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CORRECTIONS    TO    H.    0.    PUBLICATION    NO.    ^-THE   AMERICAN 
PRACTICAL  NAVIGATOR,  1914  EDITION. 

Page  108.  In  figure  No.  37,  on  right-hand  side:  For  M  read  M'. 

Page  171.   (a)  In  the  example  (fine  print),  line  4:  For  50°  50'  read  50°  58'. 

(6)  Line  5:  For  "Northward"  read  "Southward." 
Page  292.  San  Salvador  (Cat  Island)  Lighthouse,  longitude  column:  For  75.°^ 
26'  W.  read  74°  26'  W. 


CORRECTIONS  TO  THE  ABOVE-NAMED  BOOK  AND  TO  THE  USEFUL 
TABLES  (BOOK  NO.  9,  PART  II). 

Page  819.  Log.  Hav.  of  Oh.  28m.  10s.:  For  "7.75650"  read  "7.57650".  Log. 

Hav.  of  Oh.  26m.  44s.:  For  "7.35119"  read  "7.53119". 

Page  831.  Nat.  Hav.  of  26°  10'  30":  Omit  characteristic  1. 

Page  865.  Log.  Hav.  4h.  32m.  3s.:  For  ".49226"  read  ".49526." 

Page  866.  Log.  Hav.  4h.  37m.  54s.:  For  ".31147"  read  ".51147". 
Page  832,  Nat.  Hav.  of  27°  06'  45",  for  .05994  read  .06494. 

Page  896,  Nat.  Hav.  of  107°  14'  15",  for  .46817  read  .64817. 

Page  909,  Log.  Hav.  of  8h.  29m.  40s.,  for  .990515  read  9.90615. 

Page  910,  Nat.  Hav.  of  128°  02',  for  0.90806  read  0.80806. 

Page  915,  Nat.  Hav.  of  149°  01',  for  .92666  read  .92866. 

Page  917,  Nat.  Hav.  of  156°  24',  for  .85818  read  .95818. 

liJUlS  WEULE  CO. 
Chfnnofnetefsand  Hautlcal  liistrnnents 

BCX)KS  ON  NAVIGATION,  MX:. 

AOSMCT  roa 

U.S.  GO^^NMCNT  CHAHTS  *n0  •U8L«C*T"^NS 

9t,.iCllU»IIUSTMSilRFIIIilUtt4.UL 


No.  9 


American  Practical  Navigator 

An  Epitome  of  Navigation  and 
Nautical  Astronomy 


ORIGINALLY  BY 

NATHANIEL  BOWDITCH,  LL.  D. 


RE-EDITED  AND  PUBUSHED  IN  THE 

UNITED  STATES  HYDROGRAPHIC  OFFICE 

BY  DIRECTION  OF  THE  SECRETARY  OF  THE  NAVY. 
IN  ACCORDANCE  WITH  THE  ACTS  OF  CONGRESS 


WASHINGTON 

GOVERNMENT  PRINTING  OFTICE 

1914 


STATUTES  OF  AUTHORIZATION. 

There  shall  be  a  Hydrographic  Office  attached  to  the  Bureau  of  Navigation  in 
the  Navy  Department,  for  the  improvement  of  the  means  for  navigating  safely 
the  vessels  of  the  Navy  and  of  the  mercantile  marine,  by  providing,  under  the 
authority  of  the  Secretary  of  the  Navy,  accurate  and  cheap  nautical  charts,  sailing 
directions,  navigators,  and  manuals  of  instructions  for  the  use  of  aU  vessels  of  the 
United  States,  and  for  the  benefit  and  use  of  navigators  generally.     (R.  S.  431.) 

The  Secretary  of  the  Navy  is  authorized  to  cause  to  be  prepared,  at  the  Hydro- 
graphic  Office  attached  to  the  Bureau  of  Navigation  in  the  Navy  Department, 
maps,  charts,  and  nautical  books  relating  to  and  required  in  navigation,  and  to 
publish  and  furnish  them  to  navigators  at  the  cost  of  printing  and  paper,  and  to 
purchase  the  plates  and  copyrights  of  such  existing  maps,  charts,  navigators,  sail- 
ing directions,  and  instructions,  as  he  may  consider  necessary,  and  when  he  may 
deem  it  expedient  to  do  so,  and  under  such  regulations  and  instructions  as  he  may 
prescribe.     (R.  S.  432.) 


37 


I>A.RT    I. 


TEXT  AND  APPENDICES. 


ZSIOHZ 


Digitized  by  the  Internet  Archive 

in  2008  with  funding  from 

Microsoft  Corporation 


http://www.archive.org/details/epitomenavigatOObowdrich 


CONTENTS   OF   P^RT   I. 


Page. 

Abbreviations 7 

Chapter     I.  Definitions  relating  to  Navigation 9 

II.  Instruments  and  Accessories  in  Navigation 11 

III.  The  Compass  Error 36 

IV.  Piloting 56 

V.  The  Sailings 72 

VI.  Dead  Reckoning 84 

VII.  Definitions  relating  to  Nautical  Astronomy 87 

VIII.  Instruments  employed  in  Nautical  Astronomy 91 

IX.  Time  and  the  Nautical  Almanac 102 

X.  Correction  of  Observed  Altitudes 115 

XI.  The  Chronometer  Error 121 

XII.  Latitude 126 

XIII.  Longitude 140 

XIV.  Azimuth '. 144 

XV.  The  Sumner  Line 150 

XVI.  The  Practice  of  Navigation  at  Sea 169 

XVII.  Marine  Surveying 189 

XVIII.  Winds 206 

XIX.  Cyclonic  Storms 212 

XX.  Tides 225 

XXI.  Ocean  Currents 232 

XXII.  Ice  and  its  Movements  in  the  North  Atlantic  Ocean 238 

Appendix  I.  Extracts  from  the  American  Ephemeris  and  Nautical  Almanac  for  the  year  1915 

which  have  reference  to  examples  for  that  year  given  in  this  work 248 

II.  A  collection  of  Forms  for  working  Dead  Reckoning  and  various  Astronomical  Sights, 

with  notes  explaining  their  application  under  all  circumstances 254 

III.  Explanation  of  certain  Rules  and  Principles  of  Mathematics  of  use  in  the  Solution 

of  Problems  in  Navigation 266 

IV.  Maritime  Positions  and  Tidal  Data 278 

Index 358 

5 


ABBREVIATIONS  USED  IN  THIS  WORK. 


Alt.  (or  ft) Altitude. 

a.  m Ante  meridian. 

Amp Amplitude. 

App Apparent. 

App.  t Apparent  time. 

Art Astronomical. 

Art.  t Astronomical  time. 

Aug Augmentation. 

Az.  (orZ) Azimuth. 

C Coiu*se. 

0.  C Chronometer  correction. 

0— W Chronometer  minus  watch. 

Chro.  t Chronometer  time. 

Co.  L Co.  latitude. 

Col Column. 

Corr Correction. 

Cos Cosine. 

Cosec Cosecant. 

Cot Cotangent. 

d  (or  Dec.) Declination. 

D  (or  D.Lo) Difference  longitude. 

Dep Departure. 

Dev Deviation. 

Diff Difference. 

Dirt Distance. 

DL Difference  latitude. 

D.  R Dead  reckoning. 

E.,  Ely East,  easterly. 

Elap.  t Elapsed  time. 

Eq.  t Equation  of  time. 

F Longitude  factor. 

/ Latitude  factor. 

G.  (or  Gr.) Greenwich. 

G.  A.  T Greenwich  apparent  time. 

G.  M.  T Greenwich  mean  time. 

G.  S.  T Greenwich  sidereal  time. 

h Altitude. 

H Meridian  altitude. 

H.  A.  (or  t) Hour  angle. 

Hav Ilaversine. 

H.  D Hourly  difference. 

H.  P.  (or  Hor.  par.).  .Horizontal  parallax. 

Hr-s Hour-s. 

H.  W High  water. 

1.  C Index  correction. 

L.  (or  Lat.) Latitude. 

L.  A.  T Local  apparent  time. 

L.  M.  T Local  mean  time. 


L.  S.  T Local  sidereal  time. 

Lo.  (or  Long.) Longitude. 

Log Logarithm. 

Lun.  Int Lunitidal  interval. 

L.  W Low  water. 

X Longitude. 

m Meridional  difference. 

Merid Meridian  or  noon. 

Mag Magnetic . 

M.  D Minute's  difference. 

Mid Middle. 

Mid.  L Middle  latitude. 

M.  T Mean  time. 

nat Natural. 

N.,  Nly North,  northerly. 

N.  A.  (orNaut.  Aim.)  Nautical  Almanac. 

•Np Neap. 

Obs Observation. 

p  (or  P.  D.) Polar  distance. 

p.  c Per  compass. 

jP.  D.  (or  p) Polar  distance. 

P.  L.  (or  Prop.  Log.). Proportional  logarithm, 

p.  m Post  meridian. 

p.  &  T Parallax  and  refraction. 

Par Parallax. 

R.  A Right  ascension. 

R.  A.  M.  S Right  ascension  mean  sun. 

Red Reduction. 

Ref Refraction. 

S.,  Sly South,  southerly. 

S.  D Semidiameter. 

Sec Secant. 

Sid Sidereal. 

Sin Sine. 

Spg Spring. 

t Hour  angle. 

T Time. 

Tab Table. 

Tan Tangent. 

Tr.  (or  Trans.) Transit. 

Var Variation. 

Vert Vertex  or  vertical. 

W.,  Wly West,  werterly. 

W.  T Watch  time. 

z Zenith  distance. 

Z Azimuth. 

6 Auxiliary  angle. 

X Difference  longitude  in  tima. 


SYMBOLS. 


O       The  Sun.        • 
(C        The  Moon. 
*       A  Star  or  Planet. 
T3  C  Alt.  upper  limb, 
d  ^  Alt.  lower  limb, 
(t)  ^  Azimuthal  angle. 


A  a  ..Alpha. 
B  ^  ..Beta. 
r  Y  .. Gamma. 
J  d  ..Delta. 
E  e  .. EpsUon. 
Z  C  ..Zeta. 
H  7)  ..Eta. 
e  6  .  .Theta. 
/   e  .. Iota. 
K  K  .. Kappa. 
A  X  ..Lambda. 
M  it.MvL. 


GREEK    LETTEBS. 


Degrees. 
Minutes  of  Arc. 
Seconds  of  Arc. 
Hours. 

Minutes  of  Time. 
Seconds  of  Time. 


N  V Nu. 

S  ^ Xi. 

0  o Omicron. 

niz PL 

P  p Rho. 

1  a  (C).-. Sigma. 
T  X Tau. 

Y  a Upsilon. 

<f<j> Phi. 

Xr Chi. 

7^ Psi. 

Q  u) Omega. 


CHAPTER  I. 

DEFINITIONS  EELATING  TO  NAVIGATION. 


1.  That  science,  generally  termed  Navigation,  which  affords  the  knowledge 
necessary  to  conduct  a  ship  from  point  to  point  upon  the  earth,  enabling  the  mariner 
to  determine,  with  a  sufficient  degree  of  accuracy;,  the  position  of  his  vessel  at  any 
time,  is  properly  divided  into  two  branches:  Navigation  and  Nautical  Astronomy. 

2.  Navigation,  in  its  limited  sense,  is  that  branch  which  treats  of  the  determina- 
tion of  the  position  of  the  ship  by  reference  to  the  earth,  or  to  objects  thereon.  It 
comprises  (a)  Piloting,  in  which  the  position  is  ascertained  from  visible  objects 
upon  the  earth,  or  from  soundings  of  the  depth  of  the  sea,  and  (6)  Dead  Reckoning, 
in  which  the  position  at  any  moment  is  deduced  from  the  direction  and  amount  of 
a  vessel's  progress  from  a  known  point  of  departure. 

3.  Nautical  Astronomy  is  that  branch  of  the  science  which  treats  of  the  deter- 
mination of  the  vessel's  place  by  the  aid  of  celestial  objects — the  sun,  moon,  planets, 
or  stars. 

4.  Navigation  and  Nautical  Astronomy  have  been  respectively  termed  Geo- 
Navigation  and  Celo- Navigation,  to  indicate  the  processes  upon  which  they  depend. 

5.  As  the  method  of  piloting  can  not  be  employed  excepting  near  land  or  in 
moderate  depths  of  water,  the  navigator  at  sea 
must  fix  his  position  either  ly  dead  reckoning  or  by 
observation  of  celestial  objects;  the  latter  method  is 
more  exact,  but  as  it  is  not  always  available,  the 
former  must  often  be  depended  upon. 

6.  The  Earth. — The  Eartn  is  an  oblate 
spheroid,  being  a  nearly  spherical  body  slightly 
flattened  at  the  poles;   its  longer  or   equatorial 

axis  measures  about  7,927  statute  miles,  and  its  El 1 h— I frrr— iw 

shorter  axis,  around  which  it  rotates,  about  7,900 
statute  miles. 

The  Earth  (assumed  for  purposes  of  illustra- 
tion to  be  a  sphere)  is  represented  in  figure  1. 

The  Axis  of  Rotation,  usually  spoken  of  simply 
as  the  Axis,  is  rP'. 

The  Poles  are  the  points,  P  and  P',  in  which  P' 

the  axis  intersects  the  surface,  and  are  designated,  fio.  i. 

respectively,  as  the  North  Pole  and  the  South  Pole. 

The  Equator  is  the  great  circle  EQMW,  formed  by  the  intersection  with  the 
earth's  surface  of  a  plane  perpendicular  to  the  axis;  the  equator  is  equidistant  from 
the  poles,  every  point  upon  it  boin^90°  from  each  pole. 

Meridians  are  the  great  circles  JPQP',  PMP',  PM'P',  formed  by  the  intersection 
with  the  earth's  surface  of  planes  secondary  to  the  equator  (that  is,  passing  through 
its  poles  and  therefore  perpendicular  to  its  plane). 

Parallels  of  Latitude  are  small  circles  NTn,  N'n'T',  formed  by  the  intersection 
with  the  earth's  surface  of  planes  passed  parallel  to  the  equator. 

The  Latitude  of  a  place  on  the  surface  of  the  earth  is  the  arc  of  the  meridian 
intercepted  between  the  equator  and  that  place.  Latitude  is  reckoned  North  and 
South,  from  the  equator  as  an  origin,  through  90°  to  the  poles;  thus,  the  latitude 
of  the  pomt  T  is  MT,  north,  and  of  the  pomt  T',  MT',  north.  The  Difference  of 
Latitude  between  any  two  places  is  the  arc  of  a  meridian  intercepted  between  their 
parallels  of  latitude,  and  is  called  North  or  South,  according  to  direction;  thus,  the 
difference  of  latitude  between  T  and  T'  is  Tn'  or  T'n,  north  from  T  or  south  from  T'. 

The  Longitude  of  a  place  on  the  surface  of  the  earth  is  the  arc  of  the  equator  inter- 
cepted between  its  meridian  and  that  of  some  place  from  which  the  longitude  is 


p 

lr\  \ 

"l            Ql               JM 

M' 

10  DEFISriTION  RELATING  TO  NAVIGATION. 

reckoned.  Longitude  is  measured  East  or  West  through  180°  from  the  meridian  of 
a  designated  place,  such  meridian  being  termed  the  Prime  Meridian;  the  prime 
meridian  used  by  most  nations,  including  the  United  States,  is  that  of  Greenwich, 
England.  If,  in  the  figure,  the  prime  meridian  be  PGQP',  then  the  longitude  of  the 
point  T  is  QM,  east,  and  of  T',  QM',  east.  The  Difference  of  Longitude  oetween  any 
two  places  is  the  arc  of  the  equator  intercepted  between  their  meridians,  and  is  called 
East  or  West,  according  to  direction ;  thus,  the  difference  of  longitude  between  T  and 
T'  is  MM',  east  from  M  or  west  from  M'.  The  Departure  is  the  linear  distance, 
measured  on  a  parallel  of  latitude,  between  two  meridians;  unlike  the  various  quanti- 
ties previously  defined,  departure  is  reckoned  in  miles;  the  departure  between  two 
meridians  varies  with  the  parallel  of  latitude  upon  which  it  is  measured;  thus,  the 
departure  between  the  meridians  of  T  and  T'  is  the  number  of  mUes  corresponding 
to  the  distance  Tn  in  the  latitude  of  T,  or  to  ti'T'  in  the  latitude  of  T'. 

The  curved  line  which  joins  any  two  places  on  the  earth's  surface,  cutting  all  the 
meridians  at  the  same  angle,  is  called  the  Rhumb  Line,  Loxodromic  Curve,  or  Equiaiv- 
gular  Spiral.  In  the  figure  this  line  is  represented  by  TrT'.  The  constant  angle 
which  tnis  line  makes  with  the  meridians  is  called  the  Course;  and  the  length  of  tne 
line  between  any  two  places  is  called  the  Distance  between  those  places. 

The  unit  of  linear  measure  employed  by  navigators  is  the  Nautical  or  Sea  Mile, 
or  Knot.  This  unit  is  defined  in  the  United  States  of  America  as  being  6,080.27 
feet  in  length  and  equal  to  one-sixtieth  part  of  a  degree  of  a  great  circle  of  a  sphere 
whose  surface  is  equal  in  area  to  the  area  of  the  surface  of  the  earth. 

The  nautical  mUe  is  not  exactly  the  same  in  all  countries,  but,  from  the  navi- 
gator's standpoint,  the  various  lengths  adopted  do  not  differ  materially. 

Since,  upon  the  ocean,  latitude  has  been  capable  of  easier  and  more  accurate 
determination  than  longitude,  it  might  naturally  be  expected  that  there  exists  an 
intimate  fixed  relation  between  the  nautical  mile  and  the  minute  of  latitude  (or  the 
length  of  that  portion  of  a  meridian  which  subtends  at  the  earth's  center  the  angular 
measure  of  one  minute);  but  on  account  of  the  fact  that  the  earth  is  not  a  perfect 
sphere,  a  fixed  relation  does  not  exist,  and  the  arc  of  a  meridian  that  subtends  an 
angle  of  1'  at  the  center  of  the  earth  varies  slightly  in  length  from  the  Equator  to 
the  poles,  being  6,045.95  feet  at  the  Equator  and  6,107.85  feet  at  the  poles.  Its 
average  length  is  1,852.201  meters,  or  6,076.82  feet.  Accordingly  in  France, 
Germany,  and  Austria  the  nautical  mile  is  1,852  meters,  2,025.41  yards,  or  6,076.23 
feet. 

For  purposes  of  navigation  the  nautical  mUe  is  assumed  to  be  equal  to  a  minute 
of  latitude  in  all  parts  of  the  world;  and,  hence,  when  a  vessel  changes  her  position 
to  the  north  or  south  by  1  nautical  mile,  it  may  always  be  considered  that  the  latitude 
has  changed  1'.  Owing  to  the  fact  that  the  meridians  converge  toward  the  poles, 
the  difference  of  longitude  produced  by  a  change  of  position  of  1  mile  to  the  east 
or  west  wUl  vary  with  the  latitude ;  thus,  a  departure  of  1  mile  will  equal  a  difference  of 
longitude  of  1'  at  the  Eguator,  but  of  more  than  1'  at  any  higher  latitude,  being  in 
fact  equal  to  I'.l  of  longitude  in  latitude  30°  and  to  2'  of  longitude  in  latitude  60°. 

In  England  the  nautical  mile,  corresponding  to  the  Admiralty  Jcnot,  is  regarded 
as  having  a  length  of  6,080  feet. 

The  statute  mile  of  5,280  feet,  which  is  employed  in  land  measurements,  is 
commonly  used  in  navigating  river  and  lake  vessels.  This  is  notably  the  case  on  the 
Great  Lakes  of  America,  but  with  the  recognition  of  the  advantages  to  be  gained  by 
the  practice  of  nautical  astronomy  in  the  navigation  of  these  vessels,  the  use  of  the 
nautical  mile  is  extending. 

The  Great  Circle  Track  or  Course  between  any  two  places  is  the  route  between 
those  places  along  the  circumference  of  the  great  circle  which  joins  them.  In  the 
figure  this  line  is  represented  by  Tj/T'.  From  the  properties  of  a  great  circle  (which  is  a 
circle  upon  the  earth's  surface  formed  by  the  intersection  of  a  plane  passed  through 
its  center)  the  distance  between  two  points  measured  on  a  great  circle  track  is  shorter 
than  the  distance  upon  any  other  line  which  joins  them.  Except  when  the  two 
points  are  on  the  same  meridian  or  when  both  he  upon  the  equator,  the  great  circle 
track  will  always  differ  from  the  rhumb  line,  and  the  great  circle  track  wUl  intersect 
each  intervening  meridian  at  a  different  angle. 


CHAPTER  II. 

INSTRUMENTS  AND  AOOESSOEIES  IN  NAYIGATION. 


DIVIDEBS  OB  COMPASSES. 


7.  This  instrument  consists  of  two  legs  movable  about  a  loint,  so  that  the 
points  at  the  extremities  of  the  legs  may  be  set  at  any  required  distance  from  each 
other.  It  is  used  to  take  and  transfer  distances  ana  to  describe  arcs  and  circles. 
When  used  for  the  former  purpose  it  is  termed  dividers,  and  the  extremities  of  both 
legs  are  metal  points;  when  used  for  describing  arcs  or  circles,  it  is  called  a  compass, 
and  one  of  the  metal  points  is  replaced  by  a  pencil  or  pen. 


PABALLEIi  BULEBS. 


8.  Parallel  rulers  are  used  for  drawing  lines  parallel  to  each  other  in  any  direc- 
tion, and  are  particularly  useful  in  transferring  the  rhumb-Une  on  the  chart  to  the 
nearest  compass-rose  to  ascertain  the  course,  or  to  lay  oflF  bearings  and  courses. 


PBOTBACTOB. 

9.  This  is  an  instrument  used  for  the  measurement  of  angles  upon  paper; 
there  is  a  wide  variation  in  the  material,  size,  and  shape  in  which  it  may  be  made. 
(For  a  description  of  the  Three  Armed  Protractor,  see  art.  428,  Chap.  XVII.) 

THE  CHIP  liOO. 

10.  This  instrument,  for  measuring  the  rate  of  sailing,  consists  of  three  parts; 
viz,  the  log-chip,  the  log-line,  and  the  log-glass.  A  light  substance  thrown  from  the 
ship  ceases  to  partake  of  the  motion  oi  the  vessel  as  soon  as  it  strikes  the  water, 
and  wUl  be  left  behind  on  the  surface;  after  a  certain  interval,  if  the  distance  of  the 
ship  from  this  stationary  object  be  measured,  the  approximate  rate  of  sailing  will 
be  given.  The  log-chip  is  the  float,  the  log-line  is  the  measure  of  the  distance,  and 
the  log-glass  defines  the  interval  of  time. 

The  log-chip  is  a  thin  wooden  quadrant  of  about  5  inches  radius,  loaded  with 
lead  on  the  circular  edge  sufficiently  to  make  it  float  upright  in  the  water.  There 
is  a  hole  in  each  corner  of  the  log-chip,  and  the  lo^-line  is  knotted  in  the  one  at  the 
apex;  at  about  8  inches  from  the  end  there  is  seized  a  wooden  socket;  a  piece  of 
line  of  proper  length,  being  knotted  in  the  other  holes,  has  seized  into  its  bight  a 
wooden  peg  to  fit  snugly  into  the  socket  before  the  log-chip  is  thrown;  as  soon  as 
the  line  is  checked  this  peg  pulls  out,  thus  allowing  the  log-chip  to  be  hauled  in 
with  the  least  resistance. 

The  log-line  is  about  150  fathoms  in  length,  one  end  made  fast  to  the  log-chip, 
the  other  to  a  reel  upon  which  it  is  wound.  At  a  distance  of  from  15  to  20  fathoms 
from  the  log-chip  a  permanent  mark  of  red  bunting  about  6  inches  long  is  placed 
to  allow  sufficient  stray  line  for  the  log-chip  to  clear  the  vessel's  eddy  or  wake.  The 
rest  of  the  fine  is  divided  into  lengths  of  47  feet  3  inches  called  Jcnots,  by  pieces  of 
fish-line  thrust  through  the  strands,  with  one,  two,  three,  etc.,  knots,  according  to 
the  number  from  stray-line  mark;  each  knot  is  further  subdivided  into  five  equal 
lengths  of  two-tenths  of  a  knot  each,  marked  by  pieces  of  white  rag. 

The  length  of  a  knot  depends  upon  the  number  of  seconds  which  the  log-glass 
measures;  the  length  of  each  knot  must  bear  the  same  ratio  to  the  nautical  mile 
(^  of  a  degree  of  a  great  circle  of  the  earth,  or  6,080  feet)  that  the  time  of  the  glass 
does  to  an  hour. 

U 


12  INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 

In  the  United  States  Navy  all  log-lines  are  marked  for  log-glasses  of  28  seconds, 
for  which  the  proportion  is : 

3600  :  6080  =  28"  :  x, 

X  being  the  length  of  the  knot. 
Hence, 

a;  =  47".29,  or  47"  3'«. 

The  speed  of  the  ship  is  estimated  in  knots  and  tenths  of  a  knot. 

The  log-glass  is  a  sand  glass  of  the  same  shape  and  construction  as  the  old  hour- 
glass. Two  glasses  are  used,  one  of  28  seconds  and  one  of  14  seconds;  the  latter  is 
employed  when  the  ship  is  going  at  a  high  rate  of  speed,  the  number  of  knots  indi- 
cated on  a  Hne  markea  for  a  28-second  glass  being  doubled  to  obtain  the  true  rate 
of  speed. 

11.  The  log  in  all  its  parts  should  be  frequently  examined  and  adjusted;  the 

})eg  must  be  found  to  fit  sufficiently  tight  to  keep  the  log-chip  upright;  the  log- 
ine  shrinks  and  stretches  and  should  often  be  verified;  the  log-glass  should  be 
compared  with  a  watch.  One  end  of  the  glass  is  stopped  with  a  cork,  by  removing 
which  the  sand  may  be  dried  or  its  quantity  corrected. 

12.  A  ground  log  consists  of  an  ordinary  log-hne,  with  a  lead  attached  instead 
of  a  chip;  in  shoal  water,  where  there  are  no  well-defined  objects  available  for  fixing 
the  position  of  the  vessel  and  the  course  and  speed  are  influenced  by  a  tidal  or  other 
current,  this  log  is  sometimes  used,  its  advantage  being  that  the  lead  marks  a  sta- 
tionary point  to  which  motion  may  be  referred,  whereas  the  chip  would  drift  with 
the  stream.  The  speed,  which  is  marked  in  the  usual  manner,  is  the  speed  over 
the  ground,  and  the  trend  of  the  fine  gives  the  course  actually  made  good  by  the 
vessel. 

THE  PATENT  LOG. 

13.  This  is  a  mechanical  contrivance  for  registering  the  distance  actually  run 
by  a  vessel  through  the  water.  There  are  various  types  of  patent  logs,  but  for  the 
most  part  they  act  upon  the  same  principle,  consisting  of  a  registering  device,  a  fly 
or  rotator,  and  a  lo^  or  towline;  the  rotator  is  a  small  spincue  with  a  number  of 
blades  extending  radially  in  such  manner  as  to  form  a  spiral,  and,  when  drawn  through 
the  water  in  the  direction  of  its  axis,  rotates  about  that  axis  after  the  manner  of  a 
screw  propeller;  the  rotator  is  towed  from  the  vessel  by  means  of  a  log  or  towline 
from  30  to  100  fathoms  in  length,  made  fast  at  its  apex,  the  line  being  of  special 
make,  so  that  the  turns  of  the  rotator  are  transmitted  through  it  to  the  worm  shaft 
of  the  register,  to  which  the  inboard  end  of  the  line  is  attached;  the  registering 
device  is  so  constructed  as  to  show  upon  a  dial  face  the  distance  run,  according  to 
the  number  of  turns  of  its  worm  shaft  due  to  the  motion  of  the  rotator;  the  register 
is  carried  at  some  convenient  point  on  the  vessel's  quarter;  it  is  frequently  found 
expedient  to  rig  it  out  upon  a  small  boom,  so  that  the  rotator  will  be  towed  clear 
of  the  wake. 

14.  Though  not  a  perfect  instrument,  the  patent  log  affords  a  means  of  deter- 
mining the  vessel's  speed  through  the  water.  It  will  usually  be  found  that  the 
indications  of  the  log  are  in  error  by  a  constant  percentage,  and  the  amount  of  this 
error  should  be  determined  by  careful  experiment  and  applied  to  all  readings. 

Various  causes  may  operate  to  produce  inaccuracy  of  working  in  the  patent 
log,  such  as  the  bending  of  the  blades  of  the  rotator  by  accidental  blows,  fouling  of 
the  rotator  by  seaweed  or  refuse  from  the  ship,  or  mechanical  wear  of  parts  of  the 
register.  The  length  of  the  towUne  has  much  to  do  with  the  working  of  the  log, 
and  by  varying  the  length  the  indications  of  the  instrument  may  sometimes  be 
adjusted  when  the  percentage  of  error  is  small;  it  is  particularly  important  that  the 
line  shall  not  be  too  short.  The  readings  of  the  patent  log  can  not  be  depended  upon 
for  accuracy  at  low  speeds,  when  the  rotator  does  not  tow  horizontally,  nor  in  a  head 
or  a  foUowing  sea,  when  the  effect  depends  upon  the  wave  motion  as  well  as  upon 
the  speed  of  the  vessel. 

15.  Electrical  registers  for  patent  logs  are  in  use,  the  distance  recorded  by  the 
mechanical  register  being  communicatea  electrically  to  some  point  of  the  vessel 
which  is  most  convenient  for  the  purposes  of  those  charged  with  the  navigation. 


17  fathoms  from  the  lead,  same  as  at  7  fathoms. 

20  fathoms  from  the  lead,  with  2  knots. 

25  fathoms  from  the  lead,  with  1  knot. 

30  fathoms  from  the  lead,  with  3  knots. 

35  fathoms  from  the  lead,  with  1  knot. 

40  fathoms  from  the  lead,  with  4  knots. 

And  so  on. 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION.  18 

16.  A  number  of  instruments  based  upon  different  physical  principles  have 
been  devised  for  recording  the  speed  of  a  vessel  through  the  water  and  have  been 
used  with  varying  degrees  of  success.  Of  these  the  hydrauUc  speed  indicator,  known 
as  the  Nicholson  Ship  Log,  affords  an  instance. 

17.  The  revolutions  of  the  screw  propeller  afford  in  a  steamer  the  most  valuable 
means  of  detennining  a  vessel's  speed  through  the  water.  The  number  of  revolu- 
tions per  knot  must  be  carefully  determined  for  the  vessel  by  experiment  under 
varying  conditions  of  speed,  draft,  and  foulness  of  bottom. 

THE  LEAD. 

18.  This  device,  for  ascertaining  the  depth  of  water,  consists  essentially  of  a 
suitably  marked  line,  having  a  lead  attached  to  one  of  its  ends.  It  is  an  invaluable 
aid  to  the  navigator  in  shallow  water,  particularly  in  thick  or  foggy  weather,  and  is 
often  of  service  when  the  vessel  is  out  of  sight  of  land. 

Two  leads  are  used  for  soundings — the  hand-lead,  weighing  from  7  to  14  pounds, 
with  a  Une  marked  to  about  25  fathoms,  and  the  deep-sea  lead,  weighing  from  30  to 
100  pounds,  the  hne  being  100  fathoms  or  upward  in  length. 

Lines  are  generally  marked  as  follows : 

2  fathoms  from  the  lead,  with  2  strips  of  leather. 

3  fathoms  from  the  lead,  with  3  strips  of  leather. 
5  fathoms  from  the  lead,  with  a  white  rag. 
7  fathoms  from  the  lead,  with  a  red  rag. 
10  fathoms  from  the  lead,  with  leather  having  a 

hole  in  it. 
13  fathoms  from  the  lead,  same  aa  at  3  fathoms. 
15  fathoms  from  the  lead,  same  as  at  5  fathoms. 

Fathoms  which  correspond  with  the  depths  marked  are  called  marks;  the  inter- 
mediate fathoms  are  called  deeps;  the  only  fractions  of  a  fathom  used  are  a  half 
and  a  quarter. 

A  practice  sometimes  followed  is  to  mark  the  hand-lead  line  in  feet  around  the 
critical  depths  of  the  vessel  by  which  it  is  to  be  used. 

Lead  lines  should  be  measured  frequently  while  wet  and  the  correctness  of  the 
marking  verified.  The  distance  from  the  leadsman's  hand  to  the  water's  edge  should 
be  ascertained  in  order  that  proper  allowance  may  be  made  therefor  in  taking 
soundings  at  night. 

19.  The  deep-sea  lead  may  be  armed  by  filling  with  tallow  a  hole  hollowed  out 
in  its  lower  end,  by  which  means  a  sample  of  the  bottom  is  brought  up. 

THE  SOUNDING  MACHINE. 

20.  This  machine  possesses  advantages  over  the  deep-sea  lead,  for  which  it  is 
a  substitute,  in  that  soundings  may  be  obtained  at  great  depths  and  with  rapidity 
and  accuracy  without  stopping  the  ship.  It  consists  essentially  of  a  stand  holding 
a  reel  upon  which  is  wound  the  sounding  wire,  and  which  is  controlled  by  a  suitable 
brake.  Crank  handles  are  provided  for  reeling  in  the  wire  after  the  sounding  has 
been  taken.  Attached  to  the  outer  end  of  the  wire  is  the  lead,  which  has  a  cavity 
at  its  lower  end  for  the  reception  of  the  tallow  for  arming.  Above  the  lead  is  a 
cylindrical  case  containing  the  depth-registering  mechanism;  various  devices  are  in 
use  for  this  purpose,  aU  depending,  however,  upon  the  increasing  pressure  of  the 
water  with  increasing  depths. 

21.  In  the  Lord  Kelvin  macMne  a  slender  glass  tube  is  used,  sealed  at  one  end 
and  open  at  the  other,  and  coated  inside  with  a  chemical  substance  which  changes 
color  upon  contact  with  sea  water;  this  tube  is  placed,  closed  end  up,  in  the  metal 
cylinder;  as  it  sinks  the  water  rises  in  the  tube,  the  contained  air  being  compressed 
with  a  force  dependent  upon  the  depth.  The  limit  of  discoloration  is  marked  by  a 
clearly  defined  line,  and  the  depth  oi  the  sounding  corresponding  to  this  Une  is  read 
off  from  a  scale.  Tubes  that  have  been  used  in  comparatively  shallow  water  may 
be  used  again  where  the  water  is  known  to  be  deeper. 

22.  A  tube  whose  inner  surface  is  ground  has  been  substituted  for  the  chemical- 
coated  tube,  ground  glass,  when  wet,  showing  clear.     The  advantage  of  these  tubes 


14 


INSTEUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


is  that  they  may  be  used  an  indefinite  number  of  times  if  thoroughly  dried.  To 
facilitate  drying,  a  rubber  cap  is  fitted  to  the  upper  end,  which,  when  removed, 
admits  of  a  circulation  of  the  air  through  the  tube. 

23.  As  a  substitute  for  the  glass  tubes  a  mechanical  depth  recorder  contained  in  a 
suitable  case  has  been  used.  In  this  device  the  pressure  of  the  water  acts  upon  a 
piston  against  the  tension  of  a  spring.  A  scale  with  an  index  pointer  records  the 
depth  reached.     The  index  pointer  must  be  set  at  zero  before  each  soimding. 

24.  Since  the  action  of  the  sounding  machine,  when  glass  tubes  are  used, 
depends  upon  the  compression  of  the  air,  the  barometric  pressure  of  the  atmosphere 
must  be  taken  into  account  when  accurate  results  are  required.  The  correction 
consists  in  incredsing  the  indicated  depth  by  a  fractional  amount  according  to  the 
following  table: 


Bar.  reading. 

Increase.               1 

// 

29.75 
30.00 
30.50 
30.75 

One-fortieth. 
One- thirtieth. 
One-twentieth. 
One-fifteenth. 

THE  MARINER'S  COMPASS. 

25.  The  Mariner's  Compass  is  an  instrument  consisting  either  of  a  single 
magnet,  or,  more  usually,  of  a  group  of  magnets,  which,  being  attached  to  a  graduated 
circle  pivoted  at  the  center  and  allowed  to  swing  freely  in  a  horizontal  plane,  has  a 
tendency,  when  not  affected  by  disturbing  magnetic  features  within  the  ship,  to  lie 
with  its  magnetic  axis  in  the  plane  of  the  earth's  magnetic  meridian,  thus  affording  a 
means  of  determiniag  the  azimuth,  or  horizontal  angular  distance  from  that  meridian, 
of  the  ship's  course  and  of  all  visible  objects,  terrestrial  or  celestial. 

26.  The  circular  card  of  the  compass  is  divided  on  its  periphery  into  360°, 
frequently  numbered  from  0°  at  North  and  South  to  90°  at  East  and  West;  also 
into  thirty-two  divisions  of  11 1°  each,  called  points,  the  latter  being  further  divided 
into  half-points  and  quarter-points;  still  finer  subdivisions,  eighth-points,  are  some- 
times used,  though  not  indicated  on  the  card,  A  system  of  numbering  the  degrees 
from  0°  to  360°,  always  increasing  toward  the  right,  is  shown  in  figure  2.  This 
system  is  in  use  in  the  United  States  Navy  and  by  the  mariners  of  some  foreign 
nations,  and  its  general  adoption  would  carry  with  it  certain  undoubted  advantages. 

27.  Boxing  the  Compass  is  the  process  of  naming  the  points  in  their  order,  and  is 
one  of  the  first  things  to  oe  learned  oy  the  young  mariner.  The  four  principal  points 
are  called  cardinal  points  and  are  named  North,  South,  East,  and  West;  each  differs 
in  direction  from  the  adjacent  one  by  90°,  or  8  points.  Midway  between  the  cardinal 
points,  at  an  angular  distance  of  45°,  or  4  points,  are  the  inter-cardinal  pomts,  named 
according  to  their  position  Northeast,  Southeast,  etc.  Midway  between  each 
cardinal  and  inter-cardinal  point,  at  an  angular  distance  of  22^°,  or  2  points,  is  a 
point  whose  name  is  made  up  of  a  combination  of  that  of  the  cardinal  with  that  of 
the  inter-cardinal  point:  North-Northeast,  East-Northeast,  East-Southeast,  etc.  At 
an  angular  distance  of  1  point,  or  11  i°,  from  each  cardinal  and  inter-cardinal  point 
(and  therefore  midway  between  it  and  the  22i°-division  last  described),  is  a  point 
which  bears  the  name  of  that  cardinal  or  inter-cardinal  point  joined  by  the  word  by 
to  that  of  the  cardinal  point  in  the  direction  of  which  it  lies:  North  by  East,  Northeast 
by  North,  Northeast  by  East,  etc. 


INSTRUMENTS  AND   ACCESSORIES  IN   NAVIGATION. 


15 


In  boxing  by  fractional  points,  it  is  evident  that  each  division  may  be  referred  to 
either  of  the  whole  points  to  which  it  is  adjacent;  for  instance,  NE.  by  N.  i  N.  and 
NNE.  i  E.  would  describe  the  same  division.  It  is  the  custom  in  the  United  States 
Navy  to  box  from  North  and  South  toward  East  and  West,  excepting  that  divisions 
adjacent  to  a  cardinal  or  inter-cardinal  point  are  always  referred  to  that  point;  as 


Fig.  2. 


N.  i  E.,  N.  by  E.  i  E.,  NNE.  ^  E.,  NE.  ^  N.,  etc.  Some  mariners,  however,  make  it  a 
practice  to  box  from  each  cardinal  and  inter-cardinal  point  toward  a  22i°-point  (NNE., 
ENE.,  etc.);  as  N.  ^  E.,  N.  by  E.  i  E.,  NE.  by  N.  ^  N.,  NE.  ^  N.,  etc. 

The  names  of  the  whole  points,  together  with  fractional  points  (according  to  the 
nomenclature  of  the  United  States  Navy),  are  given  in  the  following  table,  which 


16 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


shows  also  the  degrees,  minutes,  and  seconds  from  North  or  South  to  which  each 
division  corresponds: 


NORTH  TO   EAST. 

North: 

N.iE 

N.iE 

N.f  E 

N.by  E 

N.byE.  iE 

N.byE.  ^E 

N.byE.fE 

NNE 

NNE.  iE 

NNE.^E 

NNE.  JE 

NE.  byN 

NE.f  N 

NE.  *N 

NE.IN 

NE 

NE.iE 

NE.iE 

NE.f  E 

NE.byE 

NE.  byE.iE.... 

NE.  byE.  iE.... 

NE.  byE.  |E.... 
ENE 

ENE.  iE 

ENE.  iE 

ENE.  JE 

E.byN 

E.fN 

E.^N 

E-iN 

SOUTH   TO   WEST 
South 

S.iW 

S.iW 

S.f  W 

S.  byW 

S.byW.iW 

S.  byW.  iW 

S.byW.iW 

SSW 

SSW.  iW 

SSW.  iW 

SSW.  fW 

SW.  byS 

SW.  JS 

SW.  iS 

SW.  iS 

SW 

SW.iW 

SW.^W 

SW.fW 

SW.  by  W 

SW.  by  W.  iW... 

SW.  by  W.  iW... 

SW.byW.  fW... 
WSW 

WSW.  iW 

WSW.  iW 

WSW.  JW 

W.byS 

W.|S 

W.iS 

W.iS 


Points. 


i 
i 

i 
I 

^ 

2 
2i 

^ 

2f 

3 

3i 

3i 

3i 

4 

^ 

4i 

4i 

5 

5i 

H 

5| 

6 

6i 

6i 

H 

7 

n 

7i 


16 

16i 

16i 

16i 

17 

17i 

17i 

17i 

18 

18i 

18^ 

18J 

19 

19i 

19i 

19J 

20 

20i 

20i 

20i 

21 

21i 

21i 

21} 

22 

22i 

22i 

22} 

23 

23i 

23i 

23} 


Angular 
measure. 


2  48  45 
5  37  30 
8  26  15 
11  15  GO 
14  03  45 
16  52  30 
19  41  15 
22  30  00 
25  18  45 
28  07  30 
30  56  15 
33  45  00 
36  33  45 
39  22  30 
42  11  15 
45  00  00 
47  48  45 
50  37  30 
53  26  15 
56  15  00 
59  03  45 
61  52  30 
64  41  15 
67  30  00 
70  18  45 
73  07  30 
75  56  15 
78  45  00 
81  33  45 
84  22  30 
87  11  15 


180  00  00 
182  48  45 
185  37  30 
188  26  15 
191  15  00 
194  03  45 
196  52  30 
199  41  15 
202  30  00 
205  18  45 
208  07  30 
210  56  15 
213  45  00 
216  33  45 
219  22  30 
222  11  15 
225  00  00 
227  48  45 
230  37  30 
233  26  15 
236  15  00 
239  03  45 
241  52  30 
244  41  15 
247  30  00 
250  18  45 
253  07  30 
255  66  15 
258  45  00 
261  33  45 
264  22  30 
267  11  15 


EAST  TO   SOUTH. 


East..... 

E.iS 

E.iS 

E.f  S 

E.by  S 

ESE.  }E 

ESE.  iE 

ESE.  iE 

ESE 

SE.  byE.  }E. 

SE.  byE.  iE. 

SE.  byE.  iE. 
SE.byE 

SE.}E 

SE.iE 

SE.iE 


Points. 


SE.. 

SE.iS 

SE.iS 

SE.}S 

SE.byS 

SSE.  }E 

SSE.iE 

SSE.  iE 

SSE 

S.byE.fE 

S.byE.iE 

S.byE.iE 

S.byE 

S.}E 

S.iE 

S.iE 

WEST  TO   NORTH. 

West 

W\iN 

W.iN 

W.}N 

W.byN 

WNW.  }  W 

WNW.  iW^ , 

WNW.  iW 

WNW 

NW.  by  W.  }  W.  . 

NW.  by  W.  i  W. . 

NW.  by  W.  iW.. 
NW.bvW 

NW.  }  W 

NW.  iW 

NW.  iW 

NW 

NW.  iN 

NW.  iN 

NW.  f  N 

NW.byN 

NNW.  f  W 

NNW.  iW 

NNW.  iW 

NNW 

N.by  W.  }  W 

N.  by  W.  iW 

N.by  W.  iW.... 
N.by  W 

N.}  W 

N.  iW 

N.iW 

North 


8 

8i 

8i 

8} 

9 

9i 

9} 
10 
lOi 
lOi 
10} 

11 
ni 

Hi 
11} 

12 

m 

12i 

12} 

13 

13i 

13i 

13} 

14 

14i 

Hi 

14} 

15 

15i 

15i 

15} 


21 

2-li 

24i 

24} 

25 

25i 

25i 

25} 

26 

26i 

26i 

26} 

27 

27i 

27i 

27} 

28 

28i 

23* 

28} 

29 

29i 

29i 

29} 

30 

30i 

30i 

30} 

31 

31i 

31i 

31} 

32 


Angular 
measure. 


90  00  00 
92  48  45 
95  57  30 
98  26  15 
101  15  GO 
104  03  45 
106  52  30 
109  41  15 
112  30  00 
115  18  45 
118  07  30 
120  56  15 
123  45  GO 
126  33  45 
129  22  30 
132  11  15 
135  00  GO 
137  48  45 
140  37  30 
143  26  15 
146  16  GO 
149  03  45 
151  52  30 
154  41  15 
157  30  GO 
160  18  45 
163  07  30 
165  66  15 
168  45  GO 
171  33  45 
174  22  30 
177  11  15 


270  00  00 
272  48  45 
275  37  30 
278  26  15 
281  15  GO 
284  03  45 
286  52  30 
289  41  15 
292  30  00 
295  18  45 
298  07  30 
300  56  15 
303  45  00 
306  33  45 
309  22  30 
311  11  15 
315  00  GO 
317  48  45 
320  37  30 
323  26  15 
326  15  00 
329  03  45 
331  52  30 
334  41  15 
337  30  GO 
340  18  45 
343  07  30 
345  56  15 
348  45  GO 
351  33  45 
354  22  30 
357  11  15 
360  00  00 


INSTRUMENTS  AND   ACCESSORIES  IN    NAVIGATION,  17 

28.  The  compass  card  is  mounted  in  a  bowl  which  is  carried  in  gimhals,  thus 
enabhng  the  card  to  retain  a  horizontal  position  while  the  ship  is  pitching  and  rolling. 
A  vertical  black  line  called  the  lubber's  line  is  marked  on  the  inner  surface  of  the  bowl, 
and  the  compass  is  so  mounted  that  a  line  joining  its  pivot  with  the  lubber's  line  is 
parallel  to  the  keel  line  of  the  vessel;  thus  the  lubber's  line  always  indicates  the  com- 
pass direction  of  the  ship's  head. 

29.  According  to  the  purpose  which  it  is  designed  to  fulfill,  a  compass  is  desig- 
nated as  a  Standard,  Steering,  Check,  or  Boat  Compass.  On  United  States  naval  ves- 
sels additional  compasses  are  designated  as  follows :  Maneuvering,  battle,  auxiliary 
battle,  top,  and  conning-tower  compasses. 

30.  There  are  two  types  of  magnetic  compass  in  use,  the  liquid  or  wet  and  the 
dry;  in  the  former  the  bowl  is  filled  with  liquid,  the  card  being  thus  partially  buoyed 
with  consequent  increased  ease  of  working  on  the  pivot,  and  the  liquid  further  serving 
to  decrease  the  vibrations  of  the  card  when  deflected  by  reason  oi  the  motion  of  the 
vessel  or  other  cause.  On  account  of  its  advantages  the  liquid  compass  is  used  in 
the  United  States  Navy. 

31.  The  Navy  Service  7^-inch  Liquid  Compass. — ^This  consists  of  a  skeleton 
card  7i  inches  in  diameter,  made  of  tinned  brass,  resting  on  a  pivot  in  liquid,  with 
provisions  for  two  pairs  of  magnets  syrnmetrically  placed. 

The  magnet  system  of  the  card  consists  of  four  cyHndrical  bundles  of  steel  wires; 
these  wires  are  laid  side  by  side  and  magnetized  as  a  bundle  between  the  poles  of  a 
powerful  electro-magnet.  They  are  afterwards  placed  in  a  cylindrical  case,  sealed, 
and  secured  to  the  card.  Steel  wires  made  up  into  a  bundle  were  adopted  because 
they  are  more  homogeneous,  can  be  more  perfectly  tempered,  and  for  the  same  weight 
give  greater  magnetic  power  than  a  sohd  steel  bar. 

Two  of  the  magnets  are  placed  parallel  to  the  north  and  south  diameter  of  the 
card,  and  on  the  chords  of  15  (nearly)  of  a  circle  passing  through  their  extremities. 
These  magnets  penetrate  the  air  vessel,  to  which  tney  are  soldered,  and  are  further 
secured  to  the  bottom  of  the  ring  of  the  card.  The  other  two  magnets  of  the  system 
are  placed  parallel  to  the  longer  magnets  on  the  chords  of  45°  (nearly)  of  a  circle 
passing  through  their  extremities  and  are  secured  to  the  bottom  of  the  ring  of  the  card. 

The  card  is  of  a  curved  annular  type,  the  outer  ring  being  convex  on  the  upper 
and  inner  side,  and  is  graduated  to  read  to  one-quarter  point,  a  card  circle  being 
adjusted  to  its  outer  edge  and  divided  to  half  degrees,  with  legible  figures  at  each 
3°,  for  use  in  reading  bearings  by  an  azimuth  circle  or  in  laying  the  course  to  degrees. 

The  card  is  provided  with  a  concentric  spheroidal  air  vessel,  to  buoy  its  own 
weight  and  that  of  the  magnets,  allowing  a  pressure  of  between  60  and  90  grains  on 
the  pivot  at  60°  F.;  the  weight  of  the  card  in  air  is  3,060  grains.  The  air  vessel  has 
within  it  a  hollow  cone,  open  at  its  lower  end,  and  provided  with  the  pivot  bearing 
or  cap,  containing  a  sapphire,  which  rests  upon  the  pivot  and  thus  supports  the 
card;  the  cap  is  provided  with  adjusting  screws  for  accurately  centering  the  card. 
The  pivot  is  fastened  to  the  center  of  the  bottom  of  the  bowl  by  a  flanged  plate  and 
screws.  Through  this  plate  and  the  bottom  of  the  bowl  are  two  smafl  holes  which 
communicate  with  the  expansion  chamber  and  admit  of  a  circulation  of  the  liquid 
between  it  and  the  bowl.     The  pivot  is  of  gun  metal  with  an  iridium  cap. 

The  card  is  mounted  in  a  bowl  of  cast  bronze,  the  glass  cover  of  which  is  closely 
packed  with  rubber,  preventing  the  evaporation  or  leakage  of  the  liquid,  which  entirely 
fills  the  bowl.  This  liquid  is  composed  of  45  per  cent  pure  alcohol  and  55  per  cent 
distilled  water,  and  remains  liquid  below  —10°  F. 

The  lubber's  line  is  a  fine  line  drawn  on  an  enameled  plate  on  the  inside  of  the 
bowl,  the  inner  surface  of  the  latter  being  covered  with  an  insoluble  white  paint. 

Beneath  the  bowl  is  a  metaUic  self-adj^isting  expansion  chamber  of  elastic  metal, 
by  means  of  which  the  bowl  is  kept  constantly  full  without  the  show  of  bubbles  or  the 
development  of  undue  pressure  caused  by  the  change  in  volume  of  the  liquid  due 
to  changes  of  temperature. 

The  rim  of  the  compass  bowl  is  made  rigid  and  its  outer  edge  turned  strictly 
to  gauge  to  receive  the  azimuth  circle. 

32.  The  Dry  Compass. — The  Lord  Kelvin  Compass,  which  may  be  regarded 
as  the  standard  for  the  dry  type,  consists  of  a  strong  paper  card  with  the 
central  parts  cut  away  and  its  outer  edge  stiffened  by  a  thm  aluminum  ring.     The 

21594°— 14 2 


18  INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 

pivot  is  fitted  with  an  iridium  point,  upon  which  rests  a  small  light  aluminum  boss 
fitted  with  a  sapphire  bearing.  Radiating  from  this  boss  are  32  silk  threads  whose 
outer  ends  are  made  fast  to  the  inner  edge  of  the  compass  card;  these  threads  sustain 
the  weight  of  the  suspended  card,  and  as  they  possess  some  elasticity,  tend  to  decrease 
the  shocks  due  to  motion. 

Eight  small  steel  wire  needles,  3\  to  2  inches  long,  are  secured  normally  to  two 
parallelsilk  threads,  and  are  slung  from  the  aluminum  rim  of  the  card  by  other  silk 
threads  which  pass  through  eyes  in  the  ends  of  the  outer  pair  of  needles.  The  needles 
are  below  the  radial  threads,  thus  keeping  the  center  of  gravity  low. 

33.  The  Gyro  Compass. — This  compass,  which  has  recently  been  developed, 
consists  essentially  of  a  rapidly  spinning  rotor,  usually  driven  by  a  three-phase 
alternating  current  of  electricity,  at  a  rate  varying  according  to  the  type,  from 
8,000  to  21,000  revolutions  per  minute,  and  so  suspended  that  it  automatically 
places  its  axis  approximately  in  the  direction  of  the  geographical  meridian  and 
permits  of  the  reading  of  the  heading  of  the  ship,  unaffected  by  any  magnetic  influ- 
ence, from  a  graduated  compass  card  like  that  in  use  on  magnetic  compasses.  From 
the  "master  compass,"  which  may  be  located  in  a  compartment  below,  electrical 
connections  are  made  to  "repeating  compasses"  on  the  bridge,  in  the  conning  tower, 
or  in  the  steering-engine  room,  so  that  the  ship's  true  heading  may  be  transmitted 
to  any  desired  part  of  the  vessel. 

The  action  of  the  gyro  compass,  affected  as  it  is  by  the  earth's  rotation  under  it, 
conforms  to  Foucault's  general  law  that  "a  spinning  body  tends  to  swing  around 
so  as  to  place  its  axis  parallel  to  the  axis  of  any  impressed  forces,  and  so  that  its  direc- 
tion of  rotation  is  the  same  as  that  of  the  impressed  forces,"  Small  corrections, 
depending  upon  the  latitude,  course,  and  speed,  can  be  readily  computed  for  applica- 
tion to  the  gyro  compass  readings  either  mechanically  or  by  reference  to  tables. 

34.  The  Azimuth  Circle. — This  is  a  necessary  fitting  for  all  compasses 
employed  for  taking  bearings — that  is,  noting  the  directions — of  either  celestial  or 
terrestrial  objects.  The  instrument  varies  widely  in  its  different  forms;  the  essential 
features  which  all  share  consist  in  (a)  a  pair  of  sight  vanes,  or  equivalent  device,  at 
the  extremities  of  the  diameter  of  a  circle  that  revolves  concentrically  with  the 
compass  bowl,  the  line  of  sight  thus  always  passing  through  the  vertical  axis  of  the 
compass;  and  (&)  a  system,  usually  of  mirrors  and  prisms,  by  which  the  point  of  the 
compass  card  cut  by  the  vertical  plane  through  the  line  of  sight — in  other  words, 
the  compass  direction — is  brought  into  the  field  of  view  of  the  person  making  the 
observation.  In  some  circles,  for  observing  azimuths  of  the  sun  advantage  is 
taken  of  the  brightness  of  that  body  to  reflect  a  pencil  of  light  upon  the  card  in 
such  a  manner  as  to  indicate  the  bearing;  such  an  azimuth  circle  is  used  in  the 
United  States  Navy. 

The  azimuth  circles  should  be  tested  occasionally  for  accuracy.  This  can  best 
be  done  by  mounting  a  standard  compass  on  a  tripod  m  a  nonmagnetic  spot  on  shore, 
in  a  locality  where  the  variation  has  been  accurately  determined.  The  observed 
compass  bearing  of  the  sun  should,  of  course,  be  the  same  as  the  computed  magnetic 
bearing  at  any  instant,  the  difference  between  the  two,  if  any,  being  eo[ual  to  the 
error  of  the  compass  or,  what  is  more  likely,  the  error  of  the  azimuth  circle.  Any 
doubt  in  the  matter  may  be  removed  by  the  use  of  two  or  more  compasses.  It  will 
be  frequently  found  that  the  error  of  the  azimuth  circle  varies  with  the  sun's  altitude; 
this  is  due  to  the  fact  that  the  axis  of  the  mirror  is  not  normal  to  the  plane  passing 
through  the  sun,  the  5-sided  prism,  and  the  center  of  the  mirror. 

35.  Binnacles. — Compasses  are  mounted  for  use  in  stands  known  as  Binnacles, 
of  which  there  are  two  principal  types — the  Compensating  and  the  Noncom'pensating 
Binnacle,  so  designated  according  as  they  are  or  are  not  equipped  with  appliances  by 
which  the  deviation  of  the  compass,  or  error  in  its  indications  due  to  disturbing 
magnetic  features  within  the  ship  may  be  compensated. 

Binnacles  may  be  of  wood  or  of  some  nonmagnetic  metal;  all  contain  a  compass 
chamber  within  which  the  compass  is  suspended  in  its  gimbal  ring,  the  knife  ed^es 
upon  which  it  is  suspended  resting  in  V-shaped  bearings;  an  appropriate  method  is 
supplied  for  centering  the  compass.  A  hood  is  provided  for  the  protection  of  the 
compass  and  for  lighting  it  at  night.  Binnacles  must  be  rigidly  secured  to  the  deck 
of  the  vessel  in  such  position  that  the  lubber's  line  of  the  compass  gives  true  indications 
of  the  direction  of  the  ship's  head. 


INSTRUMENTS  AND  ACCESSOBIES  IN    NAVIGATION.  19 

The  position  of  the  various  binnacles  on  shipboard  and  the  height  at  which  they 
carry  the  compass  must  be  chosen  with  regard  to  the  purpose  which  the  compass  is 
to  serve,  having  in  mind  the  magnetic  conditions  of  the  ship. 

Compensatmg  binnacles  contain  the  appliances  for  carrymg  the  various  correctors 
used  in  tne  compensation  of  the  deviation  of  the  compass.  These  consist  of  (a)  a 
system  of  permanent  magnets  for  semicircular  deviation,  placed  in  a  magnetic 
chamber  lymg  immediately  beneath  the  compass  chamber,  so  arranged  as  to  permit 
variation  m  the  height  and  number  of  the  magnets  employed;  (b)  a  pair  of  arms 
projecting  horizontally  from  the  compass  chamber  and  supporting  masses  of  soft 
iron  for  quadrantal  deviation;  (c)  a  central  tube  in  the  vertical  axis  of  the  binnacle 
for  a  permanent  magnet  used  to  correct  the  heeling  error;  and  (d)  an  attachment, 
sometimes  fitted,  for  securing  a  vertical  soft-iron  rod,  or  ''Flinders  bar,"  used  in 
certain  cases  for  correction  of  a  part  of  the  semicircular  deviation.  An  explanation 
of  the  various  terms  here  used,  together  with  the  method  of  compensating  the  com- 
pass, will  be  given  in  Chapter  III. 


THE  PELOBTJS. 


36.  This  instrument  consists  of  a  circular  flat  metallic  ring,  mounted  in  gimbals, 
upon  a  vertical  standard  at  some  point  on  board  ship  affording  a  clear  view  for  taking 
bearings.  The  inner  edge  of  this  ring  is  engraved  in  degrees — the  360°  and  the  180° 
marks  indicating  a  fore-and-aft  line  parallel  to  the  keel  of  the  ship.  Within  this 
ring  a  ground-glass  dial  is  pivoted  concentrically.  This  ground-glass  dial  has  painted 
upon  it  a  compass  rose  divided  into  points  and  subdivisions  and  into  360  .  This 
dial  is  capable  of  revolution,  but  may  be  clamped  to  the  outside  ring.  Pivoted 
concentrically  with  the  flat  ring  and  tne  glass  dial  is  a  horizontal  bar  carrying  at 
both  of  its  extremes  a  sight  vane,  or,  mounted  upon  the  bar  and  parallel  to  it,  a 
telescope  containing  cross  wires.  This  sight-vane  bar  can  be  clamped  in  any  position 
independently  of  the  ground-glass  dial,  which  can  be  moved  freely  beneatn  it.  An. 
indicator  showing  the  direction  the  sight-vane  bar  points  can  be  read  upon  the  com- 
pass card  on  the  glass  dial. 

The  instrument  is  used  for  taking  bearings  of  distant  objects,  and,  at  times, 
may  be  more  convenient  than  the  standard  compass  for  that  purpose  on  account  of 
the  better  view  commanded  by  its  position,  as  well  as  because  it  may  be  made  to 
eliminate  compass  errors  from  observed  bearings,  thus  reducing  the  bearings  observed 
to  magnetic  or  true  bearings.  If  the  glass  dial  be  revolved  until  the  degree  of 
demarcation  which  is  coincident  with  the  right-ahead  marking  on  the  flat  ring  is  the 
same  as  that  which  points  to  the  lubber's  line  of  the  standard  compass,  then  all 
directions  indicated  by  the  glass  will  be  parallel  to  the  corresponding  directions  of 
the  standard  compass,  and  all  bearings  taken  by  the  pelorus  will  be  identical  with 
those  taken  by  the  compass  (leaving  out  of  the  question  the  difference  due  to  the 
distance  which  separates  them).  If  it  is  known  that  the  ship's  compass  has  a  certain 
error  due  to  deviation  of  the  compass  and  if  the  glass  dial  be  set  to  allow  for  this 
deviation,  then  aU  bearings  read  from  the  pelorus  will  be  magnetic.  If  the  dial  be 
set  allowing  for  both  deviation  and  variation  of  the  compass,  then  all  bearings  read 
will  be  true.  It  should  be  noted,  however,  that  the  bearings  taken  by  pelorus  will 
be  accurate  only  when  the  ship  is  on  her  exact  course  by  standard  compass.  For 
this  reason  it  is  usual  to  take  a  bearing  by  pelorus,  at  the  same  time  noting  the 
heading  by  standard  compass,  and  clamping  the  sight  vane;  then,  moving  the  glass 
dial  until  the  direction  opposite  the  dead-ahead  mark  is  the  same  as  that  noted  by 
the  standard  compass,  the  bearing  observed  (corrected  for  the  variation  and  for  the 
deviation  of  the  heading  at  the  instant  of  observation)  will  be  the  true  bearing. 

The  pelorus  described  above  is  of  the  most  modem  type  and  is  fitted  for  illu- 
minating the  glass  dial  from  below  in  order  to  facihtate  night  work. 

Peloruses  whose  dials  are  controlled  by  a  master  gyroscopic  compass  of  course 
indicate  at  once  the  true  bearing  of  the  object  observed. 

When  fitted  with  a  telescope  the  pelorus  may  be  used  to  take  the  azimuth  of 
stars. 

The  standard  compass  is  usually  located  in  the  ship  in  the  central  fore-and-aft 
line  which  is  established  from  the  builders'  marks  placed  in  th^t  vicinity.     The; 


20  INSTRUMENTS  AND  ACCESSOEIES  IN    NAVIGATION. 

standard  compass  being  located,  all  peloruses  may  be  oriented  from  it  by  any  one 
of  the  following  methods : 

(a)  Bv  making  the  azimuth  of  a  celestial  body,  taken  by  the  pelorus,  coincide 
with  the  smiultaneous  azimuth  of  the  same  body  taken  by  the  standard  compass. 

(&)  By  a  similar  process  with  distant  objects;  and  the  parallax  may  be  entirely 
eliminated  in  an  apparently  near  object,  in  view  of  the  moderate  distance  that 
usually  separates  the  two  instruments  on  board  ship. 

(c)  By  reciprocal  bearings  between  the  correct  instrument  and  the  instrument 
to  be  estaolished;  it  is  evident  that  if  the  lubber  lines  of  the  two  instruments  are 
both  in  the  direction  of  the  keel  line,  the  bearing  of  the  sight  vane  of  each  from  the 
other  (one  being  reversed)  should  coincide. 

{d)  By  computing  the  angle  subtended  at  the  pelorus  by  the  fore-and-aft  line 
through  the  pelorus  and  the  line  drawn  through  the  pelorus  to  the  jack  staff,  and 
setting  the  pelorus  at  this  angle  and  sighting  on  the  jack  staff. 

THE  CHART. 

37.  A  nautical  chart  is  a  miniature  representation  upon  a  plane  surface,  in 
accordance  with  a  definite  system  of  projection  or  development,  of  a  portion  of  the 
navigable  waters  of  the  world.  It  generally  includes  the  outline  of  the  adjacent 
land,  together  with  the  surface  forms  and  artificial  features  that  are  useful  as  aids 
to  navigation,  and  sets  forth  the  depths  of  water,  especially  in  the  near  approaches 
to  the  land,  by  soundings  that  are  fixed  in  position  by  accurate  determinations. 
Except  in  charts  of  harbors  or  other  localities  so  limited  that  the  curvature  of  the 
earth  is  inappreciable  on  the  scale  of  construction,  a  nautical  chart  is  always  framed 
over  with  a  network  of  parallels  of  latitude  and  meridians  of  longitude  in  relation 
to  which  the  features  to  be  depicted  on  the  chart  are  located  and  drawn;  and  the 
mathematical  relation  between  the  meridians  and  parallels  of  the  chart  and  those 
of  the  terrestrial  sphere  determines  the  method  of  measurement  that  is  to  be  employed 
on  the  chart  and  the  special  uses  to  which  it  is  adapted. 

38.  There  are  three  principal  systems  of  projection  in  use:  {a)  the  Mercator, 
(&)  the  polyconic,  and  (c)  the  gnomonic;  of  these  theMercatorisbyfarthe  most  generally 
used  for  purposes  of  navigation  proper,  while  the  polyconic  and  the  gnomonic  charts 
are  employed  for  nautical  purposes  in  a  more  restricted  manner,  as  for  plotting 
surveys  or  for  facilitating  great  circle  sailing. 

39.  The  Mercator  Projection. — The  Mercator  Projection,  so  called,  may  be 
said  to  result  from  the  development,  upon  a  plane  surface,  of  a  cylinder  which  is 
tangent  to  the  earth  at  the  equator,  the  various  points  of  the  earth's  surface  having 
been  projected  upon  the  cylinder  in  such  manner  that  the  loxodromic  curve  or 
rJiumh  line  (art.  6,  Chap.  I)  appears  as  a  right  line  preserving  the  same  angle  of 
bearing  with  respect  to  the  intersected  meridians  as  does  the  ship's  track. 

In  order  to  realize  this  condition,  the  line  of  tangency,  which  coincides  with  the 
earth's  equator,  being  the  circumference  of  a  right  section  of  the  cylinder,  will  appear 
as  a  right  line  on  the  development;  while  the  series  of  elements  of  the  cylinder 
corresponding  to  the  projected  terrestrial  meridians  will  appear  as  equidistant  right 
lines,  parallel  to  each  other  and  perpendicular  to  the  equator  of  the  chart,  main- 
taining the  same  relative  positions  and  the  same  distance  apart  on  that  equator  as 
the  meridians  have  on  the  terrestrial  spheroid.  The  scries  of  terrestrial  parallels 
will  also  appear  as  a  system  of  right  lines  parallel  to  each  other  and  to  the  e(][uator, 
and  will  so  intersect  the  meridians  as  to  form  a  system  of  rectangles  whose  altitudes, 
for  successive  intervals  of  latitude,  must  be  variable,  increasing  from  the  equator  in 
such  manner  that  the  angles  made  by  the  rhumb  line  with  the  meridian  on  tne  chart 
may  maintain  the  required  equality  with  the  corresponding  angles  on  the  spheroid. 

40.  Meridional  Parts. — At  the  equator  a  degree  of  longitude  is  equal  to  a 
degree  of  latitude,  but  in  receding  from  the  equator  and  approaching  the  pole,  while 
the  degrees  of  latitude  remain  always  of  the  same  length  (save  for  a  shght  change 
due  to  the  fact  that  the  earth  is  not  a  perfect  sphere),  the  degrees  of  longitude  become 
less  and  less. 

Since,  in  the  Mercator  projection,  the  degrees  of  longitude  are  made  to  appear 
everywhere  of  the  same  length,  it  becomes  necessary,  in  order  to  preserve  the  proper- 


INSTRUMENTS  AND  ACCESSORIES  IN    NAVIGATION.  21 

tion  that  exists  at  different  parts  of  the  earth's  surface  between  degrees  of  latitude 
and  degrees  of  longitude,  that  the  former  be  increased  from  their  natural  lengths, 
and  such  increase  must  become  greater  and  greater  the  higher  the  latitude. 

The  length  of  the  meridian,  as  thus  increased,  between  the  equator  and  any 
given  latitude,  expressed  in  minutes  at  the  equator  as  a  unit,  constitutes  the  number 
of  Meridional  Parts  corresponding  to  that  latitude.  The  Table  of  Meridional  Parts 
or  Increased  Latitudes  (Table  3),  computed  for  every  minute  of  latitude  between  0° 
and  80°,  affords  faciUties  for  construct'mg  charts  on  the  Mercator  projection  and  for 
solving  problems  in  Mercator  saihng. 

41.  To  Construct  a  Mercator  Chart." — If  the  chart  for  which  a  projection 
is  to  be  made  includes  the  equator,  the  values  to  be  measured  off  are  given  directly 
by  Table  3.  If  the  equator  does  not  come  upon  the  chart,  then  the  parallels  of 
latitude  to  be  laid  down  should  be  referred  to  a  prindpaZ  parallel,  preferably  the  lowest 
parallel  to  be  drawn  on  the  chart.  The  distance  of  any  other  parallel  of  latitude 
from  the  principal  parallel  is  then  the  difference  of  the  values  for  the  two  taken  from 
Table  3. 

The  values  so  found  may  either  be  measured  off,  without  previous  numerical 
conversion,  by  means  of  a  diagonal  scale  constructed  on  the  chart,  or  they  may  be 
laid  down  on  the  chart  by  means  of  any  properly  divided  scale  of  yards,  meters,  feet, 
or  miles,  after  having  been  reduced  to  the  scale  of  proportions  adopted  for  the  chart. 

If,  for  example,  it  be  required  to  construct  a  chart  on  a  scale  of  one-quarter  of  an 
inch  to  five  minutes  of  arc  on  the  equator,  a  diagonal  scale  may  first  be  constructed, 
on  which  ten  meridional  parts,  or  ten  minutes  of  arc  on  the  equator,  have  a  length 
of  half  an  inch. 

It  may  often  be  desirable  to  adapt  the  scale  to  a  certain  allotment  of  paper.  In 
this  case,  the  lowest  and  the  highest  parallels  of  latitude  mav  first  be  drawn  on  the 
sheet  on  which  the  transfer  is  to  be  made.  The  distance  between  these  parallels 
may  then  be  measured,  and  the  number  of  meridional  parts  between  them  ascertained. 
Dividing  the  distance  by  this  number  will  then  give  the  length  of  one  meridional 
part,  or  the  quantity  by  which  all  the  meridional  parts  taken  from  Table  3  must  be 
multiplied.  This  quantity  will  represent  the  scale  of  the  chart.  If  it  occurs  that  the 
limits  of  longitude  are  a  governing  consideration,  tne  case  may  be  similarly  treated. 

Example:  Let  a  projection  be  required  for  a  chart  of  14°  extent  in  longitude 
between  the  parallels  of  latitude  20°  30'  and  30°  25',  and  let  the  space  allowable  on 
the  paper  between  these  parallels  measure  10  inches. 

Entering  the  column  in  Table  3  headed  20°,  and  running  down  to  the  line  marked 
30'  in  the  side  column,  will  be  found  1248.9;  then,  entering  the  column  30°,  and 
running  down  to  the  line  25',  will  be  found  1905.5.  The  difference,  or  1905.5  — 
1248.9  =  656.6,  is  the  value  of  the  meridional  arc  between  these  latitudes,  for  which 
1'  of  arc  of  the  equator  is  taken  as  the  unit.     On  the  intended  projection,  therefore, 

1'  of  arc  of  longitude  will  measure   „_-  '  =0.0152  inch,  which  wiU  be  the  scale  of  the 

d5o.d 

chart.  For  the  sake  of  brevity  call  it  0.015.  By  this  quantity  aU  the  values  derived 
from  Table  3  will  have  to  be  multiplied  before  laying  them  down  on  the  projection,  if 
they  are  to  be  measured  on  a  diagonal  scale  of  one  inch. 

Draw  in  the  center  of  the  sheet  a  straight  line,  and  assume  it  to  be  the  middle 
meridian  of  the  chart.  Construct  very  carefully  on  this  line  a  perpendicular  near 
the  lower  border  of  the  sheet,  and  assume  this  perpendicular  to  be  the  parallel  of 
latitude  20°  30':  this  will  be  the  southern  inner  neat  line  of  the  chart.  From  the 
intersection  of  tne  lines  lay  off  on  the  parallel,  on  each  side  of  the  middle  meridian, 
seven  degrees  of  longitude,  or  distances  each  equal  to  0.015X60X7  =  6.3  inches; 
and  through  the  points  thus  obtained  draw  lines  parallel  to  the  middle  meridian, 
and  these  wiU  be  the  eastern  and  western  neat  lines  of  the  chart. 

In  order  to  construct  the  parallel  of  latitude  for  21°  00',  find,  in  Table  3,  the 
meridional  parts  for  21°  00',  which  are  1280.8.  Subtracting  from  this  number  the 
number  for  20°  30',  and  multiplying  the  difference  by  0.015,  we  obtain  0.478  inch, 
which  is  the  distance  on  the  chart  between  20°  30'  and  21°  00'.     On  the  meridians 

o This  construction  for  the  purpose  of  plotting  lines  of  position  in  ordinary  navigation  will  often  be  unnecessary  if  use  is 
made  of  the  Position  Plotting  Sheets  published  by  the  Hydrographic  Office. 


22  INSTRUMENTS  AND  ACCESSORIES  IN    NAVIGATION. 

lay  off  distances  equal  to  0.478  inch,  and  through  the  three  points  thus  obtained 
draw  a  straight  line,  which  will  be  the  parallel  of  21°  00'. 

Proceed  in  the  same  manner  to  lay  down  all  the  parallels  answering  to  full 
degrees  of  latitude;  the  distances  wiU  be  respectively: 

O^^.OIS  X  (1344.9  - 1248.9)  =  1.440  inches. 
0*''.015  X  (1409.5  -  1248.9)  =  2.409  inches. 
O'^'.IOS  X  (1474.5  - 1248.9)  =  3.384  inches,  etc. 

Thus  wiU  be  shown  the  parallels  of  latitude  22°  00',  23°  00',  24°  00',  etc.  FinaUy, 
lay  down  in  the  same  way  the  parallel  of  latitude  30°  25',  which  will  be  the  northern 
inner  neat  line  of  the  chart. 

A  degree  of  longitude  will  measure  on  this  chart  0^".015X60  =  0*^9.  Lay  off, 
therefore,  on  the  lowest  parallel  of  latitude  drawn  on  the  chart,  on  a  middle  one,  and 
on  the  highest  parallel,  measuring  from  the  middle  meridian  toward  each  side,  the 
distances  of  0'°.9,  1'°.8,  2*°. 7,  3'°. 6,  etc.,  in  order  to  determine  the  points  where 
meridians  answering  to  full  degrees  cross  the  parallels  drawn  on  the  chart.  Through 
the  points  thus  found  draw  the  meridians.  Draw  then  the  outer  neat  lines  of  the 
chart  at  a  convenient  distance  outside  of  the  inner  neat  lines,  and  extend  to  them  the 
meridians  and  parallels.  Between  the  inner  and  outer  neat  lines  of  the  chart  sub- 
divide the  degrees  of  latitude  and  longitude  as  minutely  as  the  scale  of  the  chart  will 
permit,  the  subdivisions  of  the  degrees  of  longitude  being  found  by  dividing  the 
degrees  into  equal  parts,  and  the  subdivisions  of  the  degrees  of  latitude  being  accu- 
rately found  in  the  same  manner  as  the  full  degrees  of  latitude  previously  described, 
though  it  will  generally  be  found  sufficiently  exact  to  make  even  subdivisions  of  the 
degrees,  as  in  tne  case  of  the  longitude. 

The  subdivisions  between  the  two  eastern  as  well  as  those  between  the  two 
western  neat  lines  wiU  serve  for  measuring  or  estimating  terrestrial  distances.  Dis- 
tances between  points  bearing  North  and  South  of  each  other  may  be  ascertained 
by  referring  them  to  the  subdivisions  between  the  same  parallels.  Distances  repre- 
sented by  fines  at  an  angle  to  the  meridians  (loxodromic  lines)  may  be  measured 
by  taking  between  the  dividers  a  small  number  of  the  subdivisions  near  the  middle 
latitude  of  the  line  to  be  measured,  and  stepping  them  off  on  that  line.  If,  for 
instance,  the  terrestrial  length  of  a  line  running  at  an  angle  to  the  meridians  between 
the  parallels  of  latitude  of  24°  00'  and  29°  00' oe  req[uired,  the  distance  shown  on  the 
neat  space  between  26°  15'  and  26°  45'  (  =  30  nautical  miles)  may  be  taken  between 
the  dividers  and  stepped  off  on  that  line. 

4:2.  Coast  lines  and  other  positions  are  plotted  on  the  chart  by  their  latitude 
and  longitude.  A  chart  may  be  transferred  from  any  other  projection  to  that  of 
Mercator  by  drawing  a  system  of  corresponding  parallels  of  latitude  and  meridians 
over  both  charts  so  close  to  each  other  as  to  form  minute  squares,  and  then  the  lines 
and  characters  contained  in  each  square  of  the  map  to  be  transferred  may  be  copied 
by  the  eye  in  the  corresponding  squares  of  the  Mercator  projection. 

Since  the  unit  of  measure,  the  mile  or  minute  of  latitude,  has  a  different  value 
in  every  latitude,  there  is  an  appearance  of  distortion  in  a  Mercator  chart  that  covers 
any  large  extent  of  surface;  for  instance,  an  island  near  the  pole  will  be  represented 
as  being  much  larger  than  one  of  the  same  size  near  the  equator,  due  to  the  different 
scale  used  to  preserve  the  character  of  the  projection. 

43.  The  Polyconic  Projection. — ^This  projection  is  based  upon  the  develop- 
ment of  the  earth's  surface  on  a  series  of  cones,  a  different  one  for  each  parallel  of 
latitude,  each  one  having  the  parallel  as  its  base,  and  its  vertex  in  the  point  where  a 
tangent  to  the  earth  at  that  latitude  intersects  the  earth's  axis.  The  degrees  of 
latitude  and  longitude  on  this  chart  are  projected  in  their  true  length,  and  the  general 
distortion  of  the  figure  is  less  than  in  any  other  method  of  projection,  the  relative 
magnitudes  bein^  closely  preserved. 

A  straight  hne  on  the  polyconic  chart  represents  a  near  approach  to  a  great 
circle,  making  a  slightly  different  angle  with  each  successive  meridian  as  the  meridians 
converge  toward  the  pole  and  are  theoretically  curved  lines;  but  it  is  only  on  charts 
of  large  extent  that  this  curvature  is  apparent;  the  parallels  are  also  curved,  this 
fact  being  apparent  to  the  eye  upon  all  excepting  the  largest  scale  charts. 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


23 


This  method  of  projection  is  especially  adapted  to  the  plotting  of  surveys;  it 
is  also  employed  to  some  extent  in  the  charts  of  the  United  States  Coast  and  Geodetic 
Survey. 

44.  Gnomonic  Projection. — ^This  is  based  upon  a  system  in  which  the  plane 
of  projection  is  tangent  to  the  earth  at  some  ^iven  point;  the  eye  of  the  spectator 
is  situated  at  the  center  of  the  sphere,  where,  bemg  at  once  in  the  plane  of  every  great 
circle,  it  will  see  all  such  circles  projected  as  straight  lines  where  the  visual  rays 
passing  through  them  intersect  the  plane  of  projection.  In  a  gnomonic  chart,  tne 
straight  Ime  between  any  two  points  represents  the  arc  of  a  great  circle,  and  is  there- 
fore the  shortest  line  between  those  points. 

Excepting  in  the  polar  regions,  for  which  latitudes  the  Mercator  projection  can 
not  be  constructed,  the  gnomonic  charts  arc  not  used  for  general  navigating  purposes. 
Their  greatest  application  is  to  afford  a  ready  means  of  finding  the  course  and  distance 
at  any  time  in  great  circle  sailing,  the  method  of  doing  wmch  will  be  explained  in 
Chapter  V. 

45.  Meridians  Adopted  in  the  Construction  of  Charts. — ^The  nautical 
charts  published  b^  the  United  States  are  based  upon  the  meridian  of  Greenwich, 
and  this  meridian  is  also  the  origin  of  longitudes  in  use  on  the  nautical  charts  pub- 
lished by  the  Governments  of  Argentina,  Austria,  Belgium,  Brazil,  Chile,  Denmark, 
Germany,  Great  Britain,  Holland  (for  all  charts  published  at  Batavia  and  for  some 
pubUshed  at  I'he  Hague),  Italy,  Japan,  Norwav,  Russia,  and  Sweden. 

In  addition  to  the  meridian  of  Greenwich,  tlie  meridian  of  Pulkowa  Observatory, 
at  St.  Petersburg,  in  longitude  30°  19'  40"  east  of  Greenwich,  is  sometimes  referred 
to  in  the  Russian  charts.  At  one  time  the  Royal  Observatory  at  Naples,  in  longitude 
14°  15'  26"  east  of  Greenwich,  was  referred  to  in  the  Italian  charts,  and  the  observatory 
at  Christiania,  in  longitude  10°  43'  23"  east  of  Greenwich,  was  referred  to  in  the 
Norwegian  charts. 

The  French  charts  are  based  upon  the  meridian  of  the  Observatory  at  Paris, 
which  has  been  determined  to  be  in  longitude  2°  20'  14.6"  east  of  Greenwich.  The 
longitudes  of  a  few  Dutch  charts  published  at  The  Hague  are  reckoned  from  the 
meridian  of  the  west  tower  of  Wester  Kirk  at  Amsterdam,  which  is  in  longi- 
tude 4°  53'  01.5"  east  of  Greenwich.  All  Portuguese  charts  constructed  on  a 
scale  of  1:100,000  refer  exclusively  to  the  meridian  of  the  observatory  of  Lisbon 
Castle,  which  is  9°  07'  54.86"  west  of  Greenwich;  Portuguese  charts  on  a  scale  of 
1:50,000  carry  two  ^aduations,  one  based  on  the  meridian  of  Greenwich,  the  other 
on  the  meridian  of  Lisbon  Castle.  In  Spain  the  meridian  of  San  Fernando  Observa- 
tory, at  Cadiz,  which  is  m  longitude  6°  12'  18"  west  of  Greenwich,  is  used. 

46.  Quality  of  Bottom. — The  following  table  shows  the  qualities  of  the 
bottom,  as  expressed  on  charts  of  various  nations: 


United  States. 

English. 

French. 

ItAlian. 

Spanish. 

German. 

Clay 

C. 

Clay 

..cl. 

Argile 

...A. 

Argila 

•arg. 

Arcillo  or  Barro.arc. 

Lehm 

....L. 

Coral 

Co. 

Coral 

..crl. 

Corail 

.Cor. 

Corfillo 

.crl. 

Coral cl. 

Korallen 

..Kor. 

Gravel 

G. 

Gravel 

...g. 

Gravier 

..Gr. 

RenaorGhiaja.gh. 

Cascfijo Co. 

Kies 

....k. 

Mud 

M. 

Mud 

..m. 

Vase 

...V. 

Fango 

...f. 

Fango  or  Luno...F. 

Schlamm 

.Schl. 

Rocky 

rky. 

Rock 

..rk. 

Roche 

...R. 

Roccia 

...r. 

Piedra  or  Roca.  P.  or  r. 

Felsig 

..Fls. 

Sand 

8. 

Sand 

...s. 

Sable 

...S. 

S£bbia  or  Artoa. .  s. 

Arena A. 

Sand 

...8d. 

Shells 

Sh. 

ShelLi 

..sh. 

CoquUle 

.Coq. 

Conchiglia.... 

.  ..c. 

Conchuela ca. 

Muacheln 

....M. 

Stone 

St. 

Stones 

..St. 

Pierre 

...P. 

Pletre 

..p. 

Piedra P. 

Stein 

...St. 

Weed 

....Wd. 

Weed 

.wd. 

Herb 

...n. 

Alga 

.alg. 

Alga A. 

Gras 

..Grs. 

Fine 

fne. 

crs. 

stf. 

sft. 

bk. 

rd. 

Fine 

Coarse 

Stiff 

Soft 

Black 

Red 

...c. 
..stf. 
..sft. 
.bUc. 
..rd. 

Fin 

Gros 

Dure 

MoUe 

Noire 

Rouge 

Jaune 

..to. 
....g. 
....d. 
...m. 

n. 

r. 

Fino 

Fina f. 

Gruesa g. 

Tenaz 

Fein 

Grob 

Schlick 

Weich 

Schwarz 

Roth 

f. 

Coarse 

Grosso 

...gb. 
....sk. 

Stifl 

T«iina«» 

Soft 

Molle 

Blando bdo. 

Negro n. 

Rojo r. 

Amarillo am. 

.Wch. 

Black 

Nero 

.schw. 

Red 

Rosse.. 

r. 

YeUow.... 

yi- 

ey. 

YeUow 

...y. 

....j. 

Giallo 

Gelb 

g. 

Gray 

24 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


47.  Measures  of  Depth. — The  following  table  shows  the  units  of  measure 
employed  in  expressing  the  soundings  in  the  more  modern  nautical  charts  of  foreign 
nations  together  with  their  equivalents  in  the  units  of  measure  used  in  the  charts 
published  by  the  United  States : 


Nationality  of 
chart. 


Argentine.. . 
Austrian 


Belgian . 
Chilean . 
Danish . 
Dutch.. 


French. . 
German. 
Italian.. 


Unit  of  soundings. 


Metro . . . 
Metro . . . 
or  faden . 
Metre . . . 
Metro . . . 

favn 

vadem... 
or  metre. 
Metre . . . 

do... 

Metro . .  - 


Equivalent  in  United 
States  units. 


Feet. 


Fathoms. 


3.281 
3.281 
6.223 


281 
281 
176 
905 
281 
281 
3.281 
3.281 


0.547 
0.547 
1.037 
0.547 
0.547 
1.029 
0.984 
0.547 
0.547 
0.547 
0.547 


Nationality  of 
diart. 


Japanese . . 
Norwegian 

Portuguese 
Russian.. . 
Spanish... 

Swedish... 

British 


Unit  of  soundings. 


Fathom. 
Metre . . 
or  favn . 
Metro . . 
Sajene.. 
Metro . . 
or  braza 
Metre . . 
or  famn. 
Fathom, 


Equivalent  in  United 
States  units. 


6.000 

3.281 
6.176 
3.  281 
6.000 
3.281 
5.492 
3.281 
5.844 
6.000 


Fathoms. 


1.000 
0.547 
1.029 
0.547 
1.000 
0.547 
0.914 
0.  547 
0.974 
1.000 


FiQ.  3. 


the 
the 


THE     BAROMETER. 

48.  The  harometer  is  an  instrument  for  measuring  the  pres- 
sure of  the  atmosphere,  and  is  of  great,  service  to  the  mariner 
in  affording  a  knowledge  of  existing  meteorological  conditions 
and  of  the  probable  changes  therein.  There  are  two  classes  of 
barometer — mercurial  and  aneroid. 

49.  The  Mercurial  Barometer. — This  instrument,  in- 
vented by  Torricelli  in  1643,  indicates  the  pressure  of  the  atmos- 
phere by  the  height  of  a  column  of  mercury. 

If  a  glass  tube  of  uniform  internal  diameter  somewhat 
more  than  30  inches  in  length  and  closed  at  one  end  be  com- 
pletely filled  with  pure  mercury,  and  then  placed,  open  end 
down,  in  a  cup  of  mercur;^  (the  open  end  having  been  tempo- 
rarily sealed  to  retain  the  liquid  during  the  process  of  inverting), 
it  will  be  found  that  the  mercury  in  the  tube  will  fall  until  the 
top  of  the  column  is  about  30  inches  dbove  the  level  of  that 
which  is  in  the  cup,  leaving  in  the  upper  part  of  the  tube  a 
vacuum.  Since  the  weight  of  the  column  of  mercury  thus  left 
standing  in  the  tube  is  equal  to  the  pressure  by  which  it  is  held 
in  position — namely,  that  of  the  atmospheric  air — it  follows  that 
the  height  of  the  column  is  subject  to  variation  upon  variation  of 
that  pressure;  hence  the  mercury  falls  as  the  pressure  of  the 
atmosphere  decreases  and  rises  as  that  pressure  increases.  The 
mean  pressure  of  the  atmosphere  is  equal  to  nearly  15  pounds 
to  the  square  inch;  the  mean  height  of  the  barometer  is  about 
30  inches. 

50.  In  the  practical  construction  of  the  barometer  the  glass 
tube  which  contains  the  mercury  is  encased  in  a  brass  tube,  the 
latter  terminating  at  the  top  in  a  ring  to  be  used  for  suspension, 
and  at  the  bottom  in  a  flange,  to  which  the  several  parts  form- 
ing the  cistern  are  attached.  The  upper  part  of  the  brass 
tube  is  partially  cut  away  to  expose  the  mercurial  column  for 
observation;  abreast  this  opening  is  fitted  a  scale  for  measur- 
ing the  height,  and  along  the  scale  travels  a  vernier  for  exact 
reading;  the  motion  of  the  vernier  is  controlled  by  a  rack  and 
pinion,  the  latter  having  a  milled  head  accessible  to  the  observer, 
by  which  the  adjustment  is  made.  In  the  middle  of  the  brass 
tube  is  fixed  a  thermometer,  the  bulb  of  which  is  covered  from 


Fig.  4. 


outside  but  open  toward  the  mercury,  and  which,  bein^  nearly  in  contact  with 
glass  tube,  inaicates  the  temperature  of  the  mercury  and  not  that  of  the  external 


INSTBUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


25 


air;  the  central  position  of  the  column  is  selected  in  order  that  the  mean  temperature 
may  be  obtained — a  matter  of  importance,  as  the  temperature  of  the  mercurial 
column  must  be  taken  into  account  in  every  accurate  application  of  its  reading. 

51.  In  the  arrangement  of  further  details  mercurial  barometers  are  divided 
into  two  classes,  according  as  they  are  to  be  used,  as  Standards  (fig.  4)  on  shore,  or 
as  Sea  Barometers  (fig.  3)  on  shipboard. 

In  the  Standard  Barometer  the  scale  and  vernier  are  so  graduated  as  to  enable 
an  observer  to  read  the  height  of  the  mercurial  column  to  the  nearest  0.002  inch, 
while  in  the  Sea  Barometer  the  reading  can  not  be  made  closer  than  0.01  inch. 

The  instruments  also  differ  in  the  method  of  obtaining  the  true  height  of  the 
mercurial  column  at  varying  levels  of  the  liquid  in  the  cistern.  It  is  evident  that 
as  the  mercury  in  the  tube  rises,  upon  increase  of  atmospheric  pressure,  the  mercury 
in  the  cistern  must  fall ;  and,  conversely,  when  the  mercurial  column  falls  the  amount 
of  fluid  in  the  cistern  will  thereby  be  increased  and  a  rise  of  level  will  occur.  As  the 
height  of  the  mercurial  column  is  required  above  the  existing  level  in  the  cistern, 
some  means  must  be  adopted  to  obtain  the  true  height  under  varying  conditions. 
In  the  Standard  Barometer  the  mercury  of  the  cistern  is  contained  in  a  leather  bag, 
against  the  bottom  of  which  presses  tne  point  of  a  vertical  screw,  the  milled  head 
of  the  screw  projecting  from  the  bottom  of  the  instrument  and  thus  placing  it  under 
control  of  the  observer.  By  this  means  the  surface  of  the  mercury  in  the  cistern 
(which  is  visible  through  a  glass  casing)  may  be  raised  or  lowered  until  it  exactly 
coincides  with  that  level  which  is  chosen  as  the  zero  of  the  scale,  and  which  is  indicated 
by  an  ivory  pointer  in  plain  view. 

In  the  Sea  Barometer  there  is  no  provision  for  adjusting  the  level  of  the  cistern 
to  a  fixed  point,  but  compensation  for  the  variable  level  is  made  in  the  scale  gradu- 
ations ;  a  division  representing  an  inch  On  the  scale  is  a  certain  fraction  short  of  the 
true  inch,  proper  allowance  being  thus  made  for  the  rise  in  level  which  occurs  with 
a  fall  of  the  column,  and  for  the  reverse  condition. 

Further  modification  is  made  in  the  Sea  Barometer  to  adapt  it  to  the  special 
use  for  which  intended.  The  tube  toward  its  lower  end  is  much  contracted  to  prevent 
the  oscillation  of  the  mercurial  column  known  as  "pumping,"  which  arises  from  the 
motion  of  the  ship ;  and  just  below  this  point  is  a  trap  to  arrest  any  small  bubbles 
of  air  from  finding  their  way  upward.  Tne  instrument  aboard  ship  is  suspended  in 
a  revolving  center  ring,  in  gimbals,  supported  on  a  horizontal  brass  arm  which  is 
screwed  to  the  bulkhead;  a  vertical  position  is  thus  maintained  by  the  tube  at  all 
times. 

62.  The  vernier  is  an  attachment  for  facilitating  the  exact  reading  of  the  scale 
of  the  barometer,  and  is  also  applied  to  many  other  instruments  of  precision,  as,  for 
example,  the  sextant  and  theodolite.  It  consists  of  a  metal  scale  similar 
in  general  construction  to  that  of  the  instrument  to  which  it  is  fitted,  and 
arranged  to  move  alongside  of  and  in  contact  with  the  main  scale. 

The  general  principle  of  the  vernier  requires  that  its  scale  shall  have 
a  total  length  exactly  equal  to  some  whole  number  of  divisions  of  the  scale 
of  the  instrument  and  that  this  length  shall  be  subdivided  into  a  number 
of  parts  equal  to  1  more  or  1  less  than  the  number  of  divisions  of  the 
instrument  scale  which  are  covered;  thus,  if  a  space  of  9  divisions  of  the 
main  scale  be  designated  as  the  length  of  the  vernier,  the  vernier  scale 
would  be  divided  into  either  8  or  10  parts. 

Suppose  that  a  barometer  scale  be  divided  into  tenths  of  an  inch  and 
that  a  length  of  9  divisions  of  such  a  scale  be  divided  into  10  parts  for  a 
vernier  (fig.  5) ;  and  suppose  that  the  divisions  of  the  vernier  be  numbered 
consecutively  from  zero  at  the  origin  to  10  at  the  upper  extremity.  If,  now, 
by  means  of  the  movable  rack  and  pinion,  the  bottom  or  zero  division  of  the 
vernier  be  brought  level  with  the  top  of  the  mercurial  column,  and  that 
division  falls  into  exact  coincidence  with  a  division  of  the  main  scale,  then 
the  height  of  the  column  wiU  correspond  with  the  scale  reading  indicated. 
In  such  a  case  the  top  of  the  vernier  will  also  exactly  coincide  with  a 
scale  division,  but  none  of  the  intermediate  divisions  wiU  be  evenly  abreast 
of  such  a  division;  the  division  marked  *'l"  will  fall  short  oi  a  scale 
division  by  one-tenth  of  1  division  of  the  scale,  or  by  0^01  inch;  that  marked  "2"  by 
two-tenths  of  a  division,  or  0.02  inch;  and  so  on.     If  the  vernier,  instead  of  having 


Fig.  5. 


26 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


the  zero  coincide  with  a  scale  division,  has  the  division  "1"  in  such  coincidence, 
it  follows  that  the  mercurial  column  stands  at  0.01  inch  above  that  scale  division 
which  is  next  below  the  zero;  for  the  division  "2,"  at  0.02  inch;  and  similarly  for 
the  others.  In  the  case  portrayed  in  figure  5,  the  reading  of  the  column  is  29.81 
inches,  the  scale  division  next  below  the  zero  being  29.80  inches,  while  the  fact  that 
the  first  division  is  abreast  a  mark  of  the  scale  shows  that  0.01  inch  must  be  added 
to  this  to  obtain  the  exact  reading. 

Had  an  example  been  chosen  in  which  8  vernier  divisions  covered  9  scale 
divisions — that  is,  where  the  number  of  vernier  divisions  was  1  less  than  the  number 
of  scale  divisions  covered — the  principle  would  still  have  applied.  But,  instead  of 
the  length  of  1  division  of  the  vernier  falling  short  of  a  division  of  the  scale  by  one- 
tenth  the  length  of  the  latter,  it  would  have  fallen  beyond  by  one-eighth.  ^  To  read  in 
such  a  case  it  would  therefore  be  necessary  to  number  the  vernier  divisions  from 
up  downward  and  to  regard  the  subdivisions  as  -^  instead  of  0.01  inch. 

It  is  a  general  rule  that  the  smallest  measure  to  which  a  vernier  reads  is  equal 
to  the  lengm  of  1  division  of  the  scale  divided  by  the  number  of  divisions  of  the 
vernier;  hence,  by  varying  either  the  scale  or  the  vernier,  we  may  arrive  at  any 
subdivision  that  may  be  desired. 

53.  The  Sea  Barometer  is  arranged  as  described  for  the  instrument  assumed  in 
the  illustration;  the  scale  divisions  are  tenths  of  an  inch,  and  the  vernier  has  10 
divisions,  whence  it  reads  to  0.01  inch.  It  is  not  necessary^  to  seek  a  closer  reading, 
as  complete  accuracy  is  not  attainable  in  observing  the  height  of  a  barometer  on  a 
vessel  at  sea,  nor  is  it  essential.  The  Standard  Barometer  on  shore,  however,  is 
capable  of  very  exact  reading;  hence  each  scale  division  is  made  equal  to  half  a 
tenth,  or  0.05  inch,  while  a  vernier  covering  24  such  divisions  is  divided  into  25  parts; 
hence  the  column  may  be  read  to  0.002  inch. 

54.  To  adjust  the  vernier  for  reading  the  height  of  the  mercurial  column  the 
eye  should  be  brought  exactly  on  a  level  with  the  top  of  the  column;  that  is,  the  line 
of  sight  should  be  at  right  angles  to  the  scale.  _  When  properly  set,  the  front  and 
rear  edges  of  the  vernier  and  the  uppermost  point  of  the  mercury  should  all  be  in 
the  line  of  sight.  A  piece  of  white  paper,  held  at  the  back  of  the  tube  so  as  to  reflect 
the  light,  assists  in  accurately  setting  the  vernier  by  day,  while  a  small  bull's-eye 
lamp  held  behind  the  instrument  enables  the  observer  to  get  a  correct  reading  at 
night.  When  observing  the  barometer  it  should  hang  freely,  not  being  inclined  by 
holding  or  even  by  touch,  because  any  inclination  will  cause  the  column  to  rise  in 
the  tube. 

55.  Other  things  being  equal,  the  mercury  wiU  stand  higher  in  the  tube  when 
it  is  warm  than  when  it  is  cold,  owing  to  expansion.  For  the  purposes  of  comparison, 
all  barometric  observations  are  reduced  to  a  standard  which  assumes  32°  F.  as  the 
temperature  of  the  mercurial  column,  and  62°  F.  as  that  of  the  metal  scale;  it  is 
therefore  important  to  make  this  reduction,  as  well  as  that  for  instrumental  error 
(art.  67),  in  order  to  be  enabled  to  compare  the  true  barometric  pressure  with  the 
normal  that  may  be  expected  for  any  locality.  The  following  table  gives  the  value 
of  this  correction  for  each  2°  F.,  the  plus  sign  showing  that  the  correction  is  to  be 
added  to  the  reading  of  the  ship's  barometer  and  the  minus  sign  that  it  is  to  be 
subtracted : 


Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

0 

20 
22 
24 
26 
28 
30 
32 
34 
36 
38 

Inch. 
+0.02 
+0.02 
+0.01 
+0.01 
0.00 
0.00 
-0.01 
-0.02 
-0.02 
-0.03 

0 

40 

42 
44 
46 
48 
50 
52 
54 
56 

1        58 

1 

Inch.. 

-0.03 

-0.04 

-0.04 

-0.05 

-0.05 

-0.06 

-0.06 

-0.07 

-0.07 

-0.08 

0 

60 
62 
64 
66 
68 
70 
72 
74 
76 
78 

Inch. 

-0.09 

-0.09 

-0.09 

-0.10 

-0.10 

-0.11 

-0.12 

-0.12 

-0.13 

-0.13 

o 

80 
82 
84 
86 
88 
90 
92 
94 
96 
98 

Inch. 

-0.14 

-0.14 

-0  15 

-0.15 

-0.  16 

-0.  16 

-0.17 

-0.17 

-0.18 

-0.18 

INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION.  27 

As  an  example,  let  the  observed  reading  of  the  mercurial  barometer  be  29.95 
inches,  and  the  temperature  as  given  by  the  attached  thermometer  74°;  then  we  have: 

// 

Observed  height  of  the  mercury 29.  95 

Correction  for  temperature  (74°) —0. 12 

Height  of  the  mercury  at  standard  temperature 29.  83 

66.  The  Aneroid  Barometer. — This  is  an  instrument  in  which  the  pressure 
of  the  air  is  measured  by  means  of  the  elasticity  of  a  plate  of  metal.  It  consists  of  a 
cylindrical  brass  box,  the  metal  in  the  sides  being  very  thin;  the  contained  air  having 
been  partially,  though  not  completely,  exhausted,  the  box  is  hermetically  sealed. 
When  the  pressure  of  the  atmosphere  increases  the  inclosed  air  is  compressed,  the 
capacity  oi  the  box  is  diminished,  and  the  two  flat  ends  approach  each  other;  when 
the  pressure  of  the  atmosphere  decreases,  the  ends  recede  from  one  another  in  conse- 
quence of  the  expansion  of  the  inclosed  air.  By  means  of  a  combination  of  levers, 
wiis  motion  of  the  ends  of  the  box  is  communicated  to  an  index  pointer  which  travels 
over  a  graduated  dial  plate,  the  mechanical  an-angement  being  such  that  the  motion 
of  the  ends  of  the  box  is  magnified  many  times,  a  very  minute  movement  of  the  box 
maldng  a  considerable  difference  in  the  indication  of  the  pointer.  The  graduations 
of  the  aneroid  scale  are  obtained  by  comparison  with  the  correct  readings  of  a  standard 
mercurial  barometer  under  normal  and  reduced  atmospheric  pressure. 

The  thermometer  attached  to  the  aneroid  barometer  is  merely  for  convenience 
in  indicating  the  temperature  of  the  air,  but  as  regards  the  instrument  itself  no  cor- 
rection for  temperature  can  be  applied  with  certainty.  Aneroids,  as  now  manufac- 
tured, are  almost  perfectly  compensated  for  temperature  by  the  use  of  different 
metals  having  unequal  coefficients  of  expansion;  tney  ought,  therefore,  to  show  the 
same  pressure  at  all  temperatures. 

The  aneroid  barometer,  from  its  small  size  and  the  ease  with  which  it  may  be  trans- 

Eorted,  can  often  be  usefully  employed  under  circumstances  where  a  mercurial 
arometer  would  not  be  available.  It  also  has  an  advantage  over  the  mercurial 
instrument  in  its  greater  sensitiveness,  and  the  fact  that  it  gives  earlier  indications 
of  change  of  pressure.  It  can,  however,  be  relied  upon  only  when  frequently  com- 
pared with  a  standard  mercurial  barometer;  moreover,  considerable  care  is  required 
m  its  handling;  while  slight  shocks  will  not  ordinarily  affect  it,  a  severe  jar  or  faaock 
may  change  its  indications  by  a  large  amount. 

Wlien  in  use  the  aneroid  barometer  may  be  suspended  vertically  or  placed  flat, 
but  changing  from  one  position  to  another  ordinarily  makes  a  sensible  change  in  the 
readings;  the  instrument  should  always,  therefore,  be  kept  in  the  same  position,  and 
the  errors  determined  by  comparisons  made  while  occupying  its  customary  place. 

67.  Comparison  of  Barometers. — To  determine  the  reliability  of  tne  ship's 
barometer,  whether  mercurial  or  aneroid,  comparisons  should  from  time  to  time  be 
made  with  a  standard  barometer.  Nearly  all  instruments  read  either  too  hi^jh  or  too 
low  by  a  small  amount.  These  errors  arise,  in  a  mercurial  barometer,  from  the 
improper  placing  of  the  scale,  lack  of  uniformity  of  caliber  of  the  glass  tube,  or 
similar  causes;  in  an  aneroid,  which  is  less  accurate  and  in  which  there  is  even  more 
necessity  for  frequent  comparisons,  errors  may  be  due  to  derangement  of  any  of  the 
various  mechanical  features  upon  which  its  working  depends.  The  errors  of  the 
barometer  should  be  determined  for  various  heights,  as  they  are  seldom  the  same  at 
all  parts  of  the  scale. 

In  the  principal  ports  of  the  world  standard  barometers  are  observed  at  specified 
times  each  day,  and  the  readings,  reduced  to  zero  and  to  sea  level,  are  puoUshed. 
It  is  therefore  only  necessary  to  read  the  barometer  on  shipboard  at  those  times 
and,  if  a  mercurial  instrument  is  used,  to  note  the  attached  thermometer  and  apply 
the  correction  for  temperature  (art.  55).  It  is  evident  that  a  comparison  of  the 
heights  by  reduced  standard  and  by  the  ship's  barometer  wiU  give  the  correction  to 
be  applied  to  the  latter,  including  the  instrumental  error,  the  reduction  to  sea  level, 
and  the  personal  error  of  the  observer.  In  the  United  States,  standard  barometer 
readings  are  made  by  the  Weather  Bureau. 

Aneroid  barometers  may  be  adjusted  for  instrumental  error  by  moving  the  index 
hand,  but  this  is  usually  done  only  in  the  case  of  errors  of  considerable  magnitude. 


28  INSTRUMENTS  AND  ACCESSOEIES  IN   NAVIGATION. 

58.  Determination  of  Heights  by  Barometer. — The  barometer  may  be 
used  to  determine  the  difference  in  heights  between  any  two  stations  by  means  of 
the  difference  in  atmospheric  pressure  between  them.  An  approximate  rule  is  to 
allow  0.0011  inch  for  each  difference  in  level  of  1  foot,  or,  more  roughly,  0.01  inch 
for  every  9  feet. 

A  very  exact  method  is  afforded  by  Babinet's  formula.  If  Bo  and  B  represent 
the  barometric  pressure  (corrected  for  all  sources  of  instrumental  error)  at  the  lower 
and  at  the  upper  stations  respectively,  and  to  and  t  the  corresponding  temperatures  of 
the  air;  then, 

TJ      T> 

Diff .  in  height  =  C  X  t3°  .  ^ ; 
if  the  temperatures  be  taken  by  a  Fahrenheit  thermometer, 

C  (in  feet)  =52,  494  (l  +  ^""^qqq^^); 
if  a  centigrade  thermometer  is  used, 

C  (in  meters)  =  16,000(^1  +^^^)- 

THE  THERMOMETER. 

59.  Tlie  Thermometer  is  an  instrument  for  indicating  temperature.  In  its 
construction  advantage  is  taken  of  the  fact  that  bodies  are  expanded  by  heat  and 
contracted  by  cold.  In  its  most  usual  form  the  thermometer  consists  of  a  bulb  filled 
with  mercury,  connected  with  a  tube  of  very  fine  cross-sectional  area,  the  liquid 
column  rising  or  falling  in  the  tube  according  to  the  volume  of  the  mercury  due  to  the 
actual  degree  of  heat,  and  the  height  of  the  mercury  indicating  upon  a  scale  the 
temperature;  the  mercury  contained  in  the  tube  moves  in  a  vacuum  produced  by 
the  expulsion  of  the  air  through  boiling  the  mercury  and  then  closing  the  top  of  the 
tube  by  means  of  the  blowpipe. 

There  are  three  classes  of  thermometer,  distinguished  according  to  the  method 
of  graduating  the  scale  as  follows:  the  FakrenTieit,  in  which  the  freezing  point  of 
water  is  placed  at  32°  and  its  boUing  point  (under  normal  atmospheric  pressure)  at 
212°;  the  Centigrade,  in  which  the  freezing  point  is  at  0°  and  the  boilmg  point  at 
100°;  and  the  Reaumur,  in  which  these  pomts  are  at  0°  and  80°,  respectively.  The 
Fahrenheit  thermometer  is  generally  used  in  the  United  States  and  England.  Tables 
will  be  found  in  this  work  for  the  interconversion  of  the  various  scale  readings 
(Table  31). 

60.  The  thermometer  is  a  valuable  instrument  for  the  mariner,  not  only  by 
reason  of  the  aid  it  affords  him  in  judging  meteorological  conditions  from  the  tem- 
perature of  the  air  and  the  amount  of  moisture  it  contains,  but  also  for  the  evidences 
it  furnishes  at  times,  through  the  temperature  of  the  sea  water,  of  the  ship's  position 
and  the  probable  current  that  is  being  encountered. 

61.  The  thermometers  employed  in  determining  the  temperature  of  the  air 
(wet  and  dry  bulb)  and  of  the  water  at  the  surface,  should  be  mercurial,  and  of  some 
standard  make,  with  the  graduation  etched  upon  the  glass  stem;  they  should  be 
compared  with  accurate  standards,  and  not  accepted  if  their  readings  vary  more 
than  1  °  from  the  true  at  any  point  of  the  scale. 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


29 


62.  The  diy-bulb  thermometer  gives  the  temperature  of  the  free  air.  The 
wet-bulb  thermometer,  an  exactly  similar  instrument,  the  bulb  of  which  is  surrounded 
by  an  envelope  of  moistened  clotn,  gives  what  is  known  as  the  temperature  of  evapora- 
tion, which  is  always  somewhat  less  than  the  temperature  of  the  free  air.  From  the 
difference  of  these  two  temperatures  the  observer  may  determine  the  proximity  of 
the  air  to  saturation;  that  is,  how  near  the  air  is  to  that  point  at  which  it  will  be 
obliged  to  precipitate  some  of  its  moisture  (water  vapor)  in  the  form  of  liquid.  With 
the  envelope  of  the  wet  bulb  removed,  the  two  thermometers  should  read  precisely 
the  same ;  otherwise  they  are  practically  useless. 

The  two  thermometers,  the  wet  and  the  dry  bulb,  should  be  hung  within  a  few 
inches  of  each  other,  and  the  surroundings  should  be  as  far  as  possible  identical.  In 
practice  the  two  thermometers*  are  gener- 
ally inclosed  within  a  small  lattice  case,  such 
as  that  shown  in  figure  6 ;  the  case  should  be 
placed  in  a  position  on  deck  remote  from  any 
source  of  artificial  heat,  sheltered  from  the 
direct  rays  of  the  sun,  and  from  the  rain  and 
spray,  but  freely  exposed  to  the  circulation 
of  the  air;  the  door  should  be  kept  closed 
except  during  the  process  of  reading.  The 
cloth  envelope  of  the  wet  bulb  should  be 
a  single  thickness  of  fine  muslin,  tightly 
stretched  over  the  bulb,  and  tied  with  a  fine 
thread.  The  wick  which  serves  to  carry  the 
water  from  the  cistern  to  the  bulb  should 
consist  of  a  few  threads  of  lamp  cotton,  and 
should  be  of  sufficient  length  to  admit  of  two 
or  three  inches  being  coded  in  the  cistern. 
The  muslin  envelope  of  the  wet  bulb  should 
be  at  all  times  thoroughly  moist,  but  not 
dripping. 

When  the  temperature  of  the  air  falls 
to  32°  F.  the  water  in  the  wick  freezes,  the 
capillary  action  is  at  an  end,  the  bulb  in 
consequence  soon  becomes  quite  dry,  and 
the  thermometer  no  longer  shows  the  tem- 

Eerature  of  evaporation.  At  such  times  the 
ulb  should  be  thoroughly  wetted  with  ice- 
cold  water  shortly  before  the  time  of  observation,  using  for  this  purpose  a  camel's 
hair  brush  or  feather;  by  this  process  the  temperature  oithe  wet  bulb  is  temporarily 
raised  above  that  of  the  dry,  but  oiJy  for  a  brief  time,  as  the  water  quickly  freezes; 
and  inasmuch  as  evaporation  takes  place  from  the  surface  of  the  ice  thus  formed 
precisely  as  from  the  surface  of  the  water,  the  thermometer  will  act  in  the  same  way 
as  if  it  had  a  damp  bulb.  The  wet-bulb  thermometer  can  not  properly  read  higher 
than  the  dry,  and  if  the  reading  of  the  wet  bulb  should  be  the  higher,  it  may  always 
be  attributed  to  imperfections  in  the  instruments. 


a  Called  a  psyohrometer. 


30 


INSTRUMENTS  AND  ACCESSORIES  IN    NAVIGATION. 


63.  Knowing  the  temperature  of  the  wet  and  dry  bulbs,  the  relative  humidity 
of  the  atmosphere  at  the  time  of  observation  may  be  found  from  the  following  table: 


Tempera- 

DifEerence  between  dry-bulb  and  wet-bulb  readings. 

lure  of  the 
air,  dry- 
bulb  ther- 

1° 

2° 

3° 

4° 

5° 

6° 

8° 

9° 

10* 

mometer. 

0 

Per  ct. 

Per  ct. 

Per  ct. 

Per  a. 

Per  ct. 

Per  ct. 

Per  ct. 

Per  ct. 

Ptr  ct. 

Per  ct. 

24 

87 

75 

62 

50 

38 

26 

26 

88 

76 

65 

53 

42 

30 

28 

89 

78 

67 

56 

45 

34 

24 

30 

90 

79 

•68 

58 

48 

38 

28 

32 

90 

80 

70 

61 

51 

41 

32 

23 

34 

90 

81 

72 

63 

53 

44 

35 

27 

36 

91 

82 

73 

64 

55 

47 

38 

30 

22 

38 

92 

83 

75 

66 

57 

50 

42 

34 

26 

40 

92 

84 

76 

68 

59 

52 

44 

37 

30 

22 

42 

92 

84 

77 

69 

61 

54 

47 

40 

33 

26 

44 

92 

85 

78 

70 

63 

56 

49 

43 

36 

29 

46 

93 

85 

79 

72 

65 

58 

51 

45 

38 

32 

48 

93 

86 

79 

73 

66 

60 

53 

47 

41 

35 

50 

93 

87 

80 

74 

67 

61 

55 

49 

43 

37 

52 

94 

87 

81 

75 

69 

63 

57 

51 

46 

40 

64 

94 

88 

82 

76 

70 

64 

69 

53 

48 

42 

56 

94 

88 

82 

77 

71 

65 

60 

55 

50 

44 

58 

94 

89 

83 

78 

72 

67 

61 

56 

51 

46 

60 

94 

89 

84 

78 

73 

68 

63 

58 

53 

48 

62 

95 

89 

84 

79 

74 

69 

64 

59 

54 

50 

64 

95 

90 

85 

79 

74 

70 

65 

60 

56 

51 

66 

95 

90 

85 

80 

75 

71 

66 

61 

57 

53 

68 

95 

90 

85 

81 

76 

71 

67 

63 

68 

64 

70 

95 

90 

86 

81 

77 

72 

68 

64 

60 

66 

72 

95 

91 

86 

82 

77 

73 

69 

65 

61 

67 

74 

95 

91 

86 

82 

78 

74 

70 

66 

62 

68 

76 

95 

91 

87 

82 

78 

74 

70 

66 

63 

59 

78 

96 

91 

87 

83 

79 

75 

71 

67 

63 

60 

80 

96 

92 

87 

83 

79 

75 

72 

68 

64 

61 

82 

96 

92 

88 

84 

80 

76 

72 

69 

65 

62 

84 

96 

92 

88 

84 

80 

77 

73 

69 

66 

63 

86 

96 

92 

88 

84 

81 

77 

73 

70 

67 

63 

88 

96 

92 

88 

85 

81 

77 

74 

71 

67 

64 

90 

96 

92 

88 

85 

81 

78 

74 

71 

68 

65 

The  table  may  be  readily  understood.  For  example,  if  the  temperature  of  the 
air  (dry  bulb)  be  60°,  and  the  temperature  of  evaporation  (wet  bulb)  be  56°,  the 
difference  being  4°,  look  in  the  column  headed  ''Temperature  of  the  air"  for  60°, 
and  for  the  figures  on  the  same  line  in  column  headed  4°;  here  78  will  be  found, 
which  means  that  the  air  is  78  per  cent  saturated  with  water  vapor;  that  is,  that  the 
amount  of  water  vapor  present  in  the  atmosphere  is  78  per  cent  of  the  total  amount 
that  it  could  carry  at  the  given  temperature  (60°).  This  total  amount,  or  saturation, 
is  thus  represented  hj  100,  and  if  there  occurred  any  increase  of  the  quantity  of 
vapor  beyond  this  point,  the  excess  would  be  precipitated  in  the  form  of  liquid. 
Over  the  ocean's  surface  the  relative  humidity  is  generally  about  90  per  cent,  or  even 
higher  in  the  doldrums;  over  the  land  in  dry  wmter  weather  it  may  fall  as  low  as 
40  per  cent. 

64.  The  sea  water  of  which  the  temperature  is  to  be  taken  should  be  drawn  from 
a  depth  of  3  feet  below  the  surface,  the  bucket  used  being  weighted  in  order  to  sink 
it.  The  bulb  of  the  thermometer  should  remain  immersed  m  the  water  at  least 
three  minutes  before  reading,  and  the  reading  should  be  made  with  the  bulb 
immersed. 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION.  31 

THE  LOG  BOOK. 

65.  The  Log  Book  is  a  record  of  the  ship's  cruise,  and,  as  such,  an  important 
accessory  in  the  navigation.  It  should  afford  all  the  data  from  which  the  position 
of  the  ship  is  estabhshed  by  the  method  of  dead  reckoning;  it  should  also  comprise 
fl,  record  of  meteorological  observations,  which  should  be  made  not  only  for  the  purpose 
of  foretelling  the  weather  during  the  voyage,  but  also  for  contribution  to  the  general 
fund  of  knowledge  of  marine  meteorolo^. 

66.  A  convenient  form  for  recordmg  the  data,  which  is  employed  for  the  log 
books  of  United  States  naval  vessels,  is  shown  on  page  32 ;  beside  the  tabulated  matter 
thus  arranged,  to  whicli  one  page  of  the  book  is  devoted,  a  narrative  of  the  miscella- 
neous events  of  the  day,  written  and  signed  by  the  proper  officers,  appears  upon  the 
opposite  page. 


32 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


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INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 


33 


67.  For  the  most  part,  the  nature  of  the  information  called  for,  with  the  method 
of  recording  it,  will  be  apparent,  A  brief  explanation  is  here  given  of  such  points 
as  seem  to  require  it. 

68.  The  Wind. — In  recording  the  force  of  the  wind  the  scale  devised  by  the 
late  Admiral  Sir  F.  Beaufort  is  employed.  According  to  this  scale  the  wind  varies 
from  0,  a  calm,  to  12,  a  hurricane,  the  greatest  velocity  it  ever  attains.  In  the  lower 
grades  of  the  scale  the  force  of  the  wind  is  estimated  from  the  speed  imparted  to  a 
man-of-war  of  the  early  part  of  the  nineteenth  century  sailing  full  and  by;  in  the 
higher  grades,  from  the  amount  of  sail  which  the  same  vessel  could  carry  when 
close-hauled.  The  scale,  with  the  estimated  velocity  of  the  wind  in  both  statute  and 
nautical  miles  per  hour,  is  as  follows : 


Conditions. 

Velocity. 

Mean  pressure 

in  pounds 

per  square 

foot. 

Force  of  wind. 

Statute  miles  per 
hour. 

Nautical  miles  per 
hour. 

0— r.filni 

Full-rigged  ship,  all  sails  set,  no  headway. . 

Just  sufficient  to  give  steerage  way 

Speed  of  1  or  2  knots,  "full and  by  " 

Speed  of  3  or  4  knots, "  full  and  by  " 

Speed  of  5  or  6  knots, "  full  and  by  " 

All  plain  sail, "  full  and  by  " 

Oto  3 
8 
13 
18 
23 
28 
34 
40 
48 

56 

65 

75 

90  and  over. 

Oto  2.6 
6.9 
11.3 
15.6 
20.0 
24.3 

29.  r, 

34.7 
41.6 

48.6 

56.4 

65.1 

78. 1  and  over. 

0.03 

1. — Light  air 

0.23 

2.— Light  breeze 

3.— Gentle  breeze 

4.— Moderate  breeze . . . 

0.62 
1.2 
1.9 
2.9 

6 —Strong  breeze 

7.— Moderate  gale 

8. — Fresh  gale 

Topgallantsails  oversingle-reefed  topsails. . 

4.2 
6.9 

Treble-reefed  topsails  (or   reefed  upper 
topsails  and  courses). 

Close-reefed  topsails  and  courses  (or  lower 
topsails  and  courses). 

Close-reefed  main  topsail  and  reefed  fore- 
sail (or  lower  main  topsail  and  reefed 
foresail). 

8.4 

9. — Strong  gale 

10.— Whole  gale 

11.— Storm 

11.5 
15.5 

20.6 

Under  bare  poles 

29.6 

69.  Wlien  steaming  or  sailing  with  any  considerable  speed,  the  apparent  direc- 
tion and  force  of  the  wind,  as  determined  from  a  vane  flag,  or  peimant  aboard  ship, 
may  differ  materially  from  the  true  direction  and  force,  the  reason  being  that  the 
air  appears  to  come  from  a  direction  and  with  a  force  dependent,  not  only  upon  the 
wind  itself,  but  also  upon  the  motion  of  the  vessel.  For  instance,  suppose  tnat  the 
wind  has  a  velocity  of  20  knots  an  hour  (force  4),  and  take  the  case  of  two  vessels, 
eachsteaming  20  knots,  the  first  with  the  wind  dead  aft,  the  second  with  the  wind  dead 
ahead.  The  former  vessel  will  be  moving  with  the  same  velocity  as  the  air  and  in 
the  same  direction;  the  velocity  of  the  wind  relatively  to  the  ship  will  thus  be  zero; 
on  the  vessel  an  apparent  calm  wiU  prevail  and  the  pennant  wiU  hang  up  and  down. 
The  latter  vessel  will  be  moving  with  the  same  velocity  as  the  air,  but  in  the  opposite 
direction;  the  relative  velocity  of  the  two  will  thus  be  the  sum  of  the  two  velocities, 
or  40  knots  an  hour,  and  on  the  second  vessel  the  wind  will  apparently  have  the 
velocity  corresponding  very  nearly  with  a  fresh  gale.  Again,  it  might  be  shown  that 
in  the  case  of  a  vessel  steaming  west  at  the  rate  of  20  knots,  with  the  wind  blowing 
from  north  with  the  velocitv  of  20  knots  an  hour,  the  velocity  with  which  the  air 
strikes  the  ship  as  a  result  oi  the  combined  motion  wiU  be  28  knots  an  hour,  and  the 
direction  from  which  it  comes  will  be  NW.  If,  therefore,  the  effect  of  the  speed  of 
the  ship  is  neglected  the  wind  wiU  be  recorded  as  NW.,  force  6,  when  in  reahty  it  is 
north,  force  4. 

In  order  to  make  a  proper  allowance  for  this  error  and  arrive  at  the  true  direction 
and  force  of  the  wind.  Table  32  may  be  entered  with  the  ship's  speed  and  the  apparent 
direction  and  force  of  the  wind  as  arguments,  and  the  true  direction  and  force  will 
be  found. 

21594°— 14 3 


34  INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION. 

70.  Weather. — To  dssignate  the  weather  a  series  of  symbols  devised  by  the 
late  Admiral  Beaufort  is  employed.  The  system  employed  in  the  United  States  Navy 
is  as  follows : 

b. — Clear  blue  sky.  p.— Passing  showers  of  rain, 

c— Clouds.  5.— Squally  weather. 

d. — Drizzling,  or  light  rain.  r. — Rainy  weather,  or  continuous  rain. 

/. — Fog,  or  foggy  weather.  s. — Snow,  snowy  weather,  or  snow  falling. 

g. — Gloomy,  or  dark,  stormy-looking  weather.  t. — Thunder. 

h. — Hail.  u. — Ugly  appearances,  or  threatening  weather. 

I. — Lightning.  ■?;.— Variable  weather, 

m.— Misty  weather.  w.— Wet,  or  heavy  dew. 

o._Overcast.  2.— Hazy  weather. 

To  indicate  great  intensity  of  any  feature,  its  symbol  may  be  underlined;  thus: 
r.,  heavy  rain. 

~  71.  Clouds. — The  following  are  the  principal  forms  of  clouds,  named  in  the 
order  of  the  altitude  above  the  earth  at  which  they  usually  occur,  beginning  with  the 
most  elevated.     The  symbols  by  which  each  is  designated  follows  its  name : 

1.  Cirrus  (Ci.). — Detached  clouds,  dehcate  and  fibrous  looking,  taking  the 
form  of  feathers,  generally  of  a  white  color,  sometimes  arranged  in  belts  which  cross 
a  portion  of  the  sky  in  great  circles,  and,  by  an  effect  of  perspective,  converging  toward 
one  or  two  opposite  points  of  the  horizon. 

2.  Cirro-Stratus  (Ci.-S.). — A  thin,  whitish  sheet,  sometimes  completely  cover- 
ing the  sky  and  only  giving  it  a  whitish  appearance,  or  at  others  presenting,  more  or 
less  distinctly,  a  formation  hke  a  tangled  web.  This  sheet  often  produces  halos 
around  the  sun  and  moon. 

3.  CiRRO-CuMULUS  (Ci.-Cu.). — Small  globular  masses  or  white  flakes,  having 
no  shadows,  or  only  very  slight  shadows,  arranged  in  groups  and  often  in  lines. 

4.  Alto-Cumulus  (A.-Cu.). — Rather  large  globular  masses,  white  or  grayish, 
partially  shaded,  arranged  in  groups  or  lines,  and  often  so  closely  packed  that  their 
edges  appear  confused.  The  detached  masses  are  generally  larger  and  more  compact 
at  the  center  of  the  group;  at  the  margin  they  form  into  finer  flakes.  They  often 
spread  themselves  out  in  lines  in  one  or  two  directions. 

5.  Alto-Stratus  (A.-S.). — A  thick  sheet  of  a  gray  or  bluish  color,  showing  a 
briUiant  patch  in  the  neighborhood  of  the  sun  or  moon,  and  which,  without  causing 
halos,  may  give  rise  to  coronas.  This  form  goes  through  all  the  changes  like  the 
Cirro-Stratus,  but  its  altitude  is  only  half  so  great. 

6.  Strato-Cumulus  (S.-Cu.). — Large  globular  masses  or  rolls  of  dark  cloud, 
frequently  covering  the  whole  skv,  especially  in  winter,  and  occasionally  giving  it 
a  wavy  appearance.  The  layer  of  Strato-Cumulus  is  not,  as  a  rule,  very  thick,  and 
patches  of  blue  sky  are  often  visible  through  the  intervening  spaces.  All  sorts  of 
transitions  between  this  form  and  the  Alto-Cumulus  are  noticeable.  It  may  be 
distinguished  from  Nimbus  by  its  globular  or  rolled  appearance  and  also  because  it 
does  not  bring  rain. 

7.  Nimbus  (N.). — Rain  clouds;  a  thick  layer  of  dark  clouds,  without  shape  and 
with  ragged  edges,  from  which  continued  rain  or  snow  generally  falls.  Through  the 
openings  of  these  clouds  an  upper  layer  of  Cirro-Stratus  or  Alto-Stratus  may  almost 
invariably  be  seen.  If  the  layer  of  Nimbus  separates  into  shreds  or  if  small  loose 
clouds  are  visible  floating  at  a  low  level  underneath  a  large  nimbus,  they  may  be 
described  as  Fracto-Nimbus  (Fr.-N.),  the  "scud"  of  sailors. 

8.  Cumulus  (Cu.). — Wool-pack  clouds;  thick  clouds  of  which  the  upper  surface 
is  dome-shaped  and  exhibits  protuberances,  while  the  base  is  horizontal.  When 
these  clouds  are  opposite  the  sun  the  surfaces  usually  presented  to  the  observer  have 
a  greater  brilliance  than  the  margins  of  the  protuberances.  When  the  light  falls 
aslant,  they  give  deep  shadows;  when,  on  the  contrary,  the  clouds  are  on  the  same 
side  as  the  sun,  they  appear  dark,  with  bright  edges.  The  true  Cumulus  has  clear 
superior  and  inferior  limits.  It  is  often  broken  up  by  strong  winds,  and  the  detached 
portions  undergo  continual  changes.  These  may  be  distinguished  by  the  name  of 
Fracto-Cumulus  (Fr.-Cu.). 


INSTRUMENTS  AND  ACCESSORIES  IN   NAVIGATION.  35 

9,  CuMULO-NiMBUS  (Cu-N.). — The  thunder-cloud  or  shower-cloud;  heavy 
masses  of  clouds  rising  in  the  form  of  mountains,  turrets,  or  anvils,  generally  having 
a  sheet  or  screen  of  fibrous  appearance  above,  and  a  mass  of  clouds  similar  to  Nimbus 
underneath.  From  the  base  there  usually  fall  local  showers  of  rain  or  of  snow 
(occasionally  hail  or  soft  hail). 

10.  Stratus  (S.). — A  horizontal  sheet  of  lifted  fog;  when  this  sheet  is  broken 
up  into  irregular  shreds  by  the  wind  or  by  the  summits  of  mountains,  it  may  be 
distinguished  by  the  name  of  Fracto-Stratus  (Fr.-S.). 

72.  In  the  scale  for  the  amount  of  clouds  0  represents  a  sky  which  is  cloudless 
and  10  a  sky  which  is  completely  overcast. 

73.  State  of  Sea. — The  state  of  the  sea  is  expressed  by  the  following  system 

of  symbols : 

B. — Broken  or  irregular  sea.  M. — ^Moderate  sea  or  Hwell. 

C. — Chopping,  short,  or  cross  sea.  R. — Rough  sea. 

G.— Ground  swell.  5.— Smooth  sea. 

//.—Heavy  sea.  T.— Tide-rips. 
L. — Long  rolling  sea. 

Note. — There  are  various  pubhcations  issued  by  the  Hydrographic  Office 
dealing  with  special  features  of  navigation,  which  should  be  regularly  consulted. 
Among  the  most  important  of  these  are : 

P%lot  charts  of  the  various  oceans  furnish  information  regarding  the  drift  of 
derelicts,  ice,  and  floating  obstructions,  the  tracks  of  storms,  average  conditions  of 
wind  and  weather,  ocean  currents,  magnetic  variation,  etc. 

Hydrographic  Bulletin,  weekly,  gives  more  detailed  facts  than  the  Pilot  Charts 
regarding  ice,  wrecks,  and  derelicts;  also  items  on  port  facilities,  use  of  oil 
to  calm  the  sea,  and  miscellaneous  items  of  use  and  interest  to  mariners. 

Daily  Memorandum,  published  at  the  main  office  at  Washington,  also  makes 
public  these  items  through  the  Branch  Hydrographic  Offices. 

Notice  to  Mariners,  weekly,  gives  changes  in  aids  to  navigation  (lights,  buoyage, 
harbor  constructions),  dangers  to  navigation  (rocks,  shoals,  banks,  bars),  important 
new  soundings,  and,  in  general,  all  such  facts  as  affect  mariners'  charts,  manuals,  and 
pilots  or  sailing  directions. 


*      CHAPTER  III. 
THE  COMPASS  EEKOE. 


CAUSES  OF  THE  ERROR. 

74.  The  properties  of  magnets  are  such  that  when  two  magnets  are  near  enough 
together  to  exert  a  mutual  influence,  those  poles  which  possess  like  magnetism  repel 
each  other,  and  those  which  possess  unlike  magnetism  attract  each  other. 

The  earth  is  a  magnetized  body,  and  acts  like  a  great  spherical  magnet  with 
poles  of  unlike  magnetism  situated  within  the  Arctic  and  Antarctic  circles  close  to 
longitudes  97°  west  and  155°  east  of  Greenwich,  respectively.  In  common  with 
magnets,  the  earth  is  surrounded  by  a  region  in  which  magnetic  influence  is  exercised 
upon  the  compass,  giving  the  magnetic  needle  a  definite  direction  in  each  locality 
and  causing  the  end  which  we  name  the  north  pole  of  the  compass  to  be  directed  in 
general  toward  the  region  of  the  magnetic  pole  in  the. geographical  north  and  the 
south  end  toward  the  region  of  the  magnetic  pole  in  the  geographical  south. 

The  north  end  of  the  compass — north-seeking,  as  it  is  sometimes  designated  for 
clearness — will  be  that  end  which  has  opposite  polarity  to  the  earth's  north  magnetic 
pole,  or,  otherwise  stated,  which  possesses  like  magnetism  with  the  earth's  south 
magnetic  pole. 

75.  By  reason  of  the  fact  that  the  magnetic  pole  in  each  hemisphere  differs  in 
geographical  position  by  a  large  and  unequal  amount  from  the  geographical  pole, 
we  are  made  aware  that  the  earth  is  not  magnetized  symmetrically  with  reference 
to  the  geographical  poles.  Hence  the  directive  influence  of  the  earth's  magnetism 
will  not  in  general  cause  the  compass  needle  to  pomt  in  the  direction  of  the  true 
meridian,  but  each  compass  point  will  differ  from  the  corresponding  true  point  by 
an  amount  varying  according  to  the  geographical  locality.  The  angle  representing 
this  difference  is  the  Variation  of  the  Compass,  sometimes  also  called  the  Magnetic 
Declination.  It  is  the  angle  between  the  plane  of  the  true  meridian  and  a  vertical 
plane  passing  through  a  freely  suspended  magnetic  needle  influenced  solely  by  the 
earth's  magnetism. 

The  variation  not  only  changes  as  one  travels  from  place  to  place  on  the  earth, 
being  different  in  different  localities,  but  in  every  locahty,  besides  the  minor  periodic 
movements  of  the  needle  known  as  the  diurnal,  monthly,  and  annual  variations, 
which  are  not  of  material  concern  to  the  mariner,  there  is  a  progressive  change 
which  extends  through  centuries  of  time  and  amounts  to  large  alterations  in  the 
pointing  of  the  compass.  In  taking  account  of  the  effect  produced  by  the  variation 
of  the  compass,  the  navigator  must  therefore  be  sure  that  the  variation  used  is 
correct  not  only  for  the  place,  but  also  for  the  time  under  consideration. 

Occasionally  the  magnetic  needle  is  subject  to  spasmodic  fluctuations  of  the 
earth's  magnetism  lasting  from  a  brief  period  to  several  days.  These  are  called 
magnetic  storms,  and  are  due  to  sudden  changes  in  the  electric  currents  which  cir- 
culate within  the  earth  and  in  the  region  surrounding  the  earth.  They  come  appar- 
entlj^  at  random,  and^  may  occur  nearly  simultaneously  over  the  whole  world  or  be 
restricted  to  a  certain  region.  The  range  of  their  effect  upon  the  compass  does 
not  often  exceed  the  half  of  a  degree  in  the  lower  latitudes,  and  hence  the  navigator 
need  only  be  concerned  with  them  in  the  higher  latitudes  where  he  may  look  to  the 
aurora  as  an  indication  of  their  occurrence. 

76.  Besides  the  error  thus  produced  in  the  indications  of  the  compass,  a  further 
one,  due  to  Local  Attraction,  ma,j  arise  from  extraneous  influences  due  to  natural 
magnetic  attraction  in  the  vicinity  of  the  vessel.     Instances  of  this  are  quite  common 

36 


THE  COMPASS  EKROB. 


37 


when  a  ship  is  in  port,  as  she  may  be  in  close  proximity  to  vessels,  docks,  machinery, 
or  other  masses  of  iron  or  steel.  It  is  also  encountered  in  the  shallow  waters  of  the 
sea  in  localities  where  the  mineral  substances  in  the  earth  itself  possess  magnetic 
qualities — as,  for  example,  at  certain  places  in  Lake  Suj)erior  and  at  others  oflF  the 
coast  of  Australia.  When  due  to  the  last-named  cause,  it  may  be  a  source  of  great 
danger  to  the  mariner,  but,  fortunately,  the  number  of  localities  subject  to  local 
attraction  is  limited.  The  amount  of  this  error  can  seldom  be  determined  except 
by  survey;  if  known,  it  might  properly  be  included  with  the  variation  and  treated 
as  a  pai't  thereof. 

77.  In  addition  to  the  variation,  the  compass  ordinarily  has  a  still  further 
error  in  its  indications,  which  arises  from  the  effect  exerted  upon  it  by  masses  of 
magnetic  metal  within  the  ship  itself.  This  is  known  as  the  Deviation  of  the  Compass. 
For  reasons  that  will  be  explained  later,  it  differs  in  amount  for  each  heading  of  the 
ship,  and,  further,  the  character  of  the  deviations  undergoes  modification  as  a  vessel 
proceeds  from  one  geographical  locality  to  another. 

APPLYING  THE  COMPASS  ERROR. 

78.  From  what  has  been  explained,  it  may  be  seen  that  there  are  three  methods 
by  which  bearings  or  courses  may  be  expressed:  (a)  true,  when  they  refer  to  the 
angular  distance  from  the  earth's  geographical  meridian;  (b)  magnetic,  when  they 
refer  to  the  angular  distance  from  the  earth's  magnetic  meridian,  and  must  be  cor- 
rected for  variation  to  be  converted  into  true;  and  (c)  hy  compass,  when  they  refer 
to  the  angular  distance  from  the  north  indicated  by  the  compass  on  a  given  heading 
of  the  ship,  and  must  be  corrected  for  the  deviation  on  that  heading  for  conversion 
to  magnetic,  and  for  both  deviation  and  variation  for  conversion  to  true  bearings  or 
courses.  The  process  of  applying  the  errors  under  all  circumstances  is  one  of  which 
the  navigator  must  make  mmself  a  thorough  master;  the  various  problems  of  con- 
version are  constantly  arising;  no  course  can  be  set  nor  bearing  plotted  without 
involving  the  application  of  this  problem,  and  a  mistake  in  its  solution  may  produce 
serious  consequences.  The  stuaent  is  therefore  urged  to  give  it  his  most  careful 
attention. 

79.  When  the  effect  of  a  compass  error,  whether  arising  from  variation  or  from 
deviation,  is  to  draw  the  north  end  of  the  compass  needle  to  the  right,  or  eastward, 
the  error  is  named  east,  or  is  marked  +  ;  when  its  effect  is  to  draw  the  north  end  of 
the  needle  to  the  left  or  westward,  it  is  named  west,  or  marked  — . 


Figures  7  and  8  represent,  respectively,  examples  of  easterly  and  westerly  errors. 
In  both  cases  consider  that  the  circles  represent  the  observer's  horizon,  N  and  S 
being  the  correct  north  and  south  points  in  each  case.  If  N'  and  S'  represent  the 
corresponding  points  indicated  by  a  compass  whose  needle  is  deflected  by  a  compass 
error,  then  in  the  first  case,  the  north  end  of  the  needle  being  drawn  to  the  right  or 
east,  the  error  will  be  easterly  or  positive,  and  in  the  second  case,  the  north  end  of  the 
needle  being  drawn  to  the  left  or  west,  the  compass  error  will  be  westerly  or  negative. 


38  THE  COMPASS  ERROR. 

Considering  figure  7,  if  we  assume  the  easterly  error  to  amount  to  one  point, 
it  will  be  seen  that  if  a  direction  of  N.  by  W.  is  indicated  by  the  compass,  the  correct 
direction  should  be  north,  or  one  point  farther  to  the  right.  If  the  compass  indicates 
north,  the  correct  bearing  is  N.  by  E.;  that  is,  still  one  point  to  the  right.  If  we 
follow  around  the  whole  card,  the  same  relation  wUl  be  found  in  every  case,  the 
corrected  bearing  being  always  one  point  to  the  right  of  the  compass  bearing. 
Conversely,  if  we  regard  figure  8,  assuming  the  same  amount  of  westerly  error,  a 
compass  bearing  of  N.  by  E.  is  the  equivalent  of  a  correct  bearing  of  north,  which  is 
one  point  to  the  left;  and  this  rule  is  general  throughout  the  circle,  the  corrected 
direction  being  always  to  the  left  of  that  shown  by  the  compass. 

80.  Having  once  satisfied  himseK  that  the  general  rule  holds,  the  navigator 
may  save  the  necessity  of  reasoning  out  in  each  case  the  direction  in  which  the  error 
must  be  applied,  and  need  only  charge  his  mind  with  some  single  formula  which  will 
cover  all  cases.     Such  a  one  is  the  following: 

When  the  correct  direction  is  to  the  right,  the  error  is  east. 

The  words  correct-right-east,  in  such  a  case,  would  be  the  key  to  all  of  his  solutions. 
With  easterly  error,  if  he  had  a  compass  course  to  change  to  a  corrected  one,  he 
would  know  that  to  obtain  the  result  the  error  must  be  applied  to  the  right;  and, 
if  it  were  desired  to  change  a  correct  course  to  one  indicated  by  compass,  the  error 
would  be  applied  to  the  left.  If  a  correct  bearing  is  to  be  compared  with  a  compass 
bearing  to  find  the  compass  error,  when  the  correct  bearing  is  to  the  right,  the 
error  is  easterly;  and  when  the  correct  bearing  is  to  the  left,  the  error  is  westerly. 

81.  It  must  be  remembered  that  the  word  east  is  equivalent  to  right  in  dealing 
with  the  compass  error,  and  west  to  left,  even  though  they  involve  an  apparent 
departure  from  the  usual  rules.  If  a  vessel  steers  NE.  by  compass  with  one  point 
easterly  error,  her  corrected  course  is  NE.  by  E.;  but  if  she  steers  SE.,  the  corrected 
course  is  not  SE.  by  E.,  but  SE.  by  S.  Another  caution  may  be  necessary  to  avoid 
confusion;  the  navigator  should  always  regard  himself  as  facing  the  point  under 
consideration  when  he  applies  an  error;  one  point  westerly  error  on  South  will  bring 
a  corrected  direction  to  S.  by  E.;  but  if  we  applied  one  point  to  the  left  of  South 
while  looking  at  the  compass  card  in  the  usual  way — north  end  up- — S.  by  W.  would 
be  the  point  arrived  at,  and  a  mistake  of  two  points  would  be  the  result. 

82.  In  the  foregoing  explanation  reference  has  been  made  to  '  'correct"  directions 
and  "compass  errors"  without  specifying  "magnetic"  and  "true"  or  "variation" 
and  "deviation."  This  has  been  done  in  order  to  make  the  statements  apply  to  all 
cases  and  to  enable  the  student  to  grasp  the  subject  in  its  general  bearing  without 
confusion  of  details. 

Actually,  as  has  already  been  pointed  out,  directions  given  may  be  true,  magnetic, 
or  by  compass.  By  applying  variation  to  a  magnetic  bearing  we  correct  it  and  make 
it  true,  by  applying  a  aeviation  to  a  compass  bearing  we  correct  it  to  magnetic,  and 
by  applying  to  it  the  combined  deviation  and  variation  we  correct  it  to  true.  Wliich- 
ever  of  these  operations  is  undertaken,  and  whichever  of  the  errors  is  considered,  the 
process  of  correction  remains  the  same ;  the  correct  direction  is  always  to  the  right, 
when  the  error  is  east,  by  the  amount  of  that  error. 

Careful  study  of  the  following  examples  will  aid  in  making  the  subject  clear: 

Examples:  A  bearing  taken  by  a  compass  free  from  deviation  is  76°;  variation, 
5°  W.;  required  the  true  bearing.     71°. 

A  bearing  taken  by  a  similar  compass  is  NW.  by  W.  ^  W.;  variation,  \  pt.  W.; 
required  the  true  bearing.     NW.  by  W.  |  W. 

A  vessel  steers  153°  by  compass;  deviation  on  that  heading,  3°  W.;  variation 
in  the  locality,  12°  E.;  required  the  true  course.     162°. 

A  vessel  steers  S.  by  W,  ^  W.;  deviation,  \  pt.  W.;  variation,  1  pt.  E.;  required 
the  true  course.     SSW.  \  W. 

It  is  desired  to  steer  the  magnetic  course  322°;  deviation,  4°  E.;  required  the 
course  by  compass.     318°. 

The  true  course  between  two  points  is  found  to  be  W.  "^  N.;  variation,  \\  pt. 
E.;  no  deviation;  required  the  compass  course.     W.  f  S. 

True  course  to  be  made,  55°;  aeviation,  7°  E.;  variation,  14°  W.;  required  the 
course  by  compass.     62°. 


THE  COMPASS  EBROB.  39 

A  vessel  passing  a  range  whose  direction  is  known  to  be  200°,  magnetic,  observes 
the  bearing  by  compass  to  be  178°;  required  the  deviation.     22°  E. 

The  sun's  observed  bearing  by  compass  is  91°;  it  is  found  by  calculation  to  be 
84°  (true);  variation,  8°  W.;  required  the  deviation.     1°  E. 

FINDING  THE  COMPASS  ERROR. 

83.  The  variation  of  the  compass  for  any  given  locality  is  found  from  the 
charts.  A  nautical  chart  always  contains  information  from  which  the  navigator  is 
enabled  to  ascertain  the  variation  for  any  place  within  the  region  embraced  and 
for  any  year.  Beside  the  information  thus  to  be  acquired  from  local  charts,  special 
charts  are  published  showing  the  variation  at  all  points  on  the  earth's  surface. 

84.  The  deviation  of  the  compass,  varying  as  it  does  for  every  ship,  for  every 
heading,  and  for  every  geographical  locality,  must  be  determined  by  the  navigator, 
for  which  purpose  various  metnods  are  available. 

Whatever  method  is  used,  the  ship  must  be  swung  in  azimuth  and  an  observa- 
tion made  on  each  of  the  headings  upon  which  the  deviation  is  required  to  be  known. 
If  a  new  iron  or  steel  ship  is  being  swung  for  the  first  time,  observations  should  be 
made  on  each  of  the  twenty-four  15°  rhumbs  into  which  the  compass  card  is  divided. 
At  later  swings,  especiall}^  after  correctors  have  been  applied,  or  in  the  case  of  wooden 
ships,  twelve  15°  rhumbs  will  suffice — or,  indeed,  only  six.  In  case  it  is  not  prac- 
ticable to  make  observations  on  exact  15°  rhumbs,  they  should  be  made  as  near 
thereto  as  practicable  and  plotted  on  the  Napier  diagram  (to  be  explained  hereafter), 
whence  the  deviations  on  exact  15°  rhumbs  may  be  found. 

85.  In  swinging  ship  for  deviations  the  vessel  should  be  on  an  even  keel  and  all 
movable  masses  of  iron  in  the  vicinity  of  the  compass  secured  as  for  sea,  and  the  com- 
pass accurately  centered  in  the  binnacle.  The  vessel,  upon  being  placed  on  any  head- 
mg,  should  be  steadied  there  for  three  or  four  minutes  before  the  observation  is  made, 
in  order  that  the  compass  card  may  come  to  rest  and  the  magnetic  conditions  assume 
a  settled  state.  To  assure  the  greatest  accuracy  the  ship  should  first  be  swung  to 
starboard,  then  to  port,  and  the  mean  of  the  two  deviations  on  each  course  taken. 
Ships  may  be  swung  under  their  own  steam,  or  with  the  assistance  of  a  tug,  or  at 
ancnor,  where  the  action  of  the  tide  tends  to  turn  them  in  azimuth  (though  in  this 
case  it  is  difficult  to  get  them  steadied  for  the  requisite  time  on  each  heading),  or  at 
anchor,  by  means  of  springs  and  hawsers. 

86.  The  deviation  of  all  compasses  on  the  ship  may  be  obtained  from  the  same 
swing,  it  being  required  to  make  observations  mth  tne  standard  only.  To  accomplish 
this  it  is  necessary  to  record  the  ship's  head  by  all  compasses  at  the  time  of  steadying 
on  each  even  rhumb  of  the  standard;  applying  the  deviation,  as  ascertained,  to  the 
heading  by  standard,  gives  the  magnetic  heads,  with  which  the  direction  of  the  ship's 
head  by  each  other  compass  may  be  compared,  and  the  deviation  thus  obtained. 
Then  a  complete  table  of  deviations  may  be  constructed  as  explained  in  article  94. 

87.  There  are  four  methods  for  ascertaining  the  deviations  from  swinging; 
namely,  by  reciprocal  hearings,  by  hearings  of  the  sun,  by  ranges,  and  by  a  distant 
ohject. 

88.  Reciprocal  Bearings. — One  observer  is  stationed  on  shore  with  a  spare 
compass  placed  in  a  position  free  from  disturbing  magnetic  influences;  a  second 
observer  is  at  the  standard  compass  on  board  ship.  At  the  instant  when  ready  for 
observation  a  signal  is  made,  and  each  notes  the  bearing  of  the  other.  The  bearing 
by  the  shore  compass,  reversed,  is  the  magnetic  bearing  of  the  shore  station  from  the 
ship,  and  the  difference  between  this  and  the  bearing  by  the  ship's  standard  compass 
represents  the  deviation  of  the  latter. 

In  determining  the  deviations  of  compasses  placed  on  the  fore-and-aft  amidship 
line,  when  the  distribution  of  magnetic  metal  to  starboard  and  port  is  symmetrical, 
the  shore  compass  may  be  replaced  by  a  dumb  compass,  or  pelorus,  or  by  a  theodolite 
in  which,  for  convenience,  the  zero  of  the  horizontal  graduated  circle  may  be  termed 
north;  the  reading  of  the  shore  instrument  wUl,  of  course,  not  represent  magnetic 
directions,  but  by  assuming  that  they  do  we  obtain  a  series  of  fictitious  deviations, 
the  mean  value  of  which  is  the  error  common  to  all.  Upon  deducting  this  error 
from  each  of  the  fictitious  deviations,  we  obtain  the  correct  values. 


40  THE   COMPASS  EBBOB. 

If  ship  and  shore  observers  are  provided  with  watches  which  have  been  com- 
pared with  one  another,  the  times  may  be  noted  at  each  observation,  and  thus 
afford  a  means  of  locating  errors  due  to  misunderstanding  of  signals. 

89.  Bearings  of  the  Sun. — In.  this  method  it  is  required  that  on  each  heading 
a  bearing  of  the  sun  be  observed  by  compass  and  the  time  noted  at  the  same  moment 
by  a  chronometer  or  watch.  By  means  which  will  be  explained  in  Chapter  XIV,  the 
true  bearing  of  the  sun  may  be  ascertained  from  the  known  data,  and  this,  compared 
with  the  compass  bearing,  gives  the  total  comjiass  error;  deducting  from  the  compass 
error  the  variation,  there  remains  the  deviation.  The  variation  used  may  be  that 
given  by  the  chart,  or,  in  the  case  of  a  compass  affected  only  by  symmetrically  placed 
u'on  or  steel,  may  be  considered  equal  to  the  mean  of  all  the  total  errors.  Other 
celestial  bodies  may  be  observed  for  this  purpose  in  the  same  manner  as  the  sun. 

This  method  is  important  as  being  the  most  convenient  one  available  for  deter- 
mining the  compass  error  at  sea.  When  adjusting  compasses  much  time  will  be 
saved  by  this  simple  modification  of  a  detail: 

Instead  of  tabulating  magnetic  azimuths  for  given  stated  times  in  advance,  draw 
on  cross-section  paper  a  curve  whose  ordinates  are  minutes  of  local  apparent  time  and 
whose  abscissae  are  degrees  of  magnetic  azimuth,  that  is,  true  azimuth  corrected  for 
variation.  Then  for  any  given  instant  (the  navigator's  watch  being  set  to  local 
apparent  time)  the  magnetic  azimuth  may  be  read  directly  from  the  curve.  The 
difference  between  the  magnetic  azimuth  of  the  sun  and  its  compass  bearing  is,  of 
course,  the  deviation  of  the  compass  on  that  particular  heading. 

90.  Ranges. — In  many  localities  there  are  to  be  found  natural  or  artificial 
range  marks  which  are  clearly  distinguishable,  and  which  when  in  line  lie  on  a  known 
magnetic  bearing.  By  steaming  about  on  different  headings  and  noting  the  compass 
bearing  of  the  ranges  each  time  of  crossing  the  line  that  they  mark,  a  series  of  devia- 
tions may  be  obtained,  the  deviation  of  each  heading  being  equal  to  the  difference 
between  the  compass  and  the  magnetic  bearing. 

91.  Distant  Object. — A  conspicuous  object  is  selected  which  must  be  at  a  con- 
siderable distance  from  the  ship  and  upon  which  there  should  be  some  clearly  defined 
point  for  taking  bearings.  The  direction  of  this  object  by  compass  is  observed  on 
successive  headings.  Its  true  or  magnetic  bearing  is  then  found  and  compared  with 
the  compass  bearings,  whence  the  deviation  is  obtained. 

The  true  or  the  magnetic  bearing  may  be  taken  from  the  chart.  The  magnetic 
bearing  may  also  be  found  by  setting  up  a  compass  ashore,  free  from  foreign  magnetic 
disturbance,  in  range  with  the  object  and  the  ship,  and  observing  the  bearing  of  the 
object;  or  the  magnetic  bearing  may  be  assumed  to  be  the  mean  of  the  compass 
bearings. 

In  choosing  an  object  for  use  in  this  method  care  must  be  taken  that  it  is  at  such 
a  distance  that  its  bearing  from  the  ship  does  not  practically  differ  as  the  vessel 
swings  in  azimuth.  If  the  ship  is  swung  at  anchor,  the  distance  should  be  not  less 
than  6  miles.  If  swung  under  way,  the  object  must  be  so  far  that  the  parallax 
(the  tangent  of  which  may  be  considered  equal  to  half  the  diameter  of  swinging 
divided  by  the  distance)  shall  not  exceed  about  30'. 

92.  In  all  of  the  methods  described  it  will  be  found  convenient  to  arrange  the 
results  in  tabular  form.  In  one  column  record  the  ship's  head  by  standard  compass, 
and  abreast  it  in  successive  columns  the  observations  from  which  the  deviation  is 
determined  on  that  heading,  and  finally  write  the  deviation  itself.  When  the  result 
of  the  swing  has  been  worked  up,  another  table  is  constructed  showing  simply  the 
headings  and  the  corresponding  deviations.  This  is  known  as  the  Deviation  Table 
of  the  compass.  If  compensation  is  to  be  attempted,  this  table  is  the  basis  of  the 
operation;  if  not,  the  deviation  tables  of  the  standard  and  steering  compass  should 
be  posted  in  such  place  as  to  be  accessible  to  all  persons  concerned  with  the  naviga- 
tion of  the  ship. 


THE  COMPASS  ERROR. 


41 


93.  Let  it  be  assumed  that  a  deviation  table  has  been  found  and  that  the  values 

are  as  follows: 

Deviation  table. 


Ship's  head  by  standard  compass.  Deviation, 


North 0 

15 
30 

NE 45 

60 
75 

East : 90 

105 
120 

SE 135 

150 
165 


-15  29 

-14  53 

-13  16 

-11  19 

-  9  69 

-  9  42 

-  9  06 

-  9  01 

-  7 

-  5 

-  2 


51 
54 
16 


+  8    29 


Ship's  head  by  standard  compass. 


South 180 

195 
210 

SW 225 

240 
255 

West 270 

285 
300 

NW 315 

330 
345 


DeviatioE 

. 

+17 

52 

+23 

47 

+27 

07 

+25 

35 

+21 

57 

+15 

54 

+  9 

56 

+  1 

56 

-  4 

09 

-10 

20 

-13 

37 

-16 

01 

We  have  from  the  table  the  amount  of  deviation  on  each  compass  heading; 
therefore,  knowing  the  ship's  head  by  compass,  it  is  easy  to  pick  out  the  corresponding 
deviation  and  thus  to  obtain  the  magnetic  neading.  But  if  we  are  given  the  magnetic 
direction  in  which  it  is  desired  to  steer  and  have  to  find  the  corresponding  compass 
course,  the  problem  is  not  so  simple,  for  we  are  not  given  deviations  on  magnetic 
heads,  and  where  the  errors  are  large  it  may  not  be  assumed  that  thev  are  the  same 
as  on  the  corresponding  compass  headings.  For  example,  with  the  deviation  table 
just  given,  suppose  it  is  required  to  determine  the  compass  heading  corresponding 
to  165°,  magnetic. 

The  deviation  corresponding  to  165°,  per  compass,  is  +8^°.  If  we  apply  this 
to  165°,  magnetic,  we  have  156^  as  the  compass  course.  But,  consulting  tne  table, 
it  may  be  seen  that  the  deviation  correspondmg  to  156^°,  per  compass,  is  +2\°,  and 
therefore  if  we  steer  that  course  the  magnetic  direction  will  be  159°,  and  not  165°, 
as  desired. 

A  way  of  arriving  at  the  correct  result  is  to  make  a  series  of  trials  until  a  course 
is  arrived  at  which  fulfills  the  conditions.     Thus,  in  the  example  given: 


First  trial. 

Mag.  course  desired 165° 

Trydev.  on  165° 8^°  E. 


Trial  comp.  course. 
Dev.  onl56i° 


156i= 
2J= 


Second  trial. 

Mag.  course  desired 165° 

Try  dev.  on  160° 5°  E. 


Trial  comp.  course 160° 

Dev.  on  160° 5° 


Mag.  course  made  good 165° 

This  happens  to  be  exactly  the  compass  course 
required.  But  it  often  occurs  that  further  trials 
may  be  necessary. 


Mag.  course  made  good 159° 

Since  this  assumption  carries  the  course  6°  too  far 
to  the  left,  assume  next  a  deviation  on  a  course  3^° 
farther  to  the  right  than  the  one  used  here. 

94.  The  Napier  Diagram. — A  much  more  expeditious  method  for  the  solution 
of  this  problem  is  afforded  by  the  Napier  Diagram,  and  as  that  diagram  also  f  aciUtates 
a  number  of  other  operations  connected  with  compass  work  it  should  be  clearly 
understood  by  the  navigator.  This  admits  of  a  graphic  representation  of  the  table 
of  deviations  of  the  compass  by  means  of  a  curve ;  besides  furnishing  a  readj  means 
of  converting  compass  into  magnetic  courses  and  the  reverse,  one  of  its  chief 
merits  is  that  if  the  deviation  has  been  determined  on  a  certain  number  of  head- 
ings it  enables  one  to  obtain  the  most  probable  value  of  the  deviation  on  any 
other  course  that  the  ship  may  head.  The  last-named  feature  renders  it  useful  in 
making  a  table  of  deviations  oi  compasses  other  than  the  standard  when  their  errors 
are  found  as  described  in  article  86. 

95.  The  Napier  diagram  (fig.  9)  represents  the  margin  of  a  compass  card  cut 
at  the  north  point  and  straightened  into  a  vertical  line;  for  convenience,  it  is  usually 
divided  into  two  sections,  representing,  respectively,  the  eastern  and  western  semi- 
circles. The  vertical  line  is  of  a  convenient  length  and  divided  into  twenty-four 
equal  parts  corresponding  to  the  15°  rhumbs  of  the  compass,  beginning  at  the  top 


42 


THE   COMPASS  ERROR. 


with  North  and  continuing  around  to  the  right;  it  is  also  divided  into  360  degrees, 
which  are  appropriately  marked. 

To  obtain  a  complete  curve,  a  sufficient  number  of  observations  should  be  taken 
while  the  ship  swings  through  an  entire  circle.  Generally,  observations  on  every 
alternate  15°  rhumb  are  enough  to  establish  a  good  curve,  but  in  cases  where  the 
maximum  deviation  reaches  40°  it  is  preferable  to  observe  on  every  15°  rhumb. 


CempaM  eeursas  en  dotted  liaes. 


Magnetic  eeunes  on  solid  Bnet. 


FROM  0°  NORTH  TO  180°  SOUTH 


DEVIATION 
EAST 


FROM  180°  SOUTH  TO  360°  NORTH 

DEVIATION  DEVIATION 

WEST  soum  EAST 


Curv*    of    Total    Oeviation 

Curve   of    Semicircular    Component 

Curve    of    Quadraniat     Component 

Fig.  9. 


ITie  cfurve  shown  in  the  full  line  on  figure  9  corresponds  to  the  table  of  deviations 
given  in  article  93. 

From  a  given  compass  course  to  find  the  corresponding  magnetic  course,  through  the 
point  of  the  vertical  Hne  representing  the  given  compass  course  draw  a  line  parallel 
to  the  dotted  lines  until  the  curve  is  intersected,  and  from  the  point  of  intersection 
draw  another  line  parallel  to  the  plain  Hues;  the  point  on  the  scale  where  this  last 


THE  COMPASS  EEROE. 


43 


line  cuts  the  vertical  line  is  the  magnetic  course  sought.  The  correctness  of  this 
solution  will  be  apparent  when  we  consider  that  the  60°  triangles  are  equilateral,  and 
therefore  the  distance  measured  along  the  vertical  side  will  equal  the  distance  meas- 
ured along  the  inclined  sides — that  is,  the  deviation;  and  the  direction  will  be  correct, 
for  the  construction  is  such  that  magnetic  directions  will  be  to  the  right  of  compass 
directions  when  the  deviation  is  easterly  and  to  the  left  if  westerly. 

From  a  given  magnetic  course  to  find  the  corresponding  compass  course,  the  process 
is  the  same,  excepting  that  the  first  line  drawn  should  follow,  or  be  parallel  to,  the 
plain  lines,  and  tne  second,  or  return  Hne,  should  be  parallel  to  the  dotted;  and  a 
proof  similar  to  that  previously  employed  will  show  the  correctness  of  the  result. 
As  an  example,  the  problem  given  in  article  93  may  be  solved  by  the  diagram,  and 
the  result  will  be  found  to  accord  with  the  solution  previously  ^veji. 

The  vertical  line  is  intersected  at  each  15°  rhumb  by  two  Imes  inclined  to  it  at 
an  angle  of  60°,  that  line  which  is  inclined  upward  to  the  right  being  drawn  plain 
and  the  other  dotted. 

To  plot  a  curve  on  the  Napier  diagram,  if  the  deviation  has  been  observed  with 
the  ship's  head  on  given  compass  courses  (as  is  usually  the  case  with  the  standard 
compass),  measure  off  on  the  vertical  scale  the  number  of  degrees  corresponding  to 
the  deviation  and  lay  it  down — to  the  right  if  easterly  and  to  the  left  if  westerly — 
on  the  dotted  line  passing  through  the  point  representing  the  ship's  head;  or,  if  the 
observation  was  not  made  on  an  even  15°  rhumb,  then  lay  it  down  on  a  line  drawn 
parallel  to  the  dotted  ones  through  that  division  of  the  vertical  line  which  represents 
the  compass  heading;  if  the  deviation  has  been  observed  with  the  ship  on  given 
magnetic  courses  (as  when  deviations  by  steering  compass  are  obtained  by  noting 
the  ship's  head  during  a  swing  on  even  15°  rhumbs  of  the  standard),  proceed  in  the 
same  way,  excepting  that  the  deviation  must  be  laid  down  on  a  plain  line  or  a  line 
parallel  thereto.  ^  Mark  each  point  thus  obtained  with  a  dot  or  small  circle,  and  draw 
a  free  curve  passing,  as  nearly  as  possible,  through  all  the  points. 

THE  THEORY  OF  DEVIATION.a 

96.  Features  of  the  Earth's  Magnetism. — It  has  already  been  stated  that 
the  earth  acts  like  a  great  spherical  magnet,  with  a  pole  in  each  hemisphere  which  is 
not  coincident  with  the  geographical  pole;  it  has 
also  a  magnetic  equator  which  lies  close  to,  but 
not  coincident  with,  the  geographical  equator. 

A  magnetic  needle  freely  suspencled  at  a 
point  on  the  earth's  surface,  and  undisturbed  by 
any  other  than  the  earth's  magnetic  influence, 
will  lie  in  the  plane  of  the  magnetic  meridian 
and  at  an  an^le  with  the  horizon  depending  upon 
the  geographical  position. 

The  magnetic  elements  of  the  earth  which 
must  be  considered  are  shown  in  figure  10. 
The  earth's  total  force  is  represented  in  direction 
and  intensity  by  the  Hne  AB.  Since  compass 
needles  are  mechanically  arranged  to  move  only 
in  a  horizontal  plane,  it  oecomes  necessary,  when 
investigating  the  effect  of  the  earth's  magnetism 
upon  them,  to  resolve  the  total  force  into  two 
components  which  in  the  figure  are  represented 
by  AC  and  AD.  These  are  known,  respectively, 
as  the  horizontal  and  vertical  components  of  the 
earth's  total  force,  and  are  usually  designated  as 
H  and  Z.  The  angle  CAB,  which  the  line  of  direction  makes  with  the  plane  o 
the  horizon,  is  called  the  magnetic  inclination  or  dip,  and  denoted  by  6. 

It  is  clear  that  the  horizontal  component  will  reduce  to  zero  at  the  magnetic 
poles,  where  the  needle  points  directly  downward,  and  that  it  will  reach  a  maximum 

o  As  it  is  probable  that  the  student  will  not  have  practical  need  of  a  knowledge  of  the  theory  of  deviation  and  the  compensation 
of  the  compass  until  after  he  has  mastered  all  other  subjects  pertaining  to  Navigation  and  Nautical  Astronomy,  it  may  be  considered 
preferable  to  omit  the  remainder  of  this  chapter  at  first  and  return  to  it  later. 


K>rizontal  Force  »H 


44  THE   COMPASS  ERROR. 

at  the  magnetic  equator,  where  the  free  needle  hangs  in  a  horizontal  direction.     The 
reverse  is  true  of  the  vertical  conrponent  and  of  the  angle  of  dip. 

Values  representing  these  diflferent  terms  may  be  found  from  special  charts. 

97.  Induction;  Hard  and  Soft  Iron. — When  a  piece  of  unmagnetized  iron 
or  steel  is  brought  within  the  influence  of  a  magnet,  certain  magnetic  properties  are 
immediately  imparted  to  the  former,  which  itseu  becomes  magnetic  and  continues  to 
remain  so  as  long  as  it  is  within  the  sphere  of  influence  of  the  permanent  magnet; 
the  magnetism  that  it  acquires  under  these  circumstances  is  said  to  be  induced,  and 
the  properties  of  induction  are  such  that  that  end  or  region  which  is  nearest  the  pole 
of  the  influencing  magnet  will  take  up  a  polarity  opposite  thereto.  If  the  magnet  is 
withdrawn,  the  induced  magnetism  is  soon  dissipated.     If  the  magnet  is  brought  into 

Eroximity  again,  but  with  its  opposite  pole  nearer,  magnetism  will  again  be  induced, 
ut  this  time  its  polarity  wiU  be  reversed.  A  further  property  is  that  if  a  piece  of  iron 
or  steel,  while  temporarily  possessed  of  magnetic  qualities  through  induction,  be 
subjected  to  blows,  twisting,  or  mechanical  violence  of  any  sort,  the  magnetism  is 
thus  made  to  acquire  a  permanent  nature. 

The  softer  the  metal,  from  a  physical  point  of  view,  the  more  c[uickly  and  thor- 
oughly will  induced  magnetism  be  dissipated  when  the  source  of  influence  is  with- 
drawn; hard  metal,  on  the  contrary,  is  slow  to  lose  the  effect  of  magnetism  imparted 
to  it  in  any  way.  Hence,  in  regarding  the  different  features  which  affect  deviation, 
it  is  usual  to  denominate  as  hard  iron  that  which  possesses  retained  magnetism  of  a 
stable  nature,  and  as  soft  iron  that  which  rapidly  acquires  and  parts  with  its  mag- 
netic qualities  under  the  varying  influences  to  which  it  is  subjected. 

98.  Magnetic  Properties  Acquired  by  an  Iron  or  Steel  Vessel  in 
Building. — The  inductive  action  of  the  earth's  magnetism  affects  all  iron  or  steel 
within  its  influence,  and  the  amount  and  permanency  of  the  magnetism  so  induced 
depends  upon  the  position  of  the  metal  with  reference  to  the  earth's  total  force, 
upon  its  character,  and  upon  the  degree  of  hammering,  bending,  and  twisting  that  it 
undergoes. 

An  iron  bar  held  in  the  line  of  the  earth's  total  force  instantly  becomes  magnetic; 
if  held  at  an  angle  thereto  it  would  acquire  magnetic  properties  dependent  for  their 
amount  upon  its  incHnation  to  the  line  of  total  force;  when  held  at  right  angles  to 
the  line  there  would  be  no  effect,  as  each  extremity  would  be  equally  near  the  poles 
of  the  earth  and  aU  influence  would  be  neutraUzed.  If,  whUe  such  a  bar  is  in  a 
magnetic  state  through  inductive  action,  it  should  be  hammered  or  twisted,  a  certain 
magnetism  of  a  permanent  character  is  impressed  upon  it,  which  is  never  entirely 
lost  unless  the  bar  is  subjected  to  causes  equal  and  opposite  to  those  that  produced 
the  first  effect. 

A  sheet  of  iron  is  affected  by  induction  in  a  similar  way,  the  magnetism  induced 
by  the  earth  diffusing  itself  over  the  entire  plate  and  separating  itseff  into  regions 
of  opposite  polarity  divided  by  a  neutral  area  at  right  angles  to  the  earth's  line  of 
total  force.  If  the  plate  is  hammered  or  bent,  this  magnetism  takes  up  a  permanent 
character. 

If  the  magnetic  mass  has  a  third  dimension,  and  assumes  the  form  of  a  ship,  a 
similar  condition  prevails.  The  whole  takes  up  a  magnetic  character;  there  is  a 
magnetic  axis  in  the  direction  of  the  line  of  total  force,  with  poles  at  its  extremities 
and  a  zone  of  no  magnetism  perpendicular  to  it.  The  distribution  of  magnetism 
win  depend  upon  the  horizontal  and  vertical  components  of  the  earth's  force  in  the 
locality  and  upon  the  direction  of  the  keel  in  building;  its  permanency  will  depend 
upon  the  amount  of  mechanical  violence  to  which  the  metal  has  been  subjected  by 
the  riveting  and  other  incidents  of  construction,  and  upon  the  nature  of  the  metal 
employed. 

99.  Causes  that  Produce  Deviation.— There  are  three  influences  that 
operate  to  produce  deviation;  namely,  {a)  sub'permanent  jnagnetism;  (h)  transient 
rnagnetism  induced  in  vertical  soft  iron,  and  (c)  transient  magnetisnri  induced  in  hori- 
zontal soft  iron.    Their  effect  will  be  explained. 

Sub'permanent  magnetism  is  the  name  given  to  that  magnetic  force  which  origi- 
nates in  the  ship  while  building,  through  the  process  explained  in  the  preceding 
article;  after  the  vessel  is  launched  and  has  an  opportunity  to  swing  in  azimuth, 
the  magnetism  thus  induced  wiU  suffer  material  diminution  until,  after  the  lapse  of 


THE   COMPASS  ERROR.  45 

a  certain  time,  it  will  settle  down  to  a  condition  that  continues  practically  unchanged; 
the  magnetism  that  remains  is  denominated  subpermanent.  The  vessel  will  then 
approximate  to  a  permanent  magnet,  in  which  the  north  polarity  will  lie  in  that 
region  which  was  north  in  building  and  the  south  polarity  (that  which  exerts  an 
attracting  influence  on  the  north  pole  of  the  compass  needle)  in  the  region  which 
was  south  in  building. 

Transient  magnetism  induced  in  vertical  soft  iron  is  that  developed  in  the  soft 
iron  of  a  vessel  through  the  inductive  action  of  the  vertical  component  only  of  the 
earth's  total  force,  and  is  transient  in  nature.  Its  value  or  force  m  any  given  mass 
varies  with  and  depends  upon  the  value  of  the  vertical  component  at  the  place, 
and  is  proportional  to  the  sine  of  the  dip,  being  a  maximum  at  the  magnetic  pole 
and  zero  at  the  magnetic  equator. 

Transient  rrmgnetism  induced  in  horizontal  soft  iron  is  that  developed  in  the  soft 
iron  of  a  vessel  through  the  inductive  action  oi  the  horizontal  component  oiAj  of 
the  earth's  total  force,  and  is  transient  in  nature.  Its  value  or  force  in  any  given 
mass  varies  with  and  depends  upon  the  value  of  the  horizontal  component  at  the 
place,  and  is  proportional  to  the  cosine  of  the  dip,  being  a  maximum  at  the  magnetic 
equator  and  reducing  to  zero  at  the  magnetic  pole. 

The  needle  of  a  compass  in  any  position  on  board  ship  will  therefore  be  acted 
upon  by  the  earth's  total  force,  together  with  the  three  forces  just  described.     The 

Eoles  of  these  forces  do  not  usually  lie  in  the  horizontal  plane  of  the  compass  needle, 
ut  as  this  needle  is  constrained  to  act  in  a  horizontal  plane,  its  movements  will  be 
affected  solely  by  the  horizontal  components  of  these  lorces,  and  its  direction  will 
be  determined  by  the  resultant  of  those  components. 

The  earth's  force  operates  to  retain  the  compass  needle  in  the  plane  of  the 
magnetic  meridian,  but  the  resultant  of  the  three  remaining  forces,  when  without 
this  plane,  deflects  the  needle,  and  the  amount  of  such  deflection  constitutes  the 
deviation. 

100k  Classes  of  Deviation. — Investigation  has  developjed  the  fact  that  the 
deviation  produced  as  described  is  made  up  of  tlu-ee  parts,  which  are  known  respec- 
tively as  semicircular,  quadrantal,  and  constant  deviation,  the  latter  being  the  least 
important.  A  clear  understanding  of  the  nature  of  each  of  these  classes  is  essential 
for  a  comprehension  of  the  methods  of  compensation. 

101.  Semicircular  Deviation  is  that  due  to  the  combined  influence,  exerted  m  a 
horizontal  plane,  of  the  subpermanent  magnetism  of  a  ship  and  of  the  magnetism 
induced  in  soft  iron  by  the  vertical  component  of  the  earth's  force.  If  we  regard  the 
effect  of  these  two  forces  as  concentrated  in  a  single  resultant  pole  exerting  an 
attractiug  influence  upon  the  north  end  of  the  compass  needle,  it  may  be  seen  that 
there  wiU  be  some  heading  of  the  ship  whereon  that  pole  will  lie  due  north  of  the 
needle  and  therefore  produce  no  deviation;  now  consider  that,  from  this  position, 
the  ship's  head  swings  in  azimuth  to  the  right;  throughout  aU  of  the  semicircle  first 
described  an  easterly  deviation  will  be  produced,  and,  after  completmg  180°,  the  pole 
will  be  in  a  position  diametericaUy  opposite  to  that  from  which  it  started,  and  wiU 
again  exert  no  influence  that  tends  to  produce  deviation.  Continuing  the  swing, 
throughout  the  next  semicircle  the  direction  of  the  deviation  produced  wdl  be  always 
to  the  westward,  until  the  circle  is  completed  and  the  ship  returns  to  her  original 
neutral  position.  From  the  fact  that  this  disturbing  cause  acts  in  the  two  semicircles 
with  equal  and  opposite  effect  it  is  given  the  name  of  semicircular  deviation. 

In  figure  9  a  curve  is  depicted  which  shows  the  deviations  of  a  semicircular  nature 
separated  from  those  due  to  other  disturbing  causes,  and  from  this  the  reason  for 
the  name  will  be  apparent. 

102,  Returning  to  the  two  distmct  sources  from  which  the  semicircular  deviation 
arises,  it  may  be  seen  that  the  force  due  to  subpermanent  magnetism  remains  constant 
regardless  of  the  geographical  position  of  the  vessel;  but  smce  the  horizontal  force 
of  the  earth,  which  tends  to  hold  the  needle  in  the  magnetic  meridian,  varies  with  the 
magnetic  latitude,  the  deviation  due  to  subpermanent  magnetism  varies  inversely  as 

the  horizontal  force,  or  as  yt;  this  may  be  readily  understood  if  it  is  considered  that 

the  stronger  the  tendency  to  cling  to  the  direction  of  the  magnetic  meridian  the  less 
will  be  the  deflection  due  to  a  given  disturbiug  force.     On  the  other  hand,  that  part 


46 


THE   COMPASS   ERROR. 


of  the  semicircular  force  due  to  magnetism  induced  in  vertical  soft  iron  varies  as  the 
earth's  vertical  force,  which  is  proportional  to  the  sine  of  the  dip;  its  effect  in  producing 
deviation,  as  in  the  preceding  case,  varies  inversely  as  the  earth's  horizontal  force — 
that  is,  inversely  as  the  cosine  of  the  dip;  hence  the  ratio  representing  the  change  of 

deviation  arising  from  this  cause  on  change  of  latitude  is  ;^^^,  or  tan  6. 

If,  then,  we  consider  the  change  in  the  semicircular  deviation  due  to  a  change 
of  magnetic  latitude,  it  will  be  necessary  to  separate  the  two  factors  of  the  deviation 
and  to  remember  that  the  portion  produced  by  subpermanent  magnetism  varies  as 

i,  and  that  due  to  vertical  induction  as  tan  d.     But  for  any  consideration  of  the 

effect  of  this  class  of  deviation  in  one  latitude  only,  the  two  parts  may  be  joined 
together  and  regarded  as  having  a  single  resultant. 

103.  Assuming  that  all  the  forces  tending^  to  produce  semicircular  deviation 
are  concentrated  in  a  single  pole  exerting  an  influence  on  the  north  pole  of  the 
compass,  it  will  be  seen  that  this  can  be  resolved  into  a  horizontal  and  a  vertical 
component,  just  as  the  earth's  magnetic  force  is  illustrated  in  figure  10.     It  is  now- 
evident,  therefore,  that  the  horizontal  component  of  this 
single  magnet  may  be  resolved  into  two  components — one 
fore-and-aft,  and  one  athwartship;    in  this  case,  the  semi- 

<>,  circular  forces  wiU  be  represented  by  two  magnets,  one  fore- 

/    and-aft  and  the  other  athwartship,  and  compensation  may 

/       be  made  by  two  separate  magnets  lying  respectively  in  the 

directions  stated,  but  with  their  north  or  repeUing  poles  in 

the  position  occupied  by  the  south  or  attracting  poles  of  the 

ship's  force. 

Figure  11  represents  the  conditions  that  have  been 
described.  Let  O  be  the  center  of  the  compass,  XX'  and 
YY',  respectively,  the  fore-and-aft  and  athwartship  Hnes  of 
the  ship,  and  OS  the  direction  in  which  the  attracting  pole  of 
the  disturbing  force  is  exerted.  Now,  if  OP  be  laid  off  on 
the  line  OS,  representing  the  amount  of  the  disturbing  force 
according  to  some  convenient  scale,  then  0&  and  Oc,  respec- 
tively, represent,  on  the  same  scale,  the  resolved  directions  of 
that  force  in  the  keel  line  and  in  the  transverse  line  of  the 
ship.  Each  of  these  resolved  forces  will  exert  a  maximum 
effect  when  acting  at  right  angles  to  the  needle,  the  athwart- 
ship one  when  the  ship  heads  north  or  south  by  compass, 
and  the  longitudinal  one  when  the  heading  is  east  or  west. 
On  any  other  heading  than  those  named  the  deviation  pro- 
duced by  each  force  will  be  a  fraction  of  its  maximum  whose 
magnitude  will  depend  upon  the  azimuth  of  the  ship's  head.  The  maximum  devia- 
tion produced,  therefore,  forms  in  each  case  a  basis  for  reckoning  all  of  the  various 
effects  of  the  disturbing  force,  and  is  called  a  coefficient. 

The  coefficient  of  semicircular  deviation  produced  by  the  force  in  the  fore-and-aft 
line  is  called  B,  and  is  reckoned  as  positive  when  it  attracts  a  north  pole  toward  the 
bow,  negative  when  toward  the  stern;  that  produced  by  the  athwartship  force  is  C, 
and  is  reckoned  as  positive  to  starboard  and  negative  to  port.  These  coefl5.cients  are 
expressed  in  degrees.* 

104.  The  coefficient  B  is  approximately  equal  to  the  deviation  on  East;  or  to 
the  deviation  on  West  with  reversed  sign;  or  to  the  mean  of  these  two.  Thus  in 
the  ship  having  the  table  of  deviations  previously  given  (art.  93),  B  is  equal  to 
-9°  06',  or  to  -9°  56',  or  to  i  (-9°  06' -9°  56')  = -9°  31'. 

The  coefficient  C  is  approximately  equal  to  the  deviation  on  North;  or  to  the 
deviation  on  South  with  reversed  sign;  or  to  the  mean  of  these  two.  In  the  example 
C  is  equal  to  -15°  29',  or  to  -17°  52',  or  to  ^  (-15°  29' -17°  52')  =- 16°  40'. 

o  It  should  be  remarked  that  in  a  mathematical  analysis  of  the  deviations,  it  would  be  necessary  to  distinguish  between  the 
approximate  coefficients,  B  and  C,  here  described,  as  als3  A,  D,  and  E,  to  be  mentioned  later,  and  the  exact  coefficients  denoted  by 
the  corresponding  capital  letters  of  the  German  alphabet,  which  latter  are  in  reality  the /orccs  producing  those  deviations  expressed 
in  terms  of  the  "  mean  force  to  north"  (Ah),  as  unit.  In  the  practical  discussion  of  the  subject  here  given,  the  question  of  the  dif- 
ference need  not  be  entered  into  further. 


Fig.  11. 


THE  COMPASS  ERROR.  47 

105.  The  value  of  the  subpermanent  magnetism  remaining  practically  constant 
under  all  conditions,  it  will  not  alter  when  the  ship  changes  her  latitude;  but  that 
due  to  induction  in  vertical  soft  iron  undergoes  a  change  when,  by  change  of  geo- 
graphical position,  the  vertical  component  of  the  earth  3  force  assumes  a  different 
value,  and  in  such  case  the  correction  by  means  of  one  or  a  pair  of  permanent  magnets 
will  not  remain  effective.  If,  however,  by  series  of  observations  in  two  magnetic 
latitudes,  the  values  of  the  coefficients  can  be  determined  under  the  diflfering  cir- 
cumstances, it  is  possible,  by  solving  equations,  to  determine  what  effect  each  force 
has  in  producing  the  semicircular  deviation;  having  done  which,  the  subpermanent 
magnetism  can  be  corrected  by  permanent  magnets  after  the  method  previously 
described,  and  the  vertical  induction  in  soft  iron  can  be  corrected  by  a  piece  of 
vertical  soft  iron  placed  in  such  a  position  near  the  compass  as  to  produce  an  equal 
but  opposite  force  to  the  ship's  vertical  soft  iron.  This  last  corrector  is  called  a 
Flinders  bar. 

Having  thus  opposed  to  each  of  the  component  forces  a  corrector  of  magnetic 
character  identical  with  its  own,  a  change  of  latitude  will  make  no  difference  m  the 
effectiveness  of  the  compensation,  for  m  every  case  the  modified  conditions  will 
produce  identical  results  m  the  disturbing  and  in  the  correcting  force. 

106.  Quadrantal  Deviation  is  that  which  arises  from  horizontal  induction  in  the 
soft  iron  of  the  vessel  through  the  action  of  the  horizontal  component  of  the  earth's 
total  force.  Let  us  consider,  in  figure  12,  the  effect  of  any  piece  of  soft  iron  which 
is  symmetrical  with  respect  to  the  compass — that 
is,  which  lies  wholly  within  a  plane  passing  through 
the  center  of  the  needle  in  either  a  fore-and-aft  or 
an  athwartship  direction.  It  may  be  seen  (a)  that 
such  iron  produces  no  deviation  on  the  cardinal 
points  (for  on  north  and  south  headings  the  fore- 
and-aft  iron,  though  strongly  magnetized,  has  no 
tendency  to  draw  the  needle  from  a  north-and-south 
line,  while  the  athwartship  iron,  being  at  right  angles 
to  the  meridian,  receives  no  magnetic  induction, 
and  therefore  exerts  no  force;  and  on  east  and 
west  headings  similar  conditions  prevail,  the  athwart- 
ship and  the  fore-and-aft  iron  having  simply  ex- 
changed positions);  and  (6)  the  direction  of  the 
deviation  produced  is  opposite  in  successive  quad- 
rants.    The  action  of  unsymmetrical  soft  iron  is  f>«-  12. 

not  quite  so  readily  apparent,  but  investigation  shows  that  part  of  its  effect  is  to 
produce  a  deviation  which  becomes  zero  at  the  inter-cardinal  points  and  is  of  oppo- 
site name  in  successive  quadrants.  From  the  fact  that  deviations  of  this  class 
change  sign  every  90°  throughout  the  circle,  they  gain  the  name  of  quadrantal  devi- 
ations. One  of  the  curves  laid  down  in  the  Napier  diagram  (fig.  9)  is  that  of  quad- 
rantal deviations,  whence  the  nature  of  this  disturbance  of  the  needle  may  be 
observed. 

107.  All  deviations  produced  by  soft  iron  may  be  considered  as  fractions  of 
the  maximum  deviation  due  to  that  disturbing  influence;  and  consequently  the 
maximum  is  regarded  as  a  coefficient,  as  in  the  case  of  semicircular  deviations. 
The  coefficient  due  to  symmetrical  soft  iron  is  designated  as  D,  and  is  considered 
positive  when  it  produces  easterly  deviations  in  the  quadrant  between  North  and 
East;  the  coefficient  of  deviations  arising  from  unsymmetrical  soft  iron  is  called  E, 
and  is  reckoned  as  positive  when  it  produces  easterly  deviations  in  the  quadrant 
between  NW.  and  NE.;  this  latter  attains  importance  only  when  there  is  some 
marked  inequality  in  the  distribution  of  metal  to  starboard  and  to  port,  as  in  the 
case  of  a  compass  placed  off  the  amidship  line. 

108.  D  is  approximately  equal  to  tne  mean  of  the  deviations  on  NE.  and  SW.; 
or  to  the  mean  of  those  on  SE.  and  NW.,  with  sign  reversed;  or  to  the  mean  of  those 
means.  In  the  table  of  deviations  given  in  article  93,  D  is  equal  to  ^(— 11°  19'  +  25° 
35')=+7°08^o^toi(  +  5°54'  +  10°200=+8°07';ortoi(7°08'  +  8°07')7=+7°37^ 
By  reason  of  the  nature  of  the  arrangement  of  iron  in  a  ship,  D  is  almost  invariably 
positive. 


48  THE   COMPASS  ERROK. 

E  is  approximately  equal  to  the  mean  of  the  deviations  on  North  and  South ;  or 
to  the  mean  of  those  on  East  and  West  with  sign  reversed ;  or  to  the  mean  of  those 
means.  In  the  example,  E  is  equal  to  ^  (-15°  29'  +  17°  52')= +1°  11';  or  to 
i  (  +  9°06'-9°560=-0°25';  or  to  i  (  +  1°  ll'-0°  25')  = +0°  23'. 

109.  Quadrantal  deviation  does  not,  like  semicircular,  undergo  a  change  upon 
change  of  magnetic  latitude ;  being  due  to  induction  in  horizontal  soft  iron,  the  magnetic 
force  exerted  to  produce  it  is  proportional  to  the  horizontal  component  of  the  earth's 
magnetism;  but  the  directive  force  of  the  needle  likewise  depends  upon  that  same 
component ;  consequently,  as  the  disturbing  force  exerted  upon  the  needle  increases, 
so  does  the  power  that  holds  it  in  the  magnetic  meridian,  with  the  result  that  on 
any  given  heading  the  deflection  due  to  soft  iron  is  always  the  same. 

110.  Quadrantal  deviation  is  corrected  by  placing  masses  of  soft  iron  (usually 
two  hollow  spheres  in  the  athwartship  line,  at  equal  distances  on  each  side  of  the 
compass) ,  with  the  center  of  mass  in  the  horizontal  plane  of  the  needle.  The  distance 
is  made  such  that  the  force  exerted  exactly  counteracts  that  of  the  ship's  iron.  As 
the  correcting  effect  of  this  iron  will,  like  the  directive  force  and  the  quadrantal 
disturbing  force,  vary  directly  with  the  earth's  horizontal  component,  the  compen- 
sation once  properly  made  will  be  effective  in  all  latitudes ;  provided  that  the  compass 
needles  are  short  and,  consequently,  exercise  little  or  no  induction  on  the  quadrantal 
correctors. 

With  compasses  such  as  the  United  States  Navy  standard  T^-inch  liquid  compass, 
the  needles  of  which  are  long  and  powerful,  it  wUl  usually  be  found  that  the  position 
of  the  spheres  must  be  changed  wdth  change  of  latitude.  This  may  be  accounted  for 
by  the  magnetism  induced  in  the  spheres  by  the  compass  needles  at  the  same  time 
and  in  the  same  manner  as  the  earth's  force.  In  this  case  the  quadrantal  correcting 
force  is  the  resultant  of  the  constant  force  due  to  the  induction  of  the  needles  in  the 
spheres  and  the  variable  force  (the  earth's  horizontal  force,  H,  varying  with  change 
in  magnetic  latitude)  due  to  the  induction  of  the  earth  in  the  spheres.  This  resultant 
of  these  two  forces  is  a  variable  force,  and,  after  a  given  quadrantal  deviation  is 
corrected  in  one  latitude  by  this  force,  the  balance  will  be  changed  upon  going  into 
another  latitude  and  the  correction  wUl  fail  to  hold  good. 

In  practice,  the  quadrantal  deviation  due  to  unsymmetrical  iron  is  seldom 
corrected;  the  correction  may  be  accomplished,  however,  by  placing  the  soft  iron 
masses  on  a  line  which  makes  an  angle  to  the  athwartship  line  through  the  center 
of  the  card. 

111.  Constant  Deviation  is  due  to  induction  in  horizontal  soft  iron  unsym- 
metrically  placed  about  the  compass.  It  has  aheady  been  explained  that  one  effect 
of  such  iron  is  to  produca  a  quadrantal  deviation,  represented  by  one  coefficient  E ; 
another  effect  is  the  constant  deviation,  so  called  because  it  is  uniform  in  amount 
and  direction  on  every  heading  of  the  ship.  If  plotted  on  a  Napier  diagram,  it  would 
appear  as  a  straight  line  parallel  with  the  initial  line  of  the  diagram. 

112.  Like  other  classes  of  deviation,  the  effect  of  the  disturbing  force  is  repre- 
sented by  a  coefficient ;  this  coefficient  is  designated  as  A,  and  is  considered  plus  for 
easterly  and  minus  for  westerly  errors.  It  is  approximately  equal  to  the  mean  of 
the  deviations  on  any  number  of  equidistant  headings.  In  the  case  previously  given, 
it  might  be  found  from  the  four  headings,  North,  East,  South,  and  West,  and  would 
then  be  equal  to  i  (-15°  29' -9°  06' +  17°  52' +  9°  56')  = +0°  48';  or  from  all  of 
the  24  headings,  when  it  would  equal  —0°  01'. 

For  the  same  reason  as  in  the  case  of  E,  the  value  of  A  is  usually  so  small  that 
it  may  be  neglected;  it  only  attains  a  material  size  when  the  compass  is  placed  off 
the  midship  hne,  or  for  some  similar  cause. 

113.  Like  quadrantal  deviation,  since  its  force  varies  with  the  earth's  horizontal 
force,  the  constant  deviation  will  remain  uniform  in  amount  in  all  latitudes.  (See 
art.  110.) 

No  attempt  is  made  to  compensate  for  this  class  of  error. 

114.  Coefficients. — The  chief  value  of  coefficients  is  in  mathematical  analyses 
of  the  deviations  and  their  causes.  It  may,  however,  be  a  convenience  to  the  practical 
navigator  to  find  their  approximate  values  by  the  methods  that  have  been  given,  in 
order  that  he  may  gain  an  idea  of  the  various  sources  of  the  error,  with  a  view  to 
ameliorating  the  conditions,  when  necessary,  by  moving  the  bionacle  or  altering  the 


THE   COMPASS  EEKOK.  49 

surrounding  iron.     The  following  relation  exists  between  the  coefficients  and  the 
deviation: 

d  =  A-\-B  sin  z' +C  cos  s'+D  sm  20'+E  cos  22', 

where  d  is  the  deviation,  and  z'  the  ship's  heading  by  compass,  measured  from 
compass  North. 

115.  Mean  Directive  Force. — The  effect  of  the  disturbing  forces  is  not  confined 
to  causing  deviations;  it  is  only  those  components  acting  at  right  angles  to  the  needle 
which  operate  to  produce  deflection;  the  effect  of  those  acting  in  the  direction  of 
the  needle  is  exerted  either  in  increasing  or  diminishing  the  directive  force  of  the 
compass,  according  as  the  resolved  component  is  northerly  or  southerly. 

It  occurs,  with  the  usual  arrangement  of  iron  in  a  vessel,  that  the  mean  effect 
of  this  action  throughout  a  complete  swing  of  the  ship  upon  all  headings  is  to  reduce 
the  directive  force — that  is,  while  it  varies  with  the  heading,  the  average  value  upon 
all  azimuths  is  minus  or  southerly.  The  result  of  such  a  condition  is  unfavorable 
from  the  fact  that  the  compass  is  thus  made  more  "sluggish,"  is  easily  disturbed 
and  does  not  return  quickly  to  rest,  and  a  given  deflecting  force  produces  a  greater 
deviation  when  the  directive  force  is  reduced.  The  usual  methods  of  compensation 
largely  correct  this  fault,  but  do  not  entirely  do  so;  it  is  therefore  the  case  that  the 
mean  combined  horizontal  force  of  earth  and  ship  to  north  is  generaUy  less  than  the 
horizontal  force  of  the  earth  alone ;  but  it  is  only  m  extreme  cases  that  this  deficiency 
is  serious. 

116.  Heeling  Error. — This  is  an  additional  cause  of  deviation  that  arises 
when  the  vessel  heels  to  one  side  or  the  other.  Heretofore  only  those  forces  have 
been  considered  which  act  when  the  vessel  is  on  an  even  keel;  but  if  there  is  an  incli- 
nation from  the  vertical  certain  new  forces  arise,  and  others  previously  inoperative 
become  effective.  These  forces  are  (a)  the  vertical  component  of  the  subpermanent 
magnetism  acquired  in  building;  (b)  the  vertical  component  of  the  induced  magnetism 
in  vertical  soft  iron,  and  (c)  the  magnetism  induced  by  the  vertical  component  of 
the  earth's  total  force  in  iron  which,  on  an  even  keel,  was  horizontal.  The  first  two 
of  these  disturbing  causes  are  always  present,  but,  when  the  ship  is  upright,  have  no 
tendency  to  produce  deviation,  simply  exerting  a  downward  pull  on  one  of  the  poles 
of  the  needle;  the  last  is  a  new  force  that  arises  when  the  vessel  heels. 

The  maximum  disturbance  due  to  heel  occurs  when  the  ship  heads  North  or 
South.  When  heading  East  or  West  there  wiU  be  no  deviation  produced,  although 
the  directive  force  of  the  needle  wiU  be  increased  or  diminished.  The  error  will 
increase  with  the  amount  of  inclination  from  the  vertical. 

117.  For  the  same  reason  as  was  explained  in  connection  with  semicircular 
deviations,  that  part  of  the  heeling  error  due  to  subpermanent  magnetism  will  vary, 

on  change  of  latitude,  as  ^,  while  that  due  to  vertical  induction  will  vary  as  tan  d. 

In  south  magnetic  latitude  the  effect  of  vertical  induction  will  be  opposite  in  direction 
to  what  it  is  in  north  latitude. 

118.  The  heeling  error  is  corrected  by  a  permanent  magnet  placed  in  a  vertical 
position  directly  under  the  center  of  the  compass.  Such  a  magnet  has  no  effect  upon 
the  compass  when  the  ship  is  upright ;  but  since  its  force  acts  in  an  opposite  direction 
to  the  force  of  the  ship  which  causes  heeling  error,  is  equal  to  the  latter  in  amount, 
and  is  exerted  under  the  same  conditions,  it  affords  an  effective  compensation.  For 
similar  reasons  to  those  affecting  the  compensation  of  B  and  C,  the  correction  by 
means  of  a  permanent  magnet  is  not  general  and  must  be  rectified  upon  change  of 
latitude. 

PBACTICAIi  COMPENSATION. 

119.  In  the  course  of  explanation  of  the  different  classes  of  deviation  occasion 
has  been  taken  to  state  generally  the  various  methods  of  compensating  the  errors  that 
are  produced.     The  practical  methods  of  applying  the  correctors  wiU  next  be  given. 

120.  Order  of  Correction. — The  following  is  the  order  of  steps  to  be  followed 
in  each  case.  It  is  assumed  that  the  vessel  is  on  an  even  keel,  that  the  compass  is 
properly  centered  in  the  binnacle,  that  aU  surrounding  masses  of  iron  or  steel  are  in 
their  normal  positions,  all  correctors  removed,  and  that  the  binnacle  is  one  in  which 

21594°— 14 4 


50  THE  COMPASS  EEROB. 

the  semicircular  deviation  is  corrected  by  two  sets  of  permanent  magnets  at  right 
angles  to  each  other. 

In  order  to  ascertain  if  the  compass  is  properly  centered  in  the  binnacle,  the 
heeling  corrector  may  be  temporarily  placed  m  its  tube  and  drawn  from  its  lowest 
to  its  highest  position ;  if  no  deflection  is  shown  by  the  needle  the  compass  is  prop- 
erly centered;  if  not  it  should  be  adjusted  by  the  screws  provided  for  the  purpose. 

1 .  Place  quadrantal  correctors  by  estimate. 

2.  Correct  semicircular  deviation. 

3.  Correct  quadrantal  deviation. 

4.  Swing  ship  for  residual  deviations. 

The  heeling  corrector  may  be  placed  at  any  time  after  the  semicircular  and 
quadrantal  errors  are  corrected.  A  Flinders  bar  can  be  put  in  place  only  after 
observations  in  two  latitudes. 

121.  The  ship  is  first  placed  on  some  magnetic  cardinal  point.  If  North  or 
South,  the  only  force  (theoretically  speaking)  which  tends  to  produce  deflection  of  the 
needle  will  be  the  athwartship  component  of  the  semicircular  force,  whose  effect  is 
represented  by  the  coefficient  C.  It  East  or  West,  the  only  deflecting  force  will  be 
the  fore-and-aft  component  of  the  semicircular  force,  whose  effect  is  represented  by 
the  coefficient  B.  This  wiU  be  apparent  from  a  consideration  of  the  direction  of  the 
forces  producing  deviation,  and  is  also  shown  by  the  equation  connecting  the  terms 
(where  A  and  E  are  zero) : 

d  =  3  sin  s'  +  C  cos  z'  +  D  sin  2z'. 

If  the  ship  is  headed  North  or  South,  z'  being  equal  to  0°  or  180°,  the  equation 
becomes  d  =  ±  C.     If  on  East  or  West,  z'  being  90°  or  270°,  we  have  d  =  ±B. 

This  statement  is  exact  if  we  regard  only  the  forces  that  have  been  considered 
in  the  problem,  but  experience  has  demonstrated  that  the  various  correctors  when 
in  place  create  certain  additional  forces  by  their  mutual  action,  and  in  order  to  correct 
the  disturbances  thus  accidentally  produced,  as  well  as  those  due  to  regular  causes, 
it  is  necessary  that  the  magnetic  conditions  during  correction  shall  approximate  as 
closely  as  possible  to  those  that  exist  when  the  compensation  is  completed ;  therefore 
the  quadrantal  correctors  should  first  be  placed  on  their  arms  at  the  positions  which 
it  is  estimated  that  they  wiU  occupy  later  when  exactly  located.  An  error  in  the 
estimate  will  have  but  slight  effect  under  ordinary  conditions.  It  should  be  under- 
stood that  the  placing  of  these  correctors  has  no  corrective  effect  while  the  ship  is  on 
a  cardinal  point.  Its  object  is  to  create  at  once  the  magnetic  field  with  which  we 
shall  have  to  deal  when  compensation  is  perfected. 

This  having  been  done,  proceed  to  correct  the  semicircular  deviation.  If  the 
ship  heads  North  or  South,  the  force  producing  deflection  is,  as  has  been  stated,  the 
athwartship  component  of  the  semicircular  force,  which  is  to  be  corrected  by  perma- 
nent magnets  placed  athwartships ;  therefore  enter  in  the  binnacle  one  or  more  such 
magnets,  and  so  adjust  their  height  that  the  heading  of  the  ship  by  compass  shall 
agree  with  the  magnetic  heading.  When  this  is  done  all  the  deviation  on  that 
azimuth  will  be  corrected. 

Similarly,  if  the  ship  heads  East  or  West,  the  force  producing  deviation  is  the 
fore-and-aft  component  of  the  semicircular  force,  and  this  is  to  be  corrected  by 
entering  fore-and-aft  permanent  magnets  in  the  binnacle  and  adjusting  the  height 
so  that  the  deviation  on  that  heading  disappears. 

With  the  deviation  on  two  adjacent  cardinal  points  corrected,  the  semicircular 
force  has  been  coinpletely  compensated.  Next  correct  the  quadrantal  deviation. 
Head  the  ship  NE.,  SE.,  SW.,  or  NW.  The  coefficients  B  and  C  having  been  reduced 
to  zero  by  compensation,  and  2z%  on  the  azimuths  named,  being  equal  to  90°  or  270°, 
the  equation  becomes  d  =  ±D.  The  soft-iron  correctors  are  moved  in  or  out  from 
the  positions  in  which  they  were  placed  by  estimate  until  the  deviation  on  the  heading 
(aU  of  which  is  due  to  quadrantal  force)  disappears.  The  quadrantal  disturbing 
force  is  then  compensated. 

122.  Determination  op  Magnetic  Headings. — To  determine  when  a  ship 
is  heading  on  any  given  magnetic  course,  and  thus  to  know  when  the  deviation  has 
been  corrected  and  the  correctors  are  in  proper  position,  four  methods  are  available: 


THE  COMPASS  ERROR.  51 

(a)  Swing  the  ship  and  obtain  by  the  best  available  method  the  deviations  on  a 
sufficient  number  of  compass  courses  to  construct  a  curve  on  the  Napier  diagram 
for  one  quadrant,  and  thus  find  the  compass  headings  corresponding  to  two  adjacent 
magnetic  cardinal  points  and  the  intermediate  intercardinal  point,  as  North,  NE., 
and  East,  magnetic."  Then  put  the  ship  successively  on  these  courses,  noting  the 
corresponding  headings  by  some  other  compass,  and  when  it  is  desired  to  head  on 
the  various  magnetic  azimuths  during  the  process  of  correction  the  ship  may  be 
steadied  upon  them  by  the  auxiliary  compass.  Variations  of  this  method  will  suggest 
themselves  and  circumstances  may  render  their  adoption  convenient.  The  compass 
courses  corresponding  to  the  magnetic  directions  may  be  obtained  from  observations 
made  with  the  auxiliary  compass  itself,  or  while  making  observations  with  another 
compass  the  headings  "by  the  auxiliary  may  be  noted  and  a  curve  for  the  latter 
constructed,  as  explained,  in  article  95,  and  the  required  headings  thus  deduced. 

(6)  By  the  methods  to  be  explained  hereafter  (Chap.  XIV),  ascertain  in  advance 
the  true  bearing  of  the  sun  at  frequent  intervals  during  the  period  which  is  to  be 
devoted  to  the  compensation  of  the  compasses;  apply  to  these  the  variation  and 
obtain  the  magnetic  Dcarings;  record  the  times  and  bearings  in  a  convenient  tabular 
form,  or,  better  still,  plot  a  curve  of  magnetic  azimuths  of  the  sun  on  cross  section  paper, 
the  coordinates  being  local  apparent  time  and  magnetic  bearings  of  the  sun,  as  described 
in  article  89.  Set  the  watch  accurately  for  the  local  apparent  time;  then  when  it 
is  required  to  steer  any  given  magnetic  course,  set  that  point  of  the  pelorus  for  the 
ship's  head  and  set  the  sight  vanes  for  the  magnetic  bearing  of  the  sun  corresponding 
to  the  time  by  watch.  Maneuver  the  ship  with  the  helm  until  the  sun  comes  on  the 
sight  vanes,  when  the  azimuth  of  the  ship  s  head  will  be  that  which  is  required.  The 
sight  vanes  must  be  altered  at  intervals  to  accord  with  the  curve  or  table  of  times 
and  bearings. 

(c)  Construct  a  curve  or  table  showing  times  and  corresponding  magnetic 
bearings  of  the  sun,  and  also  set  the  watch,  as  explained  for  the  previous  method. 
Then  place  the  sight  vanes  of  the  azimuth  circle  of  the  compass  at  the  proper  angular 
distance  to  the  right  or  left  of  the  required  azimuth  of  the  ship's  head ;  leave  them  so 
set  and  maneuver  the  ship  with  the  nelm  until  the  ima^e  of  the  sun  comes  on  with 
the  vanes.  The  course  will  then  be  the  required  one.  As  an  example,  suppose  that 
the  curve  or  table  shows  that  the  magnetic  azimuth  of  the  sun  at  tne  time  given  by 
the  watch  is  N.  87°  E.,  and  let  it  be  required  to  head  magnetic  North;  when  placed 
upon  this  heading,  therefore,  the  sun  must  bear  87°  to  the  right  or  east  of  the 
direction  of  the  ship's  head;  when  steady  on  any  course,  turn  the  sight  vane  to  the 
required  bearing  relative  to  the  keel.  Il  on  N.  11°  W.,  for  example,  turn  the  circle 
to  N.  76°  E.;  leave  the  vane  undisturbed  and  alter  course  until  the  sun  comes  on. 
The  magnetic  heading  is  then  North,  and  adjustment  may  be  made  accordingly. 

(d)  When  ranges  are  available,  they  may  be  utilized  for  determining  magnetic 
headings. 

123.  Summary  of  Ordinary  Corrections. — To  summarize,  the  following  is 
the  process  of  correcting  a  compass  for  a  single  latitude,  where  magnets  at  right 
angles  are  employed  for  compensating  the  semicircular  deviation  and  where  the  dis- 
turbances due  to  unsymmetrical  soft  iron  are  small  enough  to  be  neglected. 

First.  All  correctors  being  clear  of  the  compass,  place  the  quadrantal  correctors 
in  the  position  which  it  is  estimated  that  they  will  occupy  when  adjustment  is  com- 
plete. The  navigator's  experience  wUl  serve  in  making  the  estimate,  or  if  there 
seems  no  other  means  of  arriving  at  the  probable  position  they  may  be  placed  at  the 
middle  points  of  their  supports. 

Second.  Steady  the  ship  on  magnetic  north,  east,  south,  or  west,  and  hold  on 
that  heading  by  such  method  as  seems  best.  By  means  of  permanent  magnets  alter 
the  indications  of  the  compass  until  the  heading  coincides  with  the  magnetic  course. 
If  heading  north,  magnets  must  be  entered  north  ends  to  starboard  to  correct  easterly 
deviation  and  to  port  to  correct  westerly,  and  the  reverse  if  heading  south.  If 
heading  east,  enter  north  ends  forward  for  easterly  and  aft  for  westerly  deviations, 
and  the  reverse  if  heading  west.  (Binnacles  differ  so  widely  in  the  methods  of  carry- 
ing magnets  that  details  on  this  point  are  omitted.     It  may  be  said,  however,  that 

o  This  is  all  that  is  required  for  the  purposes  of  compensation,  but  if  there  is  opportunity  it  is  always  well  to  make  a  complete 
swing  and  obtain  a  full  table  of  deviations,  which  may  give  interesting  information  of  the  existing  magnetic  conditions. 


52  THE    COMPASS   EKKOR. 

the  magnetic  intensity  of  the  correctors  may  be  varied  by  altering  either  their  number 
or  their  distance  from  the  compass;  generally  speaking,  several  magnets  at  a  dis- 
tance are  to  be  preferred  to  a  small  number  close  to  the  compass.) 

Third.  Steady  the  ship  on  an  adjacent  magnetic  cardinal  point  and  correct  the 
compass  heading  by  permanent  magnets  to  accord  therewith  in  the  same  manner  as 
described  for  the  first  heading. 

Fourth.  Steady  the  ship  on  an  intercardinal  point  (magnetic)  and  move  the 
quadrantal  correctors  away  from  or  toward  the  compass,  keeping  them  at  equal 
distances  therefrom,  until  the  compass  and  magnetic  headings  comcide. 

Fifth.  If  time  permits,  it  is  very  important  that  the  ship  should  next  be  steadied 
on  opposite  cardinal  and  semicardinal  points  and  one-half  oi  the  remaining  deviation 
corrected  by  changing  the  position  or  number  of  the  correctors. 

The  compensation  being  complete,  the  navigator  should  proceed  immediately 
to  swing  ship  and  make  a  table  of  the  residual  deviations.  Though  the  remain- 
ing errors  will  be  small,  it  is  seldom  that  they  will  be  reduced  to  zero,  and  it  must 
never  be  assumed  that  the  compass  may  be  relied  upon  without  taking  the  devi- 
ation into  account.  Observations  on  eight  equidistant  points  will  ordinarily 
suffice  for  this  purpose. 

124,  Compensation  of  the  Compass  while  Cruising. — Every  effort  should 
be  made  to  keep  at  least  the  standard  and  steering  compasses  compensated,  as  it  is 
always  easier  to  keep  the  compasses  compensated  than  to  keep  a  deviation  table 
correct,  at  hand,  and  in  use. 

rectangular  method. 

By  the  following  method  the  compasses  may  be  kept  practically  compensated 
and,  after  the  data  are  once  obtained,  it  requires  very  little  time  or  trouble. 

After  the  first  compensation  is  completed,  or  while  it  is  bein^  done,  head  the 
ship  north  or  south  and  move  the  athwartship  magnets  up  exactly  1  inch,  noting 
by  the  bearing  of  the  sun  or  of  a  distant  object,  the  amount  and  direction  of  the 
effect  on  the  coinpass.  Then  repeat  the  observation,  lowering  the  magnets  1  inch, 
and  noting  the  eflfect.  Then  head  the  ship  east  or  west  and  take  the  same  obser- 
vations with  the  fore-and-aft  magnets.  Then  head  on  an  intercardinal  point  and 
record  the  effect  of  moving  spheres  first  in  and  then  out  an  inch  from  the  correct 
position. 

The  record  would  then  take  this  form : 

Date Latitude Longitude 

H e 

On  North,  raising  B  magnets  (6  bundles)  1  inch  (from  9.85  to  8.85)  causes  12°  3(/  Easterly  deviation, 
therefore  a  movement  of  ^i^  inch  causes  1°  15''  Ely. 
Lowering  B  magnets  (6  bundles)  1  inch  (from  9.85  to  10.85)  causes  10°  15''  Westerly  deviation, 
therefore  a  movement  of  ^nj-  inch  causes  1°  2''  Wly. 
On  East,  raising  0  magnet  (2  bundles)  1  inch  (from  10.45  to  9.45)  causes  8°  15''  Westerly  deviation, 
therefore  a  movement  of  ^  inch  causes  0°  50'  Wly. 
Lowering  0  magnet  (2  bundles)  1  inch  (from  10.45  to  11.45)  causes  6°  30^  Easterly  deviation, 
therefore  a  movement  of  rg-  inch  causes  0°  39'  Ely. 
On  Northeast,  moving  spheres  in  1  inch  (from  10.6  to  9.6)  causes  4°  15'  Westerly  deviation,  therefore  a 
movement  of  -rs  inch  causes  0°  25'  Wly. 
Moving  spheres  out  1  inch  (from  10.6  to  11.6)  causes  3°  20^  Easterly  deviation,  therefore  a  move- 
ment of  ^  inch  causes  0°  20'  Ely. 

If  now  it  is  found  at  any  time  that  there  is,  say,  1°  45''  Easterly  on  East,  it  is 
evident  that  raising  the  C  magnets  -^  inch  will  correct  it,  and  careful  observations  on 
two  adjacent  cardinal  points  and  an  inter-cardinal  point  are  enough  to  recompensate. 
This  may  ordinarily  be  done  at  no  expense  of  time  and  with  little  trouble.  More 
confidence  may  be  felt  in  the  result  it  observations  for  deviations  are  afterwards 
obtained  on  the  four  cardinal  points  and  the  mean  of  the  results  on  opposite  courses 
taken  for  the  true  value;  this  must  be  done  if  the  variation  is  uncertain.  A  new 
set  of  data  observations  should  be  taken  after  a  large  change  of  magnetic  latitude, 
but  it  will  usually  be  found  that  the  changes  are  slight. 

Theoretically  the  quadrantal  deviation,  once  corrected,  should  remain  at  zero. 
It  will  usually  be  found,  however,  that  the  position  of  the  spheres  must  be  changed 


THE    COMPASS    EEROE.  53 

with  change  of  latitude.  A  convenient  way  of  dealing  with  this  is  to  construct  a 
curve  showing  the  positions  of  the  spheres  for  varying  values  of  H.  A  similar  curve 
showing  the  position  of  the  heeling  magnet  is  also  convenient. 

Whenever  the  position  of  any  corrector  is  changed,  a  note  showing  new  position, 
date,  latitude,  longitude,  H  and  6  should  be  made  on  one  of  the  blank  leaves  of  the 
compass  record.  A  complete  record  of  this  kind  will  be  found  of  the  utmost  value 
in  keeping  track  of  the  compasses. 

125.  Correcting  the  Heeling  Error. — The  heeling  error  may  be  corrected 
by  a  method  involving  computation,  together  with  certain  observations  on  shore. 
A  more  practical  method,  however,  is  usually  followed,  though  its  results  may  be  less 
precise.  The  heeling  corrector  is  placed  in  its  vertical  tube,  N.  end  uppermost  in 
north  latitudes,  as  this  is  almost  invariably  the  required  direction;  the  ship  being  on 
a  course  near  North  or  South  and  rolling,  observe  the  vibrations  of  the  card,  which, 
if  the  error  is  material,  will  be  in  excess  of  those  due  to  the  ship's  real  motion  in 
azimuth;  slowly  raise  or  lower  the  corrector  until  the  abnormal  vibrations  disappear, 
when  the  correction  will  be  made  for  that  latitude;  but  it  must  be  readjusted  upon 
any  considerable  change  of  geographical  position. 

In  making  this  observation  care  must  be  taken  to  distinguish  the  vessel's 
"yawing"  in  a  seaway  from  the  apparent  motion  due  to  heeling  error;  for  this 
reason  it  may  be  well  to  have  an  assistant  to  watch  the  ship's  head  and  keep  the 
adjuster  informed  of  the  real  change  in  azimuth,  by  which  means  the  latter  may 
better  judge  the  effect  of  the  heeling  error. 

In  the  case  of  a  sailing  vessel,  or  one  which  for  any  reason  maintains  a  nearly 
steady  heel  for  a  continuous  period,  the  amount  of  the  heeling  error  may  be  exactly 
ascertained  by  obsei-ving  the  azimuth  of  the  sun,  and  corrected  with  greater  accuracy 
than  is  possible  with  a  vessel  which  is  constantly  rolling. 

126.  Flinders  Bar. — The  simplest  method  that  presents  itself  for  the  placing 
of  the  Flinders  bar  is  one  which  is  available  only  for  a  vessel  crossing  the  magnetic 
equator.  Magnetic  charts  of  the  world  show  the  geographical  positions  at  which  the 
dip  becomes  zero — that  is,  where  a  freely  suspended  needle  is  exactly  horizontal  and 
where  there  exists  no  vertical  component  of  the  earth's  total  ma^etic  force.  In  such 
localities  it  is  evident  that  the  factor  of  the  semicircular  deviation  due  to  vertical 
induction  disappears  and  that  the  whole  of  the  existing  semicircular  deviation  arises 
from  subpermanent  magnetism.  If,  then,  when  on  the  magnetic  equator  the  compass 
be  carefully  compensated,  the  effect  of  the  subpermanent  magnetism  will  be  exactly 
opposed  by  that  of  the  semicircular  correcting  magnets.  Later,  as  the  ship  departs 
from  the  magnetic  equator,  the  semicircular  deviation  will  gradually  acquire  a 
material  value,  which  will  be  known  to  be  due  entirely  to  vertical  induction,  and  if 
the  Flinders  bar  be  so  placed  as  to  correct  it,  the  compensation  of  the  compass  will 
be  general  for  all  latitudes. 

In  following  this  method  it  may  usually  be  assumed  that  the  soft  iron  of  the 
vessel  is  symmetrical  with  respect  to  the  fore-and-aft  hne  and  that  the  Flinders  bar 
may  be  placed  directly  forward  of  the  compass  or  directly  abaft  it,  disregarding  the 
effect  of  components  to  starboard  or  port.  It  is  therefore  merely  necessary  to 
observe  whether  a  vertical  soft  iron  rod  must  be  placed  forward  or  abaft  the  compass 
to  reduce  the  deviation,  and,  having  ascertained  this  fact,  to  find  by  expteriment  the 
exact  distance  at  which  it  completely  corrects  the  deviation. 

The  Flinders  bar  frequently  consists  of  a  bundle  of  soft  iron  rods  contained  in 
a  case,  which  is  secured  in  a  vertical  position  near  the  compass,  its  upper  end  level 
with  the  plane  of  the  needles;  in  this  method,  the  distance  remaimng  fixed,  the 
intensity  of  the  force  that  it  exerts  is  varied  by  increasing  or  decreasing  the  number 
of  rods ;  this  arrangement  is  more  convenient  and  satisfactory  than  the  employment 
of  a  single  rod  at  a  variable  distance. 

The  United  States  Navy  FUnders  bar,  Type  II,  is  made  of  carefully  annealed 
pure  soft  iron,  2  inches  in  diameter,  total  length  24  inches,  consisting  of  pieces  12 
mches,  6  inches,  3  inches,  1^  inches,  and  f  inch  (2  of  these)  long.  Hardwood  blocks 
of  the  same  dimensions  are  used  to  support  the  proper  length  of  Flinders  bar  at  the 
top  of  a  fixed  brass  tube,  which  is  secured  ordinarily  at  the  foi-ward  end  of  the  bin- 
nacle in  the  fore-and-aft  hne. 


64  THE    COMPASS    ERROK. 

It  should  be  noted,  however,  that  it  is  extremely  difficult  to  get  soft  iron  rods 
of  a  satisfactory  quaUty,  for,  after  being  placed,  they  seldom  fail  to  take  up  more 
or  less  subpermanent  magnetism.  This  magnetism,  duo  to  shock  of  gunfire,  vibra- 
tion while  cruising  or  on  speed  trials,  etc.,  is  subject  to  greater  and  more  erratic 
changes  than  that  of  the  harder  portion  of  the  hull,  and  its  proximity  to  the  compass 
intensifies  the  effect  of  the  variations  in  its  magnetic  properties. 

127.  When  it  is  not  possible  to  correct  the  compass  at  the  magnetic  equator 
there  is  no  ready  practical  method  by  which  the  Flinders  bar  may  be  placed;  the 
operation  will  then  depend  entirely  upon  computation,  and  as  a  mathematical 
analysis  of  deviations  is  beyond  the  scope  laid  out  for  this  work  the  details  of  pro- 
cedure will  not  be  gone  into;  the  general  principles  involved  are  indicated,  and 
students  seeking  more  must  consult  the  various  works  that  treat  the  subject  fully. 

It  has  been  explained  that  each  coefficient  of  semicircular  deviation  (B  and  C) 

is  made  up  of  a  subpermanent  factor  varying  as  jr  and  of  a  vertical  induction  factor 

varying  as  tan  d.     If  we  indicate  by  the  subscripts  s  and  v,  respectively,  the  parts  due 
to  each  force,  we  may  write  the  equations  of  the  coefficients: 

B^BsXjT  +  BvXtan  ^;  and 

C  =  a  X^  +  CvX  tan^. 

Now  if  we  distinguish  by  the  subscripts  ^  and  2  the  values  in  the  first  and  in  the 
second  position  of  observation,  respectively,  of  those  quantities  that  vary  with  the 
magnetic  latitude,  we  have: 

Bi  =  B,  X  jj-  +  Bv  X  tan  6^, 
B2  =  BgXtT-  +  BvXtan^2;  and 
Ci  =  Cs  X  JJ-  +  Cv  X  tan  di, 

1^2  ^^  ^s  X  XT — r  '^v  X  tan  t/2- 

The  values  of  the  coefficients  in  both  latitudes  are  found  from  the  observations 
made  for  deviations;  the  values  of  the  horizontal  force  and  of  the  dip  at  each  place 
are  known  from  magnetic  charts;  hence  we  may  solve  the  first  pair  of  equations  for 
Bs  and  By,  and  the  second  pair  for  Cg  and  Cv ;  and  having  found  the  values  of  these 
various  coefficients,  we  may  correct  the  effects  of  Bg  and  C3  by  permanent  magnets 
in  the  usual  way  and  correct  the  remainder — that  due  to  By  and  Cy — by  the  Flinders 
bar. 

Strictly,  the  FHnders  bar  should  be  so  placed  that  its  repelhng  pole  is  at  an 
angular  distance  from  ahead  equal  to  the  "starboard  angle"  01  the  attracting  pole 
of  the  vertical  induced  force,  this  angle  depending  upon  the  coefficients  By  and  Cy; 
but  since,  as  before  stated,  horizontal  soft  iron  may  usually  be  regarded  as  sym- 
metrical, Cy  is  assumed  as  zero  and  the  bar  placed  in  the  midship  line. 

128.  To  Correct  Adjustment  on  Change  of  Latitude. — 'The  compensation 
of  quadrantal  deviation,  once  properly  made,  remains  effective  in  all  latitudes,  except- 
ing as  noted  in  article  110;  but  unless  a  Flinders  bar  is  used  a  correction  of  the 
semicircular  deviation  made  in  one  latitude  will  not  remain  accurate  when  the 
vessel  has  materially  changed  her  position  on  the  earth's  surface.  With  this  in 
mind  the  navigator  must  make  frequent  observations  of  the  compass  error  during 
a  passage  and  must  expect  that  the  table  of  residual  deviations  obtained  in  the 
magnetic  latitude  of  compensation  will  undergo  considerable  change  as  that  latitude 


THE   COMPASS  ERROR.  55 

is  departed  from.  The  new  deviations  may  become  so  large  that  it  will  be  fomid 
convenient  to  readjust  the  semicircular  correcting  magnets.  This  process  is  very 
simple. 

When  correctors  at  nght  angles  are  used,  provide  for  steadying  the  ship,  by  an 
auxihary  compass  or  by  the  pelorus,  upon  two  adjacent  magnetic  cardinal  points 
(art.  122).  Put  the  ship  on  heading  North  or  South  (magnetic),  and  raise  or  lower 
the  athwartship  magnets  or  alter  their  number  until  the  deviation  disappears ;  then 
steady  on  East  or  West  (magnetic)  and  similarly  adjust  the  fore-and-ait  magnets. 
Swing  ship  for  a  new  table  of  residual  deviations. 

129.  It  must  be  borne  in  mind  that  the  compensation  of  the  compass  is  not 
an  exact  science  and  that  the  only  safeguard  is  unceasing  watchfulness  on  the  navi- 
gator's part.  As  the  ship's  iron  is  partly  "hard"  and  partly  "soft,"  the  subper- 
manent  magnetism  may  change  appreciably  from  day  to  day,  especially  in  a  new 
ship  as  the  magnetism  absorbed  in  buildmg  "shakes  out."  After  a  ship  has  been  in 
service  for  one  or  two  years,  the  magnetic  conditions  may  be  said  to  be  "settled." 
They  undergo  changes,  however,  to  a  greater  or  less  extent,  on  account  of  the  follow- 
ing influences  or  conditions: 

(a)  Continuous  steaming  on  one  general  course  for  several  days,  especially  in 
rough  weather,  or  lying  alongside  a  dock  on  one  heading  for  a  long  period. 

(6)  Shock  of  gunfire,  even  on  a  ship  that  has  been  m  commission  for  more  than 
a  year,  has  been  known  to  introduce  an  8°  error,  which  disappeared  in  the  course  of 
a  few  days. 

(c)  Extensive  alterations  or  repairs  in  the  vicinity  of  the  compass.  The  use  of 
scaling  hammers  on  a  mihtary  top  caused  a  3°  change  in  one  of  the  U.  S.  S.  Con- 
necticufs  compasses. 

(d)  Steaming  with  boilers  (especially  under  forced  draft)  whose  funnel  is  near 
the  compass  has  Deen  known  to  cause  a  change  of  more  than  10°,  the  retained  mag- 
netism being  "cooked  out." 

(e)  On  the  U.  S.  S.  Oregon,  a  groimded  searchlight  circuit  caused  a  change  of  9°. 
(/)  Ships  have  reported  changes  of  as  much  as  7°  when  struck  by  lightning  or 

after  passing  through  very  severe  thunderstorms. 

The  binnacle  fittings  must  be  carefully  inspected  from  time  to  time,  to  see  that 
the  correctors  have  not  changed  position.  At  least  once  a  year  the  quadrantal 
correctors  should  be  examined  for  polarity.  Tliis  can  be  done  by  movmg  them, 
one  at  a  time,  as  close  to  the  compass  as  practicable  and  then  revolving  them  slowly 
about  the  vertical  axis;  if  the  compass  is  deflected,  the  magnetism  should  be  removed 
by  bringing  the  sphere  to  a  low  red  heat  and  then  letting  it  cool  slowly. 

There  is  no  excuse  for  large  deviations  in  a  standard  or  steering  compass,  and  they 
should  not  he  allowed  to  exist. 


CHAPTER  IV. 
PILOTING. 


130.  Piloting,  in  tlie  sense  given  the  word  by  modern  and  popular  usage,  is  the 
art  of  conducting  a  vessel  in  channels  and  harbors  and  along  coasts,  where  landmarks 
and  aids  to  navigation  are  available  for  fixing  the  position,  and  where  the  depth  of 
water  and  dangers  to  navigation  are  such  as  to  require  a  constant  watch  to  be  kept 
upon  the  vessel's  course  and  frequent  changes  to  be  made  therein. 

PUoting  is  the  most  important  part  of  navigation  and  the  part  requiring  the  most 
experience  and  nicest  judgment.  An  error  in  position  on  the  high  seas  may  be  rectified 
by  later  observation,  but  an  error  in  position  while  piloting  usually  results  in  disaster. 
Therefore  the  navigator  should  make  every  effort  to  be  proficient  in  this  important 
branch,  bearing  in  mind  that  a  modern  vessel  is  usually  safe  on  the  high  seas  and  in 
danger  when  approaching  the  land  and  making  the  harbor. 

131.  Requisites.' — The  navigator  should  have  ready  on  approaching  the  land 
the  charts  of  the  coast  and  the  largest  scale  detail  charts  of  the  locality  at  which  he 
expects  to  make  his  landfall,  the  saOing  directions,  and  the  light  and  buoy  list,  all 
corrected  for  the  latest  information  from  the  Notices  to  Mariners  and  other  sources. 
The  usual  instruments  employed  in  navigation  should  be  at  hand  and  in  good  working 
order.  The  most  important  instrument — the  sounding  machine — should  be  in  place 
and  in  order  at  least  a  day  before  the  land  is  to  be  made.  The  importance  of  the 
sounding  machine  can  not  be  exaggerated.  The  latest  deviation  table  for  the  standard 
compass  must  be  at  hand. 

132.  Laying  the  Course. — ^Mark  a  point  upon  the  chart  at  the  ship's  position; 
then  mark  another  point  for  which  it  is  desired  to  steer;  join  the  two  by  a  line  drawn 
with  the  parallel  ruler,  and,  maintaining  the  direction  of  the  line,  move  the  ruler 
until  its  edge  passes  through,  the  center  of  the  compass  rose  and  note  the  direction. 
If  the  compass  rose  indicates  ^^rite directions,  this  will  be  the  true  course;  and  must  be 
corrected  lor  variation  and  deviation  (by  api)lying  each  in  the  opposite  direction 
to  its  name)  to  obtain  the  compass  course;  ii  it  is  a  magnetic  rose,  the  course  need 
be  corrected  for  deviation  only. 

Before  putting  the  ship  on  any  course  a  careful  look  should  be  taken  along  the 
line  over  wmch  it  leads  to  be  assured  that  it  clears  all  dangers. 

133.  Methods  of  Fixing  Position. — ^A  navigator  in  sight  of  objects  whose 
positions  are  shown  upon  the  chart  may  locate  his  vessel  by  anyone  of  the  following 
methods:  (a)  cross  bearings  of  two  known  objects;  (b)  the  bearing  and  distance  of  a 
known  object;  (c)  the  bearing  of  a  known  object  and  the  angle  between  two  known 
objects;  (d)  two  bearings  of  a  known  object  separated  by  an  interval  of  time,  with 
the  run  during  that  interval;  (e)  sextant  angles  between  three  known  objects. 
Besides  the  foregoing  there  are  two  methods  by  which,  without  obtaining  the  precise 
position,  the  navigator  may  assure  himself  that  he  is  clear  of  any  particular  danger. 
These  are:  (f)  the  danger  angle;  (g)  the  danger  bearing. 

The  choice  of  the  method  wiU  be  governed  by  circumstances,  depending  upon 
which  is  best  adapted  to  prevaiUng  conditions. 

134:,  Cross  Bearings  of  Two  Known  Objects. — Choose  two  objects  whose 
Ttosition  on  the  chart  can  be  unmistakably  identified  and  whose  respective  bearings 
from  the  ship  differ,  as  nearly  as  possible  by  90°;  observe  the  bearing  of  each,  either 
by  compass  or  pelorus,  taking  one  as  quickly  as  possible  after  the  other;  see  that 
the  ship  is  on  an  even  keel  at  the  time  the  observation  is  made,  and,  if  using  the 
pelorus,  be  sure  also  that  she  heads  exactly  on  the  course  for  wliich  the  pelorus  is  set. 
Correct  the  bearings  so  that  they  will  be  either  true  or  magnetic,  according  as  they  are 
to  be  plotted  by  the  true  or  magnetic  compass  rose  of  the  chart — that  is,  if  observed 
by  compass,  apply  deviation  and  variation  to  obtain  the  true  bearing,  or  deviation 

56 


PILOTING.  57 

only  to  obtain  the  magnetic ;  if  observed  by  pelorus,  that  instrument  should  be  set 
for  the  true  or  magnetic  heading,  according  as  one  or  the  other  sort  of  reading  is 
required,  and  no  further  correction  will  be  necessary.  Draw  on  the  chart,  by  means 
of  the  parallel  rulers,  lines  which  shall  pass  thiough  the  respective  objects  in  the 
dkection  that  each  was  observed  to  bear.  As  the  ship's  position  on  the  chart  is 
known  to  be  at  some  point  of  each  of  these  lines,  it  must  be  at  their  intersection,  the 
only  point  that  fulfills  both  conditions. 

In  figure  13,  if  A  and  B  are  the  objects  and  OA  and  OB  the  lines  passing  through 
them  in  the  observed  directions,  the  ship's  position  will  be  at  O,  their  intersection. 

The  plotting  of  a  position  from  two  bearings  is 
greatly  facilitated  by  the  use  of  a  plotter  devised  by 

Lieut.  R.  A.  Koch,  IJnited  States  Navy,  as  reference  to  (^A 

the  compass  rose  on  the  chart,  the  use  of  parallel  rulers, 
and  the  drawing  of  lines  on  the  chart  are  obviated.  A 
brief  description  of  this  plotter  and  its  uses  is  as  follows: 
All  materials  except  bolt  and  washers  are  transparent. 

A  sc[uare  (7  by  7  mches)  ruled  with  two  series  of  lines  ""^Q/^^  _     J  9 

at  nght  angles  about  one-half  inch  apart,  and  a  disk 
(7^  inches  m  diameter)  marked  in  degrees  are  placed 
on  a  central  hollow  bolt  of  brass  and  are  capable  of 
being  clamped  together  with  any  degree  of  friction  re- 
quired.   Three  arms  are  placed  so  as  to  revolve  around 

tae  same  hollow  bolt  and  can  be  clamped  together  in  «    ■" 

any  position.  In  order  to  plot  a  position  from  compass 
bearmgs  of  two  objects,  and  lay  off  a  new  course,  the  no.  is. 

zero  mark  of  the  disk  should  be  revolved  to  the  East 

or  West  of  the  true  North  and  South  line  of  the  square  by  an  amount  equal  to  the 
compass  error  in  degrees.  Two  of  the  arms  are  then  set  by  the  degrees  on  the 
disk  to  the  two  observed  compass  bearings.  The  plotter  is  then  manipulated  on  the 
chart  untn  the  two  arms  intersect  the  objects  observed  and  the  vertical  lines  on  the 
square  are  parallel  to  the  meridians  of  the  chart.  Mark  the  point  of  intersection  of 
the  arms  by  inserting  a  pencil  in  the  hollow  central  bolt.  An  arm  may  then  be  swung 
to  intersect  any  object  on  the  chart  and  the  compass  course  to  that  object  read  from 
the  disk.  This  plotter  can  also  be  used  to  obtain  the  error  of  the  compass  from 
bearings  of  three  objects  by  compass. 

135.  If  it  be  possible  to  avoid  it,  objects  should  not  be  selected  for  cross 
bearings  which  subtend  an  angle  at  the  ship  of  less  than  30°  or  more  than  150°,  as, 
when  the  lines  of  bearing  approach  parallelism,  a  small  error  in  an  observed  bearing 
gives  a  large  error  in  the  result.  For  a  similar  reason  objects  near  the  ship  should  be 
taken  in  preference  to  those  at  a  distance. 

136.  When  a  third  object  is  available  a  bearing  of  that  may  be  taken  and  plotted. 
If  this  line  intersects  at  the  same  point  as  the  other  two  (as  the  bearing  OC  of  the 
object  C  in  the  figure),  the  navigator  may  have  a  reasonable  assurance  that  his  "fix" 
is  correct;  if  it  does  not,  it  indicates  an  error  somewhere,  and  it  may  have  arisen  from 
inaccurate  observation,  incorrect  determination  or  application  of  the  deviation,  or  a 
fault  in  the  chart. 

137.  What  may  be  considered  as  a  form  of  this  method  can  be  used  when  only 
one  known  object  is  in  sight  by  taking,  at  the  same  instant  as  the  bearing,  an  altitude 
of  the  sun  or  other  heavenly  body  and  noting  the 
time;  work  out  the  sight  and  obtain  the  Sumner 
line  (as  explained  in  Chapter  XV),  and  the  mter- 
section  of   this  with  the  direction  line  from  the 

object  will  give  the  observer's  position  in  the  same  .0 

way  as  from  two  ten-estrial  bearings. 

138.  Beaeing  and  Distance  of  a  Known 
Object. — When  only  one  object  is  available,  the 
ship's  position  may  be  found  by  observing  its  bear- 
ing and  distance.  Follow  the  preceding  method  in  j-io  ■^^ 
the  manner  of  taking,  correcting,  and  plotting  the 
bearing;  then,  on  this  fine,  lay  off  the  distance  from  the  object,  which  will  give  the 

Eoint  occupied  by  the  observer.     In  figure  14,  if  A  represents  the  object  and  AO  the 
earing  and  distance,  the  position  sought  wiU  be  at  O. 


68 


PILOTING. 


The  stadimeter  is  an  instrument,  similar  to  a  sextant,  employed  in  the  United 
States  Navy,  reading  directly  the  distance  of  the  object  observed  when  set  for  the 
height  of  the  object. 

Range-findmg  instruments  are  used  in  the  United  States  Navy  for  readily 
finding  the  distance  of  an  observed  object,  and  these  instruments  do  not  require 
knowledge  of  the  height  of  the  object.  These  instruments  are  accurate  for  naviga- 
tional purposes  up  to  ten  thousand  yards. 

139.  It  is  not  ordinarily  easy  to  find  directly  the  distance  of  an  object  at  sea. 
The  most  accurate  method  is  when  its  height  is  known  and  it  subtends  a  fair-sized 
angle  from  the  ship,  in  which  case  the  angle  may  be  measured  by  a  sextant  °'  and  the 
distance  computed  or  taken  from  a  table.  Table  33  of  this  work  gives  distances  up 
to  6  miles,  corresponding  to  various  heights  and  angles.  Captain  Lecky's  ''Danger 
Angle  and  Offshore  Distance  Tables"  carries  the  computation  much  further.  The 
use  of  this  method  at  great  distances  must  not  be  too  closely  relied  upon,  as  smaU 
errors,  such  as  those  due  to  refraction,  may  throw  out  the  results  to  a  material  extent, 
but  it  affords  an  excellent  approximation;  and,  as  this  method  of  fixing  position  is 
eroployed  only  when  no  other  is  available,  the  best  possible  approximation  has  to 


sumce. 


In  measuring  vertical  angles,  strictness  requires  that  the  observation  should  be 
so  made  that  the  angle  at  the  foot  of  the  object  should  equal  90°  and  that  the  triangle 
be  a  right  triangle,  as  OMN,  figure  15,  where  the  line  OM  is  truly  horizontal,  and  not 
as  in  the  triangle  O'MN,  where  the  condition  is  not  fulfilled.  This  error  is  inappre- 
ciable, however,  save  at  very  close  distances,  when  it  may  be  sufficiently  corrected  by 
getting  down  as  low  as  possible  on  board  the  vessel,  so  that  the  eye  is  near  the  water 
line.     One  condition  exists,  however,  where  the  error  is  material — that  shown  in 


Fig.  15. 


Fig.  16. 


figure  16,  where  the  visible  shore  line  is  at  M',  a  considerable  distance  from  M,  the 
point  vertically  below  the  summit.  In  this  case  there  is  nothing  to  mark  M  in  the 
observer's  eye,  and  it  is  essential  that  aU  angles  be  measured  from  a  point  close 
down  to  the  water  line. 

If  a  choice  of  objects  can  be  made,  the  best  results  wall  be  obtained  by  observing 
that  one  which  subtends  the  greatest  angle,  as  small  errors  will  then  have  the  least 
effect. 

140.  There  is  another  method,  known  as  Buckner's  method,  for  determining 
the  distance  of  an  object,  which  is  available  under  certain  circumstances.  This 
consists  in  observing,  from  a  position  aloft,  the  angle  between  the  object  and  the 
line  of  the  sea  horizon  beyond.  By  reference  to  Table  34  will  be  found  the  distance 
in  yards  corresponding  to  different  angles  for  various  heights  of  the  observer  from 
20  to  120  feet.  The  method  is  not  accurate  beyond  moderate  distances  (the  table 
being  limited  to  5,000  yards)  and  is  obviously  only  available  for  finding  the  distance 
of  an  isolated  object,  such  as  an  islet,  vessel,  or  target,  over  which  the  horizon  may 
be  seen.  In  employing  this  method  the  higher  the  position  occupied  by  the  observer 
the  more  precise  wiU  be  the  results. 

141.  In  observing  small  angles,  such  as  those  that  occur  in  the  methods  just 
described,  it  is  sometim.es  convenient  to  measure  them  on  and  off  the  limb  of  the 
sextant.  First  look  at  the  bottom  of  the  object  and  reflect  the  top  down  into  coin- 
cidence; then  look  through  the  transparentpart  of  the  horizon  glass  at  the  top  and 
bring  the  bottom  up  by  its  reflected  ray.  The  mean  of  the  two  readings  \vill  be  the 
true  angle,  the  index  correction  having  been  eliminated  by  the  operation. 

142.  When  the  methods  of  finding  distance  by  a  vertical  or  a  horizon  angle  are 
not  available,  it  must  be  obtained  by  such  means  as  exist.  Estimate  the  distance 
by  the  appearance;  take  a  sounding,  and  note  where  the  depth  falls  upon  the  line 


a  The  use  of  the  sextant  is  explained  in  Chapter  VIII. 


PILOTING.  59 

of  bearing;  at  night,  if  atmospheric  conditions  are  normal,  consider  that  the  distance 
of  a  light  when  sighted  is  equal  to  its  maximum  range  of  visibiUty,  remembering  that 
its  range  is  stated  for  a  height  of  eye  of  15  feet;  or  employ  such  method  as  suggests 
itself  under  the  circumstances,  regarding  the  result,  however,  as  an  approximation 
only. 

143.  The  Bearing  of  a  Known  Object  and  the  Angle  between  Two 
Known  Objects. — This  method  is  seldom  employed,  as  the  conditions  always  permit 
of  cross  bearings  bemg  taken,  and  the  latter  is  generally  considered  preferable. 

Take  a  bearing  of  a  known  object  by  compass  or  pelorus  and  observe  the 
sextant  angle  between  some  two  known  objects.  The  line  of  bearing  is  plotted  as  in 
former  methods.  In  case  one  of  the  objects  of  the  observed  angle  is  that  whose 
bearing  is  taken,  the  angle  is  applied,  right  or  left  as  the  case  may  be,  to  the  bearing; 
thus  giving  the  direction  of  the  second  object,  wliich  is  plotted  from  the  compass 
rose  and  parallel  rulera.  If  the  object  whose  bearing  is  taken  is  not  one  of  the  objects 
of  the  angle,  lay  off  the  an^le  on  a  three-armed  protractor,  or  piece  of  tracing  paper, 
and  swing  it  (keeping  the  legs  or  lines  always  over  the  two  objects)  until  it  passes 
over  the  line  of  bearing,  which  defines  the  position  of  the  sliip;  there  will,  except  in 
special  cases,  be  two  points  of  interaection  of  the  line  with  the  . 

circle  thus  described,  and  the  navigator  must  know  his  position  / 

with  sufficient  closeness  to  judge  which  is  correct. 

144:.  Two  Beaeings  of  a  Known  Object. — This  is  a  most 
useful  method,  wliich  is  frequently  employed,  certain  special  / 

cases  arising  thereunder  being  particularly  easv  of  application.       A      / 
The  process  is  to  take  a  careful  bearing  and  at  tne  same  moment        \/ 
read  the  patent  log;  then,  after  runiung  a  convenient  distance,        V 
take  a  second  bearing  and  again  read  the  log,  the  difference  in  A^ 
readings  giving  the  intervening  run;  when  running  at  a  known        jV 
speed,  the  time  interval  will  also  afford  a  means  for  determining       j    N^ 
the  distance  run.  _  \. 

The  problem  is  as  follows:  In  figure  17,  given  OA,  the  direc-  ^ 

tion  of  a  known  object.  A,  at  the  fii-st  observation;   PA,  the 
direction  at  the  second  observation ;  and  OP,  the  distance  trav-  \ 

ersed  between  the  two;  to  find  hS^  the  distance  at  the  second  \ 

observation.  yiq.  n. 

Knowing  the  angle  POA,  the  angular  distance  of  the  object 
from  right  ahead  at  the  first  bearing;  OPA,  the  angular  distance  from  right  astern 
at  the  second  bearing;  and  OP,  the  distance  run;  we  have  by  Plane  Trigonometry: 

PAO  =  180°-(POA  +  OPA);  and 

AP  =  OP  X  ^f^^?^. 
smPAO 

If,  as  is  frequently  the  case,  we  desire  to  know  the  distance  of  passing  abeam,  we 
have: 

AQ=APxsinOPA. 

Tables  5A  and  5B  give  solutions  for  this  problem,  the  former  for  intervals  of 
bearing  of  quarter  points,  the  latter  for  intervals  of  two  degrees.  Tlie  first  column 
of  each  of  these  tables  gives  the  value  of  AP,  the  distance  of  the  ship  from  the  observed 
object  at  the  time  of  taking  the  last  bearing,  for  values  of  OP  equal  to  unity;  that 
is,  for  a  run  between  bearings  of  1  mile.  The  second  column  gives  AQ,  the  distance  of 
the  object  when  it  bears  abeam,  likewise  for  a  value  of  OP  of  1  mile.  When  the  run 
between  bearings  is  other  than  1  mile,  the  number  taken  from  the  table  must  be  used 
as  a  multiplier  of  that  run  to  give  the  required  distance. 

Example:  A  vessel  steermg  north  takes  a  bearing  of  a  light  NW.  i  W.;  then 
runs  4.3  miles,  when  the  bearing  is  found  to  be  WSW.  Required  the  distance  of  the 
light  at  the  time  of  the  second  bearing. 

Difference  between  course  and  first  bearing,  4^  pts. 

Difference  between  course  and  second  bearing,  10  pts. 

Multiplier  from  first  column,  Table  6A,  0.88. 

4.3  miles  X  0.  88  =  3.8  miles,  distance  at  second  bearing. 


60 


PILOTING. 


Example:  A  vessel  on  a  course  128°  takes  the  first  bearing  of  an  object  at 
154°,  and  the  second  at  182°,  running  in  the  interval  0.8  mile.  Required  the  distance 
at  which  she  will  pass  abeam. 

Difference  between  course  and  first  bearing,  26° 
Difference  between  course  and  second  bearing,  54°. 
Multiplier  from  second  column.  Table  5B,  0.76. 
0.  8  mile  X  0.76  =  0.  6  mile,  distance  of  passing  abeam. 
145.  As  has  been  said,  there  are  certain  special  cases  of  this  problem  where  it  is 
exceptionally  easy  of  application;  these  arise  when  the  multiplier  is  eq^ual  to  unity 
and  the  distance  run  is  therefore  equal  to  the  distance  from 
the  object.     When  the  angular  distance  on  the  bow  at  the 
second  bearing  is  twice  as  great  as  it  was  at  the  first  bearing, 
the  distance  of  the  object  from  the  ship  at  second  hearing  is 
equal  to  the  run,  the  multiplier  being  1.0.     For  if,  in  figure  18, 
when  the  ship  is  in  the  first  position,  O,  the  object  A  bears  a° 
on  the  bow,  and  at  the  second  position,  P,  2a°,  we  have  in  the 
triangle  APO,  observmg  that  APO  =  180°  -  2a,  and  POA  =  «r; 

PAO  =  180°  -  (POA  +  APO), 

=  180°-(aj  +  180°-2a:), 
=  a. 

Or,  since  the  angles  at  O  and  A  are  equal  to  each  other,  the  sides 
OP  and  AP  are  equal  or  the  distance  at  second  bearing  is  equal 
to  the  run.     This  is  known  as  doubling  the  angle  on  the  how. 

146.  A  case  where  this  holds  good  is  familiar  to  every 
navigator  as  the  how  and  heam  hearing,  where  the  first  bearing 
is  taken  when  the  object  is  broad  on  the  bow  (four  points  or 
45°  from  ahead)  and  the  second  when  it  is  abeam  (eight  points  or  90°  from  ahead); 
in  that  case  the  distance  at  second  bearing  and  the  distance  abeam  are  identical 
and  equal  to  the  run  between  bearings. 

147.  When  the  first  bearing  is  26^°  from  ahead,  and  the  second  45°,  the  distance 
at  wTiich  the  ohject  will  he  passed  aheam  will  equal  the  run  between  bearings.  This 
is  true  of  any  two  such  bearings  whose  natural  cotangents  differ  by  unity,  and 
the  following  table  is  a  collection  of  solutions  of  this  relation  in  which  the  pairs  of 
bearings  are  such  that,  when  observed  in  succession  from  ahead  upon  the  same  fixed 
object,  the  distance  run  between  the  bearings  wUl  be  equal  to  the  distance  of  the  fixed 
object  when  it  bears  abeam,  provided  that  a  steady  course  has  been  steered,  unaffected 
by  current  or  drift. 

The  marked  pairs  will  probably  be  found  the  most  convenient  ones  to  use,  as 
they  involve  whole  degrees  only. 

Bearings  from  ahead. 


Fig.  18. 


First. 

Second. 

First. 

Second. 

First. 

Second. 

20 

291 

28 

48i 

37 

711 

21 

31f 

*29 

51 

38 

74i 

*22 

34 

30 

53f 

39 

76| 

23 

36i 

31 

56i 

*40 

79 

24 

38f 

*32 

59 

41 

8U 

*25 

41 

33 

61  i 

42 

83i 

26 

43^ 

34 

64i 

43 

85i 

26J 

45 

35 

66f 

*44 

88 

*27 

46    • 

36 

69i 

*45 

90 

When  the  fixed  object  bears  as  per  any  entry  of  the  first  column,  take  the  time 
and  the  reading  of  the  patent  log.  Repeat  this  procedure  on  reaching  the  bearing  of 
the  adjacent  entry  in  the  second  column.  The  difference  of  the  patent-log  readings 
will  be  the  distance  at  which  the  fixed  object  will  be  passed  abeam. 


PILOTING. 


61 


This  general  solution  includes  the  26^°-45°  rule  as  well  as  the  seven-tenths  rule 
to  be  explained  later;  furthermore,  it  has  the  advantage  that  the  approximate 
determination  of  the  distance  offshore,  at  which  the  fixed  object  will  be  passed, 
need  not  wait  for  the  45°  bearmg.  There  are  two  whole-degree  pairs  by  whidi  such 
a  determination  can  be  made  before  the  45°  bearing  is  reached.  It  is  possible  to 
get  five  whole-degree  bearings  or  observations  by  the  time  the  fixed  object  bears  30° 
forward  of  the  beam,  as  follows:  22°-34°,  25°-41°,  27°-46°,  29°-51°,  32°-59°.  Of 
these,  the  last  three  should  be  reasonably  accurate;  the  acuteness  of  the  first  angle 
m  all  such  observations  accounts  for  the  discrepancies  noted  in  practice.  The  use 
of  the  table  given  above  may  be  found  to  be  more  convenient  than  the  methods  of 
plotting  about  to  be  described,  and  the  use  of  tables  5A  and  5B;  but  it  does  not  take 
the  place  of  those  methods.  Tables  5A  and  5B  cover  all  combinations  of  bearings  in 
which  the  first  bearing  is  taken  when  the  object  is  20°  or  more  on  the  bow. 

The  Seven-tenths  Rule. — If  bearings  of  the  fixed  object  be  taken  at  two  (2) 
and  four  (4)  points  on  the  bow  (22^°  and  45°),  seven-tenths  (0.7)  of  therun  between 
bearings  will  be  the  distance  at  which  the  point  will  be  passed  abeam. 

From  the  combination  of  the  seven-tenths  rule  and  the  26i°-45°  rule,  there 
follows  an  interesting  corollary,  i.  e.,  if  bearings  of  an  object  at  22^°  and  26^°  on  the 
bow  be  taken,  then  seven-thirds  (f )  of  the  distance  run  in  the  interval  will  be  the 
distance  when  abeam. 

If  a  bearing  is  taken  when  an  object  is  two  points  (22^°)  forward  of  the  beam 
and  the  run  until  it  bears  abeam  13  measured,  then  its  distance  when  abeam  is  seven- 
thirds  {^)  of  the  run.     This  rule,  particularly,  is  only  approximate. 

In  case  the  45°  bearing  on  the  bow  is  lost,  in  order  to  find  the  distance  abeam 
that  the  object  is  passed,  note  the  time  when  the  object  bears  26^°  forward  of  the 
beam,  and  again  when  it  has  the  same  bearing  abaft  the  beam;  the  distance  run  in 
this  interval  is  the  distance  of  the  object  when  it  was  abeam. 

To  steer  an  arc  course  in  order  to  round  a  light,  point,  or  other  object  without 
fixes  and  be  sure  the  course  itseM  does  not  decrease  the  initial  distance:  Provided 
there  is  no  current,  stand  on  course  until  the  light  is  at  the  required  distance,  deter- 
mined by  one  or  more  of  the  methods  described.  Immediately  bring  the  light 
abeam,  and  do  not  let  it  get  forward  of  the  beam  again,  then  tne  course  will  not 
decrease  the  initial  distance.  When  the  light  is  one-half  point  abaft  the  beam 
again  bring  it  abeam;  hold  course  until  it  is  again 
one-half  point  abaft  the  beam,  repeating  this  pro- 
cedure until  the  light  is  rounded.  A  polygon  is  thus 
circumscribed  about  the  circle,  the  nearest  approach 
to  the  light  being  the  radius  of  the  inscribed  circle. 
The  number  of  sides  of  the  polygon  may  be  in- 
creased indefinitely,  so  that  the  light  may  be  rounded, 
by  changing  the  course  just  enough  to  keep  the  light 
abeam,  after  it  is  first  brought  abeam. 

148.  There  is  a  graphic  method  of  solving  this 
problem  that  is  considered  by  some  more  convenient 
than  the  use  of  multipliers.  Draw  upon  the  chart 
the  lines  OA  and  PA  (fig.  19),  passing  through  the 
object  on  the  two  observed  bearings;  set  the  dividers 
to  the  distance  run,  OP;  lay  down  the  parallel  rulers 
in  a  direction  parallel  to  the  course  and  move  them 
toward  or  away  from  the  observed  object  until  some 
point  is  found  where  the  distance  between  the  lines 
of  bearing  is  exactly  equal  to  the  distance  between 
the  points  of  the  dividers;  in  the  figure  this  occurs 
when  the  rulers  lie  along  the  line  OP,  and  therefore  O  represents  the  position  of 
the  ship  at  the  first  bearing  and  P  at  the  second.  For  any  other  positions  O'P', 
0"P",  the  condition  is  not^ fulfilled. 

149.  Another  graphic  solution  is  given  by  the  Mooring  and  Maneuvering  Board 
and  the  various  modifications  of  it  that  are  in  use  among  navigators. 

150.  The  method  of  obtaining  position  by  two  bearings  of  the  same  object  is 
one  of  great  value,  by  reason  of  the  fact  that  it  is  frequently  necessary  to  locate  the 
ship  when  there  is  but  one  landmark  in  sight.     Careful  navigators  seldom,  if  ever. 


Fig.  19. 


62  PILOTING. 

miss  the  opportunity  for  a  bow  and  beam  bearing  in  passing  a  lighthouse  or  other 
well-plotted  object;  it  involves  little  or  no  trouble,  and  always  gives  a  feeling  of 
added  security,  however  little  the  position  may  be  in  doubt.  If  about  to  pass  an 
object  abreast  of  which  there  is  a  danger — a  familiar  example  of  which  is  when  a 
lignthouse  marks  a  point  off  which  are  rocks  or  shoals — a  good  assurance  of  clearance 
should  be  obtained  before  bringing  it  abeam,  either  by  doubling  the  angle  on  the 
bow,  or,  if  the  object  be  sighted  in  time,  by  using  any  of  the  pairs  of  bearings  tabulated 
under  article  147. 

151.  It  must  be  remembered  that,  however  convenient,  the  fix  obtained  by 
two  bearings  of  the  same  object  will  be  in  error  unless  the  course  and  distance  are 
correctly  estimated,  the  course  "made  good"  and  the  distance  ''over  the  ground" 
being  req^uired.  Difficulty  will  occur  in  estimating  the  exact  course  when  there  is 
bad  steermg,  a  cross  current,  or  when  a  ship  is  making  leeway;  errors  in  the  allowed 
run  will  arise  when  she  is  being  set  ahead  or  back  by  a  current  or  when  the  logging 
is  inaccurate.  A  current  directly  with  the  course  of  the  ship,  if  unallowed  for,  will 
give  a  determination  of  position  too  close  to  the  object  observed;  and  a  current 
directly  against  the  course  of  the  ship,  if  unallowed  for,  will  give  a  determination  of 
position  too  far  away  from  the  object  observed.  The  existence  of  such  a  current 
will  not  le  revealed  by  taking  more  than  two  successive  bearings.  All  such  observa- 
tions will  place  the  snip  on  the  same  apparent  course,  which  course  will  be  parallel 
to  the  course  made  good  and  to  the  course  steered  but  in  error  in  its  distance  from 
the  observed  object  by  an  amount  dependent  upon  the  ratio  of  the  speed  of  ship 
over  ground  to  the  speed  of  ship  by  log.  A  current  oblique  to  the  course  of  the  ship 
will  give  a  determination  of  position  which  will  be  erroneous.  The  existence  of 
such  a  current  but  not  its  amount  will  he  revealed  by  taking  more  than  two  observa- 
tions; in  this  case,  following  the  usual  method  of  plotting,  the  determination  resulting 
from  any  two  successive  bearings  \\dll  fail  to  agree  with  the  determination  from  any 
other  two.  If,  in  such  a  case,  the  observed  bearings  be  drawn  upon  the  chart  and 
the  distances  run  by  log  between  them  be  laid  down  on  the  scale  of  the  chart  upon  a 
piece  of  paper,  a  course  may  be  found  by  trial,  upon  which  course  the  intervals  of 
run  correspond  with  the  intervals  between  the  lines  of  bearing.  The  apparent  course 
thus  determined,  which  must  always  be  oblique  to  the  course  steered,  will  be  parallel 
to  the  course  actually  being  made  good,  but  v/ill  be  in  error  in  its  distance  from  the 
observed  object  by  an  amount  dependent  upon  the  ratio  of  the  speed  of  ship  over 
the  ground  to  the  speed  of  ship  by  log.  If  there  is  an  apparant  shortening  of  the 
distance  run  from  earlier  to  later  observations,  or  a  shortening  of  the  time  if  the 
speed  is  invariable,  there  is  a  component  of  set  toward  the  fixed  object.  Therefore, 
if  in  a  current  of  any  sort,  due  allowance  must  be  made,  and  it  should  be  remembered 
that  more  dependence  can  be  placed  upon  a  position  fixed  by  simultaneous  bearings 
or  angles,  when  two  or  more  objects  are  available,  than  by  two  bearings  of  a  single 
object. 

152.  Sextant  Angles  between  Three  Known  Objects, — This  method, 
involving  the  solution  of  the  three-point  prohlem,  wiU,  if  the  objects  be  well  chosen, 
give  the  most  accurate  results  of  any.  It  is  largely  employed  in  surveying,  because 
of  its  precision;  and  it  is  especially  valuable  in  navigation,  because  it  is  not  subject 
to  errors  arising  from  imperfect  Imowledgo  of  the  compass  error,  improper  logging, 
or  the  effects  of  current,  as  are  the  methods  previously  described. 

Three  objects  represented  on  the  chart  are  selected  and  the  angles  measured 
with  sextants  of  known  index  error  between  the  center  one  and  each  of  the  others. 
Preferably  there  should  be  two  observers  and  the  two  angles  be  taken  simultaneously, 
but  one  observer  may  first  take  the  angle  which  is  changing  more  slowly,  then  take 
the  other,  then  repeat  the  first  angle,  and  consider  the  mean  of  the  first  and  last 
observations  as  the  value  of  the  first  angle.  The  position  is  usually  plotted  by 
means  of  the  three-armed  protractor,  or  station-pointer  (see  art.  428,  Chap.  XVII). 
Set  the  right  and  left  angles  on  the  instrument,  and  then  move  it  over  the  chart 
until  the  three  beveled  edges  pass  respectively  and  simultaneously  through  the 
three  objects.  The  center  of  the  mstrument  will  then  mark  the  ship's  position,  which 
may  be  pricked  on  the  chart  or  marked  with  a  pencil  point  through  the  center  hole. 
When  the  three-armed  protractor  is  not  at  hand,  the  tracing-paper  protractor  will 
prove  an  excellent  substitute,  and  may  in  some  cases  be  preferable  to  it,  as,  for 


PILOTING.  63 

instance,  when  the  objects  angled  on  are  so  near  the  observer  as  to  be  hidden  by 
the  circle  of  the  instrument.  A  graduated  circle  printed  upon  tracing  paper  permits 
the  angles  being  readily  laid  off,  but  a  plain  piece  of  tracing  paper  may  be  used  and 
the  angles  marked  by  means  of  a  small  protractor.  The  tracmg-paper  protractor 
permits  the  laying  down,  for  simultaneous  trial,  of  a  number  of  angles,  where  special 
accuracy  is  sought. 

163.  The  three-point  problem,  by  which  results  are  obtained  in  this  method, 
is :  To  find  a  point  such  that  three  lines  drawn  from  this  point  to  three  given  points 
shall  make  given  angles  with  each  other. 

Let  A,  B,  and  C,  in  figure  20,  be  three  fixed  objects  on  shore,  and  from  the 
ship,  at  D,  suppose  the  angles  CDB  and  ADB  are  found  equal,  respectively,  to  40° 
and  60°. 

With  the  complement  of  CDB,  50°,  draw  the  lines  BE  and  CE;  the  point  of 
intersection  will  be  the  center  of  a  circle,  on  some  point  of  whose  circumference  the 
ship  must  be.  Then,  with  the  complement  of  the  angle  ADB,  30°,  draw  the  lines 
AF  and  BF,  meeting  at  F,  which  pomt  will  be  the  center  of  another  circle,  on  some 
point  of  whose  circumference  the  ship  must  be.  Then  D,  the  point  of  intersection 
of  the  circumference  of  the  two  circles,  will  be  the  position  of  the  ship. 

The  correctness  of  tliis  solution  may  be  seen  as  follows:  Take  the  first  circle, 
DBC;  in  the  triangle  EBC,  the  angle  at  E,  the  center,  equals  180° -2X50°  = 
2  (90°  — 50°),  twice  the  complement  of  50°,  which  is  twice  the  observed  angle;  now 
if  the  angle  at  the  center  subtended  by  the  chord  BC  equals  twice  the  observed 
angle,  then  the  angle  at  any  point  on  the  cir- 
cumference subtended  by  that  chord,  which 
equals  half  the  angle  at  the  center,  equals  the 
observed  angle;  so  the  required  condition  is 
fulfilled.  Should  either  of  the  angles  exceed 
90°,  the  excess  of  the  angle  over  90°  must  be 
laid  off  on  the  opposite  side  of  the  lines  joining 
the  stations. 

It  may  be  seen  that  the  intersection  of 
the  circles  becomes  less  sharp  as  the  centers 
E  and  F  approach  each  other;  and  finally  that 
the  problem  becomes  indeterminate  when  the 

centers    coincide,   that    is,   when    the   three  

observed  points  and  the  observer's  position  all  no.  20? 

fall  upon  the  same  circle;  the  two  circles  are 

then  identical  and  there  is  no  intersection;  such  a  case  is  called  a  "revolver,"  because 

the  protractor  wUl  revolve  aroimd  the  whole  circle,  everywhere  passing  through  the 

observed  points.     The  avoidance  of  the  revolver  and  the  employment  of  large  angles 

and  short  distances  form  the  keys  to  the  selection  of  favorable  objects. 

Generally  speaking,  the  observer,  in  judging  which  objects  are  the  best  to  be 
taken,  can  picture  in  his  eye  the  circle  passing  through  the  three  points  and  note 
whether  it  comes  near  to  his  own  position.  If  it  does,  he  must  reject  one  or  more 
of  the  objects  for  another  or  others.  It  should  be  remembered  that  he  must  avoid 
not  only  the  condition  where  the  circle  passes  exactly  through  his  position  (when 
the  problem  is  whoUy  indeterminate),  but  also  all  conditions  approximating  thereto, 
for  m  such  cases  the  circles  will  intersect  at  a  very  acute  angle,  and  the  mevitable 
small  errors  of  the  observation  and  plotting  will  produce  large  errors  in  the  result- 
ing fix. 

Without  giving  an  analysis  of  reasons,  which  may  be  found  in  various  works 
that  treat  the  problem  in  detail,  the  following  may  be  enimierated  as  the  general 
conditions  whicn  result  in  a  good  fix: 

{a)  When  the  center  object  of  the  three  lies  between  the  observer  and  a  line 
joining  the  other  two,  or  Ues  nearer  than  either  of  the  other  two. 

(&)  When  the  sum  of  the  right  and  left  angles  is  equal  to  or  greater  than  180°. 

(c)  When  two  of  the  objects  are  in  range,  or  nearly  so,  and  the  angle  to  the  third 
is  not  less  than  30°. 

{d)  When  the  three  objects  are  in  the  same  straight  line. 


64 


PILOTING. 


Fig.  21. 


A  condition  that  limits  all  of  these  is  that  angles  should  be  large — at  least  as 
large  as  30° — excepting  in  the  case  where  two  objects  are  in  range  or  nearly  so,  and 
then  the  other  angle  must  be  of  good  size.  When  possible,  near  objects  should  be 
used  rather  than  distant  ones.  The  navigator  should  not  fall  into  the  error  of 
assuming  that  objects  which  would  give  good  cuts  for  a  cross  bearing  are  necessarily 
favorable  for  the  three-point  solution. 

In  a  revolver,  the  angle  formed  by  lines  drawn  from  the  center  object  to  the 
other  two,  added  to  the  sum  of  the  two  observed  angles,  equals  180°.  A  knowledge 
of  this  fact  may  aid  in  the  choice  of  objects. 

If  in  doubt  as  to  the  accuracy  with  which  the  angles  will  plot,  a  third  angle  to 
a  fourth  object  may  be  taken.     Another  way  to  make  sure  oi  a  doubtful  fix  is  to 

take  one  compass  bearing,  by  means  of  which  even 
a  revolver  may  be  made  to  give  a  good  position. 

154.  The  Danger  Angle. — ^When  sailing  along 
a  coast,  to  avoid  sunken  rocks,  or  shoals,  or  danger- 
ous obstructions  at  or  below  the  surface  of  the  water, 
and  which  are  marked  on  the  chart,  the  navigator 
may  pass  these  at  any  desired  distance  by  using  what 
is  known  as  a  danger  angle,  of  which  there  are  two 
kinds,  namely,  the  horizontal  and  vertical  danger 
angles;  the  former  requires  two  well-marked  objects 
indicated  on  the  chart,  lying  in  the  direction  of  the 
coast,  and  sufficiently  distant  from  each  other  to 
give  a  fair-sized  horizontal  angle;  the  latter  requires 
a  well-charted  object  of  Imown  height. 

155.  In  figure  21,  let  AMB  be  a  portion  of  the 
coast  along  which  a  vessel  is  sailing  on  the  course 
CD;  A  and  B  two  prominent  objects  shown  on  the 
chart;  S  and  S'  are  two  outlying  shoals,  reefs,  or 
dangers.     In  order  to  pass  outside  of  the  danger  S' 

take  the  middle  point  of  the  danger  as  a  center  and  the  given  distance  from  the 
center  it  is  desired  to  pass  as  radius,  and  describe  a  circle.  Pass  a  circle  through 
A  and  B  tangent  to  the  seaward  side  of  the  first  circle.  To  do  this,  it  is  only  neces- 
sary to  join  A  and  B  and  draw  a  line  perpendicular  to  the  middle  of  AB,  and  then 
ascertain  by  trial  the  location  of  the  center  of  the  circle  EAB.  Measure  the  angle 
AEB,  set  the  sextant  to  this  angle,  and  remembering  that  AB  subtends  the  same  angle 
at  aU  points  of  the  arc  AEB,  the  ship  will  be  outside  the  arc  AEB,  and  clear  the 
danger  S',  as  long  as  AB  does  not  subtend  an  angle  greater  than  AEB,  to  which  the 

sextant  is  set.  At  the  same  time  in 
order  to  avoid  the  danger  S,  take  the 
middle  point  of  the  danger  S  and  with 
the  desu'ed  distance  as  a  radius  de- 
scribe a  circle.  Pass  a  second  circle 
through  A  and  B  tangent  to  this  circle 
at  G,  measure  the  angle  AGB  with  a 
protractor,  then,  as  long  as  the  chord 
AB  subtends  an  angle  greater  than 
AGB,  the  ship  wiU  be  inside  the  cir- 
cle AGB.  Therefore,  the  ship  will  pass 
between  the  dangers  S  and  S'  as  long 
as  the  angle  subtended  by  AB  is  less 
than  AEB  and  greater  than  AGB. 

156.  The  vertical  danger  angle 
involves  the  same  general  principle,  as 
can  be  readily  seen  without  explana- 
tion by  reference  to  the  figure  22  in  wliich  AB  represents  a  vertical  object  of  known 
height. 

157.  The  Danger  Bearing. — This  is  a  method  by  which  the  navigator  is  warned 
by  a  compass  bearing  when  the  course  is  leading  into  danger.  Suppose  a  vessel  to 
be  steering  a  course,  as  indicated  in  figure  23,  along  a  coast  which   must  not  be 


/"' 


/, 

/ 

/ 

V 

N       / 
\  / 

M 

T 

1/^^P^;;;^^ 

'  \ 

y  y^SeS^ 

\ 
\ 

\ 

^V-^ 

\ 
\ 
\ 
\ 

\ 

c      \ 

Fig.  22. 


PILOTING. 


65 


approached  within  a  certain  distance,  the  landmark  A  being  a  guide.  Let  the  navigator 
draw  through  A  the  line  XA,  clear  of  the  danger  at  all  points,  and  note  its  direction 
by  the  compass  rose;  then  let  frequent  bearings  be  taken  as  the  ship  proceeds,  and 
so  long  as  the  bearings,  YA,  ZA,  are  to  the  rigM  of  XA  he  may  be  assured  that  he  is 
on  the  left  or  safe  side  of  the  line. 

If,  aa  in  the  case  given,  there  is  but  one  object  in  sight  and  that  nearly  ahead,  it 
would  be  very  difficult  to  get  an  exact  position,  but  this  method  would  always  show 
whether  or  not  the  ship  was  on  a  good  course,  and  would,  in  consequence,  be  of 
the  greatest  value.  And  even  if  there  were  other  objects  visible  by  which  to  get 
an  accurate  fix  it  would  be  a  more  simple  matter  to  note,  by  an  occasional  glance 
over  the  sightvane  of  the  pelorus  or  compass,  that  the 
sliip  was  making  good  a  safe  course  than  to  be  put  to  the 
necessity  of  plotting  the  position  each  time. 

158.  It  will  occasionally  occur  that  two  natural  objects 
will  so  lie  that  when  in  range  they  mark  a  danger  bearing; 
advantage  should  be  taken  of  aU  such,  as  they  are  easier  to 
observe  than  a  compass  bearing;  but  if  in  a  locaUty  with 
which  the  navigator  has  not  had  previous  acquaintance  the 
compass  bearing  of  all  ranges  should  be  observed  and  com-  | 
pared  with  that  indicated  on  the  chart  in  order  to  make  sure 
of  the  identity  of  the  objects.  The  utility  of  ranges,  either 
artificial  or  natural,  as  guides  in  navigation,  extends  also  to 
established  lines  of  bearm^  giving  the  true  or  magnetic  direc- 
tion of  fixed  objects,  such  as  lines  of  bearing  limiting  the 
sectors  of  navigational  Ughts. 

159.  Soundings. — The  practice  should  be  followed  of 
employing  one  or  two  leadsmen  to  take  and  report  soimdings 
continuously  while  in  shoal  water  or  in  the  vicinity  of  dangers. 
The  soundings  must  not  be  regarded  as  fixing  a  position,  but  they  afford  a  check 
upon  the  positions  obtained  by  other  methods.  An  exact  agreement  with  the 
soundings  on  the  chart  need  not  be  expected,  as  there  may  bo  some  little  inaccu- 
racies in  reporting  the  depth  on  a  ship  moving  with  speed  through  the  water,  or 
the  tide  may  cause  a  discrepancy,  or  the  chart  itself  mav  lack  perfection ;  but  the 
soundings  snould  agree  in  a  general  way,  and  a  marked  departure  from  the  charac- 
teristic bottom  shown  on  the  chart  should  lead  the  navigator  to  verify  his  position 
and  proceed  with  caution ;  especially  is  this  true  if  the  water  is  more  shoal  than 
expected. 

160.  But  if  the  soundings  in  shallow  water  when  landmarks  are  in  si^ht 
serve  merely  as  an  auxiliary  guide,  those  taken  (usually  with  the  patent  sounding 
machine  or  deep-sea  lead)  when  there  exist  no  other  means  of  locatmg  the  position, 
fulfill  a  much  more  important  purpose.  In  tliick  weather,  when  approaching  or 
running  close  to  the  land,  and  at  all  times  when  the  vessel  is  in  less  than  100  fathoms 
of  water  and  her  position  is  in  doubt,  soundings  should  be  taken  continuously  and 
at  regular  intervals,  and,  with  the  character  of  the  bottom,  systematically  recorded. 
By  laying  the  soundings  on  tracing  paper,  along  a  line  which  represents  the  track  of 
the  ship  according  to  the  scale  oF  the  chart,  and  then  moving  the  paper  over  the 
chart,  keeping  the  various  courses  parallel  to  the  correspondmg  directions  on  the 
chart,  until  the  observed  soundings  agree  with  those  laid  down,  the  ship's  position 
wUl  in  general  be  quite  well  determined.  While  some  localities,  by  the  sharpness 
of  the  characteristics  of  their  soundings,  lend  themselves  better  than  others  to 
accurate  determinations  by  this  method,  there  are  few  places  where  the  mariner 
can  not  at  least  keep  out  of  danger  by  the  indications,  even  if  they  tell  him  no  more 
than  that  the  time  Has  come  when  he  must  anchor  or  he  off  till  conditions  are  more 
favorable. 

161.  Lights. — Before  coming  within  range  of  a  light  the  navigator  should 
acquaint  himself  with  its  characteristics,  so  that  when  sighted  it  will  be  recognized. 
The  charts,  sailing  directions,  and  Ught  lists  give  information  as  to  the  color,  character, 
and  range  of  visibihty  of  the  various  lights.  Care  should  be  taken  to  note  all  of 
these  and  compare  them  when  the  light  is  seen.    If  the  light  is  of  the  flashing, 

21594°— 14 5 


66  PILOTING. 

revolving,  or  intermittent  variety  the  duration  of  its  periods  should  be  noted  to 
identify  it.  If  a  fixed  light,  a  method  that  may  be  employed  to  make  sure  that  it  is 
not  a  vessel's  light  is  to  "descend  several  feet  immediately  after  sighting  it  and  observe 
if  it  disappears  from  view;  a  navigational  light  will  usually  do  so,  excepting  in  misty 
weather,  while  a  vessel's  light  will  not.  The  reason  for  this  is  that  navigational  lights 
are  as  a  rule  sufficiently  powerful  to  be  seen  at  the  farthest  point  to  which  the  ray 
can  reach  without  being  mterrupted  by  the  earth's  curvature.  They  are  therefore 
seen  at  the  first  moment  that  the  ray  reaches  an  observer  on  a  ship's  deck,  and  are 
cut  off  if  he  lowers  the  eye.  A  vessel's  light,  on  the  other  hand,  is  usually  Hmited 
by  its  intensity  and  does  not  carry  beyond  a  distance  within  which  it  is  visible  at 
all  heights. 

Care  must  be  taken  to  avoid  being  deceived  on  first  sighting  a  light,  as  there  are 
various  errors  into  which  the  inexperienced  may  fall.  The  glare  of  a  powerful  Ii»ht 
is  often  seen  beyond  the  distance  of  visibUity  of  its  direct  rays  by  the  reflection 
downward  from  particles  of  mist  in  the  air;  the  same  mist  may  also  cause  a  white 
light  to  have  a  distinctly  reddish  tinge,  or  it  may  obscure  a  light  except  within  short 
distances.  When  a  light  is  picked  up  at  the  extreme  limit  at  which  the  height  of 
the  observer  will  permit,  a  fixed  light  may  appear  flashing,  as  it  is  seen  when  the 
ship  is  on  the  crest  of  a  wave,  and  lost  when  in  the  hoUow. 

Many  lights  are  made  to  show  different  colors  in  different  sectors  within  their 
range,  and  by  consulting  his  chart  or  books,  the  navigator  may  be  guided  by  the 
color  of  the  sector  in  which  he  finds  himself;  in  such  lights  one  color  is  generally 
used  on  bearings  whence  the  approach  is  clear,  and  another  covers  areas  where 
dangers  are  to  be  encountered. 

The  visibility  of  lights  is  usually  stated  for  an  assumed  height  of  the  observer's 
eye  of  15  feet,  and  must  be  modified  accordingly  for  any  other  height.  But  it  should 
be  remembered  that  atmospheric  and  other  conditions  considerably  affect  thevisibihty, 
and  it  must  not  be  positively  assumed,  on  sighting  a  light,  even  in  perfectly  clear 
weather,  that  a  vessel's  distance  is  equal  to  the  range  of  visibiUty;  it  may  be  either 
greater  or  less,  as  the  path  of  a  ray  of  fight  near  the  horizon  receives  extraordinary 
deflection  under  certain  circumstances;  the  conditions  governing  this  deflection  are 
discussed  in  article  296,  Chapter  X. 

162.  Buoys. — While  buoys  are  valuable  aids,  the  mariner  should  always  employ 
a  certain  amount  of  caution  in  being  guided  by  them.  In  the  nature  of  things  it  is 
never  possible  to  be  certain  of  finding  buoys  in  correct  position,  or,  indeed,  of  finding 
them  at  all.  Heavy  seas,  strong  currents,  ice,  or  collisions  with  passing  vessels  may 
drag  them  from  their  places  or  cause  them  to  disappear  entirely,  and  they  are  especially 
uncertain  in  unfrequented  waters,  or  those  of  nations  that  do  not  keep  a  good  lookout 
upon  their  aids  to  navigation.  When,  therefore,  a  buoy  marks  a  place  where  a  ship 
must  be  navigated  with  caution,  it  is  well  to  have  a  danger  angle  or  bearing  as  an 
additional  gmde  instead  of  placing  too  much  dependence  upon  the  buoy  being  in 
place. ... 

Different  nations  adopt  different  systems  of  coloring  for  their  buoys;  an 
important  feature  of  many  such  systems,  including  those  adopted  by  the  tJnited 
States  and  various  other  great  maritime  nations  (though  not  aU),  consists  in  placing 
red  buoys  to  be  left  on  the  starboard  hand  of  a  vessel  entering  a  harbor  or  fairway, 
and  black  buoys  on  the  port  hand.  In  these  various  systems  the  color  and  character 
of  the  buoys  are  such  as  to  denote  the  special  purpose  for  which  they  arc  employed. 

163.  Fogs  and  Fog  Signals. — ^As  with  fights,  the  navigator  should,  in  a  fo^, 
acquaint  himself  with  the  characteristics  of  the  various  sound  signals  which  he  is 
fikely  to  pick  up,  and  when  one  is  heard,  its  periods  should  be  timed  and  compared 
with  those  given  in  the  fight  lists  to  insure  its  proper  identity. 

Experiment  has  demonstrated  that  sound  is  conveyed  through  the  atmosphere 
in  a  very  uncertain  way;  that  its  intensity  is  not  always  increased  as  its  origin  is 
approached,  and  that  areas  within  its  range  at  one  time,  will  seem  silent  at  another. 
Add  to  these  facts  the  possibifity  that,  for  some  cause,  the  signal  may  not  be  working 
as  it  should  be,  and  we  have  reason  for  observing  the  rule  to  proceed  with  the  utmost 
caution  when  running  near  the  land  in  a  fog. 

Although  the  transmission  of  sound  through  water  from  the  submarine  bells 
that  have  been  instaUed  on  many  fight  vessels  and  at  points  of  danger  is  much  more 


PILOTING.  67 

certain  than  the  transmission  of  sound  through  air  and  can  be  received  in  such  a 
way  by  vessels  equipped  with  submerged  microphones  on  each  side  as  to  enable  the 
direction  of  the  submarine  bell  to  be  approximately  determined,  yet  the  lead  continues 
to  prove  an  ever-serviceable  guide,  and  should  accordingly  be  in  constant  use. 

The  method  of  plotting  soundings  described  in  article  160  will  give  the  most 
rehable  position  that  is  obtainable.  Moreover,  the  lead  will  warn  the  navigator  of 
the  approach  to  shallow  water,  when,  if  his  position  is  at  all  in  doubt,  it  is  wisest  to 
to  anchor  before  it  becomes  too  late. 

When  running  slowly  in  a  fog  (which  caution,  as  well  as  the  law,  requires  that 
one  should  do)  it  must  be  borne  in  mind  that  the  relative  effect  of  current  is  increased; 
for  instance,  the  angle  of  deflection  from  the  course  caused  b}^  a  cross-set  is  greater  at 
low  than  at  high  speed. 

It  is  worth  remembering  that  when  in  the  vicinity  of  a  bold  bluff  shore  vessels 
are  sometimes  warned  of  a  too  close  approach  by  having  their  own  fog  signals  echoed 
back  from  the  chffs;  indeed,  from  a  knowledge  of  the  velocity  of  sound  (art.  314, 
Chap.  XI)  it  is  possible  to  gain  some  rough  idea  of  the  distance  in  such  a  case. 

When  radio-stations,  equipped  with  fog-signahng  apparatus,  send  out  simul- 
taneous radio  and  sound  signals,  distances  from  the  sending  station  can  be  found 
by  noting  the  elapsed  interval  between  the  time  of  arrival  of  radio  signal  and  sound 
signal,  and  multiplying  this  interval  expressed  in  seconds  by  the  velocity  per  second 
of  sound  in  air,  or  the  velocity  per  second  of  sound  in  water,  according  as  the 
sound  signals  are  received  through  air  or  through  water. 

By  thus  determining  the  distance  from  a  fog-signal  station  to  different  positions 
between  which  the  course  and  distance  are  known,  the  position  of  the  vessel  could 
be  approximately  found  in  a  manner  analogous  to  that  which  would  apply  in  figure  18 
if  the  distances  AO  and  AP  were  known  in  addition  to  the  length  and  direction  of  OP. 

164.  Tides  and  Currents. — The  information  relating  to  the  tides  given  on 
the  chart  and  in  other  publications  should  be  studied,  as  it  is  of  importance  for  the 
navigator  to  know  not  only  the  height  of  the  tide  above  the  plane  of  reference  of 
the  chart,  but  also  the  direction  and  force  of  the  tidal  current. 

The  plane  of  reference  adopted  for  soundings  varies  with  different  charts; 
on  a  large  number  it  is  that  of  mean  low  water,  and  as  no  plane  of  reference  above  that 
of  mean  low  water  is  ever  employed  the  navigator  may  with  safety  refer  his  sound- 
ings to  that  level  when  in  douot. 

When  traversing  waters  in  which  the  depth  exceeds  the  vessel's  draft  by  but  a 
small  margin,  account  must  be  taken  of  the  fact  that  strong  winds  or  a  high  barom- 
eter may  cause  the  water  to  fall  below  even  a  very  low  plane  of  reference.  On  coasts 
where  there  is  much  diurnal  inecjualitv  in  the  tides,  the  amount  of  rise  and  fall  can 
not  be  depended  upon^  and  additional  caution  is  necessary.  ' 

A  careful  distmction  should  be  made  between  the  vertical  rise  and  foM  of  the 
tide,  which  is  marked  at  the  transition  periods  by  a  stationary  height,  or  stand,  and 
the  tidal  current,  which  is  the  horizontal  transfer  of  water  as  a  result  of  the  difference 
of  level,  producing  the  flood  and  ehh,  and  the  intermediate  condition,  or  slack.  It 
seldom  occurs  that  the  turn  of  the  tidal  stream  is  exactly  coincident  with  the  high 
and  low  water,  and  in  some  channels  the  current  may  outlast  the  vertical  movement 
which  produces  it  by  as  much  as  three  hours,  the  effect  being  that  when  the  water 
is  at  a  stand  the  tidal  stream  is  at  its  maximum,  and  when  the  current  is  slack  the 
rise  or  fall  is  going  on  with  its  greatest  rapidity.  Care  must  be  taken  to  avoid  con- 
founding the  two. 

The  effect  of  the  tidal  wave  in  causing  currents  may  be  illustrated  by  two  simple 
cases: 

(1)  Where  there  is  a  small  tidal  basin  connected  with  the  sea  by  a  large  opening. 

(2)  Where  there  is  a  large  tidal  basin  connected  with  the  sea  by  a  small  opening. 
In  the  first  case  the  velocity  of  the  current  in  the  opening  will  have  its  maximum 

value  when  the  height  of  the  tide  within  is  changing  most  rapidly,  i.  e.,  at  a  time 
about  midway  between  high  and  low  water.  The  water  in  the  basin  keeps  at  approxi- 
mately the  same  level  as  the  water  outside.  The  flood  stream  corresponds  with  the 
rising  and  the  ebb  with  the  falling  of  the  tide. 

In  the  second  case  the  velocity  of  the  current  in  the  opening  will  have  its  maxi- 
mum value  when  it  is  high  water  or  low  water  without,  for  then  there  is  the  greatest 


68  PILOTING. 

head  of  water  for  producing  motion.  The  flood  stream  begins  about  three  hours 
after  low  water,  and  the  ebb  stream  about  three  hours  after  high  water,  slack  water 
thus  occurring  about  midway  between  the  tides. 

Along  most  shores  which  lack  features  like  bays  and  tidal  rivers,  the  current 
usually  turns  soon  after  high  water  and  low  water. 

The  swiftest  current  in  straight  portions  of  tidal  rivers  is  usually  in  the  middle 
of  the  stream,  but  in  curved  portions  the  most  rapid  current  is  toward  the  outer 
edge  of  the  curve,  and  here  the  water  will  be  deepest.  The  pilot  rule  for  best  water 
is  to  follow  the  ebb-tide  reaches. 

Conntercurrents  and  eddies  may  occur  near  the  the  shores  of  straits,  especially  in 
bights  and  near  points.  A  knowledge  of  them  is  useful  in  order  that  they  may  be 
taken  advantage  of  or  avoided. 

A  swift  current  often  occurs  in  the  narrow  passage  connecting  two  large  bodies 
of  water,  owing  to  their  considerable  difference  of  level  at  the  same  instant.  The 
several  passages  between  Vineyard  Sound  and  Buzzards  Bay  are  cases  in  point.  In 
the  Woods  Hole  Passage  the  maximum  strength  of  the  tidal  streams  occurs  near 
high  and  low  water. 

Tide  rips  are  made  by  a  rapid  current  setting  over  an  irregular  bottom,  as  at 
the  edges  oi  banks  where  the  change  of  depth  is  considerable. 

Generally  speaking,  the  rise  and  fall  and  strength  of  current  are  at  their  mini- 
mum along  straight  stretches  of  coast  upon  the  open  ocean,  while  bays,  bights,  inlets, 
and  large  rivers  operate  to  augment  the  tidal  effects,  and  it  is  in  the  vicinity  of  these 
that  one  finds  the  highest  tides  and  strongest  currents.  The  navigator  need  there- 
fore not  be  surprised  in  cruising  along  a  coast  to  notice  that  his  vessel  is  set  more 
strongly  toward  or  from  the  shore  in  passing  an  indentation,  and  that  the  evidences 
of  tide  will  appear  more  marked  as  he  nears  its  mouth.  Usually  more  complete  data 
are  furnished  in  charts  and  tide  tables  regarding  the  rise  and  fall,  and  it  irequently 
occurs  that  the  information  regarding  the  tidal  current  is  comparatively  meager;  the 
mariner  must  therefore  take  every  means  to  ascertain  for  himself  the  direction  and 
force  of  the  tidal  and  other  currents,  either  from  the  set  shown  between  successive 
well-located  positions  of  the  ship,  or  by  noting  the  ripple  of  the  water  around  buoys, 
islets,  or  shoals,  the  direction  in  which  vessels  at  anchor  are  riding,  and  the  various 
other  visible  effects  of  the  current. 

Current  arrows  on  the  chart  must  not  be  regarded  as  indicating  absolutely  the 
conditions  that  are  to  be  encountered.  They  represent  the  mean  of  the  direction 
and  force  observed,  but  the  observations  upon  which  they  are  based  may  not  be 
complete,  or  there  may  be  reasons  that  bring  about  a  departure  from  the  normal 
state. 

165.  Charts. — The  chart  should  be  carefully  studied,  and  among  other  things 
all  of  its  notes  should  be  read,  as  valuable  information  may  be  given  m  the  margm 
which  it  is  not  practicable  to  place  upon  the  chart  abreast  the  locality  affected. 

The  mariner  will  do  well  to  consider  the  source  of  his  chart  and  the  authority 
upon  which  it  is  based.  He  will  naturally  feel  the  greatest  confidence  in  a  chart 
issued  by  the  Government  of  one  of  the  more  important  maritime  nations  which 
maintains  a  well-equipped  office  for  the  especial  purpose  of  acquiring  and  treating 
hydrographic  information.  He  should  note  the  character  of  the  survey  from  which  the 
chart  has  been  constructed;  and,  finally,  he  should  be  especially  careful  that  the 
chart  is  of  recent  issue  or  bears  correction  of  a  recent  date — facts  that  should  always 
be  clearly  shown  upon  its  face. 

It  is  well  to  proceed  with  caution  when  the  chart  of  the  locality  is  based  upon 
an  old  survey,  or  one  whose  source  does  not  carry  with  it  the  presumption  of  accu- 
racy. Ev^en  if  the  original  survey  was  a  good  one,  a  sandy  bottom,  in  a  region 
where  the  currents  are  strong  or  the  seas  heavy,  is  liable  to  undergo  in  time  marked 
changes;  and  where  the  depth  is  affected  by  the  deposit  or  removal  of  silt,  as  in  the 
vicinity  of  the  estuaries  of  large  river  systems,  the  behavior  is  sometimes  most  capri- 
cious. Large  blank  spaces  on  the  chart,  where  no  soundings  are  shown,  may  be 
taken  as  an  indication  that  no  soundings  were  made,  and  are  to  be  regarded  with 
suspicion,  especially  if  the  region  abounds  in  reefs  or  pinnacle  rocks,  in  which  case 
only  the  closest  sort  of  a  survey  can  be  considered  as  revealing  all  the  dangers 
of  these  facts  must  be  duly  weighed. 


AUi 

J 


PILOTING.  69 

When  navigating  by  landmarks  the  chart  of  the  locality  which  is  on  the  largest 
scale  should  be  used.  The  hydrography  and  topography  in  such  charts  appear  in 
greater  detail,  and — a  most  important  consideration — bearings  and  angles  may  be 
plotted  with  increased  accuracy. 

To  sum  up,  the  navigator  must  know  the  exact  draft  of  the  ship  when 
approaching  the  land.  He  must  make  himself  familiar  with  every  detail  of  the 
charts  he  will  be  required  to  use  and  must  read  the  charts  in  such  a  way  as  to  be 
able  to  form  a  mental  picture  of  how  the  land  and  the  various  aids  to  navigation 
will  look  when  sighted,  remembering  that  the  position  of  the  sun  at  different  times 
of  day,  or  the  position  of  the  moon  at  night,  affects  the  appearance  of  the  land  as 
presented  to  the  navigator  approaching  from  seaward.  He  must  be  thoroughly 
lamiliar  with  the  dav,  night,  and  fog  characteristics  of  all  aids  to  navigation  in  the 
locality.  He  must  Know  the  state  of  the  tide  and  the  force  and  direction  of  the 
current  at  all  times  when  in  pilot  waters.  The  navigator,  in  making  his  plan  for 
entering  a  strange  port,  should  give  very  careful  previous  studv  to  the  chart,  and 
should  carefully  select  what  appear  to  be  the  most  suitable  marks  for  use,  also  pro- 
viding himself  with  substitutes  for  use  in  case  those  selected  as  most  suitable  should 
prove  unreliable  by  not  being  recognized  with  absolute  certainty.  It  must  be 
remembered  that  buoys  seen  at  a  distance,  in  approaching  a  channel,  are  often 
difficult  to  place  or  identify,  because  all  mav  appear  equallv  distant,  though  in 
reality  far  apart.  Ranges  should  be  noted,  if  possible,  and  the  lines  oraMm,  both 
for  leading  tnrou^  the  best  water  in  channels  and  also  for  guarding  against  par- 
ticular dangers.  For  the  latter  purpose,  safety  bearings  should  in  all  cases  be  laid 
down  where  no  suitable  ranges  oner.  Tne  courses  to  be  steered  in  entering  should 
also  be  laid  down  and  distances  marked  thereon.  If  intending  to  use  the  sextant 
and  danger  angle  in  passing  dangers,  and  especially  in  passing  between  dangers, 
the  danger  circles  should  be  plotted  and  regular  courses  planned,  rather  than  to  run 
haphazard  by  the  indications  of  the  angle  alone,  with  the  possible  trouble  to  be 
apprehended  from  wild  steering  at  critical  points. 

The  ship's  position  should  not  be  allowed  to  be  in  doubt  at  any  time,  even  in 
entering  ports  considered  safe  and  easy  of  access,  and  should  be  constantly  checked 
by  continuing  to  use  for  this  purpose  those  marks  concerning  which  there  can  be 
no  doubt  until  others  are  unmistakably  recognized. 

The  ship  should  ordinarily  steer  exact  courses  and  follow  exact  lines  as  planned 
from  the  chart,  changing  course  at  exact  points,  and,  where  the  distances  are  con- 
siderable, her  position  on  the  line  should  be  checked  at  frequent  intervals,  recording 
the  time  and  the  reading  of  the  patent  log.  This  is  desirable,  even  where  it  may 
seem  unnecessary  for  safety;  because,  if  running  by  the  eye  alone  and  the  ship's 
exact  position  be  suddenly  required,  as  in  a  sudden  squall,  fixing  at  that  particular 
moment  might  be  impossiole. 

The  habit  of  running  exact  courses  with  precise  changes  of  courses  will  be  found 
most  useful  when  it  is  desired  to  enter  port  or  pass  through  inclosed  waters  during 
fog  by  means  of  the  buoys ;  here  safety  demands  that  the  buoys  be  made  successively, 
to  do  which  requires,  if  the  fog  be  dense,  very  accurate  courses  and  careful  attention 
to  the  times,  rate  of  speed,  and  the  set  of  tne  current.  Failure  to  make  a  buoy  as 
expected  leaves  no  safe  alternative  but  to  anchor  at  once. 

It  is  a  useful  point  to  remember  that  in  passing  between  dangers  where  there 
are  no  suitable  leading  marks,  as,  for  instance,  between  two  islands  or  an  island  and 
the  main  shore,  with  dangers  extending  from  both,  a  mid-channel  course  may  be 
steered  bj^  the  eye  alone  with  great  accuracy,  as  the  eye  is  able  to  estimate  very  closely 
the  position  midway  between  visible  objects. 

In  piloting  among  coral  reefs  or  banks,  a  time  should  be  chosen  when  the  sun 
will  be  astern,  conning  the  vessel  from  aloft  or  from  an  elevated  position  forward. 
The  line  of  demarcation  between  the  deep  water  and  the  edges  of  the  shoals,  which 
generally  show  as  ^een  patches,  is  indicated  with  surprising  clearness.  This  method 
IS  of  frequent  application  in  the  numerous  passages  oi  the  Florida  keys. 

Changes  oi  course  should  in  general  be  made  by  exact  amounts,  naming  the  new 
course  or  the  amount  of  the  change  desired,  rather  than  by  ordering  the  helm  to  be 
put  over  and  then  steadying  when  on  the  desired  heading,  with  the  possibility  of  the 
attention  being  diverted  and  so  forgetting  in  the  meantime  that  the  ship  is  still 


70  PILOTING. 

swinging.  The  helmsman,  knowing  just  what  is  desired  and  the  amount  of  change 
to  be  made,  is  thus  enabled  to  act  more  intelligently  and  to  avoid  wild  steering, 
which  in  narrow  channels  is  a  very  positive  source  of  danger. 

Coast  'piloting  involves  the  same  principles  and  requires  that  the  ship's  positions 
be  continuously  determined  or  checked  as  the  landmarks  are  passed.  On  well- 
surveyed  coasts  there  is  a  great  advantage  in  keeping  near  the  land,  thus  holding 
on  to  the  marks  and  the  soundings,  and  thereby  knowing  at  all  times  the  position, 
rather  than  keeping  offshore  and  losing  the  marks,  with  the  necessity  of  again  making 
the  land  from  vague  positions,  and  perhaps  the  added  inconvenience  of  fog  or  bad 
weather,  involving  a  serious  loss  of  time  and  fuel. 

The  route  should  be  planned  for  normal  conditions  of  weather  with  suitable 
variations  where  necessary  in  case  of  fog  or  bad  weather  or  making  points  at  night, 
the  courses  and  distances,  in  case  of  regular  runs  over  the  same  route,  being  entered 
in  a  notebook  for  ready  reference,  as  well  as  laid  dowTi  on  the  chart.  The  danger 
circles  for  either  the  horizontal  or  the  vertical  danger  angles  should  be  plotted, 
wherever  the  method  can  be  usefully  employed,  and  the  angles  marked  tnereon; 
many  a  mUe  may  thus  be  saved  in  rounding  dangerous  points,  with  no  sacrifice  in 
safety.  Ranges  should  also  be  marked  in,  where  useful  for  positions  or  for  safety, 
and  also  to  use  in  checking  the  deviation  of  the  compass  by  comparing,  in  crossing, 
the  compass  bearing  of  the  range  with  its  magnetic  bearing,  as  given  by  the  chart. 

Changes  of  course  will  in  general  be  made  with  mark  or  object  abeam,  the  posi- 
tion (a  new  "departure")  being  then,  as  a  rule,  best  and  most  easily  obtained. 

In  making  the  land  in  a  fog  the  sounding  machine  must  be  kept  going  at  intervals 
of  half  an  hour  some  hours  before  it  is  expected  that  soundings  can  be  obtained. 
Several  soundings  taken  at  random  will  not  locate  a  ship,  but  on  the  contrary  may 
lead  to  disaster.  In  using  the  sounding  machine  be  careful  that  the  man  handhng 
the  tube  does  not  invert  the  tube  when  taking  it  from  the  tube  case,  as  this  would 
allow  water  to  run  toward  the  closed  end  of  the  tube,  causing  a  discoloration  of  the 
coating  and  thus  bring  about  an  incorrect  sounding.  It  is  also  essential  that  the 
lead  be  cleanly  and  freshly  armed  for  each  cast.  The  bottom  having  been  picked  up, 
a  graphic  record  of  the  soimdings  may  be  laid  down  in  the  manner  previously  described 
in  paragraph  160  and  an  approximation  made  of  the  position  oi  the  ship.  Keep  a 
sharp  lookout  for  any  landmarks  that  jnight  show  up  during  a  momentary  lifting 
of  the  fog  and  have  keen  ears  hstening  for  an  aerial  or  submarine  fog  signal.  Having 
picked  up  any  such  signal,  make  sure  to  ascertain  exactly  what  landmark  it  is. 
From  now  on  proceed  with  caution  and  determine  whether  it  is  better  to  anchor  or 
to  proceed  through  the  harbor  channel  in  the  fog.  If,  having  approached  the  land 
ana  failed  to  hear  fog  signals  at  the  time  they  were  expected  to  be  heard  and  the 
soundings  indicate  a  dangerous  proximity  to  shore,  the  only  safe  course  is  either  to 
anchor  or  to  stand  off.  When  running  slowly  in  a  fog  (which  caution,  as  well  as 
the  law,  requires  that  one  should  do)  it  must  be  borne  in  mind  that  the  relative  effect 
of  current  is  increased;  for  instance,  the  angle  of  deflection  from  the  course  caused 
by  a  cross  set  is  greater  at  low  than  at  high  speed.  It  is  worth  remembering  that 
when  in  the  vicinity  of  a  bold  bluff  shore  vessels  are  sometimes  warned  of  a  too-close, 
approach  by  having  their  own  fog  signals  echoed  back  from  the  cliffs ;  indeed,  from 
a  knowledge  of  the  velocity  of  sound  it  is  possible  to  ^ain  some  rough  idea  of  the 
distance  in  such  a  case.  Great  caution  must  be  used  in  approaching  a  bold  coast 
in  a  fog  and,  unless  soundings  can  be  got  that  will  reasonably  assure  the  navigator 
of  his  distance  from  the  coast,  the  only  safe  course  is  to  stand  off,  if  the  depth  of 
the  water  does  not  permit  of  anchoring. 

The  best  aids  at  the  disposal  of  the  navigator  when  running  in  a  fog  are  the 
sounding  machine  and  the  hand  lead,  and  the  navigator  will  do  well  to  make  great 
use  of  them.  Even  in  clear  weather  the  sounding  machine  may  be  a  great  aid  to  the 
navigator  in  verifying  his  position.  fl 

In  approaching  the  land  and  entering  harbors,  the  navigator  must  bear  in  mind  ■ 
that  rules  of  the  road  in  inland  waters  sometimes  differ  from  those  used  on  the  high 
sea,  and  should  inform  himself  of  the  boundaries  of  the  waters  where  different  rules 
of  the  road  obtain. 

166.  Records.^ — It  will  be  found  a  profitable  practice  to  pay  careful  attention 
to  the  recording  of  the  various  matter  relating  to  the  piloting  of  the  ship.     A  notebook 


PILOTING.  71 

should  be  kept  at  hand  on  deck  or  on  the  bridge,  in  which  are  to  be  entered  all  bearings 
or  angles  taken  to  fix  the  position,  all  changes  of  course,  important  soundings,  and 
any  other  facts  bearing  upon  the  navigation.  (This  book  should  be  different  from 
the  one  in  which  astronomical  sights  and  offshore  navigation  are  worked.)  The 
entries,  though  in  memorandum  form,  should  be  complete;  it  should  be  clear  whether 
bearings  and  courses  are  true,  magnetic,  or  by  compass;  and  it  is  especially  important 
that  the  time  and  patent  log  reading  should  be  given  for  each  item  recorded.  The 
value  of  this  book  will  make  itself  apparent  in  various  directions;  it  will  afford 
accurate  data  for  the  writing  of  the  ship  s  lo^;  it  will  furnish  interesting  information 
for  the  next  run  over  the  same  ground;  it  will  provide  a  means  by  which,  if  the  ship 
be  shut  in  by  fog,  rain,  or  darkness,  or  if  there  be  difficulty  in  recognizing  landmarl^ 
ahead,  the  last  accurate  fix  can  bo  plotted  and  brought  forward;  and,  finally,  if 
there  should  be  a  mishap,  the  notebook  would  fumi^  evidence  as  to  where  the 
trouble  has  been. 

The  chart  on  which  the  work  is  done  should  also  be  made  an  intelUgible  record, 
and  to  this  end  the  pencil  marks  and  lines  should  not  be  needlessly  numerous,  heavy, 
or,  long.  In  plotting  bearings,  draw  lines  only  long  enough  to  cover  the  probable 
position.  Mark  intersections  or  positions  by  drawing  a  small  circle  around  them, 
and  writing  neatly  abreast  them  the  time  and  patent  log  reading.  Indicate  the 
courses  and  danger  bearings  by  full  lines  and  mark  them  appropriately,  preferably 
giving  both  magnetic  (or  true)  and  compass  directions.  A  great  number  of  lines 
extending  in  every  direction  may  lead  to  confusion;  however  remote  the  chance 
may  seem,  the  responsibihties  of  piloting  are  too  serious  to  run  even  a  small  risk. 

Finally,  on  anchoring,  record  and  plot  the  position  by  bearings  or  angles  taken 
after  coming  to;  observe  that  the  berth  is  a  safe  one,  or,  if  in  doubt,  send  a  boat  to 
sound  in  the  vicinity  of  the  ship  to  make  sure. 


CHAPTER  V. 
THE  SAILINGS. 


167.  In  considering  a  ship's  position  at  sea  with  reference  to  any  other  place, 
either  one  that  has  been  left  or  one  toward  which  the  vessel  is  bound,  five  terms  are 
involved — the  Course,  the  Distance,  the  Difference  of  Latitude,  the  Difference  of 
Longitude,  and  the  Departure.""  The  solutions  of  the  various  problems  that  arise 
from  the  mutual  relation  of  these  quantities  are  called  Sailings. 

168.  Kinds  of  Sailings. — When  the  only  quantities  involved  are  the  course, 
distance,  difiFerence  of  latitude,  and  departure,  tne  process  is  denominated  Plane 
Sailing.  In  this  method  the  earth  is  regarded  as  a  plane,  and  the  operation  proceeds 
as  if  the  vessel  sailed  always  on  a  perfectly  level  surface.  When  two  or  more  courses 
are  thus  considered,  they  are  combined  by  the  method  of  Traverse  Sailing.  It  is 
evident  that  the. number  of  miles  of  latitude  and  departure  can  thus  be  readily 
deduced;  but,  while  one  mile  always  equals  one  minute  in  difference  of  latitude,  one 
mile  of  departure  corresponds  to  a  difference  of  longitude  that  will  vary  with  the 
latitude  in  which  the  vessel  is  sailing.  Plane  sailing  therefore  furnishes  no  solution 
where  difference  of  longitude  is  considered,  and  for  such  solution  resort  must  be  had 
to  one  of  several  methods,  which,  by  reason  of  their  taking  account  of  the  spherical 
figure  of  the  earth,  are  called  Spherical  Sailings. 

When  a  vessel  sails  on  an  east  or  west  course  along  a  parallel  of  latitude,  the 
method  of  converting  departure  into  difference  of  longitude  is  called  Parallel  Sailing. 
When  the  course  is  not  east  or  west,  and  thus  carries  the  vessel  through  various 
latitudes,  the  conversion  may  be  made  either  by  Middle  Latitude  Sailing,  in  which 
it  is  assumed  that  the  whole  run  has  been  made  m  the  mean  latitude,  or  by  Mercator 
Sailing,  in  which  the  principle  involved  in  the  construction 
of  the  Mercator  chart  (art.  39,  Chap.  II)  is  utilized. 

Great  Circle  Sailing  deals  with  the  courses  and  distances 

between  any  two  points  when  the  track  followed  is  a  great 

circle  of  the  terrestrial  sphere.     A  modification  of  this  method 

which  is  adopted  under  certain  circumstances  is  called  Corn- 

^st.  posite  Sailing. 

PLANE  SAILING. 

169.  In  Plane  Sailing,  the  curvature  of  the  earth  being 
neglected,  the  relation  between  the  elements  of  the  rhumb 
track  joining  any  two  points  may  be  considered  from  the 
plane  right  triangle  formed  by  the  meridian  of  the  place  left, 
^^'  ^-  the  parallel  of  the  place  arrived  at,  and  the  rhumb  line.     In 

figure  24,  T  is  the  point  of  departure;  T',  the  point  of  destination;  Tn,  the  meridian 
of  departure;  T'n,  the  parallel  of  destination;  and  TT',  the  rhumb  line  between  the 
points.  Let  G  represent  the  course,  T'Tn;  Dist.,  the  distance,  TT';  DL,  the  dif- 
ference of  latitude,  Tn;  and  Dep.,  the  departure,  T'n.  Then  from  the  triangle 
TT'n,  we  have  the  following: 

sin  c-^^- 
^^  ^~Dist.' 

COS  C  = 


Dist. 
Dep. 


tanC  =  j)L- 


•  For  the  definition  of  these  tenns,  see  article  6,  Chapter  I. 
72 


THE  SAILINGS. 


73 


From  these  equations  are  derived  the  following  formulaB  for  working  the  various 
problems  that  may  arise  in  Plane  Sailing: 


Given. 


Course  and  distance. 


Difference   of   latitude 
and  departure. 


Course  and  difference  of 
latitude. 


Course  and  departure. . . 


Distance  and  difference 
of  latitude. 


Distance  and  departure . 


Required. 


Formulae. 


f  Difference  of  latitude 
\Departure 

I  Course 
Distance 

Distance 

Departure 

Distance 

Difference  of  latitude 

f  Coxu-se 

I  Departure 

{Course 
Difference  of  latitude 


DL    = 
Dep.   = 

TanC= 
Dist.   = 

Dist.  = 
Dep.  = 

Dist.   = 
DL    = 

CosC  = 
Dep.  : 

SinC  = 
DL    = 


=Diet.  cos  C. 
=Dist.  sin  C. 

Dep. 
=DL  ' 

Dep. 
"sin  C ' 

DL  . 

"cos  C 

=D  L  tan  C. 

Dep. 
"sin  C 

Dep. 
"tanC* 

DL 
"Dist.  ■ 
=Dist.  sia  C. 

Dep. 
"Dist.  ■ 
=Dist.  cos  C. 


Log  D  L   =log  Dist.+log  cos  C. 
Log  Dep.  =log  Dist. -[-log  sinC. 

Log  tan  C=log  Dep.— log  D  L. 
Log  Dist.  =log  Dep.  —log  sin  C. 

Log  Dist.  =log  D  L  —log  cos  C. 
Log  Dep.  =log  D  L  -flog  tan  C. 

Log  Dist,  =log  Dep.  —log  sin  C. 
Log  D  L  =log  Dep.  — l<5g  tan  C. 

Log  cos  C=log  D  L  —log  Dist. 
Log  Dep.  =log  Dist.+log  sin  C. 

Log  sin  C  =log  Dep.  —log  Dist. 
Log  D  L  =log  Dist.  -flog  cos  C. 


170.  The  solution  of  the  plane  right  triangle  may  be  accompUshed  either  by 
Plane  Trigonometry,  by  Traverse  Tables,  or  by  construction.  If  the  former  method 
is  adopted,  the  logarithms  of  numbers  may  be  found  in  Table  42,  and  of  the  functions 
of  angles  in  Table  44.  A  more  expeditious  method  is  available,  however,  in  the 
Traverse  Tables,  which  give  by  inspection  the  various  solutions.  Table  1  contains 
values  of  the  various  parts  for  each  unit  of  Dist.  from  1  to  300,  and  for  each  quar- 
ter-point (2°  49'"),  of  C;  Table  2  contains  values  for  each  unit  of  Dist.  from  1  to 
600,  and  for  each  de^ee  of  C.  The  method  of  solving  by  construction  consists  in 
laying  down  the  various  given  terms  by  scale  upon  a  chart  or  plain  paper,  and 
measuring  thereon  the  terms  required. 

171.  Of  the  various  problems  that  may  arise,  the  first  two  given  in  the  foregoing 
table  are  of  much  the  most  frequent  occurrence.  In  the  first,  the  given  quantities 
are  course  and  distance,  and  those  to  be  found  are  difference  of  latitude  and  departure; 
this  is  the  case  where  a  navigator,  knowing  the  distance  run  on  a  given  course,  desires 
to  ascertain  the  amount  made  good  to  north  or  south  and  to  east  or  west.  In  the 
second  case  the  conditions  are  reversed;  this  arises  where  the  course  and  distance 
between  two  points  are  to  be  obtained  from  their  known  difference  of  latitude  and 
departure. 

Example  :  A  ship  sails  SW.  by  W.,  244  miles.     Required  the  difference  of  latitude  and  the  departure 
made  good. 

By  Inspection. 

In  Table  1,  find  the  course  SW.  by  W.  (5  points);  it 
occurs  at  the  bottom  of  the  page,  therefore  take  the  names 
of  the  columns  from  the  bottom  as  well;  opposite  244  in 
the  Dist.  column  will  be  seen  Lat.  135.6  and  Dep.  202.9. 


By  Computation. 


Dist.         244 
C         56°  15' 

DL        135. 6 

Dist.         244 
C         56°  ly 

Dep.     202. 9 


log        2. 38739 
log  cos  9.  74474 


2. 13213 


log    

1(^    2. 38739 
log  sin  9.  91985 

log    2. 30724 


74 


THE  SAILINGS. 


Example:  A  ship  sails  N.  5°  E.,  188  miles. 
By  CompiUation. 


Required  the  difference  of  latitude  and  the  departure. 
By  Inspection. 


Digt. 
C 


188 
5° 


log         2. 27416 
log  cos  9.  99834 


DL 

187.3 

log 

2.  27250 

Dist. 

C 

188 
5° 

log 
log 

sin 

2.  27416 
8.  94030 

In  Table  2,  find  the  course  5°;  it  occurs  at  the  top  of  the 
page,  therefore  take  the  names  of  the  columns  from  the 
top;  opposite  188  in  the  Dist.  column  will  be  seen  Lat. 
187.3  and  Dep.  16.4. 


Dep. 


16.4 


log 


1.  21446 


Example  :  A  vessel  is  bound  to  a  port  which  ia  136  miles  to  the  north  and  203  miles  to  the  west  of 
her  position.    Required  the  course  and^distance. 


Dep. 
DL 


By  Computation. 

203        log 
136        log 


2.  30750 
2. 13354 


C      (N.)  56"  IV  (W.)  log  tan  0. 17396 

Dep.  203  log         2.30750 

C  56°  11'  log  sin  9.  91951 

Dist.  244.3  log         2.38799 


By  Inspection. 

Enter  Table  1  and  turn  the  pages  until  a  course 
is  found  whereon  the  numbers  136  and  203  are 
found  abreast  each  other  in  the  columns  marked 
respectively  Lat.  and  Dep.  This  occiu-s  most  nearly 
at  the  course  for  5  points,  the  angle  being  taken 
from  the  bottom,  because  the  appropriate  names 
of  the  columns  are  found  there.  The  course  ia 
therefore  NW.  by  W.  Interpolating  for  interme- 
diate values,  the  corresponding  number  in  the 
Dist.  column  is  about  244.3. 


Example:  As  a  result  of  a  day's  run  a  vessel  changes  latitude  244  miles  to  the  south  and  makes  a 
departure  of  171  miles  to  the  east.    What  is  the  coiu-se  and  distance  made  good? 

By  Inspection. 

Enter  Table  2  and  the  nearest  agreement  will  be 
found  on  course  (S.)  35°  (E.),  the  appropriate  names 
being  found  at  the  top  of  the  page.  The  nearest 
corresfKjnding  Dist.  is  298  miles. 


By  Computation. 

Dep.                      171        log        2.23300 
DL                        244        log        2.38739 

C       (S.)  35°  02'  (E.) 

log  tan  9. 84561 

Dep.                      171 
C                     35°  02' 

log        2. 23300 
log  sin  9. 75895 

Dist. 


297. 9        log         2. 47405 


TRAVEBSE  SAILING. 


172.  A  Traverse  is  an  irregular  track  made  by  a  ship  in  sailing  on  several  different 
courses,  and  the  method  of  Traverse  Sailing  consists  in  finding  the  difference  of 
latitude  and  departure  corresponding  to  several  courses  and  distances  and  reducing 
all  to  a  single  equivalent  course  and  distance.  This  is  done  by  determining  the 
distance  to  north  or  south  and  to  east  or  west  made  good  on  each  course,  taking  the 
algebraic  sum  of  these  various  differences  of  latitude  and  departure  and  finding  the 
course  and  distance  corresponding  thereto.  The  work  can  be  most  expeditiously 
performed  by  adopting  a  tabular  form  for  the  computation  and  using  the  traverse 
tables. 

Example:  A  ship  sails  SSE.,  15  miles;  SE.,  34  miles;  W.  by  S.,  16  miles;  WNW.,  39  miles; 
S.  by  E.,  40  miles.     Required  the  course  and  distance  made  good. 


Courses. 

Dist. 

N. 

s. 

E. 

w. 

SSE. 

SE. 

W.  by  S. 

WNW. 

S.  by  E. 

S.  by  W. 

15 
34 
16 
39 
40 

14.9 

13.9 

24.0 

3.1 

39.2 

5.7 
24.0 

7.8 

15.7 
36.0 

66.8 

14.9 

80.2 
14.9 

37.5 

51.7 
37.5 

65.3 

14.2 

The  result  of  the  various  courses  is,  therefore,  to  carry  the  vessel  S.  by  W.,  66.8 
miles  from  her  original  position. 


THE  SAILINGS. 


75 


PARALLEL  SAILING. 

173.  Thus  far  the  earth  has  been  regarded  as  an  extended  plane,  and  its  spherical 
fiffure  has  not  been  taken  into  account;  it  has  thus  been  impossible  to  consider  one 
of  the  important  terms  involved — namely,  difference  of  longitude.  Parallel  Sailing 
is  the  simplest  of  the  various  forms  of  Spherical  Sailing,  being 
the  method  of  interconverting  departure  and  difference  of 
longitude  when  the  ship  sails  upon  an  east  or  west  course, 
and  therefore  remains  always  on  the  same  parallel  of  latitude. 

In  figure  25,  T  and  T'  are  two  places  in  the  same  latitude; 
P,  the  adjacent  pole;  TT',  the  arc  of  the  parallel  of  latitude 
through  the  two  places;  MM',  the  corresponding  arc  of  the 
equator  intercepted  between  their  meridians  PM  and  PM'; 
and  TT',  the  departure  on  the  parallel  whose  latitude  is 
TCM=OTC,  and  whose  radius  is  OT. 

Let  D.Lo  represent  the  arc  of  the  equator  MM',  which  is 
the  measure  of  MPM',  the  difference  of  longitude  of  the  me- 
ridians PM  and  PM';  R,  the  equatorial  radius  of  the  earth, 
CM  =  CT;  r,  the  radius  OT  of  the  parallel  TT';  and  L,  the  latitude  of  that  parallel. 

Then,  since  TT'  and  MM'  are  similar  arcs  of  two  circles,  and  are  tnerefore 
proportions,!  to  the  radii  of  the  circles,  we  have: 


TT' 


OT 
CM' 


or 


Pep.  _  r 
D.Lo~R. 


From  the  triangle  COT,  r  =  R  cos  L;  hence 

Pep.  _  R  cos  L 
P.Lo~      R 


;  or,  P.Lo=Pep.  sec.  L;  or,  Pep.  =  P.Lo  cos  L. 


Thus  the  relations  are  expressed  between  minutes  of  longitude  and  miles  of 
departure. 

174.  Two  cases  arise  under  Parallel  Sailing:  First,  where  the  difference  of 
longitude  between  two  places  on  the  same  parallel  is  given,  to  find  the  departure; 
and,  second,  where  the  departure  is  given,  to  find  the  difference  of  longitude. 

In  working  these  proolems,  the  computation  can  be  made  by  logarithms;  but 
the  traverse  tables  may  more  conveniently  be  employed.  Remembermg  that  those 
tables  are  based  upon  the  formulae, 

PL  =  Pist.  cos  C,  and  Pist.  =  PL  sec  C, 

we  may  substitute  for  the  column  marked  Lat.  the  departure,  for  that  marked  Pist. 
the  difference  of  longitude,  and  for  the  courses  at  top  and  bottom  of  the  page  the 
latitude.     The  tables  then  become  available  for  making  the  required  conversions. 

Example:  A  ship  in  the  latitude  of  49°  3CK  sails  directly  east  iintil  making  good  a  difference  of 
longitude  of  3°  30'.    Required  the  departure. 

By  Computation.  By  Inspection. 

L  49°  3(K        log  COS  9. 81254  Enter  Table  2  with  the  latitude  as  C  and  the  difference 

D.Lo.         21(y        log        2.32222  of  longitude  as  Dist.    As  the  table  is  calculated  only  to 

single  degrees,  we  must  find  the  numbers  in  the  pages  of 

49°  and  50°  and  take  the  mean.    Corresponding  to  Dist. 

210  in  the  former  is  Lat.  137.8,  and  in  the  latter  Lat.  135.0. 

The  mean,  which  is  the  required  departure,  is  136.4. 

sails  due  west  a  distance  of  215.5  miles.    Required  the 

By  Inspection. 

Entering  Table  2  with  the  latitude,  38°,  as  a  course, 
corresponding  with  the  number  215.5  in  column  of  Lat., 
is  273.5  in  the  column  of  Dist.  This  is  therefore  the 
required  difference  of  longitude,  being  equal  to  4°  33'.5. 


Dep. 

136.4 

log 

2. 13476 

Example:  A  ship 
difference  of  longituoe 

in  the  latitude  of  38 

By  Computation. 

L 
Dep. 

38° 
215.5 

log  sec 
log 

0. 10347 
2.33345 

D.Lo{4, 


273'.  5 
'33'.  5 


log 


2.43692 


MIDDLE  LATITUDE  SAILING. 


175.  When  a  ship  follows  a  course  obUquely  across  the  meridian  the  latitude  is 
constantly  changing,  and  the  method  of  converting  departure  and  difference  of 
longitude  by  Parallel  Sailing,  just  described,  ceases  to  be  applicable. 


76 


THE   SAILINGS. 


In  figure  26,  T  is  the  point  of  departure;  T',  the  point  of  destination;  P,  the 
earth's  pole;  TT',  the  rhumb  track;  tIjIT',  the  course;  Tn,  n^T',  the  respective 
parallels  of  latitude;  and  MM',  the  equator. 

The  difference  of  longitude  between  T  and  T'  is  MPM',  which  may  be  measured 
by  the  arc  of  the  equator,  MM',  intercepted  between  their  meridians.  This  corre- 
sponds to  a  departure  Tn  in  the  latitude  of  T,  and  to  the  smaller  departure  T'rii  in  the 
higher  latitude  of  T';  but  since  the  vessel  neither  makes  all  of  the  departure  in  the 
latitude  T,  nor  all  of  it  in  the  latitude  T',  the  departure  actually  made  m  the  passage 
must  have  some  intermediate  value  between  these  extremes.  Dividing  the  total 
difference  of  longitude  into  a  number  of  equal  parts  MPrnj,  m^'Pin^,  etc.,  of  such  small 
extent  that,  for  the  purposes  of  conversion,  the  change  of  latitude  corresponding  to 

each  may  be  neglected,  we  Jiave  the  total  departure  made 
p  up  of  the  sum  of  a  number  of  small  departures,  each  equal 

to  the  same  difference  of  longitude,  but  each  different  from 
the  other.     These  wUl  be  diVi  in  the  latitude  T,  d^rz 


m 


the  latitude  r^,  etc.    Hence  we  have: 

MM'  =diri  sec  MT  +  (?2''2>  sec  rriiri  +d^r^,  sec  m^rz,  +  etc. 

Now,  if  LL'  be  a  parallel  of  latitude  lying  midway 
between  Tn  and  T'%,  since  there  wiU  be  as  many  of  the 
small  parts  lying  above  as  below  it,  and  since  for  moderate 
distances  the  ratio  to  be  employed  in  the  conversion  of 
departure  and  difference  of  longitude  may  be  regarded  as 
varying  directly  with  the  latitude,  it  may  be  assumed  for 
such  distances  that  the  sum  of  all  of  the  different  small 
departures  equals  the  single  departure  between  the  merid- 
ians measured  in  the  latitude  LL',  and  therefore  that  the 
departure  obtained  by  the  method  of  plane  sailing  on  any  course  maj  be  converted 
into  difference  of  longitude  by  multiplying  by  the  secant  of  the  Middle  Latitude. 
The  method  of  conversion  based  upon  this  assumption  is  denominated  Middle 
Latitude  Sailing,  and  by  reason  of  its  convenience  and  simplicity  is  usually  employed 
for  short  distances,  such  as  those  covered  by  a  vessel  in  a  day's  run. 

176.  In  Middle  Latitude  SaUing,  having  found  the  mean  of  the  latitudes^  the 
solution  is  identical  with  that  of  Parallel  Samng  (art.  173),  substituting  the  Middle 
Latitude  for  the  single  latitude  therein  employed. 

Example:  A  ship  in  Lat.  42°  30'  N.,  Long.  58°  51'  W.,  sails  SE.  by  S.,  300  miles, 
latitude  and  longitude  arrived  at. 


From  Table  1:  Course  SE.  by  S.,  Dist.,  300,  we  find  Lat.,  249.4  S.  (4°  09'.4),  Dep. 


Required  the 
,  166.7  E. 


Latitude  left, 
DL, 


42°  SO'.  0  N. 
4    09.4  S. 


Latitude  left,  42°  SO'  N. 

Latitude  arrived  at,   38    21   N. 


Latitude  arrived  at,  38    20  . 6  N. 


Mid.  latitude, 


2)80    51 
40    25    N. 


Enter  Table  2  with  the  middle  latitude,  40°,  as  a  course;  the  difference  of  longitude  (Dist.)  cor- 
responding to  the  departure  (Lat.)  166.7  is  217.6;  entering  with  41°,  it  is  220.9;  the  mean  is  219.2  (3°  39'.2). 

Longitude  left,  58°  51'.0  W. 

D.Lo,  3    39  .2  E. 

Longitude  arrived  at,  55    11  .8  W. 

Example:  A  ship  in  Lat.  39°  42'  S.,  Long.  3°  31'  E.,  sails  S.  42°  W.,  236  mUes.    Required  the  lati- 
tude and  longitude  arrived  at.  „^ 
From  Table  2:  Course,  S.  42°  W.,  Dist.,  236  mUes;  we  find  Lat.,  175.4  S.  (2°  55'.4),  Dep.,  157.9  W. 


Latitude  left, 
DL, 


39°  42'.0  S. 
2    55  .4  S. 


Latitude  left,  39°  42'  S 

Latitude  arrived  at,  42    37  S. 


Latitude  arrived  at,  42    37  .4  S. 


Mid.  latitude, 


2)82    19 
41    09  S. 


THE   SAILINGS. 


77 


20= 


From  Table  2:  Mid.  Lat.  (course),  41°,  Dep.  (Lat.),  157.9;  we  find  D.Ix)  (Dist.),  209.3  (3°  29'.3). 

Longitude  left,  3°  SV.O  E. 

D.Lo,  3    29  .3  W. 

Longitude  arrived  at,  0    01  .7  E. 
Example:  A  vessel  leaves  Lat.  49°  57'  N.,  Long.  15°  16'  W.,  and  arrives  at  Lat.  47®  18'  N.,  Long. 
lO'  W.     Required  the  course  and  distance  made  good. 

Latitude  left  49°  57'  N.  Longitude  left,  15°  16'  W. 

Latitude  arrived  at,  47    18  N.  Longitude  arrived  at,  20    10  W. 


DL, 


f  2°  39 
\  159 
2)97'' 


D.Lo, 


4°  54' 
294' 


;}w. 


Mid.  latitude,  48    38  N. 

From  Table  2:  Mid.  Lat,  (course),  49°,  D.Lo  (Dist,),  294;  we  find  Dep.  (Lat.),  192.9. 
From  Table  2:  DL  159  S.,  Dep.  192.9  W.,  we  find  course  S.  51°  W.,  Dist.,  251  miles. 

177.  It  may  be  remarked  that  the  Middle  Latitude  should  not  be  used  when 
the  latitudes  are  of  opposite  name;  if  of  different  names  and  the  distance  is  small, 
the  departure  may  be  assumed  equal  to  the  difference  of  longitude,  since  the  meridians 
are  sensibly  parallel  near  the  equator;  but  if  the  distance  is  great  the  two  portions 
of  the  track  on  opposites  of  the  equator  must  be  treated  separately. 

178.  The  assumption  upon  which  Middle  Latitude  sailing  is  based — that  the 
conversion  may  be  made  as  if  the  whole  distance  were  sailed  upon  a  parallel  midway 
between  the  latitudes  of  departure  and  destination — while  sufficiently  accurate  for 
moderate  distances,  may  be  materially  in  error  where  the  distances  are  large.  In 
such  case,  either  the  method  of  Mercator  Saihng  (art.  179)  must  bo  employed,  or  else 
the  correction  given  in  the  following  table  should  be  applied  to  the  mean  latitude  to 
obtain  what  may  be  termed  the  latitude  of  conversion,  being  that  latitude  in  which 
the  required  conditions  are  accurately  fulfilled.  The  table  is  computed  from  the 
formula : 

cos  L,=-, 

where  Lc  represents  the  latitude  of  conversion,  and  I  and  m  are  respectively  the  differ- 
ences of  latitude  and  of  meridional  parts  (art.  40,  Chap.  II)  between  the  latitudes  of 
departure  and  destination.  <* 


Difference  of  latitude. 

Mid. 
Lat. 

Mid. 
Lat. 

1" 

2' 

«• 

4" 

6* 

6' 

7" 

8* 

9° 

10" 

12* 

14* 

W 

18' 

20' 

15 

-86 

-85 

-84 

-83 

-81 

-79 

-76 

-73 

-69 

-65 

-56 

-46 

-34 

-21 

-  6 

15 

18 

-67 

-67 

-66 

-65 

-63 

-61 

-59 

-56 

-53 

-50 

-43 

-34 

-23 

-12 

1 

18 

21 

-54 

-54 

-53 

-52 

-51 

-49 

-47 

-44 

-42 

-39 

-32 

-24 

-15 

-  5 

7 

21 

24 

-44 

-44 

-44 

-42 

-41 

-40 

-■38 

-36 

-33 

-31 

-24 

-17 

-  8 

1 

12 

24 

30 

-31 

-30 

-29 

-29 

-28 

-26 

-■24 

-23 

-20 

-18 

-12 

-  6 

1 

11 

21 

30 

35 

-23 

-22 

-21 

-21 

-19 

-18 

-17 

-15 

-12 

-10 

-  5 

2 

10 

18 

28 

36 

40 

-17 

-16 

-15 

-14 

-13 

-12 

-10 

-  8 

-  6 

-  4 

2 

8 

16 

25 

34 

40 

45 

-12 

-11 

-11 

-10 

-  8 

-  7 

-  5 

-  3 

-  1 

1 

7 

14 

22 

31 

41 

45 

50 

-  8 

-  8 

-  7 

-  6 

-  5 

-  3 

-  1 

1 

3 

6 

12 

20 

28 

38 

49 

50 

55 

-5 

-  5 

-  4 

-  3 

-  2 

0 

2 

5 

7 

10 

17 

25 

35 

46 

58 

55 

58 

-  4 

-  3 

-  3 

-  1 

0 

2 

4 

7 

10 

13 

20 

29 

39 

51 

64 

58 

60 

-  3 

-  3 

-  2 

-  1 

1 

3 

5 

8 

11 

14 

22 

32 

43 

55 

69 

60 

62 

-  3 

-  2 

-  1 

0 

2 

4 

7 

9 

13 

17 

25 

35 

46 

60 

75 

62 

64 

-  2 

-  1 

0 

1 

3 

5 

8 

11 

14 

18 

27 

38 

50 

65 

81 

64 

66 

-  2 

-  1 

0 

2 

4 

6 

9 

12 

16 

20 

30 

42 

55 

71 

89 

66 

68 

-  1 

0 

1 

2 

5 

7 

10 

14 

18 

22 

33 

46 

61 

78 

98 

68 

70 

-  1 

0 

1 

3 

5 

8 

12 

16 

20 

25 

37 

51 

67 

87 

109 

70 

72 

1 

0 

0 

2 

4 

6 

10 

13 

18 

23 

28 

41 

57 

76 

97 

123 

72 

o  The  statement  often  made  that  the  latitude  of  conversion  is  always  greater  than  the  middle  latitude  is  not  correct  when  the 
compression  of  the  earth  is  taken  into  account,  as  an  inspection  of  the  table  wiU  show;  that  statement  is  based  upon  an  assumption 
that  the  earth  is  a  perfect  sphere,  and  it  was  upon  that  assumption  that  a  table  which  appeared  in  early  editions  of  this  work  was 

computed.    The  value  of  the  compression  adopted  for  this  table  is  ^g-jgi* 


78 


THE   SAILINGS. 


Example:  A  vessel  sails  from  Lat.  10°  13''  S.  to  Lat.  20°  21'  S.,  making  a  departure  of  432  milee. 
Required  the  difference  of  longitude. 
Latitude  left,  10°  13'  S. 

Latitude  arrived  at,      20    21    S. 


2)30    34 


For  Mid.  Lat.  15°  and  Diff.  of  Lat.  10°.  Correction,  -Cy. 


Mid.  latitude,  15    17    S. 

Correction,  —  1    05 


Lc, 


14    12    S. 

L,  14°     12'  log  sec        .01348 

Dep.  432  log  2.63548 


D.Lo  445^.6         log  2.64896 

MERCATOR  SAILING. 

179.  Mercator  Sailing  is  the  method  by  which  values  of  the  various  elements 
axe  determined  from  considering  them  in  the  relation  in  which  they  are  plotted  upon 
a  chart  constructed  according  to  the  Mercator  projection. 

180.  Upon  the  Mercator  chart  (art.  39,  Chap.  II),  the  meridians  being  parallel, 
the  arc  of  a  parallel  of  latitude  is  shown  as  equal  to  the  corresponding  arc  of  the 
equator;  the  length  of  every  such  arc  is,  therefore,  expanded;  and,  in  order  that 
the  rhumb  line  may  appear  as  a  straight  line,  the  meridians  are  also  expanded  by 
such  amount  as  is  necessary  to  preserve,  in  any  latitude,  the  proper  proportion 
existing  between  a  unit  of  latitude  and  a  unit  of  longitude.  The  length  of  small 
portions  of  the  meridian  thus  increased  are  called  meridional  parts  (art.  40,  Chap.  II), 
and  these,  computed  for  every  minute  of  latitude  from  0°  to  80°,  form  the  TaJble  of 
Meridional  Parts  (Table  3),  by  means  of  which  a  Mercator  chart  may  be  constructed 
and  all  problems  of  Mercator  Sailing  may  be  solved. 

In  the  triangle  ABC  (fig.  27),  the  angle  ACB  is  the  coui-se,  C;  the  side  AC,  the 
distance,  Dist.;  the  side  BC,  the  difference  of  latitude,  DL;  and  the  side  AB,  the 
departure,  Dep.  Then  corresponding  to  the  difference  of  lati- 
tude BC  in  the  latitude  under  consideration,  if  CE  be  laid  off  to 
represent  the  meridional  difference  of  latitude,  m,  completing  the 
right  triangle  CEF,  EF  will  represent  the  difference  of  longitude, 
D.Lo.  The  triangle  ABC  gives  the  relations  involved  in  Plane 
Sailing  as  previously  described;  the  triangle  CEF  affords  the 
means  for  the  conversion  of  departure  and  difference  of  longi- 
tude by  Mercator  Sailing. 

181.  To  find  the  arc  of  the  expanded  meridian  intercepted 
between  any  two  parallels,  or  the  meridional  difference  of  latitude, 
when  both  places  are  on  the  same  side  of  the  equator,  subtract 
the  meridional  parts  of  the  lesser  latitude,  as  given  by  Table  3, 
from  the  meridional  parts  of  the  greater;  the  remainder  will  be 
the  meridional  difference  of  latitude ;  but  if  the  places  are  on  dif- 
ferent sides  of  the  equator,  the  sum  of  the  meridional  parts  will 
be  the  meridional  difference  of  latitude. 
182.  To  solve  the  triangle  CEF  by  the  traverse  tables  it  is  only  necessary  to 
substitute  meridional  difference  for  Lat.,  and  difference  of  longitude  for  Dep.  Where 
long  distances  are  involved,  carrying  the  computation  beyond  the  hmits  of  the 
traverse  table,  as  frequently  occurs  m  this  method,  either  of  two  means  may  be 
adopted:  the  problems  may  be  worked  by  trigonometrical  formulae,  using  logarithms 
or  tne  given  quantities  involved  may  all  be  reduced  by  a  common  divisor  until 
they  fall  within  the  traverse  table,  and  the  results,  when  obtained,  correspondingly 
increased.  The  former  method  is  generally  preferable,  especially  when  the  distances 
are  quite  large  and  accurate  results  are  sought.  The  formulae  for  the 
conversions  are  as  follows: 

tanC  =  — ^;  D.Lo  =  m  tan  C;  m= D.Lo  cot  C. 


DL 


Fig.  27. 


various 


D.Lo 


THE  SAILINGS.  79 

Example:  A  ship  in  Lat.  42°  30^  N.,  Long.  58°  51^  W.,  sails  SE.  by  S.,  300  miles.    Required  the 
latitude  and  longitude  arrived  at. 

From  Table  1:  Coutbc,  SE.  by  S.,  Dist.,  300;  we  find  Lat.  249.4  S.  (4°  09^4). 

Latitude  left,  42°  30^.0  N.        Merid.  parts,  +2806. 4 

DL,  4    09  .4  S. 

Latitude  arrived  at,    38    20  .6  N.         Merid.  parts,   -2480.4 

m,  326. 0 

By  Computation.  By  Inspectum. 

m  326.0        log         2. 51322  Enter  Table  1,  course  3  points;  since  the  c^uantities 

0  33°  45^  log  tan  9.  82489  involved  exceed  the  limits  of  the  table,  divide  by  2; 

f    217^8        log         2.33811  abreast -k- (Lat.),  163.0,  find —V~(Dep.),  108.9;  hence 

13°  37'!8  D.Lo=217'.8  or  3°  37'.8. 

Longitude  left,  58°  51^0  W. 

D.Lo,  3    37  .8  E. 

Longitude  arrived  at,   55    13  .2  W. 

Example:  A  ship  in  Lat.  4°  37'  S.,  Long.  21°  05''  W.,  sails  N.  14®  W.,  450  miles.    Required  the 
latitude  and  longituae  arrived  at. 

From  Table  2:  Course,  (N.)  14°  (W.),  Dist.,  450;  we  find  Lat.  436.6  N,  (7°  16'.6). 

Latitude  left,  4°  37'.0  S.         Merid.  parte,  +275.4 

DL,  7    16  .  6  N. 

Latitude  arrived  at,  2    39  . 6  N.        Merid.  parts,  +159. 0 

«  

m,  434. 4 

By  Computation.  By  Inspection. 

m  434.4       log        2.63789  From  Table  2:  Course,   14°,  m  (Lat.),  434.4,   we  find 

C       14°  log  tan  9.  39677  D.Lo  (Dep.)  108'.3  W.,  or  1°  48'.3. 


D.Lojj, 


108^  3      log         2. 03466 
48'.  3 

Longitude  left,  21°  05'.  0  W. 

D.Lo,  1    48.  3  W. 


Longitude  arrived  at,   22    53  . 3  W. 

Example:  Required  the  course  and  distance  by  rhumb  line  from  a  point  in  Lat.  42°  03'  N.,  Long. 
70°  04'  W.,  to  another  in  Lat.  36°  59'  N.,  Long.  25°  10'  W. 

Lat.  departure,     42°  03'  N.        Merid.  pts.,   +2770. 1        Long,  departure,     70°  04'  W. 
Lat.  destination,  36    59    N,        Merid.  pta.,   -2377.3        Long,  destination,  25    10  W. 

DL  {"^;}S.  »,  1^  D.LO  {^.>. 

D.Lo       2694       log  3.43040 

m  392.8       log  2.59417 


C  (S.)  81°  42' (E.)       log  tan    .83623        log  sec.   .84056 
DL  304'  log        2.48287 

Dist.       2106  log        3.32343 

The  course  is  therefore  S.  81°  42'  E.,  and  the  distance  is  2,106  miles.  Since  the 
figures  involved  are  so  large,  it  is  best  to  employ  only  the  method  by  computation. 
The  formula  by  which  the  Dist.  is  obtained  comes  from  Plane  Sailing. 

GREAT  CIRCLE  SAUilNQ. 

183.  The  shortest  distance  between  any  two  points  on  the  earth's  surface  is 
measured  by  the  arc  of  the  great  circle  which  passes  through  those  points;  and  the 
method  of  sailing  in  which  the  arc  of  a  great  circle  is  employed  for  the  track  of  the 
vessel,  taking  advantage  of  the  fact  that  it  is  the  shortest  route  possible,  is  denomi- 
nated Great  Circle  Sailing. 

184.  It  frequently  happens  when  a  great  circle  route  is  laid  down  that  it  is 
found  to  lead  across  the  land,  or  to  carry  the  vessel  into  a  region  of  dangerous  naviga- 


80  THE  SAILINGS. 

tion  or  extreme  cold  which  it  is  expedient  to  avoid;  in  such  a  case  a  certain  parallel 
should  be  fixed  upon  as  a  limit  of  jatitude,  and  a  route  laid  down  such  that  a  great 
circle  is  followed  as  far  as  the  limiting  parallel,  then  the  parallel  itself,  and  finally 
another  great  circle  to  the  port  of  destmation.  Such  a  modification  of  the  great 
circle  method  is  called  Composite  Sailing. 

185.  The  rhumh  line  (art.  6,  Chap.  I),  also  called  the  loxodromic  curve,  which 
cuts  all  the  meridians  at  the  same  angle,  has  been  largely  employed  as  a  track  by 
navigators  on  account  of  the  ease  with  which  it  may  be  laid  down  on  a  Mercator 
chart.  But  as  it  is  a  longer  line  than  the  great  circle  between  the  same  points, 
intelligent  navigators  of  the  present  day  use  the  latter  wherever  practicable.  On 
the  Mercator  chart,  however,  the  arc  of  a  great  circle  joining  two  points  (unless 
both  are  on  the  equator  or  both  on  the  same  meridian)  will  not  be  projected  as  a 
straight  line,  but  as  a  curve  which  seems  to  be  longer  than  the  rhumb  line;  hence 
the  shortest  route  appears  as  a  circuitous  one,  and  this  is  doubtless  the  reason  that 
a  wider  use  of  the  great  circle  has  not  been  made. 

It  should  be  clearly  understood  that  it  is  the  rhumb  line  which  is  in  fact  the 
indirect  route,  and  that  in  following  the  great  circle  the  vessel  is  always  heading 
for  her  port,  exactly  as  if  it  were  in  sight,  while  on  the  course  which  is  shown  as  a 
straight  line  on  the  Mercator  chart  the  vessel  never  heads  for  her  port  until  at  the 
very  end  of  the  voyage. 

186.  The  method  of  ^eat  circle  sailing  is  of  especial  value  to  steamers,  as  such 
vessels  need  not,  in  the  choice  of  a  route,  have  regard  for  the  winds  to  the  same  extent 
as  must  a  sailing  vessel;  but  even  in  navigating  vessels  under  sail  a  knowledge  of  the 
great  circle  course  may  prove  of  great  value.  For  example,  suppose  a  ship  to  be 
bound  from  Sj^dney  to  Valparaiso;  the  first  great  circle  course  is  SE.  by  S.,  while  the 
Mercator  course  is  almost  due  east.  The  distance  is  748  miles  shorter  by  the  former 
route  (if  thereat  circle  is  followed  throughout,  though  this  would  lead  to  a  latitude 
of  61°  S.).  With  the  wind  at  E.  ^  vS.  the  ship  would  he  nearer  to  the  Mercator  course 
on  the  starboard  tack,  assuming  that  she  sailed  within  six  points  of  the  wind;  but 
if  she  took  that  tack  she  would  be  increasing  her  distance  from  the  port  of  destination 
by  4^  miles  in  every  10  that  she  sailed;  while  on  the  port  tack,  heading  one  point 
farther  from  the  rhumb,  the  gain  toward  the  port  would  be  9^  miles  out  of  every  10. 
Any  course  between  East  and  SSW.  would  be  better  than  the  Mercator  course;  and 
if  tne  wind  were  anything  to  the  eastward  of  SE.  by  S.,  the  ship  would  gain  by  taking 
the  port  tack  in  preference  to  the  starboard. 

187.  As  the  great  circle  makes  a  different  angle  with  each  meridian  that  is 
crossed,  it  becomes  necessary  to  make  frec[uent  changes  of  the  ship's  course;  in 
practice,  the  course  is  a  series  of  chords  joining  the  various  points  on  the  track  line. 

If,  while  endeavoring  to  follow  a  great  circle,  the  ship  is  driven  from  it,  as  by 
unfavorable  weather,  it  will  not  serve  the  purpose  to  return  to  the  old  track  at 
convenience,  but  it  is  required  that  another  great  circle  be  laid  down,  joining  the 
actual  position  in  which  the  ship  finds  herself  with  the  port  of  destination. 

188.  The  methods  of  determining  the  great  circle  course  may  be  divided  generally 
into  four  classes;  namely,  by  Great  Circle  Sailing  Charts,  by  Computation,  by  the 
methods  of  the  Time  Azimuth,  and  by  Graphic  ApproxiTuations. 

189.  Great  Circle  Sailing  Charts. — Of  the  available  methods,  that  by  means 
of  charts  especially  constructed  for  the  purpose  is  considered  greatly  superior  to 
all  others. 

A  series  of  great  circle  sailing  charts  covering  the  navigable  waters  of  the  globe 
is  published  by  the  United  States  Hydrographic  Office.  Being  on  the  gnomonic 
projection  (art.  44,  Chap.  II),  all  great  circles  are  represented  as  straight  Unes,  and 
it  is  only  necessary  to  join  any  two  points  by  such  a  line  to  represent  the  great  circle 
track  between  them.  The  courses  and  distance  are  readily  obtainable  by  a  method 
explained  on  the  charts.  The  track  may  be  transferred  to  a  chart  on  the  Mercator 
projection  by  plotting  a  number  of  its  points  by  their  coordinates  and  joining  them 
with  a  curved  line. 

The  navigator  who  contemplates  the  use  of  great  circle  tracks  will  find  it  of  the 

freatest  convenience  to  be  provided  with  these  gnomonic  charts  for  the  regions  which 
is  vessel  is  to  traverse. 


THE  SAILINGS.  81 

190.  By  Computation. — This  method  consists  in  determining  a  series  of  points 
on  the  great  circle  by  their  coordinates  of  latitude  and  longitude,  plotting  them  upon 
a  Mercator  chart,  and  tracing  the  curve^  that  P 

joins  them.  The  first  point  determined  is  the 
vertex,  or  point  of  liighest  latitude,  even  when, 
as  sometimes  occurs,  it  falls  without  that  por- 
tion of  the  great  circle  which  joins  the  points 

of  departure  and  destination.  X  ^ ^g 

In  figure  28,  A  represents  the  point  of  /    ^ — -         V 

departure;  B,  the  point  of  destination;  AVB,     . 
the  great  circle  joining  them,  with  its  vertex    ^ '  f     as 

at  V;  and  P,  the  pole  of  the  earth.  '°'    ' 

Let  C'a  =  PAB,  the  initial  course; 

Cb  =  PBA,  the  final  course; 
La,  Ly,  IjB  =  the  latitudes  of  the  respective     points  A,   V,   B  =  (90°  — PA), 
(90° -PV),  (90° -PB). 
Lo^,  Lo^v,  LoBv  =  the  differences  of  longitude  between  A  and  B,  A  and  V,  B  and  V, 
respectively,  =  APB,  APV,  BPV. 
D  =  the  great  circle  distance  between  A  and  B;  and 
9?  =  an  auxiliary  angle  introduced  for  the  computation. 
We  then  have : 

tan  ^=cos  Lo^B  cot  Lb; 
cot  CA  =  cot  Lo^B  cos  (La  +  9>)  cosec  fp\ 
cot  D =cos  Ca  tan  (Lj^  +  <p) ; 
cos  Lv  =  sin  Cj^  cos  L^;  , 
cot  Loat  =  tan  C^  sin  Ij^- 
By  these  formulae  are  determined  the  initial  course  and  the  total  distance  by 
great  circle;  also  the  latitude  of  the  vertex  and  its  longitude  with  respect  to  A.     By 
mterchanging  the  subscript  letters  ^  and  b  throughout,  we  should  obtain  the  final 
course,  and  tne  longitude  of  the  vertex  with  respect  to  B;  also  the  same  total  distance 
and  latitude  of  the  vertex  as  before. 

In  performing  this  computation,  strict  regard  must  be  had  to  the  signs  of  the 
quantities.  If  the  points  of  departure  and  destination  are  in  different  latitudes,  the 
latitude  of  one  of  these  points  must  be  regarded  as  negative  with  respect  to  the  other, 
and  they  must  be  marked  with  opposite  signs.  Should  Loj^y  or  Lobv  assume  a 
negative  value,  it  indicates  that  the  vertex  does  not  lie  between  A  and  B,  and  is  to 
be  laid  off  accordingly. 

To  find  other  points  of  the  ^eat  circle,  M,  N,  etc.,  let  their  latitudes  be  repre- 
sented by  Ijm,  I^,  etc.,  and  their  longitudes  from  the  vertex  by  Lovm,  Loyy,  etc.; 
then 

tan  La  =  tan  Ly  cos  Loy^;  or,  cos  Loyi,  =  tan  I^m  cot  Ly; 
tan  Ljj  =  tan  Ly  cos  Loy^;  or,  cos  Lovu  =  tan  L^  cot  Ijy; 
and  so  on.  By  these  formulae  intervals  of  longitude  from  the  vertex  of  5°,  10°,  or 
any  amount,  may  be  assumed,  and  the  corresponding  latitudes  deduced;  or  any 
latitude  may  be  assumed  and  its  corresponding  interval  of  longitude  from  the 
vertex  found.  Two  positions  will  result  from  each  solution,  and  the  appropriate 
ones  may  be  chosen  by  keeping  in  mind  the  signs  involved. 

Example:  Given  two  places,  one  in  Lat.  40°  N.,  Long.  70°  W.,  the  other  in  Lat.  30°  S.,  Long.  10° 
W.,  find  the  great  circle  distance  between  them;  also  the  initial  course,  and  the  longitude  of  equator 
crossing. 

La=+40°;  Lb=-30°;  Loab=60°. 

Load  60°  cos  9. 69897.. cot  9.76144 

Lb     -  30°    cot  (-)  .23856 

La  +40°  cos   9. 88425  Bin  9. 80807 

<p  -  40°  54^  tan  (-) 9.  93753.. cosec  (-)  .18393 

(La+^)  -     0°  54'    cos  9.  99995  tan  (-)  8. 19616 

Ca  131°  24'  or  S.  48° 36' E-... cot     (-)9.  94532  cos  (-)  9.82041  sin  9.87513  tan  (-)     .05472 

D  89°  24'  or  5,364  miles cot  8.01657 

Ly  +  54°  56'    cos  9.  75938 

Loav         -  53°  54'    cot  (-)   9. 86279 

21594°— 14 6 


82 


THE   SAILINGS. 


The  initial  course  is  therefore  S.  48°  36'  E.,  and  the  distance  5,364  nautical 
miles.  (It  may  be  found  that  the  course  by  rhumb  line  is  S.  38°  45'  E.  and  the 
distance  5,386  miles.)  The  vertex  of  the  great  circle  is  in  Lat.  54°  56'  N.,  and  is 
53°  54'  in  longitude  from  the  point  A,  in  a  direction  away  from  B;  hence  it  is  in 
Long.  123°  54'  W.  To  find  the  longitude  of  equator  crossing  let  Lm  =  0°;  then  in 
the  equation, 

cos  LovM  =  tan  Lm  cot  Ly, 

since  tan  L^  equals  zero,  cos  Lovm  also  equals  zero,  or  the  longitude  interval  from 
the  vertex  is  90°,  which  is  evident  from  the  properties  of  the  great  circle:  therefore 
the  longitude  of  equator  crossing  is  123°  54'  W.— 90°  =  33°  54'  W. 

191.  By  Time  Azimuth  Methods. — A  convenient  method  of  obtaining  the  initial 
and  final  comses  in  great  circle  sailing  is  afforded  by  the  tables  and  graphic  methods 
which  are  prepared  for  the  solution  of  the  Time  Azimuth  problem  (art.  352,  Chap. 
XIV).  It  will  be  found  by  comparison  that  if  the  latitude  of  the  point  of  departure 
be  substituted  for  the  latitude  of  the  observer  in  that  ploblem,  the  latitude  of  desti- 
nation for  the  declination  of  the  celestial  body,  and  the  longitude  interval  for  the 
hour  angle,  the  solution  for  the  initial  course  will  coincide  with  that  for  the  azimuth; 
by  interchanging  the  latitudes  of  the  points  of  departure  and  destination  the  final 
course  wiU  be  similarly  obtained.  Advantage  may  thus  be  taken  of  the  various 
methods  provided  for  facilitating  the  determination  of  the  azimuth  to  ascertain 
the  great  circle  courses  from  one  point  to  another. 

192.  By  Graphic  Approximations. — Of  the  numerous  methods  that  fall 
within  this  class  only  two  need  be  given. 

193.  By  the  use  of  a  Terrestrial  Globe  the  two  given  points  between  which  the 
great  circle  track  is  required  may  be  joined  by  the  shortest  line  between  them,  either  by 
means  of  a  piece  of  thread  or  by  moving  the  globe  until  they  are  bi  ought  to  the  fixed 
horizon  which  is  usually  provided;  the  coordinates  of  the  various  points  of  the  track 
are  then  transferred  to  the  chart.  The  number  of  minutes  of  arc,  as  measured  on 
the  scale  of  the  horizon  between  the  points,  equals  the  number  of  miles  of  distance; 
if  there  be  no  Jiorizon,  the  measure  may  be  made  by  a  thiead  along  the  equator  or  a 
meridian. 

194:.  The  Method  of  Professor  Airy  consists  in  drawing  on  the  chart  a  rhumb 
Hne  joining  the  two  points,  and  erecting  at  its  middle  point  a  perpendicular;  the 
following  table  should  then  be  entered  with  the  middle  latitude  as  an  argument,  and 
the  "corresponding  parallel"  of  latitude  taken  out  (noting  whether  it  is  the  same 
or  opposite  in  name  to  the  middle  latitude) ;  where  this  parallel  is  intersected  by  the 
perpendicular  that  was  drawn  wiU  be  the  center  from  which  may  be  swept  an  arc 
approximately  representing  tue  great  circle  between  the  two  points. 


Middle  lati- 

Correspond- 

^JfliHiG 

Middle  lati- 

Correspond- 

^Jqtyjp 

tude. 

ing  parallel. 

tude. 

ing  parallel. 

20 

81  13 

Opposite. 

o 

52 

11  33 

Opposite. 

22 

78  16 

Do. 

54 

6  24 

Do. 

24 

74  59 

Do. 

56 

1  13 

Do. 

26 

71  26 

Do. 

58 

4  00 

Same. 

28 

67  38 

Do. 

60 

9  15 

Do. 

30 

63  37 

Do. 

62 

14  32 

Do. 

32 

59  25 

Do. 

64 

19  50 

Do. 

34 

55  05 

Do. 

66 

25  09 

Do. 

36 

50  36 

Do. 

68 

30  30 

Do. 

38 

46  00 

Do. 

70 

35  52 

Do. 

40 

41  18 

Do. 

72 

41  14 

Do. 

42 

36  31 

Do. 

74 

46  37 

Do. 

44 

31  38 

Do. 

76 

52  01 

Do. 

46 

26  42 

Do. 

78 

57  25 

Do. 

48 

21  42 

Do. 

80 

62  51 

Do. 

50 

16  39 

Do. 

THE   SAILINGS.  83 

COMPOSITE  SAILING. 

195.  It  has  already  been  stated  that  when,  for  any  reason,  it  is  impracticable 
or  unadvisable  to  follow  the  great  circle  track  to  its  highest  latitude,  a  Umiting  parallel 
is  chosen  and  the  route  modmed  accordingly.  This  method  is  denominated  Composite 
Sailing. 

196.  The  shortest  track  between  points  where  a  fixed  latitude  is  not  exceeded 
is  made  up  as  follows : 

1.  A  great  circle  through  the  point  of  departure  tangent  to  the  luniting  parallel. 

2.  A  course  along  the  parallel. 

3.  A  great  circle  through  the  point  of  destination  tangent  to  the  limiting  parallel. 
The  composite  track  may  be  determined  by  Great  Circle  Sailing  Chart,  by 

Compyiation,  or  by  Oraphic  Approximation. 

197.  On  a  Great  Circle  Sailing  Chart,  draw  lines  from  the  points  of  departure 
and  destination,  respectively,  tangent  to  the  Umiting  parallel;  transfer  these  great 
circles  to  a  Mercator  chart  in  the  usual  manner,  bv  the  coordinates  of  several  points, 
including  in  each  case  the  point  of  tangency  to  tne  parallel.  FoUow  the  first  ^eat 
circle  to  the  parallel;  then  foUow  the  parallel;  then  the  second  great  circle. 
Determine  great  circle  courses  and  distances  from  the  gnomonic  chart  as  thereon 
described ;  determine  the  distance  along  the  parallel  by  Parallel  Sailing. 

198.  By  computation,  the  problem  consists  in  finding  the  ^eat  circles  which 
pass,  respectively,  through  the  points  of  departure  and  destination  and  have  their 
vertices  in  the  latitude  of  the  limiting  parallel.  Resuming  the  designation  of  terms 
already  employed  (art.  190),  we  have: 

cos  LoyA  =  tan  L^  cot  Ly; 
cos  LovB  =  tan  L^  cot  Ly; 

where  Loy^  and  Loy„  represent  the  distances  in  longitude  from  A  and  from  B  to  the 
respective  points  oi  tangency;  other  features  of  each  of  the  great  circles  may  be 
determined  in  the  usual  manner. 

Example:  A  vessel  in  Lat.  30*  S.,  Long.  18°  W.,  is  bound  to  a  point  in  Lat.  39**  S.^  Long.  145°  E., 
and  it  is  decided  not  to  go  south  of  the  parallel  of  55°  S.  Find  the  longitude  of  reaching  that  parallel 
and  the  longitude  at  which  it  should  be  left. 

La=30°S.;    Lb  =  39°S.;  Lv  =  55°S. 
Loa  =  18°  W. ;  Lob  =  145°  E. 


La      30°             tan  9. 76144 
Lv      65°              cot  9.84523 

LOVB 

Lob 

39°  tan  9.  90837 
55°                 cot  9.84523 

Lova  66°  09' E.  cos  9.  60667 
Loa    18    00  W. 

55°  27'  W.  cos    9.  75360 

145    00    E. 

Lov    48    09  E.  Loy      89    33    E. 

199.  A  graphic  approximation  to  the  coniposite  track  may  be  obtained  by  drawing 
a  straight  line  between  the  ^ven  points  on  a  Mercator  chart  and  erecting  at  its  middle 
point  a  pCTpendicular,  which  should  be  extended  until  it  intersects  the  limiting 
parallel.  Then  through  this  intersection  and  the  two  points  describe  the  arc  of  a 
circle,  and  this  will  approximate  to  the  shortest  distance  within  the  assigned  limit 
of  latitude.  * 

200.  A  terrestrial  globe  may  be  employed  for  the  determination  of  the  composite 
track;  the  method  of  its  use  will  suggest  itself. 

201.  Another  approximation  is  obtained  by  joining  the  two  points  with  a  single 
great  circle,  and  following  this  to  its  intersection  with  the  limiting  parallel;  thence 
sailing  along  the  parallel  until  the  great  circle  is  again  intersected;  then  resuming 
the  circle  and  following  it  to  the  destination. 


CHAPTER  VI. 

DEAD  BECKONING. 


202.  Dead  Reckoning  \s  the  process  by  which  the  position  of  a  ship  at  any  instant 
is  found  by  applying  to  the  last  well-determined  position  the  run  that  has  since  been 
made,  using  for  the  purpose  the  ship's  course  and  the  distance  indicated  by  the  log. 

203.  Positions  by  dead  reckonmg,  also  spoken  of  as  positions  hy  account,  differ 
from  those  determined  by  bearings  of  terrestrial  objects  or  by  observations  of  celestial 
bodies  in  being  less  exact,  as  the  correctness  of  dead  reckoning  depends  upon  the 
accuracy  of  the  estimate  of  the  run,  and  this  is  always  liable  to  be  at  fault  to  a  greater 
or  less  extent.  The  course  made  good  by  a  ship  may  differ  from  that  which  it  is 
believed  that  she  is  making  good,  by  reason  of  imperfect  steering,  improper  allowance 
for  compass  error  and  leeway,  and  the  effects  of  unknown  currents;  the  allowed 
distance  over  the  ground  may  be  in  error  on  account  of  inaccurate  logging  and 
unknown  currents. 

Notwithstanding  its  recognized  defects  as  compared  with  the  more  exact  methods, 
the  dead  reckoning  is  an  invaluable  aid  to  the  mariner.  It  affords  him  a  means  of 
plotting  the  position  of  the  ship  at  any  desired  time  between  astronomical  deter- 
minations; it  also  gives  him  an  approximate  position  at  the  moment  of  taking 
astronomical  observations  which  is  a  great  convenience  in  working  up  those  observa- 
tions; and  finally  it  affords  the  only  available  means  of  determining  the  location  of 
a  vessel  at  sea  during  those  periods  (which  may  continue  for  several  days  together) 
when  the  weather  is  such  as  to  render  the  observation  of  celestial  bodies  an  impos- 
sibility. 

204.  Taking  Departube. — ^Before  losing  sight  of  the  land,  and  preferably 
while  objects  remain  in  good  view,  it  is  the  duty  of  the  navigator  to  taTce  a  departure; 
this  consists  in  fixing  the  position  of  the  ship  by  the  best  means  available  (Chap.  TV), 
and  using  this  position  as  the  origin  for  dead  reckoning.  There  are  two  methods  of 
reckoning  the  departure.  The  first  and  simpler  consists  in  taking  from  the  chart  the 
latitude  and  longitude  of  the  position  found,  and  applying  the  future  run  thereto. 
The  other  requires  that  the  bearing  and  distance  of  an  object  of  known  latitude  and 
longitude  be  found;  the  position  of  the  object  then  forms  the  basis  of  the  reckoning, 
and  the  reversed  direction  of  the  bearing,  with  the  distance,  forms  the  first  course 
and  distance ;  thus  it  may  be  considered  that  the  ship  starts  from  the  position  of  the 
object  and  sails  to  the  position  where  the  bearing  was  taken;  the  correction  for 
deviation  in  such  a  case  should  be  that  due  to  the  heading  of  the  ship  when  the  bearing 
was  taken.  Each  time  that  a  new  position  is  determined  it  is  used  as  a  new  departure 
for  the  dead  reckoning. 

This  meaning  of  the  term  departure  should  not  be  confounded  with  the  other, 
which  refers  to  the  distance  run  toward  east  or  west. 

205.  Methods. — ^The  working  of  dead  reckoning  merely  involves  an  application 
of  the  methods  of  Traverse  Sailing  (art.  172)  arid  Middle  Latitude  Sailing  (art.  175), 
as  explained  in  Chapter  V. 

The  various  compass  courses  are  set  down  in  a  column,  and  abreast  each  are 
written  the  errors  by  reason  of  which  the  course  steered  by  compass  differs  from  the 
true  course  made  good  over  the  ground;  thence  the  true  course  made  good  is  deter- 
mined and  recorded;  next,  the  distance  is  written  in,  and  afterwards,  by  means  of 
Tables  1  or  2  (according  as  the  courses  are  expressed  in  quarter  points  or  degrees),  the 
difference  of  latitude  and  departure  are  found,  separate  columns  being  kept  for 
distances  to  the  north,  south,  east,  and  west. 

When  the  position  of  the  ship  at  any  moment  is  required,  add  up  all  the  differ- 
ences of  latitude  and  departure,  and  write  in  the  column  of  the  greater  the  difference 
between  the  northing  and  southing,  and  the  easting  and  westing.  Apply  the  differ- 
ence of  latitude  to  the  latitude  of  the  last  determined  position,  which  will  give  the 

84 


DEAD  EECKONING. 


85 


latitude  by  D.  R.,  and  from  which  may  be  found  the  middle  latitude;  with  the 
middle  latitude  find  the  difference  of  longitude  corresponding  to  the  departure,  apply 
this  to  the  longitude  of  last  position,  and  the  result  will  be  the  longitude  by  D.  R. 

The  employment  of  the  tabular  form  will  be  found  to  facilitate  the  work  and 
guard  against  errors.  It  will  be  a  convenience  to  include  in  that  form  columns 
showing  the  hour,  together  with  the  reading  of  the  patent  log  (if  used)  each  time 
that  the  course  is  changed  or  the  dead  reckoning  worked  up. 

The  emi)loyment  oi  minutes  and  tenths  in  dead  reckoning  rather  than  minutes 
and  seconds  is  recommended. 

Example:  A  vessel  under  sail  heading  NE.  f  E.  (on  which  course  deviation  is 
\  pt.  Easterly)  takes  departure  from  Cape  Henry  lighthouse  (see  Appendix  IV  for 
position),  bearing  SSW.  J  W.  per  compass,  distant  1.4  miles.  She  then  sails  on  a 
series  of  courses,  with  errors  and  distances  as  indicated  below;  wind  about  SE.  by  E. 
Required  the  position  by  dead  reckoning ;  also  the  course  and  distance  made  good  by 
dead  reckoning. 


Comp.  course. 

Var. 

Dev. 

Leeway. 

Error. 

True  course. 

Dist.        N. 

S. 

E. 

w. 

D.  Lo. 

NNE.  iE. 
NE.  i  E. 
S.  by  W. 
ENE. 
S.  iE. 
NE.  iN. 

Made  good. 

iW. 
iW. 
iW. 
iW. 
iW. 
iW. 

iE. 
iE. 

0 
iE. 

0 
iE. 

iW. 
iE. 

*w. 

iE. 
iW. 

iW. 
iW. 
iW. 

iW. 

0 
iW. 

NNE.  iE. 
NE.  i  E. 
S.  iW. 

NE.byE.  iE. 
S.iE. 
NE.  byN. 

NE.  iE. 

L4 
27.6 
3L5 
14.2 
11.0 
87.0 

1.3 
18.5 

7.3 

72.3 

31.2 
ILO 

0.6 
20.5 

12.2 
0.5 

48.3 

4.6 

97.0 

96.5 

99.4 
57.2 

42.2 

82.1 

77.5 

4.6 

Point  of  departure, 
Kun, 

By  D.  R. 


Latitude. 
36°  55^  6  N. 
57  . 2  N. 

37    52  .  8  N. 


Mid.  L.,  37' 


Longitude. 
76°  00^  5  \V. 
1    37.  OE. 

74    23.  5  W. 


Example:  A  eteamer's  position  by  observation  at  noon,  patent  log  reading  27.3,  is  Lat.  49°  15''  N., 
Long.  7°  32''  W.  Thence  sne  steers  262°  (per  compass),  the  total  compass  error  on  that  course  being 
20°  W.,  until  12.30,  at  which  time,  patent  log  reading  33.9,  the  course  is  changed  to  260°  (p.  c),  same 
error.  At  4.12,  patent  log  80.5,  sights  are  taken  from  which  it  is  found  that  the  true  longitude  is  8°  46''  W., 
and  the  compass  error  19°  W,  At  6.15,  patent  log  reading  6.1,  a  sight  is  taken  from  which  it  is  found 
that  the  true  latitude  is  48°  34^  30^^  N.  At  8  p.  m.  the  patent  log  reads  27.5.  Required  the  positions  by 
D.  R.  at  each  sight  and  at  8  o'clock. 


Time. 

Comp.  course. 

Error. 

True  course. 

Pat.  Log, 

Dist. 

S. 

W. 

D.Lo. 

Noon. 

12.30 

4.12 

6.15 
8.00 

262° 
260° 

260° 
260° 

20°  W. 
20°  W. 

19°  W. 
19°  W. 

242° 
240° 

241° 
241° 

27.3 
33.9 
80.5 

6.1 
27.5 

6.6 
46.6 

25.6 
21.4 

3.1 
23.3 

5.8 
40.3 

70.3 
34.1 
27.9 

26.4 
12.4 
10.4 

46.1 
22.4 
18.7 

Latitude. 
Byobs.atnoon,  49°  15^0  N. 

Run  to  4.12  sight,  26  .4  S. 


By  D.  R.  at  4.12  sight,     48    48  .6  N. 
12  .4  S. 


By  obs.  at  4.12  sight, 
Run  to  6.15  sight. 


By  D.  R.  at  6.15  sight,    48    36  .2  N. 


By  obs.  at  6.15  sight,       48    34  .5  N. 
Run  to  8  p.  m.,  10  .4  S. 


Mid.  L.,  49' 


Mid.  L.,  49' 


Mid.  L.,  48' 


Longitude. 
7°  32^0  W. 
1     10  .3  W. 


8    42  .3  W. 


8    46  .0  W. 
34  .1  W. 


9    20  .1  W. 


27  .9  W. 


ByD.  R.  at8p.  m.,        48    24  .1  N. 


9    48  .0  W. 


86 


DEAD  RECKONING. 


206.  Allowance  for  Current. — When  a  vessel  is  sailing  in  a  known  current 
whose  strength  may  be  estimated  with  a  fair  degree  of  accuracy,  a  more  correct 
position  may  be  arrived  at  by  regarding  the  set  and  drift  of  the  current  as  a  course  and 
distance  to  be  regularly  taken  account  of  in  the  dead  reckoning. 

Example:  A  vessel  in  the  Gulf  Stream  at  a  point  where  the  current  is  estimated  to  set  48°  at  the 
rate  of  1.8  miles  an  hour,  sails  183°  (true),  making  9.5  knots  an  hour  through  the  water  for  3*»  30™.  Middle 
latitude  35°.     Required  the  course  and  distance  made  good. 


True  course. 

Dist. 

N. 

S. 

E. 

W. 

D.  Lo. 

Run 
Current 

Made  good 

183° 
48° 

174° 

33.3 
6.3 

29.3 

4.2 

33.3 

4.7 

1.7 

3.6 

29.1 

3.0 

207.  Finding  the  Current. — It  is  usual,  upon  obtaining  a  good  position  by 
observation  (as  the  navigator  usually  does  at  noon),  to  compare  that  position  with 
the  one  obtained  by  dead  reckoning,  and  to  attribute  such  discrepancy  as  may  be 
found  to  the  effects  of  current.  It  has  already  been  pointed  out  that  other 
causes  than  the  motion  of  the  water  tend  to  make  the  dead  reckoning  inaccurate, 
so  that  it  must  not  be  assumed  that  currents  proper  are  thus  determuied  with  com- 
plete correctness. 

Current  is  said  to  have  set  and  drift,  referring  respectively  to  the  direction  toward 
which  it  is  flowing  and  the  velocity  with  which  it  moves. 

It  is  evident  that,  in  calculating  current  by  the  method  of  comparing  positions 
by  observation  with  those  by  account,  the  navigator  must  limit  himself  to  the  periods 
during  which  the  dead  reckoning  has  been  brought  forward  independently,  without 
receivmg  any  corrections  due  to  new  points  of  departure.  In  case  it  is  desired  to 
find  the  current  covering  a  period  during  which  iresh  departures  have  been  used, 
as  from  noon  to  noon,  find  the  algebraical  sums  of  all  the  differences  of  latitude  and 
longitude  from  the  table,  and  apply  these  to  the  latitude  and  longitude  of  original 
departure — that  of  the  preceding  noon;  this  gives  the  position  from  the  ship's  run 
proper,  and  the  difference  between  this  and  the  position  by  observation  gives  the  set 
and  drift  for  the  twenty-four  hours ;  if  an  allowance  has  been  made  for  current,  as 
explained  in  the  preceding  article,  that  must  be  omitted  in  bringing  up  the  position 
which  is  to  take  account  of  the  run  only. 

208.  Day's  Run. — It  is  usual  to  calculate,  each  day  at  noon,  the  ship's  total  run 
for  the  preceding  twenty-four  hours.  Having  the  positions  at  noon  of  each  day,  the 
course  and  distance  between  them  is  found  as  explained  in  article  175,  Chapter  V. 
The  position  by  observation  is  used  in  each  case,  if  such  has  been  foimd;  otherwise, 
the  position  by  dead  reckoning. 

Example:  At  noon,  January  22,  the  position  of  a  vessel  by  observation  was  Lat.  35"  lO'  N.,  Long. 
134°  OV  W.  During  the  next  24  hours,  the  run  by  account  was  GO.l  miles  north  and  153.2  miles  east. 
At  noon,  January  23,  the  position  by  observation  was  Lat.  3G°  03'  N.,  Long.  131°  14'  W.  Required 
the  position  by  D.  R.  at  the  latter  time;  also  the  run  and  current  for  the  24  hours. 


By  oba.,  noon,  22d, 
Run, 


Latitude. 
35°  lO'.O  N. 
1    00  .1  N. 


By  D.  R.,  noon,  23d,    36    10  .1  N. 


Mid.  L.,  36° 
[Dep.,  153.2  E.] 
p.Lo.,  189.4  E. 


Longitude. 
134°  Ol'.O  W. 
3    09  .4  E. 


130    51  .6  W. 


By  obs.,  noon,  23d, 
Current, 


36    03  .0  N. 
6.9S. 


[D.Lo.,  22.4  W.j     131     14  .0  W. 
[Dep.,    18.1  W.J  22.4    W. 


Current  for  24  hours,  6.9  S.,  18.1  W.=249°,  19.4  miles. 
Current  per  hour,  249°,  0.8  mile. 


By  obs.,  noon,  23d, 
By  obs.,  noon,  22d, 


Latitude. 
36°  03'.0  N. 
35    10  .ON. 


Run,  0    53  .0  N. 

Run  for  24  hours,  53.0  N.,  135.1  E.=68°,  146  miles. 


Mid.  L.,  36° 
p.Lo.,  167.  OE. 
Dep.,  135.1 


Longitude. 
131°  14'.0  W. 
134    01.0  W. 


2    47  .0  E. 


CHAPTER  VII. 
DEFINITIONS  EELATING  TO  NAUTICAL  ASTEONOMY. 


209.  Nautical  Astronomy,  or  Celo- Navigation,  has  been  defined  (art.  3,  Chap.  I) 
as  that  branch  of  the  science  of  Navigation  in  which  the  position  of  a  ship  is  deter- 
mined by  the  aid  of  celestial  objects — the  sun,  moon,  planets,  or  stars. 

210.  The  Celestial  Sphere. — An  observer  upon  the  surface  of  the  earth 
appears  to  view  the  heavenly  bodies  as  if  they  were  situated  upon  the  surface  of  a 
vast  hollow  sphere,  of  which  his  eye  is  the  center.  In  reality  we  know  that  this 
apparent  vault  has  no  existence,  ana  that  we  can  determine  only  the  relative  directions 
of  the  heavenly  bodies — not  their  distances  from  each  other  or  from  the  observer. 
But  by  adopting  an  imaginary  spherical  surface  of  an  infinite  radius,  the  eye  of  the 
observer  bemg  at  the  center,  the  places  of  the  heavenly  bodies  can  be  projected  upon 
this  Celestial  Sphere,  or  Celestial  Concave,  at  points  where  the  lines  joining  them  with 
the  center  intersect  the  surface  of  the  sphere.  Since,  however,  the  center  of  the  earth 
should  be  the  point  from  which  all  angular  distances  are  measiu-ed,  the  observer, 
by  transferring  himself  there,  will  find  projected  on  the  celestial  sphere,  not  only 
the  heavenly  bodies,  but  the  imaginary  points  and  circles  of  the  earth's  surface. 
The  actual  position  of  the  observer  on  the  surface  will  be  projected  in  a  point  called 
the  zenith;  the  meridians,  eauator,  and  all  other  lines  and  points  may  also  be  projected. 

211.  An  observer  on  tne  earth's  surface  is  constantly  changing  his  position  with 
relation  to  the  celestial  bodies  projected  on  the  sphere,  thus  giving  to  the  latter  an 
apparent  motion.  This  is  due  to  three  causes:  First,  the  diurnal  motion  of  the  earth, 
arising  from  its  rotation  upon  its  axis;  second,  the  annual  motion  of  the  earth, 
arising  from  its  motion  about  the  sun  in  its  orbit;  and  third,  the  actual  motion  of 
certain  of  the  celestial  bodies  themselves.  The  changes  produced *by  the  diurnal 
motion  are  different  for  observers  at  different  points  upon  the  earth,  and  therefore 
depend  upon  the  latitude  and  longitude  of  the  observer.  But  the  changes  arising 
from  the  other  causes  named  are  independent  of  the  observer's  position,  and  may 
therefore  be  considered  at  any  instant  in  their  relation  to  the  center  of  the  earth. 
To  this  end  the  elements  necessary  for  any  calculation  are  tabulated  in  the  Nautical 
Almanac  from  data  based  upon  laws  which  have  been  found  by  long  series  of  observa- 
tions to  govern  the  actual  and  apparent  motion  of  the  various  bodies. 

212.  The  Zenith  of  an  observer  on  the  earth's  surface  is  the  point  of  the  celestial 
sphere  vertically  overhead.     The  Nadir  is  the  point  vertically  beneath. 

213.  The  Celestial  Horizon  is  the  great  cuxle  of  the  celestial  sphere  formed  by 
passing  a  plane  through  the  center  of  the  earth  at  right  angles  to  the  line  which  joins 
that  point  with  the  zenith  of  the  observer.  The  celestial  horizon  differs  somewhat 
from  the  Visihle  Horizon,  which  is  that  line  appearing  to  an  observer  at  sea  to  mark 
the  intersection  of  earth  and  sky.  This  difference  arises  from  two  causes:  First,  the 
eye  of  the  observer  is  always  elevated  above  the  sea  level,  thus  permitting  him  a 
range  of  vision  exceeding  90°  from  the  zenith;  and  second,  the  observer's  position 
is  on  the  surface  instead  of  at  the  center  of  the  earth.  These  causes  give  rise,  respec- 
tively, to  dip  of  the  horizon  and  parallax,  which  will  be  explained  later  (Chap.  X). 

214.  In  ngure  29  the  celestial  sphere  is  considered  to  be  projected  upon  the 
celestial  horizon,  represented  by  NESW.;  the  zenith  of  the  observer  is  projected  at 
Z,  and  that  pole  of  the  earth  which  is  elevated  above  the  horizon,  assumed  for  illus- 
tration to  be  the  north  pole,  appears  at  P,  the  Elevated  Pole  of  the  celestial  sphere. 
The  other  pole  is  not  shown  in  the  figure. 

87 


88 


DEFINITIONS  RELATING   TO   NAUTICAL  ASTRONOMY. 


216.  The  Equinoctial,  or  Celestial  Equator,  is  the  great  cu-cle  formed  by  extending 
the  plane  of  the  earth's  equator  until  it  intersects  the  celestial  sphere.  It  is  shown 
in  the  figure  in  the  line  EQW.  The  equinoctial  intersects  the  horizon  in  E  and  W, 
its  east  and  west  points. 

216.  Hour  Circles,  Declination  Circles,  or  Celestial  Meridians  are  great  cii'cles 
of  the  celestial  sphere  passing  through  the  poles;  they  are  therefore  secondary  to 
the  equinoctial,  and  may  be  formed  by  extending  the  planes  of  the  respective  terres- 
trial meridians  until  they  intersect  the  celestial  sphere.  In  the  figure,  PB,  PS,  PB', 
are  hour  circles,  and  that  one,  PS,  which  contains  the  zenith  and  is  therefore  formed 
by  the  extension  of  the  terrestrial  meridian  of  the  observer,  intersects  the  horizon  in 
N  and  S,  its  north  and  south  points. 

217.  Vertical  Circles,  or  Circles  of  Altitude,  are  great  circles  of  the  celestial 
sphere  which  pass  through  the  zenith  and  nadir;  they  are  therefore  secondary  to 
the  horizon.  In  the  figure,  ZH,  WZE,  NZS,  are  projections  of  such  circles,  which 
being  at  right  angles  to  the  plane  of  projection,  apj)ear  as  straight  lines.  The  vertical 
circle  NZS,  which  passes  through  the  poles,  coincides  with  the  meridian  of  the 
observer.  The  vertical  circle  WZE,  whose  plane  is  at  right  angles  to  that  of  the 
meridian,  intersects  the  horizon  in  its  eastern  and  western  points,  and,  therefore, 

at  the  points  of  intersection  of  the  equinoc- 
tial; this  circle  is  distinguished  as  the  Prime 
Vertical. 

218.  The  Declination  of  any  point  in 
the  celestial  sphere  is  its  angular  distance 
from  the  equinoctial,  measured  upon  the 
hour  or  declination  circle  which  passes 
through  that  point;  it  is  designated  as 
North  or  South  according  to  the  direction 
of  the  point  from  the  equinoctial;  it  is  cus- 
tomary to  regard  north  declinations  as 
positive  ( + ),  and  south  declinations  as  nega- 
tive (— ).  In  the  figure,  DM  is  the  declina- 
tion of  the  point  M.  Declination  upon  the 
celestial  sphere  corresponds  with  latitude 
upon  the  earth. 

219.  The  Polar  Distance  of  any  point 
is  its  angular  distance  from  the  pole  (gen- 
erally, the  elevated  pole  of  an  observer), 
measured  upon  the  hour  or  declination  circle 
passing  through  the  point;  it  must  therefore 

equal  90°  minus  the  declination,  if  measured  from  the  pole  of  the  same  name  as  the 
declination,  or  90°  plus  the  declination,  if  measured  from  the  pole  of  opposite  name. 
The  polar  distance  of  the  point  M  from  the  elevated  pole  P  is  PM. 

220.  The  Altitude  of  any  point  in  the  celestial  sphere  is  its  angular  distance 
from  the  horizon,  measured  upon  the  vertical  circle  passing  through  the  point;  it 
is  regarded  as  positive  when  the  body  is  on  the  same  side  of  the  horizon  as  the  zenith. 
The  altitude  of  the  point  M  is  HM. 

221.  The  Zenith  Distance  of  any  point  is  its  angular  distance  from  the  zenith, 
measured  upon  the  vertical  circle  passing  through  the  point;  the  zenith  distance 
of  any  point  which  is  above  the  horizon  of  an  observer  must  therefore  equal  90° 
minus  the  altitude.    The  zenith  distance  of  M,  in  the  figure,  is  ZM. 

222.  The  Hour  Angle  of  any  point  is  the  angle  at  the  pole  between  t>e  meridian 
of  the  observer  and  the  hour  circle  passing  through  that  point;  it  may  also  be  regarded 
as  the  arc  of  the  equinoctial  intercepted  between  those  circles.  It  is  measured 
toward  the  west  as  a  positive  direction  through  the  twenty-four  hours,  or  360  degrees, 
which  constitute  the  interval  between  the  successive  returns  to  the  meridian,  due 
to  the  diurnal  rotation  of  the  earth,  of  any  point  in  the  celestial  sphere.  The  hour 
angle  of  M  is  the  angle  QPD,  or  the  arc  QD. 

223.  The  Azimuth  of  a  point  in  the  celestial  sphere  is  the  an^le  at  the  zenith 
between  the  meridian  of  the  observer  and  the  vertical  circle  passing  through  the 


Fig.  29. 


DEFINITIONS  RELATING  TO   NAUTICAL  ASTRONOMY.  89 

point;  it  may  also  be  regarded  as  the  arc  of  the  horizon  intercepted  between  those 
circles.  It  is  measured  from  either  the  north  or  the  south  point  of  the  horizon 
(usually  that  one  of  the  same  name  as  the  elevated  pole)  to  the  east  or  west  through 
180°,  and  is  named  accordingly;  as,  N.  60°  W.,  or  S.  120°  W.  The  azimuth  of  M  is 
the  angle  NZH,  or  the  arc  NH,  from  the  north  point,  or  the  angle  SZH,  or  the  arc 
SH,  from  the  south  point  of  the  horizon. 

224:.  The  Amplitude  of  a  point  is  the  angle  at  the  zenith  between  the  prime 
vertical  and  the  vertical  circle  of  the  point;  it  is  measured  from  the  east  or  the  west 
point  of  the  horizon  through  90°,  as  W.  30°  N.  It  is  closely  allied  with  the  azimuth 
and  may  always  be  deduced  therefrom.  In  the  figure,  the  amplitude  of  H  is  the 
angle  WZH,  or  the  arc  WH.  The  amplitude  is  only  used  with  reference  to  points 
in  the  horizon. 

225.  The  Ecliptic  is  the  great  circle  representing  the  path  in  which,  bv  reason 
of  the  annual  revolution  of  the  earth,  the  sun  appears  to  move  in  the  celestial  sphere; 
the  plane  of  the  ecliptic  is  inclined  to  that  of  the  ec[uinoctial  at  an  angle  of  23  27^', 
and  this  inclination  is  called  the  obliguity  of  the  ecliptic.  The  ecliptic  is  represented 
by  the  great  circle  CVT. 

226.  The  Equinoxes  are  those  points  at  which  the  ecliptic  and  the  equinoctial 
intersect,  and  when  the  sun  occupies  either  of  these  positions  the  days  and  n^hts 
are  of  equal  length  throughout  the  earth.  The  Vernal  Equinox  is  that  one  at  which 
the  sun  appears  to  an  observer  on  the  earth  when  passing  from  southern  to  northern 
declination,  and  the  Autumnal  Equinox  that  one  at  which  it  appears  when  passing 
from  northern  to  southern  declination.  The  Vernal  Equinox  is  also  designated  as 
the  First  Point  of  Aries,  and  is  used  as  an  origin  for  reckoning  right  ascension ;  it  is 
indicated  in  the  ngure  at  V. 

227.  The  Solstitial  Points,  or  Solstices,  are  points  of  the  ecliptic  at  a  distance 
of  90°  from  the  equinoxes,  at  which  the  sun  attains  its  highest  declination  in  each 
hemisphere.  They  are  called  respectively  the  Summer  and  the  Winier  Solstice, 
according  to  the  season  in  which  tne  sun  appears  to  pass  these  points  in  its  path. 
The  Summer  Solstice  is  indicated  in  the  figure  at  U. 

228.  The  RigJit  Ascension  of  a  point  is  the  angle  at  the  pole  between  the  hour 
circle  of  the  point  and  that  of  the  First  Point  of  Aries;  it  may  also  be  regarded  as 
the  arc  of  the  equinoctial  intercepted  between  those  circles.  It  ls  measured  from 
the  First  Point  oi  Aries  to  the  eastward  as  a  positive  direction,  tlirough  twenty-four 
hours  or  360  degrees.     The  right  ascension  of  the  point  M'  is  YD'. 

229.  Celestial  Latitude  is  measured  to  the  north  or  south  of  the  ecliptic  upon 
great  circles  secondary  thereto.  Celestial  Longitude  is  measured  upon  the  ecliptic 
from  the  First  Point  of  Aries  as  an  origin,  being  regarded  as  positive  to  the  eastward 
throughout  360°. 

230.  Coordinates. — In  order  to  define  the  position  of  a  point  in  space,  a  system 
of  lines,  angles,  or  planes,  or  a  combination  of  these,  is  used  to  refer  it  to*  some  fixed 
line  or  plane  adopted  as  the  primitive ;  and  the  lines, 

angles,  or  planes  by  which  it  is  thus  referred  are  called  H 

coordinates. 

231.  In  figure  30  is  shown  a  system  of  rectilinear 
coordinates  for  a  plane.     A  fixed  line  FE  is  chosen,  and                D 
in  it  a  definite  point  C,  as  the  origin.     Then  the  posi- 
tion of  a  point  A  is  defined  by  CB  =  a:,  the  distance  F C 

from  the  origin,  C,  to  the  foot  of  a  perpendicular  let 

fall  from  A  on  FE;  and  by  AB=y,  the  length  of  the 

perpendicular.     The  distance  x  is  called  the  ahsdssa 

and  y  the  ordinate.     Assuming  two  intersecting  right  fiq.  30. 

lines  FE  and  HI  as  standard  lines  of  reference,  the 

location  of  the  point  A  is  defined  by  regarding  the  distances  measured  to  the  right 
hand  of  HI  and  above  FE  as  positive;  those  to  the  left  hand  of  HI  and  below  FE 
as  negative. 

An  exemplification  of  this  system  is  found  in  the  chart,  on  which  FE  is  represented 
by  the  equator,  HI  by  the  prime  meridian;  the  coordinates  x  and  y  being  the  longitude 
and  latitude  of  the  point  A. 

232.  The  great  circle  is  to  the  sphere  what  the  straight  fine  is  to  the  plane; 
hence,  in  order  to  define  the  position  of  a  point  on  the  surface  of  a  sphere,  some  great 


y 


E 


B 


90  DEFINITIONS  RELATING   TO   NAUTICAL  ASTRONOMY. 

circle  must  be  Eelected  as  the  primary,  and  some  particular  point  of  it  as  the  origin. 
Thus,  in  figure  31,  which  represents  the  case  of  a  sphere,  some  fixed  great  circle, 
CBQ,  is  selected  as  the  axis  and  called  the  primary;  and  a  point  C  is  chosen  as  the 

origin.  Then  to  define  the  position  of  any  point  A,  the  ab- 
scissa X  equals  the  distance  from  C  to  the  point  B,  where 
the  secondary  great  circle  through  A  intersects  the  primary; 
the  ordinate  y  equals  the  distance  of  A  from  the  primary 
measmed  on  the  secondary — that  is,  a;  =  CB  and  y  =  AB. 

233.  In  the  case  of  the  earth,  the  primary  selected  is 
the  equator  (its  plane  being  perpendicular  to  the  earth's 
axis),  and  upon  this  are  measured  the  abscissae,  while  upon 
the  secondaries  to  it  are  measured  the  ordinates  of  all 
points  on  the  earth's  surface.  The  initial  point  for  refer- 
ence on  the  equator  is  determined  by  the  prime  meridian 
chosen,  West  lon^tudes  and  North  latitudes  being  called 
positive,  East  longitudes  and  South  latitudes,  negative. 

234.  In  the  case  of  the  celestial  sphere,  there  are  four  systems  of  coordinates 
in  use  for  defining  the  position  of  any  point;  these  vary  according  to  the  circle 
adopted  as  the  primaiy  and  the  point  used  as  an  origin.     They  are  as  follows: 

1.  Altitude  and  azimuth. 

2.  Dechnation  and  hour  angle.  ^ 

3.  Declination  and  right  ascension. 

4.  Celestial  latitude  and  longitude. 

235.  In  the  system  of  Altitude  and  Azimuth,  the  primary  circle  is  the  celestial 
horizon,  the  secondaries  to  which  are  the  vertical  circles,  or  circles  of  altitude.  The 
horizon  is  intersected  by  the  celestial  meridian  in  its  northern  and  souttiern  points, 
of  which  one — usually  that  adjacent  to  the  elevated  pole — is  selected  as  an  origin 
for  reckoning  coordinates.  The  azimuth  indicates  in  which  vertical  circle  the  point 
to  be  defined  is  found,  and  the  altitude  gives  the  position  of  the  point  in  that  circle. 
In  figure  29  the  point  M  is  located,  according  to  this  system,  by  its  azimuth  NH 
and  altitude  HM. 

236.  In  the  system  of  Declination  and  Hour  Angle,  the  primaiy  circle  is  the 
equinoctial,  the  secondaries  to  which  are  the  circles  of  declination,  or  hour  circles. 
The  point  of  origin  is  that  point  of  intersection  of  the  equinoctial  and  celestial 
meridian  wliich  is  above  the  horizon.  The  hour  angle  indicates  in  which  declina- 
tion circle  the  point  to  be  defined  is  found,  and  the  declination  gives  the  position 
of  the  point  in  that  circle.  In  figure  29  the  point  M  is  located,  according  to  this 
system,  by  its  hour  angle  Q,D  and  declination  DM. 

237.  In  the  system  of  Declination  and  Right  Ascension,  the  primary  and  seconda- 
ries are  the  same  as  in  the  system  just  described,  but  the  point  of  origin  differs,  being 
assumed  to  be  at  the  First  Point  of  Aries,  or  vernal  equinox.  The  right  ascension 
indicates  in  which  declination  circle  the  point  to  be  defined  may  be  found,  and  the 
declination  gives  the  position  in  that  circle.  In  figure  29  the  point  M'  is  located  by 
VD',  the  right  ascension,  and  D'M',  the  dechnation.  It  should  be  noted  that  this 
system  differs  from  the  preceding  in  that  the  position  of  a  point  is  herein  referred  to 
a  fixed  point  in  the  celestial  sphere  and  is  independent  of  the  zenith  of  the  observer 
as  well  as  of  the  position  of  the  earth  in  its  diurnal  motion,  while,  in  the  system  of 
declination  and  hour  angle,  both  of  these  are  factors  in  determining  the  coordinates. 

238.  In  the  system  of  Celestial  Latitude  and  Longitude,  the  primary, circle  is  the 
ecliptic;  the  point  of  origin,  the  First  Point  of  Aries.  The  method  of  reckoning  by 
this  system,  which  is  of  only  slight  importance  in  Nautical  Astronomy,  will  appear 
from  the  definitions  of  celestial  latitude  and  longitude  already  given  (art.  229). 


CHAPTER  VIII. 
mSTEUMENTS  EMPLOYED  IN  NAUTICAL  ASTEONOMY. 


THE  SEXTANT. 

239.  Tho  sextant  is  an  instrument  for  measuring  the  angle  between  two  objects 
by  bringing  into  coincidence  at  the  eye  of  the  observer  rays  of  light  received  directly 
from  the  one  and  by  reflection  from  the  other,  the  measure  bein^  afforded  by  the 
inclination  of  the  reflecting  surfaces.  By  reason  of  its  small  dimensions,  its  accuracy, 
and,  above  aU,  the  fact  that  it  does  not  require  a  permanent  or  a  stable  mounting 
but  is  available  for  use  under  the  conditions  existing  on  shipboard,  it  is  a  most 
important  instrument  for  the  purposes  of  the  navigator.  While  the  sextant  is  not 
capable  of  the  same  degree  of  accuracy  as  fixed  instruments,  its  measurements  are 
sufficiently  exact  for  navigation. 

240.  Description. — A  usual  form  of  the  sextant  is  represented  in  figure  32. 
The  frame  is  of  brass  or  some  similar  aUoy.  The  graduated  arc,  AA,  generally  of 
silver,  is  marked  in  ai)pro- 

priate  divisions ;  in  the  micr  _  M 

sextants,  each  division  rep- 
resents 10',  and  tho  vernier 
affords  a  means  of  reading 
to  10".  A  wooden  handle, 
H,  is  provided  for  holding 
the  instrument.  The  index 
mirror,  M,  and  Twrizon  mir- 
ror, m,  are  of  plate  glass, 
and  are  silvered,  though  the 
upper  half  of  the  horizon 
glass  is  left  plain  to  allow 
direct  rays  to  pass  thi'ough 
unobstructed.  To  give 
greater  distinctness  to  the 
images,  a  small  telescope,  E, 
is  placed  in  the  lino  of  sight ; 
it  is  supported  in  a  ring,  K, 
which  can  be  moved  by  a 
screw  in  a  direction  at  right 

angles  to  the  plane  of  the  sex-  Pio.  32. 

tant,  thus  shifting  the  axis 

of  the  telescope,  and  therefore  the  plane  of  reflection;  this  plane,  however,  always 
remains  parallel  to  that  of  the  instrument,  the  motion  of  the  telescope  being  intended 
merely  to  regulate  the  relative  brightness  of  the  direct  and  reflected  ima^e.  In  the 
ring,  K,  are  small  screws  for  the  purpose  of  adjusting  the  telescope  by  making  its  axis 

Earallel  with  the  plane  of  the  sextant.  The  vernier  is  carried  on  the  end  of  an  index 
ar  pivoted  beneath  the  index  mirror,  M,  and  thus  travels  along  the  graduated  scale, 
affording  a  measure  for  any  change  of  incUnation  of  the  index  mirror;  a  reading  glass, 
R,  attached  to  the  index  bar  and  turning  upon  a  pivot,  S,  facilitates  the  reading  of 
vernier  and  scale.  The  index  mirror,  M,  is  attached  to  the  head  of  the  index  bar,  with 
its  surface  perpendicular  to  the  plane  of  the  instrument;  an  adjusting  screw  is  fitted 
at  the  back  to  permit  of  adjustment  to  the  perpendicular  plane.  The  fixed  glass  m, 
half  silvered  and  half  plain,  is  called  the  Jwrizon  glass,  as  it  is  through  this  that  the 

91 


92  INSTRUMENTS  EMPLOYED  IN    NAUTICAL  ASTRONOMY. 

horizon  is  observed  in  measuring  altitudes  of  celestial  bodies;  it  is  provided  with 
screws,  by  which  its  perpendicularity  to  the  plane  of  the  instrument  may  be 
adjusted.  At  P  and  Q  are  colored  glasses  of  different  shades,  which  may  be  used 
separately  or  in  combination  to  protect  the  eye  from  the  intense  Hght  oi  the  sun. 
In  order  to  observe  with  accuracy  and  make  the  images  come  precisely  in  contact,  a 
tangent  screw,  B,  is  fixed  to  the  mdex,  by  means  of  which  the  latter  may  be  moved 
with  greater  precision  than  by  hand ;  but  this  screw  does  not  act  until  the  index  is 
fixed  by  the  screw  C  at  the  back  of  the  sextant;  when  the  index  is  to  be  moved  any 
considerable  amount,  the  screw  C  is  loosened;  when  it  is  brought  near  to  ite 
required  position  the  screw  must  be  tightened,  and  the  index  may  then  be  moved 
gradually  by  the  tangent  screw. 

Besides  the  telescope,  E,  the  instrument  is  usually  provided  with  an  inverting 
telescope,  I,  and  a  tube  without  glasses,  F ;  also,  with  a  cap  carrying  colored  glasses, 
which  may  be  put  on  the  eye  end  of  the  telescope,  thus  dispensing  with  the  necessity 
for  the  use  of  tlie  colored  shades,  P  and  Q,  and  eliminating  any  possible  errors  which 
might  arise  from  nonparaUelism  of  their  surfaces. 

The  latest  type  of  sextant  furnished  to  the  United  States  Navy  is  fitted  with  an 
endless  tangent  screw  which  carries  a  micrometer  drum  from  which  the  seconds  of 
arc  are  read.  By  pressure  of  the  thumb  the  tangent  screw  is  released  and  the  index 
bar  may  be  moved  to  any  position  on  the  arc  by  hand,  where  the  tangent  screw  is 
again  thrown  into  gear  by  releasing  the  pressure  of  the  thumb.  The  endless  tangent 
screw  is  accomplished  by  cutting  the  edge  of  the  arc  with  the  worm  teeth  into  which 
the  tangent  screw  gears.  At  night  the  reading  of  this  sextant  is  facilitated  by  a 
small  electric  light  carried  on  it  and  supplied  by  a  batteiy  contained  in  the  handle. 

241.  The  vernier  is  an  attachment  for  facilitating  the  exact  reading  of  the  scale 
of  a  sextant,  by  which  ahquot  parts  of  the  smallest  divisions  of  the  graduated  scale 
are  measured.  The  principle  of  the  sextant  vernier  is  identical  with  that  of  the 
barometer  vernier,  a  complete  description  of  which  will  be  found  in  article  52,  Chapter 
II.  The  arc  of  a  sextant  is  usually  divided  into  120  or  more  parts,  each  division 
representing  1°;  each  of  these  degree  divisions  is  further  subdivided  to  an  extent 
dependent  upon  the  accuracy  of  reading  of  which  the  sextant  is  capable.  In  the 
instruments  lor  finer  work,  the  divisions  of  the  scale  correspond  to  10'  each,  and  the 
vernier  covers  a  length  corresponding  to  59  such  divisions,  which  is  subdivided  into 
60  parts,  thus  permitting  a  reading  of  10";  all  sextants,  however,  are  not  so  closely 
graduated. 

Whatever  the  limits  of  subdivision,  all  sextants  are  fitted  with  verniers  which 
contain  one  more  division  than  the  length  of  scale  covered,  and  in  which,  therefore, 
scale-readings  and  vernier-readings  increase  in  the  same  direction — toward  the  left 

hand.  To  read  any  sextant,  it  is  merely 
necessary  to  observe  the  scale  division  next 
F  below,  or  to  the  right  of,  the  zero  of  the 
'^  vernier,  and  to  add  thereto  the  angle  cor- 
responding to  that  division  of  the  vernier 
scale  which  is  most  nearly  in  exact  coin- 
cidence with  a  division  of  the  instrument 
scale. 

242.  Optical  Principle. — ^When    a 

ray  of  light  is  reflected  from  a  plane  surface, 

the  angle  of  incidence  is  equal  to  the  angle 

_  of  reflection.     From  this  it  may  be  proved 

PiQ  33_  that  when  a  ray  of  light  undergoes  two 

reflections  in  the  same  plane  the  angle  be- 
tween its  first  and  its  last  direction  is  equal  to  twice  the  inclination  of  the  reflecting 
surfaces.     Upon  this  fact  the  construction  of  the  sextant  is  based. 

In  figure  33,  let  B  and  C  represent  respectively  the  index  mirror  and  horizon 
mirror  of  a  sextant;  draw  EF  perpendicular  to  B,  and  CF  perpendicular  to  C;  then 
the  angle  CFB  represents  the  incUnation  of  the  two  mirrors.  Suppose  a  ray  to  pro- 
ceed from  A  and  undergo  reflection  at  B  and  at  C,  its  last  direction  being  CD;  then 
ADC  is  the  angle  between  its  first  and  last  directions,  and  we  desire  to  prove  that 
ADC  =  2  CFB. 


INSTRUMENTS  EMPLOYED  IN  NAUTICAL  ASTRONOMY.  93 

From  the  equality  of  the  angles  of  incidence  and  reflection: 

ABE=EBC,  and  ABC  =  2  EBC; 
BCF  =  FCD,  and  BCD  =  2  BCF. 

From  Geometry: 

ADC  =  ABC  -  BCD  =  2  (EBC  -  BCF)  =  2  CFB, 

which  is  the  relation  that  was  to  be  proved ._ 

24:3.  In  the  sextant,  since  the  index  mirror  is  immovably  attached  to  the  index 
arm,  which  also  carries  the  vernier,  it  follows  that  no  change  can  occur  in  the  incUna- 
tion  between  the  index  mirror  and  the  horizon  mirror,  excepting  such  as  is  registered 
by  the  travel  of  the  vernier  upon  the  scale. 

If,  when  the  index  mirror  is  so  placed  that  it  is  nearly  parallel  with  the  horizon 
mirror,  an  observer  direct  the  telescope  toward  some  weU-defined  object,  there  wiU 
be  seen  in  the  field  of  view  two  separate  images  of  the  object;  and  if  the  inclination 
of  the  index  mirror  be  slightly  changed  by  moving  the  index  bar,  it  will  be  seen  that 
while  one  of  the  images  remains  fixed  the  other  moves.  The  fixed  image  is  the  direct 
one  seen  through  the  unsilvered  p^rt  of  the  horizon  glass,  while  the  movable  image 
is  due  to  rays  reflected  by  the  index  and  horizon  mirrors.  When  the  two  images 
coincide  these  mirrors  must  be  parallel  (assuminjj  that  the  object  is  sufficiently  distant 
to  disregard  the  space  which  separates  the  mirrors;  in  this  position  of  the  index 
mirror  the  vernier  indicates  the  true  zero  of  the  scale.  If,  however,  instead  of 
observing  a  single  object,  the  instrument  is  so  placed  that  the  direct  ray  from  one 
object  appears  in  coincidence  with  the  reflected  ray  of  a  second  object,  then  the  true 
angle  between  the  objects  will  be  twice  the  angle  of  inclination  between  the  mirrors, 
or  twice  the  angle  measured  by  the  vernier  from  the  true  zero  of  the  scale.  To  avoid 
the  necessity  of  doubling  the  angle  on  the  scale,  the  latter  is  so  marked  that  each 
half  degree  appears  as  a.  whole  degree,  whence  its  indications  give  the  whole  angle 
directly. 

244.  Adjustments  of  the  Sextant. — ^The  theory  of  the  sextant  requires  that, 
for  accurate  indications,  the  foUowing  conditions  be  fulfilled: 

(a)  The  two  surfaces  of  each  mirror  and  shade  glass  must  be  parallel  planes. 
(h)  The  graduated  arc  or  limb  must  be  a  plane,  and  its  graduations,  as  well  as 
those  of  the  vernier,  must  be  exact. 

(c)  The  axis  must  be  at  the  center  of  the  limb,  and  perpendicular  to  the  plane 
thereof. 

(d)  The  index  and  horizon  glasses  must  be  perpendicular,  and  the  line  of  sight 
parallel  to  the  plane  of  the  limb. 

Of  these,  only  the  last  named  ordinarily  require  the  attention  of  the  navigator 
who  is  to  make  use  of  the  sextant;  the  others,  which  may  be  called  the  permanent 
adjustments,  should  be  made  before  the  instrument  leaves  the  hands  of  the  maker, 
and  with  careful  use  will  never  be  deranged. 

245.  The  Adjustment  of  the  Index  Mirror  consists  in  making  the  reflecting 
surface  of  this  mirror  truly  perpendicular  to  the  plane  of  the  sextant.  In  order  to 
test  this,  set  the  index  near  the  middle  of  the  arc,  then,  placing  the  eye  very  nearly 
in  the  plane  of  the  sextant  and  close  to  the  index  mirror,  observe  whether  the  direct 
image  of  the  arc  and  its  image  reflected  from  the  mirror  appear  to  form  one  continuous 
arc;  if  so,  the  glass  is  perpendicular  to  the  plane  of  the  sextant;  if  the  reflected  image 
appears  to  droop  from  the  arc  seen  directly,  the  glass  leans  backward ;  if  it  seems  to 
rise,  the  glass  leans  forward.  The  adjustment  is  made  by  the  screws  at  the  back  of 
the  mirror. 

246.  The  Adjustment  of  the  Horizon  Mirror  consists  in  making  the  reflecting 
surface  of  this  mirror  perpendicular  to  the  plane  of  the  sextant.  The  index  mirror 
having  been  adjusted,  if,  in  revolving  it  by  means  of  the  index  arm,  there  is  found 
one  position  in  which  it  is  parallel  to  the  horizon  glass,  then  the  latter  must  also  be 
perpendicular  to  the  plane  of  the  sextant.  In  order  to  test  this,  put  in  the  telescope 
and  direct  it  toward  a  star;  move  the  index  until  the  reflected  image  appears  to  pass 
the  direct  image;  if  one  passes  directly  over  the  other  the  mirrors  must  be  parallel; 


94  INSTRUMENTS  EMPLOYED  IN   NAUTICAL  ASTRONOMY. 

if  one  passes  on  either  side  of  the  other  the  horizon  glass  needs  adjustment,  which  is 
accomplished  b}^  means  of  the  screws  attached. 

The  sea  horizon  may  also  be  used  for  making  this  adjustment.  Hold  the  sextant 
vertically  and  bring  the  du-ect  and  the  reflected  images  of  the  horizon  line  into  coin- 
cidence; then  incline  the  sextant  until  its  plane  makes  but  a  small  angle  with  the 
horizon;  if  the  images  still  coincide  the  glasses  are  parallel;  if  not,  the  horizon  glass 
needs  adjustment. 

247.  The  Adjustment  of  the  Telescope  must  be  so  made  that,  in  measuring 
angular  distances,  the  line  of  sight,  or  axis  of  the  telescope,  shall  be  parallel  to  the 
plane  of  the  instrument,  as  a  deviation  in  that  respect,  in  measuring  large  angles, 
will  occasion  a  considerable  error.  To  avoid  such  error,  a  telescope  is  employed  in 
which  are  placed  two  wires,  parallel  to  each  other  and  equidistant  from  the  center 
of  the  telescope ;  by  means  oi  these  wires  the  adjustment  may  be  made.  Screw  on 
the  telescope,  and  turn  the  tube  containing  the  eyeglass  tiU  the  wires  are  parallel 
to  the  plane  of  the  instrument;  then  select  two  clearl;;/^  defined  objects  whose  angular 
distance  must  be  not  less  than  90°,  because  an  error  is  more  easily  discovered  when 
the  angle  is  great;  bring  the  reflected  image  of  one  object  into  exact  coincidence 
with  the  direct  image  of  the  other  at  the  inner  wire;  then,  by  altering  slightly  the 
position  of  the  instrument,  make  the  objects  appear  on  the  other  wire;  if  the  contact 
still  remains  perfect,  the  axis  of  the  telescope  is  in  its  right  situation ;  but  if  the  two 
objects  appear  to  separate  or  lap  over  at  the  outer  wire  the  telescope  is  not  parallel, 
and  it  must  be  rectified  by  turning  one  of  the  two  screws  of  the  ring  into  which  the 
telescope  is  screwed,  having  previously  unturned  the  other  screw;  by  repeating  this 
operation  a  few  times  the  contact  will  be  precisely  the  same  at  both  wires,  and  the 
axis  of  the  telescope  will  be  parallel  to  the  plane  of  the  instrument. 

Another  method  of  making  this  adjustment  is  to  place  the  sextant  upon  a  table 
in  a  horizontal  position,  look  along  the  plane  of  the  limb,  and  make  a  mark  upon  a 
wall,  or  other  vertical  surface,  at  a  distance  of  about  20  feet;  draw  another  mark 
above  the  first  at  a  distance  equal  to  the  height  of  the  axis  of  the  telescope  above 
the  plane  of  the  limb;  then  so  adjust  the  telescope  that  the  upper  mark,  as  viewed 
through  the  telescope,  faUs  midway  between  the  wires.  Some  sextants  are  accom- 
panied by  small  sights  whose  height  is  exactly  equal  to  the  distance  between  the 
telescope  and  the  plane^  of  the  limb ;  by  the  use  of  these,  the  necessity  for  employing 
the  second  mark  is  avoided  and  the  adjustment  can  be  very  accurately  made. 

248.  The  errors  which  arise  from  defects  in  what  have  been  denominated  the 
permanent  adjustments  of  the  sextant  may  be  divided  into  three  classes,  namely: 
Errors  due  to  faulty  centering  of  the  axis,  called  eccentricity;  errors  of  graduation; 
and  errors  arising  from  lack  of  parallelism  of  surfaces  in  index  mirror  and  in  shade 
glasses. 

The  errors  due  to  eccentricity  and  faulty  graduation  are  constant  for  the  same 
angle,  _  and  should  be  determined  once  for  all  at  some  place  where  proper  facilities 
for  doing  the  work  are  at  hand;  these  errors  can  only  be  ascertained  by  measuring 
known  angles  with  the  sextant.  If  angles  of  10°,  20°,  30°,  40°,  etc.,  are  first  laid 
off  with  a  theodolite  or  similar  instrument  and  then  measured  by  the  sextant,  a 
table  of  errors  of  the  sextant  due  to  eccentricity  and  faulty  graduation  may  be  made, 
and  the  error  at  any  intermediate  angle  found  by  interpolation;  this  table  will 
include  the  error  of  graduation  of  the  theodolite  and  also  the  error  due  to  inaccurate 
reading  of  the  sextant,  but  such  errors  are  small.  Another  method  for  determining 
the  combined  errors  of  eccentricity  and  graduation  is  by  measuring  the  angular 
distance  between  stars  and  comparing  the  observed  and  the  computed  arc  between 
them,  but  this  process  is  liable  to  inaccuracies  by  reason  of  the  uncertainty  of  allow- 
ances for  atmospheric  refraction. 

Errors  of  graduation,  when  lar^e,  may  be  detected  by  "stepping  off"  distances 
on  the  graduated  arc  with  the  vermer;  place  the  zero  of  the  vernier  in  exact  coinci- 
dence with  a  division  of  the  arc,  and  observe  whether  the  final  division  of  the  vernier 
also  coincides  with  a  division  of  the  arc;  this  should  be  tried  at  numerous  positions 
of  the  graduated  limb,  and  the  agreement  ought  to  be  perfect  in  every  case. 

The  error  due  to  a  prismatic  index  mirror  may  be  found  by  measuring  a  certain 
unchangeable  angle,  then  taking  out  the  glass  and  turning  the  upper  edge  down, 
and  measuring  the  angle  again;  half  the  difference  of  these  two  measures  will  be 
the  error  at  that  angle  due  to  the  mirror.     From  a  number  of  measures  of  angles 


INSTRUMENTS  EMPLOYED  IN   NAUTICAL  ASTRONOMY.  95 

in  this  manner,  a  table  similar  to  the  one  for  eccentricity  and  faulty  ^aduation  can 
be  made;  or  the  two  tables  m.&j  be  combined.^  When  possible  to  avoid  it,  however, 
no  sextant  should  be  used  in  which  there  is  an  index  mirror  which  produces  a  greater 
error  than  that  due  to  the  probable  error  of  reading  the  scale.  Mirrors  having  a 
greater  angle  than  2"  between  their  faces  are  rejected  for  use  in  the  United  States 
Navy.  Index  mirrors  may  be  roughly  tested  by  noting  if  there  is  an  elongated 
image  of  a  well-defined  point  at  large  angles. 

Since  the  error  due  to  a  prismatic  horizon  mirror  is  included  in  the  index  cor- 
rection (art.  249),  and  consequently  applied  alike  to  all  angles,  it  may  be  neglected. 

Errors  due  to  prismatic  shade  glasses  can  be  determined  by  measuring  angles 
with  and  without  the  shade  glasses  and  noting  the  difference.  They  may  also  be 
determined,  where  the  glasses  are  so  arranged  that  they  can  be  turned  through  an 
angle  of  180°,  by  measuring  the  angle  first  with  the  glass  in  its  usual  position  and 
then  reversed,  and  taking  the  mean  of  the  two  as  the  true  measure. 

249.  Index  Error.^ — The  Index  Error  of  a  sextant  is  the  error  of  its  indications 
■  due  to  the  fact  that  when  the  index  and  horizon  mirrors  are  parallel  the  zero  of  the 

vernier  does  not  coincide  with  the  zero  of  the  scale.  Having  made  the  adjustments 
of  the  index  and  horizon  mirrors  and  of  the  telescope,  as  previously  described,  it  is 
necessary  to  find  that  point  of  the  arc  at  which  the  zero  of  the  vernier  falls  when  the 
two  mirrors  are  parallel,  for  all  angles  measured  by  the  sextant  are  reckoned  from 
that  point.  If  this  point  is  to  the  left  of  the  zero  of  the  limb,  aU  readings  will  be 
too  great;  if  to  the  right  of  the  zero,  all  readings  will  be  too  small. 

if  desirable  that  the  reading  should  be  zero  when  the  mirrors  are  parallel,  place 
the  zero  of  the  vernier  on  zero  of  the  arc;  then,  by  means  of  the  adjusting  screws  of 
the  horizon  glass,  move  that  glass  until  the  direct  and  reflected  images  of  the  same 
object  coincide,  after  which  the  perpendicularity  of  the  horizon  ^lass  should  again  be 
verified,  as  it  may  have  been  deranged  by  the  operation.  This  adjustment  is  not 
essential,  since  the  correction  may  readily  do  determined  and  applied  to  the  reading. 
In  certain  sextant  work,  however,  such  as  surveying,  it  will  be  very  convenient  to 
be  relieved  of  the  necessity  of  con-ecting  each  angle  observed.  The  sextant  should 
never  be  relied  upon  for  maintaining  a  constant  index  correction,  and  the  error 
should  be  ascertained  frequently.  It  is  a  good  practice  to  verify  the  correction  each 
time  a  sight  is  taken. 

250.  The  Index  Correction  may  be  found  (a)  by  a  star,  (6)  by  the  sea  horizon, 
and  (c)  by  the  sun. 

(a)  Bring  the  direct  and  reflected  images  of  a  star  into  coincidence,  and  read  off 
the  arc.  The  index  correction  is  numerically  equal  to  this  reading,  and  is  positive 
or  negative  according  as  the  reading  is  on  the  right  or  left  of  the  zero. 

(o)  The  same  method  may  be  employed,  substituting  for  a  star  the  sea  horizon, 
though  this  will  be  found  somewhat  less  accurate. 

(c)  Measure  the  apparent  diameter  of  the  sun  by  first  bringing  the  upper  limb 
of  the  reflected  image  to  touch  the  lower  limb  of  the  direct  image,  and  then  cringing 
the  lower  limb  of  the  reflected  image  to  touch  the  upper  limb  of  the  direct  image. 

Denote  the  readings  in  the  two  cases  by  r  and  r  ;  then,  if  S  =  apparent  diameter 
of  the  sun,  and  R  =  the  reading  of  the  sextant  when  the  two  images  are  in  coincidence, 
we  have: 

r  =R  +  S, 
r'  =  R-S, 
R  =  i  {r  +  r'). 

As  R  represents  the  error,  the  correction  will  be  —  R.  Hence  the  rule:  Mark  the 
readings  when  on  the  arc  with  the  negative  sign;  when  off,  with  the  positive  sign; 
then  the  index  correction  is  one-half  the  algebraic  sum  of  the  two  readings. 

Example  :  The  sun's  diameter  is  measured  for  index  correction  as  follows :  On 
the  arc,  31'  20";  off  the  arc,  33'  10".     Required  the  correction. 

On  the  arc,      -31'  20" 
Off  the  arc,      +33    10 

2)+    1    50 

I.  C,  +   0    55 


96  INSTRUMENTS  EMPLOYED  IN    NAUTICAL  ASTRONOMY. 

251.  From  the  equations  previously  given,  it  is  seen  that: 

S=i  (r-r'); 

hence,  if  the  observations  are  correct,  it  will  be  found  that  the  sun's  semidiamoter, 
as  given  in  the  Nautical  Almanac  for  the  day  of  observation,  is  equal  to  one-half  the 
algebraic  difference  of  the  readings.  If  required  to  obtain  the  index  correction  with 
great  precision,  several  observations  should  be  taken  and  the  mean  used,  the  accuracy 
being  verified  by  comparing  the  tabulated  with  the  observed  semidiameter.  If  the 
sun  is  low,  the  horizontal  semidiameter  should  be  observed,  to  prevent  the  error  that 
may  arise  from  unequal  refraction. 

252.  Use  of  the  Sextant, — ^To  measure  the  angle  between  any  two  visible 
objects,  point  the  telescope  toward  the  lower  one,  if  one  is  above  the  other,  or  toward 
the  left-hand  one,  if  they  are  in  nearly  the  same  horizontal  plane.  Keep  this  object 
in  direct  view  through  the  unsilvcred  part  of  the  horizon  glass,  and  move  the  index 
arm  imtil  the  image  of  the  other  object  is  seen  by  a  double  reflection  from  the  index 
mirror  and  the  silvered  portion  of  the  horizon  glass.  Having  gotten  the  direct 
image  of  one  object  into  nearly  exact  contact  with  the  reflected  image  of  the  other, 
clamp  the  index  arm  and,  by  means  of  the  tangent  screw,  complete  the  adjustment 
so  that  the  contact  may  be  perfect;  then  read  the  limb. 

In  measuring  the  altitude  of  a  celestial  body  above  the  sea  horizon,  it  is  necessary 
that  the  angle  shall  be  measured  to  that  point  of  the  horizon  which  lies  vertically 
beneath  the  object.  To  determine  this  point,  the  observer  should  move  the  instru- 
ment sUghtly  to  the  right  and  left  of  the  vertical,  swinging  it  about  the  line  of  sight 
as  an  axis,  taking  care  to  keep  the  object  in  the  middle  of  the  field  of  view.  The 
object  will  appear  to  describe  the  arc  of  a  circle,  and  the  lowest  point  of  this  arc 
marks  the  true  vertical. 

The  shade  glasses  should  be  employed  as  may  be  necessary  to  protect  the  eye 
when  observing  objects  of  dazzling  brightness,  such  as  the  sun,  or  the  horizon  when 
the  sun  is  reflected  from  it  at  a  low  altitude.  Care  must  be  taken  that  the  images 
are  not  too  bright  or  the  eye  wiU  be  so  affected  as  to  interfere  with  the  accuracy  of 
the  observations. 

253.  Choice  of  Sextants. — ^The  choice  of  a  sextant  should  be  governed  by  the 
kind  of  work  which  is  required  to  be  done.  In  rough  work,  such  as  surveying,  where 
angles  need  only  be  measured  to  the  nearest  30''  the  radius  maybe  as  small  as  6  inches, 
which  wiU  permit  easy  reading,  and  the  instrument  can  be  correspondingly  lightened. 
Where  readings  to  10''  are  desired,  as  in  nice  astronomical  work,  the  radius  should  be 
about  7i  inches,  and  the  instrument,  to  be  strongly  built,  should  weigh  about  3J 
pounds. 

The  parts  of  an  instrument  should  move  freely,  without  binding  or  gritting.  The 
eyepieces  should  move  easily  in  the  telescope  tubes;  the  bracket  for  carrying  tne  tele- 
scope should  be  made  very  strong.  It  is  frequently  found  that  the  parallehsm  of 
the  line  of  sight  is  destroyed  in  focusing  the  eyepiece,  either  on  account  of  the  loose- 
ness of  the  fit  or  because  of  the  telescope  bracket  being  weak.  The  vernier  should 
lie  close  to  the  limbs  to  prevent  paraUax  in  reading.  If  it  is  either  too  loose  or  too 
tight  at  either  extremity  of  its  travel,  it  may  indicate  that  the  pivot  is  not  perpendicu- 
lar. The  baUs  of  the  tangent  screw  should  fit  snugly  in  their  sockets,  so  that  there 
may  be  no  lost  motion. 

Where  possible,  the  sextant  should  always  be  submitted  to  expert  exammation 
and  test  as  to  the  accuracy  of  its  permanent  adjustments  before  acceptance  by  the 
navigator. 

254.  Kesilvering  Mirrors. — Occasion  may  sometimes  arise  for  resflvering  the 
mirrors  of  a  sextant,  as  they  are  always  liable  to  be  damaged  by  dampness  or  other 
causes.  For  this  purpose  some  clean  tin  fofl  and  mercury  are  required.  Upon  a 
piece  of  glass  about  4  mches  square  lay  a  piece  of  tin  foil  whose  dimensions  exceed  by 
about  a  quarter  of  an  inch  in  each  direction  those  of  the  glass  to  be  sflvered;  smooth 
out  the  foil  carefuUy  by  rubbing;  put  a  small  drop  of  mercury  on  the  foil  and  spread 
it  with  the  finger  over  the  entire  surface,  being  careful  that  none  shall  find  its  way 
under  the  foil;  then  put  on  a  few  more  drops  of  mercury  until  the  whole  surface  is 
fluid.  The  glass  which  is  to  be  silvered  having  been  carefully  cleaned,  it  should  be 
laid  upon  a  piece  of  tissue  paper  whose  edge  just  covers  the  edge  of  the  foil  and 


I 


INSTRUMENTS  EMPLOYED  IN   NAUTICAL  ASTEONOMY.  97 

transferred  carefully  from  the  paper  to  the  tin  foil,  a  gentle  pressure  being  kept  upon 
the  glass  to  avoid  the  formation  of  bubbles;  finally,  place  tne  mirror  face  downward 
and  leave  it  in  an  inclined  position  to  allow  the  surplus  mercury  to  flow  off,  the  latter 
operation  being  hastened  bv  a  strip  of  tin  foil  at  its  lower  edge.  After  five  or  six 
hours  the  tin  foil  around  the  edges  may  be  removed,  and  the  next  day  a  coat  of 
varnish  made  from  spirits  of  wine  and  red  sealing  wax  should  be  apphed.  For  a 
horizon  mirror  care  must  be  taken  to  avoid  silvermg  the  plain  half.  The  mercury 
drawn  from  the  foU  should  not  be  placed  with  clean  mercury  with  a  view  to  use  in  the 
artificial  horizon  or  the  whole  will  be  spoiled. 

255.  Octants  and  Quintants. — rroperly  speaking,  a  sextant  is  an  instrument 
whose  arc  covers  one-sixth  of  a  complete  circle,  and  which  is  therefore  capable  of 
measuring  an  angle  of  120°.  Other  instruments  are  made  which  are  identical  in 
principle  with  the  sextant  as  heretofore  described,  and  which  differ  from  that  instru- 
ment only  in  the  length  of  the  arc.  These  are  the  octant,  an  eighth  of  a  circle,  by 
which  angles  may  be  measured  to  90°,  and  the  quirdant,  a  fifth  of  a  circle,  whicn 
measures  angles  up  to  144°.  The  distinction  between  these  instruments  is  not 
always  carefuUy  made,  and  in  such  matters  as  have  been  touched  upon  in  the  fore- 
going articles  the  sextant  may  be  regarded  as  the  type  of  all  kindred  reflecting 
mstruments. 

THE  ABTiriCIAL  HORIZON. 

256.  The  Artificial  Horizon  is  a  small,  rectangular,  shallow  basin  of  mercury, 
over  which,  to  protect  the  mercury  from  agitation  by  the  wind,  is  placed  a  roof 
consisting  of  two  plates  of  glass  at  ri^ht  angles  to  each  other.  The  mercury  affords 
a  perfectly  horizontal  surface  which  is  at  tne  same  time  an  excellent  mirror.  The 
different  parts  of  an  artificial  horizon  are  furnished  in 

a  compact  form,  a  metal  bottle  being  provided  for 
containing  the  mercury  when  not  in  use,  together 
with  a  suitable  funnel  for  pouring. 

If  MN,  in  figure  34,  is  the  horizontal  surface  of 
the  mercury;  S'B  a  ray  of  light  from  a  celestial 
object,  inciaent  to  the  surface  atB;  BA  the  reflected 
ray;  then  an  observer  at  A  will  receive  the  ray  BA 
as  if  it  proceeded  from  a  point  S*,  whose  angular 
depression,  MBS",  below  the  horizontal  plane  is 
equal  to  the  altitude,  JMBS',  of  the  object  above 
that  plane.  If,  then,  SA  is  a  direct  ray  from  the 
object  parallel  to  S'B,  an  observer  at  A  can  measure 
with  the  sextant  the  angle  SAS"  =  S'BS"  =  2  S'BM,  by 
bringing  the  image  of  the  object  reflected  by  the 
index  mirror  into  coincidence  with  the  image  S"  re- 
flected by  the  mercury  and  seen  through  the  horizon 
glass.  The  instrumental  measure,  corrected  for  in- 
dex error,  will  be  double  the  apparent  altitude  of  the  fig.  34. 
body. 

The  sun's  altitude  will  be  measured  by  bringing  the  lower  limb  of  one  image  to 
touch  the  upper  limb  of  the  other.  Half  the  corrected  instrumental  reading  wfll  be 
the  apparent  altitude  of  the  sun's  lower  or  upper  limb,  according  as  the  lower  or  upper 
limb  of  the  reflected  image  was  the  one  employed  in  the  observation. 

In  observations  of  the  sun  with  the  artificial  horizon,  the  eye  is  protected  by  a 
suigle  dark  glass  over  the  eyepiece  of  the  telescope  through  which  direct  and  reflected 
rays  must  pass  alike,  thereby  avoiding  the  errors  that  might  possibly  arise  from  a 
difference  in  the  separate  shade  glasses  attached  to  the  frame  of  the  sextant. 

The  glasses  in  the  roof  over  the  mercury  should  be  made  of  plate  glass,  with 
perfectly  paraUel  faces.  If  they  are  at  all  prismatic,  the  observed  altitude  will  be 
erroneous.  The  error  may  be  removed  by  observing  a  second  altitude  with  the  roof 
reversed,  and,  in  general,  by  taking  one-half  of  a  set  of  observations  with  the  roof  in 
one  position  and  the  other  half  with  the  roof  reversed.  On  the  rare  occasions  when 
the  atmosphere  is  so  calm  that  the  unsheltered  mercury  will  remain  undisturbed, 
most  satisfactory  observations  may  be  made  by  leaving  off  the  roof. 
21594°— 14 7 


98  INSTRUMENTS  EMPLOYED  IN    NAUTICAL  ASTRONOMY. 

257.  In  setting  up  an  artificial  horizon,  care  should  be  taken  that  the  basin  is 
free  from  dust  and  other  foreign  matter,  as  small  particles  floating  upon  the  surface 
of  the  mercury  interfere  with  a  perfect  reflection.  The  basin  should  be  so  placed 
that  its  longer  edge  lies  in  the  direction  in  which  the  observed  body  will  bear  at  the 
middle  of  the  observations.  The  spot  selected  for  taking  the  sights  should  be  as 
free  as  possible  from  causes  which  will  produce  vibration  of  the  mercury,  and  pre- 
cautions should  be  taken  to  shelter  the  horizon  from  the  wind,  as  the  mere  placing 
of  the  roof  will  not  ordinarily  be  sufficient  to  accomplish  this.  Embedding  the  root 
in  earth  serves  to  keep  out  the  wind,  while  setting  the  whole  horizon  upon  a  thick 
towel  or  a  piece  of  such  material  as  heavy  felt  usually  affords  ample  protection  from 
wind,  tends  to  reduce  the  vibrations  from  mechanical  shocks,  and  also  aids  in  keeping 
out  the  moisture  from  the  ground.  In  damp  climates  the  roof  should  be  kept  dry 
by  wiping,  or  the  moisture  deposited  from  tne  inclosed  air  will  form  a  cloud  upon 
the  glass. 

Molasses,  oil,  or  other  viscous  fluid  may,  when  necessary,  be  employed  as  a 
substitute  for  mercury. 

258.  Owing  to  the  perfection  of  manufacture  that  is  required  to  insure  accuracy 
of  results  with  the  artificial  horizon,  navigators  are  advised  to  accept  only  such 
instrument  as  has  satisfactorily  stood  the  necessary  tests  to  prove  the  correctness  of 
its  adjustment  as  regards  the  glasses  of  the  roof. 

THE  CHRONOMETER. 

259.  The  Chronometer  is  simply  a  correct  time  measurer,  differing  from  an 
ordinary  watch  in  having  the  force  of  its  mainspring  rendered  uniform  by  means  of 
a  variable  lever.  Owing  to  the  fact  that  on  a  sea  voyage  a  chronometer  is  exposed 
to  many  changes  of  temperature,  it  is  furnished  with  an  expansion  balance,  formed 
of  a  combination  of  metals  of  different  expansive  qualities,  which  produces  the 
required  compensation.  In  order  that  its  working  maj^  not  be  deranged  by  the 
motion  of  the  ship  in  a  seaway,  the  instrument  is  carried  in  gimbals. 

As  the  re^larity  of  the  chronometer  is  essential  for  the  correct  determination 
of  a  ship's  position,  it  is  of  the  greatest  importance  that  every  precaution  be  taken 
to  insure  the  accuracy  of  its  indications.  There  is  no  more  certain  way  of  doing 
this  than  to  provide  a  vessel  with  several  of  these  instruments — preferably  not  less 
than  three — m  order  that  if  an  irregularity  develop  in  one,  the  fact  may  be  revealed 
by  the  others. 

260.  Care  of  Chronometers  on  Shipboard. — ^The  box  in  which  the  chro- 
nometers are  kept  should  have  a  permanent  place  as  near  as  practicable  to  the  center 
of  motion  of  the  ship,  and  where  it  will  be  free  from  excessive  shocks  and  jars,  such 
as  those  that  arise  from  the  engines  or  from  the  firing  of  heavy  guns;  the  location 
should  be  one  free  from  sudden  and  extreme  changes  of  temperature,  and  as  far 
removed  as  possible  from  masses  of  vertical  iron.  The  box  should  contain  a  separate 
compartment  for  each  chronometer,  and  each  compartment  should  be  lined  with 
baize  cloth  padded  with  curled  hair,  for  the  double  purpose  of  reducing  shocks  and 
equalizing  tne  temperature  within.  An  outer  cover  of  baize  cloth  should  be  pro- 
vided for  the  box,  and  this  should  be  changed  or  dried  out  frequently  in  damp 
weather.  The  chronometers  should  aU  be  placed  with  the  XII  mark  in  the  same 
position. 

For  transportation  for  short  distances  by  hand,  an  instrument  should  be  rigidly 
clamped  in  its  gimbals,  for  if  left  free  to  swing,  its  performance  may  be  deranged  by 
the  violent  oscillations  that  are  imparted  to  it. 

For  transportation  for  a  considerable  distance,  as  by  express,  the  chronometer 
should  be  allowed  to  run  down,  and  should  then  be  dismounted  and  the  balance 
corked. 

261.  Since  it  is  not  possible  to  make  a  perfect  instrument  which  will  be  unin- 
fluenced by  the  disturbing  causes  incident  to  a  sea  voyage,  it  becomes  the  duty  of 
the  navigator  to  determine  the  error  and  to  keep  watch  upon  the  variable  rate  of  the 
chronometer. 

The  error  of  the  chronometer  is  the  difference  between  the  time  indicated  and  the 
standard  time  to  which  it  is  referred — usually  Greenwich  mean  time. 
The  amount  the  chronometer  gains  or  loses  daily  is  the  daily  rate. 


INSTRUMENTS   EMPLOYED  IN    NAUTICAL  ASTRONOMY. 


99 


The  indications  of  a  chronometer  at  any  given  instant  require  a  correction  for 
the  accumulated  error  to  that  instant;  and  this  can  be  found  if  the  error  at  any 
given  time,  together  with  the  daily  rate,  are  known. 

262.  Winding. — Chi-onometers  are  ordinarily  constructed  to  run  for  56  hours 
without  rewinding,  and  an  indicator  on  the  face  always  shows  how  many  hours 
have  elapsed  since  the  last  winding.  To  insure  a  uniform  rate,  they  must  be  wound 
regularly  every  day,  and,  in  order  to  avoid  the  serious  consequences  of  their  running 
down,  the  navigator  should  take  some  means  to  guard  against  neglecting  this  duty 
through  a  fault  of  memory.  To  wind,  turn  the  chronometer  gently  on  its  side, 
enter  the  key  in  its  hole  and  push  it  home,  steadying  the  instrument  with  the  hand, 
and  wind  to  the  left,  the  last  half  turn  being  made  so  as  to  bring  up  gently  against 
the  stop.  After  winding,  cover  the  keyhole  and  return  the  instrument  to  its  natural 
position.  Chronometers  should  always  be  wound  in  the  same  order  to  prevent 
omissions,  and  the  precaution  taken  to  inspect  the  indicators,  as  a  further  assurance 
of  the  proper  performance  of  the  operation. 

After  winding  each  day,  the  comparisons  should  be  made,  and,  with  the  reading 
of  the  maximum-and-minimum  thermometer  and  other  necessary  data,  recorded  in 
a  book  kept  for  the  purpose.^ 

The  maximum-and-minimum  thermometer  is  one  so  arranged  that  its  highest 
and  lowest  readings  are  marked  by  small  steel  indices  that  remain  in  place  until 
reset.  Every  chronometer  box  should  be  provided  with  such  an  instrument,  as  a 
knowledge  of  the  temperature  to  which  chronometers  have  been  subjected  is  essential 
in  any  analysis  of  the  rate.  To  draw  down  the  indices  for  the  purpose  of  resetting, 
a  magnet  is  used.  This  magnet  should  be  kept  at  all  times  at  a  distance  from  the 
chronometers. 

263.  Comparison  of  Chronometers. — ^The  instrument  believed  to  be  the  best 
is  regarded  as  the  Standard,  and  each  other  is  compared  with  it.  It  is  usual  to  desig- 
nate the  Standard  as  A,  and  the  others  as  B,  C,  etc.  Chronometers  are  made  to 
boat  half  seconds,  and  any  two  may  be  compared  by  following  the  beat  of  one  with 
the  ear  and  of  the  other  with  the  eye. 

To  make  a  comparison,  say  of  A  and  B,  open  the  boxes  of  these  two  instruments 
and  close  all  others.  Get  the  cadence  and,  commencing  when  A  has  just  completed 
the  beat  of  some  even  5-second  division  of  the  dial,  count  ** half-one-half -two-haK- 
three-haK-four-half-five,"  glancing  at  B  in  time  to  note  the  position  of  its  second  hand 
at  the  last  count;  the  seconds  indicated  by  A  will  be  five  greater  than  the  number 
at  the  beginning  of  the  count.  The  hours  and  minutes  are  also  recorded  for  each 
chronometer,  and  the  subtraction  made.  A  good  check  upon  the  accuracy  is  afforded 
by  repeating  the  operation,  taking  the  tick  n-om  B. 

Where  necessary  for  exact  work,  it  is  possible  to  estimate  the  fraction  between 
beats,  and  thus  make  the  comparison  to  tenths  of  a  second;  but  the  nearest  half 
second  is  sufficiently  exact  for  the  purposes  of  ordinary  navigation  at  sea. 

264.  The  following  form  represents  a  convenient  metnod  of  recording  com- 
parisons : 


Stand.  A,  No.  777. 


Chro.  B,  No.  1509. 


Chro.  0,  No.  1802. 


Date,  1903. 

Designation  of 
comparisons. 

Chro.  B 

with 
Stand.  A. 

2ddifl. 

Chro.  C 

with 
Stand.  A. 

2ddifl. 

Therm. 

Bar. 

Rfiinarks. 

Max. 

Min. 

Air. 

January 

Stand.  A. 
BandC. 

Difference. 

h.   m.   s. 
1  13  40 
1  12  2L5 

s. 

h.     m.     s. 

1  14  20 

2  04  11 

s. 

• 

63 

O 

59 

60 

30.07 

Found    errors 
by  time- 
ball. 

1  18.5 

11  10  09 

2 

Stand.  A. 
B  and  C. 

Difference. 

1  16  30 
1  15  10 

+L5 

1  17  00 

2  06  51.  5 

-0.5 

64 

58 

57 

30.12 

Left    New 
York    for 
San  Juan, 
P.  R. 

1  20 

11  10  08.  5 

100  INSTRUMENTS  EMPLOYED  IN   NAUTICAL  ASTRONOMY. 

265.  The  secorid  difference  in  the  form  is  the  difference  between  the  comparisons 
of  the  same  instruments  for  two  successive  days.  When  a  vessel  is  equipped  with 
only  one  chronometer  there  is  nothing  to  indicate  any  irregularity  that  it  may  develop 
at  sea — and  even  the  best  instruments  may  imdergo  changes  from  no  apparent  cause. 
When  there  are  two  chronometers,  the  second  difference,  which  is  equal  to  the  algebraic 
difference  between  their  daily  rates,  remains  uniform  as  long  as  the  rates  remain 
uniform,  but  changes  if  one  of  the  rates  undergoes  a  change;  in  such  a  case,  there  is 
no  means  of  knowing  which  chronometer  has  departed  from  its  expected  performance, 
and  the  navigator  must  proceed  with  caution,  giving  due  faith  to  the  indications  of 
each.  If,  however,  there  are  three  chronometers,  an  irregularity  on  the  part  of  one 
is  at  once  located  by  a  comparison  of  the  second  differences.  Tnus,  if  the  predicted 
rates  of  the  chronometers  were  such  as  to  give  for  the  second  difference  of  A-B,+ 
1^.5,andof  A— C,  —  0^5,  suppose  on  a  certain  day  those  differences  were  ^-4^5and  — 0^5, 
respectively;  it  would  at  once  be  suspected  that  the  irregularity  was  in  B,  and  that 
that  chronometer  had  lost  3^  on  its  normal  rate  during  the  preceding  day.  Suppose, 
however,  the  second  differences  were  +4^.5  and  +2^.5;  it  would  then  be  apparent 
that  A  had  gained  3^. 

266.  Temperature  Curves. — Notwithstanding  the  care  taken  to  eliminate  the 
effect  of  a  change  of  temperature  upon  the  rate  of  a  chronometer,  it  is  rare  that  an 
absolutely  perfect  compensation  is  attained,  and  it  may  therefore  be  assumed  that  the 
rates  of  aU  chronometers  vary  somewhat  with  the  temperature.  Where  the  voyage 
of  a  vessel  is  a  long  one  and  marked  changes  of  climate  are  encountered,  the  accu- 
mulated error  from  the  use  of  an  incorrect  rate  may  be  very  material,  amounting  to 
several  minutes'  difference  of  longitude.  Careful  navigators  will  therefore  take  every 
means  to  guard  against  such  an  error.  By  the  employment  of  a  temperature  curve  in 
connection  with  the  chronometer  rate  the  most  satisfactory  results  are  arrived  at. 

267.  There  should  be  furnished  with  each  chronometer  a  statement  showing 
its  daily  rate  under  various  conditions  of  temperature ;  and  this  may  be  supplemented 
by  the  observations  of  the  navigator  during  the  time  that  the  chronometer  remains 
on  board  ship.  With  all  available  data  a  temperature  curve  should  be  constructed 
which  wiU  indicate  graphically  the  performance  of  the  instrument.  It  is  most  con- 
venient to  employ  for  this  purpose  a  piece  of  "  profile  paper,"  on  which  parallel  lines 
are  ruled  at  equal  intervals  at  right  angles  to  each  other.  Let  each  horizontal  line 
represent,  say,  a  degree  of  temperature,  numbered  at  the  left  edge,  from  the  bottom 
up ;  draw  a  vertical  line  in  red  ink  to  represent  the  zero  rate,  and  let  all  rates  to  the 
right  be  'plus,  or  gaining,  and  those  to  the  left  minus,  or  losing;  let  the  intervals 
between  vertical  lines  represent  intervals  of  rate  (as  one-tenth  of  a  second)  numbered 
at  the  top  from  the  zero  rate;  then  on  this  scale  plot  the  rate  corresponding  to  each 
temperature;  when  there  are  several  observations  covering  one  height  of  the  ther- 
mometer, the  mean  mav  be  used.  Through  all  the  plotted  points  draw  a  fair  curve, 
and  the  intersection  of  this  curve  with  each  temperature  line  gives  the  mean  rate 
at  that  temperature.  The  mean  temperature  given  by  the  maximum  and  minimum 
thermometer  shows  the  rate  to  be  used  on  any  day. 

268.  Hack  or  Comparing  Watch. — In  order  to  avoid  derangement,  the  chro- 
nometers should  never  be  removed  from  the  permanent  box  in  which  they  are  kept 
on  shipboard.  When  it  is  desired  to  mark  a  certain  instant  of  time,  as  for  an  astro- 
nomical observation  or  for  obtaining  the  chronometer  error  by  signal,  the  time  is 
marked  by  a  ''hack"  (an  inferior  chronometer  used  for  this  purpose  only),  or  by  a 
comparing  watch.  Careful  comparisons  are  taken — preferably  both  before  and 
afterwards — and  the  chronometer  time  at  the  required  instant  is  thus  deduced.  The 
correction  represented  by  the  chronometer  time  minus  the  watch  time  (twelve  hours 
being  added  to  the  former  when  necessary  to  make  the  subtraction  possible)  is  referred 
to  asC-W. 

Suppose,  for  example,  the  chronometer  and  watch  are  compared  and  their 
indications  are  as  follows : 

Chro.  t.,     5*^  27'^  30" 
W.  T.,    -2    36    45.5 

C-W,        2    50     44.5 


INSTRUMENTS  EMPLOYED  IN   NAUTICAL  ASTRONOMY.  101 

If  then  a  sight  is  taken  when  the  watch  shows  S**  01°°  27^.5,  we  have: 

W.  T.,        3^  01"  27».5 
C-W,    +2    50    44.5 


Chro.  t.,     5    52     12.0 

It  may  occur  that  the  values  of  C  —  W,  as  obtained  from  comparisons  before  and 
after  marking  the  desired  time,  wiU  vary;  in  that  case  the  value  to  be  used  will  be 
the  mean  of  the  two,  if  the  time  marked  is  about  midway  between  comparisons,  but 
if  much  nearer  to  one  comparison  than  the  other,  allowance  should  be  made  accord- 
ingly- 

Thus  suppose,  in  the  case  previously  given,  a  second  comparison  had  been  taken 

after  the  sight  as  follows: 

Chro.  t.,      6''   12°>  45« 
W.  T.,      -3     21     59.5 


C-W,         2     50     45.5 

The  sight  having  been  taken  at  about  the  middle  of  the  interval,  the  C  — W  to 
be  used  would  be  the  mean  of  the  two,  or  2^  50"  45*.0. 

Let  us  assume,  however,  that  the  second  comparison  showed  the  following: 

Chro.  t.,  6''  38"  25" 

W.  T.,  -3     47    39 


C-W,  2     50     46 

Then,  the  sight  having  been  taken  when  onljr  about  one-third  of  the  interval 
had  elapsed  between  the  first  and  second  comparisons,  it  woidd  be  assumed  that 
onlv  one-third  of  the  total  change  in  the  C  — W  had  occurred  up  to  the  time  of  sight, 
and  the  value  to  be  used  would  be  2''  50"  45*.0. 

269.  It  is  considered  a  good  practice  always  to  subtract  watch  time  from 
chronometer  time,  whatever  the  relative  values,  and  thus  to  employ  C  —  W  invariably 
as  an  additive  correction.  It  is  equally  correct  to  take  the  other  difference,  W  — C, 
and  make  it  sub  tractive ;  it  may  sometimes  occur  that  a  few  figures  will  thus  be  saved, 
but  a  chance  for  en'or  arises  from  the  possibility  of  inadvertently  using  the  wrong 
sign,  which  is  almost  impossible  by  the  other  method.  Thus,  the  foUowmg  example 
may  be  taken: 

(C,      lO''  57"  38"   W,     11^  42"  35" 
W,    -11  42  35    C,    -10  57  38 


Comparison' 


Sight 


C-W,  11  15  03  W-C,   0  44  57 

W,  11  50  21  W,     11  50  21 

C-W,  +11  15  03  W-C,  -  0  44  57 

,C,  11  05  24  C,      11  05  24 


CHAPTER  IX. 
TIME  AND  THE  NAUTICAL  ALMANAC. 


270.  The  subjects  of  Time  and  the  Nautical  Almanac  are  two  of  the  most 
important  ones  to  be  mastered  in  the  study  of  Nautical  Astronomy,  as  they  enter 
into  every  operation  for  the  astronomical  determination  of  a  ship's  position.  They 
will  be  treated  in  conjunction,  as  the  two  are  interdependent. 

METHODS  OF  BECKONING  TIME. 

271.  The  instant  at  which  any  point  of  the  celestial  sphere  is  on  the  meridian 
of  an  observer  is  termed  the  transit,  culmination,  or  meridian  passage  of  that  point; 
when  on  that  half  of  the  meridian  w^hich  contains  the  zenith,  it  is  designated  as 
superior  or  upper  transit;  when  on  the  half  containing  the  nadir,  as  inferior  or  lower 
transit. 

272.  Three  different  kinds  of  time  are  employed  in  astronomy — (a)  apparent 
or  solar  time,  (6)  mean  time,  and  (c)  sidereal  t%me.  These  depend  upon  the  hour 
angle  from  the  meridian  of  the  points  to  which  they  respectively  refer.  The  point 
of  reference  for  apparent  or  solar  time  is  the  Center  of  ike  Sun;  for  mean  time,  an 
imaginary  point  called  the  Mean  Sun;  and  for  sidereal  time,  the  Verrwl  Equinox, 
also  called  the  First  Point  of  Aries. 

The  unit  of  time  is  the  Day,  which  is  the  period  between  two  successive  transits 
over  the  same  branch  of  the  meridian  of  the  point  of  reference.  The  day  is  divided 
into  24  equal  parts,  called  Hours;  each  hour  is  divided  into  60  equal  parts,  called 
Minutes,  and  each  minute  into  60  equal  parts,  called  Seconds. 

273.  Apparent  or  Solar  Time. — Tne  hour  angle  of  the  center  of  the  sun  affords 
a  measure  of  Apparent  or  Solar  Time.  An  Apparent  or  Solar  Day  is  the  interval  of 
time  between  two  successive  transits  over  the  same  meridian  of  the  center  of  the 
sun.  It  is  Apparent  Noon  when  the  sun's  hour  circle  coincides  with  the  celestial 
meridian.  This  is  the  most  natural  and  direct  measure  of  time,  and  the  unit  of 
time  adopted  by  the  navigator  at  sea  is  the  apparent  solar  day.  Apparent  noon  is 
the  time  when  tne  latitude  can  be  most  readily  determined,  and  the  ordinary  method 
of  determining  the  longitude  by  the  sun  involves  a  calculation  to  deduce  the  apparent 
time  first. 

Since,  however,  the  intervals  between  the  successive  returns  of  the  sun  to  the 
same  meridian  are  not  equal,  apparent  time  can  not  be  taken  as  a  standard.  The 
apparent  day  varies  in  length  from  two  causes :  first,  the  sun  does  not  move  in  the 
equator,  the  great  circle  perpendicular  to  the  axis  of  rotation  of  the  earth,  but  in  the 
ecliptic;  and,  secondly,  the  sun's  motion  in  the  ecliptic  is  not  uniform.  Sometimes 
the  sun  describes  an  arc  of  57'  of  the  ecliptic,  and  sometimes  an  arc  of  61'  in  a  day. 
At  the  points  where  the  ecliptic  and  equmoctial  intersect,  the  direction  of  the  sun's 
apparent  motion  is  inclined  at  an  angle  of  23°  27'  to  the  equator,  whUe  at  the  solstices 
it  moves  in  a  direction  parallel  to  the  equator. 

274.  Mean  Time. — ^To  avoid  the  irregularity  of  time  caused  b;;^  the  want  of 
uniformity  in  the  sun's  motion,  a  fictitious  sun,  called  the  Mean  Sun,  is  supposed  to 
move  in  the  equinoctial  with  a  uniform  velocity  that  equals  the  mean  velocity  of  the 
true  sun  in  the  ecliptic.  This  mean  sun  is  regarded  as  being  in  coincidence  with  the 
true  sun  at  the  vernal  equinox,  or  First  Point  of  Aries. 

Mean  Time  is  the  hour  angle  of  the  mean  sun.  A  Mean  Day  is  the  interval 
between  two  successive  transits  of  the  mean  sun  over  the  meridian.  Mean  Noon  is 
the  instant  when  the  mean  sun's  hour  circle  coincides  with  the  meridian. 

102 


TIME  AND  THE   NAUTICAL  ALMANAC.  103 

Mean  time  lapses  uniformlv;  at  certain  times  it  agrees  with  apparent  time, 
while  sometimes  it  is  behind,  and  at  other  times  in  advance  of  it.  It  is  this  time  that 
is  measured  by  the  clocks  in  ordinary  use,  and  to  this  the  chronometers  used  by 
navigators  are  regulated. 

275.  The  difference  between  apparent  and  mean  time  is  called  the  Equation  of 
Time;  by  this  quantity,  the  conversion  from  one  to  the  other  of  these  times  may  be 
made.  Its  magnitude  and  the  direction  of  its  application  may  be  found  for  any 
moment  from  the  Nautical  Almanac. 

276.  Sidereal  Time. — Sidereal  Time  is  the  hour  an^le  of  the  First  Point  of 
Aries.  This  point,  which  is  identical  with  the  vernal  equinox,  is  the  origin  of  all 
coordinates  oi  right  ascension.  Since  the  position  of  the  point  is  fixed  in  the  celestial 
sphere  and  does  not,  like  the  sun,  moon,  and  planets,  have  actual  or  apparent  motion 
therein,  it  shares  in  this  respect  the  properties  of  the  fixed  stars.  It  may  therefore 
be  said  that  intervals  of  sidereal  time  are  those  which  are  measured  by  the  stars. 

A  Sidereal  Day  is  the  interval  between  two  successive  transits  of  tne  First  Point 
of  Aries  across  the  same  meridian.  Sidereal  Noon  is  the  instant  at  which  the  hour 
circle  of  the  First  Point  of  Aries  coincides  with  the  meridian.  In  order  to  interconvert 
sidereal  and  mean  times  an  element  is  tabulated  in  the  Nautical  Almanac.  This  is 
the  Sidereal  Time  of  Mean  Noon,  which  is  also  the  Right  Ascension  of  the  Mean  Sun. 

277.  Civil  and  Astronomical  Time. — The  Civtl  Day  commences  at  midnight 
and  comprises  the  twenty-four  hours  until  the  following  midnight.  The  hours  are 
counted  from  0  to  12,  from  midnight  to  noon;  then,  again,  from  0  to  12,  from  noon 
to  midnight.  Thus  the  civil  day  is  divided  into  two  periods  of  twelve  hours  each, 
the  first  of  which  is  marked  a.  m.  (ante  meridian),  while  the  last  is  marked  p.  m. 
(post  meridian). 

The  Astronomical  or  Solar  Day  commences  at  noon  of  the  civil  day  of  the  same 
date.  It  comprises  twenty-four  hours,  reckoned  from  0  to  24,  from  noon  of  one  day 
to  noon  of  the  next.  Astronomical  time  (apparent  or  mean)  is  the  hour  angle  of  the 
sun  (true  or  mean)  measured  to  the  westward  throughout  its  entire  circuit  from  the 
time  of  its  upper  transit  on  one  day  to  the  same  instant  of  the  next. 

The  civil  day,  therefore,  begins  twelve  hours  before  the  astronomical  day,  and 
a  clear  imderstanding  of  this  fact  is  all  that  is  required  for  interconverting  these 
times.     For  example: 

January  9,  2  a.  m.,  civil  time,  is  January  8,  14'',  astronomical  time. 

January  9,  2  p.  m.,  civil  time,  is  January  9,  2^,  astronomical  time. 

278.  Hour  Angle. — The  Tiour  angle  of  a  heavenly  body  is  the  angle  at  the 
pole  of  the  celestial  concave  between  the  declination  circle  of  the  heavenly  body 
and  the  celestial  meridian.  It  is  measured  by  the  arc  of  the 
celestial  equator  between  the  declination  circle  and  the  celestial 
meridian. 

In  figure  35  let  P  be  the  pole  of  the  celestial  sphere,  of  which 
VMQ  is  the  equator,  PQ  the  celestial  meridian,  and  PM,  PS, 
PV  the  declination  circles  of  the  mean  sun,  a  heavenly  body, 
and  the  First  Point  of  Aries,  respectively. 

Then  QPM,  or  its  arc  QM,  is  the  hour  angle  of  the  mean 
sun,  or  the  mean  time ;  QPS,  or  QS,   the  hour  angle  of  the  fig.  35. 

heavenly  body;  QPV,  or  QV,  the  hour  angle  of  the  First  Point 
of  Aries,  or  the  sidereal  time;  VPQ,  or  VQ,  the  right  ascension  of  the  meridian;  VPS, 
or  VS,  the  right  ascension  of  the  heavenly  body;  and  VPM,  or  VM,  the  right  ascen- 
sion of  the  mean  sun. 

279.  Time  at  Different  Meridians. — The  hour  angle  of  the  true  sun  at  any 
meridian  is  called  the  local  aj^'parent  time;  that  of  the  mean  sun,  the  local  mean  time; 
that  of  the  First  Point  of  Anes,  the  local  sidereal  time.  The  hour  angles  of  the  same 
body  and  points  from  Greenwich  are  respectively  the  Greenwich  apparent,  mean, 
and  sidereal  times.  The  difference  between  the  local  time  at  any  meridian  and  the 
Greenwich  time  is  ec[ual  to  the  longitude  of  that  place  from  Greenwich  expressed 
in  time;  the  conversion  from  time  to  arc  may  be  effected  by  a  simple  mathematical 
calculation  or  by  the  use  of  Table  7. 

In  comparing  corresponding  times  of  different  meridians  the  most  easterly 
meridian  may  be  distinguished  as  that  at  which  the  time  is  greatest  or  latest. 


104  TIME  AND  THE   NAUTICAL  ALMANAC. 

In  figure  36  PM  and  PM'  represent  the  celestial  meridians  of  two  places,  PS 
the  declination  circle  through  the  sun,  and  PG  the  Greenwich  meridian ;  let  Tq  =  the 
Greenwich  time  =  GPS ; 

Tii  =  the  corresponding  local  time  at  all  places  on  the  meridian  PM  =  MPS; 
Tji'  =  the  corresponding  local  time  at  all  places  on  the  meridian  PM'  =  M'PS; 
Lo  =  west  longitude  of  meridian  PM  =  GPM ;  and 
Lo'  =  east  longitude  of  meridian  PM'  =  GPM'. 

If  west  longitudes  and  hour  angles  be  reckoned  as  positive, 
and  east  longitudes  and  hour  angles  as  negative,  we  have : 

Lo  =  To-Tm;  and 
Lo'  =  Tq-Tm';  therefore 
Lo-Lo'=Tm'-T„. 

Thus  it  may  be  seen  that  the  difference  of  longitude  be- 
tween two  places  equals  the  difference  of  their  local  times. 
Fig.  36.  This  relation  may  be  shown  to  hold  for  any  two  meridians 

whatsoever. 
Both  local  and  Greenwich  times  in  the  above  formulae  must  be  reckoned  west- 
ward, always  from  their  respective  meridians  and  from  O'*  to  24^;  in  other  words,  it 
is  the  astronomical  time  which  should  be  used  in  aU  astronomical  computations. 

The  formula  Lo  =  T^ — Tm  is  true  for  any  kind  of  time,  solar  or  sidereal ;  or,  in  general 
terms,  Tq  and  T^  are  the  hour  angles  of  any  point  of  the  sphere  at  the  two  meridians 
whose  difference  of  longitude  is  Lo.  S  may  be  the  sun  (true  or  mean)  or  the  vernal 
equinox. 

280.  Finding  the  Greenwich  Time, — Since  nearly  every  computation  made 
by  the  navigator  requires  a  knowledge  of  the  Greenwich  date  and  time  as  a  pre- 
liminary to  the  use  of  the  Nautical  Almanac,  the  first  operation  necessary  is  to 
deduce  from  the  local  time  the  corresponding  Greenwich  date,  either  exact  or  approxi- 
mate, and  thence  the  Greenwich  time  expressed  astronomically. 
The  formula  is: 

Tq  =  T^+Lo, 

rememDering  that  west  longitudes  are  positive,  east  longitudes  are  negative.     Hence 
the  following  rule  for  converting  local  to  Greenwich  time : 

Having  expressed  the  local  time  astronomically,  add  the  longitude  if  west, 
subtract  it  u  east;  the  result  is  the  corresponding  Greenwich  time. 

Example:  In  longitude  81**  15''  W.  the  local  time  is,  April,  15"^  10''  17™  30'  a.  m.     Required  the 
Greenwich  time. 

Local  Ast.  time,  April,      14'*  22''  17°  30' 
Longitude,  +     5  25    00 


Greenwich  time,  15     3  42    30 

Example:  In  longitude  81°  15'  E.  the  local  time  is,  August,  5"*  2^  10™  30»  p.  m.     Required  the  Green- 
wich time. 

Local  Ast.  time,  August,     5"*    2'*  10™  30' 
Longitude,  —     5   25    00 


Greenwich  time,  4   20  45    30 

Example:  In  longitude  17°  28'  W.  the  local  time  is.  May,  1"*  3**  10™  p.  m.     Required  the  Greenwich 
time. 

Local  Ast.  time.  May,  l-^  3^  10™  00" 

Longitude,  +    1    09    52 


Greenwich  time,  1    4    19    52 

Example:  In  longitude  125°  30^  E.  the  local  time  is,  May,  1^  8''  10™  30»  a.  m.     Required  the  Green- 
wich time. 

Local  Ast.  time,  April,     30^  20^  10™  30* 
Longitude,  -      8    22    00 


Greenwich  time,  30    11    48    30 


umb  and  the  nautical  almanac.  105 

281.  From  the  preceding  article  we  have: 

To=Tu+Lo;  hence, 
TM=Ta-Lo; 

thus  it  will  be  seen  that,  to  find  the  local  time  corresponding  to  any  Greenwich  time, 
the  above  process  is  simply  reversed. 

Since  aU  observations  at  sea  are  referred  to  chronometers  regulated  to  Greenwich 
mean  time,  and  as  these  instruments  are  usually  marked  on  the  dial  from  0**  to  12^,  it 
becomes  necessary  to  distinguish  whether  it  is  a.  m.  or  p.  m.  at  Gneenwich.  Therefore 
an  approximate  knowledge  of  the  longitude  and  local  time  is  necessary  to  determine 
the  Greenwich  date. 

Example:  In  longitude  &^  00°»  00*  W.,  about  S""  30"  p.  m.  April  15th,  the  Greenwich  chronometer 
read  8^  25",  and  was  fast  of  Gr,  time  3"  15'.     Required  the  local  astronomical  time. 


Approx.  local  time,         150  S^*  30"         Gr.  chro.,                 8"  25"  00» 
Longitude,                   +        5    00           Corr.,                     -        3    15 

Gr.  Ast.  time  15*^,  8''  21° 
Longitude,            —5    00 

'45* 
00 

Approx.  Gr.  time,            15    8    30           Gr.  Ast.  time  15'',     8    21    45 

Local  Ast.  time  15*,  3    21 

45 

Example:  In  longitude  S^  00"  00*  E.,  about  8  a.  m.  May  3d,  the  Gr. 
fast  of  Gr.  time  3"  15».     Required  the  local  astronomical  time. 

chro.  read  3"  15"  20»,  and 

was 

Approx.  local  time,  May,     2'»  20''          Gr.  chro.,                  3*"  15"  20* 
Longitude,                              —    5           Corr.,                        —     3    15 

Gr.  Ast.  time  2^,  IS^  12" 
Longitude,          +  5  00 

05« 
00 

Approx.  Gr.  time,                 2    15           Gr.  Ast.  time  2^,     15    12  05 

Local  Ast.  time  2'',  20   12 

05 

THE  NAUTICAL  AT.MANAC.a 

282,  The  American  Ephermeris  and  Nautical  Almanac  is  divided  into  three  parts 
as  follows:  Part  I,  Ephemeris  for  the  meridian  of  Greenwich,  gives  the  ephemerides 
of  the  sun  and  moon,  the  geocentric  and  heliocentric  positions  of  the  major  planets, 
the  sun's  coordinates,  and  other  fundamental  astronomical  data  for  equidistant 
intervals  of  Greenwich  mean  time;  Part  II,  Ephemeris  for  the  meridian  of  Washington 
gives  the  ephemerides  of  the  fixed  stars,  sun,  moon,  and  major  planets  for  transit 
over  the  meridian  of  Washington,  and  Part  III,  Phenomena,  contains  predictions  of 
phenomena  to  be  observed  with  data  for  their  computation.  Tables  are  also  appended 
for  the  interconversion  of  mean  and  sidereal  time  and  for  finding  the  latitude  and 
azimuth  by  an  altitude  of  Polaris. 

The  American  Nautical  Almanac  is  a  smaller  book  made  up  of  extracts  from  the 
"Ephemeris  and  Almanac"  just  described,  and  is  designed  especially  for  the  use  of 
navigators,  being  adapted  to  the  meridian  of  Greenwich.  It  contams  the  position 
of  the  sun  and  moon,  together  with  the  ephemerides  of  the  planets  Mercury,  Venus, 
Mars,  Jupiter,  and  Saturn,  and  the  mean  places  of  200  fixed  stars;  solar  and  lunar 
echpses  are  described,  and  the  tables  for  the  interconversion  of  mean  and  sidereal 
time  and  for  finding  the  latitude  by  Polaris  are  included. 

The  elements  dependent  upon  the  sun  and  moon  are  placed  at  the  beginning  of 
the  book,  arranged  according  to  the  months  of  the  year;  twelve  pages  are  devoted 
to  each  month,  numbered  in  Roman  notation  from  I  to  XII.  Of  these,  page  I  con- 
tains the  Apparent  Right  Ascension  and  Declination  of  the  sun  and  the  Eciuation  of 
Time  for  the  instant  of  Greenwich  apparent  noon;  throughout  the  remaining  eleven 
pages  Greenwich  mean  time  forms  the  basis  of  reckoning.  Page  I  is  used  in  compu- 
tations from  observations  that  depend  upon  the  time  of  the  sun's  meridian  passage, 
at  which  instant  the  local  apparent  time  is  0*»,  and  the  Greenwich  apparent  time  is 
equal  to  the  longitude,  if  west,  or  to  24**  minus  the  longitude,  if  east;  this  page  there- 
fore affords  a  means  for  reducing  the  elements  for  such  observations  from  a  knowl- 
edge of  the  longitude  alone.  In  aU  other  observations  the  calculation  is  made  for 
some  definite  instant  of  Greenwich  mean  time  (usually  as  noted  by  the  chronometer), 
in  which  case  Pages  II  to  XII  are  employed. 

0  See  extracts  from  Ephemeris  and  Nautical  Almanac  for  1915,  Appendix  I. 


106  TIME  AND  THE   NAUTICAL  ALMANAC. 

283.  Reduction  of  Elements. — The  reduction  of  elements  in  the  Nautical 
Almanac  is  usually  accomplished  by  Interpolation,  but  in  certain  cases  where  extreme 
precision  is  necessary  the  method  of  Second  Differences  must  be  used. 

The  Ephemeris,  being  computed  for  the  Greenwich  meridian,  contains  the  right 
ascensions,  declinations,  equations  of  time,  and  other  elements  for  given  equidistant 
intervals  of  Greenwich  time.  Hence,  before  the  value  of  any  of  these  quantities  can 
be  found  for  a  given  local  time  it  is  necessary  to  determine  the  corresponding  Green- 
wich time.  Should  that  time  be  one  for  which  the  Nautical  Almanac  gives  the 
value  of  the  required  element,  nothing  more  is  necessary  than  to  emplojr  that  value. 
But  if  the  time  falls  between  the  Almanac  times,  the  required  quantity  must  be 
found  by  interpolation. 

The  Almanac  contains  the  rate  of  change  or  difference  of  each  of  the  principal 
quantities  for  some  unit  of  time,  and,  unless  great  precision  is  required,  the  first 
differences  only  need  be  regarded.  In  order  to  use  the  difference  columns  to  advan- 
tage, the  Greenwich  date  should  be  expressed  in  the  unit  of  time  for  which  the 
difference  is  given.  Thus,  for  using  the  hourly  differences,  the  Greenwich  time 
should  be  expressed  in  hours  and  decimal  parts  of  an  hour;  when  using  the  differences 
for  one  minute,  the  time  should  be  in  minutes  and  decimal  parts  of  a  minute.  Instead 
of  using  decimal  parts,  some  may  prefer  the  use  of  aliquot  parts. 

Since  the  quantities  in  the  Almanac  are  approximate  numbers,  ^ven  to  a  cer- 
tain decimal,  any  interpolation  of  a  lower  order  than  that  decimal  is  unnecessary 
work.  Moreover,  since,  in  computations  at  sea,  the  Greenwich  time  is  more  or  less 
inexact,  too  great  refinement  need  not  be  sought  in  reducing  the  Almanac  elements. 

Simple  interpolation  assumes  that  the  differences  of  the  quantities  are 
proportional  to  the  differences  of  the  times;  in  other  words,  that  tne  differences 
given  in  the  Almanac  are  constant;  this  is  seldom  the  case,  but  the  error  arising  from 
the  assumption  will  be  smaller  the  less  the  interval  between  the  times  in  the  Almanac. 
Hence  those  quantities  which  vary  most  irregularly  are  given  for  the  smallest  units 
of  time;  as  the  variations  are  more  regular,  the  units  for  which  the  differences  are 
given  increase. 

In  takmg  from  the  Almanac  the  elements  relating  to  the  fixed  stars  the  data 
may  be  found  either  in  the  table  which  gives  the  "mean  place"  of  each  star  for  the 
year  or  in  that  which  gives  the  "apparent  place"  occupied  by  each  one  on  every 
tenth  day  throughout  the  year.  As  the  annual  variation  of  position  of  the  fixed 
stars  is  small,  the  results  wiU  not  vary  greatly  whichever  table  may  be  used.  Yet, 
as  it  is  proper  to  seek  always  the  greatest  attainable  accuracy,  the  use  of  the  table 
showing  the  exact  positions  is  recommended.  That  table  is,  however,  published  in 
the  "Ephemeris  and  Nautical  Almanac"  only,  and  is  omitted  from  tne  abridged 
"Nautical  Almanac;"  hence,  where  the  larger  book  is  not  at  hand,  the  table  of  mean 
places  must  be  employed. 

284.  To  find  from  the  Nautical  Almanac  a  required  element  for  any  given  time 
and  place,  it  is  first  necessary  to  express  the  time  astronomically  and  to  convert  it 
to  Greenwich  time  and  date.  Then  take  from  the  Almanac,  for  the  nearest  given 
preceding  instant,  the  required  quantity,  together  with  its  corresponding  "Diff.  for 
1^"  or  "Diff.  for  1™,"  noting  the  name  or  sign  in  each  case;  for  the  sun  use  Page  I 
of  the  proper  month  in  the  Almanac  when  apparent  time  is  to  be  the  basis  for  correc- 
tion, but  otherwise  use  Page  II.  Multiply  the  "Diff.  for  1^"  by  the  number  of  hours 
and  fraction  of  an  hour,  or  the  "Diff.  for  1""  by  the  number  of  minutes  and  fraction 
of  a  minute,  corresponding  to  the  interval  between  the  time  for  which  the  quantity 
is  given  in  the  Almanac  and  the  time  for  which  required ;  apply  the  correction  thus 
obtained,  having  regard  to  its  sign. 

A  modification  of  this  rule  may  be  adopted  if  the  time  for  which  the  quantity  is 
desired  falls  considerably  nearer  a  subsequent  time  given  in  the  Almanac  than  it  does 
to  one  preceding;  in  this  case  the  interpolation  may  be  made  backward,  the  sign  of 
appHcation  of  the  correction  being  reversed. 


1 


TIME  AND  THE   NAUTICAL  ALMANAC.  107 

Example:  At  a  place  in  longitude  81°  15'  W.,  April  17,  1915,  find  the  sun's  declination  and  the 
equation  of  time  at  apparent  noon. 

,     Long.=81°  15'  W.  G.  A.  T.=17'»  6^  25«»=17«»+5''.42. 


Dec.,  17<»  0^, 
Corr., 

(+) 

+ 

+ 
4- 

4 

10" 

'  11'  32".  4  N. 
4    47  .9 

Eq.  t.,  1710",  0'»12M7 
Corr.,                       4          3.22 

Dec,  17*  5^  25", 

10 

16    20  . 3  N. 

Eq.  t.,  17<»5»'25'°,       0     15.39 

H.  D., 
G.  A.  T., 

53".  12 
5".  42 

H.  D.,  4-  0'.595 
G.  A.  T.,                 4-        5\  42 

Corr., 

/    287".  91 
\4'  47".  9 

Corr.,  4-  3V225 
(Subtract  from  apparent  time.) 

Example:  At  a  place  in  longitude  81"  15'  E.,  April  17, 1915,  find  the  sun's  declination  and  the  equa- 
tion of  time  at  apparent  noon. 

Long.=81°  15'  E.  G.  A.  T.=16'»  18*  35»=17'»-5''.42. 


Dec.,  17<»  C, 
Corr., 

(+) 

> 
+ 

10° 

11'  32".  4  N. 
4    47  .9 

Eq.  t.,  171  oh^  Qm  i2».  17 
Corr.,                       -          3.22 

Dec.,  W  IS**  35» 

10 

06    44  .5  N. 

Eq.  t.,  16*  18"  35«,     0    08  .  95 

H.D., 
G.  A.  T., 

53".  12 
5»'.42 

H.  D.,  4-  OV  595 
G.  A.T.,                 -        5".  42 

Corr., 

r    287".  91 
14'  47".  9 

Corr.,                       -        3".  225 

Example:  April  15,  1915,  at  11"  55™  30*  a.  m.,  local  mean  time,  in  Long.  81°  15' W.,  required  the 
declination  and  semidiameter  of  the  sun,  the  equation  of  time,  and  the  right  ascension,  declination, 
horizontal  parallax,  and  semidiameter  of  the  moon  and  Jupiter. 

Local  mean  time,  14*  23"  55"  30* 

Longitude,  4         5"  25"  00' 


[15<*    5"  20"  30* 
Greenwich  mean  time,]  lo^   5"  20".  5 
[151    5".  34 

For  the  Sun. 

Dec.,0",    (4-)    9°  28'  42".  4  N.  S.  D.,  15' 58".2  Eq.  t.,  0",      0*  17* .  09 

Corr.,  4-  4    48  .1  (Same  aa  at  G.  A.  Noon.)  Corr.,  -  3 .   33 


Dec,  9    33    30  .5  N.  Eqt.  t..  e     13 .   76 


4 

48  . 

1 

9 

33 

30 

.5N. 

53" 

5" 

.95 
.34 

H.  D.,  4-  53".  95  H.  D.,        -  0«.624 

G.  M.  T.,     4  5". 34  G.  M.  T.,   4-         5".   34 


Corr.,  4{ 


288". 09  Corr.,  -        3'  .   33 

4'  48".  09  (Subtract  from  mean  time.) 

For  the  Moon. 


R.A.,5i>,   2k  16" 39". 20      DflC.,  S*,  (+)18''  49*  29».4  N.     Hot.  Par.,  0<>,   64'  13'.  9     S.  D.,0«,   14'  48».2 
Corr.,    +     40  .30     Corr.,     +    3  36  .5       Corr.,       -    2.8     Con.,        -         0  .7 


R.  A.,     2  17  19.60     Dec.,       18  53  05  .9N.     Hor.  Par.,     64  11  .  1     S.  D.,     14  47.5 


M.  D.,        +  1».966  M.  D.,  +  10».66  H.  D.,  -         0'.53  H.  D.,       -         C.W 

No.  min.,  +  20".    5  No.  min.,     +  20".  5  G.  M.  T.,  +         5*.34  G.  M.  T.,  +         S«'.34 


64' 

13'. 
2  . 

.   9 
.  8 

64 

11  , 

,   1 

+ 

0'.63 
6>'.34 

Corr., 


Corr.,         +  40«.3O  r,^  j./  216'.  48  Corr.,  -         2'.83  Corr.,        -         0».99 

For  Jupiter. 

Dec,  0",   (-)  6°  13'  33".  6  S.  Hor.  Par.,  IS",       1".  5 

Corr.,         4  1   05  . 1 


R.  A.,  0", 
Corr., 

23"  11"57» 
4              10 

.49 
.68 

R.  A., 

23    12    08 

.17 

H.D., 
G.  M.  T., 

4                 2' 
4               5" 

.00 
.34 

Dec, 

6    12    28  .5  8 

H.  D., 
G.  M.  T., 

4                12".  20 
4-                  5".  34 

S.  D.,  151,  16".  4 


Corr.,  +  10».68  Corr.,  4-  60".   1 


108  TIME  AND  THE   NAUTICAL  ALMANAC. 

285.  Should  greater  precision  be  required  than  that  attainable  by  simple  inter- 
polation, resort  must  be  had  to  the  reduction  for  second  differences. 

The  differences  between  successive  values  of  the  quantities  given  in  the  Nautical 
Almanac  are  called  the  first  differences;  the  di£ferences  between  successive  first 
differences  are  called  the  secona  differences.  Simple  interpolation,  which  satisfies 
the  necessities  of  sea  computations,  assumes  the  first  differences  to  be  constant; 
but  if  the  variation  of  the  first  differences  be  regarded,  a  further  interpolation  is 
required  for  the  second  difference. 

The  difference  for  a  imit  of  time  in  the  American  Nautical  Almanac  abreast  any 
element  expresses  the  rate  at  which  the  element  is  changing  at  that  precise  instant 
of  Greenwich  time.  Now,  regarding  the  second  difference  as  constant,  the  first 
difference  varies  uniformly  with  the  Greenwich  time;  therefore  its  value  may  be 
found  for  any  intermediate  time  by  simple  interpolation. 

Hence  the  following  rule  for  second  differences:  Employ  the  interpolated  value 
of  the  first  difference  which  corresponds  to  the  middle  of  the  interval  for  which  the 
correction  is  to  be  computed. 

Example:  For  the  Greenwich  date  1915,  AprU,  10<*  IS'*  25™  30%  find  the  moon's  declination. 


Dec, 
Corr. 

18^   (-)4°  56' 
+           6 

4    50 

39'^  7  S. 
09  .5 

30  . 2  S. 

First  diff., 
Corr., 

M.  D., 

No.  min., 

Corr., 

+14'^  487 
+  0   .002 

Second  diff., 
Interval, 

Corr., 

+0'^  009 
+0^ .  213 

Dec., 

+14   .489 
+25°».5 

+(/'.  002 

,  /  369^'.  5 
+16^09^'.  5 

The  difference  for  one  minute  being  + 14''. 487  at  18^^,  and  + 14 ".496  at  IQ'^,  the 
difference  for  one  minute  undergoes  a  change  of  +0''.009  during  one  hour.  The 
time  for  which  it  is  desired  to  obtain  the  difference  is  at  the  middle  instant  between 
18^  0"^  and  18^  25'^.5— that  is,  at  18»^  12'".75,  or  its  equivalent,  18^.213.  With  a 
change  of  +0".009  in  one  hour,  the  change  in  0^.213  is  readily  obtainable;  correcting 
the  minute's  difference  at  18^.0  accordingly,  the  process  of  correcting  the  declination 
becomes  the  same  as  in  simple  interpolation. 

CONVEBSION  OF  TIMES. 

286.  Conversion  of  Time  is  the  process  by  which  any  instant  of  time  that  is 
defined  accordiag  to  one  system  of  reckoning  may  be  defined  according  to  some 
other  system;  and  also  by  which  any  interval  of  time  expressed  in  imits  of  one 
system  may  be  converted  mto  units  of  another. 

287.  Sidereal  and  Mean  Time. — ^Mean  time  is  the  hour  angle  of  the  Mean 
Sun;  sidereal  time  is  the  hour  angle  of  the  First  Point  of  Aries.     Since  the  Right 

Ascension  of  the  Mean  Sun  is  the  angular  distance  between 
the  hour  circles  of  the  First  Point  of  Aries  and  of  the  Mean 
Sun,  mean  time  may  be  converted  into  sidereal  time  by  adding 
to  it  the  Right  Ascension  of  the  Mean  Sun ;  and  similarly,  sidereal 
time  may  be  converted  into  mean  time  by  subtracting  from  it 
the  Right  Ascension  of  the  Mean  Sun. 

This  is  explained  in  figure  37,  which  represents  a  projec- 
tion of  the   celestial  sphere  upon  the   equator.     If  P  be  the 
pole;  QPQ',  the  meridian;  V,  the  First  Point  of  Aries;  M,  the 
position  of  the  mean  sun  (west  of  the  meridian) ;  then  QPV,  or 
Q  the  arc  QV,  is  the  sidereal  time ;  QPM,  or  the  arc  QM,  is  the 

Fig.  37.  mean  time;  and  VPM,  or  the  arc  VM,  is  the  Right  Ascension 

of  the  Mean  Sun.     From  this  it  wiQ  appear  that: 

QV  =  QM  +  VM,  or 
Sidereal  time  ==  Mean  time  +  Right  Ascension  of  Mean  Sun. 


TIME  AND  THE   NAUTICAL  ALMANAC.  109 

If  the  mean  sun  be  on  the  opposite  side  of  the  meridian,  at  M',  then  the  mean 
time  equals  24^  — M'Q.     In  this  case: 

QV  =  yM'-M'Q,  or 

Sidereal  time  =  Right  Ascension  of  Mean  Sun—  (24'*— Mean  time), 
=  Right  Ascension  of  Mean  Sun + Mean  time  — 24**. 

Right  ascension  being  measured  to  the  east  and  hour  angle  to  the  west,  the 
sidereal  time  wiU  therefore  always  equal  the  sum  of  these  two;  but  24**  must  be  sub- 
tracted when  the  sum  exceeds  that  amount. 

From  the  preceding  equations,  we  also  have: 

QM  =  QV-VM;  and 
M'Q  =  VM'-QV,  or 

(24''-M'Q)  =  (24»'+QV)  -  VM'. 

From  this  it  may  be  seen  that  the  mean  time  equals  the  sidereal  time  minus 
the  Right  Ascension  of  the  Mean  Sun,  but  the  former  must  be  increased  by  24** 
when  necessary  to  make  the  subtraction  possible. 

288.  Apparent  and  Mean  Times. — ^Apparent  time  is  the  angle  between  the 
meridian  and  the  hour  circle  which  contains  the  center  of  the  sun;  mean  time  is  the 
angle  between  the  meridian  and  the  hour  circle  which  contains  the  mean  sun.  Since 
the  equation  of  time  represents  the  angle  between  the  hour  circles  of  the  mean  and 
apparent  suns,  it  is  clear  that  the  conversion  of  mean  time  to  apparent  time  may  be 
accomplished  by  the  application  of  the  equation  of  time,  with  its  proper  sign,  to 
the  mean  time ;  and  the  reverse  operation  oy  the  application  of  the  same  quantity, 
in  an  opposite  direction,  to  the  apparent  time. 

The  resemblance  of  these  operations  to  the  interconversion  of  mean  and  sidereal 
times  may  be  observed  if,  in  figure  37,  we  assume  that  PV  is  the  hour  circle  of  the 
true  Sim,  PM  remaining  that  of  the  mean  sun;  tiien  the  arc  QM  will  be  the  mean 
time;  QV,  the  apparent  time;  and  VM,  the  equation  of  time;  whence  we  have  as 
before : 

QV  =  QM  +  VM,  or 
Apparent  time  =  Mean  time  +  Equation  of  time ; 

the  equation  of  time  will  be  positive  or  negative  according  to  the  relative  position  of 
the  two  suns. 

289.  Sidereal  and  Mean  Time  Intervals. — The  sidereal  year  consists  of 
366.25636  sidereal  days  or  of  365.25636  mean  solar  days.  If,  therefore,  M  be  any 
interval  of  mean  time,  and  S  the  corresponding  interval  of  sidereal  time,  the  relations 
between  the  two  may  be  expressed  as  loUows : 

8^366.25636^ 

M     365.25636     ^•^^^^'^^^' 

M    365.25636 
S~366.  25636  ~"'^^^''^^^- 

Therefore,  S  =  1 .  0027379  M  =  M  + .  0027379  M ; 
M  =  0.9972696  S  =S  -.0027304  S. 

If  M=24'*,  8  =  24'' +3™  56'.6;  or,  in  a  mean  solar  day,  sidereal  time  gains  on 
mean  time  3™  56^.6,  the  gain  each  hour  being  9^.8565. 

If  8  =  24**,  M  =  24'*  — 3™  65*.9;  or,  in  a  sidereal  day,  mean  time  loses  on  sidereal 
time  3*"  55^9,  the  loss  each  hour  being  9^8296. 

If  M  and  8  be  expressed  in  hours  and  fractional  parts  thereof, 

S  =  M  +  9«.8565M; 
M- S-9«.8296S. 

Tables  for  the  conversion  of  the  intervals  of  mean  into  those  of  sidereal  time 
and  the  reverse  are  based  upon  these  relations.  Tables  8  and  9  of  this  work  give 
the  values  for  making  these  conversions,  and  similar  tables  are  to  be  foimd  in  the 
Nautical  Almanac. 


110  TIME  AND  THE   NAUTICAL  ALMANAC. 

290.  To  Convert  Mean  Solar  into  Sidereal  Time. — Apply  to  the  local  mean 
time  the  longitude,  adding  if  west  and  subtracting  if  east,  and  thus  obtain  the  Green- 
wich mean  time.  Take  from  the  Nautical  Almanac  the  Right  Ascension  of  the  Mean 
Sun  at  Greenwich  mean  noon,  and  correct  it  for  the  Greenwich  mean  time  by  Table  9 
or  by  the  hourly  difference  of  9*.857.  Add  to  the  local  mean  time  this  corrected 
right  ascension,  rejecting  24^  if  the  sum  is  greater  than  that  amount.  The  result 
wSl  be  the  local  sidereal  time. 

Example:  April  22,  1915,  in  Long.  81°  15'  W.,  the  local  mean  time  is  2^'  00"  00'  p.  m.    Required 
the  corresponding  local  sidereal  time: 

L.  M.  T.,        22<J  2^  00°"  00*         R.  A.  M.  S.,  22i  O'',  l*"  57"  50'.86        L.  M.  T.,  2^  OO"*  00* 

Long.,     +  5    25    00  Red.  for  T"  25""  (Tab.  9),  +        1     13.10        R.  A.  M.  S.,+1    59    03.96 

G.  M.  T.,       22    7    25    00  R.  A.  M.  S.,  7'»  25™,  1    59    03.96        L.  S.  T.,  3    59    03.96 

Example:  April  22,  1915,  in  Long.  75°  E.,  the  local  mean  time  is  4^  00"  00*  a.  m.     Required  the 
local  sidereal  time. 

L.  M.  T.,      21^  16^  00"  00*         R.  A.  M.  S.,  21^  O^*,  l"*  53"  54*. 31        L.M.T.,  21^  16»'  00"  00* 

Long.,    -  5    00    00  Red.  for  IV'  (Tab.  9),  +         1    48  .42        R.  A.  M.  S.,+1    55    42  .73 

G.  M.  T.,   21  11  00  00    R.  A.  M.  S.,  ll^       1  55  42.73    L.S.T.,  21  17  55  42.73 

In  these  examples  the  reduction  of  the  R.  A.  M.  S.  has  formed  a  separate  operas 
tion  in  order  to  make  clear  the  process.  It  would  be  as  accurate  to  add  together 
directly  L.  M.  T.,  R.  A.  M.  S.,  and  Red.,  and  the  work  would  thus  be  rendered  more 
brief. 

291.  To  Convert  Sidereal  into  Mean  Solar  Time. — ^Take  from  the  Nautical 
Almanac  the  Right  Ascension  of  the  Mean  Sun  for  Greenwich  mean  noon  of  the 
given  astronomical  day,  and  apply  to  it  the  reduction  for  longitude,  either  by  Table  9 
or  by  the  hourly  difference  of  9^.857,  and  the  result  will  be  the  Right  Ascension  of 
the  Mean  Sun  at  local  mean  noon,  which  is  equivalent  to  the  local  sidereal  time  at 
that  instant.  Subtract  this  from  the  given  local  sidereal  time  (adding  24^  to  the 
latter  if  necessary),  and  the  result  will  be  the  interval  from  local  mean  noon,  expressed 
in  units  of  sidereal  time.  Convert  this  sidereal  time  interval  into  a  mean  time  interval 
by  subtracting  the  reduction  as  given  by  Table  8  or  by  the  hourly  difference  of  9^.830; 
the  result  will  be  the  local  mean  time. 

Example:  April  22,  1915,  a.  m.,  in  Long.  75°  E.,  the  local  sidereal  time  is  17''  55"  42".73.     What  is 
the  local  mean  time? 

Astronomical  day,  April  21. 

L.  S.  T.,  17''  55"  42'.73  R.  A.  M.  S.,  Or.  21^  0",  1"  53"  54'.31 

R.  A.  M.  S.,  -  1    63    05  .03  Red.  for  -5h  long.  (Tab.  9),         -  49  .28 


Sid.  interval  from  L.  M.  noon,  16    02    37.70  R.  A.  M.  S.,  local  0",  1    53    05.03     ' 

Red.  for  sid.  interval  (Tab.  8) ,  2    37  .  70 

L.  M.  T.,  21*  16    00    00  .00 

Example:  April  22,  1915,  p.  m.,  at  a  place  in  Long.  81°  15^  W.,  the  sidereal  time  is  Z^  59"  03'.96. 
What  is  the  corresponding  mean  time? 

Astronomical  day,  April  22. 

L.  S.  T.,  3"  59"  03'.96  R.  A.  M.  S.,  Gr.  22''  0",  1"  57"  50«.86 

R.  A.  M.  S.,  -1    58    44  .25  Red.  for  +5"  25"  long.  (Tab.  9),  +        0    53  .39 

Sid.  interval  from  L.M.Noon,    2    00    19.71  R.  A.  M.  S.,  local  0",  1    58    44.25 

Red.  for  sid.  interval  (Tab.  8),  -      0    19  .71 

L.  M.  T.,  22^  2    00    00  .00 

292.  To  Convert  Mean  into  Apparent  Time  and  the  Reverse. — ^Find  the 
Greenwich  time  corresponding  to  the  given  local  time.  If  apparent  time  is  given,  find 
the  Greenwich  apparent  time  and  take  the  equation  of  time  from  Page  I  of  the 
Almanac.  If  mean  time,  find  the  Greenwich  mean  time  and  take  the  equation  of 
time  from  Page  II.  ^  Correct  the  equation  of  time  for  the  required  instant  and  apply 
it  with  its  proper  sign  to  the  given  time. 


I 


TIME   AND  THE   NAUTICAL  ALMANAC.  Ill 

Example:  April  21,  1915,  in  Long,  81°  15''  W.,  find  the  local  apparent  time  corresponding  to  a  local 
mean  time  of  S*"  05"  00"  p.  m. 

L.  M.  T.,  21'»    S^  05"'  00* 
Long.,      +        5    25    00 

G.  M.  T.,    21    8    30    00 


L.  M.  T.,  21*  3"  05°  00* 

Eq.  t.,  +       1  10  .78 

Eq.  t.,  0",  1"»  06«.27 
Corr.,  +     4  .51 

L.A.T.,  21  3  06  10.78 

Eq.  t.,    1  10  .78 
H.  D.,   +    0-.5^i 
G.  M.  T.,  +   S^.^ 

Corr.,        +       4'. 513 
{Add  to  mean  time.) 

Example:  April  3,  1915,  in  Long.  81**  15'  E.,  the  local  apparent  time  is  S**  45™  00'  a.  m.     Required 
the  mean  time. 

L.  A.  T.,        2^  20»"  45«  00* 
Long.,       -         5   25    00 

G.  A.  T.,        2    15    20     00 


L.A.T., 
Eq.  t.. 

2^  20^  45"'  00" 
+       3  43.59 

Eq,  t.,  0^, 
Corr., 

Eq.  t., 

H.D., 
G.  A.  T., 

3°  55'.  16 
11 .  57 

L.  M.  T., 

2  20  48  43.59 

3  43  .  59 

0«.755 
+    15^  33 

Corr.,  -         11«.57 

(Add  to  apparent  time.) 

293.  To  Find  the  Houe  Angle  of  a  Body  from  the  Time,  and  the 
Reverse. — In  figure  37,  if  M  and  M'  represent  the  positions  of  celestial  bodies 
instead  of  those  of  the  mean  sun  as  before  assumed,  then  the  hour  angles  of  the 
bodies  will  be  Q  M  and  24^  — M'  Q,  respectively,  and  their  right  ascensions  will  be 
V  M  and  V  M'. 

As  before,  we  have : 

QV    =QM+VM, 

=VM'-M'Q; 
QM    =QV-VM; 
M'Q  =VM'-VQ,  or 
(24''-M'  Q)  =(24'»  +  Q  V)  -V  M'. 

Substituting,  therefore,  Tiour  angle  of  the  hody  for  mean  time,  and  right  ascejision 
of  the  hody  for  Hight  Ascension  of  the  Mean  Sun,  the  rules  previously  given  for  the 
conversion  of  mean  and  sidereal  times  will  be  applicable  for  the  conversion  of  hour 
angle  and  sidereal  time.  Thus,  the  sidereal  time  is  equal  to  the  sum  of  the  right 
ascension  of  the  body  and  its  hour  angle,  subtracting  24*'  when  the  sum  exceeds 
that  amount;  and  the  hour  angle  equals  the  sidereal  time  minus  the  right  ascension 
of  the  body,  24**  being  added  to  the  former  when  necessary  to  render  the  subtraction 
possible. 

Example:  In  Long.  81°  15'  W.,  on  April  25,  1915,  at  12''  10»  30*  (astronomical)  mean  time,  find  the 
hour  angle  of  Sirius. 

L.  M.  T.,       12"  10»  30'  L.  M.  T.,  12"  lO""  30* 

Long.,      +    5  25    00  R.  A.  M.  S.,  0",  +    2  09    40.53 

Red.  (Tab.  9),     +         2    53.39 

G.  M.  T.,       17  35    30 


L.  S.  T.,  14   23    03.92 

R.  A.  Sirius,       -     6  41    24.67 


H.  A.  Sirius,  7  41    39.25 

Example:  May  9, 1915,  Arcturus  being  2"  27*  42'.52  east  of  the  meridian,  find  the  local  sidereal  time. 

24"00'»00*  H.  A.,        21"32»17'.48 

H.  A.,     2  27    42.52  E.  R.  A.,  +  H   11    49.99 


H.  A.,  21   32     17.48  W.  L.  S.  T.,    11   44    07.47 
Or  thus: 

H.  A.,     -  2"  27"' 42".  52 

R.  A.,     +  14   11    49.99 

L.  S.  T.,      11  44    07.47 


112 


TIME  AND  THE   NAUTICAL  ALMANAC. 


294.  Many  navigators  find  the  conversion  of  time  much  simplified  and  more 
easily  grasped  by  rou^y  plotting  the  elements  as  they  are  presented  in  any  given 
case,  in  a  figure  drawn  on  the  plane  of  the  celestial  equator.  Noting  the  known  ele- 
ments and  the  elements  requu-ed  to  be  found,  a  study  of  the  figure  shows  very 
quickly  how  to  combine  the  Known  elements  to  get  the  unknown  elements. 

Following  this  method,  the  examples  of  articles  290,  291,  and  293  are  here 
solved  as  an  alternative  to  the  preceding  treatment,  since  it  is  found  that,  for  many 
who  have  learned  this  method  of  procedure  in  the  beginning,  every  difficulty  in 
reckoning  or  converting  time  has  been  obviated.     Although  the  explanation  may 

appear  somewhat  long,  the  actual  plotting  and  solution 
01  any  given  case  take  only  a  few  seconds  when  the 
method  is  understood.  In  the  figures,  P  represents  the 
elevated  pole;  Q,  the  intersection  of  the  local  meridian 
with  the  equator;  G,  the  intersection  of  the  meridian 
of  Greenwich  with  the  equator;  V,  the  First  Point  of 
Aries  (Vernal  Equinox);  S^,  the  mean  sun;  Sa,  the 
apparent  sun;  and  %,  a  star  or  planet. 

First  Example  of  Article  290.     (See  Figure  38.) 

Draw  a  circle  to  represent  the  plane  of  the  celestial 
equator,  P  being  the  projection  of  the  pole,  and  PQ  the 
projection  of  the  local  meridian.  From  P  draw  the 
projection  of  the  hour  circle  of  the  Greenwich  meridian 
which  (since  the  longitude  is  west)  is  laid  off  to  the  right 
or  eastward  of  the  local  meridian  so  that  the  arc  Q(l 
equals  the  longitude.  The  arrow  indicates  westerly  direction  and  shows  the  direction  in 
wliich  the  hour  circles  of  the  heavenly  bodies  move  around  the  circle  on  the  earth's  axis. 
The  L.  M.  T.  being  p.  m.,  we  lay  off  the  hour  circle  of  the  mean  sun  to  the  westward 
of  the  local  meridian  so  that  the  arc  QS^  equals  the  L.  M.  T.  We  see  at  once  from 
the  figure  that  the  G.  M.  T.  (the  position  of  the  hour  circle  of  the  mean  sun,  Sm,  with 
reference  to  the  Greenwich  meridian)  is  the  arc  GQSm,  which  ecjuals  Long.  +  L.  M.  T. 
Having  thus  found  the  G.  M.  T.,  we  can  find  the  right  ascension  of  the  mean  sun  at 
that  instant  from  the  Nautical  Almanac  (picked  out  for  the  day  and  corrected  for  the 
G.  M.  T.)  which,  in  this  case,  is  I''  59°^  03^96.  The  correction  is  ( + )  or  additive  to  the 
angle  which  represents  the  R.  A.  M.  S.  for  Greenwich  Mean  Noon  because  this  angle 

has  been  increased  by  this  amount  owing  to  the 
gain  of  the  Vernal  Ec^^uinox  over  the  mean  sun  for 
the  angle  through  which  the  mean  sun  has  traveled 
from  the  Greenwich  meridian.  The  mean  sun  is  to 
the  eastward  of  the  Vernal  Equinox  by  the  amount 
of  its  right  ascension.  We  therefore  lay  off  PV, 
the  hour  circle  of  the  Vernal  Equinox,  so  that  the 
arc  VSm  equals  the  R.  A.  M.  S.  Since  the  L.  S.  T. 
equals  the  H.  A.  of  the  Vernal  Equinox,  we  see  at 
once  from  the  figure  that  the  L.  S.  T.  equals  R.  A.  M. 
S.  +  L.M.T. 


Fig.  38. 


Second  Example  of  Article  290.  (See  Figure  39.) 


TVest 


Fig.  39. 


Draw  a  circle  to  represent  the  plane  of  the  celes- 
tial equator.  Project  the  pole  P  and  the  local  me- 
ridian JPQ.  Draw  the  arrow  pointed  west  to  show  the 
direction  in  which  the  hour  circles  move.  Since  the  longitude  is  east,  we  know  that 
the  Greenwich  meridian  is  to  the  westward  of  the  local  meridian,  and  we  draw  PG,  the 
Greenwich  meridian,  so  that  the  arc  QG  equals  the  longitude,  equals  5  hours.  Since 
the  L.  M.  T.  is  4*'  00°^  00»  a.  m.,  we  know  that  it  will  be  12^^-4^^  equals  W  before  the 
sun  crosses  the  local  meridian;  hence  we  lay  off  the  arc  QSm  to  equal  the  sun's 
H.  A.,  which  equals  8**,  and  draw  PSm,  the  hour  circle  of  the  mean  sun.  We  see 
from  the  figure  that  the  hour  angle  of  the  mean  sun  from  Greenwich  (G.  M.  T.)  is 
equal  to  24^*  —  (Long.  4-  H.  A.  Sm),  and  that,  since  the  mean  sun  must  travel  around 
the  arc  to  the  west  from  Sm  to  G  to  make  the  time  0  hours  on  April  22  at 


TIME   AND    THE   NAUTICAL   ALMANAC. 


113 


FlQ.  40. 


Greenwich,  the  date  must  be  April  21,  and  the  G.  M.  T.  is  11  hours.  For  this 
Greenwich  date,  we  get,  from  tne  Nautical  Almanac  (corrected  for  G.  M.  T.)  the 
R.  A.  M.  S.  equal  to  1^  55™  42^.73,  which  is  the  amount  the  hour  circle  of  the  mean 
sun  is  to  the  eastward  of  the  hour  circle  of  the  Vernal  Equinox.  The  correction  is  + 
or  additive  for  the  reason  given  in  the  preceding  example.  Lay  ofif  the  arc  SmV 
equal  to  the  II .  A.  M.  S.  and  draw  the  hour  circle  of  the  Vernal  Equinox  PV. 
An  uispection  of  the  figure  shows  us  that  the  L.  S.  T.  is  the  arc  QGV  which  is  equal 
to  the  Long.  +  G.  M.  T.  +  R.  A.  M.  S.,  or  to  the  L.  M.  T.  +  the  R.  A.  M.  S. 
We  also  see  that  L.  M.  T.  equals  the  Long.  +  G.  M.  T. 

First  Example  of  Article  291.    (See  Figure  40.) 

Draw  the  figure  as  shown,  laying  off  the  longitude 
equal  to  5  hours  east,  to  the  westward  from  Q,  thus 
finding  the  Greenwich  meridian  G.  The  given  L.  S.  T. 
is  18  hours,  so. lay  off  QV  (equal  to  18  hours)  to  the 
westward  from  Q,  giving  the  j)osition  of  V,  the  Vernal 
Equinox  or  First  Point  of  Aries,  for  the  instant  de- 
sired. The  problem  is  to  plot  the  position  of  the 
mean  sun  at  this  instant,  and  thence  find  its  local 
hour  angle,  or  the  L.  M.  T.  We  plot  this  position  of 
the  mean  sun  by  laying  off  its  right  ascension  to 
the  eastward  from  V.  The  R.  A.  M.  S.  is  found  from 
the  Almanac  for  a  particular  instant  which  is  at 
Greenwich  mean  noon  of   the  astronomical   date, 

April  21,  and  which  we  find  is  1*»  53"  54'.31.  Plot  in  Sn^,  over  the  Greenwich  merid- 
ian and  lay  off  tliis  angle  GVj,  to  the  westward  from  G,  giving  us  the  position  of  V 
at  Greenwich  mean  noon.  As  we  are  reckoning  hour  angles  from  the  local  meridian, 
we  must  move  the  sun  back  to  Q  and  find  the  position  Vj  at  the  instant  of  local  mean 
noon.  To  find  Vj  we  must  find  the  angle  QV3  which  will  be  less  than  GV^,  as  the 
First  Point  of  Anes  always  advances  faster  towards  the  west  than  the  mean  sun. 
The  amount  of  this  gain  of  the  Vernal  Equinox  over  the  mean  sun  depends  on  the 
angular  distance  through  which  the  mean  sun  travels,  i.  e.,  in  this  case  from  Q  to 
G  equals  the  longitude,  equals  5  hours.  From  Table  9  we  find  the  gain,  which  is 
represented  by  the  sector  Cj  in  the  figure,  to  be  49".28  for  the  5  hours,  so  that  QV, 
equals  GVi-49".28,  equals  l**  53"*  54».31-49«.28,  equals  1*^  53""  05«.03.  Now  we 
have  the  position  Vj  lor  the  instant  of  time  when  the  mean  sun  was  at  Q,  that  is 
for  the  position  8^2  or  local  mean  noon.  For  the  instant  of  time  desired  the  Vernal 
Equinox  is  not  at  V2  but  at  V  and  at  this  instant  we  must  find  Sni2.  The  Vernal 
Equinox  has  moved  from  V,  to  the  westward  to  V  or  through  the  arc  V,  V  which 
equals  QV-QV2,  equals  I?'' 55"°  42«.73  - 1^  53""  05«.03,  equals  16^  02°>  37».70,  which 
is  caUed  a  sidereal  interval.  During  tliis  travel  of  the 
Vernal  Equinox  the  mean  sun  wUl  lose  a  certain  an- 
gular amount  on  the  Vernal  Equinox,  depending  on 
the  travel  of  the  latter,  which  travel  is  16^  02''^  37^70. 
From  Table  8,  we  find  for  tliis  travel  that  the  loss 
will  be  2""  37''.70,  which  is  represented  by  the  sector 
Ca  in  the  figure,  so  that  the  angle  QSm  is  V,  V  — 2°' 


37«.70,  equals  IQ^  02'°  37«.70-2'"  37«.70,  equals  16'' 
OO""  00*,  which,  from  the  figure,  equals  the  desired  L. 
M.  T. 

Second  Example  of  Article  291.    (See  Figure  41.) 

Draw  the  figure  as  shown,  laving  off  the  lon^tude 
equal  to  5^  west,  to  the  eastward,  from  Q,  thus  nnding 
the  Greenwich  meridian  G.  The  problem  is  similar 
to  the  above  problem  except  that  in  moving  the  mean 
sun  from  G  to  Q  we  see  tnat  the  angle  Smi  V^  is  in- 
creased to  find  Siia2  V2,  as  the  Vernal  Equinox  has  gained  a  certain  amount  on  the 
mean  sun  during  the  travel  of  the  sun  to  the  westward  from  G  to  Q.  For  the  travel 
of  V2  to  V,  the  mean  sun  will  travel  from  Smj  to  Sm,  losing  a  certain  amount  on  the 
Vernal  Equinox  for  the  travel  of  V,  V  of  the  latter,  and  we  find  QS^  equals  the  L.  M.  T. 
21594°— 14 8 


Fig.  41. 


114 


TIME   AND    THE   NAUTICAL   ALMANAC. 


Fig.  42. 


First  Example  of  Article  293.    (See  Figure  42.) 

Draw  the  figure  as  explained  above,  using  longitude  given  equals  5  hours  west, 
and  L.  M.  T.  given,  12  hours  (  +  ).  Then  G.  M.  T.  equals  12  +  5  or  17  hours  (+ )  of 
April  25.     For  this  instant  of  time  the  mean  sun  is  plotted  at  Sm. 

Now  the  problem  is,  knowing  the  positions  of  G,  Q, 
and  Sm,  to  find  the  position  of  the  given  star  on  the  di- 
agram, and  thence  its  local  hour  angle.  If  we  can  find 
the  relative  angles  from  the  mean  sun  and  from  the 
star  to  some  third  object,  we  can  plot  this  third  object 
and  find  the  rec[uired  hour  angle  of  the  star.  The  third 
object  is  the  First  Point  of  Aries  (the  Vernal  Equinox) 
and  the  angles  from  the  mean  sun  and  from  the  star 
are  the  right  ascensions  of  the  mean  sun  and  the  star. 
The  right  ascension  of  the  mean  sun  is  found  from  the 
Almanac,  not  for  the  instant  we  want,  but  for  the 
Greenwich  mean  noon  of  the  date.  This  R.  A.  must 
be  increased  by  a  correction  for  the  angle  through 
which  the  mean  sun  has  traveled  since  noon,  —  the 
G.  M.  T.  In  the  problem  the  E.  A.  M.  S.  so  increased 
is  2  hours,  so  we  fay  off  SmV  from  Sm  to  the  westward 
2  hours,  plotting  the  position  of  the  Vernal  Equinox  at  the  desired  instant.  From 
the  Almanac  we  find  the  R.  A.  of  the  star  to  be  6  hours,  and  we  lay  off  V  *  equal 

to  6  hours   to  the  eastward.    The  required  local  hour 
V  angle  of  the  star  is  then  Q  *  whicn  equals  QSni  + 

VSm-V  *  equals  L.  M.  T.  +  R.  A.  M.  S.-R.  A.  equals 
12i^+2^-6'»  equals  8  hours. 

Second  Example  of  Article  293.    (See  Figure  43.) 

Draw  the  figure  as  before.  The  problem  is,  know- 
ing the  position  of  the  star  at  a  certain  instant,  to  find 
the  L.  S.  T.,  so  we  must  plot  the  position  of  the  star, 
then  that  of  the  Vernal  Equinox.  The  local  hour  angle 
of  the  latter  is  the  required  L.  S.  T. 

The  hour  angle  of  the  star  is  given  as  2  hours,  bear- 
ing east  from  the  meridian,  so  lay  off  Q  sfc  =2  hours  to 
the  east  from  Q.  Now  find  from  the  Almanac  the  R.  A. 
of  the  ;ic  which  is  14  hours,  and  lay  off  >|c  V  equal  to  14''  to 
the  westward  from  3\^ .  The  L.  S.  T.  is  then  QV,  equals 
V  *  —  Q  *,  equals  the  R.  A.  *  —  H.  A.  *,  equals  14^  —  2^  equals  12  hours. 

When  doubt  exists  as  to  the  Greenwich  date  the  navigator,  by  plotting  the  data 
in  exactly  the  same  way  as  explained  above,  can  at  once  remove  aU  doubt  on  the 
subject  and  can  get  the  correct  G.  M.  T. 


TVest 

Fig.  43. 


CHAPTER  X. 
OOEEEOTION  OF  OBSEEVED  ALTITUDES. 


294.  The  true  altitude  of  a  heavenly  body  at  any  place  on  the  earth's  surface 
is  the  altitude  of  its  center,  as  it  would  be  measured  by  an  observer  at  the  center  of 
the  earth,  above  the  plane  passed  through  the  center  of  the  earth  at  right  angles 
to  the  direction  of  the  zenith. 

The  observed  altitude  of  a  heavenly  body,  as  measured  at  sea,  may  be  converted 
to  the  true  altitude  by  the  application  of  the  following-named  corrections:  Index 
Correction,  Dip,  Refraction,  Parallax,  and  Semidiameter.  The  corrections  for  parallax 
and  semidiameter  are  of  inappreciable  magnitude  in  observations  of  the  fixed  stars, 
and  with  planets  are  so  small  that  they  need  only  be  regarded  in  refined  calculations. 
In  observations  with  the  artificial  horizon  there  is  no  correction  for  dip. 

For  theoretical  accuracy,  the  corrections  should  be  applied  in  the  order  in  which 
they  are  named,  but  in  ordinary  nautical  practice  the  order  of  application  makes 
no  material  difference,  except  in  the  case  of  the  parallax  of  the  moon  as  explained 
in  article  306;  and  hence,  instead  of  turning  to  the  separate  tables  referred  to  in  the 
following  articles  as  containing  these  corrections,  their  combined  amount,  given  in 
Table  46,  may  be  applied  to  observed  altitudes  of  the  sun,  the  planets,  and  the  stars, 
after  the  manner  shown  in  article  308. 

INDEX  CORRECTION. 

295.  This  correction  is  fully  explained  in  articles  249  and  250,  Chapter  VIII. 

REFRACTION. 

296.  It  is  known  by  various  experiments  that  the  rays  of  light  deviate  from 
their  rectilinear  course  m  passing  obliquely  from  one  medium  into  another  of  a 
different  density;  if  the  latter  be  more 
dense,  the  ray  will  be  bent  toward  the  per- 
pendicular to  the  line  of  junction  of  the 
media;  if  less  dense,  it  will  be  bent  away 
from  that  perpendicular. 

The  ray  of  light  before  entering  the 
second  medium  is  called  the  in.ident  ray; 
after  it  enters  the  second  medium  it  is 
called  the  refracted  ray,  and  the  difference  of 
direction  of  the  two  is  called  the  refraction. 

The  rays  of  li^ht  from  a  heavenly  body 
must  pass  through  the  atmosphere  before 
reaching  the  eye  of  an  observer  upon  the 
surface  of  the  earth.  The  earth's  atmos- 
phere is  not  of  a  uniform  density,  but  is 
most  dense  near  the  earth's  surface,  gradu- 
ally decreasing  in  density  toward  its  upper 
limit;  hence  the  path  of  a  ray  of  light,  by 
passing  from  a  rarer  medium  into  one  con- 
tinually increasing  density  becomes  a  curve, 
which  is  concave  toward  the  earth.     The 

last  direction  of  the  ray  is  that  of  a  tangent  to  the  curved  path  at  the  eye  of  the 
observer,  and  the  difference  of  the  direction  of  the  ray  before  entering  the  atmosphere 
and  this  last  direction  constitutes  the  refraction. 

297.  To  illustrate  this,  consider  the  earth's  atmosphere  as  shown  in  figure  44; 
let  SB  be  a  ray  from  a  star  S,  entering  the  atmosphere  at  B,  and  bent  into  the  curve 
BA;  then  the  apparent  direction  of  the  star  is  AS',  the  tangent  to  the  curve  at  the 
point  A,  the  retraction  being  the  angle  between  the  lines  BS  and  AS'.     If  CAZ  is 

115 


116 


CORRECTION   OF   OBSERVED  ALTITUDES. 


the  vertical  line  of  the  observer,  by  a  law  of  optics  the  vertical  plane  of  the  observer 
which  contains  the  tangent  AS'  must  also  contain  the  whole  curve  BA  and  the  incident 
ray  BS.  Hence  refraction  increases  the  apparent  altitude  of  a  star  without  affecting 
its  azimuth. 

At  the  zenith  the  refraction  is  nothing.  The  less  the  altitude  the  more  obliquely 
the  rays  enter  the  atmosphere  and  the  greater  will  be  the  refraction.  At  the  horizon 
the  retraction  is  the  greatest. 

298.  The  refraction  for  a  mean  state  of  the  atmosphere  (barometer  30'°,  Fahr. 
thermometer  50°)  is  given  in  Table  20  A;  the  combined  refraction  and  sun's  parallax 
in  Table  20  B;  and  the  combined  refraction  and  moon's  parallax  in  Table  24. 

Since  the  amount  of  the  refraction  depends  upon  the  density  of  the  atmosphere, 
and  the  density  varies  with  the  pressure  and  the  temperature,  which  are  indicated 
by  the  barometer  and  thermometer,  the  true  refraction  is  found  by  applying  to  the 
mean  refraction  the  corrections  to  be  found  in  Tables  21  and  22;  these  are  deduced 
from  Bessel's  formulae,  and  are  regarded  as  the  most  reliable  tables  constructed.  It 
should  be  remembered,  however,  that  under  certain  conditions  of  the  atmosphere  a 
very  extraordinary  deflection  occurs  in  rays  of  light  which  reach  the  observer's  eye 
from  low  altitudes  (that  is,  from  points  near  the  visible  horizon),  the  amount  of 
which  is  not  covered  by  the  ordinary  corrections  for  pressure  and  temperature ;  the 
error  thus  created  is  discussed  under  Di'p  (art.  301) ;  on  account  of  it,  altitudes  less 
than  10°  should  be  avoided. 

Example:  Required  the  refraction  for  the  apparent  altitude  5°,  when  the  thermometer  is  at  20® 
and  the  barometer  at  SO'^.e?. 

The  mean  refraction  by  Table  20  A  is,        9'  52''' 
The  correction  for  height  of  barometer  is,  +  13 
The  correction  for  the  temperature,  +  42 


10  47 


True  refraction, 

299.  The  correction  for  refraction  should  always  be  subtracted,  as  also  that 
for  combined  refraction  and  parallax  of  the  sim ;  the  correction  for  combined  refrac- 
tion  and  parallax  of  the  moon  is  invariably  additive. 

DIP. 

300.  Dip  of  the  Horizon  is  the  angle  of  depression  of  the  visible  sea  horizon  below 
the  true  horizon,  due  to  the  elevation  of  the  eye  of  the  observer  above  the  level  of 
the  sea. 

In  figure  45  suppose  A  to  be  the  position  of  an  observer  whose  height  above  the 
level  of  the  sea  is  AB.     CAZ  ia  the  true  vertical  at  the  position  of  the  observer,  and 

AH  is  the  direction  of  the  true  horizon,  S 
being  an  observed  heavenly  body.  Draw 
ATH'  tangent  to  the  earth's  surface  at  T. 
Disregardmg  refraction,  T  will  be  the  most 
distant  point  visible  from  A.  Owing  to 
refraction,  however,  the  most  distant  visi- 
ble point  of  the  earth's  surface  is  more  re- 
mote from  the  observer  than  the  point  T, 
and  is  to  be  found  at  a  point  T',  in  figure 
46.  But  to  an  observer  at  A  the  point  T' 
will  appear  to  lie  in  the  direction  of  AH", 
the  tangent  at  A  to  the  cm-ve  AT'.  If  the 
vertical  plane  were  revolved  about  CZ  as 
an  axis,  the  line  AH  would  generate  the 
plane  of  the  true  horizon,  while  the  pomt 
T'  would  generate  a  small  circle  of  the 
terrestrial  sphere  called  the  Visible  or  Sea 
Horizon.  The  Dip  of  the  Horizon  is 
HAH'',  being  the  angle  between  the  true 
horizon  and  the  apparent  direction  of  the 
sea  horizon.  Values  of  the  dip  are  given 
m  Table  14  for  various  heights  of  the  observer's  eye,  and  in  the  calculation  of  the 
table  allowance  has  been  made  for  the  effect  of  atmospheric  refraction  as  it  exists 
under  normal  conditions. 


FlO.  45. 


CORRECTION   OF   OBSERVED  ALTITUDES. 


117 


FlQ.  46. 


301.  The  fact  must  be  emphasized,  however,  that  under  certain  conditions  the 
deflection  of  the  raj  in  its  path  from  the  horizon  to  the  eye  is  so  irregular  as  to  give  a 
value  of  the  dip  widely  different  from  that  which  is  tabulated  for  the  mean  state  of 
atmosphere.  These  irregularities  usually  occur  when  there  exists  a  material  differ- 
ence between  the  temperature  of  the  sea  water  and  that  of  the  air,  and  they  attain  a 
maximum  value  in  calm  or  nearly  cahn  weather,  when  the  lack  of  circulation  permits 
the  air  to  arrange  itself  in  a  series  of  horizontal  strata  of  different  densities,  the  denser 
strata  being  below  when  the  air  is  warmer,  and  the  reverse  condition  obtaining  when 
the  air  is  cooler.  The  effect  of  such  an  arrangement  is  that  a  ray  of  light  from  the 
horizon  in  passing  through  media  of  different  densities,  undergoes  a  refraction  quite 
unlike  that  whicn  occurs  in  the  atmosphere  of  much  more  nearly  homogeneous 
density  that  exists  under  normal  conditions. 

Various  methods  have  been  suggested  for  computing  the  amount  of  dip  for 
different  relative  values  of  temperature  of  air  and  water,  but  none  of  these  afford  a 
satisfactory  solution,  there  behig  so  many  ele- 
ments involved  which  are  not  susceptible  of 
determination  by  an  observer  on  shipboard 
that  it  will  always  be  difficult  to  arrive  at 
results  that  may  be  depended  upon. 

As  the  amount  of  difference  between  the 
actual  and  tabulated  values  of  the  dip  due  to 
this  cause  may  sometimes  be  very  consider- 
able— reliable  observations  having  frequently 
E laced  it  above  10',  and  values  as  high  as  32' 
aviag  been  recorded — it  is  necessary  for  the 
navigator  to  be  on  his  guard  against  the 
errors  thus  produced,  and  to  reco^ze  the 
possible  inaccuracy  of  all  results  derived  from 
observations  taken  under  unfavorable  condi- 
tions. Without  attempting  to  give  any  method 
for  the  determination  of  the  amount  of  the  ex- 
traordinary variation  in  dip,  the  following  rules  may  indicate  to  the  navigator  the  con- 
ditions under  which  caution  must  be  observed,  and  the  direction  of  probable  error: 

(a)  A  displacement  of  the  horizon  should  always  be  suspected  when  there  is  a 
marked  difference  between  the  temperatures  of  air  and  sea  water;  this  fact  should 
be  especially  kept  in  miad  in  regions  such  as  those  of  the  Red  Sea  and  the  Gulf 
Stream,  where  the  difference  frequently  exists. 

(&)  The  error  in  the  tabulated  value  of  the  dip  will  increase  with  an  increase  in  the 
difference  of  temperature,  and  will  diminish  with  an  increase  in  the  force  of  the  wind. 

(c)  The  error  will  decrease  with  the  height  of  the  observer's  eye;  hence  it  is 
expedient,  especially  when  error  is  suspected,  to  make  the  observation  from  the  most 
elevated  position  available. 

(d)  When  the  sea  water  is  colder  than  the  air  the  visible  horizon  is  raised  and  the 
dip  is  decreased;  therefore  the  true  altitude  is  greater  than  that  given  by  the  use  of 
the  ordinary  dip  table.  When  the  water  is  warmer  than  the  air,  the  horizon  is 
depressed  and  the  dip  is  increased.  At  such  times  the  altitude  is  really  less  than  that 
found  from  the  use  of  the  table. 

The  same  cause,  it  may  be  mentioned  here,  affects  the  kindred  matter  of  the 
visibihty  of  objects.  When  the  air  is  warmer,  terrestrial  objects  are  sighted  from  a 
greater  distance  and  appear  higher  above  the  horizon  than  under  ordinary  conditions. 
When  the  water  is  warmer  than  the  air,  the  distance  of  visibility  is  reduced,  and 
terrestrial  objects  appear  at  a  less  altitude. 

302.  What  has  been  said  heretofore  about  the  dip  supposes  the  horizon  to  be 
free  from  all  intervening  land  or  other  objects;  but  it  often  happens  that  an  obser- 
vation is  required  to  be  taken  from  a  ship  sailing  along  shore  or  at  anchor  in  harbor, 
when  the  sun  is  over  the  land  and  the  shore  is  nearer  the  ship  than  the  visible  sea 
horizon  would  be  if  it  were  unconfined;  in  this  case  the  dip  will  be  different  from 
that  of  Table  14,  and  wiU  be  greater  the  nearer  the  ship  is  to  that  point  of  the  shore 
to  which  the  sun's  image  is  brought  down.  In  such  case  Table  15  gives  the  dip  at 
different  heights  of  the  eye  and  at  different  distances  of  the  ship  from  the  land. 

303.  The  dip  is  always  to  be  subtracted  from  the  observed  altitude. 


118 


COKEECTION   OF   OBSERVED  ALTITUDES. 


PARALLAX. 

304.  The  'parallax  of  a  heavenly  body  is,  in  general  terms,  the  an^le  between 
two  straight  lines  drawn  to  the  body  from  different  points.  But  in  Nautical  Astron- 
omy geocentric  parallax  is  alone  considered,  this 
being  the  difference  between  the  positions  of  a 
heavenly  body  as  seen  at  the  same  instant  from 
the  center  or  the  earth  and  from  a  point  on 
its  surface. 

The  zenith  distance  of  a  body,  S  (fig.  47), 
seen  from  A,  on  the  surface  of  the  earth,  is  ZAS; 
seen  from  C  it  is  ZCS;  the  parallax  is  the  dif- 
ference of  these  angles,  ZAS  — ZCS=ASC. 

Parallax  in  altitude  is,  then,  the  angle  at 
the  heavenly  body  subtended  by  the  radius 
of  the  earth. 

If  the  heavenlj^  body  is  in  the  horizon  as 
at  H',  the  radius,  being  at  right  angles  to  AH', 
subtends  the  greatest  possible  angle  at  the 
star  for  the  same  distance,  and  this  angle  is 
called  the  horizontal  parallax.  The  parallax 
is  less  as  the  bodies  are  farther  from  the  earth, 
as  will  be  evident  from  the  figure. 


Fig.  47 


Let  par.  =  parallax  in  altitude,  ASC; 

Z  =  SAZ,  the  apparent  zenith  distance  (corrected  for  refraction); 

R=AC,  the  radius  of  the  earth;  and 

D  =  CS,  the  distance  of  the  object  from  the  center  of  the  earth. 

Then,  since  SAC  =  180°-SAZ,  the  triangle  ASC  gives: 

R  sin  Z 


sm  par.  = 


D 


and 


If  the  object  is  in  the  horizon  at  H',  the  ai^le  AH'C  is  the  horizontal  parallax, 
denoting  it  by  H.  P.  the  right  triangle  AH'C  gives: 


sinH.  P.=§. 


R. 


Substituting  this  value  of  j^  in  the  above, 

sin  par.  =  sin  H.  P.  sin  Z. 

If  h=SAIl',  the  apparent  altitude  of  the  heavenly  body,  then  Z  =  90°  —  A;  hence, 

sin  par.  =sin  H.  P.  cos  h. 

Since  par.  and  H.  P.  are  always  small,  the  sines  are  nearly  proportional  to  the 
angles;  hence, 

par.  =  H.  P.  cos  7i. 

306.  The  Nautical  Almanac  gives  the  horizontal  parallax  of  the  moon,  as  well 
as  of  the  planets  Mercury,  Venus,  Mars,  Jupiter,  Saturn,  Uranus,  and  Neptune. 

In  Table  16  will  be  found  the  values  of  the  sun's  parallax  for  altitude  intervals 
of  5°  or  10°,  while  Table  20  B  contains  the  combined  values  of  the  sun's  parallax 
and  the  refraction.  In  Table  24  is  given  the  parallax  of  the  moon,  combined  with 
the  refraction,  at  various  altitudes  and  for  various  values  of  the  horizontal  parallax. 


COREECTION  OF   OBSERVED  ALTITUDES. 


119 


I 


306.  Parallax  is  always  additive;  combined  parallax  and  refraction  additive  in 
the  case  of  the  moon,  but  subtractive  for  the  sun. 

As  the  correction  for  parallax  of  the  moon  is  so  large,  it  is  essential  that  it  be 
taken  from  the  table  with  considerable  accuracy;  the  corrections  for  index  correc- 
tion, semidiameter,  and  dip  should  therefore  be  applied  first,  and  the  "approximate 
altitude"  thus  obtained  snould  be  used  as  an  argument  in  entering  Table  24  for 
parallax  and  refraction. 

SEMTDLA  TVrRTEB. 

307.  The  semidiameter  of  a  heavenly  body  is  haK  the  angle  subtended  by  the 
diameter  of  the  visible  disk  at  the  eye  of  the  observer.  For  the  same  body  the 
semidiameter  varies  with  the  distance;  thus,  the  difference  of  the  sun's  semidiameter 
at  different  times  of  the  year  is  due  to  the  change  of  the  earth's  distance  from  the 
sun;  and  similarly  for  the  moon  and  the  planets. 

In  the  case  oi  the  moon,  the  earth's  radius  bears  an  appreciable  and  considerable 
ratio  to  the  moon's  distance  from  the  center  of  the  earth;  hence  the  moon  is  materially 
nearer  to  an  observer  when  in  or  near  his  zenith  than  when  in  or  near  his  horizon, 
and  therefore  the  semidiameter,  besides  having  a  menstrual  change,  has  a  semi- 
diurnal one  also. 

The  increase  of  the  moon's  semidiameter  due  to  increase  of  altitude  is  called  its 
augmentation.    This  reduction  may  be  taken  from  Table  18. 

The  semidiameters  of  the  sun,  moon,  and  planets  are  given  in  their  appropriate 
places  in  the  Nautical  Almanac. 

The  semidiameter  is  to  be  added  to  the  observed  altitude  in  case  the  lower  limb 
of  the  body  is  brought  into  contact  with  the  horizon,  and  to  be  subtracted  in  the 
case  of  the  upper  limb.  When  the  artificial  horizon  is  used,  the  limb  of  the  reflected 
image  is  that  which  determines  the  sign  of  this  correction,  it  being  additive  for  the 
lower  and  subtractive  for  the  upper. 

Example:  May  6, 1915,  the  observed  altitude  of  the  sun's  upper  limb  was  62*  KK 40''';  I.  C,  +  3'  10"; 
height  of  the  eye,  25  feet.    Bequired  Uie  true  altitude. 


Obs.  alt.  ^, 
Corr., 

True  alt., 


62°  lO'  40" 
18    04 


I.e. 


+    3'  10" 


Required  the  true  altitude. 


61 

52    36 

S.  D.  (Naut.  Aim.), 

dip  (Tab.  14), 

p.  &  r.  (Tab.  20  B), 

-  15' 

-  4 

53" 

54 

27 

-  21 

14 

Corr., 

-  18' 

04" 

s  as  observed  with 

an  artificial  horizon  was  50"  5S 

►'30* 

Obs. 

I.e. 

2  alt.  9|e, 

50° 

59^  30" 
1    30 

2)50    58    00 


Obs.  alt.,  25    29    00 

ref.  (Tab.  20  A),  -  2    02 


True  alt., 


25    26    58 


Example:  April  16,  1915,  observed  altitude  of  Venus  53°  26'  10";  I.  C,  +  2'  30";  height  of  eye, 
20  feet.    Required  the  true  altitude. 


Obs.  alt.  *,  53°  26'  10" 
Corr.,        -  2    32 

53    23    38 


r.  (Tab.  17),       +  0'  04" 
+  2    30 


rd! 


Hor.  Par.  (Naut.  Aim.),  7" 


+  2    34 


dip  (Tab.  14),        -  4'  23" 
ref.  (Tab.  20  A),    -        43 


Corr., 


-  5    06 

-  2'  32" 


120  CORRECTION    OF   OBSERVED  ALTITUDES. 

Example:  May  6,  1915,  at  13''  24"»  G.  M.  T.,  the  observed  altitude  of  the  moon's  lower  limb  was  25* 
3(K  SO''';  I.  G.,-V  30''';  height  of  eye,  20  feet.     Required  the  true  altitude. 

Obs.  alt.£,  25°  30^  30^''  S.  D.  (Naut.  Aim.),  +15'  3^  Hor.  Par.  (Naut.  Aim.)  56'  SI"' 

Ifit.  corr.,  +  9    45  Aug.  (Tab.  18),         +        07 

Approx.  alt.,              25    40    15                                               +15    38 
p.  &  r.  (Tab.  24),    +        49    14  

dip  (Tab.  14),  -  4'  23'' 

True  alt.,  26    29    29  I.  C,  -  1    30 

-  5    53 

Istcorr.,  +  9'  45" 

Or,  the  following  modification  may  be  adopted: 

Obs.  alt. C,         25°  30'  30"  S.  D.,         +15'  31"         H.  P.,  3411"         log  3. 53288 

1st  cor.,  +  7    44  Aug.,  +        07  App.  alt.,    25°  38'  cos  9.95500 

Approx.  alt.,       25    38    14                               +15    38  „„^  f    3075"  log  3.48788 

pir^,  +        51    15  P^'         151'  15"  ^ 

dip.  -  4'  23" 

True  alt.,  26    29    29  ret,  -  2    01 

I.  C,  -  1    30 

-  7    54 
Istcorr.,    +  7'  44" 

308.  The  corrections  for  dip,  parallax,  refraction,  and  semidiameter,  which 
must  be  applied  to  the  observed  altitude  of  a  star  or  of  the  sun's  lower  limb  in  order 
to  obtain  the  true  altitude,  have  been  combined  in  Table  46.  This  is  done  in  order 
to  save  the  time  and  labor  involved  in  referring  to  separate  tables  of  these  corrections. 

The  tabulated  correction  for  an  observed  altitude  of  a  star  combines  the  mean 
refraction  and  the  dip;  and  that  for  the  observed  altitude  of  the  sun's  lower  limb, 
the  mean  refraction,  the  dip,  the  parallax,  and  the  mean  semidiameter,  which  is 
taken  as  16'.  A  supplementary  table,  taking  account  of  the  variation  of  the  sun's 
semidiameter  in  the  different  months  of  the  year,  is  given  in  connection  with  the 
main  table. 

Thus,  in  the  first  example  under  article  324,  we  may,  when  variations  from  the 
mean  state  of  the  atmosphere  (barometer  30  inches,  Fahr.  thermometer  50°)  are 
left  out  of  consideration,  proceed  as  follows: 

Measured  altitude Q.     =40°  04'  00" 

I.e.    =+       3    00 

Correction  from  Table  46,  height  of  eye  20  feet.    +10'   35"         40     07     00 
Supplementary  table  for  June  21 —   0     14  10     21 

Truealtitude 40     17     21 


CHAPTER  XI. 
THE  OHEONOMETEE  EEEOE. 


309.  It  has  already  been  explained  (art.  261,  Chap.  VIII)  that  the  error  of  a 
chronometer  is  the  difference  between  the  time  indicated  by  it  and  the  correct  standard 
time  to  which  it  is  referred;  and  that  the  daily  rate  is  the  amount  that  it  gains  or 
loses  each  day.  In  practice,  chronometer  errors  are  usually  stated  with  reference  to 
Greenwich  mean  time.  It  is  not  required  that  either  the  error  or  the  rate  shall  be 
zero,  but  in  order  to  be  enabled  to  determine  the  correct  time  it  is  essential  that  both 
rate  and  error  be  known  and  that  the  rate  shall  have  been  uniform  since  its  last 
determination. 

310.  Determining  the  Rate. — Since  all  chronometers  are  subject  to  some 
variation  in  rate  under  the  changeable-conditions  existing  on  shipboard,  it  is  desirable 
to  ascertain  a  new  rate  as  often  as  possible.  The  process  of  obtaining  a  rate  involves 
the  determination  of  the  error  on  two  different  occasions  separated  by  an  interval 
of  time  of  such  length  as  may  be  convenient;  the  change  of  error  during  this  interval, 
divided  by  the  number  of  days,  gives  the  daily  rate. 

Example:  On  March  10,  at  noon,  found  chronometer  No.  576  to  be  0™  32».5  fast  of  G.  M.  T. ;  on  March 
20,  at  noon,  the  same  chronometer  waa  0™  48''.0  fast  of  G.  M.  T.    What  was  the  rate? 

Error,  March  10^  0",  +0»  32*.  5 

Error,  March  20'*  0",  +0    48  .  0 


Change  in  10  days,  +      15  ,  5 

Daily  rate,  +        1'.55 

The  chronometer  is  therefore  gaining  1^.55  per  day. 

311.  Determining  Error  from  Rate.— The  error  on  any  given  day  being 
known,  together  with  the  daily  rate,  to  find  the  error  on  any  other  day  it  is  only 
necessary  to  multiply  the  rate  by  the  number  of  days  that  may  have  elapsed  and 
to  apply  the  product  with  proper  sign  to  the  given  error. 

Example:  On  December  17  a  chronometer  is  S"  27'. 5  slow  of  G.  M.  T.  and  losing  0'.47  daily.     What 
is  the  error  on  December  26? 

Error  Dec.  17,  -3°  27V5  Daily  rate,  -0'.47 

Correction,        —        4  .2  No.  days,  9 

Error  Dec.  26,  -3    31.7  Corr.,  -4.23 

The  chronometer  is  therefore  slow  of  G.  M.  T.  on  December  26,  3™  3P.7. 

312.  It  is  necessary  to  distinguish  between  the  signs  of  the  chronometer  correc- 
tion and  of  the  chronometer  error.  A  chronometer  fast  of  the  standard  time  is 
considered  as  having  a  positive  error,  since  its  readings  are  positive  to  (greater  than) 
those  of  an  instrument  showing  correct  time;  but  the  same  chronometer  has  a 
negative  correction,  as  the  amount  must  be  subtracted  to  reduce  chronometer  readings 
to  correct  readings. 

313.  Numerous  methods  are  available  for  determining  the  error  of  a  chronometer 
in  port.     The  principal  of  these  wiU  be  given. 

BY  TIME  SIGNALS. 

314.  In  nearly  all  of  the  important  ports  of  the  world  a  time  signal  is  made  each 
day  at  some  defined  instant.  In  many  cases  this  consists  in  the  dropping  of  a  time 
ball — the  correct  instant  being  given  telegraphically  from  an  observatory.  In  a 
number  of  places  where  there  is  no  time  ball  a  signal  may  be  received  on  the  instru- 
ments at  the  telegraph  offices,  whereby  mariners  may  ascertain  the  errors  of  their 
chronometers.  Such  signals  are  to  be  had  in  almost  every  port  of  the  United  States, 
and  similar  signals  are  being  sent  out  from  Government  radio  stations,  so  that 
it  is  now  possible  to  find  the  error  of  the  chronometer  on  board  ships  fitted  with 

121 


122  THE  CHEONOMETEE  EEEOE. 

receiving  instruments  when  lying  in  port  and  also  when  underway  within  radio 
distance  of  these  stations. 

The  time  signal  may  be  given  by  a  gunfire  or  other  sound,  in  which  case  allowance 
must  be  made  by  the  observer  for  the  length  of  time  necessary  for  the  sound  to  travel 
from  the  point  of  origin  to  his  position.  Sound  travels  1,090  leet  per  second  at  32°  F., 
and  its  velocity  increases  at  the  rate  of  1.15  feet  per  second  with  each  degree  increase 
of  temperature*    If  V  be  the  velocity  of  sound  in  feet  per  second  at  the  existing 

temperature,  and  D  the  distance  in  feet  to  be  traversed,  ^  is  the  number  of  seconds 

to  be  subtracted  from  the  chronometer  reading  at  the  instant  of  hearing  the  signal 
to  ascertain  the  reading  at  the  instant  the  signal  was  made. 

This  method  of  obtaining  the  chronometer  error  consists  in  taking  the  difference 
between  the  standard  time  and  chronometer  time  at  the  time  of  observation  and 
marking  the  result  with  appropriate  sign. 

Example:  A  time  ball  drops  at  5^  0™  0',  G.  M.  T.,  and  the  reading  of  a  chronometer  at  the  same 
moment  is  4''  57™  52».5.     "What  is  the  chronometer  error? 

G.  M.  T.,  5^  00™  00» 

Chro.  t.,  4    57     52.5 


Chro.  error,    -        2    07  .  5 
That  is,  chronometer  is  slow  2™  07'. 5;  chronometer  correction  additive. 

BY  TRANSITS. 

315.  The  most  accurate  method  of  finding  the  chronometer  correction  is  by 
means  of  a  transit  instrument  well  adjusted  in  the  meridian,  noting  the  times  of 
transit  of  a  star  or  the  limbs  of  the  sun  across  the  threads  of  the  instrument. 

At  the  instant  of  the  body's  passage  over  the  meridian  wire,  mark  the  time  by 
the  chronometer.  The  hour  angle  at  the  instant  is  0^;  therefore  the  local  sidereal 
time  is  equal  to  the  right  ascension  of  the  body  in  the  case  of  a  star,  or  the  local 
apparent  time  is  0**  in  the  case  of  the  sun's  center.  By  converting  this  sidereal  or 
apparent  time  into  the  corresponding  mean  time  and  applj^ing  the  longitude,  the 
Grreenwich  mean  time  of  transit  is  given.  By  comparing  with  this  the  time  shown 
by  chronometer  the  error  is  found. 

Example:  1915,  May  9  (Ast.  day),  in  Long.  44°  39''  E.,  observed  the  transit  of  Arcturus  over  the 
middle  wire  of  the  telescope,  the  time  noted  by  a  chronometer  regulated  to  Greenwich  mean  time  being 
&"  05"  33V5.     Required  the  error. 

L.  S.  T.  (R.  A.  *),  14"  11™  49*.  99 

Long.,  -     2    58     36 


G.  S.  T., 

R.  A.  M.  S.,9<»0^, 

11 
-     3 

13 
04 

13 
52 

.99 
.31 

Sid.  int.  from  O*", 
Reduction  (Tab.  8), 

8 

08 

1 

21 
20 

.68 
.01 

G.  M.  T., 
Chro.  t., 

8 
8 

07 
05 

01 
33 

.67 
.50 

Chro.  slow,  1     28  .  17 

Example:  June  25,  1915,  in  Long.  60°  E.,  observed  the  transit  of  both  limbs  of  the  sun  over  the 

meridian  wire  of  the  telescope,  noting  the  times  by  a  chronometer.  Find  the  error  of  the  chronometer 
on  G.  M.  T. 

Transit  of  western  limb,          &"  04™  02».  5  Eq.  t.,    2™  12*.  64 

Transit  of  eastern  limb,  8    06     20 . 0  

H.  D.,    +  0».530 

Chro.  time,  loc.  app.  noon,     8    05     11.25  Long.,     —           4'' 

L.  A.  T.,  loc.  app.  noon,         0"  00™  00*  Corr.,      -   2".  120 

Eq.  t.,  +  2     10.52  

Eq.  t.,    2™  10*.  52 


L.  M.  T.,  loc.  app.  noon,  0  02  10  .  52               Add  to  apparent  time. 

Long.,                                -  4  00  00 

G.  M.  T.,  loc.  app.  noon,  8  02  10  .  52 

Chro.  time,  loc.  app.  noon,  8  05  11 .  25 

Chro.  fast,  3  00  .  73 


THE  CHRONOMETER  ERROR. 


BY  A  SINGLE  ALTITXTDE  (TIME  SIGHT). 


123 


316.  The  problem  involved  in  this  solution,  by  reason  of  its  frequent  application 
in  determining  the  longitude  at  sea,  is  one  of  the  most  important  ones  in  Nautical 
Astronomy.  It  consists  in  finding  the  hour  angle  from  ^iven  values  of  the  altitude, 
latitude,  and  polar  distance.  The  hour  angle  thus  obtamed  is  converted  by  means 
of  the  lon^tude  and  equation  of  time  in  the  case  of  the  sun,  or  longitude  and  ri^ht 
ascension  m  the  case  of  other  celestial  bodies,  into  Greenwich  mean  time;  and  this, 
compared  with  the  chronometer  time,  gives  the  error. 

317.  It  should  be  borne  in  mind  that  the  most  favorable  position  of  the  heavenly 
body  for  time  observations  is  when  near  to  the  prime  vertical.  When  exactly  in 
the  prime  vertical  a  small  error  in  the  latitude  produces  no  appreciable  effect. 
Therefore,  if  the  latitude  is  uncertain,  good  results  may  be  obtained  by  observing  the 
sun  or  other  body  when  bearing  east  or  west.  If  observations  are  made  at  the  same 
or  nearly  the  same  altitude  on  each  side  of  the  meridian  and  the  mean  of  the  results 
is  taken,  various  errors  are  eliminated  of  which  it  is  otherwise  impossible  to  take 
account,  and  a  very  accurate  determination  is  thus  afforded. 

318.  With  a  sextant  and  artificial  horizon  or  good  sea  horizon,  several  altitudes 
of  a  boay  should  be  observed  in  quick  succession,  noting  in  each  case  the  time  as  shown 
by  a  hack  chronometer  or  comparing  watch  whose  error  upon  the  standard  chronom- 
eter is  known.  Condensing  the  observation  into  a  brief  interval  justifies  the  assump- 
tion that  the  altitude  varies  uniformly  with  the  time.  A  very  satisfactory  method 
is  to  set  the  sextant  in  advance  at  definite  Latervals  of  altitude  and  note  the  time  as 
contact  is  observed. 

319.  Correct  the  observed  altitude  for  instrumental  and  other  errors,  reducing 
the  apparent  to  the  true  altitude. 

If  the  sun,  the  moon,  or  a  planet  is  observed,  the  declination  is  to  be  taken  from 
the  Nautical  Almanac  for  the  time  of  the  observation.  If  the  chronometer  correction 
is  not  approximately  known  and  it  is  therefore  impossible  to  determine  the  Greenwich 


mean  time  of  observation  with  a  fair  degree  of  accuracy,  the  first  hour  angle  found 
will  be  an  approximate  one ;  the  declination  corrected  by  this  new  value  of  the  time 
will  produce  a  more  exact  value  of  the  hour  angle,  and  the  operation  may  be  repeated 
until  a  sufficiently  precise  value  is  determined. 

320.  In  figures  48  and  49  are  given: 

AM  ==^,  the  altitude  of  the  body  M; 

DM  =d,  the  declination;  and. 

Q'Z  =  L,  the  latitude  of  the  place. 

In  the  astronomical  triangle  rMZ  there  may  be  found  from  the  foregoing: 

ZM = z,  the  zenith  distance  of  the  body,  =  90  °  -  Ji; 


124 


THE   CHRONOMETER  ERROR. 


PM=2),  the  polar  distance,  =  90°  ±(?;  and 
PZ  =co.L,  tne  co-latitude  of  the  place,  =  90"^  — L. 

From  these  data  it  is  required  to  find  the  angle  MPZ  the  hour  angle  of  the 
body,  =  t.    This  is  given  by  the  formula : 


sm^ 


1  ^_co3  ^  (^+L  +  p)sin  ^  (L  +  p  —  Ti) 
^  cos  L  sin  p 


If  we  let  s  =  l  (Ji  +  h+p),  this  becomes: 

sin  ^  if  =  V  sec  L  cosec  p  cos  s  sin  (s  —  h). 

The  polar  distance  is  obtained  by  adding  the  declination  to  90°  when  of  different 
name  from  the  latitude  and  subtracting  it  from  90°  when  of  the  same  name.  Like 
latitude  and  altitude,  it  is  always  positive. 

If  the  sun  is  the  body  observed,  the  resulting  hour  angle  is  the  local  apparent 
time  and  is  to  be  taken  from  the  a.  m.  or  p.  m.  column  of  Table  44  according  as  the 
altitude  is  observed  in  the  forenoon  or  afternoon.  If  the  moon,  a  star,  or  a  planet 
be  taken,  the  hour  angle  is  always  found  in  the  p.  m.  column. 

Local  apparent  time  as  deduced  from  an  observation  of  the  sun  is  converted  to 
local  mean  time  by  the  application  of  the  equation  of  time;  then,  by  adding  the 
longitude  if  west  and  subtracting  it  if  east,  the  Greenwich  mean  time  is  obtained. 

The  hour  angle  of  any  other  body,  added  to  its  right  ascension  when  it  is  west  of 
the  meridian  at  observation  or  subtracted  therefrom  when  east,  gives  the  local  sidereal 
time,  which  may  be  reduced  to  Greenwich  sidereal  time  by  the  application  of  the 
longitude,  and  thence  to  Greenwich  mean  time  by  methods  previously  explained, 

A  comparison  of  the  Greenwich  mean  time  with  the  chronometer  time  of  sight 
gives  the  error  of  the  chronometer. 

Example:  January  20,  1915,  p.  m.,  in  Lat.  48°  41' (KK'  S.,  Long.  69°  03'  00"  E.,  observed  a  series 
of  altitudes  of  the  sun  with  a  sextant  and  artificial  horizon;  mean  double  altitude,  59°  03'  IC',  images 
approaching;  mean  of  times  by  comparing  watch,  4''  40™  66";  C — ^W,  7*^  23"*  25»;  index  correction, —1'  SO''; 
approximate  chronometer  correction,  —0™  10'.    What  was  the  exact  chronometer  error? 


W.T., 
C— W, 


4'*40°'56'    Obs.2alt.^,    59°  03'  10"    Dec,        20°  17'  41".  9  S.      Eq.  t.,10™  57«.22 


7    23    25      I.  C, 


1    30 


Chro.  t.,  0    04    21 

App.  CO.,      -        0    10 

App.G.M.T.,    0    04    11    Tor 


S.  D. 


H.  D.,      +  31".  8        H.  D.,   +      0».76 

0''.07        G.M.T.,        0^07 


29    30    50 
+  14    43 


+  2".  226        Corr.,     +    0".053 


+ 


2)59    01    40      G.M.T., 
Corr., 
Dec,        20°  17'  39".  7  S.    Eq.  t.,     10">57».3 


29    45    33 


69°  42'  20" 


16'  17" 


(Add  to  apparent 
time.) 


s 

a — h 


p.  &  r., 

Corr., 
29°  45'  33" 
48    41    00 
69    42    20 

2)148    08    53 

74    04    27 
44    18    54 


1'  34" 


L.  A.  T.,    4^  SO™  26*.  7 


+ 

sec 
cosec 


cos 
sin 


sin  i  { 


14'  43" 


. 18031 
. 02783 


9. 43837 
9.  84423 

2)19. 49074 

9.74537 


4"*  30™  28V  7 
+      10    57  .3 


L.  A.  T., 
Eq.  t., 

L.  M.  T., 
Long., 

G.  M.  T., 

Chro.  t., 


Ohro.  slow,       0    00    51  . 0 


4 

41 

24 

.0 

-4 

36 

12 

.0 

0 

05 

12 

.0 

0 

04 

21 

.0 

THE   CHRONOMETER  ERROR.  126 

Example:  May  18,  1915,  p.  m.,  in  Lat.  8°  03'  22'^  S.,  Long.  34°  51'  57''  W.,  observed  a  series  of 
altitudes  of  the  star  Arcturus,  east  of  the  meridian,  using  artificial  horizon:  mean  double  altitude, 
60''  10';  mean  watch  time,  &"  aO""  32»;  C— W,  2"  20""  59V5;  I.  C,  +2'  00".    Find  the  true  error  of  the 


I 


chronometer. 

W.  T., 
0— W, 

6h  50™32» 
2    20    59.5 

Obs.  2  a 
LC, 

ref., 
A, 

sec 
cosec 

COS 

sin 
sin  ^  t 

It.  *,        60° 

+ 

lO' 
2 

'  00" 
00 

R.  A.  * 
Dec.  *, 

S..0^ 

from  0", 
h.  8), 

19°  37 

"50'.0 
'   12".  8  N 

Chro.  t. 

,     9    11    3L5 

30"  04'  20" 
8    03    22 
109    37    13 

2)60 
30 

12 

06 
1 

00 

00 
40 

109°  37 

14*  11"" 
-  3    36 

'  13" 

h 

L 

30 

.00431 
.02598 

9. 44365 
9. 84022 

04 

20 

R.  A.  *, 
H.  A., 

L.  S.  T., 
Long., 

G.  S.  T., 
R.  A.  M. 

Sid.  int. 
Red. (Ta 

G.  M.  T. 

Chio.  t., 

Chro.  slo 

50'.  0 
01 

P 

10 
+  2 

12 
-  3 

35 

19 

55 
40 

49  .0 

27  .8 

16  .8 
21  .3 

s 
ih-h 

2)147    44    55 

73    52    28 
43    48    08 

Z^  36"'  01*  E. 

H.  A. 

2)19. 31416 
9.  65708 

9 

14 
1 

55  .5 
30  .9 

9 
9 

13 
11 

24  .6 
31  .5 

1 

53  .1 

BT  DOUBLE  ALTITTrDES  OB  ALTTTITDES  ON  OPPOSITE  SIDES  OF  THE  MERIDIAN. 

320.  Instead  of  relying  on  a  single  determination  of  the  chronometer  error  from 
altitudes  on  one  side  of  the  meridian,  it  is  better  to  observe  the  same  body  on  both 
sides  of  the  meridian,  and,  if  possible,  at  about  the  same  altitude.  The  error  of  the 
chronometer  having  been  found  from  each  set  of  sights,  the  mean  is  taken  as  the 
correct  error,  and  this  mean  wdll  probably  be  nearer  the  true  error  than  the  result 
from  either  set;  the  effect  of  the  constant  errors  of  latitude,  instrument,  and  observer, 
being  opposite  in  the  two  cases,  will  be  eUminated  by  takmg  the  mean. 


b 


CHAPTER  XII. 
LATITUDE. 


BY  MERIDIAN  ALTITTJDE. 

321.  The  latitude  of  a  place  on  the  surface  of  the  earth,  being  its  angular 
distance  from  the  equator,  is  measured  by  an  arc  of  the  meridian  between  the  zenith 
and  the  equator,  and  hence  is  equal  to  the  declination  of  the  zenith;  therefore,  if  the 
zenith  distance  of  any  heavenly  body  when  on  the  meridian  be  known,  together  with 
the  declination  of  the  body,  the  latitude  can  be  found. 

Let  figure  50  represent  a  projection  of  the  celestial  sphere  on  the  plane  of  the 
meridian  NZS;  O,  the  center  of  the  sphere;  NS,  the  horizon;  P  and  P',  the  poles  of 

the  sphere;  QOQ',  the  equator;  Z,  the  zenith  of  the 
observer.^  Then,  by  the  above  definition,  ZQ  will 
be  the  latitude  of  the  observer;  and  NP,  the  altitude 
of  the  elevated  pole,  will  also  equal  the  latitude. 

Let  M  be  the  position  of  a  heavenly  body  north 
of  the  ec[uator,  but  south  of  the  zenith;  QM  =  (?,  its 
declination;  MS  =  ^,  its  altitude;  and  ZM  =  2  =  90'* 
—  li,  its  zenith  distance. 

From  the  figure  we  have: 

QZ  =  (^H-MZ,  or 

lj  =  d-\-z. 

By  attending  to  the  names  of  z  and  d,  marking 

Fig.  50.  the  zenith  distance  north  or  south  according  as  the 

zenith  is  north  or  south  of  the  body,  the  above 

equation  may  be  considered  general  for  any  position  of  the  body  at  upper  transit, 

as  M,  M',  M^'. 

In  case  the  body  is  below  the  pole,  as  at  M'" — that  is,  at  its  lower  culmination — 
the  same  formula  may  be  used  by  substituting  180°  — d  for  d.  Another  solution  is 
given  in  this  case  by  observing  that: 

NP  =  PM'"  +  NM'",  or 
L=2)  +  L 

322.  A  common  practice  at  sea  is  to  commence  observing  the  altitude  of  the 
sun's  lower  limb  above  the  sea  horizon  about  10  minutes  before  noon,  and  then,  by 
moving  the  tangent-screw,  to  foUow  the  sun  as  long  as  it  rises;  as  soon  as  the  highest 
altitude  is  reached,  the  sun  begins  to  fall  and  the  lower  hmb  will  appear  to  dip. 
"Wlien  the  sun  dips  the  reading  of  the  limb  is  taken,  and  this  is  regarded  as  the 
meridian  observation. 

It  will,  however,  be  found  more  convenient,  and  frequently  more  accurate,  for 
the  observer  to  have  his  watch  set  for  the  local  apparent  time  of  the  prospective  noon 
longitude,  or  to  know  the  error  of  the  watch  thereon,  and  to  regard  as  the  meridian 
altitude  that  one  which  is  observed  when  the  watch  indicates  noon.  This  wiU  save 
time  and  try  the  patience  less,  for  when  the  sun  transits  at  a  low  altitude  it  may 
remain  "on  a  stand,"  without  appreciable  decrease  of  altitude  for  several  minutes 
after  noon;  moreover,  this  method  contributes  to  accuracy,  for  when  the  conditions 
are  such  that  the  motion  in  altitude  due  to  change  of  hour  angle  is  a  slow  one,  the 
motion  therein  due  to  change  of  the  observer's  latitude  majr  be  very  material,  and 
tJius  have  considerable  influence  on  the  time  of  the  sun's  dipping.  This  error  is  large 
enough  to  take  account  of  in  a  fast-moving  vessel  making  a  course  in  which  there  is  a 
good  deal  of  northing  or  southing. 

126 


LATITUDE. 


127 


In  observing  the  altitude  of  any  other  heavenly  body  than  the  sun,  the  watch 
time  of  transit  should  previously  be  computed  and  the  meridian  altitude  taken  by 
time  rather  than  by  the  dip.  This  is  especially  important  with  the  moon,  whose 
rapid  motion  in  declination  may  introduce  stUl  another  element  of  inaccuracy. 

323.  The  watch  time  of  transit  for  the  sun,  or  other  heavenly  body,  may  be 
found  by  the  forms  given  below,  knowing  the  prospective  longitude,  the  chronometer 
error,  and  the  amount  that  the  watch  is  slow  of  the  chronometer.  In  this  connection, 
article  404  describing  the  method  of  setting  the  watch  to  L.  A.  T.  may  be 
profitably  read. 


For  the  Sun. 

L,  A.  T.  noon, 

Long.  (+if  west),  ± 

G.  A.  T., 

Eq.  t.,  ± 

G.  M.  T., 

C.  C.  (sign  reversed),        T 

Chro.  time, 

C— W, 

Watch  time  noon, 


For  other  Bodies. 

h 


0^  00"  00* 


L.  S.  T.  transit, 

Long.  (+rf  -west), 

G.  S.  T., 

R.  A.  M.  S.,  O*", 

Sid  int.  from  0^, 

Red.  (Tab.  8), 

G.  M.  T., 

C.  C.  (sign  reversed), 

Chro.  time, 

O-W, 

Watch  time  transit. 


(Right  ascension. 


T 


324.  From  the  observed  altitude  deduce  the  true  altitude,  and  thence  the  true 
zenith  distance.  Mark  the  zenith  distance  North  if  the  zenith  is  north  of  the  body 
when  on  the  meridian.  South  if  the  zenith  is  south  of  the  body. 

Take  out  the  declination  of  the  body  from  the  Nautical  Almanac  for  the  time 
of  meridian  passage,  having  regard  for  its  proper  sign  or  name. 

The  algebraic  sum  of  the  declination  and  zenith  distance  will  be  the  latitude. 
Therefore,  add  together  the  zenith  distance  and  the  declination  if  they  are  of  the 
same  name,  but  take  their  difference  if  of  opposite  names;  this  sum  or  difference 
will  be  the  latitude,  which  will  be  of  the  same  name  as  the  greater. 


Example:  At  sea,  June  21,  1915,  in  Long.  60°  W.,  the  observed  meridian  altitude  of  the  sun's  lower 
limb  was  40°  V;  sun  bearing  south;  I.  C.,+3''  (f;  height  of  the  eye,  20  feet;  required  the  latitude. 

Obs.  alt.,       40°  04'  OO''               S.  D.,      +15^46''''           Dec,  23°  26'  54'''.  3    X. 

Corr.,  +        13    21  I.  C,      +  3    00  

H.  D.,  +                 1".  05 

Long.,  4''. 


*, 

40  17 

21 

dip 
p.  &  r.. 

+18 

-  4' 
,-  1 

46 

X 

49°  42' 
23  26 

39^  N. 
59  N. 

23^ 
02 

L. 

73  09 

38  N. 

-  5 

25 

Corr.,      +  4f.  20 

Dec.,  23°  26'  59"   N. 


Corr.,      +13'  21" 

Example:  At  sea,  April  14, 1915,  in  Long.  140°  E.,  the  observed  meridian  altitude  of  the  sun's  lower 
limb  was  81°  15'  30";  sun  bearing  north;  I.  C.,-2'  30";  height  of  the  eye,  20  feet. 


Obs.  alt.,       81°  15'  30" 
Corr.,  +  8    58 


S.  D.,     +15'  58" 


2, 


81    24    28 

8°  35'  32"  S. 
8    58    37    N. 

0    23    05   N. 


Dec, 

H.D.,    +" 
Long.,     - 


9°  07'  03".  5    N. 


Corr., 


Corr.,      -        I 
Dec, 


54".  33 
9"  .33 

506".  9 
8'  26".  9 


8°  58'  37"       N. 


+  8'  58" 

Example:  At  sea,  May  15,  1915,  in  Long.  0°,  the  observed  meridian  altitude  of  the  sun's  lower 
limb  was  30°  13'  10";  sun  bearing  north:.  I.  C.,+1'  30";  height  of  the  eye,  15  feet. 

Obs.  alt.,       30°  13'  10" 
+        12    02 


Corr. 


S.  D., 
LC, 


+15'  51" 
+  1    30 


Dec,  Gr.  tf",  18°  40'  34"  N. 


30    25  12 

59°  34'  48"  S. 

18    40  34    N. 

40    54  14    8. 


dip, 
p.  &  r. 


+17    21 

-  3'  48" 

-  1    31 


Corr,; 


128  LATITUDE. 

Example:  January  1,  1915,  the  observed  meridian  altitude  of  Sirius  was  53°  23'  4(/\  bearing  bouth: 
I.  C.,+5'  0'';  height  of  the  eye,  17  feet. 

Obs.  alt.,        53°  23'  4(/'  I.  C,      +  5'  (Xy  Dec.  *,     16°  35'  51"  S. 

Corr.,  +  15  

dip,  -  4'  02" 


\ 


h,  53    23    55  ref.,         -        43 


2,  36°  36'  05"  N. 

d,  16    35    51    S. 


Corr., 


L,  20    00    14    N. 

Example:  June  13,  1915,  in  Long.  65°  W.,  and  in  a  high  northern  latitude,  the  meridian  altitude  of 
the  sun's  lower  limb  was  8°  16'  10"  below  the  pole;  height  of  the  eye,  20  feet;  I.  C,  0'  00". 
Greenwich  apparent  time  of  lower  culmination,  June  13,  16^  20™  (=Long.4-12^). 

Obs.  alt.,         8°  16'  10"  S.  D.,  +15'  47"  Dec,  23°  10'  20".  4    N. 

Corr.,         +  5     12  

dip,  -  4    23  H.  D., 

h,  8    21    22  p.  &  r.,  -  6    12  G.  M.  T 

2,                     81°  38'  38"  S.  -10  35  ^ 

180° -rf,   156  47  08  N.  ^^"■' 

Corr.,    +  5  12 

75  08  30  N.  Dec.      23°  12'  52"   N. 

Alternative  method. 
h,  8°  21'  22"  p, 

p,  66    47    08 

180° -rf,         156°  47'  08" 

L,  75    08    30    N. 

Example:  Jime  26,  1915,  in  Long,  80°  W.,  the  observed  meridian  altitude  of  the  moon's  upper  limb 
59°  6'  40",  bearing  south;  I.  C,  +2'  0";  height  of  the  eye,  19  feet. 

h,  59"  18'  BO*  Obs.  alt.,  59°  06'  40'  O.  M.  T.,  Gr.  trans.,  ll^  SO^-.g  Dec.  (Hi-),     26»  63'  30".0      S. 

— — —  — — ^  Corr.forLong.(Tab.ll),  +       14.5  -^— — — — 

Z,  30°  41'  30"  N.        I.e.,  +         2'  00"  M.D.,        +  3''.848 

4,26    51    52    S.  — — —  L.  M.  T.,  local  trans.,         12    05.4  No.  min.,  +  25n>.4 

"'  Long.,  +  5    20  .0  ■ — 

L,  3    49    38    N.        Aug.,  -  15  Corr.,         +|       j,  |p^ 


23° 

10' 

20".  4 

+ 

9".  29 
le'^  .33 

+ 

V 

151".  7 
31".  7 

23° 

12' 

52" 

66° 

47' 

08" 

waa 


I.e., 

alt., 
lab.  2 

+ 

2'  00" 

S.D., 
Aug., 
dip, 

- 

16'  37" 

15 

4    16 

- 

21    08 

1st  Corr. 

- 

19'  08" 

3"" 

58' 
!4),+ 

'  47'  32" 
30    68 

G.  M.  T.,  local  trans.,      +17    25.4 


Dec.,  26"  51'  52*     S. 


Hor.  Par.,  60'  52*. 2 

n,  59    18    30 

Example:  At  sea,  September  16,  1915,  in  Long.  75°  E.,  the  observed  meridian  altitude  of  Jupiter 
waa  51°  25'  24",  bearing  north;  I.  C,  +3'  0";  height  of  the  eye,  16  feet. 

Obs.  alt.,  51°  25'  24"      par.,  +0'  01"     O.  M.  T.,  Gr.  trans.,   llh  59«'.5      Dec.,         3°  58'  31". 6  S. 
Corr.,    -    1  41       I.  C,  +3  00      Corr.  for  Long.,     +    0  .9 


H.D.,  -      8".  03 

h,                  61  23  43            +3  01      L.M.T.,  local  trans.,   12  00.4      G.  M.  T.,  7''. 00 

■^^— -  — "      Long.,  —  5  00  .0  . 

Z,                  38°  36'  17"  S.     dip,   -3'  55"                      Corr.,  -     56".  21 

G.  M.  T.,  local  trans.,   7  00  .4 


Dec.,  3°  59'  28"   8. 


2.        38°  36'  17"  S.     dip,   -3'  55" 
d,  3  59  28  S.    ref:,   -   47 

L,       42  35  45  8.         -4  42 

— —  H.  P.,  2".2 

Corr.,  -1'  41"  par.  (Tab.  17),        1' 

325.  Constant. — In  working  a  meridian  altitude,  especially  the  daily  noon 
observation  of  the  sun,  it  is  frequently  a  convenience  to  arrange  the  terms  so  that 
all  computation,  excepting  the  application  of  the  observed  altitude,  is  completed 
beforehand;  then  the  ship's  latitude  will  be  known  immediately  after  the  sight  haa 
been  taken,  it  being  necessary  only  to  add  or  subtract  the  altitude.     (See  art.  323.) 

It  is  assumed  that  the^  noon  longitude  will  be  sufficiently  accurately  known  in 
advance  to  enable  the  navigator  to  correct  the  declination;  also  the  approximate 
meridian  altitude  to  correct  the  parallax  and  refraction;  if  the  latter  is  not  known, 
it  may  readily  be  found  from  the  declination  and  approximate  latitude. 

Generally  speaking, 

Lat.  =  Zenith  distance  +  Dec., 
=  90 ° -True  alt. + Dec, 
=  90°- (Obs.  alt.  +  Corr.)  +  Dec, 
=  (90°  +  Dec-Corr.) -Obs.  alt., 


LATITUDE. 


129 


in  which  the  quantity  (90°  + Dec.  —  Corr.)  may  be  termed  a  Constant  for  the  meridian 
altitude  of  the  day,  as  it  remains  the  same  regardless  of  what  the  observed  altitude 
may  prove  to  be.  The  constant  having  been  worked  up  before  the  observation  is 
made,  the  latitude  will  be  known  as  soon  as  the  observed  altitude  is  applied. 

To  avoid  the  confusion  that  might  arise  from  the  necessity  of  combining  the 
terms  algebraically  according  to  their  diiBFerent  names,  it  may  be  convenient  to  divide 
the  problem  into  four  cases  and  lay  down  rules  for  the  arithmetical  combination  of 
the  terms,  disregarding  their  respective  names  as  follows : 

Case  I.  Lat.  and  Dec.  same  name,  Lat.  greater,  +90°  +  Dec.  — Corr. —  Obs.  alt. 
Case  II.  Lat.  and  Dec,  same  name,  Dec.  greater,  —  90°  + Dec.  +  Corr.  +  Obs.  alt. 
Case  III.  Lat.  and  Dec.  opposite  names,  +90°  — Dec. —  Corr. —  Obs.  alt. 

Case  IV.  Lat.  and  Dec.  same  name,  lower  transit,  +  90°  —  Dec.  +  Corr.  +  Obs.  alt. 

The  correctness  of  such  an  arrangement  will  become  readily  apparent  from  an 
inspection  of  figure  42.  The  assumption  has  been  made  that  the  correction  to  the 
observed  altitude  is  positive;  when  this  is  not  true  the  sign  of  the  correction  must 
be  reversed. 

As  examples  of  this  method,  the  first,  second,  third,  and  fifth  of  the  examples 
previously  given  illustrating  the  meridian  altitude  will  be  worked,  using  the  constant; 
the  details  by  which  Corr.  and  Dec.  are  obtained  are  omitted,  being  the  same  as  in 
the  originals. 


1st  Example. 

Case  I. 

+  90°  00'  00» 
Dec.,         +  23    26    69 
Corr.,        -         13    21 

2d  Example. 

Case  II. 

-90°  00'  oof 
Dec.,          +  8    68    37 
Corr.,         +         8    58 

3d  Example. 

Case  III. 

+90°  00'  00» 
Dec.,          -18    40    34 
Corr.,          -        12    02 

5th  Example. 

Case  I  r. 
+90°  00'  00* 
Dec.,          -23    12   52 
Con.,          +         5    12 

Constant, +  113    13    38 
Obs.  alt.,  -  40    04    00 

Constant,  —80    52    25 
Obs.  alt.,    +81    15    30 

Constant,  +71    07    24 
Obs.  alt.,    -30    13    10 

Constant,  +66    62   20 
Obs.  alt.,    +  8    16    10 

Lat.,               73    09    38  (N.) 

Lat.,               0    23    05  (N.) 

Lat.,              40    54    14(8.) 

Lat.                75    08    30  (N.) 

BY  REDUCTION  TO  THE  MERIDIAN. 

326.  Should  the  meridian  observation  be  lost,  owing  to  clouds  or  for  other 
reason,  altitudes  may  be  taken  near  the  meridian  and  the  times  noted  by  a  watch 
compared  with  the  cnronometer,  from  which,  knowing  the  longitude,  the  hour  angle 
may  be  deduced. 

If  the  observations  are  within  26"  from  the  meridian,  before  or  after,  the  correc- 
tion to  be  applied  to  the  observed  altitude  to  reduce  it  to  the  meridian  altitude  may 
be  found  by  mspection  of  Tables  26  and  27.  Table  26  contains  the  variation  of  the 
altitude  for  one  minute  from  the  meridian,  expressed  in  seconds  and  tenths  of  a 
second.  Table  27  contains  the  product  obtained  by  multiplying  the  square  of  the 
minutes  and  seconds  by  the  change  of  altitude  in  one  minute. 

Let  a  =  change  of  altitude  (in  seconds  of  arc)  in  one  minute  from  the  meridian : 
H= meridian  altitude; 
A.  =  corrected  altitude  at  observation;  and 
<  =  interval  from  meridian  passage. 
The  value  of  the  reduction  to  the  meridian  altitude  of  each  altitude  is  found  by 
the  formula: 

U^h+at', 

a  being  found  in  Table  26,  and  at^  in.  Table  27;  hence  the  following  rule: 

Find  the  hour  angle  of  the  body  in  minutes  and  seconds  of  time.  Take  from 
Table  26  the  value  of  a  corresponding  to  the  declination  and  the  latitude.  Take 
from  Table  27  the  value  of  at^  corresponding  to  the  a  thus  found  and  to  the  interval, 
in  minutes  and  seconds,  from  meridian  passage.  This  quantity  will  represent  the 
amoxmt  necessary  to  reduce  the  corrected  altitude  at  the  time  of  observation  to  the 
corrected  altitude  at  the  meridian  passage;  it  is  always  additive  when  the  body  is 
near  upper  transit,  and  always  to  be  subtracted  when  near  lower  transit. 

If  tne  mean  of  a  number  of  sights  is  to  be  taken,  determine  each  reduction  sepa- 
rately, take  the  mean  of  all  the  reductions,  and  apply  it  to  the  mean  of  the  altitudes; 

21594°— 14 9 


130  LATITUDE. 

it  is  incorrect,  in  such  a  case,  to  take  the  mean  of  the  times  and  work  the  sight  with 
this  single  value  of  t.  The  differences  of  altitude  being  small,  the  parallax  and 
refraction  will  be  sensibly  the  same  for  all,  and  one  computation  of  the  correction  to 
the  observed  altitude  will  suffice. 

Knowing  the  meridian  altitude,  the  latitude  is  to  be  found  as  previously  explained. 

327.  When  several  sights  are  taken,  the  most  expeditious  method  of  calculating 
will  be  to  find  first  the  watch  time  of  transit,  and  thence  obtain  the  hour  angle  of  each 
observation  by  comparing  the  watch  time  of  observation.  The  watch  time  of  transit 
may  be  found  as  already  explained  (art.  323)  for  computing  that  quantity  as  a  guide 
in  taking  the  meridian  altitude,  but  the  hour  angle  thus  obtained  is  subject  to  a 
correction.  The  difference  between  watch  time  of  transit  and  watch  time  of  observa- 
tion gives  the  watch  time — that  is,  the  mean  time — elapsing  between  transit  and 
observation.  A  fixed  star  covers  in  that  time  an  angle  corresponding  to  the  sidereal 
and  not  to  the  mean  time  interval,  and  a  reduction  should  be  made  accordingly  to 
give  its  true  hour  angle  at  the  instant  of  observation.  A  planet's  hour  angle  should 
be  corrected  in  the  same  way  (for  we  may  disregard  its  very  smaU  change  in  right 
ascension).  The  correction  may  be  entirely  neglectedin  the  case  of  the  sun,  as  the 
difference  between  mean  and  apparent  time  intervals  is  immaterial.  The  reduction 
of  the  hour  angle  in  the  case  of  the  moon  becomes  rather  cumbersome,  so  much  so 
that  it  is  better  to  find  the  hour  angle  of  this  body  by  the  more  usual  method  of 
converting  watch  time  to  G.  M.  T.,  and  thence  to  L.  S.  T.,  and  finding  the  difference 
between  the  latter  and  the  R.  A. ;  an  additional  reason  for  this  is  that  the  G.  M.  T. 
of  observation  must  be  known  exactly,  with  the  moon,  for  the  correction  of  the 
declination  (art.  330). 

328.  Table  26  includes  values  of  the  latitude  up  to  60°,  and  those  of  the  declina- 
tion up  to  63°,  thus  taking  in  aU  frequented  waters  of  the  globe  and  aU  heavenly 
bodies  that  the  navigator  is  likely  to  employ.  No  values  of  a  are  given  when  the 
altitudes  are  above  86  °  or  below  6  °,  as  the  method  of  reduction  to  the  meridian  is 
not  accurate  when  the  body  transits  very  near  the  zenith,  and  the  altitudes  themselves 
are  questionable  when  very  low.  In  case  it  is  desired  to  find  the  change  of  altitude 
in  one  minute  from  noon  for  conditions  not  given  in  the  tables,  it  may  be  computed 
by  the  formula: 

1''.9635  cos  L  cos  d 
~        sin  (L — d) 

In  working  sights  by  this  method  where  great  accuracy  is  required,  as  in  deter- 
mining latitudes  on  shore  for  surveying  purposes,  it  is  well  to  compute  the  a  rather 
than  to  take  it  from  the  table,  as  one  is  thus  enabled  to  employ  the  value  as  found  to 
the  second  decimal  place. 

Due  regard  must  be  paid  to  the  names  of  the  declination  and  latitude  in  working 
this  formula;  if  they  are  of  opposite  names,  the  declination  is  negative,  and  L  and  a 
should  be  added  together  to  obtain  L — d. 

329.  Table  27  contains  values  of  af^  up  to  the  limits  within  which  the  method 
is  considered  to  apply  with  a  fair  degree  of  accuracy.  It  must  not  be  understood 
that  the  plan  of  reduction  to  the  meridian  is  not  available  for  wider  limits,  but  it 
would  seem  preferable  to  employ  the  ^'  0"  formula,  described  hereafter,  when  the 
hour  angle  falls  beyond  that  for  which  the  table  is  computed.  On  the  other  hand, 
the  reduction  is  not  exact  in  all  cases  covered  by  the  table ;  while  sufficiently  so  for 
sea  navigation,  the  limits  given  are  far  too  wide  for  the  precise  determinations 
required  in  surveying,  where  the  aim  should  be  to  observe  bodies  under  such  conditions 
that  the  total  reduction  aP  shall  not  exceed  1'. 

330.  It  should  be  kept  clearly  in  mind  when  employing  the  method  of  reduction 
to  the  meridian  that  the  resulting  latitude  is  that  of  the  ship  at  the  instant  of  observa- 
tion, and  to  bring  it  up  to  noon  the  run  must  be  applied.  The  declination  should 
properly  be  corrected  for  the  instant  of  observation;  with  the  sun  or  a  planet,  it  is 
sufficiently  accurate  to  use  the  declination  at  meridian  passage,  unless  the  interval 
from  the  meridian  be  quite  large ;  but  the  moon's  declination  changes  so  rapidly  that 
the  exact  time  of  observation  must  be  used  in  its  correction  when  working  with 
this  body. 


I 


LATITUDE. 


131 


Example:  In  latitude  47°  S.,  having  previously  worked  up  the  constant  for  meridian  altitude, 
78°  42'  W,  observed  altitude  of  sun  near  meridian,  31°  IV  50";  Dec.  11°  N.;  watch  time,  IP  40"  21», 
watch  fast  of  L.  A.  T.,  7".     Find  the  latitude. 


Watch  time, 
Watch  fast, 

11"  40™  21* 
07 

Obs.  alt.,   31° 

IV 
10 

50" 
24 

L.  A.  T., 

11     40     14 

Mer.  alt.,   31 
Constant,    78 

22 
42 

14 
10 

t, 

igm  46» 

a  (Tab.  26), 


of 2  (Tab.  27), 


Lat., 


47     19    56  S. 


1". 


ri".0=  6'  30" 
I     .6=3    54 

1  .6=10    24 


Example:  At  sea,  July  12,  1915,  in  Lat.  50°  N.,  Long.  40°  W.,  observed  circum-mendian  altitude  of 
the  sun's  lower  limb,  61°  48'  30",  the  time  by  a  chronometer  regulated  to  Greenwich  mean  time  being 
-2™  30';  I.  C,  -3'  0";  height  of  the  eye,  15  feet.    Find  the  latitude. 


2*' 41°  39';  chro.  corr. 
Chro.  t.,      2^  41«»39' 


c.  c,    - 

2 

30 

G.M.T.,      2 
Eq.  t.,    - 

39 

5 

09 
19 

G.A.  T.,    2 
Long.,    -  2 

33 
40 

50 
00 

L.  A.  T.,  11 

53 

50 

6    10 


"Corr., 

h, 

S.  D., 

dip, 
p.  <fe  r. 
I.e., 


Corr.,      + 


61°  48'  30" 
+  8    31 


Dec,        22°  05'  51". ON. 


61 

57 

01 

+ 

15' 

46" 

E 

3 
0 
3 

48 
27 
00 

- 

7 

15 

H.  D.,  - 
Long., 

Corr.,    — 

Dec., 


20".  1 
2\7 


54".  3 


22°  04'  57"      N. 


Eq.  t., 

5™  17». 

87 

H.  D., 
Long., 

+        0'. 

2^ 

34 

7 

Corr., 

+ 

.92 

Eq.  t.,        5"»  18'.  8 
(Subtract  from  mean 
time.) 


8    31 


h,       61°  57'  01" 
at\+         1    35 


H, 

61 

58 

36 

y. 

28 
22 

01 
04 

24  N. 
57  N. 

L, 

50 

06 

21  N. 

a  (Tab.  26), 
<rt»  (Tab.  27), 


2".  5 

12".  0=1'  16" 
0  .  5=0    19 
2  .  5=1    35 


Example:  May  31,  1915,  in  Lat.  30°  15'  N.,  Long.  5"  25'»  42'  W.,  about  9  p.  m.,  observed  with  a 
eextant  and  artificial  horizon  a  series  of  altitudes  of  Spica;  mean  observed  double  altitude  98°  06'  34"; 
noted  times  as  enumerated  below  by  a  watch  compared  with  a  chronometer  which  was  2™  33'  fast  of 
G.  M.  T.;  C-W,  5^  29""  40';  I.  C,  -3'  00".     Find  the  latitude. 

R.  A.  *  (L.  S.  T.  transit),     13"  20'°  45'.  5 


Long., 

G.  S.  T., 

R.  A.  M.  S.  Gr.  0", 

Sid.  int.  from  tf", 
Red.  (Tab.  8), 

G.  M.  T., 

C.  C.  (sign  reversed), 

Chro.  time  transit, 
C-W, 

Watch  time  traneit, 


+5  25  42 


I.e., 


18    46 
4     31 

27  .5 
36  .6 

14     14 
2 

50  .9 
20  .0 

ref., 

14     12 

+          2 

30  .9 
33 

14    15 
-  5    29 

03  .9 
40 

8    45 
Intervals 

24 
from  transit. 

Watch  times. 

Mean  time. 

Sid.  time." 

&"  36™  01'.  0 

-  9°  23'.  0 

-  9»"24' 

38    02  . 5 

7    21  .5 

7    23 

40    50  . 0 

4    34  .0 

4    35 

43    33  . 0 

1    51  .0 

1    51 

45    50  . 5 

+  0    26  . 5 

+  0    27 

48    28  . 5 

3    04  .5 

3    05 

50    29  . 0 

5    05  .0 

5    06 

52     16  . 0 

6    52  .0 

6    53 

55    55  . 5 

10    31  .5 

10    33 

c,98° 

06' 
3 

34" 
00 

R.  A.  *, 

Dec., 

a  (Tab.  26), 

13"  20™  45'.  5 

10°  43'   24"  S. 

2;98 
49 

03 
01 

34 

47 
50 

2".  5 

49 

00 

57 

a(2  (Tab.  27). 


2. 0  0.  5  2.  5 

2'  56"  0'  44"  3'  40" 

1  49  0  27  2  16 

0  42  0  10  0  52 

0  07  0  02  0  09 

0  00  0  00  0  00 

0  19  0  04  0  23 

0  52  0  13  1  05 

1  35  0  23  1  58 
3  42  0  55  4  37 


h,         49°  00'  57" 
at',   +    1  40 


H, 

49 

02 

37 

I 

40 
10 

57 
43 

23  N. 

24  S. 

L, 

30 

13 

59  N. 

9)15  00 


1  40 


132 


LATITUDE. 


Example:  August  6,  1915,  Lat.  59°  S.,  Long.  175*  27'  E.,  during  evening  twilight,  obaerved  an 
altitude  of  Achernar,  near  lower  transit,  26°  52'';  watch  time,  4''  31"°  12»;  C-W,  0^  18™  07';  chro.  fast  of 
G.  M.  T.,  12°»  42»;  I.  C.,+1'  2(y';  height  of  eye,  24  ft.  Find  hour  angle  by  both  methods;  thence  the 
latitude. 


L;f:1r.\wer  trans.}     l^*'  34-  36'. 4 
Long.,  -  11    41      48 


R.  A.  M.  S.  Gr.  5*  0^,  - 

Sid.  int., 

Red.  (Tab.  8),  - 

G.  M.  T., 

CO.  (sign  reversed),     + 

Chro.  time, 
C-W, 

Watch  time  transit. 
Watch  time  obs., 

.    fMean  time, 
\Sid.  time, 

Obs.  alt.  >fi, 

I.e.,        + 

dip, 

ret.,  — 


Corr., 
P, 


1 

8 

52 
51 

48 
49 

.4 
.4 

17 

00 
2 

59 

47 

.0 
.3 

16 

58 

12 

11 

42 

.7 

5 
0 

10 

18 

53 
07 

.7 

4 
4 

52 
31 

46 
12 

.7 

26° 

21 
21 

52' 

34 
38 

00" 

.7 
3 

V 

20'' 

1 

48" 
55 

6 

43 

5' 

23" 

26° 

46' 
4 

37" 
40 

26 
32 

41 
20 

57 
31 

Watch  time, 
C-W, 

Chro.  t., 

C.  C, 


4h   3im  12. 

+    0    18    07 

4    49    19 
12    42 


G.  M.  T.  5<»  16    36    37 

R.  A.  M.  S.  Gr.  5<»  0^,  +     8    51    49.  4 


Red.  (Tab.  9), 

G.  S.  T., 
Long., 

L.  S.  T., 

R.  A.  *  +W 


+ 


2    43.7 


1    31  10. 1 

+  11    41  48 

13     12  58. 1 

13    34  36. 4 

21  38.3 


R.  A.  *, 

1"  34»  36'.4 

Dec, 

57°  39'  29"  S. 

p. 

32°  20'  31" 

a  (Tab.  26;, 
af  (Tab.  27), 

0".6 
4'  40" 

59    02    28  S. 


331.  Advantages  are  gained  in  working  out  meridian  attitudes  and  reductions  to 
the  meridian,  in  finding  the  constant  for  a  meridian  altitude  or  a  reduction  to  the 
meridian,  and  in  predicting  the  approximate  altitude  of  a  body  to  be  observed  on 
or  near  the  meridian,  by  projecting,  in  a  quickly  and  roughly  drawn  diagram  on  the 
plane  of  the  meridian  of  the  observer,  the  known  data  entering  into  the  problem. 
The  diagram  or  figure  will  show  at  once  how  to  combine  the  data  to  find  the  required 

result,  and  its  use  tends  greatly  to  accuracy.  It 
is  ontv  necessary  to  know  the  meaning  of  the  terms 
already  defined  and  to  remember  the  single  principle 
that  the  latitude  of  a  place  is  equal  to  the  declination 
of  its  zenith. 

In  every  case  draw  a  circle  (a  rough  approxima- 
tion will  do)  to  represent  the  plane  of  the  meridian,  as 
in  figure  51.     The  center  O  is  the  position  of  the  ob- 
server.    Draw  a  horizontal  line  through  O,  marking 
its  intersection  with  the  circumference  on  the  right- 
hand  side  S,  and  on  the  left-hand  side  N.    Erect  a 
perpendicular  to  this  fine  at  O,  and  mark  its  inter- 
section with  the  circumference  Z.    The  line  NS  is 
the  horizon;  Z  is  the  zenith.    The  arc  ZS  is  that  por- 
tion of  the  meridian  between  the  zenith  and  the  south 
point  of  the  horizon;  the  arc  ZN  is  that  portion  of  the 
meridian  between  the  zenith  and  the  north  point  of  the  horizon.     If  the  meridian 
altitude  of  a  body  is  known  (i.  e.,  its  altitude  above  the  horizon  on  the  meridian), 
and  if  it  is  known  whether  it  bears  to  the  southward  or  to  the  northward,  its  posi- 


FiG.  51. 


LATITUDE.  133 

tion  can  be  projected  at  once  on  the  figure.  Having  the  position  of  the  heavenly 
body  on  the  meridian  and  knowing  the  declination  of  the  Dody,  it  is  evident  where 
to  draw  in  the  projection  of  the  equator.  Having  the  projection  of  the  equator, 
the  angular  distance  between  the  equator  and  the 
zenith  (i.  e.,  the  declination  of  the  zenith)  is  the 
latitude. 

Thus  in  figure  52,  supposing  the  meridian  alti- 
tude of  any  heavenly  body,  M,  nas  been  observed, 
and  that  at  the  time  of  observation  it  was  bearing 
south;  also  that  the  declination,  <?,  of  the  body  was 
south.  It  is  known  that  the  true  altitude,  It,  = 
observed  altitude  ±  altitude  corr.  Since  the  body 
bears  south,  if  the  true  altitude  is  h,  the  position 
of  the  body,  M,  can  be  located  by  laying  oflF  the 
arc  SM==A,,  or  by  drawing  OM  so  that  the  angle 
SOM  =  A^.     This  ^ves  the  position  of  the  heavenly 

body  on  the  mendian.    Since  this  body  is  south  of  

the  equator  by  the  amount  of  the  declination,  the  fiq.62. 

position  of  the  equator  may  be  drawn  by  laving  off 

the  angle  MOQ=o.  OQ  is  the  projection  of  the  equator,  and  the  arc  ZQ(or  the 
angle  ZOQ),  being  the  declination  of  the  zenith,  is  equal  to  the  latitude.  The  for- 
mula for  finding  the  latitude  may  be  written  by  inspection  of  the  figure: 

L  =  90°-  (A+<Z)  =  90°-^-<?.  (1) 

Since  ^=obs.  alt.  ±  corr., 

L= 90**  -  obs.  alt.  ±  corr. - d.  (2) 

By  a  similar  process  formulae  may  be  written  for  determining  the  approximate 
altitvde  of  the  heavenly  body  when  on  the  meridian  and  for  getting  a  noon  constant. 
TTie  former  is  necessary  to  get  the  altitude  correction  before  takmg  the  sight;  the 
latter,  so  that  the  latitude  may  be  obtained  as  soon  as  the  altitude  is  read  Kom  the 
sextant.  In  these  cases  the  D.  K.  latitude  and  longitude,  wliich  have  to  be  worked  out 
in  advance  for  noon,  are  used.  The  longitude  is  used  to  get  the  correction  to  be  applied 
to  the  declination  taken  from  Page  I,  Nautical  Almanac,  for  the  day,  to  give  the  correct 
declination  at  Local  Apparent  Noon  at  the  noon  position.  Kiiowing  the  approximate 
latitude  and  the  declination,  they  are  projected  on  the  figure  in  this  way.  If  the 
latitude  is  north,  the  zenith  is  to  the  northward  of  the  equator  by  the  amount  of 
the  latitude,  and  to  get  the  position  of  the  equator  lay  off  the  angle  ZOQ=Lat.  If 
the  latitude  were  south,  the  equator  would  of  course  be  on  the  north  side  of  the 
zenith  by  the  amount  of  the  latitude,  and  OO  would  be  on  the  north  side  of  the 
circle.  Having  the  position  of  the  equator,  draw  in  the  position  of  the  heavenly 
body  by  laying  it  off  to  the  north  side  or  to  the  south  side  of  the  equator  according 
to  the  amount  and  direction  of  its  declination.  The  angle  between  the  horizon  and 
the  heavenly  body  will  be  the  altitude  of  the  body.  This  is  the  usual  method  of 
plotting,  and  all  that  has  to  be  done  is  to  lay  the  angles  off  on  the  proper  sides, 
marking  them  appropriately,  and  then  write  down  the  formulae.  Suppose  it  is 
required  to  find  the  approximate  noon  altitude.  An  inspection  of  the  figure  shows 
that 

approx.  h  =-90°-(L-\-d)  where  L  is  the  D.  R.  Lat.  (3) 

Suppose  it  is  required  to  find  the  constant  (K)  for  a  meridian  altitude.  It  is 
seen  from  the  figure  that 

L=90°-?i-<Z=90°-obs.  alt.±corr.-d 
=  K  —obs.  alt. 
or 

K=90°±corr.-<?.  (4) 

In  the  same  way  any  combination  may  be  plotted,  and  the  correct  formulae 
may  be  written  out  at  once.  Suppose  on  a  certain  day  it  is  found  that  at  noon  the 
position  will  be  approximately  Lat.  10°  S.,  Long.  30°  15'  W.,  and  that  the  declina- 
tion of  the  sun  at  noon,  taken  from  Page  I,  Nautical  Almanac,  and  corrected  for 


134  LATITUDE. 

the  longitude,  is  20**  30'  S.,  and  it  is  desired  to  find  the  approximate  noon  altitude 
and  obtain  the  constant,  K.  Draw  the  circle  representing  the  plane  of  the  meridian 
(see  fig.  53),  draw  NS  representing  the  horizon,  and  OZ  representing  the  line  to 
the  zenith.  Since  the  approximate  latitude  is  10°  S,  the  equator  must  be  10°  north 
of  the  zenith,  and  OQ  is  drawn  to  the  north  of  Z  so  that  the  angle  ZOQ=  10°.     OQ 

is  then  the  projection  of  the  equator.     The  body  being 
Z      -KM  20°  30'  south  of  the  equator,  lay  oflp  OM  so  that  the 

Q^ 1 — "^  angle  QOM=20°  30'.     SOM  will  be  the  approximate 

altitude,  and  the  formula  for  it  is 

approx.  Ti=90°  +  lj-d,  (5) 

it  is  also  seen  that 

h+d-90°  =  ohs.  alt .  ± corr.  +  <? - 90°  =  K  +  obs.  alt. 

K=±corr.+<?-90°. 

If,  instead  of  the  formulae  for  a  meridian  altitude, 

the  formulae  for  a  reduction  to  the  meridian  are  re- 

FiG.  53.  quired,  there  is  no  change  in  the  figure  or  the  method. 

The  altitude  observed  before  or  after  noon  is  corrected 
to  make  it  the  noon  altitude  by  the  formula  h  =  7b'  +  ai^,  where  h  is  the  noon  alti- 
tude, A'  the  altitude  observed  t  minutes  before  or  after  noon,  and  a  the  rate  of 
change  of  altitude  near  noon.     So  that  in  the  case  shown  in  figure  53 

L=A+c?-90°=A'  +  a<2  +  (?-90°  =  ob3.  alt.±corr.  +  (rf2  +  <?-90°  =  K+obs.  alt.      (6) 

or  » 

K  =  ±  corr.  -\-aP  +  d-  90**. 

The  formula  for  the  approximate  value  of  Ti,  as  shown  in  (5),  is  used  for  getting 
the  altitude  correction  in  this  case,  as  the  slight  difference  in  altitude  makes  no 
change  in  the  correction. 

The  formula  for  latitude,  given  in  ecjuation  (6),  is  the  formula  for  the  latitude  at 
noon  at  the  point  where  the  observation  was  taken.  ^  But  a  ship  steaming  on  a 
course  does  not  remain  at  that  point,  and  what  is  desired  is  the  correct  latitude  of 
the  ship's  position  at  noon.  It  L'  represents  the  latitude  of  the  place  where  the 
observation  was  taken,  and  L  the  latitude  of  the  place  where  the  ship  is  at  noon, 
then  L=L'±  JL,  where  JLis  the  change  in  latitude  from  the  time  of  observation 
until  noon.  This  is  taken  from  the  Traverse  Tables.  But  from  equation  (6)  it  is 
seen  that  L'  =  obs.  alt.  ±  corr. +  a<'  +cZ  — 90° 

.•.L=L'±JL=obs.  alt.±corr.  +  a<2+c?-90°±JL. 
=         K  +  obs.  alt. 
or 

K=  ±corr.  +  a^  +  (?-90°±JL. 

BY  A  SINGLE  ALTITUDE  AT  A  GIVEN  TIME. 

332.  This  observation  should  be  limited  to  conditions  where  the  body  is  within 
three  hours  of  meridian  passage  and  where  it  is  not  more  than  45°  from  the  nieridian 
in  azimuth;  also  where  the  declination  is  at  least  3°.  On  the  prime  vertical  the 
solution  by  this  method  is  inexact,  and  when  the  hour  angle  is  6'',  or  the  declination 
0°,  it  is  impracticable. 

The  problem  is:  Given  the  hour  angle,  declination,  and  altitude;  to  find  the 
latitude.  The  solution  is  accomplished  by  letting  faU,  in  the  usual  astronomical 
triangle,  a  perpendicular  from  the  body  to  the  meridian,  and  considering  separately 
the  distances  on  the  meridian,  from  the  pole  and  zenith,  respectively,  to  the  point 
of  intersection  of  the  perpendicular;  the  sum  or  difference  of  these  distances  is  the 
co-latitude. 


LATITUDE. 


135 


Following  the  usual  designation  of  terms  and  introducing  the  auxiliaries  cf>' 
and  0",  the  formulae  are  as  follows: 

tan  (f)"  =  tan  d  sec  t; 

cos  4>'  =  sin  h  sin  cj)"  cosec  d; 

The  terms  0'  and  (j)"  will  have  different  directions  of  application  according  to 
the  position  of  the  body  relative  to  the  observer.  From  a  knowledge  of  the 
approximate  latitude,  the  method  of  combining  them  will  usually  be  apparent ;  it  is 
better,  however,  to  have  a  definite  plan  for  so  doing,  and  this  may  be  based  upon  the 
following  rule : 

Mark  (p"  north  or  south,  according  to  the  name  of  the  declination;  mark  ^' 
north  or  south,  according  to  the  name  of  the  zenith  distance,  it  being  north  if  the 
body  bears  south  and  east  or  south  and  west,  and  south  if  the  body  bears  north  and 
east  or  north  and  west.  Then  combine  ^"  and  <j)'  according  to  their  names;  the 
result  wiU  be  the  latitude,  except  in  the  case  of  bodies  near  lower  transit,  when 
180°—  (f)"  must  be  substituted  for  ^^  to  obtain  the  latitude. 

It  may  readily  be  noted  that  if  we  substitute  4>"  ^or  declination  and  ^'  for  zenith 
distance,  the  problem  takes  the  form  of  a  meridian  altitude;  indeed,  the  method 
resolves  itself  mto  the  finding  of  the  zenith  distance  and  declination  of  that  point  on 
the  meridian  at  which  the  latter  is  intersected  by  a  perpendicular  let  fall  from  the 
observed  body. 

The  time  should  be  noted  at  the  instant  of  observation,  from  which  is  foimd  the 
local  time,  and  thence  the  hour  angle  of  the  celestial  object. 

If  the  sun  is  observed,  the  hour  angle  is  the  L.  A.  T.  in  the  case  of  a  p.  m.  sight, 
\oT  12'*— L.  A.  T.  for  an  a.  m.  sight.  If  any  other  body,  the  hour  angle  may  be  found 
as  hitherto  explained. 

Example:  June  7, 1915,  in  Lat.  30''  25'  N.,  Long.  81"  25'  3(K''  W.,  by  account;  chro.  time,  6»»  22"  52*; 
oba.  Q  75°  13'  bearing  south  and  west;  I.  C.-3'  W;  height  of  the  eye,  25  feet;  chro.  corr.-2'»  36V 
i th€  "    "     " 


Find  the  latitude. 


Chro.  t., 
c.c, 


22'"  52« 
2    36 


G.  M.  T., 

Kq.  t., 

O.  A.  T., 
Long., 


6  20  16 

+  1  29 

6  21  45 

-  5  25  42 


Obs.  alt.  Q,       75'  13'  00' 
Corr.,  +        7    39 

ft. 
S.D., 


75    20    39 


Dec., 

H.  D.,  +' 

G.  M.  T.,     + 


22"*  40' 44*.  9  N.       Eq.  t., 


IB  31*  .84 


15*  .34 
6^  .3 


dip 


L.A.T.-<,      {j» 


Oh  56»03«  W. 
00'  45* 


>r.. 


.C, 


+  15'  47" 

-  4'  54' 

-  14 

-  3    00 


Corr., 
Dec., 


tt 


96'  .6 
1'  36'  .6 


22' 42'  22* 


H.  D., 
a.  M.  T., 

Corr., 


Eq.  t.,  1"  29«  .  » 

{Add  to  mean  time.) 


-  8    08 


Corr.,  + 

14*'  (K/  45'' 
22    42    22 


7'  yy 


tan 


.01312 
9.  62163 


coeec        .  41341 


h  75    20    39 

^"  23    19    45  N. 

<i'  7    00    00   N. 


tan       9. 63475 


sin 
sin 


9.  98563 
9.69771 

9.  99675 


Lat        30    19    45  N. 

Example:  May  22,  1915,  p.  m.,  in  Lat.  6°  20'  S.  by  account,  Long.  30®  21'  30"  W. 
7'»  35™  10';  observed  altitude  of  moon's  upper  limb,  68°  30'  00",  bearing  north  and  east;  I 
height  of  eye,  26  feet;  chro.  fast  of  G.  M.  T.,  1™  37'.5.    Required  the  latitude. 


;  chro.  time, 
.  0.,-3'00*; 


Chro.  t., 

c.c, 


G.  M,  T.,  7 

R.  A.  M.  S.,    +  3 
Eed.CTab.  9),  + 


G.S.T., 
R.A.  C, 


7'>  aS""  10* 
1    37.5 


33    32.5 

56    07.5 

1    14.5 


Obs.  alt.  ^,  68°  30'  00* 


S.D., 
Aug., 


15'  40' 

0  15 

5  00 

3  00 


R.  A.  CCT*"),  lOh  35m  321 .28 

+ 


Dec.  (7»'),      7' 18' 28'.  2  N. 


11 

-10 


30    54.5 
36    39 


-        23    55 


H.A.fromGr.,    0 
Long.,  2 


54    16 
01    26 


W 
W 


Ist  Corr., 


Approx.  alt.,        68°  06'  05' 
p.*r.(Tab.24),+        21    02 

U,  68    27    07 


M.  D., 
No.  min., 

Corr., 

R.  A., 


1«  .99 
33«>.54 


66". 74 
'06>.7 


10^36»39« 


M.  D.,      - 
No.  mm., 

Corr.,       - 
Dec., 


Hor.Par., 


14'  .86 
33".  54 


/  498' 

\      8'     IS*      - 
T  10'    10"     N. 


67'  W 


U6°  47'  30* 


136  LATITUDE, 

t  16°  47'  30"  sec         .01892 

d  7    10    10  tan       9.09964  coeec        .90377 


h  68    27    07  Bin  9.96854 

^'  7    29    07  N.  tan       9. 11856  an  9. 11485 


i/  13    51    45  S.  COS  9.98716 

Lat.         6    22    38  S. 

Example:  August  6, 1915,  p.  m.,  in  Lat.  52°  47'  S.  by  D.  R.,  Long.  146°  32'  E.,  observed  altitude  of 
Acheraar,  near  lower  transit,  24°  01'  20"  bearing  south  and  west;  watch  time,  &"  48™  22»;  C— W,  9^  4&* 
27';  chro.  corr.  on  G.  M.  T.,+l»  57«;  height  of  eye,  18  feet;  I.  C.+l'  00".    Find  the  latitude. 

Watch  time,  6^  48"'  22*  Obs.  alt.*,  24°  01'  20"  R.  A.  *,  l^"  34°  36'  .4 

C-W,  +9    46    27  Oorr.,        -  5     19 


Chro.  t.,  4    34    49  h,  23    56    01 

CO.,  +  1    57  

I.  C,        +  1'  00" 


Dec.,      57°  39'  29"  S. 


G.  M.  T.,  5<',  16    36    46 

R.  A.  M.  S.,        +  8    51    49.4  dip,  -  4'  09" 

Red.  (Tab.  9),     +  2    43. 7  ref.,  -  2    10 


G.  S.  T., 
R.  A.  * 

Gr., 

t 
d 

h 

180< 

Trfit 

1    31 
1    34 

19.1 
36.4 

Corr, 

rHK 

-          6    19 

coaec 

ein 
ein 

coe 

5'  19^ 

see  .08290 
tan  .  19846 

H.  A.  from 
Long., 

0    03 
9    46 

17  E. 
08  E. 

H.  A., 

9    42 

51 W. 

/  2'>  17«  09' 
[34°  17'  15" 

34°  17'  15^ 
57    39    29 

23    56    01 
'-<p"117    37    02  S. 

64    49    13  N. 

.  07321 

tan  .28136 
POLE  STAR. 

9.  60818 
9.  94747 

9.  62886 

52 

47     49  S. 
BY 

If  the  sidereal  time  is^ 


333.  This  method,  confined  to  northern  latitudes,  is  available  when  the  star 
Polaris  and  the  horizon  are  distinctly  visible,  the  time  of  the  observation  being  noted 
at  the  moment  the  altitude  is  measured. 

Reduce  the  observed  altitude  of  Polaris  to  the  true  altitude. 
Reduce  the  recorded  time  of  observation  to  the  local  sidereal  time. 

^less  than  Ih  29.2m,  subtract  it  from  Ih  29.2m; 
between  Ih  29.2m  and  13h  29.2m,  subtract  Ih  29.2m 

from  it; 
greater  than  13h  29.2m,  subtract  it  from  2oh  29.2m; 
and  the  remainder  is  the  hour-angle  of  Polaris. 

With  this  hour-angle  take  out  the  correction  from  Table  I  of  the  Nautical 
Almanac,  and  add  it  to  or  subtract  it  from  the  true  altitude,  according  to  its  sign. 
The  result  is  the  approximate  latitude  of  the  place. 

Example:  1915,  August  5,  at  10''  40™  30»  p.  m.  local  mean  solar  time,  in  longitude  59°  west  of  Green- 
wich, suppose  the  true  altitude  of  Polaris  to  be  33°  20' 0",  required  the  latitude  of  the  place. 

Local  astronomical  mean  time lO''  40°  30* 

Reduction  from  Table  9  for  lO''  40"»  30* +        01    45 

Greenwich  sidereal  time  of  mean  noon,  August  5 8    51    49 

Reduction  from  Table  9  for  longitude  (=3'' 56°  west,  or  plus) -\-        00    39 

Sum  (having  regard  to  signs)  is  equal  to  local  sidereal  time 19    34    43 

25"  29°  12» 
Subtract  sidereal  time 19    34    43 


Remainder  is  equal  to  hour  angle  of  Polaris 5    54    29 


LATITUDE.  137 

True  altitude +33«  20^  00^ 

Correction  from  Table  I  of  the  Nautical  Almanac —  57 

Approximate  latitude  of  the  place +33    19    03 

Observations  of  Polaris  for  latitude  should  be  made  when  practicable  near  the 
times  of  upper  or  of  lower  culminations  (hour  angle  O*'  or  12^).  However,  at  sea, 
if  made  near  elongation  (hour  angle  e**  or  18**),  the  hour  angle,  and  hence  the  local 
time,  should  be  known  within  one  minute. 

334.  The  latitude  may  be  approximately  found  from  an  altitude  of  Polaris  by 
computation  from  the  formula: 

Ij  =  h±p  cos  t, 
in  which, 

h  =  tY\ie  altitude,  deduced  from  the  observed  altitude; 

2?= polar  distance  =  90  °—<?,   the  apparent  declination  being  taken  from   the 
Nautical  Almanac  for  the  time  of  observation. 

t  =  star's  hour  angle. 

Keduce  the  recorded  time  of  observation  to  the  local  sidereal  time. 

Take  out,  from  the  Nautical  Almanac,  the  apparent  right  ascension  of  Polaris 
for  the  time  of  observation. 

Subtract  the  apparent  right  ascension  from  the  local  sidereal  time,  and  the 
remainder  will  be  the  hour  angle. 

To  the  log  cosine  of  the  hour  angle  add  the  logarithm  of  the  polar  distance  in 
minutes;  the  mmiber  corresponding  to  the  resulting  logarithm  will  be  a  correction 
in  minutes  to  be  subtracted  from  the  star's  true  altitude  to  find  the  latitude  when  the 
hour  angle  is  less  than  6^  or  more  than  IS**,  and  to  be  added  to  the  star's  true  altitude 
to  find  the  latitude  when  the  hour  angle  is  more  than  6**  and  less  than  IS**. 

Example:  June  11,  1915,  from  an  observed  altitude  of  Polaris,  the  true  altitude  was  found  to  be 
29°  5''  55'^.  The  time  noted  by  a  Greenwich  chronometer  was  IS**  41™  26*;  chro.  corr.— 2™  22* ;  Long. 
5^  25°  42'  W. 

Chro.  time,              13"  41"' 26'  h,  29°  05'  55''  R.  A.  *,                 1"  28°  .39" 

C.  C,                    -          2    22  pcoat,  +  1    08    54                                                 

Dec,                     88°  51'  03"  N. 

G.  M.  T.,  ll'',         13    39    04  Lat.,  30    14    49  N.                                         — — 

R.  A.  M.  S.,        +  5     14    59  „  f  1°  08'  57" 

Red.  (Tab.  9),     +          2    15  '^'  I  68'.9 

p,  68'.9  log             1.83822 

G.  S.  T.,  18    56    18  «,  179°30'45"cos  (-)     9.99998 

R.  A.  *,  -  1    28    39  

«^^«/  /68'.9lo<?   (-)  1.83820 

H.  A.  fromGr.,      17    27    39  W.  p  cos  i,  •^1008,54// 

Long.,  5    25    42  W. 

H.  A.,  12    01    57  W. 

,  f  ll*"  58""  03'  E. 

''  \179°  30'  45" 

If  the  computation  is  extended  according  to  the  following  formula,  inserting  the 
value  of  p  in  seconds  of  arc: 

Lt  =  h±p  cos  t-\-^p^  sin  I"  sin^  t  tan  A, 

the  resulting  latitude  is  subject  to  no  greater  error  than  1";  but  if  p  cos  t  is  the  only 
correction  applied  to  the  altitude  of  Polaris,  as  in  the  above  example,  the  resulting 
latitude,  while  subject  to  little  error  when  Polaris  is  observed  near  the  meridian,  wiD 
have  an  error,  when  t  =  Q  hours,  increasing  with  the  altitude  and  amounting  to  1' 
when  ^^  =  54°  and  to  3'  when  ^  =  68°  30'. 

DETERMINATION  ON  SHORE. 

335.  In  finding  the  latitude  on  shore  all  the  methods  are  available  that  have 
been  heretofore  explained  for  employment  in  finding  the  latitude  at  sea,  provided 
only  that  an  artificial  horizon  (art.  256)  be  supplied  to  take  the  place  of  the  natural 
horizon  of  the  sea  in  obtaining  a  measurement,  by  the  sextant,  or  the  altitude  of  the 
celestial  body.     In  addition,  other  methods  may  be  conveniently  employed,  involving 


138  LATITUDE. 

the  use  of  a  theodolite  or  an  altazimuth  instrument,  which  the  observer  at  sea  is 
precluded  from  using  because  the  employment  of  such  instruments  requires  a  steady 
platform. 

If  the  observation  is  to  be  made  with  a  theodolite  or  altazimuth,  the  instrument 
must  first  be  placed  level  so  that  the  line  of  collimation  of  the  telescope  revolves  in 
the  plane  of  the  true  meridian.  This  may  be  accomplished  by  means  of  laying  off  a 
true  meridian  from  the  true  bearing  of  a  terrestrial  object  from  the  instrument,  as 
determined  by  the  observation  described  in  articles  360  and  361. 

The  altitude  of  the  celestial  body  is  then  measured  by  bringing  the  horizontal 
cross  wire  of  the  telescope  on  the  body  at  the  instant  the  body  transits  the  meridian 
or  crosses  the  vertical  cross  wire  of  the  telescope,  and  then  reading  the  vertical 
circle. 

The  latitude  is  then  deduced  from  the  formula,  L  =  <?+0,  after  applying  the  proper 
corrections  for  index  error,  parallax,  and  refraction.  The  correction  for  index  error 
is  obtained  by  bringing  the  telescope  to  a  horizontal  position,  as  indicated  by  the 
level  tube  attached  to  the  telescope,  and  taking  the  corresponding  reading  of  the 
vertical  circle  immediately  before  and  after  each  observation. 

By  observing  the  altitude  of  each  of  two  stars  with  approximately  the  same 
zenith  distance,  one  north  of  the  zenith  and  one  south  of  the  zenith,  a  mean  value 
for  latitude  resulting  from  the  two  observations  may  be  obtained  which  is  not 
affected  by  the  error  in  estimating  the  absolute  value  of  the  astronomical  refraction, 
but  simply  by  the  error  in  estimating  a  very  small  difference  of  refraction  of  two 
stars  at  nearly  the  same  altitude. 

This  method  of  determining  the  latitude  of  a  station  is  known  as  the  Horrebow- 
Talcott  method,  and  consists  or  the  measurement  of  the  small  differences  of  zenith 
distance  of  two  stars  which  transit  at  about  the  same  time  on  opposite  sides  of  the 
zenith.  The  effect  of  this  procedure  is  the  attainment  of  greater  precision  due  to 
the  increased  accuracy  of  a  differential  measurement  over  the  corresponding  absolute 
measurement,  the  ehmination  of  the  use  of  a  graduated  circle  in  the  measurement, 
and  the  fact  that  the  computed  result  is  not  affected  by  the  error  in  estimating  the 
absolute  value  of  the  astronomical  refraction,  but  simply  by  the  error  in  estimating 
a  very  small  difference  of  refraction  of  two  stars  at  nearly  the  same  altitude. 

After  measuring  the  difference  of  meridional  zenith  distances  of  two  stars  which 
transit  at  about  the  same  time  on  opposite  sides  of  the  zenith  and  with  nearly  the 
same  zenith  distances,  the  latitude  may  be  deduced  from  the  following  formula : 

Let  (?  =  declination  of  star  south  of  zenith. 
d!  =  declination  of  star  north  of  zenith. 
2  =  zenith  distance  of  star  south  of  zenith. 
z'  =  zenith  distance  of  star  north  of  zenith. 
Then  h  =  d  +  z 
lj  =  d'-z' 

2lj  =  d  +  d'+z-2' 
L  =  i(d  +  d')  +  ^(z-z'); 

that  is,  the  latitude  is  equal  to  one-half  the  sum  of  the  declinations  plus  one-half  the 
difference  of  zenith  distances.  The  form  of  instrument  used  in  measuring  the  differ- 
ences of  zenith  distances  is  known  as  a  zenith  telescope,  and  consists  of  a  telescope 
mounted  on  a  horizontal  axis  supported  by  an  upright  or  uprights  in  such  a  manner 
that  it  can  be  revolved  about  a  vertical  axis.  A  vertical  circle  is  attached  to  the 
telescope  for  use  in  setting  the  telescope  at  the  proper  inclination  with  the  horizontal 
to  bring  a  particular  star  mto  the  fieldf  of  the  telescope.  A  level  tube  is  also  attached 
to  the  telescope  for  use  in  bringing  the  telescope  to  the  same  inclination  when  observ- 
ing on  each  of  a  pair  of  stars.  The  eyepiece  of  the  telescope  is  fitted  with  a  micro- 
meter screw  which  operates  a  movable  horizontal  cross  wire  with  which  the  bisections 
of  the  image  of  the  observed  body  are  made. 

The  process  of  observing  for  difference  of  zenith  distances  is  as  follows :     If  the 

first  star  of  the  pair  of  stars  to  be  observed  has  a]  g^^^u  [zenith  distance  the  telescope 
is  revolved  about  its  vertical  axis  until  it  pointsjgQy^jj^[in  the  plane  of  the  meridian. 


¥ 


LATITUDE.  139 

The  approximate  mean  zenith  distance  of  the  two  stars  is  then  set  oflF  on  the  vertical 
circle,  and  the  level  bubble  brought  to  the  center  of  the  tube.  When  the  star  appears 
in  the  field  of  the  telescope  the  horizontal  cross  wire  is  brought  to  bisect  the  star 
and  such  bisection  retained  until  the  star  crosses  the  vertical  cross  wire  of  the  tele- 
scope. The  micrometer  head  is  then  read.  The  telescope  is  then  revolved  through 
180°  about  its  vertical  axis  and  brought  to  the  same  inclination  with  the  horizontal 
by  moving  the  telescope  itself  about  its  horizontal  axis  until  the  level  bubble  is  at 
the  center  of  the  tube.  In  like  manner  the  second  star  is  bisected  by  the  horizontal 
cross  wire  and  the  micrometer  head  again  read.  The  difference  between  the  two 
micrometer  readings  gives  the  difference  of  zenith  distances  of  the  two  stars  in  terms 
of  divisions  of  the  micrometer,  which  when  multipUed  by  the  known  angular  value 
of  one  division  of  the  micrometer  gives  the  angular  difference  of  the  zenitn  distances 
of  the  two  stars. 


CHAPTER  XIII. 
LONGITUDE. 


336.  The  longitude  of  a  position  on  the  earth's  surface  is  measured  by  the  arc 
of  the  equator  intercepted  between  the  jyrime  meridian  and  the  meridian  passing 
through  the  place,  or  by  the  angle  at  the  pole  between  those  two  meridians. 

Meridians  are  great  circles  of  the  terrestrial  sphere  passing  through  the  poles. 

The  mime  meridian  is  that  one  assumed  as  the  origin,  passing  through  the 
location  of  some  principal  observatory,  such  as  Greenwich,  Paris,  or  Washington.  That 
of  Greenwich  is  tne  prime  meridian  not  only  for  English  and  American  navigators,  but 
for  those  of  many  other  nations. 

Secondary  meridians  are  those  connected  with  the  primary  meridian,  directly 
or  indirectly,  by  exchange  of  telegraphic  time  signals. 

Tertiary  meridians  are  those  connected  with  secondaries  by  carrying  time  in  the 
most  careful  manner  with  all  possible  corrections. 

Longitude  is  found  by  taking  the  difference  between  the  hour  angle  of  a  celestial 
body  from  the  prime  mendian  and  its  hour  angle,  at  the  same  instant,  from  the  local 
meridian.  In  determinations  ashore  the  hour  angle  from  the  prime  meridian  may 
be  found  either  from  chronometers  or  from  telegraphic  signals;  the  local  hour  angle 
may  be  found  by  transit  instrument  or  by  sextant.  In  determinations  at  sea  the 
chronometer  and  sextant  give  the  only  means  available. 

DETERMINATION  ON  SHORE. 

337.  Telegraphic  Determination  of  Secondary  Meridians. — In  order  to 
locate  with  accuracy  the  positions  of  prominent  points  on  the  coasts,  it  is  necessary 
to  refer  them,  by  chronometric  measurements,  to  secondary  meridians  of  longitude 
which  have  been  determined  with  the  utmost  degree  of  care. 

Before  the  establishment  of  telegraphic  cables,  this  was  attempted  principally 
through  the  observation  of  moon  culminations,  which  seemed  always  to  carry  witlh 
them  unavoidable  errors,  or  by  transporting  to  and  fro  a  large  number  of  chronometers 
between  the  principal  observatory  and  the  position  to  be  located;  and  in  this  method 
it  can  be  conceived  that  errors  would  be  involved,  no  matter  how  thorough  the 
theoretical  compensation  for  error  of  the  instruments. 

By  the  aid  of  telegraph  and  radio,  differences  of  longitude  are  determined  with 
great  accuracy,  and  an  ever-increasing  number  of  secondary  meridional  positions  are 
thus  established  over  the  world;  these  afford  the  necessary  bases  in  carrying  on  the 
surveys  to  map  correctly  the  various  coast  lines,  and  render  possible  the  publication 
of  rehable  and  accurate  navigators'  charts. 

338.  To  determine  telegraphically  the  difference  of  longitude  between  two  points, 
a  small  observatory  containing  a  transit  instrument,  chronograph,  break-circuit 
sidereal  chronometer,  and  a  set  of  telegraph  instruments  is  estabUshed  at  each  of  the 
two  points,  and,  being  connected  by  a  temporary  wire  with  the  cable  or  land  line  at 
each  place,  the  two  observatories  are  placed  in  telegraphic  communication  with  each 
other. 

By  naeans  of  transit  observations  of  stars,  the  error  of  the  chronometer  at  each 
place  on  its  own  local  sidereal  time  is  well  determined,  and  the  chronometers  are 
then  accurately  compared  by  signals  sent  first  one  way  and  then  the  other,  the  times 
of  sending  and  receiving  being  very  exactly  noted  at  the  respective  stations.  The 
error  of  each  chronometer  on  local  sidereal  time  being  appUed  to  its  reading,  the 
difference  between  the  local  times  of  the  two  places  may  be  found,  and  consequently 
the  difference  of  longitude.  The  time  of  transmission  over  the  telegraph  Une  is 
eliminated  by  sending  signals  both  ways.     By  the  employment  of  chronometers 

140 


LONGITUDE.  141 

keeping  sidereal  time,  the  computation  is  simplified,  though  mean-time  chronometers 
may  be  used. 

339.  Establishment  of  Tertiary  Meridians. — Let  it  be  supposed  that  the 
meridional  distance  between  A  and  B  is  to  be  measured,  of  which  A  is  a  secondary 
meridional  position  accurately  determined,  and  B  a  tertiary  meridional  position  to 
be  determined. 

If  possible,  two  sets  of  observations  should  be  taken  at  A  to  ascertain  the  errors 
and  rates  of  the  chronometers.  The  run  is  then  made  to  B,  and  observations  made 
to  determine  local  time,  and  hence  the  difference  of  longitude;  and  on  the  same  spot 
altitudes  of  the  sun,  or  of  a  number  of  pairs  of  stars,  or  both,  should  be  taken  to 
determine  the  latitude. 

Now,  if  chronometer  rates  could  be  rehed  on  to  be  uniform,  this  measurement 
would  suffice,  but  since  variations  may  always  arise,  the  run  back  to  A  should  be 
made,  or  to  another  secondary  meridional  position,  C,  and  new  rates  there  obtained. 
Finally,  the  errors  of  the  chronometers  on  the  day  when  the  observations  were  made 
at  the  tertiary  position  should  be  corrected  for  the  loss  or  gain  in  rate,  and  for  the 
difference  of  the  errors  as  thus  determined. 

When  opportunity  does  not  permit  obtaining  a  rcUe  at  the  secondary  meridional 
station  or  stations,  both  before  and  after  the  observations  at  B,  the  navigator  may 
obtain  the  errors  only,  and  assume  that  the  rate  has  been  uniform  between  those 
errors. 

A  modification  of  the  foregoing  method  which  may  sometimes  prove  convenient 
is  to  make  the  first  and  thirasets  of  observations  at  the  position  of  the  tertiary 
meridian,  and  the  intermediate  one  at  the  secondary  meridian ;  in  this  case  the  error 
will  be  obtained  at  the  secondary  station  and  the  rate  at  the  tertiary. 

Example:  A  vessel  at  a  station  A,  of  known  longitude,  obtained  chronometer  errors  aa  follows: 

May  27,  noon,  chro.  slow,  7™  18*.  9, 
June  3,  noon,  chro.  slow,  7    12  .  7; 

then  proceeding  to  a  station  B  a  series  of  observations  for  longitude  was  taken  on  June  17;  after  which, 
returning  to  A,  the  following  errors  were  obtained: 

July   3,  noon,  chro.  slow,  7™  00".  7, 
July  10,  noon,  chro.  slow,  6    59  . 8. 


Required  the  correct  error  on  June  17. 

May  27,          -7'"  18V  9 
June  3,           -7     12  .  7 

July   3,          -7«»  00*.  7 
July  10,         -6    59  .8 

Change,      +        6.2 

Change,      +        0.9 

Daily  rate,  +        OV  89 

Daily  rate,  +        OV  13 

Therefore,  assuming  that  these  rates  were  correct  at  the  middle  of  the  periods  for  which  they  were 
determined,  we  have, 

May  30,  Midnight,  Rate,       +0'.  89 
July   6,  Midnight,  Rate,      +0  .  13 

Change  of  rate,  37  days, 

Daily  change  of  rate, 

Change  of  rate  for   3^  days,  -0V07;  rate  June   3,  noon, +0*. 89-0* .07= +0'.  82 
Change  of  rate  for  17^  days,  -0  .37;  rate  June  17,  noon,  +0  .89-0  .37=-|-0  .  52 


Mean  daily  rate,  June  3  to  17,  4-0  .  67 

Total  change  of  error,  June  3  to  17,  +0"  09'.  38 

Error,  June  3,  -7    12  . 7 

Error,  June  17,  -7    03  . 3 

340.  Single  Altitudes. — The  determination  of  longitudes  on  shore  by  single 
altitudes  of  a  celestial  body  is  identical  in  principle  with  the  determination  at  sea 
by  that  method,  which  will  be  explained  hereafter  (art.  341).  It  may  be  remarked, 
however,  that  by  taking  observations  on  opposite  sides  of  the  meridian,  at  altitudes 
as  nearly  equal  as  posssmle,  a  means  is  afforded,  which  is  not  available  at  sea,  of  elimi- 
nating certain  constant  errors  of  observation. 


142  LONGITUDE. 

DETERMINATION  AT  SEA. 

341.  The  Time  Sight. — A  method  of  determining  longitude  at  sea  is  that  of 
the  time  sight,  sometimes  called  the  chronometer  method.  The  altitude  of  the  body 
above  the  sea  horizon  is  measured  with  a  sextant  and  the  chronometer  time  noted ; 
the  hour  angle  of  the  body  is  then  found  by  the  process  described  in  article  316, 
Chapter  XI. 

If  the  sun  is  observed,  the  hour  angle  is  equal  to  the  local  apparent  time;  the 
Greenwich  apparent  time  may  be  determined  by  applying  the  equation  of  time  to  the 
Greenwich  mean  time  as  shoAvn  by  the  chronometer;  the  longitude  is  then  equal  to 
the  difference  between  the  local  and  the  Greenwich  apparent  times,  being  east  when 
the  local  time  is  the  later  and  west  when  it  is  the  earher  of  the  two. 

If  any  other  celestial  body  is  employed,  the  hour  angle  from  the  local  meridian, 
found  from  the  sight,  is  compared  with  the  hour  angle  from  the  Greenwich  meridian  to 
obtain  the  longitude;  the  Greenwich  hour  angle  is  found  by  converting  the  Greenwich 
mean  time  into  Greenwich  sidereal  time  in  the  usual  manner,  and  then  taking  the 
difference  between  the  latter  and  the  right  ascension  of  the  body,  the  remainder  being 
marked  east  or  west,  according  as  the  Greenwich  sidereal  time  is  the  lesser  or  greater 
of  the  two  quantities;  and  as  the  local  hour  angle  may  be  marked  east  or  west  accord- 
ing to  the  side  of  the  meridian  upon  which  it  was  observed,  the  name  of  the  longitude 
will  be  indicated  in  combining  the  quantities. 

342.  As  has  been  stated,  the  most  favorable  position  of  the  celestial  body  for 
finding  the  hour  angle  from  its  altitude  is  when  nearest  the  prime  vertical,  provided 
the  altitude  is  not  so  small  as  to  be  seriously  affected  by  refraction. 

343.  In  determining  the  longitude  at  sea  by  this  method,  it  is  necessary  to 
employ  the  latitude  by  account.  This  is  seldom  exactly  correct,  and  a  chance  of 
error  is  therefore  introduced  in  the  resulting  hour  angle;  the  magnitude  of  such  an 
error  depends  upon  the  position  of  the  body  relative  to  the  observer.  The  employ- 
ment of  the  Sumner  line,  which  is  to  be  explained  in  a  later  chapter,  insures  the  navi- 
gator against  being  misled  by  this  cause,  and  its  importance  is  to  be  estimated 
accordingly. 

Example:  At  sea,  May  18,  1915,  a.  m.;  Lat.  41"  33'  N.;  Lone.  33°  30^  W.,  by  D.  R.,  the  following 
altitudes  of  the  sun's  lower  limb  were  observed,  and  times  noted  by  a  watch  compared  with  the  Green- 
wich chronometer.  Chro.  corr.,  -}-4'°  59».2;  I.  C.,-30^'';  height  of  the  eye,  23  feet;  C-W,  2^  17™  06*. 
Required  the  true  longitude. 

W.  T.,        "h  20m  IS.      Obs.  alt.  Q,  29*  35'  30"     Dec.,  19""  22'  27".9  N.  Eq.  t.,  3»>  44'.48 

20  47                   41  20  -^^^—  — ^ 

21  14                  46  10     H.  D.,  +     33".6S  H.  D.,  -   0»  .07 

" "  -  G.  M.  T.,  -   2'>.3 


G.M.T.,17d,   21  42  60.5     S.  D.,    +    15'  50"     p,      70"  38'  49" 
Eq.t.,     +     3  44.6 


G.  A.  T.,     21  4€  35. 1     p.  &  r., 
J.r 


dip, 
.  & 
C, 


29    41 
+            9 

00 
04 

29    50 

04 

+          15' 

-  4' 

-  1 

-  0 

50 

42' 
34 
30 

Mean,       7  20  45.3    Mean,     *»  ,x  w  

C-W,     +  2  17  06      Corr.,    +     9  04      r^„                 /   77".4       Corr.,    +   0«  .16 
^"i        -    \i'   17"  

Chro.  t.,       9  37  61.3     h,  29  50  04  ————  Eq.t,     3">  44«.6 

C.  C,  +  4  59. 2  _— — _     Dec.,    19°  21'  11"   N. 

(.Add  to  mean  time.) 


Dec.,         19"'  22' 

27".9 

H.  D.,       + 
G.  M,  T.,  - 

33".6S 
2h.3 

Corr.,        -    {j, 
Dec.,        19°  21' 

77".4 
17" 

11" 

Corr.,       +  9'  04" 

h  29°  50^  04* 

L  41    33    00  Bee  .12588 

p  70    38    49  coeec  .02526 


cos  9. 51229 

Bin  9. 81852 


2)142 

01    53 

8 

S-h 

71 
41 

00    57 
10    53 

G.  A.  T. 
L.  A.  T. 

2P 
19 

46"  35' 
32    38.5 

2)19.  48195 
an  it      9.  74097 


T^r.^  i  2"  IS'"  56*.51tt, 

lx)ng.         "Iggo  29/  og//  yN. 


LONGITUDE. 


143 


Example:  At  sea,  April  16,  1915,  p.  m.,  in  Lat.  11°  47'  S.,  Long.  0*  W  E.,  by  D.  R.,  observed  an 
altitude  of  the  star  Aldebaran,  west  oi  the  meridian,  23°  IS'  2(K';  chronometer  time,  1^  01™  35* ;  chro- 
nometer fast  of  G.  M.  T.,  2™  27»;  I.  C,  -2'  m"\  height  of  eye,  26  feet.    What  was  the  longitude? 


1^  Ol™  35» 

-        2    27 


Chro.  t., 
CO., 

G.  M.  T., 

R.  A.  M.  S., 
Red.  (Tab.  9), 

G.  S.  T., 
R.  A.  *, 


H.  A.  from  Gr.,      4    03    15    W. 


6 

58 

58 

+1 

34 

11.5 

+ 

1 

08.8 

8 

34 

18.3 

4 

31 

03.0 

Corr., 


9    15 


Obs.alt.  *, 

23°  13'  20^ 

R.A.  *,     4"  31"  03*.  0 

Corr., 

9     15 

Dec,        16°  20^   29"  N 

*, 

23    04    05 

p,            106°  20^    29" 

I.e., 

2'  00" 

dip, 
ref., 

5    00 

2     15 

23°  04'  05" 
11    47    00 
106    20    29 

2)141    11    34 

70    35    47 
47    31    42 


Or.  H.  A. 
H.A. 


4"  03™  15»  W. 
4    05    42  W. 


.00925 
. 01791 


9.  52143 
9. 86783 

2)19. 41642 


sin  i  <       9.  70821 


see 
cosec 


cos 
eia 


^°g-         t    0°  36'  45"/*^- 

Example:  At  sea,  April  17,  1915,  a.  m.,  in  Lat.  25°  12'  S.,  Long.  31°  32'  W.,  by  D.  R.,  observed  an 
altitude  of  the  planet  Jupiter,  east  of  the  meridian,  32°  46'  10";  watch  time,  5^  48°"  02«;  C-W,  2"  05»  42»; 
G.  C,  +2"»  18';  I.  C,  +1'  30";  height  of  eye,  18  feet.    Required  the  longitude. 


W.  T., 

c-w, 

Chro.  t., 
C.  C, 


Red.  (Tab.  9), 

G.  S.  T., 
R.  A.  *, 

H.A. from  Gr., 


5»  48»02« 
2    05    42 


7 

+ 

53 
2 

44 

18 

19 
+  1 

+ 

56 

34 

3 

02 

11.5 

16.5 

21 
23 

33 
13 

30.0 
24.8 

1    39    55  E. 


Obs.al1 
Corr , 

t.  *,  32*  46' 

-          4 

10* 
09 

R.  A.  (17<>  0»), 

H.  D., 
G.  M.  T., 

Corr., 

R.A., 

23k  13m  33..  0 

Dec.( 

H.  D. 
Q.M. 

Corr., 

Dec., 

V, 

17«l  Ok),    6*  03' 

51*.  0  B. 

+                   2".0 
4''.1 

-                 8«.2 

+ 
T.,     - 

12'  1 

», 

32    42 

01 

4>>.l 

LC, 

+          1' 

30' 

49*. « 

dip, 
ref 

-  4' 

-  1 

09» 
30 

23''  13-  24».8 

6'  04' 

41'      8. 

83*65' 

19* 

-         A    39 


Corr.,        — 


32" 

25 

83 


4'  09* 

42' 

12 

55 


01" 

00 

19 


2)141    49    20 


coeec 


.04343 
.00245 


70 
38 


54 
12 


40 

39 


Gr.H.A. 
H.A. 

Long.         I 


1"  39™  55«  E. 
3    46    26  E. 


2'»  06™  31* 
31°  37'  45' 


>) 


W. 


008 

sin 


9.  51459 
9.  79138 

2)19. 35185 


sin  ^  t       9.  67592 


CHAPTER  XIV. 
AZIMUTH. 


34:4:.  The  azimuth  of  a  body  has  been  defined  (art.  223,  Chap.  VII)  as  the  arc 
of  the  horizon  intercepted  between  the  meridian  and  the  vertical  circle  passing  through 
the  body;  and  the  amplitude  (art.  224)  as  the  arc  measured  between  the  position  of 
the  body  when  its  true  altitude  is  zero  and  the  east  or  west  point  of  the  horizon. 
The  amphtude  is  measured  from  the  east  point  at  rising  and  from  the  west  point  at 
setting,  and,  if  added  to  or  subtracted  from  90°,  will  agree  with  the  azimuth  of  the 
body  when  in  the  true  horizon.  The  azimuth  is  usually  measured  from  the  north  point 
of  the  horizon  in  north  latitude,  and  from  the  south  point  in  south  latitude,  through 
180°  to  the  east  or  west;  thus,  if  a  body  bore  N.  by  E.,  its  azimuth  would  be  named 
N.  lli°  E.  in  north,  or  S.  168f  °  E.  in  south  latitude. 

The  determination  of  the  azimuth  of  a  celestial  body  is  an  operation  of  frequent 
necessity.  At  sea,  the  comparison  of  the  true  bearing  with  a  bearing  by  compass 
affords  the  only  means  of  ascertaining  the  error  of  the  compass  due  to  variation  and 
deviation;  on  shore,  the  azimuth  is  required  in  order  to  furnish  a  knowledge  of  the 
variation,  and  is  further  essential  in  all  surveying  operations,  the  true  direction  of 
the  base  Une  being  thus  obtained. 

345.  There  are  various  methods  of  obtaining  the  true  azimuth  of  a  celestial 
body,  which  will  be  described  as  follows:  (a)  Amplitudes,  (6)  Tim^  Azimuths,  (c) 
Altitude  Azimuths,  (d)  Time  and  Altitude  Azimuths.  A  further  method,  by  meana 
of  the  Summer  line,  will  be  explained  later  (Chap.  XV).  Still  another  operation 
pertains  to  this  subject,  namely:  (e)  The  determmation  of  the  True  Bearing  of  a 
Terrestrial  Olject 

AMPLITUDES. 

346.  The  method  of  obtaining  the  compass  error  by  amplitudes  consists  in 
observing  the  compass  bearing  of  the  sun  or  other  celestial  body  when  its  center  is 
in  the  true  horizon,  the  true  bearing,  under  such  conditions,  being  obtained  by  a 
short  calculation.  Since  the  true  horizon  is  not  marked  by  any  visible  line  (differing 
as  it  does  from  the  visible  horizon  by  reason  of  the  effects  of  refraction,  parallax,  and 
dip),  allowance  may  be  made  for  the  difference  by  an  estimate  of  the  eye,  or  else  the 
observation  may  be  made  in  the  visible  horizon  and  a  correction  applied. 

347.  When  the  center  of  the  sun  is  at  a  distance  above  the  horizon  equal  to  its 
own  diameter  it  is  almost  exactly  in  the  true  horizon ;  at  such  a  time,  note  its  bearing 
by  compass,  and  also  note  (as  in  all  observations  for  determining  compass  error) 
the  ship's  head  by  compass,  and  the  angle  and  direction  of  the  ship's  heel. 

Or,  note  the  bearing  at  the  instant  at  which  the  center  of  the  body  is  in  the  visible 
horizon;  in  the  case  of  the  sun  and  moon,  the  correct  bearing  at  that  time  may  be 
most  accurately  ascertained  by  taking  the  mean  of  the  bearings  when  the  upper  and 
the  lower  limbs  of  the  disk  are  just  appearing  or  disappearing. 

348.  To  find  the  true  amplitude  hy  computation,  there  are  given  the  latitude,  L, 
and  declination,  d.     The  quantities  are  connected  by  the  formula, 

sin  Amp. = sec  L  sin  d, 

from  a  solution  of  which  the  amplitude  is  obtained. 

To  find  the  true  amplitude  hy  inspection  enter  Table  39  with  the  declination  at 
the  top  and  the  latitude  in  the  side  column;  under  the  former  and  opposite  the  latter 
will  be  given  the  true  amplitude.  To  obtain  accurate  results,  interpolate  for  minute" 
of  latitude  and  declination. 

144 


AZIMUTH.  145 

To  reduce  the  observed  amplitude  when  taken  in  the  visible  horizon  to  what  it 
would  have  been  if  taken  in  the  true  horizon,  enter  Table  40  with  the  latitude  and 
declination  to  the  nearest  degree  and  apply  the  correction  there  found  to  the 
observed  amplitude;  the  result  will  be  the  corrected  amplitude  by  compass,  which, 
by  comparison  with  the  true  ampUtude,  gives  the  compass  error.  When  the  body 
observed  is  the  sun,  a  star,  or  a  planet,  apply  the  correction,  at  rising  in  north  lati- 
tude or  at  setting  in  south  latitude,  to  the  right,  and  at  setting  in  north  latitude  or 
at  rising  in  south  latitude,  to  the  left.  For  the  moon,  apply  half  the  correction  in 
a  contrary  direction. 

Example:  At  sea,  iu  Lat,  11°  29^  N.,  the  observed  bearing  of  the  sun,  at  the  time  of  rising,  when 
its  center  was  estimated  to  be  one  diameter  above  the  visible  horizon,  was  E.  31°  N.;  corrected 
declination  22°  32'  N.     Required  the  compass  error. 

By  computation.  By  inspection  ( Table  39) . 

L    11°  29'  sec  .00878  L,  11°.5N.\t,  ,^  „^^  „  ooo  n  m 

d     22    32  sin  9.58345  rf/ 22  .5  N./^"^®  *°^P- ^- ^S**-©  N. 

Obs.  amp.  E.  31  ,0  N. 

True  amp.      E.  23°  01'  N.   sin  9. 59223  

Obs.  amp.      E,  31    00  N.  Error,  8°.0E. 

Error,  7°  59'  E. 

Example:  At  sea,  iu  Lat,  25°  03'  S.,  the  observed  bearing  of  Venus,  when  in  the  visible  horizon  at 
rising,  was  E.  18°  30'  N.,  its  declination  being  21°  44'  N.    Required  the  compass  error. 

By  computation.  By  inspection  {Table  S9). 

L    25°  03'         sec      .04290  L,  25°.  OS.!™.  17  0.0  n  xt 

d     21    44  sin    9.56854  rf,  21  . 7  N.|  ^rue  amp.     E.  24°.  1 N. 

Obs.  amp.  E.  18°.5N.\^  „   ,„    „„ 

True  amp.    E.  24°  08'  N.  sin    9.61144  Corr.  (Tab.  40)  o.3  left./ ^°™P-*™P-  ■'^' ^^  -^  ^• 


Error,  5°.  3  W. 


Comp.  amp.  E.  18    48    N. 

Error,  5°  20'  W. 

Example:  At  sea,  in  Lat.  40°  27'  N.,  the  mean  of  the  observed  bearings  of  the  upper  and  lower 
limbs  of  tlie  moon,  when  in  contact  with  the  visible  horizon  at  setting,  was  W.  17°  S. ;  declination,  21°  12'  S. 
What  wa^  the  error  of  the  compass? 

By  computation.  By  inspection  {Table  39). 

L     40°  27'  sec      .  11863  L,  40°.  5  N.  \  m,  „  w  000  >•  a 

d      21    12  sin     9.55826  d,  21  . 2  S.  f  ^"®  *°^P- ^- 28".  4  S. 

Obs.  amp.      W.  17°  .0  S.  \p„„^  „„^  w  i«    t  a 

True  amp.     W.   28°  22'  S.     sin     9.67689  Corr.  (Tab.  40)   0.3  right.  r^^^P'^^^P- ^'^^  •''  ^• 

Error,  11°.  7  W. 


Comp.  amp.  W.    16    42    S, 
Error,  11°  40'  W. 


TIME  AZIMUTHS. 


# 


349.  In  this  method  are  given  the  hour  angle,  t,  at  time  of  observation,  the 
polar  distance,  p,  and  the  latitude,  L;  to  find  the  azimuth,  Z. 

Any  celestial  body  bright  enough  to  be  observed  with  the  azimuth  circle  may 
be  employed  for  observation;  the  conditions  are,  however,  most  favorable  for  solu- 
tion when  the  altitude  is  low. 

350.  Take  a  bearing  of  the  object,  bisecting  it  if  it  has  an  appreciable  disk, 
and  note  the  time  with  a  watch  of  known  error.  Record,  as  usual,  the  ship's  head 
by  compass  and  the  amount  of  heel.  If  preferred,  a  series  of  bearings  may  be  taken 
with  their  corresponding  times,  and  the  means  taken. 

351.  First  prepare  the  data  as  follows: 

(a)  Find  the  Greenwich  time  corresponding  to  the  local  time  of  observation. 

(6)  Take  out  the  declination  of  the  body  from  the  Nautical  Almanac;  if  the 
method  of  computation  is  employed,  the  polar  distance  and  the  co-latitude  should 
be  noted. 

(c)  Find  the  hour  angle  of  the  body  by  rules  heretofore  given. 
21594°— 14 10 


146 


AZIMUTH. 


This  having  been  done,  the  true  azimuth  may  be  determined  either  by  Time 
Azimuth  Tables,  by  the  graphic  method  of  an  Azimuth  Diagram,  or  by  Solution  of 
the  Astronomical  Triangle.  Owing  to  the  possibihty  of  more  expeditious  working, 
either  of  the  first-named  two  is  to  be  considered  preferable  to  the  last,  and  the 
navigator  is  recommended  to  supply  himself  with  a  copy;  of  a  book  of  Azimuth 
Tables,  such  as  pubhshed  by  the  Hydrographic  Office,  or  with  an  Azimuth  Diagram 
such  as  Weir's  or  Sigsbee's;  an  explanation  of  the  method  of  use  accompanies  each 
of  these. 

352.  To  solve  the  triangle: 

Let  S  =  ^  sum  of  polar  distance  and  co-Lat. 
D  =  ^  difference  of  polar  distance  and  co-Lat. 
i<  =  i  hour  angle. 
Z  =  true  azimuth. 

Then,  tan  X  =  sin  D  cosec  S  cot  ^  t; 
tan  Y  =  cos  D  sec  S  cot  ^  t; 
Z=X-HY,  orX~Y. 

First  Case. — If  the  half -sum  of  the  polar  distance  and  co-Lat.  is  less  than  90°: 
take  the  sum  of  the  angles  X  and  Y,  if  the  polar  distance  is  greater  than  the  co-Lat. ; 
take  the  difference,  if  the  polar  distance  is  less  than  the  co-Lat. 

Second  Case. — If  the  half -sum  of  the  polar  distance  and  co-Lat.  is  greater  than 
90°:  always  take  the  difference  of  X  and  Y,  which  subtract  from  180°,  and  the  result 
will  be  the  true  azimuth. 

In  either  case,  mark  the  true  azimuth  N.  or  S.  according  to  the  latitude,  and 
E.  or  W.  according  to  the  hour  angle.  It  may  sometimes  be  convenient  to  use  the 
supplement  of  the  true  azimuth,  by  subtracting  it  from  180°  and  reversing  the 
prenx  N.  or  S,,  in  order  to  make  it  correspond  to  the  compass  azimuth  when  the 
fatter  is  less  than  90°. 

The  cotangent  of  haff  the  hour  angle  may  be  found  from  Table  44  abreast  the 
whole  hour  angle  in  the  column  headed  ''Hour  P.  M." 

Example:  At  sea,  in  Lat.  30°  25''  N.,  Long.  5^  25"*  42'  W.,  the  observed  bearing  of  sun's  center  was 
N.  135°  30''  E.,  and  the  Greenwich  mean  time,  December  3,  2**  36™  11'.  The  corrected  declination  of  the 
sun  was  22°  07'  S.;  the  equation  of  time  (additive  to  mean  time),  10™  03'.  Required  the  error  of  the 
compass. 

G.M.T.(Dec.3),      2i'  36™  11'     co-Lat.,      59°  35' 
Long.,  -  5    25    42      p,  112    07 

L,M.T.(Dec.2),     21    10    29  p+co-L,  171    42 

Eq.  t.,  -1-        10    03  

S,  85    51 

L.A.T.,  21    20    32  


t 
S 
D 

X 
Y 


21139m  28*     cot  it    .44051 
85°  51'  cosec     .00114 


26    16 

50    44 
88    19 


sm 
tan 


9. 64596 
. 08761 


cot  it  .44051 
sec  1. 14045 
cos     9. 95267 


tan    L  53363 


t. 


2^  39™  28' 


p-co-L,     52°  32'     X-I-Y139    03 


D,  26    16 

True  azimuth, 
Comp.  azimuth. 

Compass  error. 


N.  139°  03'  E. 
N.  135    30    E. 


3    33    E. 


Example:  At  sea,  in  Lat.  2°  16'  N.,  the  observed  bearing  of  the  sun's  center  waa  N.  85°  15'  E:  sun's 
hour  angle,  3*'  44™  16*,  and  its  declination,  7°  38'  N.     Required  the  compass  error. 


co-Lat., 
P, 

87° 
82 

44' 
22 

p-fco-L, 

170 

06 

s, 

85 

03 

co-L-p, 

5° 

22' 

D, 


2    41 


t 
S 
D 

X 

Y 


3h  44m  16. 
85°  03' 
2    41 

5    03 

87    22 


Y-X       82    19 


True  azimuth, 
Comp.  azimuth, 

Compass  error, 


cot  i  t 

cosec 

sin 

tan 


.  27372 

.00162 

8.  67039 

8.  94573 


N.  82°  19'  E. 
N.  85    15    E. 

2    56   W 


cot  J  t 
sec 

cos 


tan 


. 27372 
1. 06406 
9. 99952 


1. 33730 


I 


AZIMUTH. 


147 


Example:  At  eea,  in  Lat.  16°  32'  S.,  observed  bearing  of  Venus  N.  56°  OO'  W.,  its  hour  angle  being 
4h  27ni  311^  an(j  j^^g  declination  23°  12''  N.    What  waa  the  error  of  the  compass? 


co-Lat.,       73°  28'       t 
p,  113    12        S 


D 


p+co-L,    186    40 
S, 


4h  27"  31* 
93°  20^ 
19    52 

27    16 
87    40 


cot  it  .  18022 
cosec  .  00074 
Bin  9. 53126 


tan 


9.  71222 


cot  i  t 

sec 

cos 


tan 


.  18022 
1. 23549 
9.  97335 


L  38906 


60    24 


19    52 


119°  36' 
True  azimuth, 
Comp.  azimutii, 

Compass  error, 


S.  119°  36'  W. 
S.  124    00  W. 


4     24  W. 


AliTITTJDE  AZIMUTHS. 

353.  This  method  is  employed  when  the  altitude  of  the  body  is  observed  at  the 
same  time  as  the  azimuth;  in  such  a  case  the  hour  an^le  need  not  be  known,  though 
the  time  of  observation  should  be  recorded  with  sufficient  accuracy  for  the  correction 
of  the  declination  of  the  sun,  moon,  or  a  planet. 

There  are  given  the  altitude,  h,  the  polar  distance,  p,  and  the  latitude,  L;  to 
find  the  azimuth,  Z. 

354.  Take  a  bearing  of  the  body  by  compass,  bisecting  it  if  the  disk  is  of 
appreciable  diameter,  and  simultaneously  measure  the  altitude;  note  the  time 
approximately.     Observe  also  the  ship's  heading  (by  compass)  and  the  heel. 

Or  a  series  of  azimuths,  with  corresponding  altitudes,  may  be  observed,  and  the 
means  employed. 

355.  Calculate  the  true  altitude  and  declination  from  the  observed  altitude 
and  the  time.     Then  compute  the  true  azimuth  from  the  following  formula: 

cos  i  Z  =  Vcos  s  cos  (s—p)  sec  L  sec  i^, 

in  which  s  =  i  (h+'L-\-p).     The  resulting  azimuth  is  to  be  reckoned  from  the  north 
in  north  latitude  and  from  the  south  in  south  latitude. 

It  may  occur  that  the  term,  (s  —  p),  will  have  a  negative  value,  but  since  the  cosine 
of  a  negative  angle  less  than  90°  is  positive,  the  result  will  not  be  affected  thereby. 

Example:  At  sea,  in  Lat.  30°  25'  N.,  the  observed  bearing  of  the  sun's  center  waa  N.  135°  30'  E., 
and  its  corrected  altitude  24°  59';  the  approximate  G.  M.  T.  was  2''.6,  the  declination  at  that  time  being 
22°  07'  S.    Required  the  compass  error. 


h 

L 
P 

24°  59' 

30  25 

112  07 

sec 
sec 

cos 

COfl 

cos 

.04267 
.06431 

2  )  167  31 

83  45 
-28  22 

69  30 
139  00 

9. 03690 
9.94445 

»i 

2 )  19. 08833 
9.  54416 

True  azimuth,    N.  139°  00'  E. 
Comp.  azimuth,  N.  135    30    E. 


Compass  error, 


3    30    E. 


TIME  AND  ALTITUDE  AZIMUTHS. 

356.  When,  at  the  time  of  observing  the  compass  bearing  of  a  celestial  body, 
the  altitude  is  measured  and  the  exact  time  noted,  the  true  azimuth  may  be  very 
expeditiously  determined,  a  knowledge  of  the  latitude  being  unnecessary. 

In  view  of  the  simplicity  of  the  computation,  this  method  strongly  commends 
itself  to  observers  not  provided  with  azimuth  tables  or  diagram. 

357.  The  observation  is  identical  with  that  of  the  altitude  azimuth  (art.  354), 
with  the  exception  that  the  times  of  observation  must  be  exactly  instead  of  approx- 
imately noted. 


148  AZIMUTH. 

358.  Ascertain  the  decimation  of  the  body  at  time  of  sight,  and  correct  the 
observed  altitude;  compute  the  hour  angle.     We  then  have: 

sin  Z  =  sin  t  cos  d  sec  It, 

from  which  the  azimuth  may  be  found. 

This  method  has  a  defect  in  that  there  is  nothing  to  indicate  whether  the  resulting 
azimuth  is  measured  from  the  north  or  the  south  point  of  the  horizon;  but  as  the 
approximate  azimuth  is  always  known,  cases  are  rare  when  the  solution  will  be  in 
question. 

Example:  At  sea,  in  Lat.  30°  25''  N.,  Long.  5^  25™  42*  W.,  the  observed  bearing  of  the  sun's  center 
was  N.  135°  30'  E.;  its  altitude  at  the  time  was  24°  59';  hour  angle,  2^  39™  28*  (39°  52'),  and  declination, 
22°  07'  S.  Find  the  compass  error.  (See  example  under  Altitude  Azimuths  and  first  example  under 
Time  Azimuths.) 

t         39°  52'  sin  9. 80686  True  azimuth,     N.  139°  04'  E. 

d        22    07  cos  9. 96681  Comp.  azimuth,  N.  135    30  E. 


h         24    59  sec     .04267 


Compass  error,  3    34  E. 


Z   S.  40°  56'  E.  sin  9.  81634 

TBtTE  BEARING  OF  A  TERRE  STRIAL  OBJECT. 

359.  Thus  far,  sea  observations  for  combined  variation  and  deviation  have  been 
discussed,  but  if  it  becomes  necessary,  as  in  surveying,  to  ascertain  the  True  Bearing 
of  a  Terrestrial  Olject,  or  to  find  the  variation  at  a  shore  station,  more  accurate 
methods  than  the  foregoing  must  be  resorted  to.  ' 

The  most  reliable  method  is  that  by  an  Astronomical  Bearing.  This  consists  in 
finding  the  true  bearing  of  some  well-defined  object  by  taking  the  angle  between  it 
and  the  sun  or  other  celestial  body  with  a  sextant  or  a  theodolite,  and  simultaneously 
noting  the  time  by  chronometer,  or  measuring  the  altitude,  or  observing  both  time 
and  altitude.     It  should  always  be  noted  whether  the  object  is  right  or  left  of  the  sun. 

360.  By  Sextant. — ^Measure  the  angular  distance  between  the  object  and  the 
sun's  limb;  and  if  there  is  a  second  observer,  measure  the  altitude  of  the  sun  at  the 
same  moment  and  note  the  time.  In  the  absence  of  an  assistant,  first  measure  the 
altitude  of  the  sun;  next,  the  an^lar  distance  between  the  sun  and  the  object;  then, 
a  second  altitude  of  the  sun,  notmg  the  time  of  each  observation.  Also  measure  the 
altitude  of  the  defined  point  above  the  sea  or  shore  horizon. 

By  Theodolite. — This  instrument  is  far  more  convenient  than  the  sextant,  for, 
being  leveled,  the  horizontal  angle  between  the  sun  and  the  object  is  at  once  given, 
no  matter  what  may  be  the  altitudes  of  the  objects.  In  case  the  altitude  of  the  sun 
is  needed,  it  may  be  read  accurately  enough  from  the  vertical  circle,  although  not  as 
finely  graduated  as  the  limb  of  the  sextant.  The  error  in  altitude  must,  however, 
be  found  by  the  level  attached  to  the  telescope,  since  it  will  usually  be  found  to  differ 
from  the  levels  of  the  horizontal  circle.  If,  in  directing  the  telescope  to  the  sun,  there 
is  no  colored  eyepiece,  an  image  of  the  sun  may  be  cast  on  a  piece  of  white  paper 
held  at  a  little  distance  from  the  eyepiece,  and  by  adjusting  the  focus  the  shadow 
of  the  cross  wires  will  be  seen. 

It  should  be  understood  that  any  celestial  body  may  be  used  as  well  as  the  sun, 
and  there  are,  in  fact,  certain  advantages  in  the  use  of  the  stars;  the  sun  is  chosen 
for  illustration,  because  it  will  usually  be  found  most  convenient  to  employ  that  body. 

361.  Find  the  true  azimuth  of  the  celestial  body  by  one  of  the  methods  pre- 
viously explained  in  this  chapter,  and  apply  to  it  the  azimuth  difference,  or  horizontal 
angle  between  the  celestial  and  the  terrestrial  body,  having  regard  to  the  direction 
of  one  from  the  other. 

To  find  the  azimuth  difference  from  sextant  observations,  change^  the  observed 
altitudes  of  the  bodies  into  apparent  altitudes  by  correcting  them  for  Index  error  of 
the  sextant,  dip,  and  semidiameter;  change  the  observed  an^lar  distance  into 
apparent  angular  distance,  by  correcting  for  index  error  and  semidiameter.  Then  if 
S  =  i  (App.  Dist.  +  App.  Alt.©  +App.  Alt.  Object),  we  have: 

cos  i  Az.  Diff .  =  Vsec  App.  Alt.©  sec  App.  Alt.  Object  cos  S  cos  (S— App.  Dist.), 
whence  the  azimuth  difference  is  deduced. 


AZIMUTH. 


149 


When  the  theodolite  is  used,  the  horizontal  angle  is  given  directly.  If  only  one 
limb  of  the  sun  is  observed,  it  will  be  necessary  to  apply  a  correction  for  semidiameter 
(S.  D.  Xsec  h),  but  it  is  usual  to  eliminate  this  correction  by  taking  the  mean  of 
observations  of  both  limbs. 

Example  :  From  a.  m.  observations,  in  Lat.  30°  25'  24'^  N.,  Long.  81°  25'  24''  W.,  obtained  the  follow- 
ing data  for  finding  the  true  bearing  of  a  station: 


Watch  time,     ll*'  22""  36' 
C-W,  5    21    18 

Chro.  corr.,    +  2    16 


Obs.  Ang.  Dist.  0,  117°  07'  Left. 
Obs.  2  a,  71°  37'  20" 

Obe.  alt.  Station,  20' 

I.  C,  zero. 


Dec.  S.,     22°  56'  27" 
Eq.  t.,    +  7°  00' 

S.  D.,  16'  17" 


Required  the  true  bearing  of  the  object. 


W.  T., 
C-W, 

Chro.  t., 
C.  C, 

G.  M.  T. 
Eq.t., 

G.  A.  T., 

Long., 


ll^*  22"36» 
5    21     18 


L.  A.T. 
t, 


4 

+ 

43 
2 

54 
16 

4 

+ 

46 

7 

10 
00 

4 

-  5 

53 
25 

10 
42 

23 

27 

28 

/O"  32™  32' 
18°  08'  00" 

Obs.  Ans.  Dist.,      117»  07'  00' 
O's  8.  D.,  +  16    17 


App.  Aag.  Dist.,      117    23    17 


2C1, 

S.  D., 

App.  Alt., 
p.  &  r., 

h. 


71°  37'  20" 


35 

48 

40 

+ 

16 

17 

36 

04 

57 

— 

1 

13 

36    03    44 


App.  Dist. 
App  Alt.  O 
App.  Alt.  Object 


8 

8-App.  Dist. 


J  At.  Diff . 
Ae.  Diff. 


117*  23' 

36    05 

20 

2)153    48 

76    54 
-40    29 


62*  30' 
125    00 


8°  08'   00" 
22    56    27 
36    03    37 

S.       9°  17'  E. 
N.   170    43    E. 


ein  9. 15069 

cos  9. 96422 

sec  . 09239 

sin  9. 20730 


seo  0.00260 
see  0.00001 


cos  9.35536 
cos  9. 88115 


True  bearing  O, 
At.  Diff., 


170"  43'  E. 
1%    00  Left. 


True  bearing  object,  N.  45'  43'  E. 


2)19.32902 
COS  9.66451 


Example:  Same  date  and  place  and  same  objects  as  in  the  preceding  example;  measurement  made 
with  a  theodolite,  angular  distance  (J),  123°  17';  object  left  of  sun.  Watch  time,  11''  16™  34".5;  watch  slow 
of  L.  A.  T.,  4™  53"  .5.    Dec.  0,  22°  56' S.     Required  the  true  bearing.     (See  article  352.) 


W.  T.,       ll''  16™34».5 
W.  slow,  4-         4    53.5 


L.  A.  T.,  23    21    28  .0 
t,  0    38    32 


co-Lat.,      59°  35' 
p,  112    56 


p+co-L, 

172 

31 

s, 

86 

15 

p— co-L, 

53 

21 

t 

s 

D 

X 
Y 


0"  38™32« 
86°  15' 
26    41 

79°  24' 
89    39 


cot  it  1.07435 
cosec  .  00093 
Bin        9. 65230 


tan 


72758 


X4-Y169    03 


D, 


26    41 


True  bearing  ©, 
Az.  Diff., 


N.  169°  03'  E. 
123    17  Left. 


True  bearing  object,  N.    45    46  E. 


cot  it  1.07436 
sec  1. 18440 
COB       9. 95110 


tan       2. 20985 


CHAPTER  XV. 
THE  SUMNER  LINE. 


DESCRIPTION  OF  THE  LINE. 

362.  The  method  of  navigation  involving  the  use  of  the  Sumner  line  takes  its 
name  from  Capt.  Thomas  H.  Sumner,  an  American  shipmaster,  who  discovered  it 
and  published  it  to  the  world.  As  a  proof  of  its  value,  tne  incident  which  led  to  its 
discovery  may  be  related : 

"  Having  sailed  from  Charleston,  S.  C,  25th  November,  1837,  bound  for  Greenock, 
a  series  of  heavy  gales  from  the  westward  promised  a  quick  passage;  after  passing 
the  Azores  the  wind  prevailed  from  the  southward,  with  thick  weather;  after  passing 
longitude  21°  W.  no  observation  was  had  until  near  the  land,  but  soundings  were 
had  not  far,  as  was  supposed,  from  the  bank.  The  weather  was  now  more  boisterous, 
and  very  thick,  and  the  wind  still  southerly;  arriving  about  midnight,  17th  December, 
within  40  miles,  by  dead  reckoning,  of  Tuskar  light,  the  wind  hauled  SE.  true,  making 
the  Irish  coast  a  lee  shore;  the  ship  was  then  kept  close  to  the  wind  and  several 
tacks  made  to  preserve  her  position  as  nearly  as  possible  until  daylight,  when, 
nothing  being  in  sight,  she  was  kept  on  ENE.  under  short  sail  with  heavy  gales.  At 
about  10  a.  m.  an  altitude  of  the  sun  was  observed,  and  the  chronometer  time  noted; 
but,  having  run  so  far  without  observation,  it  was  plain  the  latitude  by  dead  reckoning 
was  liable  to  error  and  could  not  be  entirely  relied  upon. 

The  longitude  by  chronometer  was  determined,  using  this  uncertain  latitude, 
and  it  was  found  to  be  15'  E.  of  the  position  by  dead  reckoning;  a  second  latitude 
was  then  assumed  10'  north  of  that  by  dead  reckoning,  and  toward  the  danger, 
giving  a  position  27  miles  ENE.  of  the  former  position;  a  third  latitude  was  assumed 
10'  farther  north,  and  still  toward  the  danger,  giving  a  third  position  ENE.  of  the 
second  27  miles.  Upon  plotting  these  three  positions  on  the  chart,  they  were  seen 
to  be  in  a  straight  Une,  and  this  line  passed  through  Smalls  light. 

"It  then  at  once  appeared  that  the  observed  altitude  must  have  happened  at 
all  the  three  points  and  at  Smalls  light  and  at  the  ship  at  the  same  instant." 

Then  followed  the  conclusion  that,  although  the  absolute  position  of  the  ship 
was  uncertain,  she  must  be  somewhere  on  that  line.  The  ship  was  kept  on  the  course 
ENE.,  and  in  less  than  an  hour  Smalls  light  was  made,  bearmg  ENE.  ^  E.  and  close 
aboard. 

The  latitude  by  dead  reckoning  was  found  to  be  8'  in  error,  and  if  the  position 
given  by  that  latitude  had  been  assumed  correct,  the  error  would  have  been  8  miles 
too  far  S.,  and  31'  30"  of  longitude  too  far  W.,  and  the  result  to  the  ship  might  have 
been  disastrous  had  this  wrong  position  been  adopted.  This  represents  one  of  the 
practical  applications  of  the  Sumner  line. 

The  properties  of  the  line  thus  found  will  now  be  explained. 

363.  Chicles  of  Equal  Altitude. — In  fi^re  54,  if  EE'E"  represent  the  earth 
projected  upon  the  horizon  of  a  point  A,  and  if  it  be  assumed  that,  at  some  particular 
mstant  of  tmie,  a  celestial  body  is  in  the  zenith  of  that  point,  then  the  true  altitude 
of  the  body  as  observed  at  A  will  be  90°.  In  such  a  case  the  great  circle  EE'E", 
which  forms  the  horizon  of  A,  wiU  divide  the  earth  into  two  hemispheres,  and  from 
any  point  on  the  surface  of  one  of  these  hemispheres  the  body  will  be  visible,  while 
over  the  whole  of  the  other  hemisphere  it  will  be  invisible.  The  great  circle  EE'E", 
from  the  fact  of  its  marking  the  limit  of  illumination  of  the  body,  is  termed  the  circle 
of  illumination,  and  from  any  point  on  its  circumference  the  true  altitude  of  the 
center  of  the  body  will  be  zero.     If,  now,  we  consider  any  small  circle  of  the  sphere, 

150 


THE  SUMNEB  LINE. 


151 


BB'B",  CC'C,  DD'D",  whose  plane  is  parallel  to  the  plane  of  the  circle  of  illumina- 
tion and  which  lies  withiii  the  hemisphere  throughout  which  the  body  is  visible,  it  will 
be  apparent  that  the  true  altitude  of  the  body  at  any  point  of  the  circumference  of 
one  or  these  circles  is  equal  to  its  true  altitude  at  any  other  point  of  the  same  circum- 
ference; thus  the  altitude  of  the  body  at  B  is  equal  to  its  altitude  at  B'  or  B",  and 
its  altitude  at  D  is  the  same  as  at  D'  or  D". 

It  therefore  follows  that  at  any  instant  of  time  there  is  a  series  of  positions  on 
the  earth  at  which  a  celestial  body  appears  at  the  same  given  altitude,  and  these 
positions  lie  in  the  circumference  of  a  circle  described  upon  the  earth's  surface  whose 
center  is  at  that  position  which  has  the  body  in  the  zemth,  and  whose  radius  depends 
upon  the  zenith  distance,  or — what  is  the  same  thing — upon  the  altitude.  Such 
circles  are  termed  circles  of  equal  altUvde.  It  is  important  to  note  that  an  observer 
making  an  instantaneous  transit  through  the  latitudes  and  longitudes  passed  over 
by  any  rhumb  line  or  loxodromic  curve  drawn  within  the  hemisphere  of  illuniination, 
through  the  point  A,  will 
experience  no  astronomical 
difference,  with  reference  to 
the  observed  body  in  the 
zenith  of  A,  save  an  altitude 
difference. 

364.  The  data  for  an 
astronomical  sight  comprise 
merely  the  time,  declination, 
and  altitude.  The  first  two 
fix  the  position  of  the  body 
and  may  be  regarded  as 
giving  the  latitude  and  lon- 
gitude of  that  point  on  the 
earth  in  whose  zenith  the 
body  is  found;  the  zenith 
distance  (the  complement  of 
the  altitude)  indicates  the 
distance  of  the  observer 
from  that  point ;  but  there  is 
nothing  to  show  at  which  of 
the  numerous  positions  ful- 
filling the  required  condi- 
tions the  observation  may 
have  been  taken.  A  num- 
ber of  navigators  may  meas- 
ure the  same  altitude  of  a 
bod^r  at  the  same  instant 
of  time,  at  places  thousands 
position  with  identical  data. 


of 


miles  apart;  and  each  proceeds  to  work  out  his 
so  far  as  this  sight  is  concerned.  It  is  therefore 
clear  that  a  single  observation  is  not  enough,  m  itself,  to  locate  the  point  occu- 
pied by  the  observer,  and  it  becomes  necessary,  in  order  to  fix  the  position,  to 
employ  a  second  circle,  which  may  be  either  that  of  another  celestial  body  or  that  of 
the  same  body  given  by  an  observation  when  it  is  in  the  zenith  of  some  other  point 
than  when  first  taken;  knowing  that  the  point  of  observation  lies  upon  each  of  two 
circles,  it  is  only  possible  that  it  can  be  at  one  of  their  two  points  of  intersection; 
and  since  the  position  of  the  ship  is  always  known  within  fairly  close  limits,  it  is  easy 
to  choose  the  proper  one  of  the  two.  Figure  55  shows  the  plotting  of  observations 
of  two  bodies  vertically  over  the  points  A  and  A'  upon  the  earth,  the  zenith  distances 
corresponding  respectively  to  the  radii  AO  and  A'O. 

365.  The  Sumner  Line. — In  practice,  under  the  conditions  existing  at  sea,  it 
is  never  necessary  to  determine  the  whole  of  a  circle  of  equal  altitude,  as  a  very  small 
portion  of  it  will  suffice  for  the  purposes  of  navigation ;  tne  position  is  always  known 
within  a  distance  which  will  seldom  exceed  30  mUes  under  the  most  unfavorable 
conditions,  and  which  is  usually  very  much  less;  in  the  narrow  limits  thus  required, 
the  arc  of  the  circle  will  practically  coincide  with  the  tangent  at  its  middle  point, 


152  THE   SUMNEB  LINE. 

and  may  be  regarded  as  a  straight  line.  Such  a  line,  comprising  so  much  of  the  circle 
of  equal  altitude  as  covers  the  probable  limits  of  position  of  the  observer,  is  called  a 
Sumner  line  or  Line  of  position. 

The  latter  designation  has  also  a  more  extended  meaning,  embracing  any  line, 
straight  or  curved,  which  forms  a  locus  of  the  ship's  position,  whether  it  be  obtained 
from  observations  of  celestial  bodies  or  from  bearings  or  distances  of  terrestrial 
objects. 

366.  Since  the  direction  of  a  circle  at  any  point — that  is,  the  direction  of  the 
tangent — must  be  perpendicular  to  the  radius  at  that  point,  it  follows  that  the 
Sunmer  line  always  lies  in  a  direction  at  right  angles  to  that  in  which  the  body  bears 

from  the  observer.  Thus,  in  figure  55, 
it  may  be  seen  that  m  m'  and  n  n',  the 
extended  Sumner  lines  corresponding  to 
the  bodies  at  A  and  A',  are  respectively 
perpendicular  to  the  bearings  of  the  bodies 
OA  and  OA'.  This  fact  has  a  most  im- 
portant application  in  the  employment  of 
the  Sumner  line. 

367.  Uses  of  the  Sumner  Line. — 
The  Sumner  line  is  valuable  because  it 
gives  to  the  navigator  a  knowledge  of  all 
of  the  probable  positions  of  his  vessel, 
while  a  sight  worked  with  a  single  assumed 
latitude  or  longitude  gives  but  one  of  the 
probable  positions;  it  must  be  recognized 
that,  in  the  nature  of  things,  an  error  in 
the  assumed  coordinate  will  almost  invariably  exist,  and  its  possible  effect  should 
be  taken  into  consideration;  the  line  of  position  reveals  the  difference  of  longitude 
due  to  an  error  in  the  latitude,  or  the  reverse. 

Since  the  Sumner  line  is  at  right  angles  to  the  bearing,  it  may  be  seen  that  when 
the  body  bears  east  or  west — that  is,  when  it  is  on  the  prime  vertical — the  resulting 
line  runs  north  and  south,  coinciding  with  a  meridian;  if,  in  this  case,  two  latitudes 
are  assumed,  the  deduced  longitudes  will  be  the  same.  When  the  body  bears  north 
or  south,  or  is  on  the  meridian,  the  line  runs  east  and  west,  and  becomes  identical  with 
a  parallel  of  latitude;  in  such  a  case,  two  assumed  longitudes  will  give  the  same 
latitude.  Any  intermediate  bearing  gives  a  Sumner  line  inclined  to  both  meridians 
and  parallels;  if  the  line  agrees  in  direction  more  nearly  with  the  meridian,  latitude 
should  generally  be  assumed  and  the  longitude  worked;  if  it  is  nearer  a  parallel,  the 
reverse  course  is  usually  preferable.  The  values  of  the  assumed  coordinates  may 
vary  from  10'  to  1°,  according  to  circumstances. 

368.  The  greatest  benefit  to  be  derived  from  the  Sumner  method  is  when  two 
lines  are  worked  and  their  intersection  found.  The  two  lines  may  be  given  by 
different  bodies,  which  is  generally  preferable,  or  two  different  lines  may  be  obtained 
from  the  same  body  from  observations  taken  at  different  times.  The  position 
given  by  the  intersection  of  two  lines  is  more  accurate  the  more  nearly  the  Imes  are 
at  right  angles  to  each  other,  as  an  error  in  one  line  thus  produces  less  effect  upon  the 
result.  When  two  observations  of  the  same  body  are  taken,  the  position  of  tne  ship 
at  the  time  of  first  sight  must  be  brought  forward  to  that  at  the  second  in  considering 
the  intersection ;  if,  for  example,  a  certain  line  is  determined,  and  the  ship  then  runs 
NW.  27  mUes,  it  is  evident  that  her  new  position  is  on  a  line  parallel  with  tlie  first  and 
27  mUes  to  the  NW.  of  it ;  a  second  line  being  obtained,  the  intersection  of  this  with 
the  first  line,  as  corrected  for  the  run,  gives  the  ship's  position. 

Besides  the  employment  of  two  lines  for  intersection  with  each  other,  a  single 
line  may  be  made  to  serve  various  useful  purposes  for  the  navigator.  These  are 
described  in  article  389,  Chapter  XVI. 

METHODS  OF  DETERMINATION. 

369.  There  are  three  methods  in  common  use  for  determining  the  Sumner  line: 
(a)  The  Chord  Method:  To  assume  two  values  of  one  coordinate  and  find  the 

corresponding  values  of  the  other.     Two  values  of  the  latitude  may  be  assumed  and 


THE   SUMNEB  LINE.  153 

the  longitudes  determined,  as  was  done  by  Capt.  Sumner  on  the  occasion  that  led  to 
the  discovery  of  his  method;  or  else  two  values  of  the  longitude  may  be  assumed 
and  the  latitudes  determined.  Two  points  are  fixed  in  this  way,  and  the  line  joining 
them  is  the  Sumner  line. 

(&)  The  Tangent  Method:  To  assume  either  one  latitude  or  one  longitude  and 
determine  the  corresponding  coordinate.  This  gives  one  point  of  the  Sumner  line. 
The  azimuth  of  the  observed  celestial  body  is  then  ascertained,  and  a  line  is  drawn 
through  the  determined  point  at  right  angles  to  the  direction  in  which  the  body  bore 
at  the  time  of  the  sight.     This  will  be  the  Sumner  line. 

(c)  In  accordance  with  the  method  of  Saint  Hilaire,  to  be  described  in  article 
371,  to  lay  off  from  an  assumed  geographical  position,  along  the  line  of  direction 
in  which  the  body  bore  at  the  time  of  the  sight,  the  determined  distance  to  the 
Sumner  line. 

370.  It  follows  that  if  the  Sumner  line  be  located  by  the  first  method  and  its 
direction  thus  defined,  the  azimuth  of  the  observed  body  may  be  determined  by 
finding  the  angle  made  by  the  line  with  the  meridian  and  adding  or  subtracting  90  . 

Example:  At  sea,  April  17, 1915,  a.  m.,  in  Lat.  25°  12'  S.,  Long.  31*  32'  W.,  by  D.  R.,  observed  an 
altitude  of  the  planet  Jupiter,  east  of  the  meridian,  32°  46'  10";  watch  time,  ^  48™  02»;  C-W,  2"  05"»  42»; 
C.  C,  +  2™  IS";  I.  C,  +  1'  30";  height  of  eye,  18  feet.     Reguired  the  Sumner  line. 

From  a  solution  of  this  same  problem  for  a  single  longitude  (art.  343,  Chap.  XIII),  the  following 
were  found:  H.  A.  from  Or.,  1"  39""  55»  E.;  h,  32°  42' 01'';  p,  83°  55'  19".  Assume  values  of  Lat.  25°  02' 
and  25°  22'  S. 


h          32°  42'  01" 
L,         25    02    00 
p          83     55    19 

sec 
cosec 

cos 
sin 

sin  i  t 

.04284 
.00245 

9.  51641 
9. 79057 

82— h 
Gr.H.A. 
H.A.J 

Long.j 

25°  22'  00" 

70    59    40 
38     17     39 

sec 
cosec 

COB 

sin 

ein  J  i 

.04403 
.00245 

2)141    39    20 

«i          70    49    40 
s^-h    38    07    39 

9.  51276 
9.  79218 

Gr.H.A.       1"  39™55'E. 
H.  A.,           3    46    33   E. 

2)19.  35227 
;,      9. 67613 

1"  39°55» 
3    46     19 

2)19.  35142 
Cj      9. 67571 

T^ /    2"  06™38='W 

Long.i|  3^0  39/  3o//|\V. 

/  2"  06"  24"  \^ 
\31°  36'  00"/ *^- 

A  comparison  of  these  results  with  those  obtained  by  the  solution  with  a  single 
latitude  shows  that  the  hour  angle,  and  consequently  the  longitude,  corresponding 
to  the  latitude  25°  12'  S.  are  the  means  of  those  corresponding  to  the  latitudes  here 
used;  and  therefore  that  the  assumption  that  the  Sumner  line  is  a  straight  line  is 
accurate. 

The  line  of  the  same  sight  might  also  have  been  found  as  follows : 

Working  with  the  single  latitude  25°  12'  S.,  it  was  found  that  the  corresponding 
longitude  was  31°  37'  45"  W.  Now,  by  referring  to  an  azimuth  table  or  azimuth 
diagram,  the  azimuth  corresponding  to  Lat.  25°.2  S.,  Dec.,  6°.l  S.,  H.  A.,  3**  46™.4 
E.  IS  S.  99°  23'  E.;  therefore  the  Sumner  line  extends  S.  9°  23'  E. 

The  line  may  therefore  be  defined  in  either  of  two  ways,  thus : 

.  /25°  02'   00"  S.  i  /25°  22'   00*  S. 

^431  39     30   W.  ^131     36     00   W. 

^  .  /25°  12'   00"  S.  Line  runs  S.  9°  23'  E. 

^'  ^131  37     45    W. 

By  inspection  of  the  coordinates  of  A^  and  A3  it  may  be  seen  that — 

+  20'  diff.  lat.  makes  -3'.50  diff.  long.;  or 

+  20  miles  diff.  lat.  makes  —3.2  miles  departure. 

Therefore  by  reference  to  Table  2  it  appears  that  the  line  runs  about  S.  9°  E., 
and  the  azimuth  of  the  body  is  S.  99°  E.;  thus  the  results  obtaiaed  by  the  two 
methods  agree. 


154 


THE   SUMNER  LINE. 


Example:  At  sea,  May  18,  1915,  a.  m.,  Lat.  41°  33^  N.,  Long.  33°  SO'  W.,  by  D,  K.,  the  mean  of  a 
series  of  observed  altitudes  of  the  sun's  lower  limb  was  29°  41''  00^'';  the  mean  watch  time,  7''  20™  45'. 3; 
C.  C,  +4™  59».2;  I.  C,  -30^^;  height  of  the  eye,  23  feet;  C-W,  2^  17™  06».     Required  the  Sumner  line. 

From  a  solution  of  this  same  problem  for  a  single  longitude  (art.  343,  Chap.  XIII)  the  following 
were  found:  G.  A.  T.,  21''  46™  35»;  h,  29°  50^  04'^;  p,  70°  38' 49^^  Assume  values  of  the  latitude  41°  03^ 
and  42°  03'  N. 


h  29°  50'  04" 

L,        41    03    00 
p  70    38    49 

2)141    31     53 

8i  70    45    57 

Si-A    40    55    53 


sec 
cosec 


cos 
sin 


G.A.T.,     21''  46™  35" 
L.A.T.1      19    32    39 


Long.i  I 


2"  13™56'\xx. 
33°  29'  00"/"^- 
4  /  41°  03'  00"  N. 
^4  33 


29    00    W. 


. 12255 
.  02526 


9.  51776 
9. 81634 

2)19.  48191 


sin  i  «i      9.  74096 


A  /42°  03'  00"  N. 
^H33    29    15    W. 


42°  03'  00" 


*'     7. 
s^—n 

G.  A.  T. 

L.  A.  T.. 


71 
41 

15  57 
25    53 

21'' 
19 

46™  35» 
32    38 

. 12927 
.  02526 


9.  50675 
9.  82068 

2)19.  48196 


sin  i  <2      9.  74098 


sec 
cosec 


COS 

sin 


Long.2      jg 


W. 


2"  13™57''U 
1.33°  29'  15"/^ 
+60'  diff.  lat.  makes  +0'.25  long. 
-j-60  miles  diff.  lat  makes  +0.2  mile  departure. 


Line  runs,  N.  i°  W.    Azimuth,  N.  891°  E. 


The  same  sight  worked  with  a  single  latitude,  41°  33'  N.,  as  was  done  in  the 
original  example,  with  azimuth  taken  from  tables  or  diagram,  gives : 


r4i° 

133° 


33'   00"  N.  Azimuth,      N.  89°  52'  E. 

29'   08"  W.  Line  runs,    N.     0°  08'  W. 


This  example  illustrates  the  case  in  which  an  observation  is  taken  practically 
on  the  prime  vertical;  the  azimuth  shows  the  bearing  to  be  within  0°  08'  of  true  East, 
and  the  Sumner  line  is  therefore  within  0°  08'  of  the  meridian;  a  variation  of  30' 
in  either  direction  from  the  dead  reckoning  latitude  makes  a  difference  of  only  7". 5 
in  the  longitude. 

Example:  May  22,  1915,  in  Lat.  6°  20'  S.  by  account.  Long.  30°  21'  30"  W.;  chro.  time,  7"  35™  10"; 
observed  altitude  of  moon's  upper  limb,  68°  30'  00",  bearing  north  and  east;  I.  0.,— 3'  00";  height  of 
eye,  26  feet;  chro.  fast  of  G.  M.  T.,  1™  37'.5.    Required  the  Sumner  line. 

From  a  solution  of  the  same  problem  with  a  single  longitude  (art.  332,  Chap.  XII),  the  following 
values  are  obtained:  H.  A.  from  Greenwich,  0"  54™  16»  W.;  h,  68°  27'  07";  d,  7°  10'  10"  N.  Assume 
the  longitudes  30°  10'  and  30°  30'  W. 


16° 

7 

68 

7 

14 

{ 

36' 
10 

27 

28 

05 

Sr.  H.  A. 
Long.i 

00" 
10 

07 

40  N. 

30  S. 

0"  54™16»W. 
2    00    40  W. 

Gr.  H.  A. 

Long.2 

cosec     .  90377 
sin       9. 96854 
sin       9. 11442 

0" 
2 

54™  16» 
02    00 

36' 
10 

12' 
30 

5 

,  f  1"  06™  24* 
^H16°  36'  00" 

sec     .  01849 
tan  9.09964 

1" 
.6° 

07™  44» 
56'  00" 

a/  6° 
a/  ^° 

tan  9. 11813 

sec     .  01925 
tan  9. 09964 

50"  S. 
00"  W. 

<t>\ 

cos       9. 98673 

cosec     .  90377 
sin       9. 96854 
sin       9. 11517 

Lat.i 

6 

16° 

7 

66 

7 
13 

36 

56' 
10 

27 

29 

41 

50  S. 

00" 
10 

07 

27  N. 
30  S. 

A 

^a 

tan  9. 11889 

03"  S. 
00    W. 

4^2 

cos       9. 98748 

Lat.2 

6 

12 

03  S. 

THE  SUMNER  LINE.  155 

Working  by  the  other  method,  and  finding  the  azimuth,  we  have : 


r  6° 

^30 


2l'   SO^W  LmerunsN.  38°  42'   W. 


It  might  be  shown  that  the  results  check  with  each  other,  as  in  previous  cases. 

Example:  At  sea,  July  12,  1915,  in  Lat.  50°  N.,  Long.,  40"  W.,  observed  circum-meridian  altitude 
of  the  sun's  lower  limb,  the  time  by  a  chronometer  regulated  to  Greenwich  mean  time  being  2''  41"  39»; 
chro.  corr.,  -2°>  30';  I.  C,  -3'  0^^;  height  of  the  eye,  15  feet.    Find  the  Sumner  line. 

From  the  solution  of  the  same  problem  for  a  single  latitude  (art.  330,  Chap.  XII)  the  following  values 
were  obtained:  G.  A.  T.,  2''  33°»  50';  h,  61°  57'  01''';  d,  22°  04'  57''  N.;  a  (Tab.  26),  2"  .5.    Assume  longi- 


tudes 39°  45'  and  40°  15'  W. 


Gr  H.  A.         2^  33"  50*  Gr.  H.  A.        2"  33"  50* 

Long.i  -  2    39    00  Long.,        -  2    41    00 

L  7     10 


h 

5 

10 

h 

61° 

+ 

57' 

1 

Ol'^ 
06 

H. 

61 

58 

07 

J 

28 
22 

01 
04 

53  N 
57  N 

h  61°  57'  01" 

afj*  +  2    08 

H,  61    59    09 


L,  50    06    50  N. 

The  line  given  by  these  coordinates  is  then: 


4 


50°  06'  50"  N. 
39    45    00    W. 


2.        28  00 
d                    22  04 

51  N. 
57  N. 

L,        50  05 

48  N. 

.  /50°  05'  48"  N. 
M40  15  00  W. 

This  shows  that  the  Sumner  line  lies  so  nearly  in  a  due  east-and-west  direction 
that  a  difference  of  longitude  of  30'  makes  a  difference  of  latitude  of  only  1'. 

From  the  azimuth  tables  or  diagram,  it  is  found  that  the  azimuth  of  the  sun 
corresponding  to  Lat.  50°  N.  Dec.  22°  N.  and  H.  A.  6°*  iq«  E.,  is  N.  177°  E.  Therefore, 
using  the  values  given  by  the  earlier  solution,  the  line  is  defined  as  follows: 

aI^Oo'    Oo'w.  Line  runs  N.  87°  E. 

The  direction  of  the  line  thus  given  and  of  the  one  found  from  the  double  co- 
ordinates may  be  shown  to  agree  as  in  examples  before  given. 

THE  METHOD  OF  SAINT  HIliAIBE  OB.  OP  THE  CALCULATED  ALTmiDES. 

371.  The  foregoing  parts  of  this  work  have  set  forth  that,  when  the  purpose 
of  the  navigator  is  to  find  the  latitude,  the  observed  celestial  body  should  be  situated 
on  or  near  tne  meridian  or  at  least  not  remote  from  it,  and  that  he  must  apply  different 
rules  according  as  the  body  is  on  or  near  or  more  remote  from  the  meridian;  and 
again  when  his  purpose  is  to  find  the  longitude,  the  observed  celestial  body  should 
be  situated  on  or  near  or  at  least  not  remote  from  the  prime  vertical,  and  that  he 
must  then  apply  another  set  of  rules.     It  is  also  explained  in  article  363  that  a  navi- 

tator,  who  has  measured  the  altitude  of  a  celestial  body  at  a  known  instant  of  time, 
as  really  located  his  geographical  position  on  the  circumference  of  a  circle  whose 
radius  is  equal  to  the  zenith  distance  (90°  —  Alt.)  and  whose  center  is  the  geographical 
position  of  the  celestial  body  or  that  point  on  the  earth's  surface  which  falls  vertically 
under  the  observed  body  at  the  instant  of  observation. 

It  has  been  pointed  out  that  practical  needs  are  concerned  only  with  that  portion 
of  the  circumference  of  the  circle  of  position  which  lies  in  the  vicinity  of  the  estimated 

Sosition  of  the  ship,  and,  having  seen  how  this  portion  may  be  determined  and  laid 
own  by  methods  depending  upon  the  computation  of  latitudes  and  longitudes,  we 
proceed  to  extend  our  view  to  the  accomplishment  of  this  purpose  by  a  method  which 
js  now  rapidly  growing  in  favor  among  practical  navigators,  because  it  brings  the 
whole  of  astronomical  navigation  under  a  single  rule  by  rendering  the  course  of 
procedure  the  same,  whatever  the  situation  in  the  heavens  of  the  observed  bod;^  may 
oe,  provided  only  that  the  conditions  admit  of  accurate  measurement  of  its  altitude. 


156  THE   SUMNER  LINE. 

In  figure  54,  the  circumference  of  a  circle  of  position  is  represented  as  having 
been  laid  down  from  A,  the  geographical  position  of  the  observed  body,  as  a  center, 
with  a  radius  AC  equal  to  the  zenith  distance  of  the  observed  celestial  body;  but  it 
is  evident  that  a  small  arc  of  the  circumference,  not  differing  sensibly  from  a  straight 
line  within  the  extent  of  a  Sumner  line,  may  be  determined  in  the  following  manner 
from  a  neighboring  geographical  position,  as  at  P,  inside  or  outside  of  the  circum- 
ference and  at  or  near  the  position  of  the  ship  as  given  by  dead  reckoning: 

1.  Find  the  great-circle  distance  (zenith  distance)  and  bearing  (azimuth)  of  the 
geographical  position  of  the  observed  body  A  from  the  observer's  assumed  position  P. 

2.  Take  the  difference,  in  minutes  of  arc  (nautical  miles),  between  this  zenith 
distance  AP  due  to  the  observer's  assumed  position,  and  the  zenith  distance  AC 
found  from  the  true  altitude  resulting  from  observation. 

3.  Lay  off  this  difference,  which  is  called  the  altitude-difference,  or  intercept^ 
from  the  assumed  position  P  either  away  from  or  toward  the  observed  celestial  body 
according  as  the  true  altitude  by  observation  is  less  or  greater  than  the  altitude  at 
the  assumed  position,  and  through  the  point  thus  reached  draw  a  line  at  right  angles 
to  the  bearing. 

The  line  so  drawn  will  evidently  be  a  tangent  to  the  circumference  of  the  circle 
of  position,  and  will  be  so  nearly  comcident  with  this  circumference  throughout  such 
length  as  the  Sumner  line  need  have,  in  all  those  cases  in  which  the  zenith  distance 
is  as  great  as  10°,  that  the  tangent  itself  may  be  taken  as  the  true  Hne  of  position. 
Obviously  the  only  trigonometrical  computation  that  occurs  under  this  method  is 
in  calculating  the  lengm  and  bearing  of  the  great-circle  arc  joining  the  position  P, 
which  is  assumed  or  known  from  the  dead  reckoning,  with  the  geographical  position 
A,  which  is  always  in  a  latitude  equal  to  the  declination  of  the  observed  celestial 
body  at  the  instant  of  observation  and  in  a  longitude  equal  to  the  hour  angle  of  the 
body  from  the  prime  meridian  (Greenwich).  In  the  case  of  the  sun  the  Greenwich 
hour  angle  is  expressed  by  Greenwich  apparent  time,  and  in  the  case  of  any  other 
celestial  body  the  Greenwich  hour  angle  is  found  as  explained  in  article  293,  using 
G.  M.  T.  instead  of  L.  M.  T. 

372.  Being  strictly  in  the  nature  of  calculating  the  great-circle  distance  and 
course  between  two  pomts  whose  latitudes  and  longitudes  are  given,  these  compu- 
tations may  be  made  according  to  articles  190  and  191,  Chapter  V;  but  in  practice 
it  is  unnecessary  to  do  so,  since  various  altitude  and  azimuth  tables  give  the  distance 
and  azimuth  or  true  bearing,  on  the  globe  or  on  the  celestial  sphere,  of  any  place  from 
every  other  place,  and  consequently  the  altitude  and  azimuth,  or  zenith  distance  and 
bearing,  that  any  celestial  body  would  have  at  any  given  time  to  an  observer  situated 
in  any  given  geographical  position.  So  that  an  observer  in  a  geographical  position 
as  yet  unknown,  about  to  measure  the  altitude  of  a  celestial  body  for  the  purpose 
of  deducing  geographical  position,  may  assume  beforehand  a  geographical  position 
in  the  region  of  his  station  and  find  from  the  tables  the  altitude  and  azimutn  which 
the  celestial  body  would  have  if  observed  from  the  assumed  position;  and  then, 
comparing  the  altitude  so  taken  from  the  tables  with  the  true  altitude  obtained  by 
measurement,  may  at  once  find  the  Sumner  line  by  laying  off  from  the  assumed  geo- 
graphical position  along  the  direction  of  the  bearing  an  intercept,  called  the  altitude- 
difference,  and  drawing  through  its  extremity  a  line  at  right  angles  to  the  bearing. 

After  finding  the  altitude-difference  or  intercept,  the  simplest  procedure  consists 
in  laying  it  off  on  the  chart  from  the  assumed  position  and  drawing  the  Sumner  Une 
through  its  extremity,  but  if,  for  any  reason,  this  process  is  not  desirable,  the  latitude 
and  longitude  of  the  extremity  of  the  intercept,  which  is  a  point  on  the  Sumner  line, 
called  the  "computed  point,"  may  be  found  by  the  use  of  the  Traverse  Tables,  or 
may  be  computed  directly. 

The  exact  position  of  the  observer  on  the  Sumner  line  is,  of  course,  indeterminate 
from  one  observation,  unless  either  the  latitude  or  longitude  of  the  observer's  position 
be  known  beforehand,  but  the  computed  point  will  always  be  nearer  to  the  actual 
position  of  the  observer  than  the  dead  reckoning  or  assumed  position  is.  To  obtain 
a  fix,  that  is,  to  find  the  actual  position,  it  is  necessary  to  determine  the  intersection 
of  the  first  Sumner  line  with  another  Hne  of  position,  which  may  be  another  Sumner 
line  or  a  line  of  bearing  or  any  other  line  containing  the  ship's  position  at  the  same 
time. 


THE  SUMNEE  LINE.  167 

When,  the  specially  prepared  altitude  and  azimuth  tables  are  not  preferred,  the 
required  azimuth  or  true  bearing  of  the  observed  celestial  body  may  be  taken  from 
the  time  azimuth  tables,  and  the  zenith  distance,  and  hence  the  altitude,  that  the 
observed  body  would  have  at  the  instant  of  observation  to  an  observer  in  the 
assumed  geographical  position  may  be  conveniently  computed  by  the  following 
formula : 

hav  2= hav  (L~d)-\-  cos  L  cos  d  hav  t 

or  by  the  formula  of  haversines,  which  is  rid  of  all  doubt  as  to  the  algebraical  signs 
of  the  quantities  and  requires  reference  to  only  one  trigonometrical  table: 

hav  0  =  hav  (Co.  L-P.  D.)  +  {hav  (Co.  L  +  P.  D.)-hav  (Co.  L-P.  D.)}hav  t 

These  are  modifications  of  the  fundamental  formula: 

sin  h  =  sin  L  sin  d  +  cos  L  cOs  d  cos  t, 

which  is  itseK  often  preferred  for  the  computation  of  the  altitude  from  the  latitude, 
declination,  and  hour  angle. 

In  the  computations  which  follow,  the  parts  of  the  several  formulae  have  been 
designated  as  follows : 

IN  THE  COSINE-HAVERSINE  FORMULA : 

hav  ^=co8  L  COB  d  hav  t; 
hence, 

hav  2=hav  (L-^cQ+hav  d 

IN  THE   HAVERSINE   FORMULA: 

hav  A=hav  (Co.  L+P.  D.)-hav  (Co.  L-P.  D.) 
hav  B={hav  (Co.  L+P.  D.)-hav  (Co.  L-P.  D.)}  hav  W 
hence, 

hav  2=hav  (Co.  L-P.  D.)+hav  B. 

IN   THE   SINE-COSINE   FORMULA: 

A=Bin  L  sin  d,     B=co8  L  cob  d  coa  t; 
hence, 

sin  A=A+B. 

Example.— At  sea,  May  18,  1915,  a.  m,,  Lat.  41°  33'  N. ;  Long.  33°  SO'  W.,  by  D.  R.,  the  mean  of  a 
series  of  observed  altitudes  of  the  sun's  lower  limb  was  29°  41'  00''';  the  mean  watch  time,  7^  20™  45. 3»; 
C.  C.+4"'69.2^;  I.  C.,-30";  heightof  eye,  23  feet;  C.-W.,  2"  IT-^OG'.    Required  the  Sumner  line. 

From  a  solution  of  the  same  problem  under  article  343,  Chapter  XIII,  and  article  368,  Chapter  XV,  the 
following  are  taken  from  among  the  prepared  data;  G.  A.  T.,  21^46'"  35";  P.  D.,  70°  38' 49";  /j,  29°  50' 04", 
and,  therefore,  the  measured  zenith  distance  (90°  —  h),  60°  09'  56". 

Assume  a  position  in  latitude  41°  30'  N.  and  longitude  33°  39'  30"  or  2*'  14™  38*  W.,  then  the  solution 
will  be  as  follows: 

L  41°  30'  00"  G.  A.  T.     21''  46™  35* 

Long.  2     14    38  W. 


Co.  L.      48    30    00 

P.  D.        70    38    49  L.  A.  T.    19    31    57=<. 

Note. — ^After  obtaining  the  G.  A.  T.,  it  will  be  seen  that  the  longitude  of  the  assumed  position  may 
be  so  chosen  aa  to  avoid  seconds  in  the  L.  A.  T.  or  H.  A. 

The  azimuth  found  from  the  azimuth  tables  is  N.  89°  52'  E. 

BY  THE   COSINE-HAVERSINE   FORMULA: 

t       19"  31™  57*  log  hav      9. 48392 

L     41    30    00     N.  log  cos       9. 87446 

d      19    21    11     N.  log  cos       9. 97474 


log  hav  d  9.  33312  a 


nat  hav  0  0.  21534 


L/^d 

z 

h 
h 

22°  08'  49". . . . 

60°  17'  40".... 
90°  00'  00" 

nat   hav    0.03689 

Calculated 

nat  hav    0.25223 

Calculated 
Observed 

29    42    20 
29    50    04 

Altitude-difference  7'  44" 


o  The  arrangement  of  Table  45  Is  such  as  to  obviate  the  necessity  of  taking  out  the  value  of  the  angle  in  finding  the  natural 
haversine  from  the  log.  haversine,  or  vice  versa. 


158 


THE   SUMNER  LINE. 


BY   THE   HAVERSINE   FORMULA: 


Co.  L+P.  D.     119°  08'  49^''  nat  hav    0.  74353 
Co.L-P.  D.      22    08    49    nat  hav    0.03689 


nat  hav  A 

log  hav  A 
log  hav  t 

0.  70664  o 

9.  84920 
9.  48392 

log  hav  B 

nat  hav  B 

nat  hav  (Co.  L-P.  D.) 

9.  33312 

0.  21534 
0.  03689 

nat  hav  z 
Calculated  z 

0. 25223 

60°  17'  40^' 
90    00    00 

Calculated  h 
Observed  h 

29    42    20 
29    50    04 

Altitude-difference 


BY  THE   SINE-COSINE   FORMULA: 


7/   44// 


19^^    3]^m  gy* 

292°  59'  15'' log  cos  9.  59165 

41    30    00  N        log  sin    9.82126        log  cos  9.87446 

19    21    11  N        log  sin    9.52034        log  cos  9.97474 


log  A    9.34160 
A    0.21958 


log  B  9.  44085 
B  0.27596 
A    0.21958 


Calculated  ^=29°  42'  19"       nat  Bin=A+B 


0.  49554 


^  Since  the  observed  altitude  is  higher  than  the  calculated  altitude,  the  observer's 
position  is  nearer  to  the  observed  body  than  the  assumed  position.     Consequently 
the  altitude-difference  should  be  laid  off  in  a  direction  to  the  east  and  north,  89 **  52', 
7,73  nautical  miles  from  the  assumed  position. 
Or,  by  the  Traverse  Tables: 


Course. 

Distance. 

Diflf.  Lat. 

Dep. 

Difif.  Long. 

8^°  52' 

7.73 

0'.02  N. 

7'.  73  E. 

lO'.S  E. 

Assumed  position,  Lat. 
Diff.  Lat. 


41°  30'  00"  N. 
01    N. 


Computed  point  on  Sumner  line,  41°  30'   01"  N. 


Long.  33°  39'   30"  W. 

Diff.  Long.  10     18      E. 

33°  29'    12"  W. 


The  direction  of  the  Sumner  line,  being  at  right  angles  to  the  azimuth  or  true 
bearing  of  the  observed  celestial  body,  runs  N.  0°  08'  W.  and  S.  0°  08'  E.  or  359°  52' 
and  179°  52'. 

Example:  At  sea,  May  22,  1915,  in  Lat.  6°  20'  S.  by  account.  Long.  30°  21'  30"  W.;  chro.  time, 
7^  35™  10»;  observed  altitude  of  moon's  upper  limb,  68°  30'  00",  bearing  north  and  east;  I.  C.,— 3'  00"; 
height  of  eye,  26  feet;  chro.  fast  of  G.  M.  T.,  1™  37'. 5.     Required  the  Sumner  line. 

From  a  solution  of  the  same  problem  under  article  332,  Chapter  XII,  and  again  under  article  370, 
Chapter  XV,  the  following  quantities  are  taken  from  among  the  prepared  data:  H.  A.  from  Greenwich, 
Qu  54m  iQs  -^  .  corrected  altitude,  h,  68°  27'  07";  d,  7°  10'  10"  N.  and,  hence,  P.  D.,  82°  49'  50". 

Assume  a  position  in  Lat.  6°  00'  S.  and  Long.  30°  16'  45"  W.;  then  the  solution  will  be  as  follows: 


L 

6°  00'  00"  S. 

Gr.  H.  A. 
Long. 

t 

Qh  54mi6»W 
2    01    07  W 

Co.  L 
P.  D. 

96    00    00 
82    49    50 

1    06     51 

a  The  arrangement  of  Table  45  is  such  as  to  obviate  the  necessity  of  taking  out  the  value  of  the  angle  in  finding  the  natural 
haversine  from  the  log.  haversine,  or  vice  versa. 


THE   SUMNER  LINE. 


159 


BY  THE  COSINE-HAVERSINE  P< 

( 

L 

d 

3RMULA: 

1"  06°  51* 
6°  OO'  00''  S. 
7    10    ION. 

13°  IC^IO^ 

21     14    53 
90    00    00 

loghav  8.32470 
log  C08  9.  99761 
log  cos        9.  99659 

log  hav  e  8.  31890 

L-^rf 

nat  hav  6  0.  02084 
nat  hav      0.  01315 

t 

nat  hav      0. 03399 

Calculated  h 
Observed  h 

68    45    07 
68    27    07 

Altitude-difference 

BY  THE  HAVERSINE  FORMULA : 

Co.  L+P.  D. 
Co.  L-P.  D. 

nat  hav  A 

log  hav  A 
log  hav  t 

log  hav  B 


18    00 


178°  49'  50"  nat  hav 
13    10  10    nat  hav 


nat  hav  B 

nat  hav  (Co.  L-P.  D.) 

nat  hav  z 
Calculated  z 


Calculated  h 
Observed  h 

Altitude-difference 

BY  THE  SINE-COSINE  FORMULA : 


t 

V'  06°>  51' 
16°  42'  45"  . . . 

L 
d 

6  00    00    S. 

7  10    10    N. 

log  Bin    9.01923- 
log  Bin    9. 09623 

log  A      8. 11546- 
A     =-0.01305 

0.  99989 
0.01315 

0.  98674 

9.  99420 
8. 32470 

8. 31890 

0. 02084 
0. 01315 

0. 03399 

21°  14'  53" 
90    00    00 

68    45    07 
68    27    07 

18    00 


log  cos  9.  98126 
log  cos  9.99761 
log  cos    9.99659 

log  B  9.  97546 
B  =  0.94506 
A      =-0.01305 


Calculated  ft=68°  45'  00"  nat.  sih=A+B    0.  93201 
The  azimuth  from  the  Azimuth  Tables  S.  128°  42'  E.  or  N.  51°  18'  E. 

Since  the  observed  altitude  is  lower  than  the  calculated  altitude,  the  observer's 
position  is  farther  removed  from  the  observed  body  than  the  assumed  position. 
Consequently  the  altitude-difference  should  be  laid  off  to  the  south  and  west,  231° 
18',  18.0  nautical  miles  from  the  assumed  position. 

Or,  by  the  Traverse  Tables : 


Course. 

Distance. 

Difl.  Lat. 

Dep. 

Difl.  Long. 

231i° 

18 

11'.27  S. 

14'.04  W. 

14'.12  W. 

Assumed  position,  Lat. 
Diff.  Lat. 


6°  00'  00"  S. 
11    16    S. 


Computed  point  on  Sximner  line,    6    11    16    S. 


Long.  30°  16'  45"  W. 

Diff.  Long.  14    07    W. 

30    30    52    W. 


160 


THE   SUMNER  LINE. 


The  direction  of  the  Sumner  line,  being  at  right  angles  to  the  azdmuth  or  true 
bearing  of  the  observed  body,  is  N.  38°  42^  W.  and  S.  38°  42'  E.,  or  321°  18'  and 
141°  18'. 

Example:  At  sea,  July  12,  1915,  in  Lat.  50°  N.,  Long.  40°  W.,  observed  an  ex-meridian  altitude  of 
the  sun's  lower  limb,  61°  48'  30",  the  time  by  chronometer  regulated  to  Greenwich  mean  time  being 
2"  41™  39';  chro.  corr.,— 2°^  30';  I.  C.,— 3'  00";  height  of  eye,  15  feet.     Find  the  Sumner  line. 

From  a  solution  of  the  same  problem  under  article  330,  Chapter  XII,  and  again  under  article,  370 
Chapter  XV,  the  following  quantities  are  taken  from  among  the  prepared  data;  G.A.T.,  2^  33™  50';  h, 
61°  57'  01";  d,  22°  04'  57"  N. 

Assume  a  position  in  Lat.  50°  N.,  Long.  40°  12'  30"  or  2^  40™  50»  W.,  then  the  solution  will  be  as 
follows: 


L.              50°  00'  00"  N. 

G.  A.  T. 
Long. 

L.  A.  T=f 

FORMULA : 

50°  00'   00" 
22°  04'   57" 

2"  33™  50* 
2    40    50  W. 

d 
P.  D. 

6.  36774 
9.  80807 
9.  96691 

6. 14272 

90.00014 
0.  05819 

22°  04'  57"  N. 

Co.  L        40    00    00 
P.  D.         67    55    03 

BY  COSINE-HAVERSINE 

t 

L 

d 

67    55    03 

0 

N. 
N. 

07 

00  E. 

log  hav 
log  cos 
log  cos 

log  hav  d 

nat  hav  i 
nat  hav 

nat  hav 

L~d 

27°  55'  03" 

27°  57'  07" 
90°  00'  00" 

t 

0.  05833 

Calculated  h 
Observed  h 

62    02    53 
61    57    01 

Altitude-difference 

BY  HAVERSINE  FORMULA." 

Co.  L+ P.  D. 
Co.  L-P.  D. 

nat  hav  A 

log  hav  A 
log  hav  t 

log  hav  B 


5    52 


107*  55'  03"    nat  hav 
27    65    03      nat  hav 


0.  65383 
0.  05819 

0.  59564 

9.  77498 
6.  36774 

6. 14272 


nat  hav  B 

nat  hav  (Co.  L-P.  D.) 

nat  hav  z 
Calculated  z 

Calculated  h 
Observed  h 

Altitude-difference 

BY  THE  SINE-COSINE  FORMULA: 


0.  00014 
0.  05819 

0.  05833 

27°  57' 
90    00 

07" 
00 

62 
61 

02 
57 

53 
01 

5    52 


t 

L 
d 

{p  07™00» 
1°  45'  00".... 
50    00    00  N 

22    04    57  N 

log  sin 
log  sin 

log  A 
A 

'""9.' 88425 
9.  57512 

Ic^  cos 

log  COS 
log  COS 

logB 

B 

A 

9.  99980 
9.  80807 
9.  96691 

9.  45937 
0.  28799 

9.  77478 
0.  59536 
0.  28799 

Calculated  /i=62°  02'  56" 


nat  sin 


A-fB 


0.  88335 


The  azimuth  from  the  Azimuth  Tables:  N.  176°  32'  E.  or  S.  3°  28'  E. 


THE   SUMNER  LINE. 


161 


Since  the  observed  altitude  is  lower  than  the  calculated  altitude,  the  observer's  position  is  farther 
removed  from  the  observed  body  than  the  assumed  position.  Consequently  the  altitude-difference 
should  be  laid  off  to  the  north  and  west,  356°  32^,  5.87  nautical  miles  from  the  assumed  position. 

Or,  by  the  Traverse  Tables: 


Coxirse. 

Distance. 

Difl.  Lat. 

Dep. 

Difl.  Long. 

356i° 

5.87 

5.  86  N. 

(K.  36  W. 

(y.  56  W. 

Assumed  position,  Lat. 
Diff.  Lat. 


50°  0(K  (XT  N. 
5    52    N. 


Long. 
Diff.  Long. 


40° 


12' 
0 


30'''  W. 
34^  W. 


Computed  point  of  Sumner  line        50    05    52    N. 


40°  13'  04"  W. 


The  direction  of  the  Sumner  line,  being  at  right  angles  to  the  azimuth  or  true  bearing  of  the  observed 
body,  is  N.  86°  32'  E.  and  S.  86°  32'  W.,  or  86°  32'  and  266°  32'. 

373.  In  the  first  of  the  three  foregoing  examples,  the  observed  celestial  body  is 
represented  as  being  near  the  prime  vertical;  in  the  second,  remote  from  both  the 

Enme  vertical  and  the  meridian;  and  in  the  third,  near  the  meridian.  These  examples 
ave  been  solved  in  the  preceding  chapters  by  three  dijfferent  methods  known, 
respectively,  as  the  time  sight,  the  ^'  6",  and  the  ex-meridian;  but  we  have  here 
treated  all  of  them  by  one  method,  and  nave  determined  Sumner  lines  which  are  in 
agreement  with  those  determined  by  the  various  jjrecedin^  methods.  And  it  would 
be  likewise  if  we  should  take  examples  in  which  meridian  altitudes  have  been  observed. 
Inasmuch  as  the  local  hour  angle  of  a  celestial  body  is  O''  at  the  time  of  its  passage 
across  the  meridian  of  an  observer,  the  second  member  of  the  right-hand  side  of  the 
equation  of  haversines  becomes  zero  in  cases  in  which  the  meridian  altitude  has 
been  observed,  since  the  haversine  of  0°  is  equal  to  zero.  The  equation  therefore 
reduces  to 

hav  3  =  hav  (Co.  L-P.  D.) 

or 

2=(Co.  L-P.  D.) 

which  leads  at  once  to  the  usual  formulae  given  in  article  321,  Chapter  XII,  for 
finding  the  latitude  from  a  meridian  altitude.  By  this  we  are  taught  the  full  inter- 
pretation of  a  meridian  altitude,  which  is  that  it  gives  the  latitude  of  the  intersection 
with  the  local  meridian  of  a  Sumner  line  coinciding  with  a  parallel  of  latitude. 

374.  In  addition  to  the  simplicity  which  anses  from  always  working  by  the 
same  rule,  the  navigator  has,  by  this  method,  the  further  practical  advantage  of  being 
able  to  do  the  most  of  the  work  of  obtairdng  the  Sumner  line  before  taking  the 
observation,  since,  in  clear  weather,  he  may,  in  selecting  the  assumed  geographical 
position,  assume  an  hour  angle  and  calculate  what  time  the  chronometer  or  watch 
ought  to  show  at  the  instant  when  the  celestial  body  has  this  hour  angle,  and  then 
observe  the  altitude  at  this  instant ;  or,  if  anything  should  happen  to  make  him  a  few 
seconds  late  in  getting  the  altitude,  he  may  alter  the  assumed  longitude  by  a  corre- 
sponding amount  so  as  to  make  the  hour  angle  right,  and  then  the  rest  of  the  work 
will  hold  good. 

After  correcting  the  observed  altitude  and  obtaining  from  it  the  true  altitude, 
no  more  time  need  subsequently  elapse  in  determining  the  Sumner  Une  than  is 
necessary  to  take  the  diflFerence  between  the  altitudes  found  by  calculation  and  by 
observation  and  to  rule  a  line  at  right  angles  to  the  bearing  oi  the  observed  body 
through  the  point  found  by  laying  off  this  altitude-difference  as  an  intercept  from  the 
assumed  position. 

375.  It  has  already  been  remarked  that  the  labor  of  performing  such  computa- 
tions as  the  foregoing  may  be  saved  when  a  book  of  altitude  and  azimuth  tables  is 
at  hand.  These  tables  are  arranged  to  be  entered  with  the  hour  angle,  the  declina- 
tion, and  the  latitude;  and  they  contain  the  corresponding  values  of  the  altitude 
and  azimuth.  In  the  various  books  containing  such  tables,  the  special  rules  to  be 
observed  in  their  use  are  set  forth. 

21594°— 14 11 


162  THE  SUMNEB  LINE. 

It  has  been  implied  that  when  the  akitude  of  the  observed  body  is  greater  than 
80°  and,  therefore,  the  zenith  distance  or  radius  of  the  circle  of  position  is  less  than 
10°,  the  tangent  drawn  to  the  circumference  to  represent  the  Sumner  line  could  no 
longer  be  regarded  as  coinciding  throughout  its  proper  length  with  the  arc  of  the 
circumference.  When  the  zenith  distance  is  10°,  the  departure  of  the  tangent  from 
the  circumference  is  one-tenth  of  a  mile  at  a  distance  of  10  miles  from  the  theoretical 
point  of  tangency  and  seven-tenths  of  a  mile  at  a  distance  of  30  miles  from  the 
theoretical  point  of  tangency.  These  departures  are  doubled  when  the  zenith  distance 
is  reduced  to  5°,  and  they  are  nearly  ten  times  the  amounts  stated  for  10°  when  the 
zenith  distance  is  shortened  to  1  °. 

There  is  not,  however,  any  occasion  for  resorting  to  the  proceeding  of  laying 
down  a  straight  line  as  a  substitute  for  an  arc  of  the  actual  circle  of  position  when 
the  zenith  distance  is  only  a  few  degrees  in  len^h.  In  such  cases  the  greatest  con- 
venience and  the  best  results  are  found  by  drawing  circles  of  position  directly  on  the 
navigator's  chart.  For  this  purpose  the  polyconic  chart,  being  issued  to  navigators 
throughout  all  latitudes  from  20°  to  60°  north  of  the  Equator  in  connection  with  the 
works  of  the  United  States  Coast  and  Geodetic  Survey,  and  therefore  being  available 
throughout  a  like  extent  of  south  latitude  by  mere  inversion,  is  generally  serviceable, 
because  a  chart  embracing  any  certain  parallels  of  latitude  is  available  between  these 

Parallels  of  latitude  throughout  all  longitudes;  and  the  Mercator  projection  may  also 
e  used  for  this  purpose  within  the  Tropics,  since  the  length  of  a  minute  of  latitude 
as  represented  on  this  projection  varies  but  little  within  tropical  limits.  For  instance, 
it  happens  in  crossing  the  tropical  zone  that,  for  a  day  or  so,  the  sun  is  very  near  the 
zenith— perhaps  not  more  than  1°  awaj  on  one  day  and  2°  or  3°  on  another.  In 
such  circumstances,  having  a  chart  of  smtable  scale  embracing  the  parallels  of  latitude 
of  the  region  in  which  the  ship  is  situated,  plot  the  sun's  geograpnical  position  with 
Greenwich  hour  angle  as  longitude  and  declination  as  latitude,  take  on  the  dividers  the 
zenith  distance,  or  complement  of  the  corrected  altitude,  and  draw  in  a  portion  of 
the  circumference  of  the  actual  circle  of  position  lying  near  the  position  of  the  ship 
as  ^ven  by  dead  reckoning.  Then  wait  until  the  azimuth  has  changed  30°  or  so — 
which  it  does  very  rapidly  near  noon — and  draw  a  second  similar  arc.  The  inter- 
section of  these  arcs  gives  the  ship's  position  with  accuracy.  Of  course  if  the  ship 
has  moved  in  geographical  place  m  the  interval  between  the  two  sights,  it  will  be 
necessary,  in  order  to  find  the  geographical  position  at  the  instant  of  the  second  sight, 
to  move  the  first  circle  of  position  in  direction  and  amount  equal  to  the  course  and 
distance  made  good  in  the  interval. 

FINDING  THE  INTERSECTION  OF  SUMNER  LINES. 

376.  The  intersection  of  Sumner  lines  may  be  found  either  graphically  or  by 
computation. 

(a)  Graphic  METHODS. — Each  line  may  be  plotted  upon  the  chart  of  the  locality 
in  which  the  ship  is  being  navigated,  in  accordance  with  the  data  for  its  determination 
(see  art.  367),  and  the  intersection  thus  found.  This  plan  will  commend  itself 
especially  when  the  vessel  is  near  shore,  as  the  chart  in  use  will  then  probably  be 
one  of  large  enough  scale,  and  it  will  be  an  advantage  to  see  where  the  Sumner  lines 
fall  with  reference  to  the  soundings  and  landmarks.  To  aid  the  extension  of  this 
convenient  practice  on  the  ocean,  where  the  navigator  is  usually  furnished  only  with 
a  general  chart,  position-line  plotting  sheets  have  been  provided  for  the  use  oi  navi- 
gators upon  an  ample  scale, 

(6)  Methods  by  Computation. — The  finding  of  the  intersection  of  two  Sumner 
lines  by  computation  may  be  divided  into  two  cases: 

Case  I.  When  one  line  lies  in  a  NE.-SW.  direction,  and  the  other  in  a  NW.-SE, 
direction,  as  shown  in  figure  56. 

Case  II.  When  both  lie  in  a  NE.-SW.,  or  both  in  a  NW.-SE.  direction,  as  shown 
in  figure  57. 

377.  If  each  Sumner  line  is  defined  by  the  latitude  and  longitude  of  one  of  its 
points  and  the  azimuth  of  the  celestial  body  at  right  angles  to  whose  true  bearing  the 
line  rims,  we  may  then,  by  means  of  Table  47,  find  the  longitude  of  any  other  point 
on  such  a  line  when  its  difference  of  latitude  from  the  known  point  has  been  ascer- 


THE  SUMNER  LINE. 


163 


tained.  The  numbers  in  Table  47  are  values  of  the  longitude  factor,  usually  denoted 
by  the  letter  F.  They  vary  with  the  latitude  of  the  observer  and  the  celestial  body's 
azimuth  at  right  angles  to  the  direction  of  the  line,  and  express  the  change  in  longitude 
due  to  a  change  of  1'  in  latitude  along  any  given  Sumner  line.  So  that  the  difference 
of  latitude  between  any  two  points  of  a  line,  being  multiplied  by  the  longitude  factor, 
will  give  the  difference  of  longitude  between  those  points. 

Turning  to  figures  56  and  57  and  considering  the  Simmer  lines  A^  A2  and  B^  Bj 
there  represented  to  be  defined  by  the  azimuth  at  right  angles  to  each  and  the  lati- 
tudes and  longitudes  of  the  points  A^  and  Bj,  respectively,  we  proceed  to  show  the 
relations  which  exist  for  determining  the  latitude  and  longitude  of  the  fix  at  their 
intersection  by  means  of  the  tabulated  longitude  factors.  The  line  PO  being  drawn 
perpendicular  to  the  parallel  of  latitude  through  the  points  Ai  and  B,,  the  latitude 
of  tne  intersection  will  be  a  distance  OP  from  the  common  latitude  of  A^  and  Bj,  and 
its  longitude  will  be  a  distance  A^  O  from  A^  and  B^  O  from  B^.  Let  F^  and  F2  repre- 
sent the  longitude  factors  from  Table  47  for  the  Sumner  lines  A^  A,  and  B^  Bj, 
respectively.  Then,  since  F^  is  the  difference  of  longitude  corresponding  to  a  change 
of  1'  of  latitude  along  the  line  Ai  Aj,  the  difference  of  longitude  A^  O  must  be  equal 
to  El  multiplied  into  the  number  of  minutes  of  latitude  in  uie  length  OP.     Therefore, 


and  likewise 


A,  0  =  OPxFi, 
BiO  =  OPxF,; 


Fio.  57. 


and,  since  the  known  difference  of  loiigitude  between  the  points  Aj  and  B^  is  com- 

gosed  of  the  sum  of  Aj  O  and  Bi  O  in  Case  I,  and  the  difference  of  A^  O  and  B^  O  in 
ase  II,  we  have 

A,  0  +  B.  0=Ai  Bi  =  OPxFi  +  OPxFj  =  OP  (F^  +  F^),  in  Case  I,  and 
A,  0-Bi  0=Ai  Bi  =  0PxFi-0PxF2  =  0P  (F^-Fj),  in  Case  11. 

From  which,  placing  the  known  quantities  on  the  right-hand  side  of  the  equations, 


thus: 


A  B 


0P  = 


A,B, 
F,-F„> 


in  Case  II. 


Hence,  we  obtain  the  difference  of  latitude  from  the  common  parallel  of  Aj  and  B^ 
to  tiie  point  of  intersection  by  dividing  the  known  difference  of  longitude  between 
the  points  A^  and  B^  by  the  sum  of  the  longitude  factors  of  the  respective  Sumner 
lines  in  Case  I,  and  by  their  difference  in  Case  II. 

Having  determined  OP  and  hence  the  latitude  of  the  point  of  intersection  of 
the  Smnner  line,  we  proceed  to  multiply  OP  by  F^  to  get  the  difference  of  longitude 
AjP,  and  apply  that  difference  to  the  known  longitude  of  A,  to  find  the  longitude 
of  the  point  of  intersection  P;  and  also,  as  a  check,  to  multiply  OP  by  F,  to  get  the 
difference  of  longitude  BjO,  which,  being  applied  to  the  longitude  of  h^,  gives  again 
the  longitude  of  the  point  of  intersection,  r. 


164  THE  SUMNER  LINE. 

The  following  is  a  summary  of  the  successive  steps  to  be  taken  in  following  this 
method : 

1.  Make  a  rough  sketch  of  the  Sunmer  lines  whose  intersection  is  to  be  fixed  in 
latitude  and  longitude,  classifying  them  under  Case  I  or  Case  II. 

2.  Take  from  Table  47  the  longitude  factors  F^  and  Fj,  respectively,  for  the 
Sunmer  lines. 

3.  If  the  given  coordinates  of  the  points  on  the  two  lines  have  not  a  common 
latitude,  reduce  them  to  a  common  latitude  by  multiplying  the  diflFerence  between 
the  latitudes  of  the  points  on  the  two  lines  by  the  longitude  factor  of  one  of  the 
lines  and  applying  the  product  to  the  longitude  of  the  point  on  that  line.  The 
sketch  will  show  whether  the  difference  of  longitude  is  to  be  added  or  subtracted,  and 
the  result  will  be  the  longitude  of  a  poiut  of  this  line  on  the  conamon  parallel  of 
latitude. 

4.  The  difference  between  the  longitudes  of  the  points  of  the  two  Sumner  lines, 
on  the  common  parallel,  divided  by  the  sum  of  the  longitude  factors  (Fj+Fg),  wiU 
give  the  difference  of  latitude  between  the  point  of  intersection  and  the  common 

{)arallel,  when  the  lines  are  classified  under  Case  I;  and  the  difference  between  the 
ongitudes  of  the  points  of  the  two  Sumner  lines,  on  the  common  parallel,  divided  by  the 
difference  of  the  longitude  factors  (F^  —  Fj),  will  give  the  difference  of  latitude  between 
the  point  of  intersection  and  the  common  parallel,  when  the  lines  are  classified  imder 
Case  II. 

The  sketch  wiU  show  whether  the  intersection  of  the  Sumner  lines  lies  to  the 
northward  or  southward  of  the  common  parallel,  and  hence  whether  the  difference 
of  latitude  is  to  be  added  to  or  subtracted  from  the  latitude  of  the  common  parallel. 

5.  Having  found  the  difference  of  latitude  between  the  point  of  intersection  of 
the  Sunmer  lines  and  the  common  parallel,  multiply  this  difference  by  the  longitude 
factor  of  each  line  and  apply  theproducts  each  to  the  longitude  of  its  corresponding 
line  on  the  common  parallel.  The  products  are  appHed  in  opposite  directions  in 
Case  I,  and  both  of  them  must  lead  to  the  same  longitude  for  the  point  of  intersection ; 
and  the  products  are  applied  in  the  same  direction  in  Case  II,  and  in  this  case  also 
both  of  them  must  lead  to  the  same  longitude  for  the  point  of  intersection. 

Example:  Find  the  intersection  of  the  Sumner  lines  defined  below  by  the  latitude  and  longitude  of 
a  aingle  point  on  each  and  by  the  respective  azimutlis  of  the  celestial  bodies  upon  which  the  lines  depend. 


{25°  4(/  S  "1 
115    20  E  f^zimuth,  at  right  angles  to  line,  N.  51°  E. 

^  {115°  33^5^  E  l^zimuth  at  right  aisles  to  line,  N.  72°  W. 

From  Table  47: 

Longitude  factor  for  line  A=0.89=Fi. 
Longitude  factor  for  Line  B=0.36=F2. 

Reduce  the  given  points  to  a  common  parallel  of  latitude  by  transferring  the 
point  on  line  B  to  the  latitude  of  the  point  on  line  A, 

(25°  40'  S.-25°  25'  S.)XF2=15'X0.36=  5'.4  W. 

115°  33'.5  E. 


Fig.  68.  ,  115°  28'.1  E. 


Hence  we  have  for  the  point  on  the  line  B  at  which  the  latitude  is  the  same  as  the  latitude  of  the  point 
on  the  line  A, 

B  Lll°  ^  f-Q  JAzimuth  at  right  angles  to  line,  N.  72°  W. 

We  now  have  two  Sumner  lines,  under  Case  I,  whose  common  latitude  is  25°  40^  S.  and  whose  longitudes 
on  the  common  parallel  are : 

115°  28M  E. 
115    20  .OE. 


8  .l=sDiff.  Long,  on  common  parallel. 

81  8  18  1 

Tj<  ^  p  =  gQ  !       =  j--^=«6.48  DiS.  Lat.  between  intersection  and  common  parallel. 


THE  SUMNEB  LINE. 


165 


CJorrectioDB  in  longitude: 


Long.  A 
Diff.  Long. 


115*>  20'  .00  E. 
5  .77  E. 


Intersection       115    25  .77  E. 


6.  48XF,=6.  48X0.  89=5' 
6.  48XF2=6.  48X0.  36=2 

Long.  B         115°  28'  .10  E. 
Diff.  Long.  2  .33  W. 

115    25  .77  E. 


77 
33 

Lat.  common  parallel 
Diff.  Lat. 


25°  40'.00  S. 
6  .48  S. 


25    46  .48  S. 


Example:  Find  the  intersection  of  the  Sumner  lines  defined  below: 


a|'*5°  2 J"   8  ^"  }    Azimuth,  at  right  angles  to  Une,  N.  81°  W. 
BJ^g"  25^  8  W  }    A-zimutii.  at  ""ig^*  angles  to  Une,  N.  31°  W. 


A  sketch  of  the  lines  shows  their  classification  to  be  under  Case  II. 

From  Table  47: 

Longitude  factor  for  line  A=0.24=Fi, 
Longitude  factor  for  line  B=2.57=Fj. 

Diff.  Long,  on  common  parallel=5°  25'  .8—5°  24'  .8=1'  .0. 


LO 


LO 


Fa-F,     2.57-0.24    2.33 
tion  and  common  parallel. 
Corrections  in  longitude: 


=n^o=0.429=Diff.  Lat.  between  intersec- 


0.  429XF,=0.  429X0.  24=0. 10. 
0.  429XF2=0.  429X2.  57 =L  10. 


Long.  A 
Diff.  Long. 


5°  24'  .8  W. 
0  .IE. 


Long.  B 
Diff.  Long. 


5°  25'  .8  W. 
1   .1  E. 


Lat.  common  parallel 
Diff.  Lat. 


49°  30'  .0    N. 
0  A    N. 


Intersection      5    24 .7  W. 


5  24  .7  W. 


49    30  .4    N. 


378.  If  the  two  geographical  positions  defining  two  Sumner  lines  have  a 
common  longitude  instead  of  a  common  latitude,  as  represented  in  figures  60  and  61, 
their  intersection  may  be  foimd  by  means  of  the  latitude  factors 
tabulated  in  Table  48,  in  a  manner  similar  to  the  use  of  the  lon- 
gitude factors  in  connection  with  the  Sumner  lines  whose  known 
points  have  a  common  latitude.  The  latitude  factors  vary  with 
the  latitude  of  the  observer  and  the  celestial  body's  azimuth  at 
right  angles  to  the  direction  of  the  Kne,  and  express  the  change  in 
latitude  due  to  a  change  of  1 '  in  lon^tude  along  any  given  Sumner 
line.  So  that  the  difference  of  longitude  between  any  two  points 
of  a  line  being  multiplied  by  the  latitude 
factor  will  give  the  difference  of  latitude  be- 
tween those  points. 

The  latitude  factors  of  two  Sumner  lines 
whose  intersection  is  to  be  found  are  usually 
denoted  by  the  letters  f^  and  fj,  and  the 
successive  steps  to  be  taken  in  finding  the  in- 
tersection are  here  summarized : 

1.  Make  a  rough  sketch  of  the  Sumner 
lines  whose  intersection  is  to  be  fixed  in  latitude  and  longitude, 
classifying  them  under  Case  I  or  Case  II. 

2.  Take  from   Table  48   the  latitude  factors    fj   and    f,, 
respectively,  for  the  Sumner  lines. 

3.  The  difference  between  the  latitudes  of  the  points  of 
the  two  Sumner  lines,  in   the  common  longitude,  divided  by 
the  sum  of  the  latitude  factors  (fj  +  fz),  will  give  the  difference 
of  longitude  between  the  point  of  intersection  and  the  common  meridian  when  the 
lines  are  classified  under  Case  I;  and  the  difference  between  the  latitudes  of  the 


Fig.  60. 


Fig.  61. 


166  THE   SUMNER  LINE. 

points  of  the  two  Sumner  lines,  in.  the  common  longitude,  divided  by  the  difference 
of  the  latitude  factors  (fi  —  fj),  will  give  the  difference  of  longitude  between  the  point 
of  intersection  and  the  common  meridian  when  the  lines  are  classified  under  Case  II. 

The  sketch  will  show  whether  the  intersection  of  the  Sumner  lines  Hes  to  the 
eastward  or  westward  of  the  common  meridian,  and  hence  whether  the  difference  of 
longitude  is  to  be  added  to  or  subtracted  from  the  common  longitude. 

4.  Having  found  the  difference  of  longitude  between  the  point  of  intersection 
of  the  Sumner  lines  and  the  common  longitude,  multiply  this  difference  by  the 
latitude  factor  of  each  line  and  apply  the  products  each  to  the  latitude  of  its  corre- 
sponding line  on  the  common  meridian.  The  products  are  applied  in  opposite 
directions  in  Case  I,  and  both  of  them  must  lead  to  the  same  latitude  for  the  point  of 
intersection;  and  the  products  are  applied  in  the  same  direction  in  Case  II,  and  in 
this  case  also  both  of  tnem  must  lead  to  the  same  latitude  for  the  point  of  intersection. 

Example:  Find  the  intersection  of  the  Sumner  lines  defined  below: 

M^i°  Jf  '86  w*}    Azinauth,  at  right  angles  to  line,  N.  57°.  6  W. 
■^{71°  if  86  W  }    -'Azimuth,  at  right  angles  to  line,  N.  77°  W. 

A  sketch  of  the  lines  shows  their  classification  to  be  under  Case  II. 

From  Table  48: 

Latitude  factor  for  line  A=l.  23=fi. 
Latitude  factor  for  line  B=3.  32=f,. 

Diff.  Lat.  on  common  meridian=7''.15. 

7. 15  7. 15  7. 15 

-=y.  42    Diff.  Long,  between  intersection  and  common  meridian. 


fj-fi    3.32-1.23        2.09 
Corrections  in  latitude: 


3.  42Xfi=3.  42X1.  23=  4^  20 
3.  42Xf2=3.  42X3.  32=11 .  35 


Lat.  A  40°  13'.  55  N.        Lat.  B  40°  06^.  40  N.  Long,  on  common  me- 

Diff.  Lat.  4  .  20  N.        Diff.  Lat.  11  .  35  N.      ridian  71°  14^  86  W. 

Diff.  Long.  3.  42  E. 


Intersection        40°  17^  75  N.  40°  17^  75  N. 


71°  ir.  44  W. 


379.  When  a  Sumner  line  is  defined  by  the  latitudes  and  longitudes  of  two  of 
its  points,  the  longitude  factor  for  the  line  may  be  found  by  dividing  the  difference 
between  the  longitudes  of  the  two  given  points  by  the  difference  between  their 
latitudes;  and  the  latitude  factor,  being  the  reciprocal  of  the  longitude  factor,  may 
be  found  by  dividing  the  difference  between  the  latitudes  of  the  two  given  points  by 
their  difference  of  longitude. 

The  method  of  finding  the  intersection  of  Sumner  lines  by  longitude  and  lati- 
tude factors,  described  in  articles  377  and  378,  may,  therefore,  be  applied  as  well 
when  the  lines  are  defined  by  pairs  of  geographical  positions  as  when  they  are  defined 
by  the  azimuth  and  one  geographical  position. 

380.  The  modification  of  the  methods  for  finding  the  intersection  of  two  Sumner 
lines,  where  there  is  a  rim  between  the  observations  from  which  they  are  deduced, 
will  be  readily  apparent.  It  is  known  that  at  the  time  of  taking  a  sight  the  vessel 
is  at  one  of  the  points  of  the  Sumner  line,  but  which  of  the  various  points  represents 
her  precise  position  must  remain  in  doubt  until  further  data  are  acquired.  Suppose, 
now,  that  alter  an  observation,  the  vessel  sails  a  given  distance  in  a  given  direction; 
it  is  clear  that  while  her  exact  position  is  still  undetermined  it  must  be  at  one  of  the 
series  of  points  comprised  in  a  line  parallel  to  the  Sumner  line  and  at  a  distance  and 
direction  therefrom  corresponding  to  the  course  and  distance  made  good;  hence,  if 


THE  SUMNEB  LINE.  167 

a  second  sight  is  then  taken,  the  position  of  the  vessel  may  be  found  from  the  inter- 
section of  two  lines — one,  the  Sumner  line  given  by  the  second  observation,  and  the 
other  a  line  parallel  to  the  first  Sumner  line  but  removed  from  it  by  the  amount  of 
the  intervening  run. 

Positions  may  be  brought  forward  graphically  on  a  chart  by  taking  the  course 
from  the  compass  rose  with  parallel  rulers,  and  the  distance  by  scale  with  dividers. 
If  one  of  the  methods  by  computation  be  adopted,  the  point  or  points  of  the  first 
line  are  brought  forward  by  the  traverse  tables,  using  middle  latitude  sailing.  The 
direction  of  a  Sumner  line  as  determined  from  the  azimuth  of  the  body  always 
remains  the  same,  whatever  shift  may  be  made  in  the  position  of  the  point  by  which 
the  line  is  further  defined. 

Example:  Taking  the  Sumner  lines,  which  are  defined  in  the  first  example  under  article  377,  by  the 
latitude  and  longitude  of  a  point  of  each  and  by  the  respective  azimuths  of  the  celestial  bodies  upon 
which  the  lines  depend,  as  follows: 

a|^j5°  3i'    E  1^2"""*^.  a*  "g^*  angles  to  line,  N.  51°  E. 
^{115°  33  5  E  1-A-zimuth,  at  right  angles  to  line,  N.  72"  W. 

and  supposing  the  vessel  from  which  the  observations  were  taken  that  gave  these  lines  to  have  run 
N.  54°  E.  (true)  35  miles  in  the  interval  between  the  sights,  find  the  position  of  the  vessel  at  the  time  of 
the  second  sight. 

The  point  A,  in  25°  4(K  S.  and  115°  31'  E.,  is  first  transferred  to  the  point  A^  35  miles  N.  54°  E.  (true) 
Irom  A,  by  the  method  of  Middle  Latitude  Sailing  (article  177)  by  means  of  the  Traverse  Tables,  thus: 

From  Table  2,  course  N.  54°  E. ;  Dist.,  35  miles;  we  find  Diff.  Lat.  20.5  N.,  Dep.  28.3  E.    Therefore, 

Lat.  A         25°  4fy     S.  Lat.  A  25°  4(K     S. 

Difi.  Lat.  20  .6  N.  Lat.  A'  25    19  .4  S. 


Lat.  A'       25    19  .4  S.  2)50   59  .4 


Middle  Lat.    25   29  .7 

From  Table  2,  Middle  Lat.  (course),  25i°,  Dep.  (Lat.),  28.3  E.,  we  find  Diff.  Long.  (Diat.),  31.3.  E. 
Therefore, 

Longitude  A,      116°  31'     E. 
Diff.  Long.  31  .3  E. 

Longitude  A',     116   02  .3  E. 
The  Sumner  lines  whose  intersection  is  to  be  found  are  therefore  defined  as  follows: 
A'|jjg°  J^'g  |-  JAzimuth,  at  right  angles  to  the  line,  N.  51*  E. 

B  l^^  33'  5  I  JAzimuth,  at  right  angles  to  the  line,  N.  72°  W. 

From  Table  47: 

Longitude  factor  for  line  A''=0.90=F, 
Longitude  factor  for  line  B  =0.36=F, 

Reduce  the  given  points  to  a  common  parallel  of  latitude  by  transferring  the  point  on  line  B  to  the 
latitude  of  the  point  on  line  A', 

(25°  19^.4  S-25°  25^  S.)XF2= -5.6X0.36=  2'.0  E. 

115°  33  .5  E. 


115   35  .5  E. 


Hence  we  have  for  the  point  on  the  line  B  at  which  the  latitude  is  the  same  as  the  latitude  of  the  point 
on  the  line  A', 

^A  25°  19^.4  S. 

"  \n5    35  .5  E. 


168  THE  SUM  NEE  LINE. 

We  now  have  two  Sumner  lines,  A'  and  B'',  under  Case  I,  whose  common  latitude  is  25°  19^.4  S.,  and  whose 
longitudes  on  the  common  parallel  are  116°  02''.3  and  115°  35^.5.  Hence,  the  difference  of  longitude  on 
the  common  parallel  is 

116°  02'.3  E. 

115    35  .5  E. 


26  .8=Diff,  Long,  on  common  parallel. 

9fi  Q  9A   Q  Oft   Q 

p   /p  =0  QA_LQ  M~T^&~'^^'^~^^^'  ^^^'  l^®t.ween  intersection  and  common  parallel. 


Corrections  in  longitude: 


21.3XF,=21.3X0.90=19.2 
21.3XF2=21.3X0.36=  7.6 


Long.  A'         116°  02^3  E.         Loi^.  B'        115°  35^.5  E.        Lat.  common  par.   25°  19^.4  S. 
Diff.  Long.  19  .2  W.        Diff.  Long.  7  .6  E.        Diff.  Lat.  21  .3  N. 

Intersection  115   43  .1  E.  116    43  .1  24    58  .1  S. 


CHAPTER  XVI. 

THE  PRACTICE  OF  NAVIGATION  AT  SEA. 


381.  Having  set  forth  in  previous  chapters  the  methods  of  working  dead 
reckoning  and  of  solving  problems  to  find  the  latitude,^  longitude,  chronometer 
correction,  and  azimuth  from  astronomical  observations,  it  will  be  the  aim  of  the 
present  chapter  to  describe  the  conditions  which  govern  the  choice  and  employment 
of  the  various  problems,  together  with  certain  considerations  by  which  the  navigator 
may  be  guided  in  his  practical  work  at  sea. 

382.  Departure  and  Dead  Reckoning. — On  beginning  a  voyage,  a  good 
departure  must  be  taken  while  landmarks  are  still  in  view  and  lavorably  located  for 
the  purpose;  this  becomes  the  origin  of  the  dead  reckoning,  which,  with  frequent 
new  departures  from  positions  by  observation,  is  kej)t  up  to  the  completion  of  the 
voyage,  thus  enabling  the  mariner  to  know,  with  a  fair  degree  of  accuracy,  the  posi- 
tion of  his  vessel  at  any  instant. 

At  the  moment  oi  taking  the  departure,  the  reading  of  the  patent  log  (which 
should  have  been  put  over  at  least  long  enough  previously  to  be  regularly  running) 
must  be  recorded,  and  thereafter  at  the  time  of  taking  each  sight  and  at  every  other 
time  when  a  position  is  required  for  any  purpose,  the  Tog  reading  must  also  be  noted. 
It  is  likewise  well  to  read  the  log  each  hour^  for  general  information  as  to  the  speed 
of  the  vessel  as  well  as  to  observe  that  it  is  in  proper  running  order  and  that  the 
rotator  has  not  been  fouled  by  seaweed  or  by  refuse  thrown  overboard  from  the  ship. 
It  is  a  good  plan  to  record  the  time  by  ship's  clock  on  each  occasion  that  the  log  is 
read,  as  a  supplementary  means  of  arriving  at  the  distance  will  thus  be  available  in 
case  of  doubt.  If  a  vessel  does  not  use  the  patent  lo^  but  estimates  her  speed  by 
the  number  of  revolutions  of  the  engines  or  the  indications  of  the  chip  log,  the 
noting  of  the  time  becomes  essential.  A  good  sight  is  of  no  value  unless  one  knows 
the  point  in  the  ship's  run  at  which  it  was  taken,  so  that  the  position  it  gave  may  be 
brought  forward  with  accuracy  to  any  later  time. 

383.  General  Description  of  the  Day's  Work, — ^The  routine  of  a  day's 
work  at  sea  consists  in  working  the  dead  reckoning,  an  a.  m.  time  sight  and  azimuth 
taken  when  the  sun  is  in  its  most  favorable  position  for  the  purpose,  a  meridian  alti- 
tude of  the  sun  (or,  when  clouds  interfere  at  noon,  a  sight  for  latitude  as  near  the 
meridian  as  possible),  and  a  p.  m.  time  sight  and  azimuth.  This  represents  the 
minimum  of  work,  and  it  may  be  amplified  as  circumstances  render  expedient;  but 
no  part  of  it  should  ever  be  omitted  unless  cloudy  weather  renders  its  performance 
impossible. 

384.  Morning  Sights. — ^The  morning  time  sight  and  azimuth  should  be 
observed,  if  possible,  when  the  sun  is  on  the  prime  vertical.  As  the  body  bears 
east  at  that  tune,  the  resulting  Sumner  line  is  due  north  and  south,  and  the  longitude 
will  thus  be  obtained  without  an  accurate  knowledge  of  the  latitude.  Another 
reason  for  so  choosing  the  time  is  that  near  this  point  of  the  sun's  apparent  path 
the  body  is  changing  most  slowly  in  azimuth,  and  an  error  in  noting  the  time  will 
have  the  minimum  effect  in  its  computed  bearing.  The  time  when  the  sun  will  be 
on  the  prime  vertical — that  is,  when  its  azimuth  is  90° — may  be  found  from  the 
azimuth  tables  or  the  azimuth  diagram.  Speaking  generally,  during  half  the  year 
the  sun  does  not  rise  until  after  having  crossed  the  prime  vertical,  and  is  therefore 
never  visible  on  a  bearing  of  east.  In  this  case  it  is  oest  to  take  the  observation  as 
soon  as  it  has  risen  above  the  altitude  of  uncertain  atmospheric  effects — between  10° 
and  15°. 

A  series  of  several  altitudes  should  be  taken,  partly  because  the  mean  is  more 
accurate  than  a  single  sight,  and  partly  because  an  error  in  the  reading  of  the  watch 
or  sextant  may  easily  occur  when  there  is  no  repetition.  If  the  sextant  is  set  in 
advance  of  the  altitude  on  even  five  or  ten  minute  divisions  of  the  arc,  and  the  time 

169 


170  THE   PRACTICE   OF    NAVIGATION   AT  SEA. 

marked  at  contacts,  the  method  will  be  found  to  possess  various  advantages.  As 
the  sight  is  being  taken  the  patent  log  should  be  read  and  ship's  time  recorded.  It 
is  well,  too,  to  make  a  practice  of  noting  the  index  correction  of  the  sextant  each  time 
that  the  sextant  is  used.  The  bearing  of  the  sun  by  compass  should  immediately 
afterward  be  observed,  and  the  heading  by  compass  noted,  as  also  the  time  (by  the 
same  watch  as  was  used  for  the  sight). 

Before  working  out  the  sight,  the  dead  reckoning  is  brought  up  to  the  time  of 
observation,  and  the  latitude  thus  found  used  as  the  approximate  latitude  at  sight. 
It  is  strongly  recommended  that  every  sight  he  worked  for  a  Sumner  line,  either  by 
assuming  two  latitudes,  or  by  using  one  latitude  and  the  azimuth,  or  yet  more 
advantageously  by  the  method,  of  Saint  Hilaire. 

The  compass  error  is  next  obtained.  From  the  time  sight  the  navigator  learns 
that  his  watch  is  a  certain  amount  fast  or  slow  of  L.  A.  T.,  and  he  need  only  apply 
this  correction  to  the  watch  time  of  azimuth  to  obtain  the  L.  A.  T.  at  which  it  was 
observed;  then  he  ascertains  the  sun's  true  bearing  from  the  azimuth  tables  or 
azimuth  diagram,  compares  it  with  the  compass  bearing,  and  obtains  the  compass 
error;  he  should  subtract  the  variation  by  chart  and  note  if  the  remainder,  the  devia- 
tion, agrees  with  that  given  in  his  deviation  table;  but  in  working  the  next  dead 
reckoning,  if  the  ship's  course  does  not  change,  the  total  compass  error  thus  found 
may  be  used  without  separating  it  into  its  component  parts.  It  should  be  increased 
or  decreased,  however,  as  the  ship  proceeds,  by  the  amount  of  any  change  of  the 
variation  that  the  chart  may  show. 

385.  If  there  is  any  fear  of  the  weather  bein^  cloudy  at  noon,  the  navigator 
should  take  the  precaution,  when  the  sun  has  changed  about  30°  in  azimuth,  to  observe 
a  second  altitude  and  to  record  the  appropriate  data  for  another  sight,  though  this 
need  not  actually  be  worked  unless  the  meridian  observation  is  lost.  If  it  is  required 
it  may  be  worked  for  either  a  time  sight  or  ^'  <j)"  sight,  or  by  the  Saint  Hilaire 
method,  according  to  circumstances,  and  a  second  Sumner  line  thus  obtained,  whose 
intersection  with  earher  Sumner  line,  brought  forward  for  the  run  in  the  interval 
between  the  sights,  will  give  the  ship's  position. 

386.  Noon  Sights. — Between  11  and  11.30  o'clock  (allowing  for  gain  or  loss 
of  time  due  to  the  day's  run)  the  ship's  clocks  should  be  set  for  the  L.  A.  T.  of  the 
prospective  noon  position.  The  noon  longitude  may  be  closely  estimated  from  the 
morning  sight  and  the  probable  run.  The  navigator  should  also  set  his  own  watch  for 
that  time,  to  the  nearest  minute,  and  note  exactly  the  number  of  seconds  that  it  is 
in  error.  He  may  now  compute  the  constant  (art.  325,  Chap.  XII)  for  the  meridian 
altitude.  The  daily  winding  of  the  chronometer  is  a  most  important  feature  of  the 
day's  routine,  and  may  well  be  performed  at  this  hour.  At  a  convenient  time  before 
noon,  the  observations  for  meridian  altitude  are  commenced  and  continued  until  the 
watch  shows  L.  A.  noon,  at  which  time  the  meridian  altitude  is  measured  and  the 
latitude  deduced. 

If  the  weather  is  cloudy  and  there  is  doubt  of  the  sun  being  visible  on  the  meridian 
an  altitude  may  be  taken  at  any  time  within  a  few  minutes  of  noon,  the  time  noted, 
and  the  interval  from  L.  A.  noon  found  from  the  known  error  of  the  watch.  It  is 
then  the  work  of  less  than  a  minute  to  take  out  the  a  from  Table  26,  the  af  from 
Table  27,  and  apply  the  reduction  to  the  observed  altitude  to  obtain  the  meridian 
altitude.  Indeed,  the  method  is  so  simple  that  it  may  be  practiced  every  day  and 
several  values  of  the  meridian  altitude  thus  obtained,  instead  of  only  one. 

387.  It  now  becomes  necessary  to  find  the  longitude  at  noon.  This  may  be 
done  graphically  by  a  chart  or  by  computation.  The  former  plan  needs  no  explana- 
tion. There  are  a  number  of  variations  in  the  methods  of  computation,  one  of  which 
will  be  given  as  a  type. 

By  the  ship's  run,  work  back  the  noon  latitude  to  the  latitude  at  a.  m.  time  sight. 
If  the  Sumner  line  was  f oirnd  from  two  assumed  latitudes  which  differed  +  m  minutes, 
while  the  corresponding  longitudes  differed  ±  ri  minutes,  then  1'  difference  of  latitude 

causes  ±— minutes  difference  of  longitude.     If  the  true  latitude  at  sight  is±a;  min- 

utes  from  one  of  the  assumed  latitudes,  then  ±  x  X  —  is  the  corresponding  difference  of 

longitude.  If  the  Sumner  line  was  found  from  one  assumed  latitude  and  an  azimuth, 
Z,  tne  longitude  factor  of  the  line  may  be  found  from  Table  47 ;  and  this  multipUed 


THE  PRACTICE   OF   NAVIGATION  AT   SEA.  171 

by  the  difference  between  the  true  and  assumed  latitude  will  give  the  correction  to 
be  appUed  to  the  computed  longitude  corresponding  to  the  assumed  latitude. 
Having  thus  the  longitude  at  sight,  the  longitude  at  noon  is  worked  forward  for  the 
run.  If  the  sights  show  a  considerable  current  it  should  be  allowed  for,  both  in 
working  back  the  latitude  and  in  bringing  up  the  longitude  for  the  run  between  the 
sight  and  noon. 

Examplk:  Suppose  that  an  a.  m.  time  sight,  taken  when  the  sun's  azimuth  was  S.  39"  48''  E.,  has 
given  a  longitude  of  30°  31''  W.  when  solved  with  a  dead -reckoning  latitude  of  50°  54'  N.  Suppose  that 
when  the  noon  latitude  is  worked  back  to  the  time  of  the  a.  m.  sight,  by  means  of  the  vessel  s  run,  tlie 
true  latitude  at  that  time  was  found  to  be  50°  50^  N.  The  longitude  was  thus  computed  with  a  latitude 
that  was  4''  too  much  to  the  northward.  Find  the  corresponding  error  in  longitude,  and  the  longitude 
at  the  time  of  sight. 

From  Table  47,  the  longitude  factor  of  the  Sumner  line  passing  through  the  geographical  position 
whose  latitude  is  50°  54'  N.  and  whose  longitude  is  30°  31'  W.,  at  right  angles  to  the  bearing  S.  39°  48'  E., 
is  1.91.  The  computed  longitude  is  therefore  wrong  by  4X1. 91=7'. 6;  and  according  to  the  rule  laid 
down  in  connection  with  the  Explanation  of  Table  47,  the  correction  in  longitude  must,  in  this  case, 
be  applied  to  the  eastward. 

Hence  we  have^ 

Longitude  computed  with  D.  R.  Lat.,  50°  54' N 30°    31'   \V. 

Correction  in  long,  due  to  change  of  4'  in  latitude  to  the  northward 7.  6    E. 

True  longitude  at  the  time  of  sight 30*  23.4  W. 

388.  Current  and  Run. — The  current  may  be  found  by  comparing  the  noon 
positions  as  obtained  W  observation  and  by  dead  reckoning;  and  the  day's  run  is 
calculated  from  the  difference  between  the  day's  noon  position  bv  observation  and 
that  of  the  preceding  day.  To  ''current"  is  usually  attributed  aU  discrepancies 
between  the  dead  reckoning  and  observations;  but  it  is  evident  that  this  is  not 
entirely  due  to  motion  of  the  waters,  as  it  includes  errors  due  to  faulty  steering, 
improper  allowance  for  the  compass  error,  and  inaccurate  estimate  of  the  vessel  s 
speed  through  the  water. 

The  noon  position  by  observation  becomes  the  departure  for  the  dead  reckoning 
that  follows. 

389.  Afternoon  Sights. — The  p.  m.  time  sight  and  azimuth  is  similar  to  the 
morning  observation. 

390.  Sumner  Lines. — ^By  performing  the  work  that  has  just  been  described  a 
good  position  is  obtained  at  noon  each  day,  which,  in  a  slow-moving  vessel  with 
plenty  of  sea  room,  may  be  considered  sufficient;  but  conditions  are  sucn  at  times  as 
to  render  it  almost  imperatively  necessary  that  a  more  frequent  determination  of  the 
latitude  and  longitude  bo  made.  If  the  vessel  is  near  the  land  or  in  the  vicinity  of 
off-lying  dangers,  if  she  is  running  a  great  circle  course  requiring  frequent  changes, 
if  she  is  makmg  deep-sea  soundings,  u  she  has  just  come  through  a  period  of  foggy 
or  cloudy  weather,  or  if  the  indications  are  that  she  is  about  to  enter  upon  such  a 
period,  or  if  she  is  running  at  high  speed,  it  is  obviously  inexpedient  to  await  the 
coming  of  the  next  noon  for  a  fix.  The  responsibilities  resting  upon  the  navigator 
require  that  he  shall  earlier  find  his  ship's  position;  and,  generally  speaking,  the 
greater  the  speed  made  by  the  vessel  the  more  absolute  is  tnis  requirement. 

The  key  to  all  such  determinations  will  lie  in  the  Sumner  line,  and  a  clear  under- 
standing of  the  properties  of  such  a  line  will  greatly  facilitate  the  solutions.  The 
mariner  must  keep  m  mind  two  facts :  First,  that  a  single  observation  of  a  heavenly 
body  can  never,  by  itself,  give  the  'point  occupied  by  an  observer  on  the  earth's 
surface;  and  second,  that  whenever  any  celestial  body  is  visible,  together  with 
enough  of  the  horizon  to  permit  the  measuring  of  its  altitude,  an  observer  may 
thereby  determiue  a  line  which  passes  through  his  own  position  on  the  earth's  surface 
in  a  direction  at  right  angles  to  the  bearing  of  the  body. 

It  may  readily  be  seen  that  if  two  Sumner  lines  are  determined  the  observer's 
position  must  be  at  their  intersection,  and  that  that  intersection  will  be  most  clearly 
marked  when  the  angle  between  the  lines  equals  90°;  hence,  if  two  heavenly  bodies 
are  in  sight  at  the  same  time  the  position  may  be  found  from  the  intersection  of  their 
Sumner  lines,  the  angle  of  intersection  being  equal  to  the  horizontal  angle  between 
the  bodies.  If  only  one  body  is  in  sight,  as  is  generally  the  case  when  the  sun  is 
shining,  one  line  of  position  may  be  gotten  from  an  altitude  taken  at  one  time,  and  a 
second  line  from  another  altitude  taken  when  it  has  changed  some  30°  in  azimuth — 
usually,  a  couple  of  hours  later.  Bringing  forward  the  first  line  for  the  intervening 
run,  the  intersection  may  be  found. 


172  THE  PEACTICE   OF   NAVIGATION  AT  SEA. 

With  the  general  principles  of  the  Sumner  line  clearly  before  him,  the  navigator 
will  find  no  difficulty  in  maldng  the  choice  of  available  bodies.  If  about  to  take  a 
star  sight,  and  sky  and  horizon  are  equally  good  in  all  quarters,  two  bodies  should 
be  taken  whose  azimuths  differ  as  nearly  as  jpossible  by  90  °.  If  one  body  can  be  taken 
on  or  near  the  meridian,  its  bearing  being  practically  north  or  south,  the  resulting 
Sumner  line  will  be  east  and  west — that  is,  it  may  be  said  that  whatever  the  longitude 
(within  its  known  limits)  the  latitude  will  be  the  same;  the  other  sight  may  then 
be  worked  as  a.  time  sight  with  this  single  latitude,  and  time  will  thus  be  saved.  The 
same  is  true  if  Polaris  is  observed,  and  it  is  a  very  convenient  practice  to  take  an 
altitude  of  that  star  at  dawn  and  obtain  a  latitude  for  working  the  a.  m.  time  sight 
of  the  sun.  A  similar  case  arises  when  a  body  is  observed  on  the  prime  vertical, 
its  Sumner  line  then  runs  north  and  south  and  coincides  with  a  meridian;  if  the  other 
body  is  favorably  located  for  a  tp'  cp"  sight,  it  may  be  worked  with  a  single  longitude 
and  the  latitude  thus  found  directly. 

^  If  it  is  not  possible  to  obtain  two  lines  and  thus  exactly  locate  the  ship,  the 
indications  of  a  single  line  may  be  of  great  value  to  the  navigator.  A  Sumner  line 
and  a  terrestrial  bearing  will  give  the  ship's  position  by  their  intersection  in  the  same 
manner  as  two  lines  of  position  or  two  bearings;  or  the  position  of  the  ship  on  a  line 
may  be  shown  with  more  or  less  accuracy  by  a  soundmg  or  a  series  of  soundings. 
If  the  body  be  observed  when  it  bears  in  a  direction  at  right  angles  to  the  trend  of  a 
neighboring  shore  line,  the  resulting  line  will  be  parallel  with  the  coast  and  thus 
show  the  mariner  his  distance  from  the  land,  which  may  be  of  great  importance  even 
if  his  exact  position  on  the  line  remains  in  doubt.  If  the  bearing  be  parallel  to  the 
coast  line,  then  the  Sumner  line  will  point  toward  shore;  the  value  of  a  line  that  leads 
to  the  point  that  the  vessel  is  trying  to  pick  up  is  amply  demonstrated  by  the 
experience  of  Captain  Sumner  that  led  to  the  discovery  of  the  method.  (Art.  362, 
Chap.  XV.) 

For  especially  accurate  work  three  Sumner  lines  may  be  taken,  varying  in 
azimuth  about  120°;  if  they  do  not  intersect  in  a  point,  the  most  probable  position 
of  the  ship  is  at  the  center  of  the  triangle  that  they  form. 

If  two  pairs  of  lines  be  determined,  each  pair  based  upon  observation  of  two 
bodies  bearing  in  nearly  opposite  directions  and  at  about  the  same  altitude,  the 
mean  position  that  results  from  the  intersection  of  the  four  lines  will  be  as  nearly 
as  possible  free  from  those  errors  of  the  instrument,  of  refraction,  and  of  the  observer, 
which  can  not  otherwise  be  ehminated.  This  is  fully  explained  in  article  449, 
Chapter  XVII. 

391.  Use  of  Stars,  Planets,  and  Moon. — It  may  be  judged  that  the 
employment  in  navigation  of  other  heavenly  bodies  than  the  sun  is  considered  of 
the  utmost  importance,  and  mariners  are  urged  to  familiarize  themselves  with  the 
methods  by  which  observations  of  stars,  planets,  and  the  moon  may  be  utilized  to 
reveal  to  them  the  position  of  their  vessels  at  frequent  intervals  throughout  the 
twenty-four  hours. 

It  should  be  remembered,  however,  that  in  order  to  be  of  value  these  observations 
must  be  accurate;  and  to  measure  an  accurate  altitude  of  the  body  above  the  horizon 
it  is  required  not  only  that  the  body  be  visible  but  also  that  the  horizon  be  distinctly 
in  view.  Care  should  therefore  be  taken  to  make  the  observations,  if  possible,  at 
the  time  when  the  horizon  is  plainest — that  is,  during  morning  and  evening  twilight. 
It  may  be  urgently  required  to  get  a  position  during  hours  of  darkness,  and  a  dim 
horizon  line  may  sometimes  be  seen  and  an  observation  taken,  using  the  star  telescope 
of  the  sextant;  if  the  moon  is  shining,  its  light  will  be  a  material  aid;  but  results 
obtained  from  such  sights  should  be  regarded  as  questionable  and  used  with  caution. 
Altitudes  measured,  however,  just  before  sunrise  and  just  after  sunset  are  open  to 
no  such  criticism;  a  fairly  well-practiced  observer  who  takes  a  series  of  sights  at 
such  a  time,  setting  the  sextant  for  equal  intervals  of  altitude,  will  find  the  regularity 
of  the  corresponding  time  intervals  such  as  to  assure  him  of  accuracy. 

392.  Identification  of  Unknown  Bodies. — On  account  of  the  very  great 
value  to  be  derived  from  the  use  of  stars  and  planets  in  navigation,  it  is  strongly 
recommended  that  all  navigators  f  amiharize  themselves  with  the  names  and  positions 
of  those  fixed  stars  whose  magnitude  renders  possible  their  employment  for  obser- 
vations, and  also  with  the  general  characteristics — magnitude  and  color — of  the 
three  planets  (Venus,  Jupiter,  and  Mars)  which  are  most  frequently  used.     A  study 


THE  PEACTICB   OF   NAVIGATION  AT  SEA.  178 

of  the  different  portions  of  the  heavens,  with  the  aid  of  any  of  the  numerous  charts 
and  books  which  bear  upon  the  subject,  will  enable  the  navigator  to  recognize  the 
more  important  constellations  and  single  stars  by  their  situation  with  relation  to 
each  other  and  to  the  pole  and  the  equator. 

It  may  occur,  however,  that  occasion  will  arise  for  observing  a  body  whose  name 
is  not  known,  either  because  it  has  not  been  learned,  or  because  the  surrounding 
stars  by  which  it  is  usually  identified  are  obscured  by  clouds  or  rendered  invisible 
by  moonlight  or  dayhght.  In  such  a  case  the  observer  may  estimate  the  hour  angle 
and  declination  (the  hour  angle  applied  to  local  sidereal  time  giving  the  right 
ascension),  and  the  star  or  planet  may  thus  be  recognized  from  a  chart  or  from  an 
inspection  of  the  Nautical  Almanac.  This  rough  method  will  generally  suffice  when 
the  body  is  the  only  one  of  its  magnitude  within  an  extensive  region  of  the  heavens; 
but  cases  often  arise  where  a  much  closer  approximation  is  necessary,  and  more 
exact  data  are  required  for  identification. 

393.  If  in  doubt  as  to  the  name  of  the  body  at  the  time  of  taking  the  sight,  it 
should  be  made  an  invariable  rule  to  observe  its  bearing  by  compass,  whence  the 
true  azimuth  may  be  approximately  deduced  by  applying  the  compass  error .^ 

Star  Identification  Tables  giving  simultaneous  values  of  the  declination  and 
hour  angle,  corresponding  to  the  values  of  the  latitude,  altitude,  and  azimuth  ranging 
from  0°  to  88°  in  latitude  and  altitude  and  from  0°  to  180°  in  azimuth,  are  published 
by  the  Hydrographic  Office  for  the  convenience  of  navigators.  In  the  aosence  of 
these  Star  Identification  Tables,  the  following  method  affords  a  means  of  identi- 
fication : 

sin  d  =  sin  L  sin  h  +  cos  L  cos  h  cos  Z     (1 ) 
sin  t  =  sin  Z  cos  h  sec  d  (2) 

Having  computed  the  value  of  d,  the  declination,  from  (1),  noting  carefully  the 
sign  of  cosine  Z,  the  value  of  t,  the  hour  angle,  is  computed  from  (2) .  In  the  catalogues 
and  lists  giving  the  names  and  magnitudes  of  the  stars,  they  are  tabulated  by  their 
declinations  and  right  ascensions  because  these  coordinates  are  independent  of 
diurnal  rotation,  and,  this  being  so,  it  becomes  necessary,  on  finding  the  nour  angle 
from  (2),  to  convert  it  into  right  ascension;  and  then,  with  the  values  of  the  declina- 
tion and  right  ascension  thus  found,  to  scan  the  list  of  stars  and  find  the  name  of 
that  one  whose  catalogued  coordinates  best  agree  with  these  values.  The  stars  that 
are  bright  enough  to  be  observed  with  nautical  instruments  are  so  far  apart  in  the 
firmament  that  the  identification  will  be  complete  if  the  computation  be  but  roughly 
made.  The  possibility  that  the  observed  body  may  be  a  planet  must  always  be  kept 
in  mind  in  scanning  the  star  table  or  chart. 

Example  :  At  sea,  February  26, 1915,  L.  M.  T.  6h  20m  p.  m.  Weather  overcast  and  cloudy.  Observed 
the  altitude  of  an  unknown  star  tlirough  a  break  in  the  clouds  to  be  31°  3(K  (true),  bearing  285°  (true). 
What  is  the  name  of  the  star?    Ship's  position,  by  D.  R,,  latitude  35°  2(y  N.,  longitude  60°  W. 

L    35°  20^     log  sin    9.  762    log  cos    9.  912 

h    31°  30^     log  sin    9.  718    log  cos    9. 931    log  cos    9.  931 

Z  285°  OO'     log  cos    9.  413    log  sin    9.  985 

A  0.302  log...     9.480 

B  0.180 log.  - .     9.  256 

A+B  =  0.302  +  0.180  =  0'482  =  nat  sin rf  .-.d  =  28°  49^.. .     log  sec  10.  057 

«=H.  A.=a70°=4h  40m log  sin    9.973 

Then  converting  the  hour  angle  into  right  ascension,  as  follows: 

L.  M.  T.  6^  20° 

R.  A.  M.  S.  22    21 

corr.  for  G.  M.  T  +2 

L.  S.  T.  4    43 

H.  A.  4    40 

R.  A.  0    03 

The  right  ascension  and  declination  of  the  unknown  star,  as  we  have  now  approximately  found  them, 
are  O'' 3™  and  28°  49^  N.,  respectively.  The  star  is,  therefore,  a  Andromedse,  whose  tabulated  coordi- 
nates are  right  ascension  O"^  3'"  59*  and  declinaton  28°  37'  22^'  N. 


174  THE   PBACTICE   OF   NAVIGATION   AT   SEA. 

394.  Value  of  the  Moon  in  Observations. — Next  to  the  sun,  the  most  con- 
spicuous body  in  the  heavens  is  the  moon,  and  it  may  therefore  frequently  be 
employed  by  the  mariner  with  advantage.  Owing  to  its  nearness  to  the  earth  and 
the  rapidity  with  which  it  changes  right  ascension  and  declination,  the  various  cor- 
rections entailed  render  observations  of  this  body  somewhat  longer  to  work  out, 
with  consequent  increased  chances  of  error;  and  errors  in  certam  parts  of  the  work 
will  have  more  serious  results  than  with  other  bodies;  the  navigator  will  therefore 
usually  pass  the  moon  by  if  a  choice  of  celestial  bodies  is  offered  for  a  determination 
of  position;  but  so  many  occasions  present  themselves  when  there  is  no  available 
substitute  for  the  moon  that  the  extra  time  and  care  necessary  to  devote  to  it  are 
well  repaid.  During  hours  of  daylight  it  is  often  clearly  visible,  and  its  Ime  of 
position  may  cut  with  that  of  the  sun  at  a  favorable  angle,  giving  a  good  fix  from 
two  observations  taken  at  the  same  time,  when  the  only  other  method  of  finding 
the  position  would  be  to  take  two  sights  of  the  sun  separated  by  a  time  interval  in 
which  an  imperfect  allowance  for  the  true  run  intervenmg  would  affect  the  accuracy 
of  the  result,  or  a  clouding-over  of  the  heavens  would  prevent  any  definite  result 
whatever  being  reached;  and  during  the  night,  the  gleam  upon  the  water  directly 
below  the  moon  may  define  the  horizon  and  give  opportunity  for  an  altitude  of  that 
body  when  it  is  impossible  to  take  an  observation  of  any  other.  It  has  been  the 
purpose  of  this  work  to  point  out  the  features  of  the  various  sights  wherein  the 
practice  with  the  moon  differs  from  that  of  the  sun,  stars,  or  planets;  care  and 
mtelligent  consideration  will  render  these  quite  clear. 

Besides  its  availabiUty  for  determming  Sumner  lines  of  position,  which  it  shares 
with  other  bodies,  the  moon  affords  a  means  for  ascertaining  the  Greenwich  mean 
time  independently  of  the  chronometer,  thus  rendering  it  possible  to  deduce  the 
longitude  and  chronometer  error.  This  is  accompHshed  by  the  method  of  lunar 
distances.^  If  the  Greenwich  time  given  by  an  observation  of  lunar  distance  could 
be  relied  upon  for  accuracy,  the  method  would  be  a  great  boon  to  the  navigator; 
but  this  is  not  the  case.  The  most  practiced  observer  can  not  be  sure  of  obtaining 
results  as  close  as  modem  navigation  demands,  and  the  errors  to  which  the  method 
is  subject  are  larger  than  the  errors  that  may  be  expected  in  the  chronometer,  even 
when  the  instrument  is  only  a  moderately  good  one  and  its  rate  is  carried  forward 
from  a  long  voyage.  The  method  is  not,  therefore,  recommended  for  use  except 
where  the  chronometer  is  disabled  or  where  it  is  known  to  have  acquired  some 
extraordinary  error;  and  when  lunar  distances  are  resorted  to  care  must  be  taken 
to  navigate  with  due  allowance  for  possible  inaccuracy  of  the  results.  In  this  con- 
nection it  is  appropriate  to  say  that  the  best  safeguard  against  the  dire  consequences 
that  may  result  from  a  disabled  or  unrehable  chronometer  is  for  every  vessel  to  carry 
two — or,  far  better,  three — of  those  instruments,  the  advantages  of  which  plan  are 
stated  in  article  265,  Chapter  VIII. 

395.  Employment  op  Bodies  dependent  upon  their  PosmoN, — The  prac- 
tical navigator  will  soon  observe  that  there  are  certain  conditions  in  which  bodies 
are  especially  well  adapted  for  the  finding  of  latitude,  and  others  where  the  longitude 
is  obtained  most  readily. 

Taking  the  sun  for  an  example,  when  a  vessel  is  on  the  equator  and  the  declina- 
tion is  zero,  that  body  will  rise  due  east  of  the  observer  and  continue  on  the  same 
bearing  until  noon,  when  for  an  instant  it  will  be  directly  overhead,  with  a  true 
altitude  of  90°,  and  will  then  change  to  a  bearing  of  west,  which  it  wiU  maintain 
until  its  setting.  In  such  a  case  any  observation  taken  throughout  the  day  will 
give  a  true  north-and-south  Sumner  line,  defining  longitude  perfectly,  but  giving  no 
determination  of  the  latitude,  excepting  for  a  moment  only  when  the  body  is  on  the 
meridian.     With  the  exception  noted,  all  efforts  to  determine  the  latitude  will  fail. 

The  reduction  to  the  meridian  takes  the  form  j.,  becoming  indeterminate,  and  in  the 

<f>'  (ff  sight  the  cosine  of  <}>'  wiU  assume  a  value  that  corresponds  alike  to  any  angle 
within  certain  wide  limits — the  limits  within  which  the  circle  of  equal  altitude  has 
practically  a  north-and-south  du-ection.  In  conditions  approximating  to  this  we 
may  obtain  a  longitude  position  more  easily  than  one  for  latitude,  even  within  a  few 
minutes  of  noon. 

'  The  tables  of  lunar  distances  have  been  omitted  from  the  American  Ephemeris  and  Nautical  Almanac  after  the  volume  for 
the  year  1911. 


THE  PBAOTICE   OF   NAVIGATION  AT  SEA.  175 

As  the  latitude  and  declination  separate,  conditions  become  more  favorable  for 
finding  latitude  and  less  so  for  longitude;  the  intermediate  cases  cover  a  wide  range, 
wherem  longitude  may  be  well  determined  by  observations  three  to  five  hours  from 
the  meridian,  and  latitude  by  those  within  two  hours  of  meridian  passage.  As 
extreme  conditions  are  approached  the  accuracy  of  longitude  determinations  con- 
tinues to  decrease;  at  a  point  in  60°  north  latitude,  when  the  sun  is  near  the  southern 
solstice,  its  bearing  differs  only  39°  from  the  meridian  at  rising;  or,  in  other  words, 
even  if  observed  at  the  most  favorable  position,  the  resulting  Sumner  line  is  such 
that  1'  in  latitude  makes  a  difference  of  1.3  mUes  of  departure,  or  2 '.6  of  longitude, 
and  is  far  better  for  a  latitude  determination  than  for  longitude.  And  in  nigher 
latitudes  stiU  this  condition  is  even  more  marked. 

Having  grasped  these  general  facts,  the  navigator  must  adapt  his  time  for 
taking  sights  to  the  circumstances  that  prevail,  and  when  the  sun  does  not  serve 
for  an  accurate  determination  of  either  latitude  or  longitude  the  ability  to  utilize 
the  stars,  planets,  and  moon  as  a  substitute  will  be  of  the  greatest  advantage. 

396.  USE  OF  Various  Sights. — Except  when  employing  the  method  of  Saint 
Hilaire  (Chapter  XV),  the  navigator  may  sometimes  be  in  doubt  as  to  the  best 
method  of  working  a  sight.  No  rigorous  rules  can  be  laid  down,  and  experience 
alone  must  be  his  guide.  In  a  general  way  it  may  be  well,  when  the  body  is  nearer 
to  the  prime  vertical  than  to  the  meridian,  to  work  it  for  longitude,  assuming  lati- 
tude, and  using  the  time  sight;  and  when  nearer  the  meridian  to  work  it  for  latitude, 
assuming  longitude,  by  the  (f>'  <ji"  method.  The  time  sight  is  more  generally  used 
than  the  other,  it  has  wider  limits  of  accurate  application  and  is  probably  a  little 
quicker;  but  as  the  meridian  is  approached  and  the  hour  angle  decreases  small 
errors  in  the  terms  make  large  ones  in  the  results.  The  (f>'  d)"  or  latitude  method 
should  not  ordinarily  be  employed  beyond  three  hours  from  the  meridian,  and  then 
only  when  the  body  is  withm  45°  of  azimuth  from  the  meridian  and  has  a  declina- 
tion of  at  least  3°;  with  an  hour  angle  of  6**  (90°)  or  a  declination  of  0°  the  trigono- 
metric functions  assume  such  form  that  the  method  is  not  available;  nor  does  it 
give  definite  results  when  the  azimuth  is  90°  or  thereabouts. 

When  the  body  is  close  enough  to  the  meridian  for  the  method  of  reduction  to 
the  meridian  to  be  applicable,  that  method  is  to  be  preferred  because  of  its  quickness 
and  facilitjy'.  It  should  be  noted,  however,  that,  though  close  enough  to  employ 
the  reduction,  it  may  not  be  sufficiently  correct  to  assume  that  the  body  bears  due 
north  or  south,  and  the  sight  should  be  worked  with  two  longitudes,  or  the  Sumner 
line  determined  by  the  azimuth,  unless  the  bearing  nearly  comcides  with  the  direc- 
tion of  the  meridian. 

397.  Working  to  Seconds  and  Accuracy  of  Determinations. — The  beginner 
who  seeks  counsel  from  the  more  experienced  in  matters  pertaining  to  navigation  will 
find  that  he  receives  conflicting  advice  as  to  whether  it  is  more  expedient  to  carry 
out  the  terms  to  seconds  of  arc,  or  to  disregard  seconds  and  work  with  the  nearest 
whole  minute. 

It  is  a  well-recognized  fact  that  exact  results  are  not  attainable  in  navigation  at 
sea;  the  chronometer  error,  sextant  error,  error  of  refraction,  and  error  of  observa- 
tion are  all  uncertain;  it  is  impossible  to  make  absolutely  correct  allowance  for  them, 
and  the  uncertainty  increases  if  the  position  is  obtained  by  two  observations  taken 
at  different  times,  in  which  case  an  exactly  correct  allowance  for  the  intervening 
run  of  the  ship  is  an  essential  to  the  correctness  of  the  determination.  No  navigator 
should  ever  assume  that  his  position  is  not  Hable  to  be  in  error  to  some  extent,  the 
precise  amount  depending  upon  various  factors,  such  as  the  age  of  the  chronometer 
rate,  the  quality  of  the  various  instruments,  the  reliability  of  the  observer,  and  the 
conditions  at  the  time  the  sight  was  taken;  perhaps  a  fair  allowance  for  this  possible 
error,  under  favorable  circumstances,  will  be  2  miles;  therefore,  instead  of  plotting 
a  position  upon  the  chart,  and  proceeding  with  absolute  confidence  in  the  belief  that 
the  ship's  position  is  on  the  exact  point,  one  may  describe,  around  the  point  as  a 
center,  a  circle  whose  radius  is  2  miles — if  we  accept  that  as  the  value  of  tne  possible 
error — and  shape  the  future  courses  with  the  knowledge  that  the  ship's  position  may 
be  anywhere  within  the  circle. 

It  is  on  account  of  this  recognized  inexactness  of  the  determination  of  position 
that  some  navigators  assume  that  the  odd  seconds  may  be  neglected  in  deamig  with 


176  THE   PRACTICE   OF   NAVIGATION  AT  SEA. 

the  different  terms  of  a  sight;  the  average  possible  error  due  to  this  course  is  probabty 
about  one  minute,  though  under  certain  conditions  it  may  be  considerably  more.  It 
is  possible  that,  in  a  particular  case,  the  error  thus  introduced  through  one  term 
would  be  offset  by  that  from  others,  and  the  result  would  be  the  same  as  if  the 
seconds  had  been  taken  into  account;  but  that  does  not  affect  the  general  fact  that 
the  neglect  of  seconds  as  a  regular  thing  renders  any  determination  liable  to  be  in 
error  about  one  minute.  Those  that  omit  the  seconds  argue,  however,  that  since,  in 
the  nature  of  things,  any  sight  may  be  in  error  two  minutes,  it  is  immaterial  if  we 
introduce  an  additional  possibihty  of  error  of  one  minute,  because  the  new  error  is 
as  liable  to  decrease  the  old  one  as  to  increase  it;  but  the  fallacy  of  the  argument 
will  be  apparent  when  we  return  to  the  circle  drawn  around  our  plotted  point.  The 
eccentricity  of  the  sextant  may  exactly  offset  the  improper  allowance  for  refraction, 
and  the  mistake  in  the  chronometer  error  may  offset  the  observer's  personal  error, 
but  unless  we  know  that  such  is  the  case — which  we  never  can — we  nave  no  justi- 
fication for  doing  otherwise  than  assume  that  the  ship  may  be  any  place  within  the 
2-mile  circle.  If,  now,  we  increase  the  possible  error  by  1  mile,  our  radius  of  uncer- 
tainty must  be  increased  to  3  miles,  and  the  diameter  of  the  circle,  representing  the 
range  of  uncertainty  in  any  given  direction,  is  thereby  increased  from  4  to  6  miles. 
It  is  deemed  to  be  the  duty  of  the  navigator  to  put  forth  every  effort  to  obtain 
the  most  prohahle  position  of  the  ship,  which  requires  that  he  shall  eliminate  possible 
errors  as  completely  as  it  lies  within  his  power  to  do.  By  neglecting  seconds  he 
introduces  a  source  of  error  that  might  with  small  trouble  be  avoided.  This  becomes 
of  stiU  more  importance  since  modern  instruments  and  modem  methods  constantly 
tend  to  decrease  the  probability  of  error  in  the  observation,  and  to  place  it  within 
the  power  of  the  navigator  to  determine  his  ship's  position  with  greater  accuracy. 

398.  There  is  a  more  exact  way  of  defining  the  area  of  the  ship's  possible  position 
than  that  of  describing  a  circle  around  the  most  probable  point,  as  mentioned  in  the 
preceding  article,  and  that  is  to  draw  a  line  on  each  side  of  each  of  the  Sumner  lines 
by  which  the  position  is  defined,  and  at  a  imiform  distance  therefrom  equal  to  the 
possible  error  that  the  navigator  believes  it  most  reasonable  to  assume  under  existing 
conditions;  the  parallelogram  formed  by  these  four  auxiliary  lines  marks  the  limit 
to  be  assigned  for  the  ship's  position;  this  method  takes  accoimt  of  the  errors  due 
to  poor  intersections,  and  warns  the  navigator  of  the  direction  in  which  his  position 
is  least  clearly  fixed  and  in  which  he  must  therefore  make  extra  allowance  for  the 
uncertainty  of  his  determination. 

It  must  be  remembered  in  this  connection  that  no  position  can  ever  be  obtained, 
when  out  of  sight  of  the  land,  except  from  the  intersection  of  two  Sumner  lines, 
whether  or  not  the  lines  are  actually  plotted;  thus,  a  meridian  altitude  gives  a  Sumner 
line  that  extends  due  east  and  west,  and  a  sight  on  the  prime  vertical  a  line  that 
extends  north  and  south,  though  it  may  not  have  been  considered  necessary  to  work 
the  former  with  two  longitudes  or  the  latter  with  two  latitudes. 

399.  The  Work  Book  and  Forms  for  Sights. — The  navigation  work  book, 
or  sight  book,  being  the  official  record  of  all  that  pertains  to  the  navigation  of  the 
ship  when  not  running  by  bearings  of  the  land,  should  be  neatly  and  legibly  kept, 
so  that  it  wiU  be  intelligible  not  only  to  the  person  who  performed  the  work,  but 
also  to  any  other  who  may  have  reason  to  refer  to  it. 

Each  day's  work  should  be  begun  on  a  new  page,  the  date  set  forth  clearly  at 
the  top,  and  jjreferably,  also,  a  brief  statement  of  the  voyage  upon  which  the  ship  is 
engaged.  It  is  a  good  plan  to  have  the  dead  reckoning  begin  the  space  allotted  for 
the  day,  and  then  have  the  sights  follow  in  the  order  in  which  taken.  The  page 
should  be  large  enough  to  permit  the  whole  of  any  one  sight  to  be  contained  thereon 
without  the  necessity  of  carrying  it  forward  to  a  second  page.  No  work  should  be 
commenced  at  the  bottom  of  a  page  if  there  is  not  room  to  complete  it.  Every 
operation  pertaining  to  the  working  of  the  sights  should  appear  in  the  book,  and  all 
irrelevant  matter  should  be  excluded. 

It  is  weU  to  observe  a  systematic  form  of  work  for  each  sight,  always  writing 
the  different  terms  in  the  same  position  on  the  page;  this  practice  will  conduce  to 
rapidity  and  lessen  the  chances  of  error.  In  order  to  facilitate  the  adoption  of  such 
a  method,  there  are  appended  to  this  work  (Appendix  II)  a  series  of  forms  that  are 
recommended  for  dead  reckonmg,   and  for  the  various  sights  of   the  sun,  stars. 


THE  PRACTICE   OF   NAVIGATION  AT  SEA.  177 

planets,  and  moon,  respectively.  For  beginners,  these  are  deemed  of  especial 
importance,  and  it  is  recommended  that,  until  perfect  familiarity  with  the  dif- 
ferent sights  is  acquired,  the  first  stop  in  working  out  an  observation  be  to 
write  down  a  copy  of  the  appropriate  blank  form,  indicating  the  proper  sign  of  appli- 
cation of  each  quantity  (for  which  the  notes  wiU  be  a  guide),  and  not  to  put  in  any 
figures  until  the  scheme  has  been  completely  outlined;  then  the  remainder  of  the 
work  wiU  consist  in  writing  down  the  various  quantities  in  their  proper  places  and 
performing  the  operations  indicated. 

The  navigator  may  make  up  his  work  book  by  having  printed  forms  of  the 
various  sights  which  can  be  placed  in  a  loose-leaf  binder  when  they  have  been  filled 
in  with  his  computations.  Instead  of  printed  forms  on  separate  sheets,  he  m&y 
employ  rubber  stamps  of  the  various  forms  of  sights  which  he  may  stamp  in  his 
work  book  or  on  loose  leaves. 

THE  SPECIFIC  STEPS  FOB  CABBYING  OUT  THE  DAY'S  WOBE. 

400.  The  day's  work  as  described  herein  is  so  laid  out  that  the  true  position 
at  noon  is  known  some  few  minutes  before  noon,  as,  when  cruising  in  company, 
naval  vessels  have  to  make  their  noon  position  report  by  signal  at  exactly  12  o'clock. 
When  cruising  singly  the  noon  position  need  not  be  known  until  after  12  o'clock, 
but  it  is  advisable  to  do  a  daj^'s  work  always  in  one  way,  and,  therefore,  the  plan  of 
getting  the  correct  noon  position  before  noon  wiU  be  followed. 

4:01.  The  Time  to  Take  an  A.  M.  Observation. — The  navigator  of  a  vessel 
cruising  may,  by  dead  reckoning  or  by  plotting  on  a  chart,  predict  the  approximate 
position  of  the  snip  the  following  mornmg,  and  from  that  position  may  easily  determine 
the  best  time  to  observe  the  sun  (or  other  body)  for  longitude.  Having  determined 
his  approximate  8  a.  m.  position,  he  takes  from  the  Nautical  Almanac  the  declination 
of  the  sun  for  Greenwich  noon  of  that  day.  With  the  latitude  of  the  8  a.  m.  position 
and  declination  for  the  day,  he  enters  tne  Azimuth  Tables  and  takes  out  tne  local 
apparent  time  when  the  sun  will  bear  90°.  By  getting  the  error  of  his  watch  on  local 
apparent  time  for  the  approximate  8  a.  m.  longitude,  he  may  easily  find  the  watch 
time  when  the  sun  will  bear  90°,  which  is  the  time  he  should  take  his  sight.  Suppose 
on  the  evening  of  July  18,  1915,  a  navigator  finds  that  at  8  a.  m.  the  next  day  he  will 
be  in  approximate  Lat.  35°  12'  N.,  Long,  65°  15'  W.,  and  wishes  to  find  at  what 
time  h/  his  watch  the  sun  will  be  on  the  prime  vertical.  He  compares  his  watch 
with  the  chronometer,  of  which  he  knows  the  correction,  and  which  is,  we  will  say, 
slow  1™  10^  on  G.  M,  T.,  and  finds  that  when  the  chronometer  reads,  say  ll**  59"  SO", 
the  watch  reads  7**  15"  12^,     He  then  does  the  following  work: 

He  takes  from  the  Nautical  Almanac  the  declination  and  the  equation  of  time 
for  Greenwich  mean  noon  on  July  19  and  finds  Dec.  =21°  01'  N.;  Eq.  t.  6"  03», 
subtractive  from  mean  time. 

With  Lat.  35°.2  N.,  Dec.  21°.0  N.,  enter  the  Azimuth  Tables,  and  find, 
for  a  bearing  of  90°,  the  L.  A.  T.  is  about  S^  10". 

Write  down  the  reading  of  the  chronometer  face  at  comparison 11''  59"*  30* 

Apply  the  chronometer  correction +  1    10 

G.  M.  T.  of  the  time  of  comparison 12    00    40 

Apply  equation  of  time —  6    03 

Greenwich  apparent  time  of  comparison 11    54    37 

For  Long.  65°  15' W.,  il=4'»  21°' 00*.    Apply  A 4    21    00 

At  time  of  comparison  the  L.  A.  T.  at  the  8  a.  m.  position  was 7    33    37 

At  time  of  comparison  the  watch  time  was 7    15    12 

Error  of  watch  on  L.  A.  T.  of  8  a.  m.  position 18    25  slow. 

L.  A.  T.  when  sun  is  on  prime  vertical 8    10 

Watch  time  to  take  a.  m.  observation 7    51    35 

The  observation  should  therefore  be  taken  when  the  watch  face  reads. about 
7-52,  which  will  bring  the  sun  very  close  to  the  prime  vertical. 

When  the  latitude  and  declination  are  of  different  names  the  sun  crosses  the 
prime  vertical  before  rising.  In  that  case,"  the  observation  is  taken  as  soon  as  the 
21594<*— 14 12 


178  THE  PRACTICE   OF    NAVIGATION   AT  SEA. 

sun  is  sufficiently  high  to  be  unaffected  by  any  peculiar  condition  of  the  atmosphere, 
usually  about  an  hour  after  sunrise.  The  L.  A.  T.  of  sunrise  and  sunset  is  given  at 
the  bottom  of  the  page  in  the  Azimuth  Tables.  Suppose  in  the  above  example  the 
approximate  8  a.  m.  latitude  was  35°.2  S.  instead  of  35°.2  N.  Entering  the  tables 
with  Lat.  and  Dec.  of  different  names,  we  find  the  time  of  sunrise  is  about  7  a.  m. 
The  observation  should  therefore  be  taken  at  about  8  a.  m.  L.  A.  T.,  the  watch  time 
of  which  can  be  found  in  the  same  way  as  explained  above. 

In  a  similar  manner  Azimuth  Tables  may  be  used  to  find  the  best  time  to  take 
p.  m.  observations  for  longitude. 

402.  The  Morning  Work  of  the  Navigator. — The  navigator,  having  deter- 
mined the  time  at  which  he  will  take  his  morning  observation,  is  called  sufficiently 
early  to  be  ready  for  work  about  15  minutes  before  the  time  chosen. 

The  first  thmg  the  navigator  does  is  to  check  up  his  time.  To  save  the  trouble 
of  going  below  to  compare  the  watch  with  the  standard  chronometer  each  time  that 
an  observation  is  taken,  most  navigators  keep  the  hack  chronometer  in  the  chart 
house  and  use  it  for  comparisons  during  the  day.  It  is  necessary  to  check  the  hack 
with  the  standard  chronometer  each  day  to  make  sure  of  its  error  on  G.  M.  T.  and 
rate.  This  comparison  is  made  the  first  thing  in  the  morning,  the  date,  the  error 
on  G.  M.  T.,  and  the  rate  of  the  hack  being  written  on  a  slip  of  paper  that  is  placed 
in  the  hack  case.  The  hack  is  then  taken  to  the  chart  house  and  is  used  for  the 
day's  work.  As  hack  chronometers  frequently  have  high  daily  rates,  an  additional 
correction  sometimes  has  to  be  made  for  the  rate  when  observations  have  been  taken 
some  hours  after  the  comparison.  The  hack  is  sometimes  used  for  marking  the  time 
of  observation,  and.  when  so  used,  the  G.  M.  T.  is  at  once  obtained  by  applying  the 
hack  error. 

Having  checked  up  the  hacK  chronometer,  the  navigator  then  j)repares  his 
sextant  and  takes  it,  with  his  watch  and  notebook,  to  the  place  from  which  he  takes 
his  observations.  At  about  the  time  he  has  selected  for  his  purpose,  he  observes 
altitudes  of  the  sun,  which,  with  the  corresponding  watch  times  are  noted  in  his  note- 
book. The  patent  log  is  read  while  the  observations  are  being  taken  and  the  reading 
is  entered  in  the  notebook.     The  navigator  then  goes  to  the  standard  compass  and 

fets  a  bearing  of  the  sun,  which  with  the  watch  time  of  the  bearing  and  the  compass 
eading  of  the  ship  is  entered  in  the  notebook.  Either  just  before  or  just  after 
observing  the  altitude  of  the  sun  with  the  sextant,  the  index  correction  should  be 
found  and  entered  in  the  notebook.  The  navigator  next  compares  his  watch  with 
the  hack  chronometer  and  gets  the  C-W,  which  is  also  entered  in  the  notebook. 
From  the  log  book  he  gets  the  courses  and  distances  run  from  the  last  "fix"  and 
enters  them  m  his  notebook.     This  completes  the  data  for  his  morning's  work. 

The  computations  are  then  made  in  the  navigator's  work  book.  The  first  step 
is  to  work  up  the  dead  reckoning  from  the  last  "fix"  to  the  time  of  sight.  It  may 
be  well  here  to  call  the  attention  of  the  student  to  the  fact  that  for  "distance  run" 
the  propellers  frequently  are  a  more  accurate  gauge  than  the  patent  log  which  some- 
times gets  foul.  In  a  smooth  sea  the  distance  by  revolutions  is  usually  very  accurate, 
especially  if  the  effect  of  the  condition  of  the  bottom  as  to  fouling  is  known.  In 
heavy  weather  the  patent  log  is  a  better  gauge  as  the  effects  of  the  wind  and  sea  on 
the  speed  of  the  ship  are  hard  to  determme.  But  for  distance  run  both  the  patent 
log  and  revolutions  should  be  considered,  and,  if  there  is  a  discrepancy  between 
them,  it  should  be  investigated  and  the  more  accurate  distance  should  be  used. 

Having  brought  the  dead  reckoning  up  to  the  time  of  sight,  the  latitude  so  found 
is  taken  as  the  base  of  the  computation  of  the  longitude  by  observation.  It  is 
assumed  that  the  student  is  familiar  with  the  various  methods  of  getting  a  line  of 
position  from  an  observation.  Any  one  of  the  various  methods  gives  the  same  line 
and  the  choice  of  method  is  naturally  the  choice  of  the  individual. 

Having  obtained  the  line  of  position,  the  longitude  factor  is  next  found,  as 
explained  in  article  387.  The  longitude  factor  is  used  twice,  first  to  find  the  longitude 
iby  observation  corresponding  to  the  D.  R.  latitude,  and  again  after  the  noon  latitude  is 
[determined,  to  find  the  true  noon  longitude.  As  soon  as  the  longitude  factor  has  been 
Rbbtained,  the  longitude  by  observation  corresponding  to  the  D.  R.  latitude  is  found, 
[and  it  is  this  point  on*the  line  of  position  that  is  used  for  the  rest  of  the  work  to  noon. 
[This  point,  corrected  for  run,  is  also  the  point  adopted  as  the  8  a.  m.  position,  and 


THE  PRACTICE   OF   NAVIGATION  AT  SEA.  179 

as  by  using  it  future  steps  are  simplified,  it  is  advisable  alwaj^s  to  work  from  this 
point.  Of  course,  any  other  point  on  the  line  can  be  moved  up,  and  the  final  result 
will  be  the  same,  but  the  computation  will  be  a  little  more  complicated. 

Having  obtained  the  position  at  time  of  sight  (D.  R.  Lat.,  Long,  by  obs.)  and 
the  longitude  factor,  the  navigator  next  proceeds  to  get  the  compass  error.  The 
work  he  has  akeady  performedin  getting  the  line  of  position  gives  him  certain  data 
that  will  shorten  his  work  in  finding  the  compass  error.  If  the  sight  has  been  worked 
out  as  a  Sumner  line  the  navigator,  by  tak-ng  the  L.  A.  T.  found  by  his  computation 
and  correcting  it  for  the  difference  between  the  watch  times  of  his  observation  for 
altitude  and  observation  for  azimuth,  may  obtain  at  once  the  L.  A.  T.  of  the  time 
at  which  he  took  the  sun's  azimuth.  With  this  L.  A.  T.,  and  the  Lat.  and  Dec.  used 
in  working  out  his  sight,  he  may  at  once  find  from  the  Azimuth  Tables  the  true 
bearing  of  the  sun  and  get  the  compass  error.  If  the  line  of  position  has  been 
obtained  by  one  of  the  tangent  methods,  the  navigator  has,  in  his  computation,  deter- 
mined the  true  bearing  of  the  sun  at  the  time  of  sight.  All  he  has  to  do  to  get  the 
true  azimuth  for  compass  error  is  to  correct  this  bearing  for  the  change  in  azimuth 
due  to  the  difference  in  time  between  his  observation  for  altitude  and  his  observation 
for  azimuth.     This  correction  is  easily  found  from  the  Azimuth  Tables  by  inspection. 

This  completes  the  morning  work  when  the  amount  of  work  each  day  is  a 
minimum.  When  very  accurate  positions  are  required  at  other  times  than  at 
noon,  as  for  instance,  when  a  vessel  is  scouting,  when  in  dangerous  waters, 
moving  at  high  speed,  or  when  making  a  landfall,  other  lines  of  position  are 
worked  out,  and  the  ship's  position  found  on  each  line  bj^  moving  the  next  preceding 
line  up  to  it  for  run.  For  instance,  lines  obtained  from  morning  twilight  sights  of 
the  moon,  stars,  or  planets,  may  be  run  up  to  the  8  a.  m.  line,  the  8  a.  m.  line  may 
be  run  up  to  one  taken  at  9.30  or  10,  or  later,  and  so  on.  VvTien  getting  the  position 
by  the  intersection  of  lines  moved  up  for  nm,  it  is  usual  to  perform  the  work  on  the 
plotting  charts  supplied  for  this  particular  purpose.  These  charts  are  Mercator 
projections  covering  each  5°  of  latitude  from  0°  to  60°.  The  parallels  are  numbered 
for  every  degree  of  latitude,  and  the  navigator  selects  the  chart  covering  the  latitude 
in  which  he  is  working.  The  meridians  on  these  charts,  not  being  numbered,  the 
navigator  is  left  free  to  mark  them  with  the  longitudes  through  which  he  is  working. 
The  charts  are  of  large  scale,  and,  being  on  heavy  paper,  ma}'-  be  used  over  and  over, 
lines  on  these  being  drawn  in  lightly  and  erased  when  no  longer  required. 

Intersections  of  lines  of  position  may  be  computed,  as  explained  in  Chap.  XV, 
when  there  are  no  charts  at  hand  suitable  for  plottmg  the  lines  graphically.  Special 
plotting  sheets  prepared  by  the  United  States  Hydrographic  Office  are  supphed  to 
vessels  of  the  Navy. 

4:03.  The  Work  Between  11  A.  M.  and  Noon. — Two  important  steps,  not 
usually  fully  explained  in  the  text  books,  must  be  studied.  These  are:  I'irst,  to 
determine  the  exact  run  from  the  time  of  the  a.  m.  sight  to  local  apparent  noon; 
second,  to  set  the  watches  and  clocks  to  the  local  apparent  time  of  the  place  the  ship 
will  be  at  local  apparent  noon. 

If  the  ship  has  been  making  westing,  the  watches  and  clocks  will  be  ahead 
of  the  local  apparent  time  of  the  noon  position  and  will  have  to  be  set  back  by  the 
amount  of  the  change  in  longitude.  As  the  change  of  time  is  made  between  11  a.  m. 
and  noon,  it  will  be  seen  that  the  elapsed  time  between  the  time  of  the  a.  m.  sight 
and  the  new  watch  time  of  noon  will  be  more  than  the  watch  face  shows  by  the 
amount  the  watch  has  been  set  back,  and  tliis  difference  must  be  allowed  for  in 
computing  the  run  to  noon.  In  the  same  way,  if  the  ship  has  been  making  east- 
ing, the  clocks  and  watches  will  have  to  be  set  ahead  and  the  elapsed  time  between 
the  time  of  the  a.  m.  sight  and  the  new  watch  time  of  noon  will  be  less  than  the  watch 
face  shows  bv  the  amount  the  watch  has  been  set  ahead,  and  must  be  allowed  for  in 
computing  tne  run  to  noon.  It  must  be  remembered  that  this  time  can  not  be 
computed  exactly,  but  it  can  be  approximated  very  closely  in  this  wav.  Suppose  a 
ship  has  been  steaming  on  course  66°  true,  and  the  navigator  finds  from  his  a.  m. 
observation  taken  at  watch  time,  8^  00™  03^.5,  that  the  L.  A.  T.  for  the  position, 
Lat.  by  D.  R.  38°  03'.2  N.,  Long,  by  obs.  72°  46'  18"  W.,  is  8^  17'"  45«.2.  He  sees 
at  once  that  at  8  a.  m.  his  watcn  is  already  slow  17™  41 .7"  on  L.  A.  T.     Now,  if  he 


180  THE   PRACTICE   OF    NAVIGATION   AT   SEA. 

continues  on  this  couree  66°  true,  at  a  speed  of  11.7  knots  per  hour,  the  watch  will 
be  still  slower  at  noon.  He  therefore  turns  to  the  Traverse  Tables  and  finds  that 
on  that  course  and  at  a  speed  of  11.7  knots  the  ship  will  each  hour  go  10.69  imles  to 
the  eastward,  which,  in  Lat.  38°,  makes  a  change  of  longitude  of  13'. 6  each  hour. 
Now,  from  time  of  sight  to  11  a.  m.  the  change  of  longitude  will  be  3  X  13'.6  =  40'.8 
of  longitude,  which  is  equal  to  a  further  loss  of  2™  43^.2  of  time;  but  the  watch  was 
already  slow  17*°  41^7,  so  that  at  11  a.  m.  the  watch  will  be  slow  20^"  24^9,  and 
the  time  to  noon  will  be  l*"—  (20™  25"),  the  difference  due  to  change  in  longitude  in 
39'"35^(l*'-20"'25«).  Now39°' 35^  =  0.66'^  and  thechangeof  longitude  =  0.66  X  13'.6=» 
9'.0  of  long.  =  36^.0  of  time.    Hence  the  total  amount  the  time  will  be  changed  will  be: 

Change  to  time  of  a.  m.  sight 17™41'.  7 

Change  between  a.  m.  sight  and  11  a.  m 2  43  .  2 

Change  between  11  a.  m.  and  L.  A.  noon 0  36  .  0 

Total  change 21  00. 9 

and  the  run  to  noon  will  be  4  hrs.  minus  this  change  =  3^  38™  59M  =3.65  hrs.  The 
distance  run  to  noon  will  be  3.65''  X  11'^*«.7  =  42'^.7. 

The  navigator  can  now  run  the  a.  m.  point,  determined  by  dead  reckoning 
latitude  and  longitude  by  observation,  up  to  noon,  and,  after  that  he  is  ready  to 
set  his  watch  and  clocks  to  the  time  of  the  coming  local  apparent  noon  position. 

404:.  If  the  body  observed  for  the  a.  m.  sight  was  on  or  near  the  prune  vertical, 
the  longitude  found  from  it  would  be  correct  for  the  time  of  observation,  since  an  error 
in  latitude  makes  no  change  in  the  longitude.  This  longitude  when  compared  with 
the  longitude  by  dead  reckoning  at  the  time  of  sight  will  show  if  there  has  been  an 
easterly  or  westerly  set  of  the  current,  and  the  amount  of  it.  If  a  current  is  found 
and  allowed  for,  for  the  time  of  the  run  from  time  of  sight  to  noon,  the  noon  longitude 
can  be  found  very  accurately.  If  the  heavenly  body  used  for  the  a.  m.  observation 
was  not  near  the  prime  vertical,  the  exact  easterly  or  westerly  set  can  not  be  deter- 
mined; but  a  close  approximation  to  it  can  generally  be  made  by  comparing  the 
longitude  found  by  observation  with  the  D.  R.  longitude,  and  the  current  so  found 
should  be  allowed  for  in  rimning  the  a.  m.  point  up  to  noon.  The  error  will  be 
small  and  will  give  results  sufficiently  accurate  for  ordinary  work.  Having  allowed 
for  easterly  or  westerly  current  and  having  run  the  a.  m.  position  point  by  observa- 
tion up  to  noon,  the  navigator  can  then  set  his  watch  to  local  apparent  tune  of  the 
noon  position,  and  his  watch  can  be  used  to  set  the  deck  clocks.  A  convenient  waj 
to  set  the  watch  is  as  follows:  Having  looked  at  the  hack  face  and  found  what  it 
reads,  say  4^*  09™  50^,  let  it  be  determined  to  set  the  watch  to  the  correct  local 
apparent  time  of  the  noon  position  when  the  hack  face  reads  4^*  15™  00". 

Write  down  reading  of  hack  face  at  time  watch  is  to  be  set 4^  15™  00" 

Apply  the  hack  correction  (in  this  case  hack  is  5™  38'  fast  on  G.  M.  T. ) (,  — )     5    38 

This  gives  G.  M.  T.  at  which  watch  is  to  be  set  to  L.  A.  T 4    09    22 

Apply  equation  of  time  from  Page  I,  Nautical  Almanac,  corrected  for  longitude  of  noon 
position (+)  11    38.6 

This  gives  G.  A.  T.  of  time  watch  is  to  be  set 4    21    00.6 

Now  apply  longitude  for  noon  position  (in  this  case") 4    48    02.  8 

Watch  face  should  read 11    32    58 

The  watch  is  now  to  be  set  so  that,  at  4^*  15™  00"  by  hack,  the  watch  face  will  show 
as  near  ll''  32™  58'  as  possible.  It  will  be  found,  smce  the  second  hand  of  a  watch 
can  not  be  set,  that  the  watch  cannot  be  set  to  the  exact  reading.  By  care,  however, 
the  watch  can  be  set  so  that  it  will  be  30  seconds  or  less  fast  or  slow  on  the  desired 
time.  The  number  of  seconds  the  watch  is  fast  or  slow  on  L.  A.  T.  should  be  noted 
in  the  work  book,  as  it  wiU  be  a  help  in  taking  near-noon  sights  to  get  the  correct 
L.  A.  T.  at  once  from  the  reading  of  the  watch  face  instead  of  comparing  the  watch 
again  with  the  chronometer.  The  watch  being  set  as  nearly  as  possible  to  the 
correct  L.  A.  T.  and  the  error  being  recorded,  the  deck  clocks  are  set;  and  the  navi- 
gator then  proceeds  to  work  up  his  constants  for  his  near-noon  observations  for 
latitude,  and  completes  aU  his  forms  and  fills  them  out  as  far  as  possible  before 
taking  the  observations. 


THE  PRACTICE   OF   NAVIGATION  AT  SEA.  181 

405.  Now  suppose  the  navigator  wishes  to  take  his  observations  at  15,  10,  and 
5  minutes  before  local  apparent  noon  and  desires  to  get  constants  for  these  times  to 
which  he  can  apply  his  sextant  altitudes  and  at  once  get  his  correct  noon  latitude. 
To  find  the  watch  times  at  which  he  should  take  these  observationsj  he  must  know 
the  error  of  his  watch  on  local  apparent  time  of  the  place  of  observation.  He  knows 
the  error  of  his  watch  on  the  L.  A.  T.  of  the  noon  position  (in  this  case  we  will  sup- 

Eose  the  watch  is  18^  fast).  He  knows  that  on  course  66°  true,  speed  11.7  knots,  m 
at.  38°,  that  in  1  hour  he  changes  longitude  13'.6.  Therefore  15  minutes  before 
noon  the  ship  will  be  3' A  of  longitude  west  of  where  it  will  be  at  noon  =  13».6  of  time. 
Hence  the  observation  15  minutes  before  noon  should  be  taken  at  watch  time 
11"  45"  00^  +  18^  (  =  amount  watch  is  fast  on  L.  A.  T.  of  noon  position) +  13'.6 
(  =  amount  watch  is  fast  on  L.  A.  T.  of  place  of  first  near-noon  observation)  =  11*» 
45™  31''.6.  Similarly  the  observation  taken  10™  before  noon  should  be  taken  at 
watch  time  11"  50™  00"  +  18»  +  9M  (  =  amount  watch  is  fast  on  L.  A.  T.  of  place  of 
second  observation)  =  11"  50™  27*.l.  The  observation  taken  5  minutes  before  noon 
should  be  taken  at  watch  time  11"  55™  00»+18''  +  4''.5  (  =  amount  watch  is  fast  on 
L.  A.  T.  of  place  of  third  observation)  =  11"  55™  22".5.  A  meridian  altitude  would 
of  course  be  taken  at  watch  time  12"  00™  18*. 

Having  obtained  the  watch  times  of  the  observations,  the  navigator  next  works 
out  the  constants.  These  constants  are  obtained  in  the  same  way  as  meridian 
altitude  constants  but  to  each  are  applied  two  corrections  to  the  meridian  altitude 
constant.     These  are: 

(1 )  at^  or  the  correction  to  be  applied  to  an  observed  altitude  near  noon  to  make 
it  a  meridian  altitude. 

(2)  Jh  or  the  difference  in  latitude  for  the  run  from  the  time  of  observation 
to  noon. 

In  working  out  the  constant,  the  method  of  obtaining  a  meridian  altitude  con- 
stant is  followed  and  the  two  corrections  mentioned  above  are  applied  to  it.  In 
getting  a  meridian  altitude  constant,  one  has  first  to  ascertain  the  approximate 
altitude.  If  the  student  will  in  every  case  plot  his  elements  roughly  on  the  plane 
of  the  meridian,  putting  O,  the  observer,  at  the  center,  a  horizontal  line  through  the 
O  with  the  right  end  marked  S  for  south,  and  the  left  end  N  for  north,  to  represent 
the  horizon,  and  draw  a  vertical  line  upward  from  O  (marking  its  intersection  with 
the  circle  Z)  to  represent  the  zenith,  he  can  by  inspection  write  out  his  formulae  and 
see  exactly  how  to  apply  all  corrections.  A  few  minutes'  study  will  make  this  method 
clear  and  will  fully  repay  the  very  slight  mental  effort  required  to  master  it. 

Now  suppose  L  is  the  latitude  oi  the  noon  position  and  L'  the  latitude  of  the 
point  from  wnich  the  near-noon  observation  was  taken.  Then  L  =  L'±JL  where 
JL  is  the  change  in  latitude  from  the  time  of  observation  to  noon. 

Suppose,  by  inspection  of  the  figure  we  have  drawn,  we  see  that  for  a  meridian 
altitude, 

L'  =  90°-(?-obs.  alt.±corr.  to  alt. 

Now  when  the  observed  altitude  is  taken  before  noon  the  correction  aP  has  to 
be  applied  to  it  to  bring  it  to  what  the  meridian  altitude  would  be.  Therefore,  for 
an  altitude  taken  before  noon, 

L'     =90° -d-  (obs.  alt.  +  at^)  ± corr.  to  alt. 

=  90°-<Z-obs.  alt. -a<2±  corr. 
L      =90°-<Z-obs.  alt.- a<2± corr. ±JL. 

=  K  — obs.  alt. 
OTK  =  90°-d-  af  ±  corr.  ±  JL. 

Having  the  watch  time  at  which  the  near-noon  observation  is  taken  and  K  corre- 
sponding to  it,  it  is  only  necessary  to  apply  the  observed  altitude  to  its  proper  K 
to  get  tne  correct  noon  latitude.  Havmg  the  correct  noon  latitude,  find  by  how 
many  minutes  it  differs  from  the  D.  R.  noon  latitude  and  multiply  this  difference 
by  the  longitude  factor  to  get  the  correction  to  be  applied  to  the  8.00  a.  m.  longitude 
by  observation  run  up  to  noon,  in  order  to  get  the  correct  noon  longitude.    This 


182  THE   PRACTICE   OF    NAVIGATION   AT  SEA. 

part  of  the  work  is  done  roughly  on  deck  in  the  navigator's  note  book  as  soon  as  the 
altitude  is  taken.  To  facilitate  this  work  the  navigator  writes  his  data  in  his  note 
book  in  the  following  form,  filling  the  blank  spaces  after  getting  his  altitude : 


For  watch  time 

K 

Obs.  Alt. 

11"  45">  30'.  4 
84    49    11 

11"  50'^  26'.  4 
84    53    30 

11"  55'"  22».  0 
84    55    56 

12"  00"»  18* 
84    56    29 

Noon  Lat.  by  Oba. 

Mean 

Noon  Lat.  by  D.  R. 

38°  20'   35''' 

DL 

Long,  factor  (Tab.  47) 

.65 

Corr.  in  Long. 
Noon  Long,  by  a.  m.  Obs. 

72®  00'  42" 

True  longitude  at  noon 

4:06.  Having  obtained  the  correct  noon  position  in  the  above  manner,  the 
navigator  completes  his  work  in  his  work  book  and  plots  the  ship's  position  on  the 
chart.  Having  the  correct  noon  position,  he  compares  it  with  his  previous  noon 
position  (or  point  of  departure)  and  ^ets  the  true  course  and  distance  made  good. 
Having  the  position  by  dead  reckoning  and  by  observation,  he  ^ets  the  set  and 
drift  of  the  current.  He  then  computes  the  total  distance  gone  smce  leaving  port 
and  the  distance  yet  to  go  to  his  destination.  Blank  forms  for  the  noon  report  are 
arranged  for  the  following  data: 

(1)  Lat.  by  observation. 

(2)  Long,  by  observation. 

(3)  Lat.  by  D.  R. 

(4)  Long,  by  D.  R. 

(5)  Current:  Set  and  Drift. 

(6)  Course  made  good. 

(7)  Distance  made  good  since  noon. 

(8)  Distance  made  good  since  departure. 

(9)  Distance  to  destination. 

If  the  course  sailed  is  a  rhumb  line,  and  the  ship  is  practically  on  the  line  laid 
out  as  the  track,  no  change  of  course  is  necessary.  If  the  ship  is  decidedly  off  the 
rhumb  line  course  as  laid  out,  or  is  sailing  on  a  gi'eat  circle  track  that  requires  a 
change  in  compass  course,  the  new  course  is  laid  out  as  soon  as  the  true  noon  position 
is  obtained.     This  completes  the  navigator's  work  to  noon. 

4:07.  The  Atteenoon  Work  of  the  Navigator. — In  the  afternoon  the  navi- 
gator must  take  an  observation  for  longitude.  He  selects  a  time  when  the  sun  is 
as  near  as  possible  to  the  prime  vertical,  which  time  is  determined  in  the  same  way 
as  explained  for  the  a.  m.  observation.  He  runs  his  true  noon  position  up  to  the 
time  of  his  p.  m.  observation,  making  an  allowance  for  any  evident  current  that  was 
found  at  noon.  He  then  gets  a  position  point  on  a  line  of  position  determined  from 
his  observation.  This  point  is  run  up  to  8  p.  m.  by  dead  reckoning,  which  position 
is  plotted  on  the  chart  and  completes  the  mmimum  navigation  work  for  any  day. 

When  -particularly  accurate  positions  are  required,  especially  at  8  p.  m.,  the 
navigator  takes  an  additional  observation  of  the  sun,  or  of  some  other  heavenly  body 
at  twilight,  and  gets  the  intersection  of  two  lines  of  position.  Or  he  may  get  a  line 
for  longitude  and  a  line  for  latitude  by  an  altitude  of  Polaris  or  another  star.  In 
this  way  the  navigator  may,  at  either  morning  or  evening  twilight,  get  a  very  accurate 
fix;  and  this  is  done  frequently.  In  fact,  fixes  obtained  from  observations  of  two 
heavenly  bodies  taken  at  about  the  same  time  are  the  most  accurate  fixes  that  can  be 
obtainea  at  sea,  as  the  intersection  of  the  two  lines  of  position  give  a  position  point 
that  is  correct  at  the  time,  no  matter  what  the  current  is.  Careful  navigators  wiU 
therefore  take  such  observations  and  the  student  should  prepare  himself  to  do  so. 
The  methods  of  using  position  points  obtained  in  this  way  are  exactly  the  same  as 
the  methods  of  using  the  points  already  explained. 


THE  PBACTICE   OF   NAVIGATION  AT  SEA.  183 

The  following  example  will  give  a  good  idea  of  the  minimum  day's  work  for  the 
navigator  at  sea.  The  form  laid  out  is  one  that  can  always  be  followed.  The  cosine- 
haversine  formula  is  used  for  getting  the  lines  of  position,  but  any  other  method  may 
be  substituted  for  it. 

Example:  On  October  5,  1915,  the  U.  S.  S.  Delaware  left  Hampton  Roads  for 
Lisbon.  From  the  Chesapeake  Capes  the  great  circle  course  was  followed.  The 
distance  to  Lisbon  by  great  circle  course  is  3,120  mUes.  It  is  25  miles  from  Hanapton 
Roads  to  the  point  from  which  the  departure  was  taken.  At  5  p.  m.,  with  Cape  Henry 
Light  bearing  301°  (mag.),  dist.  8.3  miles,  took  departure,  set  course  74°  (p.  s.  c.) 
(Var.  5°  W.,  Dev.  3°  W.),  and  put  over  patent  log,  reading  0.  (The  point  of  de- 
parture is  Lat.  36°  51'  59"  N.,  Long.  75°  51'  03"  W.) 

The  next  morning  by  comparison  with  the  standard,  the  hack  chronometer  was 
found  to  be  5™  38'  fast  on  G.  M.  T.  and  gaining  P.5  daily.  At  about  8  a.  m.,  patent  log, 
reading  175.0,  the  navigator  took  an  a.  m.  observation  for  longitude:  W.  T.  8**  00™ 
03«.5;  obs.  alt.  22°  55^10";  I.  C.  +  l'  50";  ht.  of  eye  40  ft.  The  navigator  then 
observed  an  azimuth  of  the  sun  as  follows:  W.  T.  8**  02™  29";  bearing  of  sun  p.  s.  c. 
125°  30';  ship's  head  74°.  He  then  compared  his  watch  with  the  hack  as  follows: 
hack  face  l**  13™  00«;  watch  face  8»*  10™  11». 

Perform  the  a.  m.  part  of  the  day's  work. 

The  ship  continues  on  same  course  at  same  speed  (11.7  knots).  When  the  hack 
face  reads  4''  15™  00*,  at  what  time  should  the  watch  be  set  to  be  on  local  apparent 
time  at  the  noon  position  % 

If  the  watch  was  set  18  seconds  fast  on  local  apparent  time  at  the  noon  position, 
work  out  constants  for  observations  for  latitude  to  be  taken  15,  10,  and  5  minutes 
before  noon  and  at  noon.     Prepare  all  forms  for  the  noon  work. 

The  observed  altitudes  near  noon  were  as  follows :  15  minutes  before,  46°  12'  30"; 
10  min.  before,  46°  16'  50";  5  min.  before,  46°  19'  20".  The  noon  alt.  was  46°  19'  40". 
The  patent  log  read  217.5  at  noon. 

Complete  the  day's  work  for  noon. 

At  noon  the  course  was  changed  *to  86°  (p.  s.  c),  Var,  10°  W.,  Dev.  4°  W. 
Steamed  untU  4p.  m.  on  this  course,  when  at  W.  T.  4''  00™  12",  obs.  alt.  of  sun 
18° 32' 40";  C-W,  A^  40™  56";  I.C,  +1'  50";  ht.  of  eye,  40  ft.;  patent  log  reading, 
264.3. 

Find  position  of  ship  at  4  p.  m.  by  observation. 

The  course  and  speed  remaining  unchanged,  find  the  8  p.  m.  position. 


184 


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CHAPTER  XVII. 

MAEINE  SUEVEYING. 


408.  Definitions. — Surveying  is  the  art  of  making  such  field  observations  and 
measurements  as  are  necessary  to  determine  positions,  areas,  elevations,  and  move- 
ments on  the  surface  of  the  earth,  giving  its  characteristic  features,  such  as,  on  land, 
the  position  of  prominent  objects,  heights,  and  depressions,  and  on  water,  the  depth, 
nature  of  bottom,  position  of  shoals,  and  velocity  of  currents. 

Topographic  Surveying  relates  to  the  land,  and  Hydrograpliic  Surveyirig  to  the 
water;  and  both  are  underlaid  by  Trigonometrical  Surveying  which,  when  it  is  carried 
on  with  high  precision  over  such  large  areas  as  to  contribute  to  form  a  basis  for 
determining  the  size  and  shape  of  the  earth,  becomes  a  department  of  Geodetic 
Surveying. 

It  is  not  deemed  appropriate  to  include  in  this  work  a  complete  treatise  on 
marine  surveying.  The  scope  of  this  chapter  will  be  to  set  forth  such  general  infor- 
mation regarding  the  principles  of  surveymg  and  the  instruments  therein  employed 
as  will  give  the  navigator  an  intelligent  understanding  of  the  subject  sujficient  to 
enable  him  to  comprehend  the  methods  by  which  marine  charts  are  made,  and,  if 
occasion  should  arise,  to  conduct  a  survey  with  such  accuracy  as  the  instruments 
ordinarily  at  hand  on  shipboard  permit.  For  a  more  detailed  discussion  of  marine 
surveying,  the  student  is  referred  to  the  various  publications  which  treat  the  subject 
exhaustively. 

INSTRUMENTS  EMPLOYED  IN  MABINE  STJUVEYING. 

409.  The  Theodolite  and  Transit. — The  Theodolite  (fig.  62)  is  an  instrument 
for  the  acciu'ate  measurement  of  horizontal  and  vertical  angles.  While  these  instru- 
ments vary  in  detail  as  to  methods  of  construction,  the  essential  principles  are  always 
identical. 

A  telescope  carrying  crosshairs  in  the  common  focus  of  the  object  glass  and 
eyepiece  is  so  mounted  as  to  have  motion  about  two  axes  at  right  angles  to  one 
another;  graduated  circles  and  verniers  are  provided  by  which  angular  motion  in 
azimuth  and  (usually)  in  altitude  may  be  measured;  and  the  instrument  is  capable 
of  such  adjustment  by  levels  that  the  planes  of  motion  about  the  respective  axes 
will  correspond  exactly  with  the  horizontal  and  the  vertical. 

The  telescope  is  carried  in  appropriate  supports  upon  a  horizontal  plate  which 
has,  immovablv  attached  to  it,  one  or  more  verniers,  and  which  revolves  just  over  a 
graduated  circle  that  is  marked  upon  the  periphery  of  a  second  horizontal  plate,  a 
means  of  measuring  the  motion  of  the  upper  plate  relative  to  the  lower  one  being 
thus  provided.  Thumb  screws  are  fitted  by  which  the  upper  plate  may  be  clamped 
to  the  lower,  and  (excepting  in  some  simpler  forms  of  the  instrument)  others  by 
which  the  lower  plate  may  be  made  immovable  in  azimuth,  or  allowed  free  motion, 
at  mil;  all  clamping  arrangements  include  slow-motion  tangent  screws  for  finer 
control. 

A  vertical  graduated  circle,  or  arc,  with  a  vernier,  clamps,  and  tangent  screws, 
is  fitted  to  most  theodolites,  for  the  measurement  of  the  angular  motion  of  the  tele- 
scope in  altitude. 

The  theodoUte  usually  carries  a  magnetic  needle,  with  a  graduated  circle  and 
vernier  for  compass  bearings.  The  instrument  is  mounted  upon  a  tripod,  and  levels 
and  leveling  screws  afford  a  means  of  bringing  the  instrument  to  a  truly  horizontal 
position. 

189 


190 


MAKINE   SURVEYING. 


The  Transit  used  in  surveying  is  a  modified  form  of  the  theodolite,  and  is 
generally  employed  where  less  accuracy  is  required ;  it  takes  its  name  from  the  fact 
that  the  telescope  ma;^  be  turned  completely  about  its  horizontal  axis,  or  transitedf 
without  removal  from  its  supports. 

410.  The  line  of  coUimation  of  a  telescope  is  an  imaginary  line  passing  through 
the  optical  center  of  the  object  glass  in  a  direction  at  right  angles  to  that  of  its  axis  of 
rotation.     This  is  also  callea  the  axis  of  coUimation.     The  line  of  sight  is  an  imaginary 

line  passing  through  the 
optical  center  of  the  ob- 
ject glass  and  the  point 
of  intersection  of  the 
cross  hairs. 

A  theodolite  or 
transit,  before  it  can  be 
used  for  the  accurate 
measurement  of  angles, 
must  be  in  adjustment 
in  the  following  re- 
spects: (a)  The  vertical 
axes  of  revolution  of 
the  upper  and  lower 
horizontal  plates  must 
be  coincident;  (&)  the 
axis  must  be  vertical 
and  the  plates  horizon- 
tal when  the  bubbles  of 
the  levels  are  in  their 
central  positions;  (c) 
the  vertical  cross  hair 
must  be  perpendicular 
to  the  horizontal  axis  of 
the  telescope;  {d)  the 
line  of  collimation  must 
coincide  with  the  Une  of 
sight;  (g)  the  horizon- 
tal axis  of  the  telescope 
must  be  perpendicular 
to  the  vertical  axis  of 
the  instrument;  (f)  the 
bubble  of  the  telescope 
level  must  stand  at  the 
middle  of  its  scale,  and 
the  vertical  circle  must 
read  zero,  when  the  line 
of  collimation  is  hori- 
zontal. 

The  last-named 

condition  maj^  be  disre- 

FiG.  62.  '  garded  if  vertical  angles 

are  not  to  be  measured. 
4:11.  The  instrument  being  in  adjustment,  to  observe  angles  it  should  be  set 
up,  leveled,  and  focused.  This  involves  placing  the  tripod  so  that  a  plumb  bob 
from  the  center  of  the  instrument  shall  hang  directly  over  the  spot  at  which  the 
measurement  is  to  be  made.  The  legs  of  the  tripod  should  be  firroly  placed  in  such 
manner  that  the  height  shall  be  convenient  for  the  observer  and  the  instrument 
shall  be  nearly  level.  Then  the  horizontal  plates  are  brought  to  a  true  level  by 
means  of  the  leveUng  screws  and  bubbles.  The  telescope  should  next  be  focused 
by  moving  the  object  glass  and  eyepiece  in  such  manner  that  the  object  sighted 


MARINE   SURVEYING.  191 

♦ 

and  the  cross  hairs  may  be  plamly  seen  and  that  the  object  will  not  appear  to  have 
motion  relatively  to  the  cross  hairs  as  the  eye  is  moved  to  the  right  or  left  of  the 
eyepiece.  This  last  condition  insures  the  cross  hairs  being  at  the  common  focus  of 
the  eyepiece  and  objective. 

To  observe  a  horizontal  angle  with  a  theodoUte  or  transit,  clamp  the  upper 
plate  to  the  lower  at  zero,  leaving  the  lower  plate  undamped;  swing  tne  telescope 
so  that  its  vertical  cross  hair  bisects  one  of  the  objects,  and  clamp  the  lower  plate; 
unclamp  the  upper  plate  and  bring  the  telescope  to  bisect  the  other  object,  and  the 
reading  of  the  vermer  on  the  scale  will  give  the  required  angle.  (Tne  final  nice 
motion  by  which  the  cross  hair  is  brought  exactly  upon  a  point  is  always  given  by 
the  tangent  screw.) 

In  taking  a  round  of  angles,  this  operation  is  repeated  successively  upon  each 
object  to  be  observed  about  the  horizon,  the  upper  plate  always  being  swung,  while 
the  lower  is  kept  where  set  upon  the  first  object,  or  origin.  The  result  will  give  the 
angular  distance  of  each  object  from  the  origin,  and,  if  the  observations  have  been 
accurately  made,  upon  finally  sighting  back  to  the  origin,  the  reading  should  be  zero. 

To  repeat  an  angle,  having  made  the  first  measurement  of  it  in  the  usual  way, 
unclamp  the  lower  circle  and  swing  back  the  telescope  until  it  again  points  to  the 
first  object,  and  clamp  it;  then  unclamp  the  upper  circle,  swing  to  the  second  object, 
and  clamp.  The  scale  reading  should  now  be  double  that  of  the  first  angle.  Repeat 
as  often  as  the  importance  of  the  angle  requires,  and  the  accepted  value  will  be  the 
final  reading  divided  by  the  number  of  measurements.  AD  angles  of  the  main 
triangulation,  and  others  of  importance  in  the  survey,  are  repeated. 

Defects  in  adjustment  of  the  instrument  may  be  eliminated  by  taldng  one 
series  of  angles  witn  the  telescope  direct  and  another  with  the  telescope  reversed.  To 
reverse  the  telescope,  revolve  it  about  its  horizontal  axis  through  180°,  then  swing 
it  about  its  vertical  axis  through  180° — in  other  words,  invert  it. 

Vertical  angles  are  measured  on  the  same  principle  as  that  described  for  hori- 
zontal ones. 

The  process  of  setting  up  the  instrument  at  a  station  and  observing  the  angles 
between  the  various  objects  that  are  visible  is  called  occupying  the  station. 

4:12.  The  Plane  Table. — This  is  an  instrument  by  which  positions  are  plotted 
in  the  field  directly  upon  a  working  sheet.  It  consists  (fig.  63)  of  a  drawing  board 
mounted  upon  a  tripod  in  such  manner  as  to  be  capable  of  motion  in  azimuth,  and 
with  faciUties  for  being  brought  to  a  perfect  level;  in  connection  with  it  is  employed 
an  aUdade,  consisting  of  a  straightedge  ruler,  upon  which  is  mounted  a  telescope 
with  cross  hairs  whose  line  of  signt  is  exactly  parallel  to  the  vertical  plane  through 
the  edge  of  the  rule.  It  is  evident  that  if  a  sheet  representing  a  chart  be  placed 
upon  such  a  board  and  turned  so  that  the  true  meridians,  as  portrayed  thereon,  Ue 
in  the  direction  of  the  earth's  meridian  at  that  place,  then  all  lines  of  bearings  on 
the  chart  will  coincide  with  the  corresponding  lines  on  the  earth's  surface;  from 
which  it  follows  that  if  the  alidade  be  so  placed  that  its  rule  passes  through  the  spot 
on  the  chart  representing  the  j)osition  of  the  observer,  while  the  telescope  is  directed 
to  some  visible  object,  the  position  of  that  object  on  the  chart  lies  somewhere  upon 
the  line  drawn  along  the  edge  of  the  rule.  Upon  this  general  principle  depend  the 
various  apphcations  of  the  plane  table. 

The  drawing  board  is  usually  made  of  several  pieces  of  well-seasoned  wood, 
tongued  and  grooved  together,  with  the  grain  running  in  different  directions  to 
prevent  warping;  about  its  edge  are  several  metal  chps  for  securing  the  paper  in 
place.  It  is  supported  upon  three  strong  brass  arms,  to  which  it  is  attached  by 
screws,  thus  permitting  its  removal  at  will.  The  arms  are  attached  to  a  horizontal 
plate  which  revolves  upon  a  second  horizontal  plate  lying  immediately  below  it;  a 
clamp  and  tangent  screw  are  fitted,  by  which  the  upper  plate,  and  with  it  the  draw- 
ing board,  may  oe  secured  to  the  lower  plate,  or  may  be  given  a  fine  motion  in  azimuth. 
Three  equidistant  lugs  of  brass,  grooved  on  the  under  side,  project  down  from  the 
lower  plate,  resting  on  screws  in  the  top  of  the  tripod,  by  which  the  instrument  is 
leveled;  when  adjusted  in  this  respect  it  is  firmly  clamped  in  position,  and,  as  the 
tripod  is  made  unusually  large,  the  adjustment  is  not  easily  deranged. 


192 


MARINE   SURVEYING. 


The  alidade  is  a  metal  straightedge  with  a  vertical  column  at  its  center,  at  the 
top  of  which  are  the  supports  which  carry  the  telescope;  a  vertical  arc  and  vernier 
are  provided  for  measuring  the  motion  of  the  telescope  in  altitude.  The  telescope 
is  usually  so  fitted  that  it  may  be  revolved  in  azimuth  tlirough  an  arc  of  exactly  180°, 
for  the  purpose  of  adjusting  the  line  of  collimation.  ^  On  top  of  the  rule  near  its  center 
is  the  level — sometimes  replaced  by  two  levels  at  right  angles — by  means  of  which  it 
may  be  seen  when  the  table  is  in  a  true  horizontal  position. 

A  magnetic  needle  mounted  in  a  rectangular  metal  box,  whose  outer  straight- 
edge is  parallel  to  the  zero  line  of  a  graduated  scale  over  which  the  needle  swings,  is 
provided  for  drawing  the  north-and-south  line  on  the  chart;  this  is  called  a  declinatoire. 


Fig.  63. 


413.  To  be  in  correct  adjustment,  a  plane  table  must  comply  with  the  following 
conditions: 

(o)  The  fiducial  edge  of  the  rule  must  be  perfectly  straight.  (&)  The  level  must 
have  the  bubble  in  its  central  position  when  the  table  is  truly  horizontal,  (c)  The 
vertical  cross  hair  must  be  perpendi(;ular  to  the  horizontal  axis  of  the  telescope. 
{d)  The  line  of  coUimation  must  coincide  with  the  line  of  sight,  {e)  The  horizontal 
axis  of  the  telescope  must  be  parallel  to  the  plane  of  the  table.  (/)  The  vertical 
circle  should  read  zero  when  the  line  of  collimation  is  horizontal. 

4:14:.  The  results  derived  from  the  use  of  the  plane  table,  like  all  others  dependent 
upon  graphic  methods,  must  be  regarded  as  less  accurate  than  those  deduced  by 
computation,  and  even  less  accurate  than  those  derived  from  the  careful  plotting  of 
theodolite  angles.  Hence  it  is  that,  in  a  careful  marine  survey,  this  mstrument 
would  be  employed  only  for  the  topography  and  shore  line. 

For  whatever  purpose  used,  the  plane  table  would  not  ordinarily  be  called  into 
requisition  until  the  survey  had  so  far  progressed  that  a  chart  could  be  furnished  the 
observer  showing  certain  stations  whose  positions  were  already  established;  with 
this  chart,  the  firat  step  would  be  to  occupy  one  of  the  determined  points.     The  table 


MARINE  SURVEYING.  193 

must  be  set  up  with  the  point  on  the  chart  directly  over  the  center  of  the  station ;  it 
must  then  be  leveled  and  the  telescope  focused  as  described  for  the  theodolite  or 
transit;  andlGLnally  it  must  he  oriented — that  is,  so  turned  in  azimuth  that  aU  lines  of 
the  chart  are  parallel  to  similar  hues  of  the  earth's  surface.  To  orient,  unclamp  the 
table  and  swmg  it  until  the  north-and-south  line  of  the  chart  is  approximately 
parallel  to  that  of  the  earth,  one  means  of  doing  which  is  afforded  by  the  declinatoire; 
place  the  alidade  so  that  the  edge  of  the  rule  passes  through  the  points  on  the  chart 
representing  the  station  occupied  and  some  second  station  which  is  clearly  in  view; 
then,  sighting  tlirough  the  telescope,  jjerfect  the  adjustment  of  the  table  by  swinging 
it  until  the  second  station  is  exactly  bisected  by  the  vertical  cross  hair,  the  final  slow 
motion  being  obtained  by  clamping  the  table  and  working  the  tangent  screw.  If  the 
adjustment  has  been  correctly  made,  the  rule  may  be  laid  along  the  line  joining  the 
station  occupied  and  any  other  on  the  chart,  and  the  telescope  will  point  exactly  to 
that  other  station. 

Being  properly  oriented,  if  the  alidade  be  so  placed  that  the  edge  of  the  rule  pass 
through  the  station  occupied  and  the  telescope  point  directly  to  some  imknown 
object  whose  position  is  to  be  determined,  then  a  line  drawn  along  the  rule  will 
contain  the  point  which  represents  the  position  of  that  object.  If,  now,  the  plane 
table  be  set  up  at  a  second  station,  oriented  for  its  new  position,  and  a  line  be  similarly 
drawn  from  that  station  toward  the  one  to  bo  estabhshed,  it  will  intersect  the  first 
line  in  the  required  point.  This  is  the  method  of  determining  positions  by  prosection. 
Actually,  the  surveyor  does  not  regard  the  point  as  well  established  until  the  inter- 
section is  checked  by  a  line  from  a  third  station. 

In  practical  work,  of  course,  each  station  is  not  occupied  separately  for  the 
determination  of  each  point;  the  instrument  is  set  up  at  a  station,  lines  are  drawn 
to  all  required  points  in  view,  and  each  line  is  appropriately  marked ;  then  a  second 
station  is  occupied,  and  the  operation  is  repeated,  and  so  on,  the  various  intersections 
being  marked  as  the  work  proceeds. 

A  second  method  of  establishing  positions  is  that  of  resection;  in  this  the  first 
line  is  drawn  from  some  known  station,  as  in  the  preceding  method,  and  the  observer 
next  proceeds  to  the  place  whose  position  is  required  and  occupies  it;  the  plane  table 
is  there  oriented  by  means  of  the  fine  already  drawn,  placing  the  edge  of  the  rule 
along  the  line,  sighting  back  toward  the  first  station,  and  swinging  the  table  until 
that  station  is  in  the  line  of  sight  of  the  telescope;  then  choose  some  other  established 
station  as  nearly  as  possible  at  right  angles  to  the  direction  of  the  first;  place  the 
edge  of  the  rule  upon  the  plotted  position  of  this  station  and  swing  the  ahdade  (the 
rule  always  being  kept  on  the  plotted  point)  until  the  object  is  bisected  by  the 
telescope  cross  hairs;  draw  this  line,  and  its  intersection  with  the  first  wiU  give  the 
required  point,  the  accuracy  of  which  can  be  checked  from  some  other  plotted  station. 

A  third  method  of  locating  a  point  is  by  means  of  a  single  bearing  from  a  known 
station,  with  the  distance  from  the  occupied  station  to  the  required  one,  the  process 
of  plotting  being  self-evident. 

A  fourth  method  is  given  by  occupying  an  undetermined  position  from  which 
three  estabhshed  stations  are  in  view;  the  point  occupied  by  the  observer  is  then 
plotted  by  an  appHcation  of  the  "three-point  problem." 

415.  It  may  be  seen  that  where  the  greatest  accuracy  is  not  essential  the  plane 
table  may  be  employed  for  plotting  aU  the  points  of  a  survey.  In  such  a  case  it  would 
only  be  necessary  to  begin  with  the  two  base  stations,  plotted  on  the  sheet  on  any 
relative  bearing  whatsoever  and  at  a  distance  apart  equal  to  the  length  of  the  base 
line  (reduced  to  scale),  as  measured  by  the  most  accurate  means  available.  The 
work  of  plotting  might  even  proceed  before  the  base  line  had  been  measured,  the 
two  stations  being  laid  off  at  any  convenient  distance  apart;  when  later  the  base 
line  was  measured,  the  scale  of  the  chart  would  be  determined,  being  equal  to  the 
distance  on  the  chart  between  base  stations  divided  by  the  length  of  the  base  Hne. 

416.  A  plane  table  could  be  improvised  on  shipboard  which  would  greatly 
facihtate  the  operation  of  any  surveying  work  that  a  vessel  not  equipped  with 
instruments  might  be  called  upon  to  perform.  A  drawing  board  could  be  mounted 
upon  a  tripod  (as,  for  example,  the  tripod  suppHed  for  compass  work  on  shore)  in 
such  manner  as  to  be  capable  of  motion  m  azimuth ;  it  could  be  brought  nearly  to  the 
horizontal,  if  no  better  means  offered,  by  moving  the  tripod  legs,  and  this  adjust- 

21594°— 14 13 


194  MARINE   SURVEYING. 

ment  could  be  proved  by  any  small  spirit  level;  sight  vanes  could  be  erected  upon 
an  ordinary  ruler  to  take  the  place  of  the  alidade;  in  case  there  was  difficulty  in 
observing  any  object  with  such  an  alidade,  because  of  its  altitude  or  for  other  reasons, 
a  horizontal  angle  might  be  observed  with  a  sextant  and  plotted  with  a  protractor. 
By  this  means  work  could  be  done  which,  even  if  it  should  lack  complete  accuracy, 
might  be  of  great  value. 

417.  The  Telemeter  and  Stadia. — ^Any  telescope  fitted  with  a  pair  of  hori- 
zontal cross  hairs  at  the  focus  may  be  used  as  a  telemeter,  and  when  accompanied 
by  a  graduated  staff,  called  a  stadia,  affords  a  means  of  measuring  distance  (up 
to  certain  limits)  with  a  close  degree  of  accuracy;  the  method  consists  in  observing 
the  number  of  divisions  of  the  scale  subtended  by  the  hairs  when  the  stadia 
is  held  perpendicular  to  the  line  of  sight  of  the  telescope,  it  being  evident 
that  the  closer  the  distance  the  fewer  divisions  wiU  appear  between  them.  The 
f  acihty  with  which  distances  can  be  measured  by  this  method  makes  it  most  important 
that  aU  telescopes  of  theodolites,  transits,  and  plane  tables  be  fitted  as  telemeters 
and  that  stadia  rods  be  provided  for  all  surveying  work. 

Speaking  approximately,  it  may  be  said  that  the  number  of  divisions  intercepted 
between  the  cross  hairs  win  vary  directly  as  the  distance  of  the  stadia  rod.  This 
would  be  exactly  true  if  we  looked  at  the  object  through  an  empty  tube,  directly 
between  the  ban's.  Since,  however,  the  rays  from  the  stadia  are  refracted  by  the 
object  glass  before  they  are  intercepted  by  the  wires,  the  statement,  to  be  absolutely 
exact,  must  be  sHghtly  modified ;  but  for  practical  surveying  work  it  may  be  accepted 
as  given. 

418.  There  are  two  methods  of  installing  the  telemeter  cross  hairs — the  first,  in 
which  they  are  immovably  secm*ed  in  the  telescope  and  always  remain  at  the  same  dis- 
tance apart,  and  the  second,  in  which  the  distance  of  the  cross  hairs  is  made  variable, 
being  under  tte  control  of  the  observer.  The  former  is  generally  regarded  as  the 
preferable  method,  and  when  it  is  employed  it  is  evident  that  the  subtended  height 
of  the  stadia  bears  a  constant  ratio  to  the  distance  of  the  staff  from  the  telescope. 
It  proves  most  convenient  in  practice  to  space  the  hairs  so  that  this  constant  ratio 
is  some  even  multiple  of  10,  for  facOity  in  converting  scale  readings  into  distance; 
it  is  also  advantageous  to  mark  the  stadia  in  the  unit  of  the  chart  scale  and  decimals 
thereof;  for  example,  if  the  ratio  of  stadia  height  to  distance  were  100,  and  the 
stadia  were  marked  in  meters  and  decimals,  a  reading  of  2.07  would  at  once  be  con- 
verted into  a  distance  of  207  meters.  Any  units  and  any  ratio  may,  however,  be 
employed,  and  for  any  given  setting  of  cross  hairs  it  is  very  easy  to  graduate  a  stadia, 
by  experiment,  for  any  desired  units;  for  example,  if  it  is  requu-ed  to  mark  the 
stadia  in  feet,  set  up  and  level  the  telescope,  measure  off  a  distance  of  exactly  100 
feet  from  it,  hold  up  an  unmarked  staff  and  mark  upon  it  the  points  intersected  by 
the  cross  hairs;  the  interval  between  these  marks  will  represent  100  feet  of  the 
scale;  divide  this  length  into  100  parts,  each  of  which  will  represent  a  distance  of 
one  foot,  and  mark  the  whole  staff^on  the  same  scale;  then  if  the  stadia  be  held  up 
at  any  distance,  the  cross  hairs  wiU  intercept  a  number  of  divisions  corresponding 
to  the  number  of  feet  of  distance. 

When  the  cross  hairs  are  movable  the  ratio  becomes  variable,  but  the  principle 
of  measuring  remains  the  same — namely,  the  distance  of  the  staff  from  the  telescope 
is  equal  to  the  existing  ratio  multiplied  by  the  distance  intercepted  on  the  scale. 

419.  The  stadia  is  made  of  a  light,  narrow  piece  of  wood  and  is  usually  hinged 
for  convenience  in  transporting.  Ordinarily  the  background  of  the  scale  is  painted 
white,  while  the  main  divisions  are  marked  in  red,  with  minor  divisions  in  black, 
and  geometrical  figures  are  employed  to  facihtate  the  reading  of  fractional  parts  of 
the  scale.  Devices  are  furnished  by  which  the  man  holding  the  stadia  may  know 
when  it  is  vertical — an  essential  condition  for  accuracy  of  measurements. 

420.  The  use  of  the  telemeter  and  stadia  for  measuriag  distances  is  limited  to 
the  distance  at  which  the  scale  divisions  can  be  accurately  read  through  the  tele- 
scope. For  fairly  close  work  and  with  the  class  of  telescope  usually  supplied  with 
surveying  instruments,  400  meters  represents  about  the  greatest  distance  at  which 
it  can  be  employed.  With  this  limitation,  the  character  of  the  survey  determines 
the  nature  of  its  employment.  In  a  careful  survey  its  greatest  use  would  be  in 
connection  with  the  tneodoHte  or  plane  table  in  putting  in  shore  lines,  contour  lines. 


MARINE   SURVEYING.  195 

and  topography  generally.     In  a  survey  where  only  approximate  results  are  sought 
it  might  afford  the  best  means  for  the  measurement  of  the  base. 

421.  If  the  telemeter  be  applied  to  a  theodolite,  transit,  or  plane  table  which  is 
fitted  with  a  graduated  vertical  arc  or  circle,  it  is  possible  to  measure  the  distance  to 
the  stadia  not  only  in  a  horizontal  but  also  in  a  vertical  direction.  In  this  case  the 
vertical  angle  must  be  observed  as  well  as  the  stadia  reading.  Tables  are  computed 
giving  the  solution  of  the  triangles  involved  when  the  stadia  rod  is  held  vertical. 

422.  In  making  a  survey  with  the  ordinary  resources  of  a  ship,  the  principle  of 
the  telemeter  and  stadia  may  be  profitably  employed,  using  a  sextant  and  improvised 
staff.  In  this  case  it  is  usual  to  have  the  stadia  of  some  convenient  fixed  length — 
as,  for  example,  10  feet — and  of  slight  width  and  thickness;  this  is  held  at  right 
angles  to  the  line  of  sight  from  the  observer,  who  notes  the  angle  subtended  by  the 
total  length;  tables  are  prepared  by  which  the  distance  corresponding  to  each  angle 
is  given. 

423.  The  Sextant. — This  instrument  is  of  the  greatest  value  in  hydrographic 
surveying.  It  is  fully  described  elsewhere  in  this  work  and  its  adjustment  explained. 
(Chap.  VIII.) 

Sextants  are  manufactured  of  a  form  especially  adapted  to  surveying  work; 
they  are  smaller  and  lighter  than  those  usually  employed  in  astronomical  observa- 
tions, but  have  a  longer  limb,  by  which  angles  may  be  measured  up  to  135°;  the 
vernier  is  marked  for  quick  reading  and  has  no  finer  graduation  than  half  minutes; 
the  telescope  has  a  large  field. 

This  instrument  is  principally  employed  in  measuring  the  horizontal  angles  by 
means  of  which  soundings  are  plotted.  It  may,  however,  be  put  to  various  uses  when 
making  an  approximate  survey,  as  has  already  been  explained.  It  should  be  remem- 
bered, in  measuring  terrestrial  angles  with  a  sextant,  that  rigorous  methods  require 
a  reduction  to  the  horizontal  if  either  of  the  objects  has  material  altitude  above  the 
horizon. 

424.  The  Level. — This  is  an  instrument  for  the  accurate  measure  of  differences 
of  elevation.  It  consists  of  a  telescope,  carried  in  a  Y-shaped  rest,  which  is  mounted 
upon  a  tripod  and  leveled  in  a  mamier  similar  to  a  theodolite;  but  it  differs  from  that 
instrument  in  that  the  telescope  is  not  capable  of  motion  about  a  horizontal  axis 
and  in  having  no  graduated  circles  for  measurements  of  altitude  and  azimuth.  The 
principle  of  its  use  contemplates  placing  the  line  of  coUimation  of  the  telescope  in  a 
truly  horizontal  plane  and  keepmg  it  so  fixed. 

425.  It  is  principally  employed  in  marine  surveying  to  determine  heights  and 
contour  lines — tne  latter  being  lines  of  equal  elevation  above  the  sea  level — and  for 
locating  bench  marks  for  tidal  observations.  (Chap.  XX.)  In  connection  with  it  is 
used  a  graduated  staff  called  a  leveling  rod,  carrying  a  conspicuous  mark,  adjustable 
in  height,  called  a  target.  To  ascertain  the  difference  or  level  between  any  two 
points,  set  up  the  level  with  the  telescope  horizontal  at  some  place  between  them; 
let  an  assistant  take  the  leveling  rod  to  one  of  the  points,  and,  while  holding  it  on  the 
ground  in  a  truly  vertical  position,  move  the  target,  under  the  direction  of  the 
observer  at  the  telescope,  to  a  point  where  it  is  exactly  bisected  by  the  horizontal 
cross  hair;  the  height  of  the  target  on  the  staff — that  is,  the  height  of  the  cross  hair 
above  the  level  or  the  first  pomt — is  then  accurately  read  with  a  vernier;  now, 
without  moving  the  level,  shift  the  rod  to  the  second  point  and  again  adjust  the 
target  and  read  it.  It  is  evident  that  a  comparison  of  tne  reading  at  the  first  posi- 
tion with  that  at  the  second  will  give  the  difference  of  height  at  the  two  pomts. 
The  difference  that  can  be  read  from  one  location  of  the  instrument  is  limited  by 
the  length  of  the  rod;  but  by  making  a  suflScient  number  of  shifts  any  difference 
may  be  measured. 

The  work  of  the  level  may  be  performed  equally  well  by  a  theodolite  whose 
telescope  is  adjusted  to  the  true  horizontal. 

426.  Heliotrope  and  Heliograph. — These  are  instruments  sometimes 
employed  in  surveying,  by  means  of  which  the  sun's  rays  may  be  reflected  in  any 
given  direction;  the  object  of  their  use  is  to  render  conspicuous  a  station  which  is 
to  be  observed  at  a  distance  and  which  would  not  otherwise  be  distinguishable. 
The  instruments  vary  widely  in  form  of  constraction  and,  in  the  absence  of  those 
made  for  the  purpose,  substitutes  may  easily  be  devised. 


196 


MARINE   SURVEYING. 


4:27.  Astronomical  Transit  Instruments. — Various  instruments  are  employed 
for  the  astronomical  determinations  necessary  in  a  marine  survey.  Among  these  are 
the  zenith  telescope  and  portable  trans-it.  While  differing  in  detail  they  consist  essen- 
tially of  a  telescope  mounted  upon  a  horizontal  axis  that  is  placed  tmly  in  the  prime 
vertical,  thus  insuring  the  revolution  of  the  line  of  coUimation  in  the  meridian;  a 
vertical  graduated  circle  and  vernier  are  supplied,  affording  a  measure  of  altitude; 
in  the  focus  are  a  number  of  equidistant  vertical  cross  hairs  or  lines;  a  small  lamp 
is  so  placed  that  its  rays  illuminate  the  cross  hairs  and  render  possible  observations 
at  night.  Latitude  is  obtained  by  observing  the  meridian  altitude  of  stars;  hour 
angle  (and  thence  longitude)  by  observing  the  times  of  their  meridian  transit,  which 
is  taken  from  the  mean  of  the  times  of  passing  all  of  the  vertical  cross  hairs. 

Excepting  in  surveys  of  a 
most  accurate  nature,  the  astro- 
nomical determination  of  position 
by  the  sextant  and  artificial  hori- 
zon is  regarded  as  satisfactory. 

428.  The  Three -Armed 
Protractor,  or  Station 
Pointer. — This  is  an  instrument 
whereby  positions  are  plotted 
on  the  principle  of  the  three- 
point  problem,"  of  which  an  ex- 
planation is  given  in  article  152, 
Chapter  IV.  It  consists  (fig.  64) 
of  a  graduated  circle  with  three 
arms  pivoted  at  the  center;  each 
arm  has  one  edge  that  is  a  true 
rule,  the  direction  of  which  always 
passes  through  the  center  of  the 
circle.  The  middle  arm  is  immov- 
ably fixed  at  the  zero  of  the  scale; 
the  right  and  left  arms  each  re- 
volve about  the  center  on  their 
own  sides,  and  are  provided  with 
verniers  giving  the  angular  dis- 
tance from  the  middle  arm.  The 
protractor  being  set  for  the  right 
and  left  angles,  it  is  so  moved  that 
the  three  arms  pass  through  the 
respective  stations,  when  the  cen- 
ter marks  the  position  of  the  ob- 
server. Center  pieces  of  various 
forms  are  provided,  being  cylin- 
drical plugs  made  to  fit  into  a 
socket  at  the  pivot,  and  by  em- 
ploying one  or  the  other  of  them 
the  true  center  may  be  pricked 
with  a  needle,  dotted  with  a  pen- 
cil, or  its  position  indicated  by  cross  hairs.  Adjustable  arms  are  provided  which 
can  be  fitted  to  the  ends  of  the  ordinary  arms  when  working  with  distant  signals. 

The  most  valuable  use  of  the  three-armed  protractor  is  in  plotting  the  positions 
of  soundings  taken  in  boats,  where  sextant  angles  between  signals  are  observed. 
It  may  occur,  however,  that  certain  shore  stations  will  be  located  by  its  use. 

429.  As  this  instrument  is  not  made  with  both  right  and  left  arms  capable  of 
being  set  to  small  angles  down  to  0°,  the  manufacturers  make  protractors  with 
either  small  right  or  smaU  left  angles.  Surveying  parties  should  be  equipped  with 
both.  In  default  of  a  three-armed  protractor,  a  piece  of  tracing  paper  may  be  made 
to  answer  its  purpose.  To  use  the  tracing  paper,  draw  a  line,  making  a  dot  on  it 
to  represent  the  center  station,  and  with  the  center  of  an  ordinary  protractor  on 


Fig.  64. 


MARINE  SURVEYING. 


197 


FlQ.  65. 


the  dot,  lay  off  the  two  observed  angles  right  and  left  of  the  line;  then,  laying  this 
on  the  plan,  move  it  about  till  the  three  lines  pass  exactly  through  the  three  stations 
observed.  The  dot  from  which  they  were  laid  off  will  be  on  the  position  of  the  observer, 
and  must  be  pricked  lightly  through  or  marked  underneath  in  pencil. 

430.  T^E  Beam  Compass. — This  instrument  (fig.  65)  is  employed  iQ_  chart 
drafting  and  performs  the  functions  of  compasses  and  dividers  when  the  distance 
that  must  be  spanned  is  beyond  the  limits  of  those  instruments  in  their  ordinary 
form.  It  consists  of  an  angular  bar  of  wood  or  metal  upon  which  two  instruments 
termed  beam  heads  are  fitted  in  such  a  manner  that  the  bar  may  slide  easily  through 
them.  A  clamping  screw  attached  to  one  side  of  the  beam  head  will  fix  it  in  any 
part  of  its  course  along  the  beam.  Upon 
each  head  a  socket  is  constructed  to  carry 
a  plain  point,  exchangeable  for  an  ink  or  a 

Eencil  point.  To  secure  accuracy  the 
eam  head  placed  at  the  end  of  the  beam 

has  a  fine  adjustment,  which  moves  the 

point  a  short  distance  to  correct  any  error 

in  the  first  rough  setting  of  the  instrument. 
This  adjustment  generally 
consists  of  a  milled-head 
screw,  which  passes  through 
a  nut  fixed  upon  the  end  of 
the  beam  head,  which  it  car- 
ries with  its  motion. 

431.  Proportional 
Dividers. — These  are  prin- 
cipally employed  for  reduc- 
ing or  enlai^ng  drawings  in 
any  ^ven  proportion.  They 
consist  (fig.  66)  of  two  narrow 

flat  pieces  of  metal  called  legs,  which  turn  upon  a  pivot  whose  position 
is  movable  in  the  direction  of  their  length.  The  ends  of  both  legs  are 
shaped  into  points  like  those  of  ordinary  dividers.  When  the  pivot  is 
fixed  at  the  middle  of  the  legs,  any  distance  measured  by  the  points 
at  one  end  is  just  equal  to  that  measured  by  those  at  the  other;  for 
any  other  location  oi  the  pivot,  however,  the  distances  thus  measured 
win  not  be  equal,  but  with  a  given  setting  of  the  pivot  any  distance 
measured  by  one  end  bears  a  fixed  ratio  to  that  measured  by  the  other. 
The  path  of  travel  of  the  pivot  is  graduated  so  that  the  ratio  may  be 
given  any  desired  value.  Being  adjusted  in  this  respect,  if  a  distance 
is  taken  off  a  chart  with  the  legs  at  one  end  of  the  instrument,  then 
those  at  the  other  end  will  show  the  same  distance  on  the  scale  of  a 
chart  enlarged  or  reduced  in  the  proportion  represented  by  the  ratio 
for  which  the  pivot  was  set. 

METHODS  Employed  in  a  hydrogbaphio  survey. 

432.  Before  commencing  a  survey  a  general  inspection  of  the  field 
is  made ;  a  hose  line  is  located  and  its  extremities  marked  by  signals; 
certain  other  positions,  known  as  main  triangulation  points,  are  selected 

Fig.  66.  and  also  marked  with  signals,  being  so  chosen  that,  starting  with  the 
base  and  proceeding  thence  from  one  to  another  of  these  points,  a 
series  of  well-conditioned  triangles  or  quadrilaterals  may  cover  the  field  of  survey. 
The  base  line  is  measured  with  the  greatest  degree  of  accuracy  which  the  resources 
of  the  survey  render  possible.  Each  extremity  of  the  base  line  and  each  other  main 
triangulation  point  is  occupied  by  an  observer  with  a  theodolite,  who  measures  the 
angles  at  each  station  between  all  the  other  stations  which  are  in  sight.  ^  An  astro- 
nomical determination  is  made  of  the  latitude  and  longitude  of  some  point  of  the 
survey  (frequently  one  of  the  extremities  of  the  base)  and  of  the  true  azimuth  of 
some  known  line  (frequently  the  base  line).  Data  are  now  at  hand  for  the  location 
upon  the  chart  of  the  oase  fine  and  main  triangulation  points. 


198  MARINE   SURVEYING. 

If  the  survey  is  one  of  considerable  extent,  it  is  expedient  to  measure  a  check  hose 
near  the  end  of  the  triangulation.  A  comparison  between  the  measured  length  of 
this  base  and  its  length  as  computed  through  the  chain  of  triangles  will  show  the 
degree  of  accuracy  and  afford  a  means  of  reconciling  discrepancies.  The  position,  of 
a  second  observation  spot  may  be  determined  for  a  similar  purpose. 

The  primary  triangulation  gives  a  skeleton  of  the  field,  but  the  points  thus 
determined  are  not  usually  close  enough  together  to  aflford  a  basis  for  all  the  detail 
work  that  must  be  done.  A  second  system  of  points  is  therefore  selected  and  signals 
erected  thereon,  and  the  position  of  these  points  is  determmed  by  a  series  of  angles 
from  the  main  triangulation  points  and  from  one  another.  This  is  known  as  the 
secondary  triangulation.  The  points  thus  located  are  used  in  the  plotting  of  the 
topography  and  hydrography.  It  is  not  essential  that  their  determination  be  as 
accurate  as  that  of  main  triangulation  points. 

The  topography  is  put  in,  and  includes  the  deUneation  of  the  features  of  the 
land — shore  Ime,  lighthouses,  beacons,  contour  lines,  peaks,  buildings,  and,  in 
short,  everything  that  may  be  recognized  by  the  navigator  and  utUized  by  him  in 
locating  the  ship's  position. 

The  hydrographic  work  is  taken  up  and  the  depth  of  water  and  character  of 
bottom  determmed  as  accurately  as  possible  for  the  complete  water  area,  especial 
care  being  taken  to  develop  all  shoals  and  dangers  to  navigation  and  to  locate  aU 
aids  to  navigation,  such  as  buoys,  lightships,  and  beacons. 

One  or  more  tidal  stations  are  established  where  observations  are  taken,  con- 
tinually and  at  frequent  intervals,  of  the  height  of  the  tide  and  direction  and  velocity 
of  the  tidal  and  other  currents,  whence  data  are  derived  for  the  reduction  of  aU  sound- 
ings to  the  plane  of  reference  and  for  the  infonnation  about  tides  and  currents  which 
is  to  appear  upon  the  chart. 

Observations  are  made  to  determine  the  magnetic  variation  and  dip,  and  the 
intensity  of  the  earth's  magnetic  force. 

4:33.  The  foregoing  represent,  in  outline,  the  various  steps  that  must  be  taken 
in  the  accumulation  of  the  data  necessary  for  the  construction  of  a  complete  hydro- 
graphic  chart.  In  the  following  paragraphs  the  details  of  the  various  operations  will 
be  more  fully  set  forth. 

The  navigator  who  is  called  upon  to  conduct  a  marine  survey  without  having 
available  the  time,  instruments,  and  general  facilities  necessary  for  the  most  thorougn 
performance  of  the  work  must  exercise  his  discretion  as  to  the  modifications  of  method 
that  he  wiU  make,  and  call  upon  his  ingenuity  to  adapt  his  means  to  the  particular 
work  in  hand. 

434.  The  Base  Line. — ^As  the  base  line  is  the  foundation  for  all  distances  on 
the  chart,  the  correctness  of  the  results  of  the  survey  will  depend  largely  upon  the 
degree  of  accuracy  with  which  it  is  measured.  The  triangulation  merely  affords  a 
measure  of  the  various  distances  as  compared  with  the  distances  between  the  two 
initial  points  from  which  it  began ;  if  that  initial  distance  is  1 ,000  feet,  we  have  cer- 
tain values  for  the  sides  of  the  various  triangles;  if  the  same  base  line  is  2,000  feet, 
the  value  of  each  side  becomes  twice  as  great  as  it  was  before;  with  the  same  triangu- 
lation, therefore,  distances  vary  directly  with  the  length  of  the  base  line;  it  may 
thus  be  seen  that  if  an  error  exists  in  measurement  which  is  only  a  small  fraction 
of  the  total  length,  the  error  will  become  much  more  material  as  the  more  distant 
points  of  the  survey  are  reached.  In  a  base  line  1,000  feet  long,  if  a  mistake  of  10 
feet  be  made  aU  distances  measured  upon  the  chart  will  be  in  error  1  per  cent,  and 
a  point  plotted  by  triangulation  10  miles  from  the  observation  spot  (the  point  at 
which  plotting  begins),  would  be  out  of  its  correct  position  one- tenth  of  a  mile. 

It  is  important  that  the  base  line  should  be  as  long  as  possible,  consistent  with 
the  distribution  and  distances  between  the  surrounding  objects  which  must  be 
depended  upon  as  triangulation  stations  for  its  expansion.  The  position  of  the  line 
must  be  such  as  to  afford  favorably  conditioned  triangles  and  quadrilaterals  with 
adjoining  main  triangulation  points,  and  its  extremities  must  be  visible  from  those 
points  and  from  each  other.  The  character  of  the  ground  and  the  facility  for  meas- 
uring will  of  course  form  an  important  consideration  in  the  choice. 

435.  In  measuring  a  base  by  tape,  chain,  or  similar  means,  a  number  of  suc- 
cessive fleets  are  made  with  the  measure,  whatever  its  nature,  the  distance  traversed 


MAEINE  SURVEYING.  199 

being  appropriately  marked  after  each  fleet,  while  an  observer,  with  a  theodoUte  or 
transit,  insures  the  measurement  being  made  accurately  along  the  line. 

436.  The  most  careful  measurements  are  made  with  a  steel  tape  300  feet  long, 
stretched  along  a  series  of  supports  at  equal  intervals  along  the  base  Une,  the  points 
of  support  being  made  exactly  horizontal  by  a  level.  A  good  form  of  support  is  a 
stake  driven  vertical  with  one  side  on  the  base  line  and  a  nail,  for  supporting  the 
tape,  driven  horizontally  into  the  stake  at  the  established  level.  The  stakes  falling 
at  the  ends  of  tape  lengths  should  be  set  sUghtly  less  than  300  feet  apart,  sawed  off 
at  the  estabhshed  level,  and  have  strips  of  zinc  tacked  on  their  tops.  The  end  of 
each  fleet  is  marked  by  a  scratch  mark  cut  in  the  strip  of  zinc  at  an  even  hundredth 
of  a  foot-division  on  the  tape,  and  the  corresponding  tape  reading  recorded.  Tapes 
for  base-line  measurement  are  usually  subdivided  to  hundredths  of  a  foot  for  a 
distance  of  10  feet  from  each  end  of  the  tape.  The  tape  is  stretched  to  a  uniform 
tension  by  a  spring  balance.  The  temperature  of  the  tape  at  each  fleet  should  be 
observed,  and  the  mean  temperature,  for  the  entire  measurement  of  the  base  deduce. 
Tapes  for  base-line  measurements  are  usually  standardized  lying  flat,  and  at  a 
temperature  of  62°  Fahrenheit.  To  reduce  the  measured  length  of  the  base  line 
to  the  true  length  the  following  corrections  to  the  measured  length  must  be  applied: 

Temperature  correction  Ct  =  +  (<^m  —  To)  L, 
where     «= coefficient  of  expansion. 

Tm=mean  temperature  at  measurement. 
To  =  standard  temperature. 
L  =  measured  length. 

Correction  for  sag  C,  =  —  ^ti  -p-  )  . 

where     L  =  measured  length. 

w  =  weight  per  inch  of  tape. 

d  =  distance  between  supports  in  inches. 

P  =  tension  in  pounds. 

By  this  method  of  measurement  the  horizontal  (listance  between  the  ends  of 
the  base  line  may  be  readily  found  to  witliin  1  part  in  250,000,  and  by  application 
of  superior  apparatus,  of  several  measures,  and  greater  care — hence,  at  an  increased 
cost— the  probable  uncertainty  may  be  reduced  to  1  part  in  500,000,  but  this  de^ee 
of  accuracy  would  not  be  necessary  except  in  very  extended  systems  of  triangulation. 

437.  A  second  method  of  base  measurement  is  with  the  surveyor's  chain. 
This  depends  for  accuracy  upon  the  surface  traversed  being  plane  and  level,  a  con- 
dition that  is  well  fulfilled  on  a  sandy  beach,  where  the  chain  is  nearly  as  accurate 
as  the  tape  and  much  more  rapid.  A  surveyor's  chain  is  usually  100  feet  long;  the 
exact  value  of  its  length  must  be  obtained  by  comparison  with  a  standard,  and  a 
correction  applied  for  expansion  or  contraction  due  to  temperature.  The  ends  of 
the  fleets  are  marked  by  steel  pins  driven  into  the  ground;  the  aUgnment  is  kept 
by  the  theodohte. 

438.  Where  neither  chain  nor  tape  is  available  substitutes  may  be  improvised 
from  sounding  wire  taken  from  the  deep-sea  sounding  machine,  or  failing  this,  from 
weU-stretched  cod  Hne. 

Measurements  made  by  the  telemeter  and  stadia  afford  a  close  approxima- 
tion to  the  true  result,  and  if  these  instruments  are  not  at  hand  the  sextant  angle 
of  a  rod  of  fixed  length  can  be  employed.  The  masthead  height  of  the  vessel  may 
be  used  in  determining  the  length  of  base  line  on  this  principle,  either  by  making 
the  ship  itself  mark  one  of  the  extremities  and  observing  the  masthead  angle  from 
the  other  extremity,  or  by  simultaneously  observmg  the  masthead  angle  from  both 
ends  of  a  shore  base,  and  also  the  three  horizontal  angles  of  the  triangle  formed  by 
the  ship  and  the  two  base  stations.  The  latter  plan  is  far  preferable  where  accuracy 
is  sought,  as,  if  the  angles  are  aU  taken  by  different  observers  at  the  same  instant 
(which  can  be  marked  by  the  hauling  down  of  a  flag),  the  error  arising  from  the 
motion  of  the  ship  about  her  anchor  is  eliminated,  and,  moreover,  the  data  furnished 
offers  a  double  solution  of  the  triangle  and  the  mean  may  be  taken  as  giving  a  closer 
result. 


200  MARINE  SURVEYING. 

439.  A  crude  method  of  estimating  distance  is  by  means  of  the  velocity  of 
sound,  though  this  would  never  be  used  where  close  results  are  expected.  Fire  a  gun 
at  one  end  of  the  distance  and  at  the  other  note  by  the  most  accurate  means  available 
the  time  between  seeing  the  flash  and  hearing  the  report.  Repeat  several  times  in 
each  direction.  The  mean  number  of  seconds  and  tenths  of  a  second  multiplied  by 
the  velocity  of  sound  per  second  at  the  temperature  of  observation  (art.  314,  Chap. 
XI)  gives  the  approximate  distance. 

4:40.  When  for  any  reason  the  existing  conditions  do  not  permit  of  a  direct 
measurement  being  made  along  the  line  between  the  two  base  stations,  recourse 
must  be  had  to  a  broken  hose,  that  is,  one  in  which  the  length  of  the  base  is  obtained 
by  reduction  from  the  measured  length  of  two  or  more  auxihary  lines.  Necessity 
for  resorting  to  a  broken  base  arises  frequently  when  the  two  stations  are  situated 
on  a  curving  shore  line  and  the  straight  line  between  them  passes  across  water,  or 
where  wooded  or  unfavorable  country  intervenes,  or  where  a  stream  must  be  crossed. 
The  most  common  form  of  broken  base  is  that  in  which  the  auxiliary  lines  run  from 
each  extremity  of  the  base  at  an  acute  angle  and  intersect;  in  addition  to  measuring 
each  of  these  lines  the  angle  formed  by  their  intersection  or  else  the  angles  formed 
by  them  with  the  base  line  must  be  observed  and  the  true  length  of  the  base  deduced 
by  solution  of  the  triangle.  The  form  that  is  most  frequently  used  where  only  a 
short  section  of  the  base  is  incapable  of  measurement  (as  is  the  case  where  a  deep 
stream  flows  across)  is  that  of  an  auxiliary  ri^ht  triangle  whose  base  is  the  required 
distance  along  the  base  line  and  altitude  a  distance  measured  along  a  line  perpen- 
dicular thereto  to  some  convenient  point;  by  this  measured  distance  and  the  angles 
which  are  observed,  the  triangle  is  solved  and  the  length  of  the  unmeasured  section 
determined. 

441.  In  a  survey  of  considerable  extent,  where  good  means  are  at  hand  for  the 
correct  determination  of  latitude  and  longitude,  a  base  line  actually  measured  upon 
the  earth  may  be  dispensed  with,  and,  instead  of  that,  the  positions  of  the  two 
stations  which  are  most  widely  separated  may  be  determined  astronomically  and 
plotted;  the  triangulation  is  then  plotted  upon  any  assumed  scale,  and  when  it  has 
been  brought  up  to  connect  the  two  stations  the  true  value  of  the  scale  is  ascertained. 
This  is  called  the  method  of  an  astronomical  base. 

442.  Signals. — ^All  points  in  the  survey  whose  positions  are  to  be  located  from 
other  stations,  or  from  which  other  positions  are  to  be  located,  must  be  marked  by 
signals  of  such  character  as  wiU  render  them  distinguishable  at  the  distance  from 
which  they  are  observed.     The  methods  of  constructing  signals  are  of  a  wide  variety. 

A  vessel  regularly  fitted  out  for  surveying  would  carry  scantlings,  lumber,  bolts, 
nuts,  naUs,  whitewash,  and  sheeting  for  the  erection  of  signals;  however  meager  the 
equipment,  the  whitewash  and  sheeting  (or  some  substitute  for  sheeting,  preferably 
half  of  it  white  and  half  dark  in  color)  should  be  provided,  if  possible,  before  begin- 
ning any  surveying  work.  Regular  tripod  signals,  which  are  quickly  erected  and 
are  visible,  under  favorable  circumstances,  for  many  miles,  are  almost  invariably 
einployed  to  mark  the  main  triangulation  stations;  among  other  advantages  the 
tripod  form  permits  the  occupation  with  the  theodolite  of  the  exact  center  of  the 
station,  and  avoids  the  necessity  for  the  reduction  which  must  otherwise  be  appUed. 
Signals  on  secondary  stations  take  an  innumerable  variety  of  forms,  the  requirement 
bemg  only  that  they  shaU  be  seen  throughout  the  area  over  which  they  are  to  be 
made  use  of;  a  whitewashed  spot  on  a  rock,  a  whitewashed  trunk  of  a  tree,  a  white- 
washed cairn  of  stones,  a  sheeting  flag,  a  piece  of  sheeting  wrapped  about  a  bush, 
or  hung,  with  stones  attached,  over  a  cliff,  or  a  whitewashed  barrel  or  box  fiUed  with 
rocks  or  earth  and  surmounted  by  a  flag,  suggest  some  of  the  secondary  signals 
that  may  be  employed;  sometimes  objects  are  found  that  are  sufficiently  distinct  in 
themselves  to  be  used  as  signals  without  further  marking,  as  a  cupola  or  tower,  a 
hut,  a  lone  tree,  or  a  bowlder;  but  it  is  seldom  that  an  object  is  not  rendered  more 
conspicuous  by  the  flutter  of  a  flag  above  it,  or  by  the  dead-white  ray  reflected  from 
a  daub  of  whitewash. 

For  convenience,  each  signal  is  given  some  short  name  by  which  it  is  designated 
in  the  records. 

For  the  sake  of  economy  in  both  time  and  labor,  steel  towers,  such  as  are  used 
to  support  windmills,  are  being  extensively  employed  by  hydrographic  parties  for 


MARINE  SUEVEYING.  201 

survey  signals.  They  are  very  easily  erected  and  dismounted,  easily  transported, 
offer  little  resistance  to  gales  oi  wind,  and  are  more  permanent  and  satisfactory  than 
signals  of  wood. 

443.  The  Main  Triangulation, — ^The  points  selected  as  stations  for  the  main 
triangulation  mark  in  outline  the  whole  area  to  be  surveyed;  they  are  close  enough 
together  to  afford  an  accurate  means  of  plotting  all  intermediate  stations  of  the 
secondary  triangulation;  and  they  are  so  placed  with  relation  to  one  another  that 
the  triangles  or  quadrilaterals  derived  from  them  are  well  conditioned.  The  points 
are  generally  so  chosen  that  small  angles  will  be  avoided.  In  order  to  fulfill  the 
other  conditions,  it  frequently  becomes  necessary  to  carry  forward  the  triangulation 
by  means  of  stations  located  on  points  a  considerable  distance  inland,  such  as  moun- 
tain peaks,  which  would  not  otherwise  be  regarded  as  properly  within  the  limits  of 
the  survey. 

Great  care  should  be  taken  in  observing  all  angles  upon  which  the  main  triangu- 
lation is  based ;  the  best  available  instrument  should  Ibe  employed ;  angles  taken 
with  a  theodolite  or  transit  should  be  repeated,  and  observed  with  telescope  direct 
and  reversed,  and  the  mean  result  taken;  if  the  sextant  is  used,  a  number  of  separate 
observations  of  each  angle  should  be  taken  and  averaged  for  the  most  probable 
value.  It  must  be  remembered  that  while,  in  any  other  part  of  the  work,  an  error 
in  an  angle  affects  only  the  results  in  its  immediate  vicinity,  an  error  in  the  main 
triangulation  goes  forward  through  all  the  plotting  that  comes  after  it. 

It  occurs  frequently  that  the  purposes  of  the  survey  are  sufficiently  well  fulfilled 
by  a  graphic  plotting  of  the  main  triangulation,  but  where  more  rigorous  methods 
prevau,  tne  results  are  obtained  by  calculation.  The  sum  of  the  angles  of  each 
triangle  is  taken,  and  if  it  does  not  exactly  equal  180°  the  values  are  adjusted  to 
make  them  comply  with  this  condition.  Li  cases  where  the  triangulation  stations 
form  a  series  of  quadrilaterals,  the  angles  of  each  quadrilateral  are  adjusted  so  as  to 
form  a  perfect  geometrical  figure.  Allowance  is  made  for  the  curvature  of  the  earth 
where  the  area  of  triangles  is  sufficiently  large  to  render  it  expedient  to  do  so.  The 
lengths  of  the  various  sides  and  the  relative  latitudes  and  longitudes  of  the  several 
stations  are  then  computed.  Each  station  may  then  be  plotted  in  its  latitude  and 
longitude  on  a  polyconic  projection,  and  a  delineation  of  the  triangulation  system 
may  thus  be  obtained  free  from  the  accumulated  errors  of  a  graphic  plotting. 

444.  The  Secondary  Triangulation. — ^The  points  of  the  secondary  triangu- 
lation are  located,  as  far  as  possible,  by  angles  from  the  main  triangulation  stations; 
these  angles,  having  less  dependent  upon  them,  need  not  be  repeated.  A  graphic 
plottmg  of  tnese  stations,  without  calculation,  wiU  suffice. 

445.  Astronomical  Work. — This  comprises  the  determination  of  the  correct 
latitude  and  longitude  of  some  point  of  the  survey,  and  of  the  true  direction  of  some 
other  point  from  the  observation  spot,  thus  furnishing  an  origin  from  which  all  posi- 
tions and  all  directions  can  be  determined  either  graphically  or  by  computation. 

The  methods  of  finding  latitude,  longitude,  and  the  true  bearmg  of  a  terrestrial 
object  are  fully  set  forth  in  previous  chapters.  The  feature  that  distinguishes  such 
work  in  surveying  from  that  of  determinmg  the  position  of  a  sliip  at  sea  lies  in  the 
greater  care  that  is  taken  to  eliminate  possible  errors. 

The  results  should  therefore  be  based  upon  a  very  large  number  of  observations, 
employing  the  best  instruments  that  are  available,  and  the  various  sights  being  so 
taken  that  probable  errors  are  offset  in  reckoning  the  mean. 

446.  By  taking  a  number  of  sights  the  observer  arrives  at  the  most  probable 
result  of  which  his  mstruments  and  nis  own  faculties  render  him  capable ;  but  this 
result  is  liable  to  an  error  whose  amount  is  indeterminate  and  which  is  equal  to  the 
algebraic  sum  of  a  number  of  small  errors  due,  respectively,  to  his  instruments 
(which  must  always  lack  perfection  in  some  details),  to  an  improper  allowance  for 
refraction  under  existing  atmospheric  conditions,  and  to  his  own  personal  error. 
Assuming,  as  we  may,  that  the  personal  error  is  approximately  constant,  these 
three  causes  give  rise  to  an  error  by  which  all  altitudes  appear  too  great  or  too  small 
by  a  uniform  but  unknown  amount.  Let  us  assume,  for  an  illustration,  that  this 
error  has  the  effect  of  making  all  altitudes  appear  30"  too  great;  if  an  observer 
attempted  to  work  his  latitude  from  the  meridian  altitude  of  a  star  bearing  south, 
the  result  of  this  unknown  error  would  give  a  latitude  30*  south  of  the  true  latitude; 


202  MARINE    SURVEYING. 

if  another  star  to  the  southward  were  observed,  this  mistake  would  be  repeated; 
but  if  a  star  to  the  north  were  taken,  the  resulting  latitude  would  be  30"  to  the 
north.  It  is  evident,  therefore,  that  the  true  latitude  will  be  the  mean  of  the  results 
of  observation  of  the  northern  and  the  southern  star,  or  the  mean  of  the  average  of 
several  northern  stars  and  the  average  of  several  southern  stars.  A  similar  process 
of  reasoning  will  show  that  errors  in  the  determination  of  hour  angle  are  offset  by 
taking  the  mean  of  altitudes  of  objects  respectively  east  and  west  of  the  meridian. 

447.  It  must  be  remembered  that  the  uniformity  of  the  unknown  error  only 
exists  where  the  altitude  remains  approximately  the  same,  as  instrumental  and  refrac- 
tion errors  may  vary  with  the  altitude;  another  condition  of  uniformity  requires  that 
the  instrument  and  the  observer  remain  the  same,  and  that  all  observations  be  taken 
about  the  same  time,  in  order  that  atmospheric  conditions  remain  unchanged;  to 
preserve  uniformity,  if  the  artificial  horizon  is  used,  the  same  end  of  the  roof  should 
always  be  the  near  one  to  the  observer;  in  taking  the  sun,  however,  as  the  personal 
error  may  not  be  the  same  for  approaching  as  for  separating  limbs,  every  series  of 
observations  should  be  made  up  of  an  equal  number  of  sights  taken  under  each 
condition. 

448.  With  aU  of  this  in  mind,  we  arrive  at  the  general  rule  that  astronomical 
determinations  shall  be  based  upon  the  mean  of  observations,  under  similar  conditions, 
of  bodies  whose  respective  distances  from  the  zenith  are  nearly  equal,  and  which 
bear  in  opposite  directions  therefrom. 

449.  This  condition  eliminates  the  sun  from  availability  for  observations  for 
latitude,  though  it  properly  admits  the  use  of  that  body  for  longitude  where  equal 
altitudes  or  single  a.  m.  and  p.  m.  sights  are  taken.  Opposite  stars  of  approximately 
equal  zenith  distance  should  always  be  used  for  latitude,  circum-meridian  altitudes 
being  observed  during  a  few  minutes  before  and  after  transit;  excellent  results  are 
also  obtained  from  stellar  observations  for  longitude;  but  very  low  stars  should  be 
avoided,  on  account  of  the  uncertainty  of  refraction,  and  likewise  very  high  ones, 
as  the  reflection  from  the  index  mirror  of  the  sextant  may  not  be  perfectly  distinct 
when  the  ray  strikes  at  an  acute  angle. 

If  there  is  telegraphic  or  radio  communication,  an  endeavor  should  be  made 
to  obtain  a  time  signal  from  a  reliable  source,  instead  of  depending  upon  the 
chronometers. 

450.  Topography. — ^The  plane  table,  with  telemeter  and  stadia,  affords  the 
most  expeditious  means  of  plotting  the  topography,  and  should  be  employed  when 
available.  Points  on  shore  may  also  be  plotted  by  sextant  angles,  using  the  three- 
point  problem,  or  by  any  other  reliable  method. 

451.  Hydrography. — The  correct  delineation  of  the  hydrographic  features 
being  one  of  the  most  important  objects  of  the  survey,  great  care  should  be  devoted 
to  this  part  of  the  work.  Soundings  are  run  in  one  or  more  series  of  parallel  lines, 
the  direction  and  spacing  of  which  depend  upon  the  scope  of  the  survey.  It  is 
usual  for  one  series  of  lines  to  extend  in  a  direction  normal  to  the  general  trend  of  the 
shore  line.  In  most  cases  a  second  series  runs  perpendicular  to  the  first,  and  in  surveys 
of  important  bodies  of  water  still  other  series  of  lines  cross  the  system  diagonally. 
In  developing  rocks,  shoals,  or  dangers  the  direction  of  the  lines  is  so  chosen  as  will 
best  illustrate  the  features  of  the  bottom.  When  lines  cross,  the  agreement  of  the 
reduced  soundings  at  their  intersection  affords  a  test  of  the  accuracy  of  the  work. 

As  the  depth  of  water  increases,  if  there  is  no  reason  to  suspect  dangers,  the 
interval  between  lines  may  be  increased. 

Lines  are  run  by  the  ship  or  boat  in  such  manner  as  to  foUow  as  closely  as  possible 
the  scheme  of  sounding  that  has  been  laid  out.  The  position  is  located  by  angles 
at  the  beginning  of  each  line,  at  each  change  of  course,  at  frequent  intervals  along 
the  line,  and  at  the  point  where  each  line  is  finished.  Soundings  taken  between 
positions  are  plotted  by  the  time  intervals  or  patent  log  distances. 

452.  There  are  a  number  of  methods  for  determining  positions  while  soimding, 
which  may  be  described  briefly  as  foUows: 

By  two  sextant  angles. — ^Two  observers  with  sextants  measure  simultaneously 
the  angles  between  three  objects  of  known  position,  and  the  position  is  located  by 
the  three-polat  problem.  This  is  the  method  most  commonly  employed  in  boat 
Work,  and  has  the  great  advantage  that  the  results  may  be  plotted  at  once  on  the 


MARINE    SURVEYING. 


203 


working  sheet  in  the  boat  and  the  lines  as  run  thus  kept  nearly  in  coincidence  with 
those  laid  out  in  the  scheme.  A  study  of  the  three-point  problem  (art.  153,  Chap. 
IV)  will  give  the  considerations  that  must  govern  in  the  selection  of  objects. 

By  two  theodolite  angles. — ^Two  stations  on  shore  are  occupied  by  observers  with 
theodolites,  and  at  certain  instants,  indicated  by  a  signal  from  the  ship  or  boat,  they 
observe  the  angular  distance  thereof  from  some  laiown  point.  The  intersection 
of  the  directionlines  thus  given  is  at  the  required  position.  This  method  is  expedi- 
tious where  the  signals  are  small  or  not  numerous.  Its  disadvantage  is  that  the 
plotting  can  not  be  kept  up  as  the  work  proceeds. 

By  one  sextant  and  one  theodolite  an^le. — ^An  observer  ashore  occupies  a  station 
with  a  theodolite  and  cuts  in  the  ship  or  boat,  while  one  on  board  takes  a  sextant 
angle  between  two  objects,  of  which  one  should  preferably  be  the  occupied  station. 
It  is  plotted  by  laying  ofiF  the  direction  line  from  the  theodolite  and  finding  with  a 
three-armed  protractor  or  piece  of  tracing  paper  at  what  point  of  that  line  the 
observed  angle  between  the  ob- 
jects is  subtended.  Its  advantages 
and  disadvantages  are  the  same  as 
those  of  the  preceding  method. 

In  running  lines  of  soundings 
offshore,  where  signals  are  lost 
sight  of,  the  best  method  is  to  get 
an  accurate  departure,  before  drop- 
ping the  land,  by  the  best  means 
that  offers,  keeping  careful  note 
of  the  dead  reckoning,  and  on  run- 
ning in  again,  to  get  a  position  as 
soon  as  possible,  note  the  drift  and 
reconcile  the  plotting  of  inter- 
mediate soundings  accordii^ly. 
Where  circumstances  require,  the 
position  may  be  located  by  astro- 
nomical observations  as  usually 
taken  at  sea. 

453.  A carefulrecord  of  sound- 
ings must  be  kept,  showing  the 
time  of  each  (so  that  proper  tidal 
correction  may  be  apphed),  the 
depth,  the  character  of  oottom,  and 
such  data  as  may  be  required  to 
locate  the  position. 

454.  The  Wire  Drag.— The 
use  of  the  lead  in  hydrographic 
surveying  does  not  absolutely  es- 
tablish a  definite  available  depth, 
as  pinnacle  obstructions  may  exist  which  are  not  detected  by  that  means.  This  is 
particularly  true  of  rocky  localities  and  those  of  coral  formation. 

In  order  to  guarantee  a  certain  depth  of  water  for  purposes  of  navigation  it  has 
become  the  practice  to  tow  through  the  waters  to  be  examined  a  line  of  wire  or  cable 
suspended  at  that  depth. 

The  drag  or  sweep  consists  essentially  of  a  horizontal  member,  known  as  the 
bottom  wire,  which  is  a  long  steel  Une  composed  of  50-foot  sections  coupled  together 
with  swivels  and  shackles.  It  is  supportea  at  each  terminal  from  an  80-pound  buoy 
by  a  chain  stirrup  line  whose  length  may  be  adjusted  from  20  to  50  leet.  There 
are  smaller  buoys  placed  at  intervals  varying  from  150  to  450  feet,  according  to  local 
conditions,  which  support  the  wire  by  means  of  steel-cable  stirrup  lines,  adjustable 
in  length  like  the  chain  stirrup  lines  on  the  terminal  buoys.  At  intermediate  50-foot 
connections,  cedar  toggles  or  floats,  which  have  a  little  more  buoyancy  than  is 
sufficient  to  support  uie  wire  between  the  stirrup  lines,  are  attached  by  means  of 
snap  hooks.  To  prevent  the  bottom  wire  from  sagging  back  as  the  drag  is  towed 
transversely  to  its  own  length  by  the  bridles  fastened  at  the  terminals,  a  leaden 


Fio.  6' 


204  MAKINB   SURVEYING. 

weight  of  165  pounds  is  suspended  from  each  of  the  terminal  stirrup  lines,  and  a 
weight  of  20  pounds  from  each  of  the  intermediate  stirrup  hnes.  The  length  of  the 
drag  may  be  varied  through  a  wide  range  to  suit  the  conditions  existing  in  the 
localities  to  be  examined.  Anj  multiple  of  50  feet  may  be  used,  but  it  is  in  general 
found  best  to  use,  in  each  division  between  two  towing  launches,  eight  sections  with 
stirrup-line  suppports  at  their  ends,  each  composed  of  from  three  to  seven  50-foot 
units.  The  towmg  launches  use  tow  Hnes  about  200  feet  in  length  bridled  to  the 
terminal  stirrup  lines  with  attachments  at  the  top  and  bottom.  During  the  towing,  as 
long  as  the  drag  is  free,  the  line  of  supporting  buoys  will  trace  out  a  paraboUc  curve 
on  the  surface  of  the  water;  but,  if  progress  should  be  interrupted  by  a  pinnacle  of 
rock  rising  in  its  path  above  the  depth  to  which  the  drag  hne  is  set,  the  paraboUc 
curve  of  the  line  of  buoys  will  immediately  become  broken  into  the  form  of  a  V, 
whose  angle  will  correspond  in  position  with  the  position  of  the  pinnacle.  The  pres- 
ence of  any  such  obstruction  is  also  registered  by  the  spring  balance  usually  attached 
to  the  towline  at  a  convenient  position  near  the  towing  vessel.  If  the  shape  of  the 
obstruction  is  such  as  to  allow  the  drag  line  to  ride  upward  upon  it,  as  may  be  with 
bowlders  and  shoals,  an  additional  indication  of  its  presence  is  afforded  by  the  falling 
over  of  the  supporting  buoys  when  the  suspended  stirrup  lines  are 
reheved  of  stram  by  tne  grounding  of  the  weights  attached  to  them. 
In  such  cases  a  tender  should  be  in  readmess  to  proceed  to  the 
indicated  point  for  the  purpose  of  taking  position  angles  to  locate 
the  spot  and  also  soundings  to  ascertain  the  characteristics  of  the 
obstruction.  Such  locaUties  are  plotted  upon  the  chart  upon 
which  the  paths  of  the  drag  line  are  being  mapped,  and  later  these 
areas  are  again  swept  with  the  drag  line  at  a  lesser  depth;  and 
this  procedure  is  continued  until  the  obstruction  is  cleared  by  the 
drag  line,  and  thus  the  least  depth  is  proved.  The  position  of  the 
drag  is  determined  by  observers  with  sextants  on  board  the  towing 
vessels  who  simultaneously  measure,  at  frequent  intervals,  the 
values  of  two  angles  between  two  pairs  of  known  objects  whose  posi- 
tions are  identified  upon  the  plotting  chart. 

The  average  speed  of  towing  is  about  IJ  knots  per  hour,  and 
the  average  area  explored  per  working  day  is  1^  square  miles, 
although  a  much  higher  rate  of  progress  is  usually  attained  in  open 
areas  under  favorable  conditions. 

455.  Tidal  Observations. — These  should  begin  as  early  as 
practicable  and  continue  throughout  the  survey,  it  being  most  im- 
portant that  they  shaU,  if  possible,  cover  the  period  of  a  lunar  month.     In  the  chap- 
ter on  tides  (Chap.  XX)  the  nature  of  the  data  to  be  obtained  is  explained. 

456.  Magnetic  Observations. — The  feature  of  the  earth's  magnetism  with 
which  the  navigator  is  most  concerned  is  the  variation,  which  is  set  forth  on  the 
chart,  and  upon  the  determination  of  which  will  depend  the  correctness  of  all  courses 
and  bearings  on  shipboard.  It  is  usually  obtained  by  noting  the  compass  direction 
from  the  observation  spot  of  the  object  whose  true  bearing  is  known  by  calculation, 
and  comparing  the  true  and  compass  bearings;  or  it  may  be  observed  by  mounting 
the  ship's  compass  in  a  place  on  shore  free  from  foreign  magnetic  influence,  and  finding 
the  compass  error  as  it  is  found  on  board.  Observations  for  dip  and  intensity  are 
also  made  when  the  proper  instruments  are  at  hand. 

457.  Running  Survey. — Where  time  and  opportunity  permit  only  a  superficial 
examination  of  a  coast  line  or  water  area,  or  where  the  interests  of  navigation  req^^uire 
no  more,  recourse  is  had  to  a  running  survey,  in  which  shore  positions  are  determmed 
and  soundings  are  made  while  the  ship  steams  along  the  coast,  stopping  only  occa- 
sionally to  fix  her  position,  and  in  which  the  assistance  of  boat  or  shore  parties  may 
or  may  not  be  employed. 

In  this  method  the  ship  starts  at  one  end  of  the  field  from  a  known  position, 
fixed  either  by  astronomical  observations  or  by  angles  or  bearings  of  terrestrial 
objects  having  a  determined  location.  Careful  compass  bearings  or  sextant  angles 
are  taken  from  this  position  to  all  objects  ashore  which  can  be  recognized,  and  a 
series  of  direction  lines  is  thus  obtained.  The  ship  then  steams  along  the  coast,  at  a 
convenient  distance  therefrom,  keeping  accurate  account  of  her  run  by  compass 


MARINE    SURVEYING.  205 

courses  and  patent  log.  From  time  to  time  other  senes  of  bearing  or  angles  are 
taken  upon  tnose  objects  ashore  which  are  to  be  located,  the  direction  lines  plotted 
from  the  estimated  position  of  the  ship,  and  the  various  objects  located  by  the 
intersections  with  their  other  direction  lines.  During  all  the  time  that  the  ship  is 
under  way,  soundings  are  taken  at  regular  intervals  and  plotted  from  the  dead  reck- 
oning. As  frequently  as  circumstances  permit,  the  ship  is  stopped  and  her  position 
located  by  the  oest  available  means,  and  the  intervening  dead  reckoning  reconciled 
for  any  current  that  may  be  found. 

If  a  steam  launch  can  be  employed  in  connection  with  a  running  survey,  it  is 
usually  sent  to  run  a  second  line  inshore  of  the  ship.  The  boat's  position  is  obtained 
by  bearings  of  objects  ashore  which  are  located  by  the  ship,  or  by  bearings  and  mast- 
head angles  of  the  ship,  or  by  such  other  means  as  offer.  The  duty  of  the  boat  is 
to  take  a  series  of  soundmgs  and  to  coUect  data  for  shore  line  and  topography. 

If  circumstances  allow  the  landing  of  a  shore  party,  its  most  important  duty  is 
to  mark  the  various  objects  on  shore  by  some  sort  of  signals  which  will  render  tnem 
unmistakable.  Beyond  this,  it  can  perform  such  of  uie  duties  assigned  to  shore 
parties  in  a  regular  survey  as  opportunity  permits. 


CHAPTER  XVIII. 
WINDS. 


458.  Wind  is  air  in  approximately  horizontal  motion.  Observations  of  the 
wind  should  include  its  true  du-ection,  and  its  force  or  velocitTp'.  The  direction  of  the 
wind  is  designated  by  the  point  of  the  compass  from  which  it  proceeds.  The  force 
of  the  wind  is  at  sea  ordinarily  expressed  in  terms  of  the  Beaufort  scale,  each  degree 
of  this  scale  corresponding  to  a  certain  velocity  in  miles  per  hour,  as  explained  in 
article  68,  Chapter  II. 

459.  The  Cause  of  the  Wind. — Winds  are  produced  by  differences  of  atmos- 
pheric pressure,  which  are  themselves  ultimately,  and  in  the  main,  attributable  to 
differences  of  temperature. 

To  understand  how  the  air  can  be  set  in  motion  by  these  differences  of  pressure, 
it  is  necessary  to  have  a  clear  conception  of  the  nature  of  the  air  itself. 

The  atmosphere  which  completely  envelops  the  earth  may  be  considered  as  a 
fluid  sea  at  the  bottom  of  which  we  live,  and  which  extends  upward  to  a  considerable 
height,  probably  200  miles,  constantly  diminishing  in  density  as  the  altitude  increases. 

The  air,  or  material  of  which  this  atmostphere  is  composed,  is  a  transparent  gas, 
which,  like  all  other  gases,  is  perfectly  elastic  and  highly  compressible.  Although 
extremely  light,  it  has  a  perfectly  definite  weight,  a  cubic  foot  of  air  at  ordinary 
pressure  and  temperature  weighing  1.22  ounces,  or  about  one  seven  hundred  and 
seventieth  part  of  the  weight  of  an  equal  volume  of  water.  In  consequence  of  this 
weight  it  exerts  a  certain  pressure  upon  the  surface  of  the  earth,  amounting  on  the 
average  to  15  pounds  for  each  square  inch.  To  accurately  measure  this  pressure, 
which  is  constantly  undergoing  slight  changes,  we  ordinarily  employ  a  mercurial 
barometer  (art.  48,  Chap.  II),  an  instrument  in  which  the  weight  of  a  column  of  air 
of  given  cross  section  is  balanced  against  that  of  a  column  of  mercury  having  an 
equal  cross  section;  and  instead  of  saying  that  the  pressure  of  the  atmosphere  is  a 
certain  number  of  pounds  on  each  square  inch,  we  say  that  it  is  a  certain  number  of 
inches  of  mercury,  meaning  thereby  that  it  is  equivalent  to  the  pressure  of  a  column 
of  mercury  that  many  inches  in  height,  and  one  square  inch  in  cross  section. 

All  gases,  air  included,  are  highly  sensitive  to  the  action  of  heat,  expanding  or 
increasing  in  volume  as  the  temperature  rises,  contracting  or  diminishing  in  volume 
as  the  temperature  falls.  Suppose  now  that  the  atmosphere  over  any  considerable 
region  of  the  earth's  surface  is  maintained  at  a  higher  temperature  than  that  of  its 
surroundings.  The  warmed  air  will  expand,  and  its  upper  layers  will  flow  off  to  the 
surrounding  regions,  cooling  as  they  go.  The  atmospheric  pressure  at  sea  level 
throughout  the  heated  areas  will  thus  be  diminished,  while  that  over  the  cii'cum- 
jacent  cooler  areas  will  be  correspondingly  increased.  As  the  result  of  this  difference 
of  pressure,  there  will  be  movement  of  the  surface  air  away  from  the  region  of  high 
pressure  and  toward  the  region  of  low,  somewhat  similar  to  the  flow  of  water  which 
takes  place  through  the  connecting  bottom  sluice  as  soon  as  we  attempt  to  fill  one 
compartment  of  a  divided  vessel  to  a  slightly  higher  level  than  that  found  in  the 
other. 

A  difference  of  atmospheric  pressure  at  sea  level  is  thus  immediately  followed 
by  a  movement  of  the  surface  air,  or  by  winds ;  and  these  differences  of  pressure  have 
their  origin  in  differences  of  temperature.  If  the  atmosphere  were  everywhere  of 
uniform  temperature  it  would  lie  at  rest  on  the  earth's  surface — sluggish,  torpid, 
and  oppressive — and  there  would  be  no  wmds.  This,  however,  is  fortunately  not 
the  case.  The  temperature  of  the  atmosphere  is  continually  or  periodically  higher 
in  one  region  than  in  another,  and  the  chief  variations  in  the  distrioution  of  tempera- 
ture are  systematically  repeated  year  after  year,  giving  rise  to  like  systematic 
variations  in  the  distribution  of  pressure. 
206 


WINDS.    .  ^  207 

460.  The  Normal  Distribution  of  Pressure. — The  winds,  while  thus  due 
primarily  to  differences  of  temperature,  stand  in  more  direct  relation  to  differences 
of  pressure,  and  it  is  from  this  point  of  view  that  they  are  ordinarily  studied. 

In  order  to  furnish  a  comprehensive  view  of  this  distribution  of  atmospheric 
pressure  over  the  earth's  surface,  charts  have  been  prepared  showing  the  average 
reading  of  the  barometer  for  any  given  period,  whether  a  month,  a  season,  or  a  year, 
and  covering  as  far  as  possible  the  entire  globe.  These  are  known  as  isobaric  charts, 
from  the  fact  that  all  points  at  which  the  barometer  has  the  same  reading  are  joined 
by  a  continuous  line  or  isobar. 

The  isobaric  chart  for  the  year  (fig.  69)  shows  in  each  hemisphere  a  well-defined 
belt  of  high  pressure  ( 30.20  inches)  completely  encircUng  the  globe,  that  in  the  northern 
hemisphere  naving  its  middle  line  about  in  latitude  35°  North,  that  in  the  southern 
hemisphere  about  m  latitude  30°  South,  these  constituting  the  so-called  meteorological 
tropics.  From  the  summit  or  ridge  of  each  of  these  belts  the  pressure  falls  off  alike 
toward  the  equator  and  toward  the  pole,  although  much  less  rapidly  in  the  former 
direction  than  in  the  latter.  The  equator  itself  is  encircled  by  a  belt  of  somewhat 
diminished  pressure  (29.90  inches),  the  middle  line  of  which  is  ordinarily  found  in 
northern  latitudes.     In  the  northern  hemisphere  the  diminution  of  pressure  on  the 

Eoleward  slope  is  much  less  marked  and  much  less  regular  than  in  the  southern 
emisphere,  minima  (29.70  inches)  occurring  in  the  North  Atlantic  Ocean  near 
Iceland  and  in  the  North  Pacific  Ocean  near  the  Aleutian  Islands,  beyond  which  the 
pressure  increases.  In  the  southern  hemisphere  no  such  minima  are  apparent,  the 
pressure  continuing  to  diminish  uninterruptedly  as  higher  and  higher  latitudes  are 
attained.  Along  the  sixtieth  parallel  of  south  latitude  the  average  barometric 
reading  is  29.30  inches. 

461.  Seasonal  Variations  of  Pressure. — As  might  be  expected  from  its 
close  relation  to  the  temperature,  the  whole  system  of  pressure  distribution  exhibits 
a  tendency  to  follow  the  sun's  motion  in  declination,  the  barometric  equator  occupy- 
ing in  July  a  position  slightly  to  the  northward  of  its  position  in  January.  In  eitner 
hemisphere,  moreover,  the  pressure  over  the  land  during  the  winter  season  is  decidedly 
above  the  annual  average,  during  the  summer  season  decidedly  below  it;  the  extreme 
variations  occurring  in  the  case  of  continental  Asia,  where  the  mean  monthly  pressure 
ranges  from  30.50  inches  during  Januaiy  to  29.50  inches  during  July.  Over  the 
northern  ocean,  on  the  other  hand,  conditions  are  reversed,  the  summer  pressures 
being  here  somewhat  the  higher.  Thus,  in  January  the  Icelandic  and  the  Aleutian 
minima  increase  in  depth  to  29.50  inches,  while  in  July  these  minima  fill  up  and  are 
well-nigh  obliterated,  a  fact  which  has  much  to  do  with  the  strength  and  irequency 
of  the  winter  gales  in  high  northern  latitudes  and  the  absence  of  these  gales  during 
the  summer.  Over  the  southern  ocean,  in  keeping  with  its  slight  contrast  between 
winter  and  summer  temperatures,  similar  variations  of  pressure  do  not  exist. 

4:62.  The  Prevailing  Winds. — ^As  a  result  of  the  distribution  of  pressure  just 
described,  there  is  in  either  hemisphere  a  continual  motion  of  the  surface  air  away 
from  the  meteorological  tropic — on  one  side  toward  the  equator,  on  the  other  side 
toward  the  pole,  the  first  constituting  in  each  case  the  trade  winds,  the  second  the 
prevailing  winds  of  higher  latitudes.  Upon  a  stationary  earth  the  direction  of  this 
motion  would  be  immediately  from  the  region  of  high  toward  the  region  of  low 
barometer,  the  moving  air  steadily  following  the  barometric  slope  or  gradient, 
increasing  in  force  to  a  gale  where  these  gradients  are  steep,  decreasing  to  a  Hght 
breeze  where  they  are  gentle,  sinking  to  a  calm  where  they  are  absent.  The  earth, 
however,  is  in  rapid  rotation,  and  this  rotation  gives  rise  to  a  force  which  exercises 
a  material  influence  over  all  horizontal  motions  upon  its  surface,  whatever  their 
direction,  serving  constantly  to  divert  them  to  the  ngM  in  the  northern  hemisphere, 
to  the  left  in  the  southern.  The  air  set  in  motion  by  the  difference  of  pressure  is 
thus  constantly  turned  aside  from  its  natural  course  down  the  barometric  gradient 
or  slope,  and  the  direction  of  the  wind  at  any  point,  instead  of  being  identical  with 
that  of  the  gradient  at  that  point,  is  deflected  by  a  certain  amount,  crossing  the 
latter  at  an  angle  which  in  practice  varies  between  45°  and  90°  (4  to  8  compass 
points),  the  wind  in  the  latter  case  blowing  parallel  to  the  isobars.  As  a  consequence 
of  this  deflection  the  northerly  winds  wmch  one  would  naturally  expect  to  imd  on 
the  equatorial  slope  of  the  belt  of  high  pressure  in  the  northern  hemisphere  become 


208 


WINDS. 


Fig.  69. 


WINDS.  209 

northeasterly — the  NE.  trade;  the  southerly  winds  of  the  polar  slope  become  south- 
westerly— the  prevailing  westerly  winds  of  northern  latitudes.  So,  too,  for  the 
southern  hemisphere,  the  southerly  winds  of  the  equatorial  slope  here  becoming 
southeasterly — the  SE.  trades;  the  northerly  winds  of  the  polar  slope  northwesterly — 
the  prevaihng  westerly  winds  of  southern  latitudes. 

463.  The  relation  here  described  as  existing  between  the  distribution  of  atmos- 
pheric pressure  and  the  direction  of  the  wind  is  of  the  greatest  importance.  It  may 
be  briefly  stated  as  follows: 

In  the  northern  hemisphere  stand  with  the  face  to  the  wind;  in  this  position 
the  region  of  high  barometer  lies  on  your  left  hand  and  somewhat  in  front  of  you; 
the  region  of  low  barometer  on  your  right  hand  and  somewhat  behind  you. 

In  the  southern  hemisphere  stand  with  the  face  to  the  wind ;  in  this  position 
the  region  of  high  barometer  lies  on  yom*  right  hand  and  somewhat  in  front  of  you ; 
the  region  of  low  barometer  on  your  left  hand  and  somewhat  behind  you. 

This  relation  holds  absolutely,  not  only  in  the  case  of  the  general  distribution  of 
pressure  and  circulation  of  the  atmosphere,  but  also  in  the  case  of  the  special  con- 
ditions of  high  and  low  pressure  which  usually  accompany  severe  gales. 

464:.  The  Trade  Winds. — The  Trade  Witids  blow  from  the  tropical  belts  of 
high  pressure  toward  the  equatorial  belt  of  low  pressure — in  the  northern  hemisphere 
from  the  northeast,  in  the  southern  hemisphere  from  the  southeast.  Over  the 
eastern  half  of  each  of  the  great  oceans  they  extend  considerably  farther  from  the 
line  and  their  original  direction  inclines  more  toward  the  pole  than  in  midocean, 
where  the  latter  is  almost  easterly.  They  are  ordinarily  looked  upon  as  the  most 
constant  of  winds,  but  while  they  may  blow  for  days  or  even  for  weeks  with  slight 
variation  in  direction  or  strength,  their  uniformity  should  not  be  exaggerated, 
liiere  are  times  when  the  trade  winds  weaken  or  shift.  There  are  regions  where 
their  steady  course  is  deformed,  notably  among  the  island  groups  of  the  South  Pacific, 
where  the  trades  during  January  and  February  are  practically  nonexistent. 
They  attain  their  highest  development  in  the  South  Atlantic  and  in  the  South  Indian 
Ocean,  and  are  everywhere  fresher  during  the  winter  than  during  the  summer  season. 
They  are  rarely  disturbed  by  cyclonic  storms,  the  occurrence  of  the  latter  within  the 
limits  of  the  trade-wind  region  being  furthermore  confined  in  point  of  time  to  the 
late  summer  and  autumn  months  of  the  respective  hemispheres,  and  in  scene  of 
action  to  the  western  portion  of  the  several  oceans.  The  South  Atlantic  Ocean 
alone,  however,  enjoys  complete  immunity  from  tropical  cyclonic  storms. 

465.  The  Doldrums. — The  equatorial  girdle  oi  low  pressure  occupies  a  position 
between  the  h^h-pressure  belt  of  the  northern  and  the  similar  belt  oi  the  southern 
hemisphere.  Throughout  the  extent  of  this  barometric  trough  the  pressure,  save 
for  the  s^ght  diurnal  oscillation,  is  practically  uniform,  and  decided  barometric 
gradients  do  not  exist.  Here,  accordingly,  the  winds  sink  to  stagnation,  or  rise  at 
most  only  to  the  strength  of  fitiul  breezes,  coming  first  from  one  point  of  the  compass, 
then  from  another,  with  cloudy,  rainy  sky  and  frequent  thimderstorms.  The  region 
throughout  which  these  conditions  prevail  consists  of  a  wedge-shaped  area,  the  base 
of  the  wedge  resting  in  the  case  of  the  Atlantic  Ocean  on  the  coast  of  Africa,  and  in 
the  case  of  the  Pacific  Ocean  on  the  coast  of  America,  the  axis  extendingwestward. 
The  position  and  extent  of  the  belt  vary  somewhat  with  the  season.  Throughout 
February  and  March  it  is  found  immediately  north  of  the  equator  and  is  of  inap- 
preciable width,  vessels  following  the  usual  sailing  routes  frequently  passing  from 
trade  to  trade  without  interruption  in  both  the  Atlantic  and  the  Pacific  Oceans. 
In  July  and  August  it  has  migrated  to  the  northward,  the  axis  extending  east  and 
west  along  the  parallel  of  7°  north,  and  the  belt  itself  covering  several  degrees  of 
latitude,  even  at  its  narrowest  point.  At  this  season  of  the  year,  also,  the  southeast 
trades  blow  with  diminished  freshness  across  the  equator  and  weU  into  the  northern 
hemisphere,  being  here  diverted,  however,  by  the  effect  of  the  earth's  rotation,  into 
southerly  and  southwesterly  winds,  the  so-called  southwest  monsoon  of  the  African 
and  Central  American  coasts. 

466.  The  Horse  Latitudes. — On  the  outer  margin  of  the  trades,  corresponding 
vaguely  with  the  summit  of  the  tropical  ridge  of  high  pressure  in  either  hemisphere, 
is  a  second  region  throughout  which  the  barometric  graoients  are  faint  and  undecided, 

21594»— 14 M 


210  WINDS. 

and  the  prevailing  winds  correspondingly  light  and  variable,  the  so-called  liorse 
latitudes,  or  calms  of  Cancer  and  of  Capricorn.  Unlike  the  doldrums,  however, 
the  weather  is  here  clear  and_ fresh,  and  the  periods  of  stagnation  are  intermittent 
rather  than  continuous,  showing  none  of  the  persistency  "v^ich  is  so  characteristic 
of  the  equatorial  region.  The  explanation  of  this  difference  will  become  obvious 
as  soon  as  we  come  to  study  the  nature  of  the  daily  barometric  changes  of  pressure 
in  the  respective  regions,  these  in  the  one  case  being  marked  by  the  uniformity  of  the 
torrid  zone,  in  the  other  sharing  to  a  limited  extent  in  the  wide  and  rapid  variations 
of  the  temperate. 

467.  The  Prevailing  Westerly  Winds. — On  the  exterior  or  polar  side  of  the 
tropical  maxima  the  pressure  again  diminishes,  the  barometric  gradients  being  now 
directed  toward  the  pole;  and  the  currents  of  air  set  in  motion  along  these  gradients, 
diverted  to  the  right  and  left  of  their  natural  course  by  the  earth's  rotation,  appear  in 
the  northern  hemisphere  as  southwesterly  winds,  in  the  southern  hemisphere  as 
northwesterly — the  prevailing  westerly  winds  of  the  temperate  zone. 

Only  in  the  southern  hemisphere  do  these  winds  exhibit  anything  approaching 
the  persistency  of  the  trades,  their  course  in  the  northern  hemisphere  bemg  subject 
to  frequent  local  interruption  by  periods  of  winds  from  the  eastern  semicircle.  Thus 
the  tabulated  results  show  that  throughout  the  portion  of  the  North  Atlantic  included 
between  the  parallels  40°-50°  North,  and  the  meridians  10°-50°  West,  the  winds 
from  the  western  semicircle  (South — NNW.)  comprise  about  74  per  cent  of  the 
whole  number  of  observations,  the  relative  frequency  being  somewhat  higher  in 
winter,  somewhat  lower  in  summer.  The  average  force,  on  the  other  hand,  decreases 
from  force  6  to  force  4  Beaufort  scale,  with  the  change  of  season.  Over  the  sea  in  the 
southern  hemisj)here  such  variations  are  not  apparent;  here  the  westerlies  blow 
through  the  entire  year  with  a  steadiness  little  less  than  that  of  the  trades  them- 
selves, and  with  a  force  which,  though  fitful,  is  very  much  greater,  their  boisterous 
nature  giving  the  name  of  the  "  Roaring  Forties "  to  the  latitudes  in  which  they  are 
most  frequently  observed. 

The  explanation  of  this  striking  difference  in  the  extra-tropical  winds  of  the  two 
halves  of  the  globe  is  found  in  the  distribution  of  atmospheric  pressure,  and  in  the 
variations  which  this  latter  undergoes  in  different  parts  of  the  world.  In  the  landless 
southern  hemisphere  the  atmospheric  pressure  after  crossing  the  parallel  of  30° 
South  diminishes  almost  uniform!;^  toward  the  pole,  and  is  rarely  disturbed  by  those 
large  and  irregular  fluctuations  which  form  so  important  a  factor  in  the  daily  weather 
of  the  northern  hemisphere.  Here,  accordingly,  a  system  of  polar  gradients  exists 
quite  comparable  in  stabiUty  with  the  equatorial  gradients  which  give  rise  to  the 
trades;  and  the  poleward  movement  of  the  air  in  obedience  to  these  gradients, 
constantly  diverted  to  the  left  by  the  efl:ect  of  the  earth's  rotation,  constitutes  the 
steady  westerly  winds  of  the  south  temperate  zone. 

468.  The  Monsoon  Winds. — The  air  over  the  land  is  warmer  in  summer  and 
colder  in  winter  than  that  over  the  adjacent  oceans.  During  the  former  season  the 
continents  thus  become  the  seat  of  areas  of  relatively  low  pressure;  during  the  latter 
of  relatively  high.  Pressure  gradients,  directed  outward  during  the  winter,  inward 
during  the  summer,  are  thus  established  between  the  land  and  the  sea,  which  exercise 
the  greatest  influence  over  the  winds  prevailing  in  the  region  adjacent  to  the  coast. 
Thus,  off  the  Atlantic  seaboard  of  the  United  States  southwesterly  winds  are  most 
frequent  in  summer,  northwesterly^  winds  in  winter;  while  on  the  Pacific  coast  the 
reverse  is  true,  the  wind  here  changing  from  northwest  to  southwest  with  the  advance 
of  the  colder  season. 

The  most  striking  illustration  of  winds  of  this  class  is  presented  by  the  monsoons 
{Mausum,  season)  of  the  China  Sea  and  of  the  Indian  Ocean.  In  January  abnormally 
low  temperatures  and  high  pressure  obtain  over  the  Asiatic  plateau,  high  tempera- 
tures and  low  pressure  oyer  Australia  and  the  nearby  portion  of  the  Indian  Ocean. 
As  a  result  of  the  baric  gradients  thus  established,  the  southern  and  eastern  coast 
of  the  vast  Asiatic  continent  and  the  seas  adjacent  thereto  are  swept  by  an  outflowing 
current  of  air,  which,  diverted  to  the  right  of  the  gradient  by  the  earth's  rotation, 
appears  as  a  northeast  wind,  covering  the  China  Sea  and  the  northern  Indian  Ocean. 
Upon  entering  the  southern  hemispliere,  however,  the  same  force  which  hitherto 


WINDS.  211 

deflected  the  moving  air  to  the  right  of  the  gradient  now  serves  to  deflect  it  to  the 
left;  and  here,  accordingly,  we  have  the  monsoon  appearing  as  a  northwest  wind, 
covering  the  Indian  Ocean  as  far  south  as  10°,  the  Arafura  Sea,  and  the  northern 
coast  of  AustraUa. 

In  July  these  conditions  are  precisely  reversed.  Asia  is  now  the  seat  of  high 
temperature  and  correspondingly  low  pressure,  Australia  of  low  temperature  and 
high  pressure,  although  the  departure  from  the  annual  average  is  by  no  means  so 
pronounced  in  the  case  of  the  latter  as  in  that  of  the  former.  The  baric  gradients 
thus  lead  across  the  equator  and  are  addressed  toward  the  interior  of  the  greater 
continent,  giving  rise  to  a  system  of  winds  whose  direction  is  southeast  in  the  southern 
hemisphere,  southwest  in  the  northern. 

Tne  northeast  (winter)  monsoon  blows  in  the  China  Sea  from  October  to  April, 
the  southwest  (summer)  monsoon  from  May  to  September.  The  former  is  marked 
by  all  the  steadiness  of  the  trades,  often  attaining  the  force  of  a  moderate  gale ;  the 
latter  appears  as  a  light  breeze,  unsteady  in  direction,  and  often  sinking  to  a  calm. 
Its  prevalence  is  frequently  interrupted  by  tropical  cyclonic  storms,  locally  known 
as  typhoons,  although  the  occurrence  of  these  latter  may  extend  well  into  the  season 
of  the  winter  monsoon. 

469.  Land  and  Sea  Breezes. — Corresponding  with  the  seasonal  contrast  of 
temperature  and  pressure  over  land  and  water,  there  is  Ukewise  a  diurnal  contrast 
which  exercises  a  similar  though  more  local  effect.  In  summer  particularly,  the  land 
over  its  whole  area  is  warmer  than  the  sea  by  day,^  colder  than  the  sea  by  night,  the 
variations  of  pressure  thus  established,  although  insignificant,  sufficing  to  evoke  a 
system  of  littoral  breezes  directed  landward  during  the  daytime,  seaward  during  the 
n^ht,  which,  in  general,  do  not  penetrate  to  a  distance  greater  than  30  miles  on  and 
offshore,  and  extend  but  a  few  hundred  feet  into  the  depths  of  the  atmosphere. 

The  sea  breeze  begins  in  the  morning  hours — ^from  9  to  11  o'clock — as  the  land 
warms.  In  the  late  aitemoon  it  dies  away.  In  the  evening  the  land  breeze  springs 
up,  and  blows  gently  out  to  sea  until  mornmg.  In  the  tropics  this  process  is  repeated 
day  after  day  with  great  regularity.  In  our  own  latitudes,  the  land  and  sea  breezes 
are  often  masked  by  winds  of  cyclonic  origin. 

4:70.  A  single  important  effect  of  the  seasonal  variation  of  temperature  and 
pressure  over  the  land  remains  to  be  described.  If  there  were  no  land  areas  to  break 
the  even  water  surface  of  the  globe,  the  trades  and  westerlies  of  the  terrestrial  circu- 
lation would  be  developed  in  the  fullest  simphcity,  with  linear  divisions  along  latitude 
circles  between  the  several  members — a  condition  nearly  approached  in  the  land- 
barren  southern  hemisphere  during  the  entire  year,  and  m  tne  northern  hemisphere 
during  the  winter  season.  In  the  summer  season,  however,  the  tropical  belt  of  high 
pressure  is  broken  where  it  crosses  the  warm  land,  and  the  air  shouldered  off  from 
the  continents  accumulates  over  the  adjacent  oceans,  particularly  in  the  northern 
or  land  hemisphere.  This  tends  to  creato  over  each  of  the  oceans  a  circular  or 
eUiptical  area  of  high  pressure,  from  the  center  of  which  the  baric  gradients  radiate 
in  all  directions,  giving  rise  to  an  outflowing  system  of  winds,  which  by  the  effect  of 
the  earth's  rotation  is  converted  into  an  outflowing  spiral  eddy  or  anticyclonic  whirl. 
The  sharp  lines  of  demarcation  which  would  otherwise  exist  between  the  several 
members  of  the  general  circulation  are  thus  obhterated,  the  southwesterly  winds  of  the 
middle  northern  latitudes  becoming  successively  northwesterly,  northerly,  and  north- 
easterly, as  we  approach  the  equator  and  round  the  area  of  high  pressure  by  the  east; 
the  northeast  tracfe  becoming  successively  southeasterly,  southerly,  and  soutnwesterly, 
as  we  recede  from  the  equator  and  round  this  area  by  the  west;  similarly  for  the  other 
hemisphere. 


CHAPTER  XIX. 
OYOLOmO  STOEMS. 


4:71.  Variations  of  the  Atmospheric  Pressure. — Tlie  distribution  of  the 
atmospheric  pressure  previously  described  (Chap.  XVIII)  and  the  attendant  circu- 
lation of  the  winds  are  those  which  become  evident  after  the  effects  of  many  disturbing 
causes  have  been  eUminated  by  the  process  of  averaging,  or  embracing  m  the  sum- 
mation observations  covering  an  extended  period  of  time.  The  distribution  of 
pressure  and  the  system  of  winds  which  actually  exist  at  a  given  instant  will  in 
general  agree  with  these  in  its  main  features,  but  may  differ  from  them  materially 
m  detail. 

Confining  our  attention  for  the  time  being  to  the  subject  of  atmospheric  pressure, 
it  may  be  said  that  this,  at  any  given  point  on  the  earth's  surface,  is  in  a  constant 
state  of  change,  the  mercurial  oarometer  rarely  becoming  stationary,  and  then  only 
for  a  few  hours  in  succession.  The  variations  which  the  pressure  undergoes  may 
be  divided  into  two  classes,  viz,  periodic,  or  those  which  are  continuously  in  opera- 
tion, repeating  themselves  within  fixed  intervals  of  time,  long  or  short ;  and  non- 
periodic  or  accidental,  which  occur  irregularly,  and  are  of  varying  duration  and 
extent. 

472.  Periodic  Variations. — Of  the  former  class  of  changes  the  most  important 
are  the  seasonal,  which  have  been  already  to  some  extent  described,  and  the  diurnal. 
The  latter  consists  of  the  daily  occurrence  of  two  barometric  maxima,  or  points  of 
highest  pressure,  with  two  intervenmg  minima.  Under  ordinary  circumstances 
with  the  atmosphere  free  from  disturbances,  the  barometer  each  day  attains  its  first 
minimum  about  4  a.  m.  As  the  day  advances  the  pressure  increases,  and  a  maximum, 
or  point  of  greatest  pressure,  is  reached  about  10  a.  m.  From  this  time  the  pressure 
diminishes,  and  a  second  minimum  is  reached  about  4  p.  m.,  after  which  the  mercury 
again  rises,  reaching  its  second  maximum  about  10  p.  m.  The  range  of  this  diurnal 
oscillation  is  greatest  at  the  equator,  where  it  amounts  to  ten  hundredths  (0.10)  of 
an  inch.  It  diminishes  with  increased  latitude,  and  near  the  poles  it  seems  to  vanish 
entirely.     In  middle  latitudes  it  is  much  more  apparent  in  summer  than  in  winter. 

473.  NoNPERioDic  Variations. — The  equatorial  slope  of  the  tropical  belt  of 
high  pressure  which  encircles  the  globe  in  either  hemisphere  is  characterized  by  the 
marked  uniformity  of  its  meteorological  conditions,  the  temperature,  wind,  and 
weather  changes  proper  to  any  given  season  repeating  themselves  as  day  succeeds 
day  with  almost  monotonous  regularity.  Here  the  diurnal  oscillation  of  the*barom- 
eter  constitutes  the  main  variation  to  which  the  atmospheric  pressure  is  subjected. 
On  the  polar  slope  of  these  belts  conditions  the  reverse  of  these  obtain,  the  elements 
which  go  to  make  up  the  daily  weather  here  passing  from  phase  to  phase  without 
regularity,  with  the  result  that  no  two  days  are  precisely  ahke;  and  as  regards 
atmospheric  pressure,  it  may  be  said  that  in  marked  contrast  with  the  unifomuty  of 
the  torrid  zone,  the  barometer  in  the  temperate  zone  is  constantly  subjected  to  non- 
periodic  or  accidental  fluctuations  of  such  extent  that  the  periodic  diurnal  variation 
IS  scarcely  apparent,  the  mercurial  barometer  at  a  given  station  frequently  rising  or 
falling  several  tenths  of  an  inch  in  twenty-four  hours. 

474.  Progressive  Areas  of  High  and  Low  Pressure. — The  explanation  of 
this  rapid  change  of  conditions  is  found  in  the  approach  and  passage  of  extensive 
areas  oi  alternately  high  and  low  pressure,  which  affect  alike,  although  to  a  different 
degree,  aU  the  barometers  coming  withm  their  scope.  The  general  direction  of 
motion  of  these  areas  is  that  of  tne  prevailing  winds;  eastward,  therefore,  in  the 
latitudes  which  are  under  consideration. 

Taken  in  conjunction,  these  areas  of  high  and  low  pressure  exercise  a  controlling 
influence  over  the  weather  changes  of  the  temperate  zones.     As  the  low  area  draws 

212 


CYCLONIC  STORMS. 


213 


near,  the  sky  becomes  overclouded,  the  prevailing  westerly  wind  falls  awaj^,  and 
is  succeeded  by  a  wind  from  some  easterly  direction,  faint  at  first,  but  increasing  as 
the  pressure  continues  to  diminish;  the  lowest  pressure  having  oeen  reached,  the 
wind  again  goes  to  the  westward,  the  barometer  starts  to  rise,  and  the  weather  clears; 
all  marKing  the  eastward  recession  of  the  low  area  and  the  approach  of  the  subsequent 

The  first  stage  in  the  development  of  the  low  is  a  slight  diminution  of  the 
atmospheric  pressure,  amounting  in  general  to  not  more  than  one  or  two  hundredths 
of  an  inch,  throughout  an  area  covering  a  more  or  less  extensive  portion  of  the  earth's 
surface,  either  land  or  water,  but  far  more  frequently  over  the  former  than  over  the 
latter.  Shortly  after  the  advent  of  this  initiatory  fall  the  decrease  of  pressm-e 
throughout  some  small  region  within  the  larger  area  assumes  a  more  decided  character, 
the  mercury  here  standing  at  a  lower  level  than  elsewhere  and  reading  successively 
higher  as  we  go  outward,  the  region  thus  becoming,  as  it  were,  the  center  of  the  whole 
barometric  depression.  A  system  of  barometric  gradients  is  by  this  means  estab- 
lished, all  directed  radially  mward,  and  in  obedience  to  these  gradients  there  is  a 
movement  of  the  surface  air  toward  the  center  or  point  of  lowest  barometer.  The 
air  once  in  motion,  however,  the  effect  of  the  earth's  rotation  is  brought  into  play 
precisely  as  in  the  case  of  the  larger  movements  of  the  atmosphere,  with  the  result 
that  the  several  currents,  instead  of  following  the  natural  course  along  these  gradients, 
are  deflected  from  them,  in  the  northern  hemisphere  to  the  right  hand,  in  the  southern 
hemisphere  to  the  left,  the  extent  of  the  deflection  being  from  4  to  8  compass  points. 


AfUieyelonk. 


NOBTBERN  HEIOSPHEBE. 


cyclonic. 


Lew. 


AtUieyclonk. 


Cyclonic, 


SOUTHEKN  HEMISPHEEE. 

Fio.  70. 
The  light  arrows  show  the  direction  of  the  gradients;  the  heavy  arrows  the  direction  of  the  winds. 

475.  Cyclones  and  Cyclonic  Circulations. — ^A  central  area  of  low  barometer 
will  thus  be  surrounded  by  a  system  of  winds  which  constantly  draw  in  toward  the 
center  but  at  the  same  time  circulate  about  it,  the  whole  forming  an  inflowing  spiral; 
the  direction  of  this  circulation  being  in  the  southern  hemisphere  with  the  motion 
of  the  hands  of  a  watch,  in  the  northern  hemisphere  opposed  to  this  motion.  Where 
the  barometric  gradients  are  steep,  these  winds  are  apt  to  be  strong;  where  they  are 
gentle,  the  winds  are  apt  to  be  weak;  where  they  are  absent,  as  is  the  case  at  the 
center  or  bottom  of  the  depression,  calms  are  apt  to  prevail. 

Around  the  center  of  the  area  of  high  pressure  a  similar  systern  of  wind  will  be 
found,  but  blowing  in  a  contrary  direction.  Here  the  barometric  gradients  are 
directed  radially  outward,  with  the  result  that  in  place  of  the  inflowing,  we  have  an 
outflowing  spiral,  the  circulatory  motion  being  right  handed  or  with  the  hands  of 
a  watch  in  the  northern  hemisphere,  left  handed  or  against  the  hands  of  a  watch  in 
the  southern. 

All  these  features  are  shown  in  the  accompanying  diagrams  (fig.  70),  which 
exhibit  the  general  character  of  cyclonic  (arouna  the  low)  and  anticyclonic  (around 
the  high)  circulations  in  the  northern  and  the  southern  hemisphere,  respectively. 


214 


CYCLONIC   STORMS. 


The  closed  curves  represent  the  isobars,  or  Hnes  along  which  the  barometric  pressure 
is  the  same;  the  short  arrows  show  the  direction  of  the  gradients,  wliich  are  every- 
where at  right  angles  to  the  isobars;  the  long  arrows  give  the  direction  of  the  winds, 
deflected  by  the  earth's  rotation  to  the  right  of  the  gradients  in  the  northern  hemi- 
sphere, to  the  left  in  the  southern. 

476.  Features  of  Cyclonic  and  Anticyclonic  Regions. — Certain  features  of 
the  two  areas  may  here  be  contrasted.  In  the  anticyclonic,  the  successive  isobars 
are  as  a  rule  far  apart,  showing  weak  gradients  and  consequently  light  winds;  the 
areas  themselves  are  of  relatively  great  extent,  and  their  rate  of  progression  is  slow. 
During  the  summer  they  originate  as  extensions  into  higher  latitudes  of  the  margins 
of  the  tropical  belts  of  high  pressure;  during  the  winter,  as  offshoots  of  the  strong 
anticyclone  which  covers  the  land  throughout  that  season.  Their  approach  and 
jjresence  is  accompanied  by  polar  or  westerly  winds,  temperature  below  the  seasonal 
average,  fair  weather,  and  clear  skies.  In  the  cyclonic  area  the  successive  isobars 
are  crowded  together,  showing  steep  gradients  and  strong  winds;  they  may  appear 
either  as  trough-like  extensions  into  the  temperate  zone  of  the  polar  belt  of  low 
pressure,  in  which  case  the  easterly  winds  proper  to  their  polar  side  are  nonexistent, 
or  (in  lower  latitudes)  as  independent  areas,  sometimes,  indeed,  as  detached  portions 
of  the  equatorial  low-pressure  belt,  which  move  eastward  and  poleward  across  the 
temperate  zone,  and  are  ultimately  merged  into  the  great  cyclonic  area  surrounding 
the  pole.  The  progress  of  these  independent  areas  is  mvariably  attended  by  the 
strong  and  steadily  shiftmg  winds,  foul  weather,  and  other  features  which  make  up 
the  ordinary  storm  at  sea.  In  the  trough-like  depressions  of  higher  latitudes  these 
features  may  or  may  not  be  observed,  their  presence  depending  upon  the  depths  of 
the  barometric  trough  and  the  steepness  of  its  slopes.  In  these,  moreover,  the 
cyclonic  circulation  is  never  completely  developed,  the  storm  winds  having  rather 
the  character  of  right  line  gales,  blowing  from  an  equatorial  or  easterly  direction 
until  the  axis  of  the  trough  is  at  hand,  and  as  this  passes  shifting  by  the  west  at  one 
bound  to  a  polar  direction. 

477.  Cyclonic  Storms. — Strong  winds  are  the  result  of  steep  barometric 
gradients.  These  may  occur  with  cyclonic  or  with  anticyclonic  areas,  the  latter 
being  exemplified  in  the  case  of  the  northei*s  in  the  Gulf  of  Mexico  and  the  north- 
westerly winter  gales  along  the  Atlantic  coast  of  the  United  States,  which  are  almost 
invariably  accompanied  by  barometers  above  the  average.  They  are,  however,  so 
much  more  frequent  in  the  case  of  areas  of  low  pressure  and  consequent  cyclonic 
circulations,  with  their  attendant  foul-weather  characteristics,  that  the  latter  are 
generally  known  as  cyclonic  storms,  i.  e.,  storms  in  which  the  wind  circulation  is 
cyclonic. 

Cyclonic  storms  may  with  convenience  be  divided  into  two  classes :  viz,  tropical, 
or  those  which  originate  near  but  not  on  the  equator;  and  extra-tropical,  or  those 
which  first  appear  in  higher  latitudes. 

478.  Tropical  Cyclonic  Storms. — The  occurrence  of  tropical  cyclonic  storms 
is  confined  to  the  summer  and  autumn  months  of  the  respective  hemispheres,  and  to 
the  western  part  of  the  several  oceans,  the  North  Atlantic,  the  North  Pacific,  the 
South  Pacific,  and  the  Indian  Ocean.  They  are  unknown  in  the  South  Atlantic 
Ocean.  Although  these  cyclonic  storms  are  all  of  the  same  essential  characteristics, 
they  have  generally  been  called  hurricanes  when  occurring  in  the  West  Indies  and  the 
region  between  Samoa  and  Australia,  typhoons  when  occurring  in  the  region  of  the 
Philippines,  and  cyclones  when  occurring  in  the  Indian  Ocean  and  its  dependent  seas. 

The  limits  of  the  regions  within  which  these  tropical  storms  originate  are  defined 
by  parallels  of  latitude  and  meridians  of  longitude  as  follows : 


Hurricanes  of  the  West  Indies 

Typhoons  of  the  Pliilippine  region 

Cyclones  of  the  Bay  of  Bengal 

Cyclones  of  the  Indian  Ocean 

Hurricanes  of  the  Samoan  region . , 


Latitude. 


12° 

5 

8 

4 
10 


to  28< 
to  20 
to  22 
to  30 
to  30 


N. 
N. 
N. 
S. 
S. 


Longitude  from 
Greenwich. 


55°     to  95" 
150       to  115 
100       to  80 
100       to  40 
160  W.  to  150 


W. 
E. 
E. 
E. 
E. 


CYCLONIC   STOEMS. 


215 


The  percentage  of  frequency  of  these  storms  in  the  different  months  of  the  year 
is  set  forth  in  the  following  table : 


Hurricanes  of  the  West  Indies. . . . 
Typhoons  of  the  Philippine  region 
Cyclones  of  the  Bay  of  Bengal .  . . . 
Cyclones  of  the  Indian  Ocean..  . . 
Hurricanes  of  the  Samoan  region .  . 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

0 

0 

0 

0 

1 

6 

4 

25 

32 

31 

1 

2 

0.4 

1 

2 

5 

9 

16 

16 

19 

14 

11 

0 

0 

0 

0 

6 

12 

19 

15 

20 

14 

10 

22 

19 

18 

15 

6 

1 

0.5 

0 

0 

1.5 

7 

29 

17.5 

28 

6 

1 

0 

0 

0 

1.5 

1 

3 

Dec. 


0 

5 

4 

10 

13 


The  yearly  average  number  of  those  occurring  in  the  West  Indian  region  is  4,  in 
the  PhiUppine  region  21,  in  the  Bay  of  Bengal  9,  in  the  Indian  Ocean  (south  of  the 
Equator)  9,  and  in  th6  region  between  Samoa  and  Australia  4. 

479.  Motion  of  the  Storm  Center. — In  the  case  of  tropical  cyclonic  storms 
there  is  always  a  tendency  for  the  barometric  depression,  impelled  by  the  general 
motion  of  the  atmosphere  in  the  trade-wind  region,  to  follow  a  path  wliich  tends  at 
once  westward  and  away  from  the  equator.  This  motion  contmues  until  the  limits 
of  the  trades  are  reached,  where  the  path  ordinarily  recurves;  and  the  subsequent 
motion  of  the  depression  is  eastward  and  toward  tne  pole,  the  disturbance  at  the 
same  time  assummg  the  features  of  the  extra-tropical  cyclonic  storm. 

Rate  of  progress  of  the  storm  center. — Within  the  tropics  in  the  northern  hemi- 
sphere, the  average  velocity  of  the  storm  center  along  the  path  is  11  miles  an  hour; 
and  in  the  latitude  of  the  recurvature  of  the  storm  this  average  is  maintained, 
although  there  are  numerous  instances  of  wide  variations  in  the  rate  of  process  here, 
and  sometimes  the  center  becomes  stationary  for  a  few  days.  In  higher  latitudes,  the 
rate  increases  to  an  average  of  16  miles  an  hour. 

In  the  southern  hemisphere,  the  average  velocity  of  progress  as  far  as  determined 
is  somewhat  less  than  in  the  northern;  and,  in  the  Indian  Ocean,  many  of  the  Mauri- 
tius cyclones  have  a  very  small  movement  of  translation,  and  these  are,  in  conse- 
quence, designated  as  stationary  cyclones. 

The  general  path  of  the  tropical  cyclonic  storm  in  either  hemisphore  and  the 
cyclonic  circulation  of  the  wind  about  the  storm  center  are  given  in  figures  73  and 
74;  that  for  the  northern  hemisphere  applying  to  the  hurricanes  of  the  West  Indies; 
that  for  the  southern  hemisphere  to  the  hurricanes  of  the  South  Pacific  Ocean. 

480.  Indications  of  the  Approach  of  Tropical  Cyclonic  Storms. — The 
premonitory  signs  of  a  tropical  cyclonic  storm  comprise,  besides  those  feeUngs  of 
personal  discomfort  which  are  common  within  the  sphere  of  atmospheric  disturbance 
of  cyclonic  storms  in  all  parts  of  the  world,  (1)  an  unsteady  barometer,  or  even  a 
cessation  of  the  diurnal  range,  which  is  constant  in  settled  weather;  (2)  a  heavy 
swell  not  caused  by  the  wind  then  blowing;  (3)  the  appearance  of  the  sky  arising 
from  the  forms  and  movements  of  the  clouds.  It  is  upon  the  concomitance  of  these 
indications,  rather  than  the  recognition  of  any  one  oi  them,  that  reliance  should  be 
placed. 

The  appearance  of  the  clouds  and  their  value  as  storm  warnings  is  described  as 
follows  by  Faura  in  the  Cyclones  of  the  Far  East,  by  Jos6  Algue,  of  the  Manila 
Observatory: 

The  best  means  for  determining  the  center  [of  a  storm]  and  for  following  up  its  movements  are  the 
observations  of  cirri,  little  clouds  of  a  very  fine  structure  and  clear  opal  color,  which  appear  aa  elongated 
feathers.  *  *  *  Long  before  the  least  sign  of  bad  weather  ia  noticeable  and  in  many  cases  when  the 
barometer  is  still  very  high — being  under  the  influence  of  a  center  of  high  pressure,  which  generally 
precedes  a  tempest — these  small  isolated  clouds  appear  in  the  upper  regions  ot  the  atmosphere.  They 
seem  to  be  piled  up  on  the  blue  vault  of  heaven  and  drawn  out  in  the  direction  of  some  point  on  the 
horizon  toward  which  they  converge.  The  first  to  present  themselves  are  few  in  number  but  well  defined 
and  of  the  most  delicate  structure,  appearing  like  filaments  bound  together  but  whose  visibility  is  lost 
before  they  reach  the  point  of  radiation.  We  often  had  an  opportunity  to  watch  them  at  the  observatory 
of  Manila,  when  the  center  was  still  600  miles  distant.  The  best  times  for  observing  the  cirri  are  sunrise 
and  sunset.  If  the  sun  is  in  the  east  and  very  near  the  horizon,  the  first  clouds  which  are  tinged  by 
the  solar  rays  are  the  cirro-strati  which  precede  the  cyclone,  and  they  are  also  the  last  to  disappear  at 
sunset,  inasmuch  as  they  overspread  the  horizon.  Such  times  are  the  best  for  determining  the  radiant 
point  of  the  cloud  streaks  and  at  the  same  time  for  ascertaining  the  direction  in  which  the  center  lies.  Later 
on  the  delicacy  of  form,  which  characterizes  this  class  of  clouds  in  its  earlier  stages,  is  lost,  and  the  clouds 


216 


CYCLONIC   STORMS. 


appeax  in  more  confused  and  tangled  forms^  like  streamers  of  feather  work,  with  central  nuclei,  which 
Btill  maintain  this  direction,  so  that  the  point  of  radiation  can  still  be  detected.  In  order  to  ascertain 
approximately  the  direction  in  which  the  center  is  advancing  in  its  movement  of  translation,  it  is  necessary 


Fig.  71.— Average  Paths  of  Hurricanes  In  the  West  Indies. 

The  small  circles  indicate  the  jwints  of  origin  of  130  storms,  which  comprise  all  the  instances 
resulting  from  the  authentic  accounts  of  a  period  of  35  years. 

dD  June  and  July  storms  ®  September  storms 

0  August  storms  O  October  storms 

to  determine  the  changes  of  the  radiant  point  at  equal  intervals  of  time  and  to  compare  them  with  the 
movements  of  the  barometer.  If  the  point  of  convergence  does  not  perceptibly  change  its  position,  but 
remains  fixed  and  immovable  for  a  long  time,  even  for  several  consecutive  days,  it  is  almost  certain  that 


CYCLONIC  STOBMS. 


217 


the  tempest  will  break  over  the  poeition  of  the  observer.     In  this  case  the  barometer  begins  to  fall  shortly 
after  the  first  cirrus  clouds  have  been  observed  and  sometimes  even  before.    At  first  it  falls  slowly,  without 


Fig.  72.— Mean  Paths  of  Typhoons. 

1.  Typhoons  In  the  Marianas. 

2.  Typhoons  formed  in  the  Pacific  which,  at  some  distance  east  of  the  meridian  of  Manila,  have  recurved  toward 

Japan. 
3  and  3a.  Typhoons  formed  in  the  Pacific  which,  near  the  meridian  of  Manila,  have  recurved  toward  Japan. 
4.  Typhoons  of  Taiwan  or  Formosa.  ' 

6  and  5a.  Typhoons  of  northern  Luzon  which  have  recurved  In  the  island  or  near  it  in  the  China  Sea. 

6.  Typhoons  which  have  crossed  Luzon  northward  of  Manila  and  continued  to  the  continent. 

7.  Typhoons  which  have  crossed  Luzon  southward  of  Manila. 

8.  Typhoons  of  the  Visavas  and  Mindanao. 

9.  Typhoons  formed  In  the  Pacific  which  have  crossed  south  of  Manila,  recurved  In  the  Cliina  Sea  between  latitudes 

10  degrees  and  20  degrees,  and  recrossed  north  of  Manila. 

10.  Typhoons  formed  in  the  China  Sea. 

11.  Typhoons  formed  in  the  Sulu  Sea  and  the  Interlsland  waters. 

completely  losing  the  diurnal  and  nocturnal  oscillatory  movements,  but  changing  somewhat  the  hours 
of  maximum  and  minimum.    The  daily  reading  is  observed  to  be  each  day  less  than  that  of  the  preceding 


218 


CYCLONIC   STOEMS. 


day.  That  part  of  the  horizon  in  the  direction  of  the  storm  begins  to  be  covered  by  a  cirrug  veil,  which 
increases  slowly  until  it  forms  an  almost  homogeneous  covering  of  the  sky.  This  veil  is  known  by  the 
name  "cirro-pallium"  of  Poey,  and  ia  that  which  causes  the  solar  and  lunar  halos,  which  are  never 
absent  when  a  storm  approaches.  Beneath  the  veil  a  few  isolated  clouds,  commonly  called  "cotton," 
appear.  They  are  much  more  numerous  and  larger  on  the  side  lying  toward  the  storm,  where  they  soon 
appear  as  a  compact  mass.  At  such  times  the  sunrises  and  sunsets  are  characterized  by  the  high  red 
tint  which  the  clouds  assume,  resembling  a  great  fire,  especially  in  the  direction  of  the  cyclone.  The 
wind  remains  fixed  at  one  point,  showing  only  a  few  variations,  which  are  due  principally  to  the  squalls, 
which  continually  exert  their  force  within  the  limits  of  the  storm.  The  low  or ' '  cotton  clouda  successively 
and  from  time  to  time  cover  the  sky,  throwing  out  occasional  squalls  of  rain  and  wind;  but,  the  squalls 
having  passed,  a  lull  ensues,  the  cirrus  veil  remaining,  and  likewise  the  hurricane  bank  of  clouds,  which 
seems  fixed  to  the  same  spot  in  the  direction  of  the  storm.    This  state  of  the  atmosphere  continues  until 

the  bank  of  clouda  invades 
the_  point  of  observation,  in 
which  case  the  squalls  will 
be  continuous  and  the  wind 
will  increase  in  violence  each 
moment. 

The  condition  of 
diminished  pressure  at- 
tending a  cyclonic 
storm  gives  rise  to  high 
waves  which  are  propa- 
gated in  all  directions 
from  such  a  storm  on 
the  ocean.  These 
waves  outrun  the  storm 
as  much  as  a  thousand 
miles,  and,  by  the  di- 
rection from  which  they 
arrive,  indicate  the 
bearing  of  the  storm's 
center. 

Although  thunder- 
storms can  not  be  con- 
sidered as  premonitory 
signs,  it  rarely  happens 
that  showers  and 
squalls  are  not  experi- 
enced from  24  to  48 
hours  in  advance  of  the 
jioma*  storm;  and  the  un- 
settled state  of  the  ba- 
rometer in  the  distant 
approaches,  varying 
from  500  to  1,000  miles 
in  advance  of  the  cen- 
ter, gives  place,  at  a 
distance  of  300  to  400 
miles,^  to  a  slow  and  steady  fall  of  the  mercurial  column.  At  the  same  time  the 
direction  and  velocity  of  the  lower  clouds  show  unmistakable  evidence  of  the 
presence  of  a  storm  and  the  bearing  of  the  center.  When  the  storm  center  is 
stiU  far  distant,  the  phenomenon  called  the  "bar  of  the  cyclone"  may  frequently  be 
seen.  This  is  a  dense  mass  of  rain  cloud  formed  about  the  center  of  tne  storm, 
giving  the  aj)pearance  of  a  huge  bank  of  black  clouds  resting  upon  the  horizon,  which 
may  retain  its  form  unchanged  for  hours.  It  is  usually  most  conspicuous  about 
sunrise  or  sunset.  When  it  is  possible  to  observe  this  bar,  the  changes  in  its  position 
at  intervals  of  a  few  hours  will  enable  the  observer  to  determine  the  direction  of 
movement  of  the  storm. 

481.  Chaeacter  of  Teopical  Cyclonic  Stoems. — Within  the  tropics  the 
storm  area  is  small,  the  region  covered  by  violent  winds  extending  in  general  not 
more  than  150  miles  from  the  center.  The  barometric  gradients  are,  however, 
exceedingly  steep,  instances  having  been  recorded  in  which  the  difference  of  pressure 


FtQ.  73. 


CYCLONIC   STORMS. 


219 


10' 


for  this  distance  amounted  to  2  inches.  In  the  typhoons  of  the  North  Pacific  Ocean 
gradients  of  one  inch  in  60  miles  are  not  infrequent.  The  successive  isobars  are 
almost  circular.  As  a  consequence  of  this  distribution  of  pressure  the  wiads  on  the 
slopes  of  the  depression  are  frequently  of  great  violence,  and  in  the  matter  of  direc- 

^  tion  they  are  more  sym- 

'fQ^,    .    .    1    I    .    .    I    I  '^°  I I    [Mqo  metrically  disposed  about 

^'^  '''      the   center   tnan  is   the 

case  with  the  larger  and 
less  regularly  shaped  de- 
pressions of  higher  lati- 
tudes. In  these  low  lati- 
tudes the  average  values 
of  the  deflection  of  the 
wind  from  the  baromet- 
ric gradient  is  in  the 
neighborhood  of  six  com- 
pass points — to  the  right 
m  the  northern  hemi- 
sphere, to  the  left  in  the 
southern. 

482.  To  Fix  the 
Bearing  op  the  Storm 
Center  from  the  Ves- 
sel.— On  this  assump- 
tion, the  following  rules 
will  enable  an  observer 
to  fix  the  bearing  of  the 
20' storm  center  from  his 
vessel: 

In  the  northern  hem- 
isphere, stand  with  the 
face  to  the  wind;  the 
storm  center  will  bear  ten 
points  to  the  observer's 
right. 

In  the  southern  hem- 
isphere, stand  with  the 
face  to  the  wind;  the 
storm  center  wiU  bear  ten 
points  to  the  observer's 
left. 

On  the  basis  of  these 
rules  the  tables  hereafter 
given  (art.  487)  show  the 
bearing  of  the  center 
corresponding  to  a  wind 
of  any  direction. 

483.  To  Fix  the  Distance  of  the  Storm  Center  from  the  Vessel. — The 
following  table,  taken  from  Piddington's  "Sailor's  Horn  Book,"  may  prove  of  some 
assistance  in  estimating  the  distance  of  the  storm  center  from  the  vessel: 


30 


180 


Fig.  74. 


Average  fall  of  the  barometer 
per  hour. 

From  0.  02  to  0.  06  in. 
From  0.  06  to  0. 08  in. 
From  0.  08  to  0. 12  in. 
From  0. 12  to  0. 15  in. 


Distance  from  the  storm 
center. 

From  250  to  150  miles. 
From  150  to  100  miles. 
From  100  to  80  miles. 
From   80  to   60  miles. 


The  table  assmnes  that  the  vessel  is  hove-to  in  front  of  the  storm  and  that  the 
latter  is  advancing  directly  toward  it. 


220  CYCLONIC  STOEMS. 

Inasmuch  as  cyclones  are  of  varying  area  and  of  different  intensities,  the  Unes  of 
equal  barometric  pressure  (isobars)  lie  much  closer  together  in  some  storms  than  in 
others,  so  that,  in  the  circumstances  of  an  observer  on  the  ocean,  the  estimation  of 
the  distance  of  the  center  by  the  height  of  the  mercurial  column  or  of  its  rate  of  fall 
must  be  somewhat  conjectural. 

484:.  To  Avoid  the  Center  of  the  Storm. — In  the  immediate  neighborhood 
of  the  center  itself  the  winds  attain  full  hurricane  force,  the  sea  is  exceedingly 
turbulent,  and  there  is  danger  of  being  taken  aback.  Every  effort  should  therefore 
be  made  to  avoid  this  region,  either  by  running  or  by  heaving- to;  and  if  recourse  is 
had  to  the  latter  maneuver,  much  depends  upon  the  selection  of  the  proper  tack; 
this  being  in  every  case  the  tack  which  will  cause  the  wind  to  draw  aft  with  each 
successive  shift. 

A  vessel  hove-to  in  advance  of  a  tropical  cyclonic  storm  will  experience  a  long 
heavy  swell,  a  falling  barometer  with  torrents  of  rain,  and  winds  of  steadily  increasing 
force.  The  shifts  of  wind  will  depend  upon  the  position  of  the  vessel  with  respect 
to  the  path  followed  by  the  storm  center.  Immediately  upon  the  path,  the  wind 
will  hold  steady  in  direction  until  the  passage  of  the  central  calm,  tne  "eye  of  the 
storm,"  after  which  the  gale  will  renew  itself,  but  from  a  direction  opposite  to  that 
which  it  previously  had.  To  the  right  of  the  path,  or  in  the  right-hand  semicircle 
of  the  storm  (the  observer  being  supposed  to  face  along  the  track),  the  wind,  as  the 
center  advances  and  passes  the  vessel,  wiU  constantly  shift  to  the  right,  the  rate  at 
which  the  successive  shifts  follow  each  other  increasing  with  the  proximity  to  the 
center;  in  this  semicircle,  then,  in  order  that  the  wind  shall  draw  aft  with  each 
shift,  the  vessel  must  be  hove-to  on  the  starboard  tack;  similarly,  in  the  left-hand 
semicircle,  the  wind  will  constantly  shift  to  the  left,  and  here  the  vessel  must  be 
hove-to  on  the  port  tack. 

These  rules  hold  alike  for  both  hemispheres  and  for  cyclonic  storms  in  all 
latitudes. 

Figure  75  represents  a  cyclonic  storm  in  the  northern  hemisphere  after  reciu*vin^. 
For  simpUcity  the  area  of  low  barometer  is  made  perfectly  circular,  and  the  center  is 
assumed  to  be  ten  points  to  the  right  of  the  direction  of  the  wind  at  all  points  within 
the  disturbed  area.  Let  us  assume  that  the  center  is  advancing  about  NNE.,  in  the 
direction  of  the  long  arrow,  shown  in  heavy  full  hne.  The  ship  a  has  the  wind  at 
ENE.;  she  is  to  the  left  of  the  track,  or  technically  in  the  navigable  semicircle. 
The  ship  h  has  the  wind  at  ESE.  and  is  in  the  dangerous  semicircle.  As  the  storm 
advances  these  ships,  if  lying  to,  a  upon  the  port  tack,  h  upon  the  starboard  tack,  as 
shown,  take  with  regard  to  the  storm  center  the  successive  positions  a,  a^,  etc.,  6,  \, 
etc.,  the  wind  of  ship  a  shifting  to  the  left,  of  ship  6  to  the  right,  or  in  both  cases 
drawing  aft,  and  thus  diminishing  the  probabihty  of  either  ship  being  taken  aback, 
a  danger  to  which  a  vessel  lying  to  on  the  opposite  tack  (i.  e.,  the  starboard  tack  In 
the  left-hand  semicircle  or  the  port  tack  in  the  right-hand  semicircle)  is  constantly 
exposed,  the  wind  in  the  latter  case  tending  constantly  to  draw  forward.  The  ship  6 
is  continually  beaten  by  wind  and  sea  toward  the  storm  track.  The  ship  a  is  drifted 
away  from  the  track,  and,  should  she  be  able  to  carry  sail,  would  soon  find  better 
weather  by  running  off  to  the  westward. 

It  must  not  be  forgotten  that  the  shifts  of  wind  will  only  occur  in  the  above  order 
when  the  vessel  is  stationary.  When  the  course  and  speed  are  such  as  to  maintain 
a  constant  relative  bearing  between  the  ship  and  storm  center,  there  will  be  no  shift 
of  wind.  Should  the  vessel  be  outrunning  the  storm,  the  wind  will  indeed  shift  in 
the  opposite  direction  to  that  given,  and  a  navigator  in  the  right  semicircle,  for 
instance,  and  judging  only  by  the  shifts  of  wind  without  taking  into  account  his  own 
run,  might  imagine  himself  on  the  opposite  side.  In  such  a  case  the  barometer  must 
be  the  guide. 

An  examination  of  figure  75  shows  how  this  is.  A  vessel  hove  to  at  the  position 
marked  &,  and  being  passed  by  the  storm  center,  will  occupy  successive  positions  in 
regard  to  the  center  from  h  to  O4,  and  wiU  experience  shifts  of  wind,  as  shown  by  the 
arrows,  from  East  through  South  to  SW.  On  the  other  hand,  if  the  storm  center 
be  stationary  or  moving  slowly  and  a  vessel  be  overtaking  it  along  the  line  from  64 
to  h,  the  wiad  will  back  from  SW.  to  East,  and  is  likely  to  convey  an  entirely  wrong 
impression  as  to  the  location  and  movement  of  the  center. 


CYCLONIO    STORMS. 


221 


485.  Dangerous  and  Navigable  Semicircles. — Prior  to  recurving,  the  winds 
in  that  semicircle  of  the  storm  which  is  more  remote  from  the  equator  (the  right- 
hand  semicircle  in  the  northern  hemisphere,  the  left-hand  semicircle  in  the  southern) 
are  liable  to  be  more  severe  than  those  of  the  opposite  semicircle.  A  vessel  hove  to 
in  the  semicircle  adjacent  to  the  equator  has  also  the  advantage  of  immunity  from 
becoming  involved  in  the  actual  center  itself,  inasmuch  as  there  is  a  distinct  tendency 
on  the  part  of  the  latter  to  move  away  from  the  equator.  For  these  reasons  the  more 
remote  semicircle  has  been  called  the  dangerous,  the  less  remote  the  navigahle. 

486.  Maneuvering. — A  vessel  suspecting  the  dangerous  proximity  of  a  tropical 
cyclonic  storm  should  lie-to  for  a  time  on  the  starboard  tack  to  locate  the  center  by 
observing  shifts  of  the  wind  and  the  behavior  of  the  barometer.    If  the  former  holds 

N 


steady  and  increases  in  force,  while  the  latter  falls  rapidly,  say  at  a  greater  rate  than 
0.03  of  an  inch  per  hour,  the  vessel  is  probably  on  the  track  of  the  storm  and  in  advance 
of  the  center.  In  this  position  the  proper  step  (providing,  of  course,  that  sea  room 
permits)  is  to  run,  keepmg  the  wind,  in  the  northern  hemisphere,  at  all  times  well  on 
the  starboard  quarter;  in  the  southern  hemisphere,  well  on  the  port;  and  thus 
constantly  increasing  the  distance  to  the  storm  center.  The  same  rule  holds  good 
if  the  observation  places  the  vessel  at  but  a  scant  distance  within  the  forward  quadrant 
of  the  dangerous  semicircle.  Here,  too,  the  natural  course  will  be  to  seek  the  navigable 
semicircle  of  the  storm,  even  though  such  a  course  involves  crossing  the  track  m 
advance  of  the  center,  always  exercising  due  caution  to  keep  the  winafrom  drawing 
too  far  aft. 


222  CYCLONIC    STORMS. 

The  critical  case  is  that  of  a  vessel  which  finds  herself  in  the  forward  quadrant 
of  the^  dangerous  semicircle  and  at  a  considerable  distance  from  the  track,  for  here 
the  shifts  of  the  wind  are  sluggish  and  the  indications  of  the  barometer  are  undecided, 
both  causes  conspiring  to  render  the  bearing  of  the  center  doubtful.  If,  upon 
heaving  to,  the  barometer  becomes  stationary,  the  position  should  be  maintained 
until  indications  of  a  rise  are  apparent,  upon  which  the  course  may  be  resumed  with 
safety  and  held  as  long  as  the  rise  contmues.  If,  however,  the  barometer  falls,  a 
steamer  should  make  a  run  to  the  NNE.  or  NE.  (southern  hemisphere,  SSE.  or  SE.), 
keeping  the  wind  and  sea  a  little  on  the  port  (southern  hemisphere,  starboard)  bow, 
and  usmg  such  speed  as  will  at  least  keep  the  barometer  stationary.  Such  a  step  will 
in  general  be  attended  with  the  assurance  that  the  present  weather  conditions  will 
in  any  case  grow  no  worse.  For  a  saiUn^  vessel,  unable  to  stand  closer  to  the  wind 
than  six  points,  the  last  maneuver  will  be  impossible,  and  driven  to  leeward  by  wind, 
sea,  and  current,  she  may  be  compelled  to  cross  the  track  immediately  in  advance 
of  the  center,  or  may  even  become  involved  in  the  center  itself.  In  this  extremity 
the  path  of  the  storm  center  during  the  past  twenty-four  hours  should  be  laid  down 
on  a  diagram  as  accurately  as  the  observations  permit,  and  the  line  prolonged  for 
some  distance  beyond  the  present  position  of  the  center.  Having  assumed  an  average 
rate  of  progress  for  the  center,  its  probable  position  on  the  line  should  be  frequently 
and  carefully  plotted,  and  the  handling  of  the  vessel  should  be  in  accordance  with 
the  diagram. 

487.  Summary  of  Rules. — The  following  summary  comprises  the  rules  of 
maneuvering,  so  far  as  they  may  be  made  general: 

NORTHERN   HEMISPHERE. 

In  the  Right  or  Dangerous  Semicircle. — Steamers  bring  the  wind  on  the  starboard 
bow,  and  make  as  much  way  as  possible;  if  obliged  to  heave  to,  do  so  head  to  sea. 
Saihng  vessels  haul  by  the  wind  on  the  starboard  tack  and  carry  sail  as  long  as  possible ; 
if  obliged  to  heave  to,  do  so  on  the  starboard  tack. 

In  the  Left  or  Navigable  Semicircle. — Bring  the  wind  on  the  starboard  quarter, 
note  the  course,  and  hold  it ;  if  obhged  to  heave  to,  do  so  on  the  port  tack,  unless  in 
a  steamer  which  behaves  better  when  hove  to  stern  to  the  sea. 

On  the  Storm  Track  in  Front  of  the  Center. — Bring  the  wind  two  points  on  the 
starboard  quarter,  and,  holding  this  course,  run  for  the  Left  Semicircle;  if  obhged 
to  heave  to,  do  so  on  the  port  tack,  unless  in  a  steamer  which  behaves  better  when 
hove  to  stern  to  the  sea. 

On  the  Storm  TracJc  in  Rear  of  the  Center. — Avoid  the  center  by  the  best 
practicable  route,  having  due  regard  to  the  tendency  of  cyclones  to  recurve  to  the 
northward  and  eastward. 

SOUTHERN   HEMISPHERE. 

In  the  Left  or  Dangerous  Semicircle. — Steamers  bring  the  wind  on  the  port  bow, 
and  make  as  much  way  as  possible;  if  obhged  to  heave  to,  do  so  head  to  sea.  SaiUng 
vessels  haul  by  the  wind  on  the  port  tack,  and  carry  sail  as  long  as  possible ;  if  obHged 
to  heave  to,  dx)  so  on  the  port  tack. 

In  the  Right  or  Navigable  Semicircle. — Bring  the  wind  on  the  port  quarter,  note 
the  course,  and  hold  it;  if  obhged  to  heave  to,  do  so  on  the  starboard  tack,  unless  in 
a  steamer  which  behaves  better  when  hove  to  stern  to  the  sea. 

On  the  Storm  TracTc  in  Front  of  the  Center. — Brin^  the  wind  two  points  on  the 
port  quarter,  and,  holding  this  course,  run  for  the  right  semicircle;  if  obliged  to 
heave  to,  do  so  on  the  starooard  tack,  unless  in  a  steamer  which  behaves  better  when 
hove  to  stern  to  the  sea. 

On  the  Storm  TracTc  in  Rear  of  the  Center. — Avoid  the  center  by  the  best  practi- 
cable route,  having  due  regard  to  the  tendency  of  cyclones  to  recurve  to  the  south- 
ward and  eastward. 


CYCLONIC    STOEMS. 


223 


The  application  of  these  rules  for  the  various  directions  of  the  wind  is  shown 
in  the  following  table: 

Storm  Table,  Northern  Hemisphere. 


Direction 
of  wind. 

Direction 
of  center. 

Observer  facing  along  storm  track. 

If  wind  shifts  toward 
the  right. 

If  wind  shifts  toward 
the  left. 

If  wind  steady  with 
falling  barometer. 

If  wind  steady  with 
rising  barometer. 

North. 

NNE. 

NE. 

ENE. 

East. 

ESE. 

SE. 

SSE. 

South. 

SSW. 

SW, 

wsw. 

West. 
WNW. 

NW. 
NNW. 

ESE. 
SE. 

SSE. 
South. 

SSW. 

SW. 
WSW. 

West. 
WNW. 

NW. 
NNW. 
North. 

NNE. 

NE. 

ENE. 

East. 

Steamers  bring  wind  on  starboard 
bow  and  make  as  much  way  as 

§ossible;  if  obliged  to  heave  to, 
0  so  head  to  sea. 
Sailing  vessels  haul  by  wind  on 
starboard  tack  and  carry  sail  as 
long  as  possible;  if  obliged   to 
heave  to,  do  so  on  starboard  tack. 

Run  SSW.          a 
RunSW.     -gS^I 
RunWSW,  ;i,o^ 
Run  West,    gSo 
Run  WNW.  £.^^ 
RunNW.     '^o 
Run  NNW.      ?  « 
Run  North,      b-  » 
Run  NNE.       ^^ 
RunNE.         ^3 
Run  ENE.       g-^ 
Run  East.       -    «" 
Run  ESE.        g-'g 
RunSE.           ^  S 
Run  SSE.        °  ? 
Run  South,      g  if 

Run  SSW.           a 
RunSW,     'gg-S' 
RunWSW,  3-K^ 
Run  West,    g  (ti  o 
Run  WNW.  SL^^ 
RunNW.     •   S^® 
Run  NNW,      tr" 
Run  North,      g  -- 
Run  NNE.       <a 
RunNE.         *^ 
Run  ENE.      P  » 
Run  East.        o.'g 
Run  ESE.        OS. 
RunSE.           00  cr 
Run  SSE.        °if 
Run  South,      g  -; 

Run  SSW.           a 
RunSW.      a-K.-2. 
RunWSW.  ^o<^ 
Run  West.   oSS 
Run  WNW.  3  "§  i 
RunNW.     ^^^ 
Run  NNW.  S  S"  « 
Run  North.  f^B'S 
Run  NNE.       g  5- 
RunNE.         ^^ 
Run  ENE.       g-^ 
Run  East.       -    * 
Run  ESE.        g-'g 
RunSE.          ao  S 
Run  SSE.        ®  o-' 
Run  South,      gjf 

o  Courses  given  are  for  wind  two  points  on  starboard  quarter,  but  it  is  preferable  to  take  wind  broad  on  quarter  If  possible. 

Storm  Table,  Southern  Hemisphere. 


Direction 
of  wind. 

Direction 
of  center. 

Observer  facing  along  storm  track. 

If  wind  shifts  toward 
the  right. 

If  wind  shifts  toward 
the  left. 

If  wind  steady  with 
falling  barometer. 

If  wind  steady  with 
rising  barometer. 

North. 

NNE. 
NE. 

ENE. 

East. 

ESE. 
SE. 

SSE. 
South. 

SSW. 

SW. 

WSW. 

West. 
WNW. 

NW. 
NNW. 

WSW. 

West. 
WNW. 

NW. 
NNW. 
North. 

NNE. 

NE. 

ENE. 

East. 

ESE. 
SE. 

SSE. 
South. 

SSW. 

sw. 

Run  SSE.            a 
Run  South.  S.Ka 
Run  SSW.    1,0,0- 
RunSW.      oKo 
RunWSW.  ^=!?S 
Run  West.    ^^^ 
Run  WNW.  g  0  ° 
RunNW.     .t^B-g 
Run  NNW.      $  ^ 
Run  North,      i  » 
Run  NNE.      p-^ 
Run  NE.         -    S 
Run  ENE.       g-'g 
Run  East.        a,  S 
Run  ESE.        °  5-* 
Run  SE.          g  « 

Steamers  bring  wind  on  port  bow 
and  make  as  much  way  as  possi- 
ble; if  obliged  to  heave  to,  do  so 
head  to  sea. 

Sailing  vessels  haul  by  wind  on 
port  tack,  and  carry  sail  aa  long 
as  possible ;  if  obliged  to  heave  to, 
do  so  on  port  tack. 

Run  SSE.            a 
Run  South,  g-g-g- 
Run  SSW.    Sk^ 
RunSW.      o'So 
RunWSW.  I^^l 
Run  West.    ^0^ 
RunWNW.g^g 
RunNW.     r%^ 
Run  NNW.      <3 
Run  North.      ®  ^ 
Run  NNE.      S>  ^ 
RunNE.          ^'g 
Run  ENE.       oS 
Run  East.        ^  5; 
Run  ESE.        °  ?. 
Run  SE.          g  - 

Run  SSE.           a 
Run  South,  "g  K.-S- 
Run  SSW,    3-0.^ 
RunSW.      gK§ 
RunWSW.  £.^  S 
Run  West.    •    ^.g 
Run  WNW.     S  » 
RunNW,         B-g 
Run  NNW,      g  ^ 
Run  North,      ^3 
Run  NNE,      ^  ' 
Run  NE,          °  ^ 
Run  ENE.       %-^ 
Run  East.        „  S 
Run  ESE,        °  5-' 
Run  SE.          g  a 

a  Courses  given  are  for  wind  two  points  on  port  quarter,  but  it  is  preferable  to  take  wind  broad  on  quarter  if  possible. 

488.  Extra-Tropical  Cyclonic  Storms, — On  turning  to  the  cyclones  of  tem- 
perate latitudes,  we  find  many  features  in  which  they  resemble  those  of  the  torrid 
zone,  but  certain  other  features  in  which  they  differ.  Their  fundamental  resemblance 
to  tropical  cyclones  is  seen  in  their  incurving  winds,  forming  an  inflowing  left-handed 
spiral  about  the  center  of  low  pressure  in  the  northern  hemisphere,  an  inflowing  right- 
handed  spiral  in  the  southern.  The  intensity  of  these  winds  varies  with  the  depth  of 
the  barometric  depression.  The  depression  itseK,  however,  in  place  of  covering  a  few 
miles,  as  is  the  case  in  the  tropics,  will  frequently  have  a  diameter  of  several  hundred 
or  even  a  thousand  miles,  and  for  some  distance  around  the  center  the  gradients  will 
have  a  tolerably  strong  value.  For  this  reason  there  is  less  concentration  of  violence 
close  to  the  center,  and  the  calm  and  clear  central  space,  or  "eye,"  is  seldom  sharply 
developed,  although  it  is  not  uncommon  to  discover  a  gradual  "weakening  or  faihng 


224 


CYCLONIC    STOBMS. 


of  the  winds,  and  sometimes  even  an  imperfect  breaking  away  of  the  clouds  as  the 
central  area  passes  over  the  observer.  The  form  of  tropical  cyclones  as  defined  by 
their  isobaric  lines  is  nearly  circular.  Extra-tropical  cyclones  are  as  a  rule  less 
symmetrical,  and  their  isobars  are  often  elongated  mto  an  oval  form,  the  longer  axis 
of  the  oval  trending  (in  the  northern  hemisphere)  between  north  and  east — about, 
therefore,  in  the  direction  of  progression.  Tne  steepest  gradients,  and  consequently 
the  strongest  winds,  are  apt  to  be  foimd  on  the  equatorial  and  westerly  sides  of  the 
depression. 

Extra-tropical  cyclones  generally  follow  an  easterly  course,  inclining  somewhat 
toward  the  pole;  but  they  occasionally  turn  to  one  side  or  the  other,  become  sta- 
tionary, or  even  move  backward.  The  velocity  of  progression  varies  from  15  to  40 
miles  an  hour.  If  they  exist  as  independent  barometric  depressions,  with  strong 
upward  gradients  on  all  sides  of  the  center,  the  cyclonic  circulation  will  be  complete, 
the  wind  shifting  with  the  sun  for  an  observer  situated  in  the  equatorial  semicircle 
of  the  storm,  against  the  sun  for  an  observer  situated  in  the  polar  semicircle. 

Important  among  these  extra-tropical  cyclonic  disturbances  are  the  pamperos 
of  the  Argentine  coast.  These  storms  are  primarily  caused  by  the  approach  and 
passage  eastward  of  an  area  of  low  pressure,  around  which  the  winds  circulate  spirally 
m  a  right-handed  direction.  They  vary  in  strength  and  duration  from  a  squall  to  a 
gale  01  great  violence.  Although  preceded  by  the  indications  which  characterize 
the  approach  of  cyclonic  storms  m  general,  yet  they  usually  break  with  such  sudden- 
ness, in  a  shift  of  wind  from  the  northward  to  the  southwestward,  that  they  may 
become  particularly  dangerous  from  this  cause  alone.  They  usually  continue  to 
blow  and  die  out  in  the  southwest  quadrant. 

489.  Storms  Along  the  Transatlantic  Steamship  Routes. — The  storms 
which  are  so  frequently  met  during  the  winter  season  along  the  steamship  routes 
between  America  and  Europe  are  not,  as  a  rule,  due  to  central  oarometric  depressions 
but  to  depressions  having  a  trough  or  V  shape,  wliich  extend  southerly  from  the 
extensive  permanent  area  of  low  pressure  havingits  center  in  the  vicinity  of  Iceland. 

They  are  not  attended  by  complete 
cyclonic  circulations,  inasmuch  as 
tne  polar  gradients  which  would 
otherwise  give  rise  to  easterly  winds 
on  this  polar  side  are  lacking.  Their 
approach  is  heralded  by  a  gradual 
hauling  of  the  wind  to  southward, 
which  is  later  followed  (at  the  time 
of  passage  of  the  central  line  of  the 
trough)  by  a  change  to  NW.,  accom- 
panied by  heavy  rain  squalls  and  a 
rapid  increase  in  force.  The  general 
distribution  of  pressure  and  the  sur- 
rounding winds  are  shown  in  figure  76.  The  changes  in  wind  and  pressure  ensue 
much  more  rapidly  in  the  case  of  a  westward-bound  vessel  than  in  that  of  one  east- 
ward bound,  tne  rate  at  which  the  observer  and  the  depression  approach  each  other 
being  in  the  former  case  the  sum  of  his  own  westward  velocity  and  the  eastward 
velocity  of  the  trough,  in  the  latter  case  the  difference  of  these  velocities. 


Hi^h 


Fig.  76. 


CHAPTER  XX. 
TIDES. 


490.  Definitions. — Tidal  phenomena  present  themselves  to  the  observer 
under  two  aspects — as  alternate  elevations  and  depressions  of  the  sea,  and  as  recur- 
rent inflows  and  outflows  of  streams.  The  word  tide,  in  common  and  general  usage, 
is  made  to  refer  without  distinction  to  both  the  vertical  and  horizontal  motions  of 
the  sea,  and  confusion  has  sometimes  arisen  from  this  double  appHcation  of  the  term ; 
in  its  strict  sense,  this  word  may  be  used  only  with  reference  to  the  changes  of  eleva- 
tion, while  the  recurrent  streams  are  properly  distinguished  as  tidal  currents. 

The  tide  rises  until  it  reaches  a  maximum  height  called  high  water  or  high  tide, 
and  then  falls  to  a  minimum  level  called  low  water  or  low  tide;  that  period  at  high  or 
low  water  marking  the  transition  between  the  tides,  during  which  no  vertical  change 
can  be  detected,  is  called  stand. 

Of  the  tidal  currents,  that  which  arises  from  a  movement  of  the  water  in  a 
direction,  generally  speaking,  from  the  sea  toward  the  land,  is  called  jlood,  and  that 
arising  from  an  opposite  movement,  ehh;  the  intermediate  period  between  the  cur- 
rents, during  which  there  is  no  horizontal  motion,  is  distinguished  as  slack.  Set  and 
drift  are  terms  appHcable  to  the  tidal  currents,  the  first  referring  to  the  direction  and 
the  second  to  the  velocity. 

Care  should  be  taken  to  avoid  confusing  the  terms  relating  to  tides  with  those 
which  relate  to  tidal  currents. 

491.  Cause. — The  cause  of  the  tides  is  the  periodic  disturbance  of  the  ocean 
from  its  position  of  equihbrium  brought  about  through  the  periodic  differences  of 
attraction  upon  the  water  particles  of  the  earth,  by  the  moon,  and  to  lesser  degree, 
by  the  sun,  on  account  of  their  relative  periodic  movements.  The  tide-producing 
force  of  the  moon  upon  a  particle  of  unit  mass  on  the  surface  of  the  earth  is  the 
difference  between  the  moon's  attraction  upon  the  given  unit  mass  and  the  moon's 
attraction  upon  the  entire  earth;  and  it  is  hkewise  with  the  sun,  only  the  magnitude 
of  the  mean  tide-producing  force  is  in  this  case  reduced  to  about  two-fiifths  of  the 
tide-producing  force  of  the  moon,  because  of  the  comparative  remoteness  of  the  sun 
from  the  earth. 

A  particle  which  has  a  tide-producing  body  in  its  zenith  or  in  its  nadir  experi- 
ences, as  the  result  of  the  attraction  of  the  tide-producing  body,  an  effect  only  in  the 
vertical  direction  as  ii  the  intensity  of  gravity  were  momentarily  lessened;  and  a 
particle  which  has  the  tide-producing  body  in  its  horizon,  being  then  practically  at 
the  same  distance  from  the  tide-producing  body  as  the  center  of  the  earth,  experi- 
ences, as  the  result  of  the  attraction  of  the  tide-producing  body,  an  effect  which  is 
practically  aU  in  the  vertical  direction  as  if  the  intensity  of  gravity  were  momentarily 
mcreased.  But  when  the  tide-producing  body  is  in  any  other  situation  with  reference 
to  an  attracted  particle,  the  attraction  is  partly  directed  in  a  vertical  line  toward  the 
center  of  the  earth  and  partly  in  a  horizontal  direction  along  the  surface  of  the  earth. 
The  vertical  components  of  the  attractions  of  the  tide-producing  bodies  can  not 
create  any  sensible  disturbance  on  the  existing  oceans ;  but  the  horizontal  components 
of  such  attractions,  tending  to  produce  horizontal  movements  oscillating  back  and 
forth  on  the  surface  of  the  earth,  are  effective  in  the  production  of  the  tides,  and,  by 
acting  upon  portions  of  the  oceans  that  are  susceptible  of  taking  up  stationary 
oscillations  in  approximate  imison  with  the  period  oi  the  tide-producing  forces,  give 
rise  to  the  dominant  tides. 

The  peculiarities  that  characterize  the  tides  of  many  localities  are  caused  by 
modifications  resulting  from  reflections  and  interferences  suffered  by  the  dependent 
waves  generated  by  the  dominant  tides.  Theory  is  not  yet  sufficiently  advanced  to 
render  practicable  the  prediction  of  the  tides  where  no  observations  have  been  made; 

21594°— 14 15  225 


226  TIDES. 

but  by  theory,  supplemented  by  the  observation  of  actual  tidal  conditions  in  a  given 
locality  during  a  certain  period  of  time,  very  accurate  predictions  of  the  time  and 
height  of  the  tides  can  be  made  for  that  locality. 

4:92.  Establishment. — High  and  low  water  occur,  on  the  average  of  the  twenty- 
eight  days  comprising  a  lunar  month,  at  about  the  same  intervals  after  the  transit 
of  the  moon  over  the  meridian.  These  nearly  constant  intervals,  expressed  in  hours 
and  miautes,  are  known,  respectively,  as  the  liigh  water  lunitidal  interval  and  low 
water  lunitidal  interval. 

The  interval  between  the  moon's  meridian  passage  at  any  place  and  the  time 
of  the  next  succeeding  high  water,  as  observed  on  the  days  when  the  moon  is  at  fuU 
or  change,  is  called  the  vulgar  (or  common)  establishment  of  that  place,  or,  sometimes, 
simply  the  estahlishment.  This  interval  is  frequently  spoken  of  as  the  time  of  Jiigh 
water  on  full  and  change  days  (abbreviated  ''H.  W.  F.  &  C.");  for  since,  on  such 
days,  the  moon's  two  transits  (upper  and  lower)  over  the  meridian  occur  about 
midnight  and  noon,  the  vulgar  estabHshment  then  corresponds  closely  with  the  local 
times  of  high  water.  When  more  extended  observations  have  been  made,  the  average 
of  aU  high  water  lunitidal  intervals  for  at  least  a  lunar  month  is  taken  to  obtain  what 
is  termed,  in  distinction  to  the  vulgar  estabHshment,  the  corrected  estahlishment  of 
the  port,  or  mean  high  water  lunitidal  interval.  In  defining  the  tidal  characteristics 
of  a  place  some  authorities  give  the  corrected  estabHshment,  and  others  the  vulgar 
establishment,  or  ''high  water,  full,  and  change;"  calculations  based  upon  the  former 
will  more  accurately  represent  average  conditions,  though  the  two  intervals  seldom 
differ  by  a  large  amount. 

Having  determined  the  time  of  high  water  by  appljring  the  estabHshment  to  the 
time  of  moon's  transit,  the  navigator  may  obtain  the  time  of  low  water  with  a  fair 
degree  of  approximation  by  adding  or  subtracting  6**  13""  (one-fourth  of  a  mean  lunar 
day) ;  but  a  closer  result  wiH  be  given  by  applying  to  the  time  of  transit  the  mean 
low  water  lunitidal  interval,  which  occupies  the  same  relation  to  the  time  of  low  water 
as  the  mean  high  water  lunitidal  interval,  or  corrected  establishment,  does  to  the 
time  of  hi^  water. 

493.  Range. — The  range  of  the  tide  is  the  difference  in  height  between  low 
water  and  high  water.  This  term  is  often  appHed  to  the  difference  existing  under 
average  conditions,  and  may  in  such  a  case  be  designated  as  the  mean  range  or  mean 
rise  and  fall  to  distin^ish  it  from  the  spring  range  or  neap  range,  which  are  the  ranges 
at  spring  and  neap  tides,  respectively. 

4:94.  Spring  and  Neap  Tides. — ^At  the  times  of  new  and  full  moon  the  relative 
positions  of  sun  and  moon  are  such  that  the  high  water  produced  by  one  of  those 
bodies  occurs  at  the  same  time  as  that  produced  by  the  other,  and  so  also  with  the 
low  waters;  the  tides  then  occurring,  caUed  s'pring  tides,  have  a  greater  range  than 
any  others  of  the  lunar  month,  and  at  such  times  the  highest  high  tides  as  weU  as 
the  lowest  low  tides  are  experienced,  the  tidal  range  being  then  at  its  maximum. 
At  the  first  and  third  quarters  of  the  moon  the  positions  are  such  that  the  hi^h  tide 
due  to  one  body  occurs  at  the  time  of  the  low  tide  due  to  the  other,  so  that  the  two 
actions  are  opposed;  this  causes  the  neap  tides,  which  are  those  of  minimum  range, 
the  high  waters  being  lower  and  the  low  waters  higher  than  at  other  periods  of  the 
month. 

Since  the  horizontal  motion  of  the  water  depends  directly  upon  the  rise  and  fall 
of  the  tides  it  foUows  that  the  currents  will  be  greatest  at  springs  and  least  at  neaps. 

The  effect  of  the  moon's  being  at  fuU  or  change  is  not  felt  at  once  in  aU  parts  of  the 
world,  and  the  greatest  range  of  tides  does  not  generally  occur  until  oncor  two  days 
thereafter;  thus,  on  the  Atlantic  coast  of  North  America,  the  highest  tides  are 
experienced  one  day,  and  on  the  Atlantic  coast  of  Europe  two  days,  afterwards, 
though  on  the  Pacific  coast  of  North  America  thev  occur  nearly  at  fuU  and  change. 

495.  The  nearer  the  moon  is  to  the  earth  the  stronger  is  its  attraction,  and  as 
it  is  nearest  in  perigee,  the  tides  will  be  larger  then  on  that  account,  and  consequently 
less  in  apogee.  For  a  Hke  reason,  the  tides  will  be  increased  by  the  sun's  action  when 
the  eartn  is  near  its  perihelion,  about  the  1st  of  January,  and  decreased  when  near 
its  apheHon,  about  the  1st  of  July. 

4:96.  The  height  of  the  tides  at  any  place  may  undergo  modification  on  account 
of  strong  prevaiHng  winds  or  abnormal  barometric  conditions,  a  wind  blowing  off 


TIDES. 


227 


the  shore  or  a  high  barometric  tending  to  reduce  the  tides,  and  the  reverse.  The 
effect  of  atmospheric  pressure  is  to  create  a  difference  of  about  2  inches  in  the  height 
of  tide  for  every  tenth  of  an  inch  of  difference  in  the  barometer, 

497.  Priming  and  Lagging. — The  tidal  day  is  the  variable  interval,  averaging 
24h  50 m^  between  two  alternate  high  or  low  waters.  The  amount  by  which  corre- 
sponding tides  grow  later  day  by  day — that  is,  the  amount  by  which  the  tidal  day 
exceeds  24'' — is  called  the  daily  retardation.  When  the  sun's  tidal  effect  is  such  as  to 
shorten  the  lunitidal  intervals,  thus  reducing  the  length  of  the  tidal  day  and  causing 
the  tides  to  occur  earlier  than  usual,  there  is  said  to  be  a.  priming  of  the  tide;  when, 
from  similar  causes,  the  interval  is  lengthened,  there  is  saia  to  be  a  lagging. 

498.  Types  of  Tides. — The  observed  tide  is  not  a  simple  wave;  it  is  a  compound 
of  several  elementary  undulations,  rising  and  falling  from  the  same  common  plane, 
of  which  two  can  be  distinguished  and  separated  by  a  simple  ^ouping  of  the 
data.  These  two  waves  are  known  as  the  semidiurnal  and  the  diurnal  tides,  be- 
cause the  first,  if  alone,  would  give  two  high  and  two  low  waters  in  a  day,  while 
the  second  would  give  but  one  high  and  one  low  water  in  an  equivalent  period 
of  time.     In  nearly  all  ports  these  two  tides  coexist,  but  the  proportion  between 

them  varies  remarkably  for  differ- 
ent seas.  The  effect  of  the  com- 
bination of  these  two  types  of 
tide  is  to  produce  a  diurnal 
inequality,  both  in  the  height  of 
two  consecutive  high  or  low 
waters,  and  in  the  mtervals  of 
time  between  their  occurrence. 
The  height  of  the  diurnal  wave 
may  be  regarded  as  reaching  a 
maximum  fortnightly,  soon  after 
the  moon  attains  its  extreme  dec- 
lination and  is  therefore  near 
one  of  the  tropics.  The  tides 
that^  then  occur  are  denominated 
tropic  tides. 

In  undertaking  to  investi- 
gate the  tides  of  a  port  it  is  im- 
portant to  ascertain  as  early  as 
possible  the  form  of  the  tide ;  that 
is^  whether  it  resembles  the  semi- 
diurnal, the  diurnal,  or  the  mixed 
type;  because  not  only  may  this  information  be  of  scientific  value,  but  the  knowledge 
thus  gained  at  the  outset  will  enable  the  observer  to  fix  upon  the  best  method  of 
keeping  his  record. 

499.  The  type  forms  referred  to  are  illustrated  in  the  diagram  in  figure  77, 
where  the  waves  are  plotted  in  curves,  using  the  times  as  abscissae  and  the  heights 
as  ordinates.  In  this  diagram,  the  curve  traced  in  the  full  line  is  a  tide  wave  of  the 
semidiurnal  type;  that  traced  by  the  dotted  line  one  of  the  diurnal;  while  the 
broken  line  is  one  of  the  mixed  type,  in  this  case  the  compound  of  the  two  others. 

In  order  to  determine  the  type  to  which  the  tide  of  any  port  belongs,  it  is  usually 
only  necessary  to  make  hourly  observations  for  a  day  or  two  at  the  date  of  the  moon's 
maximum  declination,  and  to  repeat  the  series  about  a  week  later,  when  the  moon 
crosses  the  equator.  The  reported  irregularities  of  the  rise  and  faU  at  any  place 
should  not  deter  persons  from  careful  investigation.  When  analyzed,  even  the  most 
complicated  of  tides  are  found  to  follow  some  general  law. 

500.  Tidal  Currents. — It  should  be  clearly  borne  in  mind  by  the  navigator 
that  the  periods  of  flood  and  ebb  currents  do  not  necessarily  coincide  with  those  of 
rising  and  faUing  tides,  and  that,  paradoxical  though  it  may  seem  at  first  thought, 
the  inward  set  of  the  surface  current  does  not  always  cease  when  the  water  nas 
attained  its  maximum  height,  nor  the  outward  set  when  a  minimum  height  has  been 
reached.     Under  some  circumstances  it  may  occur  that  stand  and  slack  will  be 


V 

( 

)^T"2"'.'»'^4~5''6''7''8""'"0'l0  n  12  13  M  15  16  17  18  39  20  21  22  23  24     | 

Ff, 

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3 

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2 

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2 
3 
4 

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/ 

\ 

\ 

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1  - 

p. 

- 

/ 

/ 

\,' 

/' 

/ 

/ 

\ 

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\ 

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17 

1 

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V 

V. 

- 

/- 

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f 

^- 

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L 

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T 

U'1 

' 

Semidiurnal. 


diurnal. 

FiQ.  77. 


mixed. 


228  TIDES. 

simultaneous,  while  other  conditions  may  produce  a  maximum  current  at  stand, 
with  a  maximum  rate  of  rise  or  fall  at  slack  water. 

The  varying  effects  which  will  be  produced  according  to  local  conditions  may 
be  considered  by  the  comparison  of  two  tidal  basins,  to  one  of  which  the  tide  wave 
has  access  from  the  sea  by  a  channel  of  ample  capacity,  while  the  other  has  an 
entrance  that  is  narrow  and  constricted.  In  the  first  case,  the  process  of  filling  or 
emptying  the  basin  keeps  pace  with  the  change  of  level  in  the  sea  and  is  practically 
completed  as  soon  as  the  height  without  becomes  stationary;  in  this  case  slack  and 
stand  occur  nearly  at  the  same  time,  as  do  flood  and  rise  and  ebb  and  fall.  In  the 
second  case,  the  limited  capacity  of  the  entrance  will  not  permit  the  basin  to  fill  or 
empty  as  rapidly  as  the  tide  changes  its  level  without ;  hence  there  is  still  a  difference 
of  level  to  produce  a  current  when  the  vertical  motion  in  either  direction  has  ceased 
on  the  outside,  and  for  a  considerable  time  after  motion  in  the  reverse  direction  has 
been  in  progress ;  under  extreme  conditions  it  may  even  occur  that  a  common  level 
will  not  be  established  until  mid-tide,  and  therefore  the  surface  current  at  some 
places  will  ebb  until  three  hours  after  low  water  and  flow  until  three  hours  after  high 
water. 

Localities  that  partake  of  the  nature  of  the  first  case  are  those  upon  open  coasts 
and  wide-mouthed  eights.  Examples  of  the  latter  class  will  be  found  m  narrow 
bays  and  long  channels. 

TIMES   OF  HIGH  AND  LOW  WATER. 

501.  Tide  Tables. — The  most  expeditious,  as  well  as  most  exact,  method  of 
ascertaining  the  times  of  high  and  low  water  and  other  features  of  the  tides  will  be 
by  reference  to  a  Tide  Table,  and  every  navigator  is  recommended  to  provide  him- 
self with  such  a  pubUcation.  The  United  States  Coast  and  Geodetic  Survey  pub- 
lishes annuaUy,  in  advance,  tables  giving,  for  every  day  in  the  year,  the  predicted 
time  and  height  of  the  tides  at  certain  principal  ports  of  the  world,  and  from  these, 
by  a  simple  reduction,  the  times  and  heights  at  a  multitude  of  other  ports  may 
readily  be  obtained;  data  for  ascertaining  the  tidal  currents  in  certain  important 
regions  are  also  provided.  General  tide  tables  are  also  published  by  the  govern- 
ments of  other  maritime  nations,  and  special  tables  are  to  be  had  for  many  particular 
localities. 

502.  Where  no  tide  tables  are  available,  the  method  of  calculation  by  applying 
the  lunitidal  interval  to  the  time  of  the  moon's  meridian  passage  must  be  resorted  to. 

To  do  this,  find  first  the  time  of  the  moon's  meridian  passage,  upper  or  lower, 
as  may  be  required.  The  Greenwich  mean  time  of  upper  transit  at  Greenwich  is 
given  m  the  Nautical  Almanac  (page  IV  of  the  month) ;  the  corresponding  time  of 
lower  transit  is  most  easily  found  by  taking  the  mean  of  the  two  adjacent  upper 
transits ;  to  the  Greenwich  time  of  Greenwich  transit  apply  the  correction  for  longi- 
tude given  in  Table  11  (using  the  daily  variation  of  the  moon's  meridian  passage 
shown  in  the  Almanac),  adding  in  west  and  subtracting  in  east  longitude;  the  result 
is  the  local  mean  time  of  local  transit.  Add  to  this  the  high-water  or  low-water 
lunitidal  interval  of  the  port  from  Appendix  IV,  according  as  the  time  of  high  or 
low  water  may  be  required.     The  result  is  the  time  sought. 

The  astronomical  date  must  be  strictly  adhered  to,  and  in  so  doing  it  may  be 
found  necessary  to  employ  the  time  of  a  lower  transit,  or  the  transit  of  a  preceding 
day,  to  find  the  time  of  the  tide  in  question. 

Appendix  IV  contains,  besides  the  geographical  positions  of  all  the  more 
important  positions  in  the  world,  a  series  of  tidal  data  relating  to  many  of  those 
places.  In  such  data  are  comprised  the  mean  lunitidal  intervals  for  high  and  low 
water;  also,  for  places  where  the  semi-diurnal  type  of  tide  prevails,  the  tidal  range 
at  spring  and  at  neap  tides,  and  for  those  where  the  tide  is  of  the  diurnal  type,  the 
tropic  range.    An  alphabetical  index  is  appended  to  this  table. 

The  corrected  establishment  taken  from  the  charts  may  be  substituted  for  the 
high-water  lunitidal  interval  of  the  table;  or,  with  only  slight  variation  in  the  results, 
the  vulgar  establishment  (H.  W.  F.  &  C.)  may  be  employed. 


TIDES.  229 

Example:  Find  the  times  of  the  high  and  low  waters  at  the  New  York  Navy  Yard,  occurring  next 
after  noon  on  April  15,  1915. 

G.  M.  T.  of  Gr.  tiansit,  22<J  0^  37"».7 

Corr.  for+74°  I^ng.  (Tab.  11),     +  9 


L.  M.  T.  of  local  traasit,  22    0    47 

Transit,  22*  C^  47«  Transit,  221  Qh  47111 

H.  W.  Lun.  Int.  (App.  IV),  8    44  L.  W.  Lun.  Int.  (App.  IV),  2    49 

L.  M.  T..  H.  W.,  {ly  JXn  p.  m.        ^-  ^^  T-.  L-  W..  {fp^f  J^^,  p,  ^. 

Example:  Find  the  time  of  high  water  at  the  Presidio,  San  Francisco,  Cal.,  on  the  afternoon  of 
May  7, 1915. 

G.  M.  T.  of  Gr.  transit,  6<«  19"^  06'".2 

Corr.  for+122°  Long.  (Tab.  11),    +  15 

L,  M.  T.  of  local  transit,  6    19    21 

H.  W.  Lun.  Int.  (App.  IV),  +        11    43 


L.  M.  T.,  H.  W.,  JMayV  7.04  p.  m. 

Example:  Find  the  time  of  low  water  at  Singapore  on  the  night  of  May  21, 1915. 

G.  M.  T.  of  Gr.  transit,  210  5h  52in.3 

Corr.  for-104°  Long.  (Tab.  11),    -  13 

L.  M.  T.  of  local  transit,  21    5    39 

L.  W.  Lun.  Int.  (App.  IV),  +  4    02 


L.  M.  T.,  L.  W.,  {May^21,'*9.41  p.  m. 

Example  :  Find  the  time  of  morning  high  water  and  afternoon  low  water  at  Gibraltar  on  June  19, 1915. 

G.  M.  T.  of  Gr.  upper  transit, 
G.  M.  T.  of  Gr.  upper  transit. 


19 

4h 
5 

34°'.7 
19   .0 

2)37 

09 

53  .7 

18 

+ 

16 

57 
01 

G.  M.  T.  of  Gr.  lower  transit, 
.  Corr.  for  +5°  Long.  (Tab.  11), 

L.  M.  T.  of  local  lower  trans.,         18    16    58 

Transit,  18"*  16^  58"'  Transit,  18«  16"  58"» 

H.  W.  Lun.  Int  (App.  IV),  1    35  L.  W.  Lun.  In t  (App.  IV),  7    55 

L.M.T.,  H.W.,  {june\?.33a.m.  L.  M.  T.,  L.  W.,  {jLe^9, 12.53  p.  m. 

TIDAL  OBSERVATIONS. 

503.  Since  navigators  will  frequently  have  opportunity  to  observe  tidal 
conditions,  either  in  connection  with  a  hydrographic  survey  or  otherwise,  at  places 
where  existing  knowledge  of  the  tides  is  incomplete,  an  understanding  of  the  methods 
employed  in  tidal  observations  may  be  important. 

504.  Tides. — ^For  the  proper  study  of  tides,  frequent  and  continuous  observa- 
tions are  necessary;  it  will  not  suffice  to  observe  the  heights  of  the  high  and  low 
waters  only,  even  if  they  present  themselves  as  distinct  phases,  but  the  whole  tidal 
curve  for  each  day  should  be  developed  by  recording  the  height  of  water  at  intervals, 
which,  preferably,  should  not  exceed  thirty  minutes.  Observations,  to  be  complete, 
must  cover  a  whole  limar  month;  or,  if  it  be  impracticable  to  observe  the  tides  at 
night,  the  day  tides  of  two  lunar  months  may  be  substituted. 

505 .  When  made  for  the  purposes  of  a  hydrographic  survey,  the  tidal  observations 
are  used  to  correct  the  soundings,  and  care  must  be  taken  to  make  sure  that  the 
gauge  is  placed  in  a  situation  visited  by  the  same  form  of  tide  as  that  which  occiu's 
at  the  place  where  soundings  are  being  made.    It  will  not  answer,  for  instance,  to 


230      .  TIDES. 

correct  the  soundings  upon  an  inlet  bar  by  tidal  observations  made  within  the  lagoon 
with  which  tJiis  inlet  communicates,  because  the  range  of  the  tide  within  the  lagoon 
is  less  than  upon  the  outside  coast.  A  partial  obstruction,  like  a  bridge,  or  a  natural 
contraction  of  the  channel  section,  while  it  may  not  reduce  the  total  range  of  the  tide 
or  materially  affect  the  time  of  high  or  low  tides,  will  alter  the  relative  heights  above 
and  below  at  intermediate  stages,  so  that  the  hydrographer  must  be  careful  to  see 
that  no  such  obstruction  intervenes  between  his  field  of  work  and  the  gauge. 

506.  Tidal  Currents. — Observations  for  tidal  currents  should  be  made  with 
the  same  regularity  as  for  tides;  the  intervals  need  not  ordinarily  be  more  frequent 
than  once  in  every  half  hour.  They  should  always  be  made  at  the  same  point  or 
points,  which  should  be  far  enough  from  shore  to  be  representative  of  the  conditions 
prevailing  in  the  navigable  waters.  The  ordinary  log  may  be  employed  jfor  measuring 
the  current,  but  it  is  better  to  replace  the  chip  by  a  pole  weighted  to  float  upright 
at  a  depth  of  about  fifteen  feet;  the  line  should  be  a  very  li^ht  one,  and  buoyed  at 
intervals  by  cork  floats  to  keep  it  from  sinking;  the  set  of  the  current  should  be 
noted  by  a  compass  bearing  of  the  direction  of  the  pole  at  the  end  of  the  observation. 

507.  Record. — ^The  record  of  observations  should  be  kept  clearly  and  in 
complete  form.  It  should  include  a  description  of  the  locahty  of  observation,  the 
nature  of  gauge  and  of  instruments  used  for  measuring  currents,  and  the  exact  position 
of  both  tidal  and  current  stations,  together  with  situation  and  height  of  bench  mark. 
The  time  of  making  each  observation  should  be  shown,  and  data  given  for  reduction 
to  some  standard  time.  In  extended  tidal  observations  the  meteorological  conditions 
should  be  carefully  recorded,  the  instruments  used  for  the  observations  being  properly 
compared  with  standards. 

508.  There  are  frequently  remarkable  facts  in  reference  to  tides  and  currents 
to  be  obtained  from  persons  having  local  knowledge;  these  should  be  examined  and 
recorded.  The  date  and  circumstances  of  the  highest  and  lowest  tides  ever  known 
form  important  items  of  information. 

»  509.  Planes  of  Reference. — The  'plane  of  reference  is  the  plane  to  which 
soundings  and  tidal  data  are  referred.  One  of  the  principal  objects  of  observing 
tides  when  making  a  survey  is  to  furnish  the  means  for  reducing  the  soundings  to 
this  plane.  Four  planes  of  reference  are  used;  namely,  mean  low  water,  mean  low- 
water  springs,  mean  lower  low  waters,  and  the  harmonic  or  Indian  tide  plane. 

Mean  tow  water  is  a  plane  whose  depression  below  mean  sea  level  corresponds 
with  half  the  mean  semidiurnal  range,  whde  the  depression  of  mean  low-water  springs 
corresponds  with  half  the  mean  range  of  spring  tide;  mean  lower  low  water  depends 
upon  the  diurnal  inequality  in  high  and  low  water;  the  harmonic  or  Indian  tide  plane 
was  adopted  as  a  convenient  means  of  expressing  something  of  an  approximation 
to  the  level  of  low  water  of  ordinary  spring  tides,  but  where  there  is  a  large  diurnal 
inequahty  in  low  waters  it  falls  considerably  below  the  true  mean  of  such  tides. 

As  these  planes  may  differ  considerably,  it  is  important  to  ascertain  which  plane 
of  reference  is  adopted  before  making  use  oi  any  chart  or  considering  data  concerning 
the  tides. 

510.  The  tides  are  subject  to  so  many  variations  dependent  upon  the  movements 
of  the  sun  and  moon,  and  to  so  many  irregularities  due  to  the  action  of  winds  and 
river  outflows,  that  a  very  long  series  of  observations  would  be  necessary  to  fix  any 
natural  plane.  In  consideration  of  this,  and  keeping  in  view  the  possibilities  of 
repetitions  of  the  surveys  or  subsequent  discoveries  within  the  field  of  work,  it  is 
necessary  to  define  the  position  of  the  plane  of  reference  which  has  resulted  from  any 
series  of  observations.  This  is  done  by  levehng  from  the  tide  gauge  to  a  permanent 
hench,  precisely  as  if  the  adopted  plane  were  arbitrary. 

511.  Bench  Mark. — The  plmth  of  a  lighthouse,  the  water  table  of  a  substantial 
building,  the  base  of  a  monument,  and  the  hke,  are  proper  benches;  and  when  these 
are  not  within  reach  a  mark  may  be  made  on  a  rock  not  likely  to  be- moved  or  started 
by  the  frost,  or,  if  no  rock  naturally  exists  in  the  neighborhood,  a  block  of  stone 
buried  below  the  reach  of  frost  and  plowshare  should  be  the  resort.  When  a  bench 
is  made  on  shore  it  should  be  marked  by  a  circle  of  2  or  3  inches  diameter  with  a 
cross  in  the  center  indicating  the  reference  point.  The  levelings  between  this  point 
and  the  gauge  should  be  run  over  twice  and  the  details  recorded.  A  bench  made 
upon  a  wharf  or  other  perishable  structure  is  of  little  value,  but  in  the  absence  of 


TIDES.  231 

permanent  objects  it  is  better  than  nothing.  The  marks  should  be  cut  in,  if  on  stone, 
and  if  on  wood,  copper  nails  should  be  used.  The  bench  must  be  sketched  and 
carefully  described,  and  its  location  marSed  on  the  hydrographic  sheet,  with  a  state- 
ment of  the  relative  position  of  the  plane  of  reference. 

512.  The  leveling  from  the  bench  mark  to  the  tide  gauge  may  be  done,  when  a 
leveUng  instrument  is  not  available,  by  measuring  the  difference  of  height  of  a  number 
of  intermediate  points  by  means  of  a  long  straight-edged  board,  held  horizontal  by 
the  aid  of  a  carpenter's  spirit  level,  or  even  a  plummet  square,  taking  care  to  repeat 
each  step  with  the  level  inverted  end  for  end.  A  line  of  si^ht  to  tne  sea  horizon, 
when  it  can  be  seen  from  the  bench  across  the  tide  staff,  wul  afford  a  level  line  of 
sufficient  accuracy,  especially  when  observed  with  the  telescope.  It  may  often  be 
convenient  to  combine  these  methods. 

513.  Tide  Gauges. — The  Staff  Gauge  is  the  simplest  device  for  measuring  the 
heights  of  tides,  and  in  perfectly  sheltered  localities  it  is  the  best.  It  consists  of  a 
vertical  staff  graduated  upward  in  feet  and  tenths,  and  so  placed  that  its  zero  shall 
lie  below  the  lowest  tides.  The  same  gauge  may  also  be  used  where  the  surface  is 
rough,  if  a  glass  tube  with  a  float  inside  is  secured  alongside  of  the  staff,  care  being 
taken  to  practically  close  the  lower  end  of  the  tube  so  as  to  exclude  undulations; 
readings  may  also  be  made  by  noting  the  point  midway  between  the  crest  and  trough 
of  the  waves. 

A  staff  gauge  should  always  be  erected  for  careful  tidal  observations,  even  where 
other  classes  of  gauge  are  to  be  employed,  as  it  furnishes  a  standard  for  comparison 
of  absolute  heights,  and  also  serves  to  detect  any  defects  in  the  mechanical  details 
upon  which  all  other  gauges  are  to  a  greater  or  less  extent  dependent. 

514.  Where  there  is  considerable  swell,  and  where,  from  the  situation  of  the 
gauge  or  the  great  range  of  the  tide  (making  it  inconvenient  for  the  observer  to  see 
the  figures  in  certainpositions)  the  staff  gauge  can  not  be  used,  recourse  must  be  had 
to  the  Box  Gauae.  This  gauge  consists  of  a  vertical  box,  closed  at  the  bottom,  with 
a  few  small  holes  in  the  lower  part  which  admit  sufficient  water  to  keep  the  level 
within  ec[ual  to  the  mean  level  without  but  which  do  not  permit  the  admission  of 
water  with  suflScient  rapidity  to  be  affected  by  the  waves.  Within  the  box  is  a 
copper  float;  in  some  cases  tnis  float  carries  a  graduated  vertical  rod  whose  position 
with  reference  to  a  fixed  point  of  the  box  affords  a  measure  for  the  height  of  the 
water;  in  other  gauges  of  this  class  the  float  is  attached  to  a  wire  or  cord  which 
passes  over  pulleys  and  terminates  in  a  counterpoise  whose  position  on  a  vertical 
graduated  scale  shows  the  height  of  tide. 

515.  An  Automatic  Gauge  requires  a  box  and  float  such  as  has  just  been  described. 
The  motion  of  the  float  in  rising  and  falling  with  the  tide  is  communicated  to  a  pencil 
which  rests  upon  a  moving  sheet  of  paper;  uniform  motion  is  imparted  to  the  paper 
by  the  revolution  of  a  cyhnder  driven  by  clockwork;  the  motion  of  the  pencil  mie  to 
the  tide  is  in  a  direction  perpendicular  to  the  direction  of  motion  of  the  paper,  and 
a  curve  is  thus  traced,  of  which  one  coordinate  is  time  and  the  other  height.  The 
paper,  which  is  usually  of  sufficient  length  to  contain  a  month's  record,  is  paid  out 
from  one  cyUnder,  passes  over  a  second  whereon  it  receives  the  record  and  is  rolled 
upon  a  third  cyhnder,  which  thus  contains  the  completed  tidal  sheet. 

This  gauge,  besides  giving  a  perfectly  continuous  record,  has  the  further  merit 
of  requiring  but  little  of  the  ooserver's  time.  But  its  indications,  both  of  time  and 
heights,  should  be  checked  by  occasional  comparisons  with  the  standard  clock  and 
the  staff  gauge,  the  readings  of  which  should  be  noted  by  hand  at  appropriate  points 
of  the  graphic  record. 

A  newer  type  of  automatic  gauge  prints  the  date,  the  time,  and  the  stage  of 
the  tide  every  five  minutes  on  a  paper  tape. 


CHAPTE|l  XXI. 
OCEAN  OUEEENTS. 


616.  An  ocean  current  is  a  progressive  horizontal  motion  of  the  water  occurring 
throughout  a  region  of  the  ocean,  as  a  result  of  which  all  bodies  floating  therein  are 
carried  with  the  stream. 

The  set  of  a  current  is  the  direction  toward  which  it  flows,  and  its  drift,  the  velocity 
of  the  flow. 

517.  Cause. — The  principal  cause  of  the  superficial  ocean  currents  is  the  wind. 
Every  breeze  sets  in  motion,  by  its  friction,  the  surface  particles  of  the  water  over 
which  it  blows;  this  motion  of  the  upper  stratum  is  imparted  to  the  stratum  next 
beneath,  and  thus  the  general  movement  is  commimicated,  eachlayer  of  particles  acting 
upon  the  one  below  it,  until  a  current  is  estabhshed.  The  direction,  depth,  strength, 
and  permanence  of  such  a  current  will  depend  upon  the  direction,  steadiness,  and  force 
of  the  wind;  all,  however,  subject  to  modification  on  account  of  extraneous  causes, 
such  as  the  intervention  of  land  or  shoals  and  the  meeting  of  conflicting  currents. 

A  minor  cause  in  the  generation  of  ocean  currents  is  the  difference  in  density  of  the 
sea  water  in  different  regions,  as  a  result  of  which  a  set  is  produced  from  the  more 
dense  toward  the  less  dense,  in  the  effort  to  estabhsh  equilibrium  of  pressure;  the 
difference  of  density  may  be  due  to  temperature,  the  warmer  water  near  the  equator 
being  less  dense  than  the  colder  water  oi  higher  latitudes ;  or  it  may  be  created  by  a 
difference  in  the  amount  of  contained  sahne  matter,  resulting  from  evaporation, 
freezing,  or  other  causes.  Another  minor  factor  that  may  have  influence  upon  ocean 
currents  is  the  difference  of  pressure  exerted  by  the  atmosphere  upon  the  water  in 
different  regions.  But  neither  of  the  last-mentioned  causes  may  be  regarded  as  of 
great  importance  when  compared  with  the  influence,  direct  and  indirect,  of  the  wind. 

518.  Submarine  Currents. — In  any  scientific  investigation  of  the  circulation 
of  ocean  waters  it  is  necessary  to  take  account  of  the  submarine  currents  as  well 
as  those  encountered  upon  the  surface;  but  for  the  practical  purposes  of  the  navigator 
the  surface  currents  alone  are  of  interest. 

519.  Methods  of  Determination. — The  methods  of  determining  the  exist- 
ence of  a  current,  with  its  set  and  drift,  may  be  divided  into  three  classes ;  namely, 
(a)  by  observations  from  a  vessel  occupying  a  stationary  position  not  affected  by  the 
current;  (6)  by  comparison  of  the  position  of  a  vessel  under  way  as  given  by  obser- 
vation with  that  given  by  dead  reckoning;  and  (c)  by  the  drift  of  objects  abandoned 
to  the  current  in  one  locaHty  and  reappearing  in  another. 

520.  Of  these  methods  the  first  named,  by  observations  from  a  vessel  at  anchor, 
is  by  far  the  most  accurate  and  reliable,  but  being  possible  only  under  special  circum- 
stances is  not  often  available.  The  most  valuable  information  about  ocean  currents 
being  that  which  pertains  to  conditions  in  the  open  sea,  the  great  depths  there  existing 
usually  preclude  the  possibihty  of  anchoring  a  vessel;  ships  especially  fitted  for  the 
purpose  have  at  times,  however,  carried  out  current  observations  with  excellent 
results ;  the  most  notable  achievements  in  this*  direction  are  those  of  the  survey  of 
the  Guff  Stream,  made  by  United  States  naval  officers  acting  under  the  Coast  and 
Geodetic  Survey,  during  which  the  vessel  was  anchored  and  observations  were  made 
in  positions  where  the  depths  reached  to  upward  of  2,000  fathoms. 

521.  The  method  of  determining  current  from  a  comparison  of  positions  obtained 
respectively  by  observation  and  by  dead  reckoning  is  the  one  upon  which  our  knowl- 
edge must  largely  depend.  This  method  is,  however,  always  subject  to  some  inac- 
curacy, and  the  results  are  frequently  quite  erroneous,  for  the  so-called  current  is 
thus  made  to  embrace  not  only  the  real  set  and  drift,  but  also  the  errors  of  observa- 
tion and  dead  reckoning.  In  the  case  of  a  modern  steamer  accurately  steered  and 
equipped  with  good  instruments  for  determining  the  speed  through  the  water  as  well 
as  the  position  by  astronomical  observations,  the  current  may  be  arrived  at  by  this 
method  with  a  fairly  close  degree  of  accuracy.  It  is  not  always  possible,  however, 
to  keep  an  exact  reckoning,  and  this  is  especially  true  in  sailing  vessels,  where  the 
conditions  render  it  difficult  to  determine  correctly  the  position  by  account;  this 

232 


OCEAN  CURRENTS.  233 

source  of  error  may  be  combined  with  faulty  instrumental  determinations,  giving 
apparent  currents  differing  vridely  from  those  that  really  exist. 

522.  Much  useful  knowledge  regarding  ocean  currents  has  been  derived  from 
the  observed  drift  of  objects  from  one  to  another  locality.  This  is  true  not  only  of 
the  bottles  thrown  overboard  from  vessels  with  the  particular  object  of  determining 
the  currents,  but  also  of  derehcts,  drifting  buoys,  and  pieces  of  wreckage,  which 
fulfill  a  similar  mission.  The  deductions  to  be  drawn  from  such  drift  are  of  a  general 
nature  only.  The  point  of  departure,  point  of  arrival,  and  elapsed  time  are  all  that  are 
positively  known.  The  route  followed  and  the  set  and  drift  of  current  at  different  points 
are  not  indicated,  and  in  the  case  of  objects  floating  otherwise  than  in  a  completely 
submerged  condition  account  must  be  taken  of  the  fact  that  the  drift  is  influenced 
by  the  wind.  But  even  this  general  information  is  of  great  value  in  researches  as  to 
ocean  currents,  and  navigators  who  desire  to  aid  in  the  work  of  investigation  may  do 
so  by  throwing  overboard,  from  time  to  time,  sealed  bottles  containing  a  statement 
of  date  and  position  at  which  they  are  launched. 

523.  Currents  of  the  Atlantic  Ocean. — A  consideration  of  the  currents  of 
the  Atlantic  most  conveniently  begins  with  a  description  of  the  Equatorial  Currents. 
The  effect  of  the  northeast  and  southeast  trade  winds  is  to  form  two  great  drift  cur- 
rents,^ setting  in  a  westerly  direction  across  the  Atlantic  from  Africa  toward  the 
American  continent,  whose  combined  width  covers  at  times  upward  of  fifty  degrees 
of  latitude.  These  are  distinguished  as  the  Northern  or  Soutltem  Equatorial  Currents, 
according  as  they  rise  from  the  trade  winds  of  the  northern  or  southern  hemisphere. 

Of  the  two,  the  Southern  Equatorial  Current  is  the  more  extensive.  It  nas  its 
origin  off  the  continent  of  Africa  south  of  the  Guinea  coast,  and  begins  its  flow  with 
a  daily  velocity  that  averages  about  15  miles;  it  maintains  a  general  set  of  west,  the 
portion  near  the  equator  acquiring  later,  however,  a  northerly  component,  while  the 
drift  steadily  increases  until,  on  arriving  off  the  South  American  co&st,  a  rate  of  60 
miles  is  not  uncommon.  At  Cape  San  Roque  the  current  bifurcates,  the  main  or 
equatorial  branch  flowing  along  tne  Guiana  coast,  while  the  other  branch  is  deflected 
to  the  southward. 

The  Northern  Equatorial  Current  originates  to  the  northward  of  the  Cape  Verde 
Islands  and  sets  across  the  ocean  in  a  direction  that  averages  due  west;  though 
parallel  to  the  corresponding  southern  drift,  its  velocity  is  not  so  high. 

524.  Between  tne  Northern  and  Southern  Equatorial  Currents  is  found  the 
Equatorial  Counter  Current  setting  to  the  eastward  under  the  propelling  force  of  the 
southwest  monsoon,  which  prevails  over  an  elongated  area  of  varying  extent  lying 
north  of  the  equator  and  stretching  westward  from  the  southwestern  part  of  the 
sahent  extension  of  the  continent  of  Africa.  The  extent  and  strength  of  this  current 
thus  varies  with  the  seasonal  extent  of  the  monsoon  area,  being  a  maximum  in  July 
and  August,  when  its  effect  is  apparent  to  the  westward  of  the  fiftieth  meridian  of 
west  longitude,  while  at  its  mimmum,  in  November  and  December,  its  influence  is 
but  slight  and  prevails  for  only  a  limited  distance  from  the  African  coast. 

525.  To  the  westward  of  the  region  of  the  Equatorial  Counter  Current  the 
North  and  the  South  Equatorial  Currents  unite.  A  large  part  of  the  combined 
stream  flows  into  the  Caribbean  Sea  through  the  various  passages  between  the 
Windward  Islands,  takes  up  a  course  first  to  the  westward  and  then  to  the  northward 
and  westward,  finally  arriving  off  the  extremity  of  the  peninsula  of  Yucatan;  from 
here  some  of  the  water  follows  the  shore  fine  of  the  Gulf  of  Mexico,  while  another 
portion  passes  directly  toward  the  north  Cuban  coast;  by  the  reuniting  of  these  two 
branches  in  the  Straits  of  Florida  there  is  formed  the  most  remarkable  of  aU  ocean 
currents — the  Gulf  Stream. 

From  that  portion  of  the  combined  equatorial  currents  which  fails  to  find 
entrance  to  the  Caribbean  Sea  a  current  of  moderate  strength  and  volume  takes  its 
course  along  the  north  coasts  of  Porto  Rico,  Haiti,  and  Cuba,  flows  between  the 
last-named  island  and  the  Bahamas,  and  enters  the  Gulf  Stream  off  the  Florida  coast, 
thus  adding  its  waters  to  those  of  the  main  branch  of  the  Equatorial  Current  which 
have  arrived  at  the  same  point  by  way  of  the  Caribbean,  the  Yucatan  Passage,  and 
the  Gulf. 

526.  The  Gulf  Stream,  which  has  its  origin,  as  has  been  described,  in  the  Straits 
of  Florida,  and  receives  an  accession  from  a  branch  of  the  Equatorial  Current  off 
the  Bahamas,  flows  in  a  direction  that  averages  true  north  as  far  as  the  parallel  of 


234  OCEAN   CUKRENTS. 

31°,  then  curves  sharply  to  ENE.  until  reaching  the  latitude  of  32°,  when  a  direction 
a  little  to  the  north  of  NE,  is  assumed  and  maintained  as  far  as  Cape  Hatteras;  at 
this  point  its  axis  is  about  40  miles,  while  its  inner  edge  is  in  the  neighborhood  of  20 
miles  off  the  shore.  Thus  far  in  its  flow  the  average  position  of  the  maximum  current 
is  from  11  to  20  miles  outside  the  100-fathom  curve,  disregarding  the  irregularities 
of  the  latter,  and  the  width  of  the  stream — about  40  miles — is  nearly  uniform.  From 
off  Hatteras  the  stream  broadens  rapidly  and  curves  more  to  the  eastward,  seeking 
deeper  water;  its  northern  limit  may  be  stated  to  be  60  to  80  miles  off  Nantucket 
Shoals  and  120  to  150  miles  to  the  southward  of  Nova  Scotia,  in  which  latter  place 
it  has  expanded  to  a  width  of  about  250  miles.  Farther  on  its  identity  as  the  Gulf 
Stream  is  lost,  but  its  general  direction  is  preserved  in  a  current  to  be  described  later. 

The  water  of  the  Gulf  Stream  is  of  a  deep  indi^o-blue  color,  and  its  junction 
with  ordinary  sea  water  may  be  plainly  recognized;  m  moderate  weather  the  edges 
of  the  stream  are  marked  by  ripples;  in  cool  regions  the  evaporation  from  its  surface, 
due  to  difference  of  temperature  between  air  and  water,  is  apparent  to  the  eye ;  the 
stream  carries  with  it  a  quantity  of  weed  known  as  "gulf  weed,"  which  is  familiar 
to  all  who  have  navigated  it  waters. 

In  its  progress  from  the  tropics  to  higher  latitudes  the  transit  is  so  rapid  that 
time  is  not  given  for  more  than  a  partial  cooUng  of  the  water,  and  it  is  therefore 
found  that  the  GuK  Stream  is  very  much  warmer  than  the  neighboring  waters  of  the 
seas  through  which  it  flows.  This  warm  water  is,  however,  divided  by  bands  of 
markedly  cooler  water  which  extend  in  a  direction  parallel  to  the  axis  and  are  usually 
found  near  the  edges  of  the  stream  of  warm  water.  The  most  abrupt  change  from 
warm  to  cold  water  occurs  on  the  inshore  side,  where  the  name  of  the  Cold  Wall  has 
been  given  to  that  band  which  has  appeared  to  some  oceanograohers  to  form  the 
northern  and  western  boundary  of  the  stream. 

The  investigations  of  PiUsbury  tend  to  prove  that  the  thermometer  is  only  an 
approximate  guide  to  the  direction  and  velocity  of  the  current.  Though  it  indicates 
the  limits  of  the  stream  in  a  general  way,  it  must  not  be  assumed  that  the  greatest 
velocity  of  flow  coincides  with  the  highest  temperature,  nor  that  the  northeasterly 
set  will  be  lost  when  the  thermometer  shows  a  region  of  cold  sea  water. 

The  same  authority  has  also  demonstrated  that  in  the  vicinity  of  the  land  there 
is  a  marked  variation  in  the  velocity  of  current  at  different  hours  of  the  day,  which 
may  amount  to  upward  of  2  knots,  and  which  is  due  to  the  elevation  and  depression 
of  the  sea  as  a  result  of  tidal  influences,  the  maximum  current  being  encountered  at 
a  period  which  averages  about  three  hours  after  the  moon's  transit.  Another  effect 
noted  is  that  at  those  times  when  the  moon  is  near  the  equator  the  current  presents 
a  narrow  front  with  very  high  velocity  in  the  axis  of  maximum  strength,  while  at 
periods  of  great  northerly  or  southerly  declination  the  front  broadens,  the  current 
decreasing  at  the  axis  and  increasing  at  the  edges.  These  tidal  effects  are  not, 
however,  observed  in  the  open  sea. 

The  velocity  of  the  Gulf  Stream  varies  with  the  seasons,  following  the  variation 
in  the  intensity  of  the  trade  winds,  to  which  it  largely  owes  its  origin.  The  drift  of 
the  current  under  average  conditions  may  be  stated  as  follows : 

Between  Key  West  and  Habana:  Mean  surface  velocity  in  axis  of  maximum 
current,  2 J  knots;  allowance  to  be  made  by  a  vessel  crossing  the  entire  width  of  the 
stream,  1.1  knots  per  hour. 

Off  Fowey  Rocks:  Mean  surface  velocity  in  axis,  3.5  knots;  allowance  in  crossing, 
2\  knots  per  hour. 

Off  Cape  Hatteras:  Mean  surface  velocity  in  axis,  upward  of  2  knots;  allowance 
in  crossmg  the  stream,  1 J  knots  per  hour  between  the  100-fathom  curve  and  a  point 
40  miles  outside  that  curve. 

527.  _  After  passing  beyond  the  longitude  of  the  easternmost  portions  of  North 
America,  it  is  generally  regarded  that  the  Gulf  Stream,  as  such,  ceases  to  exist;  but 
by  reason  of  the  prevalence  of  westerly  winds  the  direction  of  the  set  toward  Europe 
is  continued  until  the  continental  shores  are  approached,  when  the  current  divides, 
one  branch  going  to  the  northeastward  and  entering  the  Arctic  regions  and  the  other 
running  off  toward  the  south  and  east  in  the  direction  of  the  African  coast.  These 
currents  have  received,  respectively,  the  designations  of  the  Easterly,  Northeast,  and 
SoutJieast  Drift  Currents. 

528.  The  effect  of  the  currents  thus  far  described  is  to  create  a  general  circula- 
tion of  the  surface  waters  of  the  North  Atlantic,  in  a  direction  coinciding  with  that 


OCEAN   CUERENTS.  235 

of  the  hands  of  a  watch,  about  the  periphery  of  a  huge  ellipse,  whose  limits  of  latitude 
may  be  considered  as  20°  N.  and  40°  N.,  and  which  is  bounded  in  longitude  by  the 
eastern  and  western  continents.  The  central  space  thus  inclosed,  in  which  no  well- 
marked  currents  are  observed,  and  in  the  waters  of  which  great  quantities  of  the 
Sargasso  or  gulf  weed  are  encountered,  is  known  as  the  Sargasso  Sea. 

529.  The  Southeast  Drift  Current  carries  its  waters  to  the  northwest  coast  of 
Africa,  whence  they  foUow  the  general  trend  of  the  land  from  Cape  Spartel  to  Cape 
Verde.  From  this  point  a  largepart  of  the  current  is  deflected  to  the  eastward  close 
along  the  upper  Guinea  coast.  The  stream  thus  formed,  greatly  augmented  at  certain 
seasons  by  the  prevailing  monsoon  and  by  the  waters  carried  eastward  with  the 
Equatorial  Counter  Current,  is  called  the  Guinea  Current.  A  remarkable  character- 
istic of  this  current  is  the  fact  that  its  southern  Hmit  is  only  sUghtly  removed  from 
the  northern  edge  of  the  west-moving  Equatorial  Current,  the  effect  being  that  the 
two  currents  flow  side  by  side  in  close  proximity,  but  in  diametrically  opposite 
directions. 

530.  The  Arctic  or  Labrador  Current  sets  out  of  Davis  Strait,  flows  southward 
down  the  coasts  of  Labrador  and  Newfoundland,  and  thence  southwestward  past 
N^ova  Scotia  and  the  coast  of  the  United  States,  being  found  inshore  of  the  Gulf 
Stream.  It  brings  with  it  the  ice  so  frequently  met  at  certain  seasons  off  New- 
foundland. 

531.  Rennells  Current  was  formerly  represented  as  a  temporary  but  extensive 
stream  setting  at  times  from  the  Bay  of  Biscay  toward  the  west  and  northwest  across 
the  English  Channel  and  to  the  westward  of  Cape  Clear.  The  most  recent  investiga- 
tions fail  to  reveal  such  a  feature,  but  disclose  only  a  narrow  current  of  reaction 
moving  northward  along  the  coast  of  France  when  the  winds  have  forced  the  waters 
above  the  usual  level  at  the  head  of  the  Gulf  of  Gascoyne. 

532.  Of  the  two  branches  of  the  Southern  Equatorial  Current  which  are  formed 
by  its  bifurcation  off  Cape  San  Roque,  the  northern  one,  setting  along  the  coasts  of 
northeastern  Brazil  and  of  Guiana  and  contributing  to  the  formation  of  the  Gulf 
Stream,  has  already  been  described;  the  other,  known  as  the  Brazil  Current,  flows  to 
south  and  west,  along  the  southeastern  coast  of  Brazil,  as  far  as  the  neighborhood 
of  the  island  of  Trinidad;  here  it  divides,  one  part  continuing  down  the  coast  and 
having  some  sUght  influence  as  far  as  the  latitude  of  45°  S.,  and  the  other  curving 
around  toward  east. 

533.  The  last-mentioned  branch  of  the  Brazil  Current  is  called  the  Southern 
Connecting  Current  and  flows  toward  the  African  coast  in  about  the  latitude  of  Tristan 
da  Cunha.  It  then  joins  its  waters  with  those  of  the  general  northerly  current  that 
sets  out  of  the  Antarctic  region,  forming  a  current  which  flows  to  the  northward  along 
the  southwest  African  coast  and  eventually  connects  with  the  Southern  Equatorial 
Current,  thus  completing  the  surface  circulation  of  the  South  Atlantic. 

534:.  There  is  another  current  whose  effects  are  felt  in  the  Atlantic.  It  originates 
in  the  Pacific  and  flows  around  Cape  Horn,  and  will  be  described  in  connection  with 
the  currents  of  the  Pacific  Ocean. 

535.  CuBRENTS  OF  THE  PACIFIC  OcEAN. — As  in  the  Atlantic,  the  waters  of  the 
Pacific  Ocean,  in  the  region  between  the  tropics,  have  a  general  drift  toward  the 
westward,  due  to  the  effect  of  the  trade  winds,  the  currents  produced  in  the  two 
hemispheres  being  denominated,  respectively,  the  Northern  and  the  Southern  Equa- 
torial Currents.  These  are  separated,  as  also  in  the  case  of  the  Atlantic,  by  an  east- 
setting  stream,  about  300  miles  wide,  whose  mean  position  is  a  few  degrees  north  of 
the  equator,  and  wliich  receives  the  name  of  the  Equatorial  Counter  Current. 

536.  The  major  portion  of  the  Northern  Equatorial  Current,  after  haying 
passed  the  Marianas,  flows  toward  the  eastern  coast  of  Taiwan  in  a  WNW.  direc- 
tion, whence  it  is  deflected  northward,  forming  a  current  which  is  sometimes 
called  the  Japan  Stream,  but  which  more  frequently  receives  its  Japanese  name  of 
Kuroshiwo,  or  "  black  stream."  This  current,  the  waters  of  which  are  dark  in  color 
and  contain  a  variety  of  seaweed  similar  to  "  gulf  weed,"  carries  the  wann  tropical 
water  at  a  rapid  rate  to  the  northward  and  eastward  along  the  coasts  of  Asia  and  its 
offlying  islands,  presenting  many  analogies  to  the  Gulf  Stream  of  the  Atlantic, 

The  limits  and  volume  of  the  Kuroshiwo  vary  according  to  the  monsoon,  being 
augmented  during  the  season  of  southwesterly  winds  and  diminished  during  the  prev- 
alence of  those  from  northeast.  The  current  sets  to  the  north  along  the  east  coast 
of  Taiwan  (Formosa),  and  in  about  latitude  26°  N.  changes  its  course  to  northeast, 


236  OCEAN   CURBENTS. 

amying  at  the  extreme  southwestern  point  of  Japan  by  a  route  to  westward  of  the 
Sakishima  and  Nansei  Shoto.  A  branch  makes  off  from  the  main  stream  to  fol- 
low northward  along  the  west  coast  of  Japan,  entering  the  Sea  of  Japan  by  the  Tsu- 
shima Kaikyo;  but  the  principal  current  bends  toward  the  east,  flows  through 
Osumi  Kaikyo  and  the  passages  between  the  Tokara  Gunto,  and  runs  parallel  to  the 

feneral  trend  of  the  south  shores  of  the  Japanese  islands  of  Kiushu,  Shikoku,  and 
^  [onshu,  attaining  its  greatest  velocity  between  Bimgo  Suido  and  Kii  Suido,  where 
its  average  drift  is  between  2  and  3  laiots  per  hour.  Continuing  beyond  the  south- 
eastern extremity  of  Honshu,  the  direction  of  the  stream  becomes  somewhat  more 
northerly,  and  its  width  increases,  with  consequent  loss  of  velocity.  In  the  Kuro- 
shiwo,  as  in  the  Gulf  Stream,  the  temperature  of  the  sea  water  is  an  approximate, 
though  not  an  exact,  guide  as  to  the  existence  of  the  current. 

_  537.  Near  146°  or  147°  E.  and  north  of  the  fortieth  parallel  the  Kuroshiwo 
divides  into  two  parts.  One  of  these,  called  the  Kamchatka  Current,  flows  to  the 
northeast  in  the  direction  of  the  Aleutian  Islands,  and  its  influence  is  felt  to  a  high 
latitude.  The  second  branch  continues  as  the  main  stream,  and  maintains  a  general 
easterly  direction  to  the  180th  meridian,  where  it  is  merged  into  the  north  a^d  north- 
east drift  currents  which  are  generally  encountered  in  this  region. 

638.  A  cold  countercurrent  to  the  Kamchatka  Current  sets  out  of  Bering  Sea 
and  flows  to  the  south  and  west  close  to  the  shores  of  the  Kuril  Islands,  Hokushu 
and  Honshu,  sometimes,  like  the  Labrador  Current  in  the  Atlantic,  bringing  with  it 
quantities  of  Arctic  ice.     This  is  often  called  by  its  Japanese  name  of  Oyashiwo. 

539.  On  the  Pacific  coast  of  North  America,  from  about  50°  N.  to  the  mouth 
of  the  Gulf  of  California,  23°  N.,  a  cold  current,  200  or  300  miles  wide,  flows  with  a 
mean  speed  of  three-quarters  of  a  knot,  being  generally  stronger  near  the  land  than 
at  sea.  It  follows  the  trend  of  the  land  (nearly  SSE.)  as  far  as  Point  Concepcion 
(south  of  Monterey),  when  it  begins  to  bend  toward  SSW.,  and  then  to  WSW.,  off 
Capes  San  Bias  and  San  Lucas,  ultimately  joining  the  great  northern  equatorial  drift. 

On  the  coast  of  Mexico,  from  Cape  Corrientes  (20°  N.)  to  Cape  Blanco  (Gulf  of 
Nicoya),  there  are  alternate  currents  extending  over  a  space  of  more  than  300  miles 
in  width,  which  appear  to  be  produced  by  the  prevaihng  winds.  During  the  dry 
season — January,  February,  and  March — the  currents  generally  set  f.oward  south- 
east; during  the  rainy  season — from  May  to  October — especially  in  July,  August, 
and  September,  the  currents  set  to  northwest,  particularly  from  Cosas  Island  and 
the  Guu  of  Nicoya  to  the  parallel  of  15°. 

540.  The  Southern  Equatorial  Current  prevails  between  Hmits  of  latitude  that 
may  be  approximately  given  as  4°  N.  and  10°  S.,  in  a  broad  region  extending  from 
the  American  continent  almost  to  the  one  hundred  and  eightieth  meridian,  setting 
always  to  the  west  and  with  slowly  increasing  velocity.  In  the  neighborhood  of  the 
Fiji  Islands  this  current  divides;  one  part,  known  as  the  Rossel  Current,  continues 
to  the  westward,  following  a  route  marked  by  the  various  passages  between  the 
islands,  and  later  acquiring  a  northerly  component  and  setting  through  Torres 
Strait  and  along  the  north  coast  of  New  Guinea;  the  other  part,  caUed  the  Australia 
Current,  sets  toward  south  and  west,  arriving  off  the  east  coast  of  Austraha,  along 
which  it  flows  southward  to  about  latitude  35°  S.,  whence  it  bends  toward  southeast 
and  east  and  is  soon  after  lost  in  the  currents  due  to  the  prevailing  wind. 

541.  The  general  drift  current  that  sets  to  the  north  out  of  the  Antarctic 
regions  is  deflected  until,  upon  gaining  the  regions  to  the  southwest  of  Patagonia,  it 
has  acquired  a  nearly  easterly  set;  in  striking  the  shores  of  the  South  American 
continent  it  is  divided  into  two  branches. 

The  first,  known  as  the  Cape  Horn  Current,  maintains  the  general  easterly 
direction,  and  its  influence  is  felt,  where  not  modified  by  winds  and  tidal  currents, 
throughout  the  vicinity  of  Cape  Horn,  and,  in  the  Atlantic  Ocean,  off  the  Falkland 
Islands  and  eastern  Patagonia. 

The  second  branch  flows  northeast  in  the  direction  of  Valdivia  and  Valparaiso, 
follows  generally  the  direction  of  the  coast  lines  of  Chile  and  Peru  (though  at  times 
setting  directly  toward  the  shore  in  such  manner  as  to  constitute  a  great  danger  to 
the  navigator),  and  forms  the  important  current  which  has  been  called  variously 
the  Peruvian,  Chilean,  or  Humboldt  Current,  the  last  name  having  been  given  for  the 
distinguished  scientist  who  first  noted  its  existence.     The  principal  characteristic  of 


OCEAN  QUERENTS.  237 

the  Peruvian  Current  is  its  relatively  low  temperature.  The  direction  of  the  waters 
between  Pisco  and  Payta  is  between  north  and  northwest;  near  Cape  Blanco  the 
current  leaves  the  coast  of  America  and  bears  toward  the  Galapagos  Islands,  passing 
them  on  both  the  northern  and  southern  sides;  here  it  sets  toward  WNW.  and  west; 
beyond  the  meridian  of  the  Galapagos  it  widens  rapidlj,  and  the  current  is  lost  in 
the  equatorial  current,  near  108°  W.  As  often  happens  m  similar  cases,  the  existence 
of  a  countercurrent  has  been  proved  on  diflferent  occasions;  this  sets  toward  the 
south,  is  very  irregular,  and  extends  only  a  Httle  distance  from  shore. 

542.  Currents  of  the  Indian  Ocean. — In  this  ocean  the  currents  to  the 
north  of  the  equator  are  very  irregular;  the  periodical  winds,  the  alternating  breezes, 
and  the  changes  of  monsoon  produce  currents  of  a  variable  nature,  their  direction 
depending  upon  that  of  the  wind  which  produces  them,  upon  the  form  of  neighboring 
coasts,  or,  at  times,  upon  causes  which  can  not  be  satisfactorily  explained. 

543.  There  is,  in  the  Indian  Ocean  south  of  the  equator,  a  regular  Equatorial 
Current  which,  by  reason  of  owing  its  source  to  the  southeast  trade  winds,  corresponds 
with  the  Southern  Equatorial  Currents  of  the  Atlantic  and  Pacific.  The  limits  of 
this  west-moving  current  vary  with  the  longitude  as  well  as  with  the  season.  Upon 
reaching  about  the  meridian  of  Rodriguez  Island,  a  branch  makes  oflf  toward  the 
south  and  west,  flowing  past  Mauritius,  then  to  the  south  of  Madagascar  (on  the 
meridian  of  which  it  is  480  miles  broad),  and  thereafter,  rapidly  diminishing  its 
breadth,  forming  part  of  the  AguUias  Current  a  little  to  the  south  of  Port  Natal. 

The  main  equatorial  current  continues  westward  until  passing  the  north  end  of 
Madagascar,  where,  encountering  the  obstruction  presented  by  the  African  con- 
tinent, it  divides,  one  branch  following  the  coast  in  a  northerly,  the  other  in  a  southerly 
direction.  The  former,  in  the  season  of  the  southwest  monsoon,  is  merged  into  the 
general  easterly  and  northeasterly  drift  that  prevails  throughout  the  ocean  from  the 
northern  limit  of  the  Equatorial  C\irrent  on  the  south,  as  far  as  India  and  the  adjacent 
Asiatic  shores  on  the  north;  but  during  the  northeast  monsoon,  when  there  exists  in 
the  northern  regions  of  the  Indian  Ocean  a  westerly  drift  current  analogous  to  the 
Northern  Equatorial  Currents  produced  in  the  Atlantic  and  Pacific  bv  the  northeast 
trades,  there  is  formed  an  east-setting  Equatorial  Countercurrent,  wnich  occupies  a 
narrow  area  near  the  equator  and  is  made  up  of  the  waters  accumulated  at  the 
western  continental  boundary  of  the  ocean  by  the  drift  currents  of  both  hemispheres. 

544.  The  southern  branch  of  the  Ecjuatorial  Current  flows  to  the  south  and  west 
down  the  Mozambique  Channel,  and,  being  joined  in  the  neighborhood  of  Port  Natal 
by  the  stream  which  arrives  from  the  open  ocean,  there  is  formed  the  warm  Agulhas 
Current,  which  possesses  many  of  the  characteristics  of  the  Gulf  and  Japan  streams. 
This  current  sku-ts  the  east  coast  of  South  Africa  and  attains  considerable  velocity 
over  that  part  between  Port  Natal  and  Algoa  Bay.  During  the  summer  months  its 
effects  are  felt  farther  to  the  westward ;  during  the  winter  it  diminishes  in  force  and 
extent.  The  meeting  of  the  Agulhas  Current  with  the  cold  water  of  higher  latitudes 
is  frequently  denoted  bv  a  broken  and  confused  sea. 

Upon  arriving  at  tne  southern  side  of  the  Agulhas  Bank  the  major  part  of  the 
current  is  deflected  to  the  south,  and  then  curves  toward  east,  flowing  back  into  the 
Indian  Ocean  with  diminished  strength  and  temperature  on  about  the  fortieth 
parallel  of  south  latitude,  where  its  influence  is  felt  as  far  as  the  eightieth  meridian. 
A  small  part  of  the  stream  which  reaches  Agulhas  Bank  continues  across  the  southern 
edge  of  that  bank  before  turning  to  the  southward  and  eastward  to  rejoin  the 
major  part. 

545.  Along  the  fortieth  paraUel  of  south  latitude,  between  Africa  and  Australia, 
there  is  a  general  easterly  set,  due  to  the  branch  of  the  Agulhas  Current  already 
described,  to  the  continuation  of  the  drift  current  from  the  Atlantic  which  passes  to 
southward  of  the  Cape  of  Good  Hope,  and  to  the  westerly  winds  which  largely  prevail 
in  this  region.  At  Cape  Leeuwin,  the  southwestern  extremity  of  Australia,  this 
east-setting  current  is  divided  into  two  branches;  one,  going  north  along  the  west 
coast  of  AustraUa,  blends  with  the  Equatorial  Current  nearly  in  the  latitude  of  the 
Tropic  of  Capricorn;  the  other  preserves  the  direction  of  the  original  current  and 
has  the  effect  of  producing  an  easterly  set  along  the  south  coast  of  AustraUa. 

546.  As  in  the  other  oceans,  a  general  northerly  current  is  observed  to  set  into 
the  Indian  Ocean  from  the  Antarctic  regions. 


CHAPTER  XXII. 

ICE. AND  ITS  MOVEMENT  IN  THE  NOETH  ATLANTIC  OCEAN. 


547.  Vessels  crossing  the  Atlantic  Ocean  between  Europe  and  the  ports  of  the 
United  States  and  British  America  are  liable  to  encounter  icebergs  or  extensive 
fields  of  compact  ice,  which  are  carried  southward  from  the  Arctic  region  by  the 
ocean  currents.     It  is  in  the  vicinity  of  the  Great  Bank  of  Newfoundland  that  these 


I  APRIL 

Limiting  lines  of  the  regions 
in  which  icebergs  and  field  ice" 
have  been  reported  by  mariners 
in  the  month  of  April  for  the 
years  1904  to  1913,  inclusive. 


Fig.  78. 


masses  of  ice  appear  in  the  greatest  numbers  and  drift  farthest  southward.  The 
accompanying  charts  show  the  changeable  area  in  which  icebergs  and  field  ice  have 
been  reported  by  mariners  in  the  years  1904  to  1913  in  the  months  of  April,  May, 
and  June,  when  they  occur  in  the  greatest  number. 


238 


ICE  AND  ITS  MOVEMENT  IN  THE  NOBTH  ATLANTIC  OCEAN.  239 

The  amount  of  ice  and  its  location  and  movement  are  so  variable  from  year  to 
year,  while  the  region  occupied  in  its  formation  and  transportation  is  so  vast  and 
so  little  under  special  observation,  that  no  successful  system  of  prediction  has  as  yet 
been  instituted.  The  most  that  can  be  said  now  is  that  after  an  exceptionally  open 
winter  in  the  Arctic  we  may  expect  the  ice  to  come  south  earlier  and  in  greater  quan- 
tity. After  such  a  winter  the  East  Greenland  current  starts  the  ice  stream  around 
Cape  Farewell  from  one  to  three  months  earlier,  and  this  advancing  of  the  season  is 
reflected  by  a  corresponding  advance  in  the  Labrador  Current  and  on  the  Newfound- 
land Bank.  The  greatest  calving  at  the  glaciers  of  Greenland  follows  the  breaking 
up  of  the  shore  ice,  and  hence  the  bergs  also  start  southward  earlier  and  with  more 
freedom  after  an  open  winter. 

In  April,  May,  and  June,  from  1904  to  1913,  inclusive,  icebergs  have  been  seen 
as  far  south  as  latitude  37°  50'  north  and  as  far  east  as  longitude  38°  west.  Excej)- 
tional  drifts  have  occurred  almost  down  to  latitude  30°  north  and  between  longi- 
tudes 10°  and  75°  west,  in  these  months  as  well  as  during  other  seasons  of  the  year. 
Between  Newfoundland  and  the  fortieth  parallel  floating  ice  may  be  met  in  any 
month,  but  not  often  from  August  to  December.  On  the  Great  Bank  of  New- 
foundland bergs  generally  move  southward.  Those  that  drift  westward  of  Cape 
Race  usually  pass  between  Green  and  St.  Pierre  banks.  The  Virgin  Rocks  are 
generally  surrounded  by  ice  until  the  middle  of  April  or  the  beginning  of  May. 

548.  The  Origin  of  the  Icebergs. — Most  of  the  bergs  which  annually  appear 
in  the  North  Atlantic  orifnnate  on  the  western  coast  of  Greenland ;  a  few  come  from 
the  east  coast  and  from  Hudson  Bay.  A  small  but  productive  glacier  in  southern 
Greenland  yields  the  bluish  bergs  which  are  so  hard  to  see  at  night.  The  largest 
bergs  come  from  the  glaciers  at  Umanak  Fjord  and  Disko  Bay  (Lat.  69°  to  71°),  and 
their  height  above  water  will  rise  to  500  feet ;  but  as  they  lose  in  mass  from  that  time 
forward,  we  can  not  expect  to  find  them  of  such  gigantic  height  when  they  finally 
appear  near  the  Newfoundland  Bank. 

A  huge  ice  sheet,  formed  from  compressed  snow,  covers  the  whole  of  the  interior  of 
Greenland.  The  surface  of  this  enormous  glacier,  only  occasionally  interrupted  by 
protruding  mountain  tops,  rises  slightly  toward  the  interior  and  forms  a  watershed 
between  the  east  and  west  coasts,  whicn  is  estimated  to  be  from  8,000  to  10,000  feet 
above  the  sea.  The  outskirts  oi  Greenland,  as  they  are  called,  consist  of  a  fringe 
of  islands,  mountains,  and  promontories  surrounding  the  vast  ice-covered  central 
portion  and  varying  in  widtn  from  a  mere  border  up  to  80  miles.  Upon  the  west 
side,  below  the  parallel  of  73°  of  latitude,  it  has  an  average  width  of  about  50  miles 
and  extends  witn  little  interruption  from  Cape  Farewell  to  Melville  Bay,  a  distance 
of  something  over  1,000  miles. 

Everywnere  this  mountainous  belt  is  penetrated  by  deep  fiords,  which  reach 
to  the  inland  ice,  and  are  terminated  by  the  perpendicular  fronts  of  huge  glaciers, 
while  in  some  places  the  ice  comes  down  in  broad  projections  close  to  the  margin  of 
the  sea.  All  of  these  glaciers  are  making  their  way  toward  the  sea,  and,  as  their 
ends  are  forced  out  into  the  water,  they  are  broken  off  and  set  adrift  as  bergs.  This 
process  is  called  calving.  The  size  of  the  pieces  set  adrift  varies  greatly,  but  a  berg 
from  60  to  100  feet  to  the  top  of  its  walls,  whose  spires  or  pinnacles  may  reach  from 
200  to  250  feet  in  height  and  whose  length  may  be  from  300  to  500  yards,  is  considered 
to  be  of  ordinary  size  in  the  Arctic.  These  measurements  apply  to  the  part  above 
water,  which  is  about  one-eighth  or  one-ninth  of  the  whole  mass.  Many  authors 
^ve  the  depth  under  water  as  being  from  eight  to  nine  times  the  height  above ;  this 
IS  incorrect,  as  measurements  above  and  below  water  should  be  referred  to  mass  and 
not  to  height. 

Bergs  are  being  formed  all  the  year  round,  but  in  greater  numbers  during  the 
summer  season ;  and  thousands  are  set  adrift  each  year. 

Once  adrift  in  the  Arctic  they  find  their  way  into  the  Labrador  Current  and 
begin  their  journey  to  the  southward.  It  is  not  an  unobstructed  drift,  but  one 
attended  with  many  stoppages  and  mishaps.  Many  ground  in  the  Arctic  Basin  and 
break  up  there;  others  reach  the  shores  of  Labrador,  where  from  one  end  to  the 
other  they  continually  ground  and  float;  some  break  up  and  disappear  entirely, 
while  others  get  safely  past  and  reach  the  Grand  Bank.  The  whole  coast  of  Labrador 
is  cut  up  by  numerous  islands,  bays,  and  headlands,  shoals  and  reefs,  which  makes  the 


240 


ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATLANTIC  OCEAN. 


journey  of  all  drift  a  long  one,  and  adds  greatly  to  the  destruction  of  the  bei^s  by  stop- 

Eages  and  by  causing  mem  to  break  up.     Disintegration  is  also  hastened  by  th-eir 
reaking  away  from  the  floe  ice,  for  detached  bergs  will  melt  and  break  up  rapidly 
even  in  high  latitudes  during  the  summer. 

549.  The  Ice-Bearing  Currents. — ^The  Labrador  Current  passes  to  the 
southward  along  the  coasts  of  Bafiin  Land  and  Labrador,  and,  although  it  occasionallj 
ceases  altogether,  its  usual  rate  is  from  10  to  36  mUes  per  day.  Near  the  coast  it  is 
very  much  influenced  by  the  winds,  and  reaches  its  maximum  rate  after  those  from 


Fig.  79. 


the  northward.  The  general  drift  of  the  current  is  to  the  southward,  as  shown  by 
the  passage  of  many  icebergs,  although  occasions  have  arisen  on  which  these  have 
been  observed  to  travel  northward  without  any  apparent  reason.  The  breadth  and 
depth  of  the  current  are  not  known,  but  it  is  certam  that  it  pours  into  the  Atlantic 
enormous  masses  of  water  for  which  compensation  is  derived  from  the  warm  waters 
of  the  Atlantic  and  from  the  East  Greenland  Current  that  flows  around  Cape  Farewell. 
The  flow  of  the  Polar  Current  down  the  east  coast  of  Greenland  has  been  abundantly 
demonstrated  by  the  drift  of  vessels  that  have  been  beset  in  the  ice  pack  to  the  east- 
ward of  Greenland.    This  current  turns  around  Cape  Farewell,  with  an  ice  stream 


ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATLANTIC  OCEAN.  241 

60  miles  wide,  and  then  takes  a  northwesterly  direction  along  the  Greenland  coast 
as  far  as  the  Arctic  Circle,  where  it  meets  the  southerly  current  from  Baffin  Bay. 

550.  Drift  and  Characteristics  of  Icebergs. — Not  all  the  bergs  made  in 
any  one  season  find  their  way  south  during  the  following  one,  for  only  a  small  per- 
centage of  them  ever  reach  trans-Atlantic  routes.  So  many  delays  attend  tneir 
journey  and  so  irregular  and  erratic  is  it  that  many  bergs  seen  in  any  one  season 
may  have  been  made  several  seasons  before.  If  bergs  on  their  calving  at  once  drifted 
to  the  southward  and  met  with  no  obstructions  their  journey  of  about  1,200  to  1,500 
miles  would  occupy  from  4  to  5  months,  reckoning  the  drift  of  the  Labrador  Current 
at  10  miles  a  day,  which  may  be  making  it  too  little.  Then,  if  bergs  were  liberated 
principally  in  July  and  August  they  should  reach  trans-Atlantic  routes  in  December 
and  January,  while  we  know  this  to  be  the  rare  exception.  It  is  then  seen  what  an 
important  bearing  the  shores  of  Labrador  have  in  arresting  their  flow,  when  it  is 
known  that  bergs  are  generally  most  plentiful  in  the  late  spring  and  early  summer 
months  off  the  Bank. 

It  should  not  be  supposed  that  all  bergs  follow  the  same  course  when  set  adrift 
from  their  parent  glaciers,  for,  like  floating  bodies  at  the  head  of  a  river,  some  will 
go  direct  to  the  mouth,  others  will  go  but  a  short  distance  and  lod^e,  others  still  will 
accomplish  half  the  journey  and  remain  until  another  freshet  again  floats  them^  so 
that  in  the  end  the  d6bris  will  be  composed  iopart  of  that  of  several  years'  production. 

Bergs,  when  first  liberated  on  the  west  Greenland  shore,  are  out  of  the  strongest 
sweep  of  the  southerly  current,  and  they  may  take  some  months  to  find  their  way 
out  of  Davis  Strait,  wnUe  again  others  may  at  once  drift  iato  the  current  and  move 
unobstructed  until  dissipated  in  the  Gulf  Stream.  The  difference  in  time  of  two 
bergs  reaching  a  low  latitude,  which  were  set  adrift  the  same  day,  may  cover  a  period 
of  one  or  two  years. 

Field  ice  also  offers  an  obstruction  to  bergs,  and  a  close  season  in  the  Arctic 
may  prevent  their  liberation  to  a  great  extent,  though,  from  their  deep  submersion, 
they  act  as  ice  plows  and  aid  materially  in  breaking  up  the  vast  fields  of  ice  which 
so  often  close  the  Arctic  Basin. 

Ice  fields  are  more  affected  by  wind  than  bergs.  Bergs  owe  their  drift  almost 
entirely  to  current,  so  that  they  will  often  be  noticed  forcing  their  way  through 
immense  fields  of  heavy  ice  and  going  directly  to  windward.  Advantage  is  taken  of 
this  by  vessels  in  ice  fields,  which  often  moor  to  bergs  and  are  towed  for  miles  through 
ice  in  which  they  could  not  otherwise  make  any  headway.  This  is  accomplished  by 
sinking  an  ice  anchor  into  them  and  using  a  strong  towline,  and  as  the  berg  advances 
open  water  is  left  to  leeward  while  the  loose  ice  floats  past  on  both  sides.  For  the 
same  reason  vessels,  when  beset  by  field  ice,  run  from  tne  lee  of  one  berg  to  that  of 
another,  as  leads  may  offer  themselves. 

Instances  are  not  rare  where  icebergs  were  seen  to  drift  toward  north,  making 
15  to  24  miles  a  day,  near  the  tail  of  the  Bank  and  to  the  eastward  of  Cape  Race. 

All  ice  is  brittle,  especially  that  in  bergs,  and  it  is  wonderful  how  little  it  takes 
to  accomplish  their  destruction.  A  blow  of  an  ax  will  at  times  split  them,  and  the 
report  of  a  gun,  by  concussion,  will  accomplish  the  same  end.  They  are  more  apt 
to  break  up  in  warm  weather  than  cold,  and  whalers  and  sealers  note  this  before 
landing  on  them,  when  an  anchor  is  to  be  planted  or  fresh  water  to  be  obtained.  On 
the  coast  of  Labrador  in  July  and  August,  when  it  is  j^acked  with  bergs,  the  noise  of 
rupture  is  often  deafening,  and  those  experienced  in  ice  give  them  a  wide  berth. 

When  they  are  frozen  the  temperature  is  very  low,  so  that  when  their  surface 
is  exposed  to  a  thawing  temperature  the  tension  of  the  exterior  and  interior  is  very 
different,  making  them  not  unlike  a  Prince  Rupert's  drop.  Then,  too,  during  the 
day  water  made  by  melting  finds  its  way  into  the  crevices,  freezes,  and  hence  expands, 
and,  acting  like  a  wedge,  forces  the  berg  into  fragments.  It  is  the  greatly  increased 
surface  which  the  fragments  expose  to  the  melting  action  of  the  oceanic  waters  that 
accounts  for  the  rapid  disappearance  of  the  ice  after  it  has  reached  the  northern 
edge  of  the  warm  circulatory  drift  currents  of  the  North  Atlantic  Ocean.  If  these 
processes  of  disintegration  did  not  go  on  and  large  bergs  should  remain  intact,  several 
years  might  elapse  before  they  would  melt,  and  they  would  ever  be  present  in  the 
transoceanic  routes.  In  fact,  mstances  are  on  record  in  which  masses  of  ice,  escaping 
the  influences  of  swift  destruction  or  possessing  a  capability  for  resisting  them,  have, 

21594°— 14 16 


242 


ICE  AND  ITS  MOVEMENT  IN  THE  NOBTH  ATLANTIC  OCEAN. 


by  phenomenal  drifts,  passed  into  European  waters  and  been  encountered  from  time 
to  time  throughout  that  portion  of  the  ocean  which  stretches  from  the  British  Isles 
to  the  Azores. 

Icebergs  assume  the  greatest  variety  of  shapes,  from  those  approximating  to 
some  regular  geometric  figure  to  others  crowned  with  spires,  domes,  minarets,  and 
peaks,  while  others  stiH  are  pierced  by  deep  indentations  or  caves.  SmaU  cataracts 
fall  from  the  large  bergs,  while  from  many  icicles  hang  in  clusters  from  every  pro- 


FiQ.  80. 

jecting  ledge.  They  frequently  have  outlymg  spurs  under  water,  which  are  as 
dangerous  as  any  other  sunken  reefs.  For  this  reason  it  is  advisable  for  vessels  to 
give  them  a  wide  berth,  for  there  are  cases  on  record  where  vessels  were  seriously 
damaged  by  striking  when  apparently  clear  of  the  berg.  Among  these  is  that  of  the 
British  steamship  Nessmore,  which  ran  into  a  berg  in  latitude  41°  50'  N.,  longitude 
52°  W.,  and  stove  in  her  bows.  On  dockmg  her  a  long  score  was  found  extending 
from  abreast  her  forerigging  all  of  the  way  aft,  just  above  her  keel.     Four  frames  were 


ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATLANTIC  OCEAN.  243 

broken  and  the  plates  were  almost  cut  through.  The  ship  evidently  struck  a  pro- 
jecting spur  after  her  helm  had  been  put  over,  as  there  was  clear  water  between  her 
and  the  oerg  after  the  first  collision. 

It  is  generally  best  to  go  to  windward  of  an  iceberg,  because  the  disintegrated 
fragments  wiU  have  a  tendency  to  drift  to  leeward  while  open  water  will  be  found  to 
windward.  Serious  injury  has  occurred  to  vessels  through  the  breaking  up  or  cap- 
sizing of  icebergs.  Often  the  bergs  are  so  nicely  balanced  that  the  slightest  melting 
of  their  surfaces  causes  a  shifting  of  the  center  of  gravity  and  a  consequent  turning 
over  of  the  mass  into  a  new  position,  and  this  overturning  also  frequently  takes 
place  when  bergs,  drifting  with  the  current  in  a  state  of  delicate  equihorium,  touch 
the  ocean  bottom. 

651.  Field  Ice. — Field  ice  is  formed  throughout  the  region  from  the  Arctic 
Ocean  to  the  shores  of  Newfoundland  and  yearly  leaves  the  shore  to  find  its  way 
into  the  path  of  commerce.  Starting  with  the  Arctic  field  ice  and  coming  to  the 
southward,  we  find  this  ice  growing  l^hter,  both  in  thickness  and  in  quantity,  until 
it  disappears  entirely.  Ice  made  in  wie  Arctic  is  heavier  and  has  lived  through  a 
number  of  seasons.  After  the  short  summer  in  high  latitudes  ice  begins  to  form  on 
all  open  water,  increasing  several  feet  in  thickness  each  season.  Much  of  this  remains 
nortn  during  the  following  summer,  and,  though  it  melts  to  some  extent,  it  never 
entirely  disappears,  so  that  each  succeeding  winter  adds  to  its  thickness. 

This  contmues  from  year  to  year  until  it  reaches  12  or  15  feet  in  thickness,  often 
more.  If  it  remained  perfectly  quiet  it  would  be  of  uniform  thickness,  increasing 
with  the  latitude,  but  it  is  in  a  state  of  almost  continual  motion,  often  a  very  violent 
one,  which  causes  it  to  raft  and  pile  until  it  becomes  full  of  hummocks  and  other 
irregularities.  Immense  fields  are  detached  from  the  shore  and  from  other  fields, 
and  under  the  influence  of  winds,  currents,  and  tides  are  set  in  motion  and  kept 
continually  drifting  from  place  to  place;  after  a  snow,  thaw,  or  piling  the  whole 
becomes  cemented  together  into  solid  pieces,  when  under  the  influence  of  a  low 
temperature.  The  space  of  open  water  between  the  fields  becomes  frozen,  joining 
smaller  fields,  and  making  a  solid  pack  which  will  remain  so  untU  the  elements  again 
break  it  to  pieces.  Along  the  shores  from  headland  to  headland  the  bajs  and  inlets 
often  remain  solid  for  years,  almost  invariably  through  the  Arctic  winter,  but  in 
BaflSn  Bay  and  Davis  Strait  open  water  can  be  found  at  intervals  all  the  year  round. 

Ice  becomes  rafted  in  a  variety  of  ways.  If  two  fields  are  adrift  the  one  to 
windward  will  drift  down  on  the  one  to  leeward;  the  one  which  is  rougher  on  its 
surface  gives  the  wind  a  better  hold  and  drifts  the  faster;  fields  may  be  impelled 
towards  each  other  by  winds  from  contrary  directions.  Ice  that  is  secure  to  the 
shore  is  rafted  on  its  seaward  edge  from  contact  with  that  which  is  adrift.  Fields 
in  drifting  often  have  a  turning  motion,  which  is  caused  by  contrary  currents,  or  one 
variable  in  strength  at  different  places,  or  by  the  friction  of  a  field  coming  in  contact 
with  another  field  afloat  or  one  attached  to  the  shore.  This  rotary  motion  is  especially 
dangerous  when  a  vessel  finds  itself  between  two  fields,  A  heavy  gale  will  break  up 
the  strongest  fields  at  times  and  cause  them  to  raft  and  form  hummocks. 

Small  fragments  of  bergs  find  themselves  mingled  with  Arctic  fields  and  become 
frozen  fast.  These,  when  liberated  to  the  southward,  are  called  growlers,  and  form 
low,  dark,  indigo  colored  masses,  which  are  just  awash  and  rounded  on  top  Hke  a 
whale's  back.  They  are  very  dangerous  when  in  ice  fields  which  have  become  loose 
enough  to  permit  the  passage  of  vessels  through  them,  and  should  always  be  looked 
for;  they  can  be  seen  apparently  rising  and  sinking  as  the  sea  breaks  over  them. 

During  the  spring  and  summer  months  the  bergs,  aided  by  a  rise  of  temperature, 
so  cut  up  and  weaken  the  ice  fields  that  much  ice  is  loosened  and  begins  drifting  out 
of  the  Arctic  basin.  This  is  joined  by  that  brought  from  the  waters  of  Spitzbergen  by 
the  East  Greenland  Current,  near  the  sixty- third  parallel,  whence  it  flows  down  the 
eastern  coast  of  North  America,  reaching  Cape  Chidley  about  October  or  November. 
By  this  time  the  remaining  ice  in  the  Arctic  is  being  cemented  into  solid  fields,  while 
the  ice  cap  is  being  daily  extended  to  the  southward.  As  fast  as  fields  are  detached 
the  open  water  freezes,  and  these  masses  are  forced  to  the  southward  and  can  not 
rejoin  the  soUd  pack.  With  a  westerly  wind  ice  formed  in  Hudson  Strait  and  adjacent 
waters  is  swept  out  and  joins  the  Arctic  ice,  differing  from  it  only  in  being  a  httle 
lighter. 


244  ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATIANTIC  OCEAN. 

Ice  begins  to  form  at  Cape  Chidley  about  the  middle  of  October,  at  Belle  Isle 
about  November  1,  and  by  the  middle  of  November  or  1st  of  December,  the  whole 
coast  is  soUdly  frozen.  The  dates  given  are  approximate  and  vary  from  year  to 
year,  with  many  marked  exceptions. 

The  string  of  ice  along  the  coast  of  Labrador  extends  from  headland  to  head- 
land, including  the  outlying  islands,  and  starting  from  the  heads  of  the  bays  works 
its  way  out  to  seaward,  forming  by  the  middle  of  December  an  impassable  barrier 
to  the  shore  which  will  probably  not  be  permanently  broken  until  the  latter  part  of 
April.  This  ice  varies  m  thickness  from  12  feet  at  the  northern  extreme  to  3  or  4 
feet  at  the  southern.  During  the  entire  winter  the  Arctic  drift  is  finding  its  way 
down  the  coast,  and  is  being  continually  reinforced  by  fields  broken  from  the  Labrador 
ice.  These  continue  to  the  southward  in  the  Labrador  Current  on  an  average  of 
about  10  miles  a  day,  reaching  Belle  Isle  between  the  middle  of  January  and  the 
middle  of  February. 

The  best  example  on  record  of  a  continued  drift  from  the  Arctic  is  that  of  Cap- 
tain Tyson.  On  October  14,  1871,  he  and  a  party  of  nineteen  others  were  separated 
from  the  United  States  surveying  ship  Polaris,  in  latitude  77°  or  78°  N.,  just  south  of 
Littleton  Island,  and,  being  unable  to  regain  the  ship,  remained  on  the  floe  and 
accomplished  one  of  the  most  wonderful  journeys.  After  a  drift  of  over  1,500  miles, 
fraught  with  danger  from  beginning  to  end,  they  were  picked  up  about  six  months 
later,  April  30,  1872,  by  the  Tigress,  a  sealing  steamer  from  Newfoundland,  near  the 
Strait  of  Belleisle,  in  latitude  53°  35'  N.,  and  carried  safely  into  port. 

Much  delay  in  the  southward  movement  of  the  drift  will  be  caused  by  wiads 
from  the  southward  of  west,  as  field  ice  is  affected  more  by  wind  than  current. 
The  prevailing  wind  and  weather  will  influence  the  drift  very  greatly.  Strong 
northerly  or  northwest  winds  will  increase  its  speed,  but  contrary  winds  will  hold  it 
back.  The  string  of  shore  ice  keeps  the  northern  ice  off  the  coast  and  in  the  current. 
At  times  westerly  winds  will  also  send  the  Labrador  ice  off  the  coast  and  leave  it 
entirely  clear,  but  this  does  not  happen  often.  StiU  the  outer  Labrador  ice  is  con- 
stantly being  added  to  the  Arctic  flow.  Frequently  the  bays  remain  frozen  over 
until  June;  again,  they  are  cleared  some  years  in  April,  making  a  large  variation. 
During  the  drift  the  wind  from  northwest  to  southwest  will  clear  the  ice  off  the 
coast  and  leave  a  line  of  open  water,  but  the  ice  will  be  set  on  the  coast  by  a  northeast 
wind  and  be  rafted  and  piled.  The  appearance  of  the  ice  when  it  reaches  Belle  Isle 
and  to  the  southward  would  be  a  fair  mdication  of  the  weather  it  had  encountered 
on  its  way  down.  The  rougher  the  ice  the  more  severe  the  weather.  This  floating 
ice  string  extends  approximately  200  miles  offshore  in  the  latitude  of  Cape  Harrison, 
and  spreads  more  during  its  drift,  though  narrower  farther  north.  One  small  stream 
finds  its  way  through  the  Strait  of  Belleisle,  while  the  greater  part  continues  toward 
the  northern  limit  of  the  Gulf  Stream.  By  the  middle  of  January  the  shores  of 
Newfoundland  and  Gulf  of  St.  Lawrence  are  full  of  ice,  which  has  been  frozen  there 
and  are  opened  or  closed  by  a  favorable  or  adverse  wind.  Navigation  in  the  River 
St.  Lawrence  is  closed  about  the  middle  of  November  and  does  not  open  until  about 
May.  A  wind  from  northwest  to  southwest  will  clear  the  eastern  coast  of  Newfound- 
land, while  the  Gulf  of  St.  Lawrence  may  remain  full  of  ice  until  the  1st  of  May. 
Even  after  this  date  much  ice  is  found  in  the  Gulf  until  July,  and  by  August  or  earlier 
the  field  ice  is  replaced  in  the  Strait  of  Belleisle  by  bergs. 

In  the  bight  from  Cape  Bauld  to  Fogo  Island  a  string  of  ice  is  often  found  joining 
thesepoints,  hemming  in  the  shore  for  weeks  at  a  time. 

With  each  northwest  or  westerly  wind  the  ice  is  cleared  off  the  Newfoundland 
coast,  except  from  some  of  the  deeper  bays,  and  carried  out  to  sea,  and  frecjuently 
before  the  Arctic  and  Labrador  ice  has  passed  Belle  Isle  the  Newfoundland  ice  has 
found  its  way  as  far  south  as  latitude  45°.  In  the  same  way  the  Labrador  ice  some- 
times precedes  the  Arctic  ice,  while  all  may  arrive  at  nearly  the  same  time.  Ice 
fields  often  lose  their  identity,  as  coming  from  any  one  particular  place,  by  the  constant 
intermingling  on  its  southern  journey  with  ice  made  in  a  lower  latitude. 

With  easterly  winds  the  field  ice  and  icebergs  may  block  the  harbors  on  the 
east  coast  of  Newfoundland  until  June  or  even  July,  but  these  harbors  are  usually 
open  in  May. 


ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATLANTIC  OCEAN.  245 

Ice  leaving  the  gulf  and  river  St.  Lawrence  flows  southward  through  Cabot  Strait. 
This  strait  is  never  frozen  over  completely,  but  vessels  not  specially  built  to  encounter 
ice  can  not  navigate  it  safel3r  between  the  beginning  of  January  and  the  last  of  April  on 
account  of  the  heavy  drift  ice  which  blocks  the  passage.  Nearly  every  spring,  from 
about  the  middle  of  April  to  the  middle  of  May,  a  great  rush  of  ice  out  of  the  Gulf 
of  St.  Lawrence  causes  a  block  between  St.  Paul  Island  and  Cape  Ray.  This  block, 
which  sometimes  lasts  for  three  or  four  weeks,  and  completely  prevents  the  passage 
of  ships,  is  known  as  the  bridge.  It  is  recorded  that  300  vessels  have  at  one  time  been 
detained  by  this  obstacle. 

The  ice  usually  passes  out  of  Cabot  Strait  in  the  direction  of  Banquereau  Bank, 
with  its  eastern  edge  extending  halfway  between  Scatari  and  St.  Pierre  Islands. 
Its  path  broadens  after  it  is  through  the  strait  and  is  principally  governed  by  the 
winds,  but,  under  the  influence  of  the  current  alone,  it  drifts  southwestward,  and  in 
latitude  45°  may  be  from  10  to  75  miles  in  width.  Much  of  this  ice  is  very  heavy 
and  prevents  the  passage  through  it  of  all  vessels  that  are  not  specially  built  to  encoim- 
ter  ice. 

Ice  fields  assume  a  variety  of  shapes,  depending  upon  the  influence  of  winds 
and  currents,  and  upon  their  shape  on  being  set  adrift.  Those  loosened  in  the 
Arctic  meet  with  so  many  vicissitudes  that  they  have  entirely  lost  their  original 
form  when  a  low  latitude  is  reached,  while  those  from  Newfoundland  may  remain 
approximately  intact.  Their  extent  is  governed  by  the  same  rules  and  varies  from 
a  few  scattered  pieces  to  several  hundred  miles  in  length. 

From  off  Belle  Isle  the  field  ice  finds  its  way  south  toward  the  Gulf  Stream, 
where  no  definite  shape  can  be  given  it.  In  appearance,  if  heavy  ice,  it  will  be  white, 
covered  with  snow,  and  visible  at  a  long  distance;  even  in  foggy  weather  it  can  often 
be  seen  for  some  distance.  It  is  full  of  hummocks  and  its  surface  is  very  uneven; 
blocks  have  been  piled  upon  each  other,  others  stood  on  end,  and  the  whole  mass  will 
form  an  impenetrable  field,  through  which  vessels  can  not  force  their  way. 

If  the  ice  is  lighter  the  pans  will  be  smoother  and  more  even,  the  angles  groimd 
down  by  friction  and  turned  up  at  the  edges  like  so  many  large  pond  liUes.  If  com- 
pact, no  water  is  seen;  if  loose,  wide  leads  may  extend  through  the  whole,  or  a  little 
water  be  seen  surrounding  each  cake. 

The  appearance  must  decide  whether  a  vessel  is  warranted  in  trying  to  force 
her  way  through.  In  a  smooth  sea,  where  doubt  exists,  should  a  vessel  go  dead  slow 
into  the  mass,  there  will  be  but  little  danger  in  attempting  it,  and  if  too  heavy  she 
can  haul  out.  Often  the  weather  edge  is  the  heaviest  from  being  rafted,  when  to 
leeward  it  may  be  scattering.  An  ice  field  will  often  form  a  good  lee  for  riding  out  a 
gale  of  wind,  as  it  will  break  the  force  of  the  sea.  But  care  is  necessarj  not  to  lie 
too  close,  for  the  pans  are  often  given  such  a  force  that  they  will  stave  m  the  bows 
of  the  strongest  vessel. 

A  high  temperature  will  soften  field  ice  and  make  it  very  rotten,  so  that  the 
slightest  motion  will  cause  it  to  fall  to  pieces.  On  reaching  the  waters  of  the  Gulf 
Stream  or  a  warmer  atmospheric  temperature  it  begins  to  melt,  gets  soft  and  spongy, 
and  left  in  a  calm  will  disappear  slowly.  But,  fortunately,  there  is  seldom  a  time 
when  there  is  not  a  swell  on  the  sea,  and  this  soon  breaks  tne  pans  into  small  pieces, 
thus  bringing  a  greater  surface  in  contact  with  the  melting  agency.  A  heavy  ^ale 
will  in  a  few  hours  sometimes  cause  the  destruction  of  a  large  field  by  fracture,  fnction, 
and  continued  motion,  just  as  a  calm  cold  night  may  unite  it  in  a  solid  mass.  Bergs 
plow  their  way  through  fields,  break  them  up,  and  scatter  the  pieces,  as  in  the  Arctic. 
Snow  preserves  them  and  often  ^ives  the  pans  the  appearance  of  standing  well  out 
of  water,  and  is  misleading  in  tms  particular.  By  melting  and  afterwards  freezing 
it  adds  to  the  thickness  of  the  ice. 

552.  The  Disappearance  of  the  Ice. — The  advancmg  ice  will  have  reached, 
in  the  month  of  April,  the  northern  average  limit  of  the  Gulf  Stream;  and,  having 
spread  itself  along  this  line  both  east  and  west  of  the  fiftieth  meridian,  it  enters  the 
final  stage  of  disintegration  and  rapid  disappearance. 

After  reaching  tnis  limit  of  southward  movement,  many  bergs,  on  account  of 
their  deep  immersion,  find  their  way  to  the  westward,  even  within  the  current  of  the 
Gulf  Stream,  while  field  ice  never  follows  this  course,  a  condition  that  is  accounted 


246 


ICE  AND  ITS  MOVEMENT  IN  THE  NOBTH  ATLANTIC  OCEAN. 


for  by  the  fact  that  the  Labrador  current  here  runs  under  the  Gulf  Stream,  which 
spreads  itself  out  on  the  surface  as  an  eastward-moving  current,  consisting  of  streaks 
of  warm  water  with  colder  water  between. 

The  locality  in  which  ice  of  all  kinds  is  most  apt  to  be  found  during  the  months 
of  April,  May,  and  June  Hes  between  latitude  42°  and  45°  and  longitude  47°  and  52° 
west  of  Greenwich.  Here  the  Gulf  Stream  and  the  Labrador  Current  meet,  and  the 
movement  of  the  ice  is  influenced  sometimes  by  the  one  and  sometimes  by  the  other 
of  these  currents. 


M                                                                                   W                                                                                     40-                                                ] 

1 
1 

J 

i 

General  enveloping  lines  of  1 

i    the  region  of  icebergs  and  field  1 

1    ice.  1904-1913.                          1 

»5 

1 

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.... 

.... 

— 

-— 

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.... 

— - 

\ 

— -[ 



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[ 

— - 

„. 

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r 

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— 

■\ 



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x 

if 

h 

h  \ 

s 

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ly-s^ 

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S 

1 

'-.-Si 

>^^s 

,^......4.: 

¥ 

« 

.--, 

,.•-•; 

^ 

\ 

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Srv^^kJr*^ 

^ 

Y- 

o*'"* 

x^ 

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1 
/ 

/ 

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r 

h. 

1 

h 

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1"' 

/ 

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v'^' 

■l 

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.... 

.... 

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,,|.:. 

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/ 

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1 

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\ 

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^^ 

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Fig.  81. 


Besides  the  three  charts  of  monthly  limits  for  April,  May,  and  June,  a  fourth 
chart  is  presented  showing  the  general  limits  within  which  icebergs  and  field  ice  have 
been  encountered  during  the  same  months.  ,      .    •    i- 

653.  Signs  of  the  Proximity  of  Ice.— The  proximity  of  ice  is  mdicated  by 
the  following-described  signs : 

Before  field  ice  is  seen  from  deck  the  ice  Wink  will  often  mdicate  its  presence. 
On  a  clear  day  over  an  ice  field  on  the  horizon  the  sky  will  be  much  paler  or  hghter 
in  color  and  is  easily  distinguished  from  that  overhead,  so  that  a  sharp  lookout  should 
be  kept  and  changes  in  the  color  of  the  sky  noted. 


ICE  AND  ITS  MOVEMENT  IN  THE  NORTH  ATLANTIC  OCEAN.  247 

On  a  clear  day  icebergs  can  be  seen  at  a  long  distance,  owing  to  their  brightness; 
during  foggy  weather  they  are  first  seen  through  the  fog  as  a  black  object.  In  thick 
fog  the  first  sight  of  a  berg  is  apt  to  be  a  narrow  streak  of  dark  at  the  water  line. 

They  can  sometimes  oe  detected  hj  the  echo  f^om  the  steam  whistle  or  the 
fog  horn.  In  that  case,  by  noting  the  time  between  the  blast  of  a  whistle  and  the 
reflected  sound,  the  distance  of  tne  bei^  in  feet  may  be  approximately  found  by 
multiplying  by  550.  The  absence  of  echo  is  by  no  means  proof  that  no  bergs  are 
near,  for  unless  there  is  a  fairly  vertical  wall,  no  return  of  the  sound  waves  can  be 
expected. 

The  presence  of  icebergs  is  often  made  known  by  the  noise  of  their  breaking  up 
and  falling  to  pieces.  The  cracking  of  the  ice  or  the  falling  of  pieces  into  the  sea 
makes  a  noise  like  breakers  or  a  distant  dischai^e  of  guns,  which  may  often  be  heard 
a  short  distance. 

The  absence  of  swell  or  wave  motion  in  a  fresh  breeze  is  a  sign  that  there  is  land 
or  ice  on  the  weather  side. 

The  appearance  of  herds  of  seal  or  flocks  of  murre  far  from  land  is  an  indication 
of  the  proximity  of  ice. 

The  temperature  of  the  air  falls  as  ice  is  approached,  especially  on  the  leeward 
side,  but  generally  only  at  an  inconsiderable  distance  from  it.  The  fall  of  the  tem- 
perature of  the  sea  water  has  been  held  to  indicate  the  nearness  of  ice,  but  in  regions 
where  there  is  an  intermixture  of  cold  and  warm  currents  going  on,  as  at  the  junction 
of  the  Labrador  Current  and  the  Gulf  Stream,  the  temperature  of  the  sea  has  been 
known  to  rise  as  the  ice  is  approached.  The  special  temperature  studies  made  during 
the  ice  patrol  of  1912  have  not  settled  the  question  whether  icebergs  influence  the 
temperature  of  sea  water  to  a  measurable  extent  at  distances  of  a  imle  or  so. 

A  reliable  sign  of  icebergs  being  near  is  the  presence  of  calf  ice.  When  such 
pieces  occur  in  a  curved  line,  as  they  may  do,  especially  in  calm  weather,  the  parent 
berg  is  on  the  concave  side  of  the  curve. 

No  ship  captain  can  afford  to  trust  any  of  the  above-named  signs  to  the  exclusion 
of  a  good  lookout. 

Current  Information  Regarding  Ice  Conditions.— The  branch  hydrographic 
offices  receive  daily  the  latest  information  regarding  ice  and  other  obstructions  to 
navigation,  being  furnished  with  the  reports  of  passing  vessels  and  the  ice-patrol 
ships,  as  long  as  such  are  in  service.  The^  also  distribute  the  publications  of  the 
Hydrographic  Office  dealing  with  this  topic,  namely,  the  Hydrographic  Bulletin 
(weekly)  and  the  Pilot  Chart  (monthly),  as  well  as  the  pamphlet  on  North  Atlantic 
Ice  Patrols  (Reprint  No.  24). 


APPENDIX   I. 

EXTRACTS  FEOM  THE  AMERICAN  EPHEMERIS  AND  NAUTICAL  ALMA- 
NAC, FOR  THE  YEAR  1915,  WHICH  HAVE  REFERENCE  TO  THE 
EXAMPLES  FOR  THAT  YEAR  GIVEN  IN  THIS  WORK. 


[Extracts:  Page  I.) 
AT   GREENWICH    APPARENT   NOON. 


THE  SUN'3 


AjiparerU 
Right  Ascension. 


ft.      WJ. 


Diff.  for 
1  hour. 


A  pparent 
Decimation. 


Bifl.  for 
1  hour. 


Semi- 
diameter. 


Sidereal 
Time  of 
the  Semi- 
diameter 
passing 
the 
Meridian. 


Equation  of 

Time,  to  be 

added  to 


subtracted 
from  Appar- 
ent Time. 


Diff.  for 
1  hour. 


JANUARY. 


Tues. 

19 

Wed. 

20 

Thur. 

21 

20    1  51.77 
20    6    6.99 
20  10  21.44 

10.649 
10.618 
10.586 

20  30    7.6 

+30.83 

20  17  36.1 

31.79 

20    4  41.8 

32.73 

16  17.18 

69.75 

16  17.10 

69.65 

16  17.02 

69.55 

10  38.76 

10  57.36 

11  15.20 


0.790 
0.759 
0.727 


APRIL. 


Thur. 

1 

Fri. 

2 

Sat. 

3 

Tues. 

13 

Wed. 

14 

Thur. 

15 

Fri. 

16 

Sat. 

17 

Sun. 

18 

Mon. 

19 

Tues. 

20 

Wed. 

21 

0  39  17.25 

9.095 

0  42  55.58 

9.100 

0  46  34.04 

9.105 

1  23    9.70 

9.204 

1  26  50.74 

9.217 

1  30  32.12 

9.231 

1  34  13.82 

9.245 

1  37  55.88 

9.260 

1  41  38.30 

9.275 

1  45  21.10 

9.291 

1  49    4.28 

9.308 

1  52  47.87 

9.325 

N. 


4  13  56.4 

+57.99 

4  37    6.0 

57.80 

5    0  10.7 

57.59 

8  45  15.1 

54.70 

9    7    3.5 

54.33 

9  28  42.7 

53.94 

9  50  12.4 

63.54 

10  11  32.4 

63.12 

10  32  42.2 

62.69 

10  53  41.5 

62.25 

11  14  29.9 

51.79 

11  35     7.2 

+51.31 

16     2.05 

64.47 

16     1.77 

64.49 

16     1.49 

64.51 

15  58.70 

64.83 

15  58.43 

64.88 

15  58.16 

64.93 

15  57.89 

64.98 
65.03 

15  57.62 

15  57.36 

65.09 

15  57.10 

65.15 

15  56.84 

65.21 

15  56.59 

65.27 

4  13.33 
3  55.16 
3  37.11 
0  47.70 
0  32.23 
0  17.09 
0    2.28 


0  12.17 
0  26.27 
0  39.99 

0  53.32 

1  6.26 


0.759 
0.755 
0.749 
0.651 
0.638 
0. 624 
0. 610 

0.595 
0.580 
0.564 
0.547 
0.531 


MAY. 


Thur. 
Fri. 

Sat. 

Sun. 

Sat. 

Sun. 

Mon. 

Tues. 


49  37.97 

9.640 

53  29.62 

9.664 

57  21.85 

9.689 

1  14.67 

9.713 

24  43.88 

9.858 

28  40.76 

9.882 

32  38.21 

9.905 

36  36.22 

9.928 

N. 


16  18  29.2 

+  42.67 

16  35  25.2 

41.99 

16  52    4.7 

41.30 

17    8  27.5 

40.59 

18  40  33.9 

36.09 

18  54  50.5 

35.29 

19    8  47.9 

34.48 

19  22  25.8 

+33. 67 

15  52.91 

66.37 

15  52.68 

66.45 

15  52.46 

66.53 

15  52.24 

66.61 

15  50.95 

67.10 

15  50.75 

67.18 

15  50.56 

67.27 

15  50.37 

67.35 

24.11 
29.00 
33.32 
37.04 
47.15 
46.82 
45.93 
44.48 


0.216 
0.192 
0.167 
0.143 
0.001 
0.025 
0.049 
0.072 


Note. — Mean  Time  of  the  Seraidiameter  passing  may  be  found  by  subtracting  0«.18  from  the  Sidereal  Time. 

+  prefixed  to  the  hourly  change  of  declination  indicates  that  north  declinations  are  increa-siug  and  south  declina- 
tions are  decreasing;  —  indicates  that  north  declinations  are  decreasing  and  south  declinations  increasing. 

248 


EXTEACTS  FROM   NAUTICAL  ALMANAC. 


249 


[Extracts:  Page  I.] 
AT  GREENWICH  APPARENT  NOON— Continued. 


i 

•s 

1 

o 
1 

o 

p 

THE  SUN'S 

Sidereal 
Time  of 
the  Semi- 
diameter 
passing 

the 
Meridian. 

Equation  of 

Time,  to  be 

subtracted 

from 

Dift.  for 
1  hour. 

Apparent 
Right  Ascension. 

Piff.  for 
1  hour. 

Apparent 
Decimation. 

Difl.  for 
1  hour. 

Semi- 
diameter. 

added  to 

AppareTU 

Time. 

h.     m.      s. 

». 

.       , 

• 

'         ' 

». 

m.      s. 

s. 

JUNE. 

Mon. 
Tues. 
Sun. 
Mon. 

Tue& 
Mon. 
Fri. 

Sat. 

7 

8 

13 

14 

15 
21 
25 
26 

4  57  40.  36 
6    1  47.  98 

5  22  30.  17 
5  26  39.  24 

5  30  48.  47 

5  55  45.  61 

6  12  23.  53 
6  16  32.  78 

10.311 
10.324 
10.374 
ia381 

10.387 
10.399 
10.388 
10.383 

N.  22  40  44.  5 

22  46  40.  9 

23  10  20.  4 
23  13  51.  0 

23  16  57. 1 
23  26  54.  3 
23  25  17.  0 
23  23  50.  9 

+15.34 
14.35 
9.29 
8.27 

7.24 
+  LOS 

-  5.07 

-  4.10 

15  47.  25 
15  47. 13 
15  46.  61 
15  46.  52 

15  46.  43 
15  46.  04 
15  45.  86 
15  45.  82 

68.64 
68.68 
68.84 
68.87 

68.89 
68.95 
68.92 
68.91 

1  3L85 
1  20.  82 
0  21.  59 
0    9.11 

0.453 
0.466 
0.516 
0.623 

0.529 
0.541 
0.530 
0.525 

0  3.53 

1  21. 10 

2  12.  64 
2  25.31 

JULY. 

Sat. 
Sun. 
Mon. 

10 
11 
12 

7  14  20.  54 
7  18  25.  86 
7  22  30.  75 

10.230 
10.213 
iai95 

N.  22  21    8.  4 
22  13  41.  2 
22    5  6L  0 

-18.15 

19.11 

-20.07 

15  45.  70 
15  45.  72 
15  45.  75 

68.36 
68.30 
68.24 

5    0.82 
5    9.56 
5  17.  87 

0.372 
9.355 
0.337 

OCTOBER. 

Tnbetub- 

tracted  from 

Apparent 

Time. 

Tues. 
Wed. 
Thur. 

5 
6 

7 

12  41    0.  28 
12  44  38.  83 
12  48  17.  76 

9.099 
9.114 
9.130 

S.     4  24  53.  2 

4  48    L  7 

5  11    6.  7 

-57.92 

57.78 
-67.63 

16    L63 
16    L90 
16    2.18 

64.46 
64.51 
64.57 

11  17.  06 
11  35.  02 
11  52.  60 

0.756 
0.740 
0.724 

NOTl 

t.— Me 

+ 

an  Time  of  the  Sen 
)reflxed  to  the  houi 
ions  are  decreasing 

lidiameter  passing  may  be  found  by  subtracting  0«.18  frc 
rly  change  of  declination  indicates  that  north  declination 
;  —  indicates  that  north  declinations  are  decreasing  and 

m  the  Side 
3  are  incres 
south  decli 

real  Time. 

ising  and  south  declina- 

nations  increasing. 

250 


EXTRACTS  FROM   NAUTICAL  ALMANAC. 


[Extracts:  Page  II.] 
AT  GREENWICH  MEAN  NOON. 


Day  of 

the 
Week. 


Day  of 

the 
Month. 


THE  SUN'S 


Apparent 
Right  Ascension. 


A.    tn.    «. 


Diff.  for 
1  hour. 


Apparent 
Dechnation. 


DiS.  for 
1  hour. 


Equation  of 

Time,  to  be 

subtracted  from 


added  to  Mean 
Time. 


Diff.  for 
1  hour. 


Sidereal  Time 
or  Right  As- 
cension of 
Mean  Sun. 


JANUARY. 


Tues. 

19 

Wed. 

20 

Thur. 

21 

20 

1  49.  88 

10.647 

20 

6    5.05 

10. 616 

20  10  19.  45 

10.584 

S.  20  30  13. 1 
20  17  41.  9 
20    4  48.  0 


+30. 82 

31.78 

+32.  72 


10  38.  62 

0.790 

10  57.  22 

0.759 

11  15.  07 

0.727 

19  51  11.  27 
19  55  7.  82 
19  59    4.  38 


APRIL. 


Thur. 

1 

Fri. 

2 

Thur. 

15 

Fri. 

16 

Sat. 

17 

Tuea. 

20 

Wed. 

21 

Thur. 

22 

Fri. 

23 

Sat 

24 

Sun. 

25 

Mon, 

26 

0  39  16.  61 

9.097 

0  42  54.  99 

9.102 

1  30  32.  07 

9.232 

1  34  13.  82 

9.247 

1  37  55.  92 

9.262 

1  49    4.  42 

9.309 

1  52  48.  04 

9.326 

1  56  32.  07 

9.343 

2    0  16.  52 

9.361 

2    4    L40 

9.379 

2    7  46.  73 

9.398 

2  11  32.  52 

9.417 

N. 


4  13  52.  3 

+58. 01 

4  37    2.  2 

57.81 

9  28  42.  4 

53.95 

9  50  12.  4 

53.64 
63.12 

10  11  32.  6 

11  14  30.  7 

51.79 

11  35    8. 1 

51.32 

11  55  34.  0 

50.83 

12  15  48.  0 

50.33 

12  35  49.  9 

49.82 

12  55  39.  2 

49.29 

13  15  15.  8 

+  48.75 

4  13.  39 
3  55.  21 
0  17.  09 
0    2.28 


0  12.  17 
0  53.  33 


6.27 
18.80 
30.90 
42.57 
53.80 

4.57 


0.759 
0.755 
0.624 
0.610 

0.595 
0.547 
0.531 
0.513 
0.495 
0.477 
0.458 
0.439 


0  35    3.  22 

0  38  59.  78 

1  30  14.  98 
1  34  11.  53 


38    8.09 

49  57.  75 

53  54.  31 

57  50.  86 

1  47.  42 

5  43.  97 

9  40.  53 

13  37.  08 


MAY. 


Sun. 

Mon. 

Tues. 

Wed. 

Mon. 

Tues. 

Sun. 

Mon. 


10 
11 
12 
17 
18 
30 
31 


1  15.  26 

9.7)4 

5    8.68 

9.738 

9    2.68 

9.762 

12  57.  27 

9.787 

32  38.  84 

9.905 

36  36.  84 

9.928 

24  53.  17 

10. 177 

28  57.  65 

10. 196 

N.  17  8  29.  9 
17  24  35.  6 
17  40  23.  7 
17  55  54.  2 
19  8  50. 1 
19  22  27.  9 
21  39  9.  7 
21  48  12. 1 


+  40.59 
39.87 
39.14 
38.40 
34.47 
33.65 
23.07 

+  22.13 


37.05 
40.18 
42.74 
44.71 
45.92 
44.48 
46.84 
38.91 


0.143 
0.118 
0.094 
0.070 
0.049 
0.072 
0.321 
0.339 


4  52.  31 

8  48.  86 
12  45.  42 
16  41.  98 
36  24.  76 
40  21.  32 
27  40.  01 
31  36.  56 


To  be  added  to 


JUNE. 


subtracted  from 
Mean  Time. 


Mon. 

7 

Tues. 

8 

Sun. 

13 

Mon. 

14 

Tuea. 

15 

Sun. 

20 

Mon. 

21 

4  57  40.  63 

10. 310 

5    1  48.  22 

10.323 

5  32  30.  23 

10. 373 

5  26  39.  27 

10.380 

5  30  48.  46 

10. 386 

5  51  35.  81 

10. 399 

5  55  45.  37 

10.398 

N.  22  40  44.  9 

22  46  41.  2 

23  10  20.  4 
23  13  5L  0 

23  16  57. 1 
23  26  16.  7 
23  26  54.  3 


+  15.34 
14.35 
9.29 
8.26 

7.24 

2.08 

+   1.05 


1  31.  84 
1  20.  81 
0  21.  59 
0    9.11 


0  3.53 

1  8.08 
1  21.  08 


0.453 
0.466 
0.516 
0.523 

0.529 
0.542 
0.541 


4  59  12.  47 

5  3  9.03 
5  22  51.  82 
5  26  48.  38 

5  30  44.  94 
5  50  27.  73 
5  54  24.  29 


Note. — The  Semidiameter  for  Mean  Noon  may  be  assumed  the  same  as  that  for  Apparent  Noon. 

+prefixed  to  the  hoiu-ly  change  of  declination  indicates  that  n#rth  declinations  are  increasing 
and  south  declinations  are  decreasing;  —indicates  that  north  declinations  are  decreasing  and 
south  declinations  increasing. 


Difl.  for  1  hour. 
+9».856S. 


EXTRACTS   FROM   NAUTICAL  ALMANAC. 


251 


[Extracts:  Page  11.] 
AT   GREENWICH    MEAN   NOON-Continued. 


Day  of 

the 
Week. 

Day  of 

the 
Month. 

THE  sun's 

Kquation  of 

Time,  to  be 

subtracted  from 

Mean  Tme. 

Difr.  for 
1  hour. 

Sidereal  Time 
or  Right  As- 
cension of 
Mean  Sun. 

Apparent 
Right  Ascension. 

Diff.  for 
1  hour. 

Apparent 
Declination. 

Difl.  for 
1  hour. 

ft.    m.    s. 

s. 

O            f             ft 

" 

m.    s. 

s. 

ft.          TO.          S. 

AUGUST. 

Thur. 

Fri 

Sat. 

5 
6 

7 

8  57  44.94 

9  1  35.80 
9    5  26.07 

9.631 
9.607 
9.583 

N.  17  12  38.8 
16  56  29. 5 
16  40    3. 7 

-40.04 

40.73 

-41.41 

5  55. 56 
5  49. 86 
5  43.58 

0.225 
0.250 
0.274 

8  51  49. 38 
8  55  45. 94 
8  59  42. 50 

OCTOBER. 

Equation  of 
Time,  to  be 

added  to 
Mean  Time. 

Tues. 
Wed. 
Thur. 

5 
6 

7 

12  41    2.00 
12  44  40.  59 
12  48  19.  56 

9.100 
9.116 
9.132 

S.     4  25    4.1 

4  48  12. 9 

5  11  18. 1 

-57.93 

57.79 

-57.64 

11  17.20 
11  35.16 
11  52.74 

0.756 
0.740 
0. 724 

12  52  19.20 

12  56  15. 75 

13  0  12.30 

[Extracts:  Page  IV.] 
GREENWICH    MEAN    TIME. 


THE  MOON'S 


Day  of 

the 
Month. 


SEMIDIAMETER. 


Noon.  Midnight. 


HORIZONTAL  PARALLAX. 


Noon. 


Diff.  for 
1  hour. 


Midnight. 


Diff.  for 
1  hour. 


MBRIDULN  FA8SA0K. 


Difl.  for 
1  hour. 


Noon. 


APRIL. 


10 
11 
12 
13 
14 
15 
16 
17 
18 


15  19.5 

15  11.2 

15    3.9 

14  57.6 

14  52.3 

14  48. 2 

14  45.4 

14  44.3 

14  45. 0 

15  15.2 

15    7.4 

15    0.6 

14  54.8 

14  50. 1 

14  46.  6 

14  44. 6 

14  44.4 

14  46. 2 

56    8.78 

-1.841 

55  38. 40 

1.192 

55  11.57 

1.043 

54  48.40 

0.888 

54  29.02 

0.723 

54  13.91 

0.531 

54    3.78 

0.306 

53  59.53 

-0.041 

54    2.18 

+a270 

55  53. 14 

-1.266 

55  24. 54 

1.118 

54  59.52 

0.966 

54  38. 22 

0.808 

54  20.89 

0.631 

54    8.17 

0.424 

54    0.86 

-0.179 

53  59.92 

+0.109 

54    6.43 

0.4^0 

21  50.3 

1.75 

22  31.7 

L71 

23  12.8 

1.72 

23  54.5 

1,76 

d 

0  37.7 

1.84 

1  23.0 

1.94 

2  10.7 

2.03 

3    0.4 

ZIO 

25.7 

26.7 

27.7 

28.7 

0.0 

1.0 

2.0 

3.0 

4.0 


MAY. 


6 

7 

8 

21 

22 


15  38. 2 
15  25.5 
15  14.3 
15  22. 3 
15  35.8 


15  31.6 
15  19.7 
15  9.4 
15  28.  9 
15  43. 1 


V 

57  17.33 

-2.049 

56  30. 64 

1.831 

55  49. 77 

-1.570 

56  19. 13 

+1.925 

57    8.54 

+2.179 

56  53. 33 

-1.948 

56    9.42 

1.704 

55  31. 75 

-1.432 

56  43. 07 

+2.062 

57  35.26 

+2.270 

19    6.2 

1.88 

22.0 

19  49.8 

L77 

23.0 

20  31. 5 

L71 

24.0 

5  52.3 

1.90 

7.4 

6  37.6 

1.88 

8.4 

JUNE. 


18 
19 
20 
26 

27 


15  23. 7 
15  35. 1 

15  47.7 

16  39.7 
16  35.2 


15  29.3 
15  41.3 

15  54. 2 

16  38.0 
16  31. 1 


56  24. 15 

57  6.14 
57  52.20 
61  3.14 
60  46. 43 


+  1.647 
1.844 
+  1.981 
-0.320 
-1.061 


56  44.  55 

+1.751 

57  28.76 

1.923 

58  16.20 

+2.014 

60  57.01 

-0. 699 

60  31. 65 

-1.396 

4  34.7 

1.85 

5  19.0 

1.85 

6    3.9 

1.91 

11  50.0 

2.77 

12  55.8 

2.61 

5.7 

6.7 

7.7 

13.7 

14.7 


252 


EXTRACTS  FEOM   NAUTICAL  ALMANAC. 


[Extracts:  Pages  V-XII.J 
GREENWICH  MEAN  TIME. 


THE    moon's    right   ASCENSION    AND   DECLINATION. 


Hour. 


Right  Ascension. 


h.    m.       s. 


Difl. 
for  1  m. 


Declination. 


Did. 
for  1  m. 


Hour. 


Right  Ascension 


A.    m.       s. 


Diflf. 
for  1  m. 


Declination. 


Diff. 
for  1  m. 


SATURDAY,  APRIL  10. 


SUNDAY,  JUNE  20. 


17 
18 
19 


22  55  22.  91 

1. 8743 

22  57 

15. 

29 

1.8717 

22  59 

7. 

51 

1. 8691 

s. 


5  11  8.  6 
4  56  39.  7 
4  42  10.  2 


14.476 
14.487 
14. 496 


11  45  13. 

99 

1.9983 

11  47  13. 

97 

2.0012 

11  49  14. 

13 

2.0043 

s. 


1 

54  54. 

5 

2 

10  27. 

9 

2  26    1. 

8 

15.553 
15. 561 
15.568 


THURSDAY,  APRIL  15. 


SATURDAY,  JUNE  26. 


4  2  14  41.  37 

5  2  16  39.  20 

6  2  18  37.  24 


1.9621 
1.9656 
1.9691 


N.  18  38  53.  3 

18  49  29.  4 

19  0    0.7 


10.643 
10.562 
10.481 


16 

17 
18 


18  18  38.  81 

2. 7984 

18  21  26.  59 

2. 7940 

18  24  14.  09 

2. 7894 

26  57  14.  8 
26  53  30.  0 
26  49  33.  0 


3.643 

3.848 
4.052 


SATURDAY,  MAY  22. 


10  33  32.  76 
10  35  32.  26 
10  37  31.  78 


1.9915 
1.9918 
1.9923 


N. 


7  33  18. 1 
7  18  28.  2 
7  3  35.  2 


14.805 
14.858 
14.909 


[Extracts:  Pages  relating  to  Planets.] 
GREENWICH  MEAN  TIME. 


JUPITER. 


JXTPITER. 


AprD. 


September. 


Apparent 

Right 
Ascension. 


Noon. 


Var.  of 
R.A. 
fori 
Hour. 


Noon. 


Apparent 
Declination. 


Noon. 


Var.  of 
Dec. 
fori 

Hour. 


Noon. 


Meridian 


Apparent 

Right 
Ascension. 


Noon. 


Var.  of 
R.A. 
fori 
Hour. 


Noon. 


Apparent 
Declination. 


Noon. 


Var.  of 
Dec. 
fori 

Hour. 


Noon. 


Meridian 


23  11  57.49 
23  12  45.35 
23  13  32.95 
23  14  20.30 


«. 

+2.000 
1.990 
1.979 

+1.968 


-6  13  33.  6 
6  8  4L6 
6    3  51. 0 

-5  59    L  9 


+12.20 
12.14 
12.08 

+12.01 


h.     m. 
21  38.  9 
21  35.  7 
21  32.  6 
21  29.  4 


ft.    m.      s. 
23  39    8.02 
23  38  38.64 
23  38    9.26 


-1.223 

1.224 

-1.224 


-3  58  31.  6 
4  1  44. 1 
-4    4  56. 1 


-8.03 
8.01 
-7.99 


11  59.  5 
11  55.  1 
11  50.7 


Day  of  the  Month. 


Semidiameter 

HorizontalParallax 


6th. 


16.16 
L51 


22d. 


16.36 
1.53 


16.59 
1.55 


30th. 


Day  of  the  Month. 


16.86 
L58 


Semidiameter 

Horizontal  Parallax 


5th. 


23.64 
2.21 


13th. 


21st. 


29th. 


23.75 
2.22 


23.74 
2.22 


23.62 
2.21 


EXTRACTS  FROM  NAUTICAL  ALMANAC. 

[Extracts:  Pages  relating  to  Fixed  Stars.] 

FIXED  STA.RS. 

MEAN  PLACES  FOR  1915.  0.     (Jan.  0+'»  .732,  Washington.) 


253 


star's  Name. 

Magni- 
tude. 

Right  Ascension. 

An.  Variation. 

Declination. 

An.  Variation. 

a  Ursse  Min.     (Polaris)* 

ct  Eridani  (Achemar) 

2.1 
0.6 
1.1 
3.2 
-1.6 
1.2 
0.2 
L2 

h.    m.       ». 
1  29  15.  60 
1  34  32.  979 
4  31     2.  478 
6  17  49. 125 
6  41  24.  147 

13  20  42.776 

14  11  47.  030 
16  24  11.  574 

+28.5356 
+  2.  2364 
+  3.4400 
+  3.  6307 
+  2.  6434 
+  3. 1570 
+  2.  7355 
+  3.  6741 

+88  51     6.  49 
-57  40    6.  31 
+16  20  21.  52 
+22  33  29.  65 
-16  35  55.  77 
-10  43    4.50 
+19  37  28.  04 
-26  14  39.  44 

+18.  547 
+18.  323 
+  7.  398 

-  1.671 

-  4.  808 
-18.  848 
-18.  825 

-  8.166 

rtr  Tauri  (Aldebaran) 

u  Geminorum 

(X  Canis  Maj   (Sinus) 

ez  Virginia  (Spica) 

<T  Bootia  (Arcturus) 

(X  Scorpii  (Antares) 

*Circumpolar  Star. 
APPARENT  PLACES  FOR  THE  UPPER  TRANSIT  AT  WASHINGTON. 


a  Eridani.    {AeheriMT.) 

aTaari.    (.Aldebaran.) 

a  Canls  Majoris.    (Siriiu.) 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
South. 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
North. 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
South. 

July28.7 
Aug.  7.  7 

h.  m. 
1  34 

35.86   ^ 
36.32   * 

-57  39 

29.5     - 
29.2     ** 

Apr.  10. 1 
20.1 
30.1 

h.  tn. 
4  31 

3.08     . 
3.00     ° 
2.96     " 

+16  20 

28.7     , 
28. 6     ] 
28.5     ^ 

Jan.   0.  5 
10.5 

Apr.  10.  2 
20.2 
30.2 

h.   771. 

6  41 

25.88     - 
25. 96     ** 
24.91 
24.74   ]] 
24.60   " 

-16  35 

^^■^  a* 

53.4  ^ 

63.0     ^ 

62.5  I 
6L7     " 

a  Virginia.    {Spica.) 

a  Bootis.    {Arcturus.) 

o  Scorpii.    (Antares.) 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
South. 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
North. 

Mean  Solar 
Date. 

Right 
Ascension. 

Declination 
Stnuh. 

MaylO.4 
20.4 

30.4 
June9.  3 

h.  m. 
13  20 

45. 53     , 
45.52     I 

45. 49     ^ 
45.44     ^ 

O           / 

-10  43 

It 

24.3     , 
242     I 

24.0 
23.8     ^ 

Apr.30.  5 

May  10.  5 

20.4 

h.  m. 
14  11 

49. 95     , 
49. 99     * 
50.00     ^ 

+19  36 

69.9 

7L5    \l 
73.1    ^^ 

MaySO.  5 
June  9.  5 
19.4 
July29.  3 
Aug.  8.  3 

h.  m. 
16  24 

15.21 
15.32   " 
15.40     " 
15.30 
15.19   " 

•          t 

-26  14 

53.9     ^ 

54.3  \ 
54.6     ^ 
55.4 

55.4  ® 

APPENDIX   II. 

A  COLLECTION  OF  FORMS  FOR  WORKING  DEAD  RECKONING  AND  VARI- 
OUS ASTRONOMICAL  SIGHTS,  WITH  NOTES  EXPLAINING  THEIR 
APPLICATION  UNDER  ALL  CIRCUMSTANCES. 


(The  figures  in  parenthesis  refer  to  the  Notes  following  these  forms.) 
FORM  FOR  DAY'S  WORK,  DEAD  RECKONING. 


Time. 

Compass  Course. 

Var. 

Dev. 

Lee- 
way. 

Total 
error. 

True  Course. 

Patent 
log. 

Dist. 

N. 

S. 

E. 

^-      Long. 

i 

LatUude. 

Longitude. 

O      / 

Left  at  departure  (or  noon) 

(')N.  or  S. 

(') 

E.  orW. 

Run  to 

N.  orS. 

E.  or  W. 

By  D.  R.  at 

N.  orS. 

E.  or  W. 

Run  to 

N.  orS. 

E.  or  W. 

ByD.  R.  at 

N.  orS. 

E.  orW. 

FORM  FOR  TIME  SIGHT  OF  SUN'S  LOWER  LIMB  (SUMNER  LINE). 


W.  T. 

h. 

TO.      fi. 

C-W 

+  .. 

Chro.  t. 

C.  C. 

±  .. 

(ii)G.  M.T. 
(')  Eq.  t. 

±  ... 

G.  A.  T. 

h 

Li 
P 


Si-h 


h.     TO.     8. 

G.  A.T 

L.A.T.i 


Obs.  alt.  Q 
Corr.        ± 


(3)  S.  D.        + 
(<)  I.  C.         + 


dip  — 

p.  &r.     — 


Corr. 


log  sec 
log  cosec 


log  cos 
log  sin 


log  sin  i  h 


(5)  Dec. 

H.  D.    ± 
G.  M.  T. 

Corr.    ± 

Dec. 


(•)P 


{')U 


I  «9 


N.  or  8. 


N.orS. 


h.    TO.     «. 

G.  A.T 

L.A.T.2 


Ih.    TO.    «.' 
o  ■■■,■■■■,;}£.  or  yf. 

254 


Long.3 


h.     TO.     s. 


(")  Eq.  t. 

H.  D. 
Q.  M.  T. 

Corr. 

Eq.  t. 


log  sec 
log  cosec 


log  cos 
log  sin 


log  sin  i  tt 


E.  or  W. 


TO, 

«. 

±  . 

«. 

h. 

±  . 

S. 

TO. 

«. 

FORMS  FOR  WORK.  255 

FORM  FOB  TIME  SIGHT  OF  A  STAR  (SUMNER  LINE). 


W  T. 

+  . 

±  . 

+  .. 
+  .. 

h. 

TO.      S. 

- 

or 

Obs. 
Corr. 

h 
0)  I.  C 

dip 
ref. 

W. 

Corr. 

alt. 

0 

* .... 

±  .... 

/     // 

C-W 

Chro.  t. 

C  C 

+ 

'     II 

f»M  G.  M.T. 

RAMS 

Red.  (Tab.  9) 

1    II 

G.  S.  T. 

..  E. 

R.  A.  * 

(IS)  H.  A.  from  Gr. 

4- 

1    II 

h.    m    f. 


R.A. 


Dec.  N.  orS. 


(•)P 


A  o    '    " 

Li  logrsec  (•)  I*         logeec 

p  log  cosec  logcoeec 


«i  logcos  (*•)««  logcos 

Si-h  logsin  tfh  logsin 


h.    m.    s.  2) h.    m.    g. 

Gr.H.A E.orW.  Gr.  H.  A 

(")H.A.i  E.  or  W.  log  8ln  i  <i  H.  A.i  logsln4<» 


[      A.    tn.    «.      1  (  h.    m.    s.  I 

(»<)  Long.i  J----o""'/""«"""'U-orW.  Long.i       |-o-V  V"[e.  or  W. 


FORM  FOR  TIME  SIGHT  OF  A  PLANET  (SUMNER  LINE). 


W.T. 
C-W 

S. 
b.9 

k.  TO.   ». 
+ 

Chro.  t. 
C.  C. 

± 

(»)  G.  M.  T. 
R.  A.  M. 
Red.  (Ta 

+ 

)+ 

G.  S.  T. 
R.  A.  * 

O       1       II 

h.  TO.   8. 

o 

1    II 

Obs. 

alt. 

* 

R.  A. 

Dec. 

.... 

....N.  org. 

Corr. 

± 

^ 

II 

h 

'     ;/ 

H.D. 
G.  M.  T 

± 

h. 

H.D. 
G.  M.T 

±.... 

h. 

m  par. 

+ 

(*)  I.  c. 

+ 

Corr. 

B. 
± 

Corr. 

± 

1    II 

+ 

_«_ 

k.  TO.   S. 

o      / 

■    II 

'     // 

R.  A. 

Dec. 

....N.orS. 

dip 

- 

-^ 

— 

ref. 

— 

(•) 

P 

o     . 

'    // 

/     II 

Corr. 

a. 

(IS)  H.A.fromGr E.orW.        ref. 


For  the  remainder  of  the  work,  by  which  the  hour  angles  and  thence  the  longitudes  are  found,  employ  the  method 
given  under  "  Form  for  Time  Sight  of  a  Star  (Sumner  Line)." 


256  FOEMS  FOR  WORK. 

FORM  FOB  TIME  SIGHT  OF  MOON'S  LOWER  LIMB  (SUMNER  LINE). 


k. 

"W.  T. 

m.  «. 

or 

Obs.  alt.  ^ 

(")  S.  D. 
Aug. 

(♦)  I.  c. 

dip 

W.     1st  corr. 

Approx.  alt. 
p.<fcr.(Tab.2<l 

A 

O       / 

'     // 

h.  m.  s. 
(")R.A 

8. 

M.  D.        +  

m. 
No.  Min.  ± 

(")  Dec. 

M.  D. 
No.  min, 

Corr. 

Dec. 

(')P 

o    r    r/ 
N.orS 

C-W               +  ... 

+  .... 
+  .... 

rr 

Chro.  t. 

-1- 

C.  C.              ±  ... 

m. 
■  ± 

(")  GMT 

R.  A.  M.  S.   +  ... 

+ .... 

'     n 

8. 

Corr.         ± 

h.  m.  8. 
B.  A.              

/    // 

Red.(Tab.9)+  ... 

-j- 

G.  S.  T. 

o     r     >r 

R.  A.  C 

± .... 

O       1 

'     n 

N.orS. 

(12)  H.A.fromGr.  ... 

, E. 

0+  .... 

For  the  remainder  of  the  work,  by  which  the  hour  angles  and  thence  the  longitudes  are  found,  employ  the  method 
given  under  "Form  for  Time  Sight  of  a  Star  (Sumner  Line)." 

FORM  FOR  MERIDIAN  ALTITUDE  OF  SUN'S  LOWER  LIMB. 


o      / 


Corr. 

± 

.... 

h 

(18)2 

d 

0         / 

....N.orS. 
. ...  N.  or  8. 

Lat. 

....N.orS. 

(')S.  D.      + (i»)  Dec N.orS. 

(♦)I.C.       + 


+ 


dip        — 
p.  &r.   — 


II 

H.  D.    ±  .... 

h. 

Long.  ±  .... 

1    II 

Corr.    ±  .... 

^^^_  Q       I       II 

'    "  Dec N.orS. 

Corr.     ± 

FORM  FOR  MERIDIAN  ALTITUDE  OF  A  STAR. 

o     I      II  I    II  a    I     II 

Obs.alt.5|e («)I.  C.   + Dec N.orS. 

Corr.        ± — 


A                   dip     - 

ref.     - 

(18) «  N.orS 

d                  N.orS.  - 


Lat.  N.orS. 

Corr.  ± 


FORM  FOR  MERIDIAN  ALTITUDE  OF  A  PLANET. 


Obs.  alt.  * (")par.   + 

Corr.       ± (^)I.C.    + 


(•")  z  N.orS.  dip    - 

d  N.  or  S.  ref.    — 

Lat.  N.orS.  —  , 


I    II 
Corr.  ± 


h.  m. 

G.  M.  T.,  Gr.  trans 

Corr.  for  Long.           ± 

O      t      If 

Dec N.orS. 

L.  M.  T.,  local  trans 

Long.                          ± 

G.  M.  T.,  local  trans 

H.  D.  ± 

A. 
G.M.T 

Corr.   ± 

O      1      II 

Dec N.orS. 

FORMS  FOR  WORK. 


257 


FOBM  FOB  MERIDIAN  ALTITUDE  OF  MOON'S  LOWER  LIMB. 

"    '    "  h.  m. 


Obs.  alt.  (t 


(")2 

d 


,  N.orS.      ('«)S.D. 

N.  or  S.  Aug. 

(4)1.  C. 


Lat N.orS. 


dip 

iBt  corr 


+  .. 

+  .. 


G.  M.  T.,  Gr.  trans. 

Corr. for  Long.  (Tab.U)  ± . 

L.  M.  T.,  local  trans. 
Long.  ±. 

G.  M.  T.,  local  trans. 


(")  Dec. 


M.  D. 

± 

TO. 

No.  min. 

± 

,     n 

Corr. 

± 

Dec. 

•          t          ft 

N.orS. 


N.orS. 


Approz.  Alt. 
p.(fcr.(Tab.24)  +. 


ALTERNATIVE  FORM  FOR  MERIDIAN  ALTITUDE  OF  A  BODY.  (•>) 


±  90»  00'  00" 

{n)Dec.         ± 

Corr.        ± 


Constant  ±. 
Obs.  Alt.  ±. 

Lat. 


Rules  for  signs. 

Case    I.  Lat.  &  Dec.  same  name,  Lat.  greater +90''+Dec.— Corr.— Alt. 

Case  II.  Lut.  &  Dec.  same  name,  Dec.  greater — W+Dec.+Corr.+Alt. 

Casein.  Lat.  and  Dec.  opposite  names +90°— Dec— Corr.— Alt. 

Case  IV.  Lower  transit +90°— Dec.+Corr.+Alt 


W.  T. 

C-W  ±. 

Chro.  t. 

C.  C.  ±. 

(")  G.  M.  T. 
DEq.  t,         ±. 


N.orS. 

FORM  FOR  LATITUDE  SIGHTS  OF  SUN'S  LOWER  LIMB  (SUMNEB  LINE). 

h.    m.    s. 


Q.  A.  T. 
Long.i      ±. 

L.  A.  T.i      . 


h.   m.    «. 


(")<i 


(»)  Long.]      ±. 
L.A.T.1 


h.    m.    s. 


Obs.  alt.     Q. 
Corr.  ±- 


(»)  8.  D. 
(♦)  I.  c. 


dip 
p.  <fer. 


Corr. 


(«)  Dec. 

H.  D.      ±. 
Q.  M.  T.    . 

Corr.      ±. 
Dec. 


N.orS. 


N.orS. 


Eq.  t. 

TO.      8. 

H.D.      ±. 

a. 

h. 

G.M.T.    . 

«. 

Corr.      ±. 

TO.      S 

Eo.  t. 

h.    TO.    s. 


^'  4>"  Method. 


log  sec 

log  tan log  cosec 


h 
(U)W    —  • 

9>i'      N.  or 


log  sin 
N.orS.    log  tan log  sin 


Lat.i N.orS. 


log  cos 


log  sec  

log  tan log  cosec 


9>i"    N.orS.    log  tan. 

q>^      N.orS. 

Lat.| N.  or  S. 

21594°— 14 17 


log  sin 
log  sin 

log  cos 


(»)a 


Reduction  to  Meridian. 


h           

h 

(=«)a<i»  ± 

a«,»± 

Hi          

H] 

mzi       

d          

....N.orS. 
....N.orS. 

d 

Lat.i      N.orS. 


•    I    II 


Lat.i    N.orS. 


258 


FORMS  FOR  WORK. 
FORM  FOB  LATITUDE  SIGHTS  OF  A  STAB  (SUHNEB  LINE). 

h.  m.  8.  °     '     " 


W.  T. 
C-W 

Chro.  t. 
C.  C. 

(")  G.  M.  T. 

R.  A.  M.  S. 


Red.(Tab.g)    +. 

G.  8. T. 
R.  A.* 


(»»)  H.  A. from Gr E.orW. 

(»')Long.i  E.orW. 


h.  m.  s. 


h.  m.  B, 


(»)  LOIlg.2 


}E.orW. 


E.orW. 


(  h,  m.  s.  1 


Obs.  alt.*  . 
Corr.        ±. 


(<)I.C. 


dip 
ref. 


Corr. 


h.  m.  s. 


B.A. 
Dec. 


N.  orS. 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  9'  <p"  formula  or  the  reduction  to  the 
meridian,  employ  the  methods  given  under  "Form  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 


FORM  FOB  LATITUDE  SIGHTS  OF  A  PLANET  (SUMNEB  LINE). 


W.  T. 

+ 

± 

+ 
+ 

h. 

m. 

s. 

E. 
E. 

E. 

E 
E. 

orW. 
orW. 

orW. 

orW. 
orW. 

Obs.  alt 
Corr. 

h 

(16)  par. 
(<)  I.  C. 

dip 
ref. 

Corr. 

0      / 

* 

± 

R.  A. 

H.D. 
G.  M.  T. 

Corr. 

R.A. 

h. 

m.    t. 

0 
Dec.            

/     // 

... 

.... 

... 

C-W 

±.... 

s. 

h. 

H.D.       ± 

G.  M.  T 

ChTO.  t. 

... 

.... 

... 

h. 

C.  C. 

+ 

+ 

'     " 

(»)G.  M.  T. 
R.  A.  M.  S. 
Red.(Tab.9) 

... 

.... 

... 

±  — . 

s. 

Corr.        ±.... 

1    II 

+ 

G.  8.  T. 
R.  A.* 

A. 

m.    8. 

0 
Dec.           

1     II 

... 

.... 

/     // 

(»)  H.  A.  from  Gr 



... 

(»)  Long.] 

h. 

m. 

«. 

± 

h 

0 

1 

// 

(«)  Long.i 

h. 

m. 

c. 

h. 

m. 

s. 

d 

0 

1 

// 

N.orS. 


N.orS. 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  <f>'  <ft"  formula  or  the  reduction  to  the 
meridian,  employ  the  methods  given  under  "  Forms  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 


FORMS  FOR   WORK.  259 

FORM  FOR  LATITUDE  SIGHTS  OF  MOON'S  LOWER  LIMB  (SUMNER  LINE). 

h.  m.  s.                                                            °  '  "                               h.  m.  f.                          °  '  » 
Vv .  T.  Obs.aU.C  (")R.  A.  (")  Dec N.wS. 


Chro.  t.  {■«)  8.  D.  + M.  D.        + M.  D.        ±. 

C.  C.  ± Aug.  + m. 

(«)I.  C.  + No. min.  ± No. min.  ±. 


(")  G.  M.  T. 

R.  A.  M.  8.         + 


+ «.  '  " 

Red.  (Tab.  9)    + ,^—^.  Corr.         ± Corr.         ± 


G.  S.  T.  dip  - h.m,.t.  °'" 

R.  A.^  ..^  R.  A.  Dec.  N.orS. 


(»)  H.  A.  from  Gr E.orW.  1st  Corr. 

(»)  Long.i  E.orW. 


h.  TO.  «.  1  Approx.  alt. 

p.ikr.  (Tab.  24)  +. 


}E.orW. 


h.  m.  t. 
Long.i  E.orW. 


h.  m.  t. 


^E.orW. 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  9'  9"  formula  or  the  reduction  to  the 
meridian,  employ  the  methods  given  under  "  Forms  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 

FORM  FOR  FINDING  THE  TIME  OF  HIGH  (OR  LOW)  WATER. 

d.  h.  m. 

G.  M.  T.  of  Greenwich  transit  

(»)  Corr.  for  Long.  (Tab.  11)  ± 


L.  M.  T.  of  local  transit 
Lunitidal  int.  (App.  IV) 

L.  M.  T.  of  high  (or  low)  water 


260 


FORMS   FOR  WORK. 


FORM  FOR  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE  DIFFERENCE  FOR  LAYING  DOWN  THE 
SUMNER  LINE  BY  THE  METHOD  OP  SAINT  HILAIRE  FROM  A  SIGHT  OF  THE  SUN'S  LOWER  LIMB. 

(SINE— COSINE  FORMULA.i) 


E.  or  W. 


Dec. 

H.  D.       ± 
G.  M.  T. 
Corr.        ± 

d 


L  ± 

d  ± 


N.  or  S. 


Eq.t. 
H.  D. 

G.  M.  T. 
C!orr. 

Eq.t. 


log  COS. 

±    log  cos. 
±    log  cos. 


log  sin  

log  sin  

(Sum)logA  ±    log  B    + 

A±  B  ±     

A  ±      

nat.  sin  —    A+B 


FORM  FOR  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE  DIFFERENCE  FOR  LAYING  DOWN  THE 
SUMNER  LINE  BY  THE  METHOD  OF  SAINT  HILAIRE  FROM  A  SIGHT  OF  THE  SUN'S  LOWER  LIMB. 


(COSINE— HAVERSINE  FORMULA.^) 


h.  m.  8. 


W.  T. 

~  E.orYf. 

Dec. 
H.  D. 

G.  M.  T. 
Corr. 

d 

log  hav 

log  cos 
log  cos 
log  hav  9 
nat  hav  9 
nat  hav 
nat  hav 

C— W. 

+      

± 

Chro.  t. 

C.  C. 

±      

(")  G.  M.  T. 

± 

(T)   Eq.  t. 
G.  A.  T. 

±      

± 

Long,    of 

as-1 

sumed  Pos./  

fl.  TO.  8. 

L.A.T.=t          

L 

o     /     r/ 

d 

L~d 

2 

Calculated  h  \ 
-90°-z        I 


N.  or  S.    Eq.  t. 
H.  D. 

G.  M.  T. 
Corr. 

Eq.t. 
Obs.  alt. 


(Sum) 


(Sum) 


Q 


LC. 

+ 

Corr.  (Tab.  46). 

± 

Obs.  h 

Calculated  h 

Alt.  Diflf. 

1  Sine— cosine  formula:  sin  h  =8in  L  sin  d  +  cos  L  cos  d  cos  ( 

=  A         +  B 

*  Cosine— haversine  formula:   hav  z  =hav  (L~d)  +  cos  L  cos  d  hav  t 

=hav  (L~d)  +  hav  S 


FORMS  FOR  WORK.  261 

FORM  FOB  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE  DIFFERENCE  FOR  LAYING  DOWN  THE 
SUMNER  LINE  BY  THE  METHOD  OP  SAINT  HILAIRE  FROM  A  SIGHT  OF  THE  SUN'S  LOWER  LIMB. 

(»)  (HAVERSINE  FORMULA.!) 

h.    m.    8.                                                    °    '    "  m.    t. 

W.T.  Dec.  N.orS. 


C-W  + 

Chro.  t.  H.  D. 

C.C.  ± 


(M)  G.  M.  T. 

C)  Eq.  t.  ± 


G.  A.  T 

L.ong  o 
sumed  Pos 

L.  A.  T.=t 


G.  M.  T. 


Corr 


Long  of  as-     1  „       „, 

*  I E.orW.  Dec.  N.orS. 


Eq.  t. 

H.  D.  ±     . 

< 

G.M.T.     . 
Corr  ±    . 

h 
s 

Eq.  t. 

m.  s. 

(«)  p.  D. 
CO.  L. 


CO.  L.4- P.  D nathay 

CO.  L.— P.  D nathav 


nathay  A  (Diff.) 

log  hav  A 
log  hav  t 


:} 


Obs. 

Alt. 

Q 

I.e. 

+ 

.Corr 

.  (Tab.  46 

')± 

Obs. 

h 

Calculated  /t 

Alt. 

Diff. 

log  hav  B  (Sum) 

nat  bay  B  ^ 

nat  hay  (CO.  L- P.  D.)  I 

nat  bay  z  (Bum) 


Calculated  h\ 
-90°-«     / 


FORM  FOR  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE   DIFFERENCE   FOR  LAYING  DOWN 
THE  SUMNER  LINE  BY  THE  METHOD  OF  SAINT  HILAIRE  FROM  A  SIGHT  OF  A  STAR. 

(SINE-COSINE  FORMULA.*) 


W  T 

9) 

mGr. 
isumed  Pos. 

h. 

m.  t. 

E 
E. 

.or 
or 

W. 
W. 

Obs.  alt.* 
I.  C. 
Corr.  (Tab.  46) 

Obs.  h 

t 
L± 

d  ± 

Calculated  h 
Obs.  h 

Alt.  Diff. 

o         /        // 

log  sin 
log  sin 

log  A 

A± 

nat  sin- 

Dec.  (d) 
R.  A. 

± 

± 

o      /     n 
h.  m,  B. 

N. 

or  S. 

C-W 

+  ... 

+ 

Chro  t 

±-.- 

C.C. 

log  cos 
log  cos 
log  cos 

log  B 
B    ± 
A   ± 

(U)  G.  M.  T, 
R  A  M.  8 

O         t      II 

± 

+  ... 
+  ... 

Red.  (Tab. 

(Sum) 

o         /         // 

GST 

± 

-J- 

R.  A.* 

.      A+B 

(")  H.  A.*  fro: 
C)  Long,  of  af 

t 

o 

111.    s. 

1     II 

>  Haversine  formula:  hav  z  =  {hay  (co.  L  +  P.  D.)—  hav  (co.  L— P.D.)}hav<  +  hav  (co.  L— P.D.) 

=  hav  B  +  hav  (co.  L— P.  D.) ;  where  hav  B=hav  A  hav  t,  and  hav  A=hav  (co.  L+ 
P.D.)-hav  (CO.  L— P.D.) 
*  Sine— cosine  formula:  sin  h  =sin  L  sin  d  +  cos  L  cos  d  cos  ( 
=         A         +  B 


262 


FOEMS  FOR  WORK. 


FORM  FOB  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE  DIFFERENCE  FOR  LAYING  DOWN  THE 
SUMNER  LINE  BY  THE  METHOD  OF  SAINT  HILAIRE  FROM  A  SIGHT  OF  A  STAB. 

(COSINE-HAVERSINE  FORMULA.') 

h.  m.  s.  h.  m.  s.  °    '    " 


W.  T. 

C-W.  +. 

Chro.  t. 

C.  C.  ±. 

(»)  G.  M.  T. 

R.  A.  M.S.    +. 

Red.  (Tab.  9)  +  . 

G.  8.  T.        : 

R.  A.  *  . 

(12)  H.  A.  *    r 

from  Gr.         /' 
(«)  Long,  of         \ 
assumed  Pos.ll 
t 


L-d 


Calcu- 
lated 


log  hav 

log  cos 
log  cos 


loghavO (Smu) 

;■■} 


nat  liav9... 
nat  hav   . . . 

nat  hav    (Sum) 


\       o      /       // 

h    ) =90°-3 


.E.or\V.     Ohs.h 
.E.orW.    Alt.  diff. 


Dec.  (d ) 
R.  A. 


h.  m.  s. 


-N.  orS. 


Obs.  alt.  * 

I.e.  +. 

Corr.  (Tab.  46)-. 

Obs.  h 


F<^RM   FOB  FINDING   THE   CALCULATED   ALTITUDE  AND   THE    ALTITUDE   DIFFERENCE   FOR   LAYING  DOWN 
THE  SUMNER  LINE  BY  THE   METHOD  OF  SAINT  HILAIRE  FROM  A  SIGHT  OF  A  STAB. 

(»)  (HAVEBSINE  F0BMULA.2) 


h.  m.  I. 


h.  m.  8. 


W.  T.               

or 
or 

W, 
W. 

Dec. 
(6)  P.  D. 

CO.  L. 

CO.  L-)-P.  D. 

CO.L-P.D. 

t 

CO.  L— P.  D. 

z 

Calculated/ 
=90°-  z 

...N.  or  8. 

R.  A. 

C-W             + 

o 

Obs.  alt.  jfc 

Chro.  t.           

/     // 

I.  C.                    + 

C.  C.            ± 

nat hav  

nat hav  

Corr.   (Tab  46)— 

fii)Q.  M.  T 

ft.  m. 

R.  A.  M.S.  + 

nat  hav  A 

(Diff.) 

Obs.  A 

Red.(Tab.9)+  

log  hav  A . .  . . 

1 

Calculated  A 

s. 

G.  S.  T.            

Alt.  diff. 

O        / 

J 

R.  A.  3|(              

log  hav  B 

(Sum) 

(»)  H.A.*fromi 

Gr              / 

E. 

E. 

(W)  Long,  of  as-  \ 

nat  hav 

t                      ..  . 

nat  hav 

(Sum) 

o       / 

t 

" 

^ 

I  Cosine — ^haveraine  formula:  hav  z  =hav  (L~d)  +  cos  L  cos  d  hav  t 

=hav  (L~d)  -t-  hav  d 
»  Haveraine  formula:  hav  z  =  {hav  (co.  L  -f-  P.  D.)—  hav  (eo.  L— P.  D.)}  hav  t  +  hav  (co.  L— P.  D.) 

=  hav  B  +  hav  (co.  L— P.  D.);  where  hav  B=hav  A  hav  t,  and  hav  A==hav  (co.  L-f- 
P.  D.)-hav(co.  L-P.D.) 


FORMS    FOR    WORK. 


263 


FORM   FOR   FINDING    THE    CALCULATED   ALTITUDE    AND    THE    ALTITUDE  DIFFERENCE    FOR   LAYING 
DOWN  THE  SUMNER  LINE  BY  THE  METHOD  OP  SAINT  HILAIRE  FROM  A  SIGHT  OF  A  PLANET. 


h.  m.  s. 


W.  T. 

C-W 

+  . 

Chro.  t. 

C.  C. 

± 

(U)  Q.  M.  T. 

R.  A.  M. 

S.+ 

Red.(Tab.9)+ ( 

G.8.T ] 

R.A.*  c 

C«)H.A.*from\ 

Gr.  / E.orW. 

(*>)  Long,  of  ti»-\ 

sumed  Pes/ E.  orW. 

h.  TO.  ». 


(SINE-COSINE  FORMULA!) 

A.      TO.      8. 


R.  A. 

Dec. 

i. 

H.  D. 

±... 

h. 

H.  D. 

G.  M.  T. 

G.  M.  T. 

s. 

COIT. 

±... 

Corr. 

R.  A. 

d 

.N.  or  S.Obs.  alt. 
I.  C. 


Calculated  h 


logsin  ± 

log  sin  ± 

(8um)logA     ± 

A  ± 

nat.  sin 


Corr.(Tab.46).-. 

Obs.  h 

Calculated  ft 
Alt.  Diff. 


log  COS 
log  COS 

lug  cos 
logB 

B 


A 

•A+B 


FORM  FOR  FINDING   THE  CALCULATED   ALTITUDE   AND   THE  ALTITUDE    DIFFERENCE    FOR    LAYING 
DOWN  THE  SUMNER  LINE  BY  THE  METHOD  OF  SAINT  HILAIRE  FROM  A  SIGHT  OF  A  PLANET. 


A.  m.  ». 


(COSINE-HAVERSINE  FORMULA.') 

h.  m.  I.  h.  m,  8. 


W.  T.                .... 

(             

log  hav    

R.  A.      ... 

Dec 

N.  orS. 

o      / 
L             

log  cos     

C-W              + 

H.D.±... 

8. 

h. 

8. 

H.  D.  ±.... 

G.  M.  T 

Corr.  ±  

ri 

log  cos     

G.M.T.... 

Chro.  t.            

d            

A. 

C.C.              ± 

Ioghav0 

nat  hav 0 ..... 

(Sum)  Corr.  ±... 

I     n 

(")G.  M.  T 

•!            R.  A.      ... 

d 

o     1     tr 

Ob8.alt 

Jl- 

R.A.M.8.     + 

L~d      

nat  hav    . . . . , 

(Sum) 

Red.(Tab.9)+ 

z            

nat  hav    . . . . , 

G.  8.  T.            

o 

-W-z 

R.  A.  *            

Calcu-I 
latedAi 

I.e.     + 

Corr.  (Tab.  46)— 

E.  orW. 
E.  or  W. 

(H)  H.A.5icfrom\ 

Gr.             /  

Obs.  A 

(")  Long,  of  as-\ 

sumed  Pos.i  

Calcu-  \ 
lated  A/ 

t                       

Alt.  Diff. 

'  Sine— cosine  formula:  sin  A  =-sin  L  sin  i  +  cos  L  cos  i  cos  t 

=  A  +  B 

» Cosine — haverslne  formula:  hav  z  =hav  (L~<i)  +  cos  L  cos  d  hav  t 

-hav  (L~d)  +  hav  Q 


264 


rOBMS    FOR    WORK. 


FOEM  FOB  FINDING  THE  CALCULATED  ALTITUDE  AND  THE  ALTITUDE  DIFFERENCE  FOB  LAYING  DOWN  THE 
SUMNEB  LINE  BY -THE  METHOD  OP  SAINT  HILAIBE  FROM  A  SIGHT  OF  A  PLANET. 


h.  m.  f. 


(»)  (HAVEBSINE  FORMULA.)^ 

o      t      11 


W.  T. 

orW. 
,  or  W. 

Dec. 
H.D. 
G.  M.  T. 
Corr. 

Dec. 

(«)  P.  D. 
CO.  L 

CO.  L  +  P 
co.L-P 

R.A. 

H.D. 

G.M.T. 

Corr. 

R.  A. 

N. 

N. 

or 
or 

S. 

S. 

CO.L  +  P.D 

co.L-P.D 

h.  m. 
t                

, . .  nat  hav     

nat hav     

+ 

c-w 

II 
± 

h 

Chro.  t. 

nat  hav  A 

....(Dili.) 
...1 

C.  C. 

± 

± 

s. 

(")  G.  M.  T. 

o      /      // 

1 

+ 

9)  + 

.... 

co.L-P.D 

R  A.  M  S. 

log  hav  B 

nat  havB 

...(Sum) 

Red.  (Tab. 

nathav     

G.  S.  T. 

o     /      >r 

.D 

.D 

R.  A.  * 

nathav    

. . .  (Sum) 

(«)  H.A.*froii 

aGr 

as-i 
OS./    

E. 

E, 

h.  m.  s. 

(^)hong .  of 
sumed  P' 

s. 
± 

h. 

o      / 

Calculated  h\ 

//                              o    / 

Obs.ftlt 

" 

( 

=90°-z     / 
Obs.h             

....1.  0.       + 

Corr.  -\ 
....(Tab.  46)/ 

s. 
± 

h.  VI.  s. 

Alt.  Diff 

... 

Obs.     h     

1  Haversine  formula:  hav  z  =  {hav  (co.  L  +  P.  D.)—  hav  (co.  L— P.  D.)}  hav  t  +  hav  (co.  L— P.  D.) 

=  hav  B  +  hav  (co.  L— P.  D.);  where  hav  B=hav  A  hav  t,  and  hav  A=hav  (co.  L-l- 
P.  D.)-haT  (CO.  L-P,  D.) 


FORMS    FOR    WOfeK.  265 

NOTES  RELATING  TO  THE  FORMS. 

1.  It  is  not  necessary  to  convert  departure  Into  difference  of  longitude  for  each  course;  it  will  suflBce  to  make  one 
conversion  for  the  sum  of  all  the  departures  used  in  bringing  forward  the  position  to  any^particular  time. 

2.  In  D.  R.  it  will  be  found  convenient  to  work  Lat.  and  Long,  in  minutes  and  tenths,  rather  than  in  minutes  and 
eeconds. 

3.  If  upper  limb  is  observed,  the  correction  for  8.  D.  should  be  negative,  instead  of  positive. 

4.  A  positive  I.  C.  has  been  assiuned  for  illustration  throughout  the  forms;  if  negative,  it  should  be  included  with  the 
minus  terms  of  the  correction. 

6.  For  time  sights  and  <p'  <p"  sights,  take  Dec.  and  Eq.  t.  from  Naut.  Aim.,  p.  II  (Q.  M.  noon). 

6.  To  obtain  p,  subtract  Dec.  from  90°  if  of  same  name  as  Lat.;  add  to  90°  if  of  opposite  name. 

7.  Sign  of  Eq.  t.  that  of  application  to  mean  time. 

8.  If  Q.  A.  T.  is  later  than  L.  A.  T.,  Long,  is  west;  otherwise  it  is  east. 

9.  If  Lat.  is  exactly  known,  a  second  latitude  need  not  be  employed. 

10.  St  and  st—h  may  be  obtained  by  applying  half  the  difference  between  Li  and  In,  with  proper  sign,  to  «i  and  si—h, 
respectively. 

11.  The  G.  M.  T.  must  represent  the  proper  number  of  hours  from  noon,  the  beginning  of  the  astronomical  day;  to  obtain 
this  it  may  be  necessary  to  add  12h  to  the  Chro.  t. 

12.  H.  A.  from  Greenwich  is  the  difference  between  G.  S.  T.  and  R.  A.,  and  should  be  marked  W.  if  the  former  is  greater 
otherwise,  E. 

13.  Local  H.  A.  is  marked  E.  or  W.,  according  as  the  body  is  east  or  west  of  the  meridian  at  time  of  observation. 

14.  Subtract  local  hour  angle  from  Greenwich  hour  angle  to  obtain  longitude;  that  is,  change  name  of  local  hour  angle 
and  combine  algebraically. 

15.  The  forms  include  a  correction  for  the  parallax  of  a  planet,  but  in  most  cases  this  is  small,  and  may  be  omitted.  When 
used,  take  hor.  par.  from  Naut.  Aim.  and  reduce  to  observe  altitude  by  Table  17.  The  semidiameter  of  a  planet  may  be 
disregarded  in  sextant  work  if  the  center  of  the  body  is  brought  to  the  horizon  line. 

16.  If  upper  limb  is  observed,  the  corrections  for  8.  D.  and  Aug.  should  be  negative,  instead  of  positive. 

17.  R.  A.  and  Dec.  are  to  be  picked  out  of  Naut.  Aim.  for  nearest  hour  of  G.  M.  T.,  and  to  be  corrected  for  the  number  of 
minutes  and  tenths. 

18.  Mark  zenith  distance  N.  or  S.  according  as  zenith  is  north  or  south  of  the  body  observed;  mark  Dec.  according  to  its 
name,  subtracting  it  from  180°  for  cases  of  lower  transit;  then,  in  combining  the  two  for  Lat.,  have  regard  to  their  names. 

19.  For  meridian  altitudes,  take  Dec.  from  Naut.  Aim.,  p.  I  (G.  A.  noon). 

20.  This  form  enables  "Constant"  to  be  worked  up  before  sight  is  taken,  and  gives  latitude  directly  on  completion  of 
meridian  observation.  Longitude  and  altitude  at  transit  must  be  known  in  advance  with  sufficient  accuracy  for  correcting 
terms. 

21.  The  details  of  obtaining  Dec.  at  transit  and  correction  for  altitude  are  shown  in  the  meridian  altitude  forms  for  each 
of  the  various  bodies. 

22.  In  an  a.  m.  sight  subtract  L.  A.  T.  from  24h  to  obtain  t;  in  a  p.  m.  sight  L.  A.  T.  is  equal  to  t. 

23.  If  Long,  is  exactly  known,  a  second  longitude  need  not  be  employed. 

24.  Mark  <p"  N.  or  8.  according  to  name  of  Dec,  and  subtract  it  from  180°  when  body  is  nearer  to  lower  than  to  upper 
transit;  mark  ^'  N.  or  S.  according  as  zenith  is  north  or  south  of  the  body;  then  combine  for  Lat.  having  regard  to  the  names. 

25.  Take  a  from  Table  26  and  aP  from  Table  27. 

26.  Add  for  upper,  subtract  for  lower  transits. 

27.  Subtract  longitude  from  Greenwich  hour  angle  to  obtain  local  hoar  angle;  that  is,  change  name  of  longitude  and 
combine  algebraically. 

28.  Add  for  west,  subtract  for  east  longitude. 

29.  As  the  trigonometric  functions  are  all  haversines  in  this  solution,  the  abbreviation,  hav,  might  be  omitted,  and  the 
abbreviations,  nat  and  log,  might  be  employed  to  indicate  the  natural  haversine  and  the  log  haversine,  respectively. 


APPENDIX  III. 

EXPLANATION  OF  OEETAIN  EULES  AND  PEINOIPLES  OF  MATHEMATICS 
OF  USE  IN  THE  SOLUTION  OF  PEOBLEMS  IN  NAVIGATION. 


DECIMAL   FRACTIONS. 

Fractions,  or  Vulgar  Fractions,  are  expressions  for  any  assignable  part  of  a  unit ;  tliey  are  usually 
denoted  by  two  numbers,  placed  one  above  the  other,  with  a  line  between  them ;  thus  i  denotes  the 
fraction  one-fourth,  or  one  part  out  of  four  of  some  whole  quantity,  considered  as  divisible  into  four 
equal  parts.  The  lower  number,  4,  is  called  the  denominator  of  the  fraction,  showing  into  how  many 
parts  the  whole  is  divided ;  and  the  upper  number,  1,  is  called  the  numerator,  and  shows  how  many  of 
those  equal  parts  are  contained  in  the  fraction.  It  is  evident  that  if  the  numerator  and  denominator  be 
varied  in  the  same  ratio  the  value  of  the  fraction  will  remain  unaltered  ;  thus,  if  both  the  numerator 
and  denominator  of  the  fraction  J  be  multiplied  by  2,  3,  4,  etc.,  the  fractions  arising  will  be  f,  -rj,  -f^, 
etc.,  all  of  which  are  evidently  equal  to  J. 

A  Decimal  Fraction  is  a  fraction  whose  denominator  is  always  a  unit  with  some  number  of  ciphers 
annexed  and  the  numerator  any  number  whatever ;  as  ■^,  -rhst  Tuhsr  etc.  And  as  the  denominator  of 
a  decimal  is  always  one  of  the  numbers  10,  100,  1000,  etc.,  the  necessity  for  writing  the  denominator, 
may  be  avoided  by  employing  a  point ;  thus,  -^  is  written  .3,  and  -^  is  written  .14  ;  the  mixed  number 
Srbir,  consisting  of  a  whole  number  and  a  fractional  one,  is  written  3.14. 

In  setting  down  a  decimal  fraction  the  numerator  must  consist  of  as  many  places  as  there  are 
ciphers  in  the  denominator ;  and  if  it  has  not  so  many  figures  the  defect  must  be  supplied  by  placing 
ciphers  before  it ;  thus,  Tiif;ff=.16,  ^^^^=.016,  -nyVVTr=-0016,  etc.  And  as  ciphers  on  the  right-hand  side 
of  integers  increase  their  value  in  a  tenfold  proportion,  as  2,  20,  200,  etc.,  so  when  set  on  the  left  hand 
of  decimal  fractions  they  decrease  their  value  in  a  tenfold  proportion,  as  .2,  .02,  .002,  etc. ;  but  ciphers 
set  on  the  right  hand  of  these  fractions  make  no  alteration  in  their  value;  thus,  .2  is  the  same  as 
.20  or  .200. 

The  common  arithmetical  operations  are  performed  the  same  way  in  decimals  as  they  are  in  inte- 
gers, regard  being  had  only  to  the  particular  notation  to  distinguish  the  integral  from  the  fractional 
part  of  a  sum. 

Addition  op  Decimals. — Addition  of  decimals  is  performed  exactly  like  that  of  whole  numbers, 
placing  the  numbers  of  the  same  denomination  under  each  other,  in  which  case  the  separating  decimal 
pbints  will  range  straight  in  one  column. 

Examples. 

Inches. 
Add:         26.7  1.26  272.3267 

.0134 
2. 1576 
31.4 


Miles. 

Feet. 

26.7 

1.26 

32.15 

2.31 

143. 206 

1.785 

.003 

2.0 

Sum:      202.059  7.355  305.8977 

Subtraction  of  Decimals. — Subtraction  of  decimals  is  performed  in  the  same  manner  as  in  whole 
numbers,  observing  to  set  the  figures  of  the  same  denomination  and  the  separating  points  directly 
under  each  other. 

Examples. 


From  : 
Take: 

31. 267 
2.63 

36.75 
.026 

36. 724 

1.254 
.316 

.938 

1364.2 
25. 163 

Difference : 

28. 637 

1339. 037 

Multiplication  of  Decimals. — Multiply  the  numbers  together  as  if  they  were  whole  numbers, 
and  point  off  as  many  decimals  from  the  right  hand  as  there  are  decimals  in  both  factors  together ;  and 
when  it  happens  that  there  are  not  so  many  figures  in  the  product  as  there  must  be  decimals,  then 
prefix  such  number  of  ciphers  to  the  left  hand  as  will  supply  the  defect. 

Example  I.  _->  Example  II. 


Multiply  3. 25  by  4. 5 

3.25 
4.5 


1625 
1300 

Answer :      14.  625 

In  one  of  the  factors  is  one  decimal,  and  in  the 
other  two ;  their  sum,  3,  is  the  number  of  decimals 
of  the  product. 

266 


Multiply  .  17  by  .06 

.17 
.06 


Answer :  .  0102 


In  each  of  the  factors  are  two  decimals;  the  pro- 
duct ought  therefore  to  contain  4 ;  and,  there  being 
only  three  figures  in  the  product,  a  cipher  must  be 
prefixed. 


RULES  AND  PRINCIPLES   OF   MATHEMATICS. 


267 


Example  III. 

Example  IV. 

Multiply  0.5  by  0.7 

Multiply  .18  by  24 

0.5 

0.7 

.18 
24 

Ner:        0.35 

72 
36 

Answer:         4.32 

Division  of  Decimals.  —Division  of  decimals  is  performed  in  the  same  manner  as  in  whole  num- 
bers. The  number  of  decimals  in  the  quotient  must  be  equal  to  the  excess  of  the  number  of  decimals 
of  the  dividend  above  those  of  the  divisor;  when  the  divisor  contains  more  decimals  than  the  dividend, 
ciphers  must  be  affixed  to  the  right  hand  of  the  latter  to  make  the  number  equal  or  exceed  that  of  the 
divisoi. 


Example  I. 
Divide  14.625  by  3.25 

3.25)14.625(4.5 
13  00 


1625 
1625 


In  thi»  example  there  are  two  decimals  in  the 
divisor  and  three  in  the  dividend;  hence,  there  is 
one  decimal  in  the  quotient. 

Example  II. 

Divide  3.1  by  .0062 
Previous  to  the  division  affix  three  ciphers  to 
the  right  hand  of  3.1,  to  make  the  number  of  deci- 
mals in  the  dividend  equal  the  number  in  the 
divisor. 

.0062)3.1000(500 
3  10 


000 


Example  III. 
Divide  17.256  by  1.16 

1.16)17.25600(14.875-}- 
11  6 

565 
464 

1016 
928 

880 

812 

680 
580 

100 

By  pursuing  the  operation  further  the  quotient 
may  be  carried  out  as  many  decimal  placea  aa 
desired. 


Multiplication  of  Decimals  by  Contraction. — The  operation  of  multiplication  of  decimal  fractions 
may  be  very  much  abbreviated  when  it  is  not  required  to  retain  any  figures  beyond  a  certain  order  or 
place;  this  will  constantly  occur  in  reducing  the  elements  taken  from  the  Nautical  Almanac  from  Green- 
wich noon  to  later  or  earUer  instants  of  time. 

In  multiplying  by  this  method,  omit  writing  down  that  part  of  the  operation  which  involves 
decimal  places  below  the  required  order,  but  mental  note  should  be  made  of  the  product  of  the  first 
discarded  figure  by  the  multiplying  figure,  and  the  proper  number  of  tens  should  be  carried  over  to 
insure  accuracy  in  the  lowest  decimal  place  sought. 

Example:  Required  the  reduction  for  the  sun's  declination  for  7''. 43,  the  hourly  difference  being 
58''''.  18,  where  the  product  is  required  to  the  second  decimal. 


By  ordinary  method. 
58'M8 
7^43 


By  contraction. 

58'M8 
7\4S 


17454 
23272 
40726 

432^^2774 


1.74 

23.27 

407.26 

432.'''27 


In  the  contracted  method,  for  the  multiplier  .03  it  is  not  necessary  to  record  the  product  of  any 
figures  in  the  multiplicand  below  units;  for  the  multiplier  .4,  none  below  tenths;  but  in  each  case 
observe  the  product  of  the  left-hand  one  of  the  rejected  figures  and  carry  forward  the  number  of  tens. 


268 


EULES  AND  PRINCIPLES  OF   MATHEMATICS. 


RULES    AND    PEINCIPLES    OF    MATHEMATICS. 

Reduction  op  Decimals. — To  reduce  a  vulgar  fraction  to  a  decimal,  add  any  number  of  ciphers  to 
the  numerator  and  divide  it  by  the  denominator;  the  quotient  will  be  the  decimal  fraction.  The  decimal 
point  must  be  so  placed  that  there  may  be  as  many  figures  to  the  right  hand  of  it  as  there  were  added 
ciphers  to  the  numerator.  If  there  are  not  so  many  figures  in  the  quotient  place  ciphers  to  the  left  hand 
to  make  up  the  number. 


Example  I. 

Reduce  -^  to  a  decimal. 
50)L00 

.02  Answer. 

Example  II. 

Reduce  |  to  a  decimal. 
8)3.000 


,375  Answer. 
Example  III. 

Reduce  3  inches  to  the  decimal  of  a  foot. 

Since  12  inches=l  foot  this  fraction  is  y\. 

12)8.00 


.25  Answer. 


Example  IV. 

Reduce  15  minutes  to  the  decimal  of  an  hour. 
Since  60"^  =  1*^,  this  fraction  is  ^. 
60)15.00 


.25  Answer. 
Example  V. 
Reduce  17""  22"  to  the  decimal  of  an  hour. 


22= 
22*  =  — 
60 


0™.37. 


17°' 37  = 


17^37 

=0^289+ Answer. 


60 


Any  decimal  may  be  reduced  to  lower  denominations  of  the  same  quantity  by  multiplying  it  by  the 
number  representing  the  relation  between  the  respective  denominations. 
Example  VI.  Reduce  7.231  days  to  days,  hours,  minutes,  and  seconds. 


Answer:  7^  5^  32"»  38».4. 


0-1.231 
24 

0i'.544 
60 

0'".640 
60 

924 
462 

32"'.640 

38''.400 

51^.544 


GEOMETRY. 


Geometry  is  the  science  which  treats  of  the  description,  properties,  and  relations  of  magnitudes,  of 
which  there  are  three  kinds;  viz,  a  line,  which  has  only  length  without  either  breadth  or  thickness;  a 
surface,  comprehended  by  length  and  breadth;  and  a  solid,  which  has  length,  breadth,  and  thickness. 

Appoint,  considered  mathematically,  has  neither  length,  breadth,  nor  thickness;  it  denotes  position 
simply. 

A  line  has  length  without  breadth  or  thickness. 
A  surface  has  length  and  breadth  without  thickness. 
A  solid  has  length,  breadth,  and  thickness. 

A  straight  or  right  line  is  the  shortest  distance  between  two  points  on  a  plane  surface. 
A  plane  surface  is  one  in  which,  any  two  points  being  taken,  the  straight  line  between  them  lies 
wholly  within  that  surface. 

Parallel  lines  are  such  as  are  in  the  same  plane  and  if  extended  indefinitely  never  meet. 

A  circle  is  a  plane  figure  bounded  by  a  curved  line  of  which  every  point  is 
equally  distant  from  a  point  within  called  the  center.  The  bounding  curve  of 
the  circle  is  called  the  circumference. 

The  radius  of  a  circle,  or  semidiameter,  is  a  right  line  drawn  from  the 
center  to  the  circumference,  as  AC  (fig.  82);  its  length  is  that  distance  which 
is  taken  between  the  points  of  the  compasses  to  describe  the  circle. 

A  diameter  of  a  circle  is  a  right  line  drawn  through  the  center  and  termi- 
nated at  both  ends  by  the  circumference,  as  ACB,  its  length  being  twice  that 
of  the  radius.  A  diameter  divides  the  circle  and  its  circumference  into  two 
equal  parts. 

An  arc  of  a  circle  is  any  portion  of  the  circumference,  as  DFE. 
The  chord  of  an  arc  is  a  straight  line  joining  the  ends  of  the  arc.     It  divides 
the  circle  into  two  unequal  parts,  called  segments,  and  is  a  chord  to  them  both; 
thus,  DE  is  the  chord  of  the  arcs  DFE  and  DGE. 
A  semicircle,  or  half  circle,  is  a  figure  contained  between  a  diameter  and  the  arc  terminated  by  that 
diameter,  as  AGB  or  AFB. 


Fig.  82. 


RULES  AND  PRINCIPLES   OF   MATHEMATICS.  269 

Any  part  of  a  circle  contained  between  two  radii  and  an  arc  is  called  a  sector,  aa  GCH. 

A  quadrant  ia  half  a  semicircle,  or  one-fourth  part  of  a  whole  circle,  as  CAG. 

All  circles  are  Bupi)08ed  to  have  their  circumferences  divided  into  360  equal  parts,  called  degrees; 
each  degree  is  divided  into  60  equal  parts,  called  minutes;  and  each  minute  into  60  equal  parts,  called 
seconds;  an  arc  ia  measured  by  the  number  of  degrees,  minutes,  and  seconds  that  it  contains. 

A  sphere  is  a  solid  bounded  by  a  surface  of  which  every  point  is  equally  distant  from  a  point  within, 
which,  as  in  the  circle,  is  called  the  center.  Substituting  surface  for  circumference,  the  definitions  of  the 
radius  and  diameter,  as  given  for  the  circle,  apply  for  the  sphere. 

An  angle  is  the  inclination  of  two  intersectmg  lines,  and  is  measured  by  the  arc  of  a  circle  inter- 
cepted between  the  two  lines  that  form  the  angle,  the  center  of  the  circle  being  the  point  of  intersection. 

A  right  angle  is  one  that  is  measured  by  a  quadrant,  or  90°.  An  acute  angle  ia  one  which  is  less  than 
a  right  angle.     An  obtuse  angle  is  one  which  is  greater  than  a  right  angle. 

A  plane  triangle  is  a  figure  contained  by  three  straight  lines  in  the  same  plane. 

When  the  three  sides  are  equal,  the  triangle  ia  called  equilateral;  when  two  of  them  are  equal,  it  ia 
called  isosceles.  When  one  of  the  angles  is  90°,  the  triangle  la  said  to  be  right-angled.  When  each  angle 
is  less  than  90°,  it  is  said  to  be  acute-angled.  When  one  is  greater  than  90°,  it  ia  said  to  be  obtuse-angled. 
Triangles  that  are  not  right-angled  are  generally  called  oblique-angled. 

A  quadrilatercd  figure  is  one  bounded  by  four  sides.  If  the  opposite  sides  are  parallel,  it  is  called  a 
parallelogram.  A  parallelogram  having  all  its  sides  equal  and  ita  angles  right  angles  is  called  a  square. 
When  the  angles  are  right  angles  and  only  the  opposite  sides  equal,  it  is  called  a  rectangle. 

In  a  right-angled  triangle  the  side  opposite  the  right  angle  is  called  the  hypotenuse,  one  of  the  other 
sides  is  called  the  base,  ancf  the  third  side  is  called  the  perpendicular.  In  any  oblique-angled  triangle, 
one  side  having  been  assumed  as  a  base,  the  distance  from  the  intersection  of  the  other  two  sides  to  the 
base  or  the  base  extended,  measured  at  right  angles  to  the  latter,  ia  the  perpendicular.  In  a  parallelo- 
gram, one  of  the  sides  having  been  assumed  as  the  base,  the  distance  from  ita  opposite  side,  measured 
at  right  angles  to  ita  direction,  ia  the  perpendicular.  The  term  oMtude  ia  sometimes  substituted  for 
perpendicular  in  this  sense. 

Every  section  of  a  sphere  made  by  a  plane  is  a  circle.  A  great  circle  of  a  sphere  is  a  section  of  the 
surface  made  by  a  plane  which  passes  through  its  center.  A  smaU  circle  ia  a  section  by  a  plane  which 
intersects  the  sphere  without  passing  through  the  center. 

A  great  circle  may  be  drawn  through  any  two  points  on  the  surface  of  a  sphere,  and  the  arc  of  that 
circle  lying  between  those  points  is  shorter  than  any  other  distance  between  them  that  can  be  meaaured 
upon  the  surface.     All  great  circlea  of  a  sphere  have  equal  radii,  and  all  bisect  each  other. 

The  extremities  of  that  diameter  of  the  sphere  which  is  perpendicular  to  the  plane  of  a  circle  are 
called  the  poles  of  that  circle.  In  the  case  of  a  small  circle  the  poles  are  named  the  adjacent  pole  and 
the  remote  pole.  All  circles  of  a  sphere  that  are  parallel  have  the  same  poles.  All  points  in  the  circum- 
ference of  a  circle  are  equidistant  from  the  poles.  In  the  case  of  a  great  circle,  the  poles  are  90°  distant 
from  every  point  of  the  circle. 

Assuming  any  great  circle  as  a  primary,  all  gre&t  circlea  which  paaa  through  its  poles  are  called  ita 
secondaries.     All  secondaries  cut  the  primary  at  right  angles. 

Useful  Formulae  Derived  from  Geometry. — In  these  formulae  the  following  abbreviations  are 
adopted: 

b,  base  of  triangle  or  parallelogram.  r,  radius  of  sphere  or  circle. 

h,  perpendicular  of  triangle  or  parallelogram.  d,  diameter  of  sphere  or  circle. 

I,  height  of  cylinder  or  cone.  A,  major  axis  of  ellipse. 

It,  ratio  of  diameter  to  circumference  o,  minor  axis  of  ellipse. 

( =  3. 141593) .  «,  side  of  a  cube. 

Area  of  parallelogram  =  b  X  h. 

Area  of  triangle  =  i  b  X  h. 

Area  of  any  right-lined  figure  =  sum  of  the  areas  of  the  triangles  into  which  it  ia  divided. 

Sum  of  three  angles  of  any  triangle  =  180°. 

Circumference  of  circle  =  27Cr,  or  Ttd. 

ltd' 
Area  of  circle  =  itr^,  or  -j-. 

Angle  aubtended  by  arc  equal  to  radiua  =  57°. 29578. 

TCd^ 

Volume  of  sphere  =  —q-. 

Surface  of  sphere  =  7C(P,  or  4jrr^. 

Area  of  ellipse  =  — t~- 

Volume  of  cube  =  «*. 

Volume  of  cylinder  =  Area  of  base  X  I. 

Volume  of  pyramid  or  cone  =  Area  of  base  X   o  . 


270 


RULES  AND  PRINCIPLES   OF   MATHEMATICS. 


TRIGONOMETRIC  FUNCTIONS. 

The  trigonometric  functions  of  the  angle  formed  by  any  two  lines 
are  the  ratios  existing  between  the  sides  of  a  right  triangle  formed  by 
letting  fall  a  perpendicular  from  any  point  in  one  line  upon  the 
other  line;  no  matter  what  point  is  chosen  for  the  perpendicular 
nor  which  line,  the  ratios,  and  therefore  the  respective  functions, 
will  be  the  same  for  any  given  angle. 

Let  ABO  (fig.  83)  be  a  plane  right  triangle  in  which  C  is  the 
right  angle;  A  and  B,  the  other  angles;  c,  the  hypotenuse;  a  and 
b  the  sides  opposite  the  angles  A  and  B,  respectively.  In  considering 
the  functions  of  the  angle  A,  its  opposite  side,  a,  is  regarded  as  the 
perpendicular,  and  its  adjacent  side,  b,  as  the  base;  for  the  angle  B,  b 
is  the  perpendicular  and  a  the  base.  Then  the  various  ratios  are 
designated  as  follows: 

— ,   or  I^-P-_ ,    is  called  the  sine  of  the  angle  A,  abbreviated  sin  A; 

c  hypotenuse 

b  bas 

c  hypotenuse 


,   is  called  the  cosine  of  the  angle  A,  abbreviated  cos  A; 


a     ^^  perpendicular^   j^  ^jj^^  ^^^  tangent  of  the  angle  A,  abbreviated  tan  A; 

A,   or  ^f    , — ,   is  called  the  cotangent  of  the  angle  A,  abbreviated  cot  A; 

a  perpendicular 

T'   ^^        h  qp — '  ^^  called  the  secant  of  the  angle  A,  abbreviated  sec  A; 

_£.    or  _5^P?J??"??-,   is  called  the  cosecant  of  the  angle  A,  abbreviated  cosec  A; 
a  perpendicular 

1— cosine  A,  is  called  the  versed  sine  of  A,  abbreviated  vers  A. 

1— sine  A,  is  called  the  co-versed  sine  of  A,  abbreviated  covers  A. 

i  (1— cosine  A)  is  called  the  haversine  of  A,  abbreviated  hav  A. 

The  following  relations  may  be  seen  to  exist  between  the  various  functions: 

-: — r  =  ^  "*"  T  =  T  =  coeec  A ; 

sin  A  c       a  ' 


sec  A; 


tan  A 
sin  A 

COB  A 


1-^  r  =  ^  =  cotA; 


=  X  =  tan  A. 


Hence  the  cosecant  is  the  reciprocal  of  the  sine,  the  secant  is  the  reciprocal  of  the  cosine,  the  cotan 
gent  is  the  reciprocal  of  the  tangent,  and  the  tangent  equals  the  sine  divided  by  the  cosine. 

The  complement  of  an  angle  is  equal  to  90°  minus  that  angle,  and  thus  in  the  triangle  ABC  the 
angle  B  is  the  complement  of  A.    The  supplement  is  equal  to  180°  minus  the  angle. 

From  the  triangle  ABC,  regarding  the  angle  B,  we  have: 

6 
sin  B  =  —  =  cos  A; 

tan  B  =  —  =  cot  A; 


sec  B 


cosec  A. 


BULES  AND  PRINCIPLES   OF   MATHEMATICS. 


271 


Hence  it  may  be  seen  that  the  sine  of  an  angle  is  the  cosine  of  the  complement  of  that  angle;  the 
tangent  of  an  angle  is  the  cotangent  of  its  coniple-  » 

ment,  and  the  secant  of  an  angle  is  the  cosecant  of 
its  complement. 

The  functions  of  angles  vary  in  sign  according 
to  the  quadrant  in  which  the  angles  are  located. 

Let  AA^  and  BB'  (fig.  84)  be  two  lines  at  right 
angles  intersecting  at  the  point  O,  and  let  that  point 
be  the  center  about  which  a  radius  revolves  from 
an  initial  position  OB,  euccessively  passing  the  points 
A,  W,  A''.  In  considering  the  angle  made  by  this 
radius  at  any  position,  P^  V,  V\  V'',  with  the 
line  OB,  its  position  of  origin,  the  functions  will  g, 
depend  upon  the  ratios  existing  between  the  sides 
of  a  right  triangle  whose  base,  fe,  will  always  lie 
within  BB'',  Bnd  whose  perpendicular,  a,  will  always 
be  parallel  to  A  A'',  while  its  hypot€nuse,c  (of  a  con- 
stant length  equal  to  that  of  the  radius) ,  will  de- 
pend upon  the  position  occupied  by  the  radius. 
Kow,  if  OB  and  OA  be  regarded  as  the  positive  direc- 
tions of  the  base  and  perpendicular,  respectively, 
and  OB'  and  OA'  as  their  negative  directions,  the 
sign  of  the  hypotenuse  being  always  positive,  the 
sign  of  any  function  may  be  determined  oy  the  signs 
of  the  sides  of  the  triangle  upon  which  it  depends. 

For  example,  the  sine  of  the  angle  P'-'OB  is  -,  and  since  a  is  positive  the  quantity  has  a  positive 

value;  its  cosine  is  -,  and  as  b  is  measured  in  a  n^ative  direction  from  O  the  cosine  must  therefore  be 

negative. 

In  the  first  quadrant,  between  0°  and  90°,  all  quantities  being  positive,  all  functions  will  also  be 
positive. 

In  the  second  quadrant,  between  90°  and  180°,  sin  A  (=-)  is  positive;  cos  A  {==-)  has  a  nega- 
tive value  because  h  is  negative;  tan  A  (  =?)  is  also  negative  because  of  h.    The  cosecant,  secant,  and 

cotangent  have,  as  in  all  cases,  the  same  signs  as  the  sine,  cosine,  and  tangent,  respectively,  being  the 
reciprocals  of  those  quantities. 

In  the  third  quadrant,  between  180°  and  270°,  sin  A  (=^)  and  cos  A  {  =  ^  are  both  n^ative, 
because  both  o  and  h  have  negative  values;  tan  A  (  =r  j  is  positive  for  the  same  reason. 

In  the  fourth  quadrant,  between  270°  and  360°,  sin  A  (=^)  is  negative,  cos  A  (  =-)  is  positive, 

and  tan  A  (  =-r  j  is  also  negative. 

From  a  consideration  of  the  signs  in  the  manner  that  has  been  indicated,  the  following  relations 
will  appear: 


sin  A  =  sin  (180°  -  A)  =  -  sin  (180°  -f  A)  =  -  sin  (360°  -  A)  =  -  sin  (-  A) 
cos  A  =  -cos  (180°- A)  =  - cos  (180°  +  A)  =  cos  (360°  -  A)  =  cos  (- A). 
tan  A  = -tan  (180°  -  A)  =  tan  (180°  +  A)  =  -  tan  (360° -A)  =  -  tan  (-A' 
sin  A  =  cos  (90°  -  A)  =  -  cos  (90°  -H  A)  =  -  cos  (270°  -  A)  =  cos  (270°  -{■  A 


\: 


Any  similar  relation  may  be  deduced  from  the  figure. 

It  is  of  great  importance  to  have  careful  regard  for  the  signs  of  the  functions  in  all  trigonometrical 
solutions. 

LOGARITHMS. 

In  order  to  abbreviate  the  tedious  operations  of  multiplication  and  division  with  large  numbers,  a 
series  of  numbers,  called  Logarithms,  was  invented  by  Lord  Napier,  by  means  of  which  the  operation  of 
multiplication  may  be  performed  by  addition,  and  that  of  division  by  subtraction.  Numbers  may  be 
involved  to  any  power  by  simple  multiplication  and  the  root  of  any  power  extracted  by  simple  division. 

In  Table  42  are  given  the  logarithms  of  all  numbers,  from  1  to  9999;  to  each  one  must  be  prefixed 
an  inde%  with  a  period  or  dot  to  separate  it  from  the  other  part,  as  in  decimal  fractions;  the  logarithms 
of  the  numbers  from  1  to  100  are  given  in  that  table  with  their  indices;  but  from  100  to  9999  the  index 
is  left  out  for  the  sake  of  brevity;  it  may  be  supplied,  however,  by  the  general  rule  that  the  index  of  the 
logarithm  of  any  integer  or  mixed  number  is  always  one  less  than  the  number  of  integral  places  in  the 
natural  number.     Thus,  the  index  of  the  logarithm  of  any  number  (integral  or  mixed)  between  10  and 


272  BULES  AND  PRINCIPLES  OF   MATHEMATICS. 

100  is  1;  from  100  to  1000  it  is  2 ;  from  1000  to  10000  it  is  3,  etc. ;  the  method  of  finding  the  logarithms 
from  this  table  will  be  evident  from  the  rules  that  follow: 

To  find  the  logarithm  of  any  number  less  than  100,  enter  the  first  page  of  the  table,  and  opposite  the 
given  number  will  be  found  the  logarithm  with  its  index  prefixed.  Thus,  opposite  71  is  1.85126,  which 
IS  its  logarithm. 

To  find  the  logarithm  of  any  number  between  100  and  1000,  find  the  given  number  in  the  left-hand  col- 
umn of  the  table  of  logarithms,  and  immediately  under  0  in  the  next  column  is  a  number,  to  which  must 
be  prefixed  the  number  2  as  an  index  (because  the  number  consists  of  three  places  of  figures),  and  the 
required  logarithm  will  be  found.  Thus,  if  the  logarithm  of  149  was  required,  this  number  being  found 
in  the  left-hand  column,  against  it,  in  the  column  marked  0  at  the  top  (or  bottom)  is  found  17319,  pre- 
fixing to  which  the  index  2,  we  have  the  logarithm  of  149  =  2.17319. 

To  find  the  logarithm  of  any  number  between  1000  and  10000,  find  the  three  left-hand  figures  of  the  given 
number  in  the  left-hand  column  of  the  table  of  logarithms,  opposite  to  which,  in  the  column  that  is 
marked  at  the  top  (or  bottom)  with  the  fourth  figure,  is  to  be  found  the  required  logarithm,  to  which 
must  be  prefixed  the  index  3,  because  the  number  contains  4  places  of  figures.  Thus,  if  the  logarithm 
of  1495  was  required,  opposite  to  149,  and  in  the  column  marked  5  at  the  top  (or  bottom)  is  17464,  to 
which  prefix  the  index  3,  and  we  have  the  logarithm,  3.17464. 

To  find  the  logarithm  of  any  number  above  10000,  find  the  first  three  figures  of  the  given  number  in  the 
left-hand  column  of  the  table,  and  the  fourth  figure  at  the  top  or  bottom,  and  take  out  the  corresponding 
logarithm  as  in  the  preceding  rule;  take  also  the  difference  between  this  logarithm  and  the  next  greater, 
and  multiply  it  by  the  remaining  figure  or  figures  of  the  number  whose  logarithm  is  sought,  pointing  off 
aa  many  decimal  places  in  the  product  as  there  are  figures  in  the  multiplier.  To  facilitate  the  calcula- 
tion of  the  proportional  parts  several  small  tables  are  placed  in  the  margin,  which  give  the  correction 
corresponding  to  the  difference,  and  to  the  fifth  figure  of  the  proposed  number.  Thus,  if  the  logarithm 
of  14957  was  required,  opposite  to  149,  and  under  5,  is  17464;  the  difference  between  this  and  the  next 
greater  number,  17493,  is  29;  this  multiplied  by  7  (the  last  figure  of  the  given  number)  gives  203; 
pointing  off  the  right-hand  figure  gives  20.3  (or  20)  to  be  added  to  17464,  which  makes  17484;  to  this, 
prefixing  the  index  4,  we  have  the  logarithm  sought,  4.17484.  This  correction,  20,  may  also  be  found 
by  inspection  in  the  small  table  in  the  margin,  marked  at  the  top  29;  opposite  to  the  fifth  figure  of  the 
number,  7,  in  the  left-hand  column,  is  the  corresponding  correction,  20,  in  the  right-hand  column. 

Again,  if  the  logarithm  of  1495738  was  required,  the  logarithm  corresponding  to  149  at  the  left,  and 
5  at  the  top,  is,  as  in  the  last  example,  17464;  the  difference  between  this  and  the  next  greater  is  29; 
multiplying  this  by  738  (the  given  number  excluding  the  first  four  figures)  gives  21402;  crossing  off  the 
three  right-hand  figures  of  this  product  (because  the  number  738  consists  of  three  figures) ,  we  have  the 
correction  21  to  be  added  to  17464;  and  the  index  to  be  prefixed  is  6,  because  the  given  number  consists 
of  7  places  of  figures;  therefore  the  required  logarithm  is  6.17485.  This  correction,  21,  may  be  found  aa 
above,  by  means  of  the  marginal  table  marked  at  the  top  29,  taking  at  the  side  7.38  (or  7J  nearly),  to 
which  corresponds  21,  as  before. 

To  find  the  logarithm  of  any  mixed  decimal  number,  find  the  logarithm  of  the  number,  aa  if  it  were 
an  integer,  by  the  preceding  rules,  to  which  prefix  the  index  of  the  integral  part  of  the  given  number. 
Thus,  if  the  logarithm  of  the  mixed  decimal  149.5738  was  required,  find  the  logarithm  of  1495738,  with- 
out noticing  the  decimal  point;  this,  in  the  last  example,  was  found  to  be  17485;  to  this  prefix  the  index 
2,  corresponding  to  the  integral  part  149;  the  logarithm  sought  will  therefore  be  2.17485. 

To  find  the  logarithm  of  any  decimal  fraction  less  than  unity,  it  must  be  observed  that  the  index  of  the 
logarithm  of  any  number  less  than  unity  is  negative;  but,  to  avoid  the  mixture  of  positive  and  negative 
(juantities,  it  is  common  to  borrow  10  in  the  index,  which,  in  most  cases,  may  afterwards  be  neglected 
in  summing  them  with  other  indices;  thus,  instead  of  writing  the  index  —  1,  it  is  written  +  9;  instead 
of  —  2  we  may  write  -f  8;  and  so  on.  In  this  way  we  may  find  the  logarithm  of  any  decimal  fraction 
by  the  following  rule:  Find  the  logarithm  of  a  fraction  as  if  it  were  a  whole  nvmiber;  see  how  many 
ciphers  precede  the  first  figure  of  the  decimal  fraction,  subtract  that  number  from  9,  and  the  remainder 
will  be  the  index  of  the  given  fraction.  Thus  the  logarithm  of  0.0391  is  8.59218  —  10;  the  logarithm  of 
0.25  is  9.39794  —  10;  the  logarithm  of  0.0000025  is  4.39794  -  10,  etc.  In  most  cases  the  writing  of  —  10 
after  the  logarithm  may  be  dispensed  with,  as  it  will  be  quite  apparent  whether  the  logarithm  has  a 
positive  or  a  negative  index. 

To  find  the  number  corresponding  to  any  logarithm,  seek  in  the  column  marked  0  at  top  and  bottom 
the  next  smallest  logarithm,  neglecting  the  index;  write  down  the  number  in  the  side  column  abreast 
which  this  is  found,  and  this  will  give  the  first  three  figures  of  the  required  number;  follow  the  line 
until  the  logarithm  next  smaller  than  the  given  one  is  found,  and  the  fourth  figure  of  the  required 
number  will  be  at  the  top  and  bottom  of  the  column  in  which  this  stands;  take  the  difference  between 
this  next  smaller  logarithm  and  the  next  larger  one  in  the  table,  and  also  the  difference  between  the 
next  smaller  logarithm  and  the  given  one;  entering  the  small  marginal  table  which  has  for  its  heading 
the  first-named  difference,  and  finding  in  the  right-hand  column  of  that  table  the  last-named  difference, 
there  will^  appear  abreast  the  latter,  in  the  left-hand  column,  the  fifth  figure  of  the  required  number. 
Where  it  is  desired  to  determine  figures  beyond  the  fifth  for  the  corresponding  number,  the  difference 
between  the  next  lower  logarithm  and  the  given  one  may  be  divided  by  the  difference  between  the 
next  lower  and  next  higher  ones,  and  the  quotient  (disregarding  the  decimal  point,  but  retaining  any 
ciphers  that  may  come  between  the  decimal  point  and  the  significant  figures)  will  be  the  fifth  and  suc- 
ceeding figures  of  the  number  sought.  Having  found  the  figures  of  the  corresponding  number,  point 
off  from  the  left  a  number  of  figures  which  shall  be  one  greater  than  the  index  number,  and  there  place 
a  decimal  point.  In  this  operation  of  placing  the  decimal  point,  proi)er  account  must  be  taken  oi  the 
negative  value  of  any  index. 

Thus,  if  the  number  corresponding  to  the  logarithm  1.52634  were  required,  find  52634  in  the  column 
marked  0  at  the  top  or  bottom,  and  opposite  to  it  is  336;  now,  the  index  being  1,  the  required  number 
must  consist  of  two  integral  places;  therefore  it  is  33.6. 

If  the  number  corresponding  to  the  logarithm  2.57345  were  required,  look  in  the  column  0  and  find 
in  it,  against  the  number  374,  the  logarithm  57287,  and,  guiding  the  eye  along  that  line,  find  the  given 


BTJLES  AND  PRINCIPLES  OF   MATHEMATICS. 


273 


logarithm,  57345,  in  the  column  marked  5;  therefore  th6  mixed  number  sought  is  3745,  and  since  the 
index  is  2,  the  integral  part  must  consist  of  3  places;  therefore  the  number  sought  is  374.5.  If  the  index 
be  1  the  number  will  be  37.45,  and  if  the  index  be  0  the  number  will  be  3.745.  If  the  index  be  8, 
corresponding  to  a  number  less  than  unity,  the  number  will  be  0.03745. 

Again,  if  the  number  corresponding  to  the  logarithm  3.57811  were  required,  find,  against  378  and 
under  5,  the  logarithm  57807,  the  difference  between  this  and  the  next  greater  logarithm,  57818,  being 
11,  and  the  difference  between  57807  and  the  given  logarithm,  57811,  being  4;  in  the  marginal  table 
headed  11,  find  in  the  right-hand  column  the  number  4,  and  abreast  the  latter  appears  the  figure  4, 
which  is  the  fifth  figure  of  the  required  number;  hence  the  figures  are  37854;  pointing  off  from  the 
left  3+1=4  places,  the  number  is  3785.4. 

If  the  given  logarithm  were  5.57811,  since  the  index  5  requires  that  there  shall  be  six  places  in  the 
whole  number,  it  is  desirable  to  seek  accuracy  to  the  sixth  figure.  The  logarithmic  part  being  the 
same  as  in  the  example  immediately  preceding,  it  is  found  as  before  that  the  first  four  figures  are  3785, 
the  difference  between  the  next  lower  and  next  greater  logarithms  is  11,  and  between  the  next  lower 
logarithm  and  the  given  one  is  4;  divide  4  by  11  and  the  quotient  is  .36;  drop  the  decimal  point,  annex 
and  point  off,  and  the  number  required  is  found  to  be  378536. 

It  may  be  remarked  that  in  using  five-place  logarithm  tables  it  is  not  generally  to  be  expected  that 
results  will  be  exact  bej^ond  the  fifth  figure. 

To  show,  at  one  view,  the  indices  corresponding  to  mixed  and  decimal  numbers,  the  following 
examples  are  given: 


Mixed  number.  Logarithms. 

40943.0 Log.  4.61218 

4094.3 Log.  3.61218 

409.43 Log.  2.61218 

40.943 Log.  1.61218 

4.0943 Log.  0.61218 


Decimal  number.  Logarithms. 

0.40943 Log.  9. 61218-10 

0.040943 Log.  8. 61218-10 

0.0040943 Log.  7.61218-10 

0.00040943 Log.  6.61218-10 

0.000040943 Log.  5.61218-10 


To  perf(yrm  multiplication  by  logarithms,  add  the  logarithms  of  the  two  numbers  to  be  multiplied  and 
the  sum  will  be  the  logarithm  of  their  product. 


Example  I. 
Multiply  25  by  35. 

25 Log.  1.39794 

35 Log.  L54407 

Product,  875 Log.  2.94201 

Example  II. 


Multiply  22.4  by  1.8. 


22.4. 
1.8. 


.Log. 
■  Log. 


L 35025 
0. 25527 


Product,    40.32 Log.  1.60552 


EXAMPLB  III. 

Multiply  3.26  by  0.0026. 

3.26 Log.  0.51322 

0.0025 Log.  7.39794 

Product,  0.00815 Log.  7.91116 

Example  IV. 


Multiply  0.25  by  0.003. 


0.25.. 
0.003. 


.Log.  9.39794 
.Log.  7.47712 


Product,  0.00075 Log.  6.87506 


In  the  last  example,  the  sum  of  the  two  logarithms  is  really  16.87506—20;  this  is  the  same  as 
6.87506—10,  or,  remembering  that  the  quantity  is  less  than  unity,  simply  6.87506. 

To  perform  division  by  logarithms,  from  the  logarithm  of  the  dividend  subtract  the  logarithm  of  the 
divisor;  the  remainder  will  be  the  logarithm  of  the  quotient. 


Example  I. 
Divide  875  by  25. 

875 Log.  2.94201 

25 Log.  1.39794 

Quotient,    35 Log.  L54407 

Example  II. 


Example  III. 
Divide  0.00815  by  0.0025. 

0.00815 Log.  7.91116 

0.0025 Log.  7.39794 

Quotient,  3. 26 Log.  0.51322 

Example  IV. 


Divide  0.00075  by  0.025. 

0.00075 Log.  6.87506 

0.025 Log.  8.39794 

Quotient,  0. 03 Log.  8.47712 


Divide  40.32  by  22.4. 

40.32 Log.  1.60552 

22.4 Log.  1.35025 

Quotient,    1.8 Log.  0.25527 

In  Example  III  both  the  divisor  and  dividend  are  fractions  less  than  unity,  and  the  divisor  is  the 
lesser;  consequently  the  quotient  is  greater  than  unity.  In  Example  IV  both  fractions  are  less  than 
unity;  and,  since  the  divisor  is  the  greater,  its  logarithm  is  greater  than  that  of  the  dividend;  for  this 
reason  it  is  necessary  to  borrow  10  in  the  index  before  making  the  subtraction,  that  is,  to  regard  the 
logarithm  of  .00075  as  16.87506  —  20;  hence  the  quotient  is  less  than  unity. 

21594°— 14 18 


274 


RULES  AND  PRINCIPLES  OF   MATHEMATICS. 


The  arithmetical  complement  of  the  logarithm  of  a  number,  usually  called  the  cologarithm  of  the 
number,  and  denoted  by  colog,  is  the  remainder  obtained  by  subtracting  the  logarithm  of  the  number 
from  the  logarithm  of  unity.  It  is  therefore  the  logarithm  of  the  reciprocal  of  the  number;  and,  since  the 
effect  of  dividing  by  any  number  is  the  same  as  that  of  multiplying  by  its  reciprocal,  it  follows  that,  in 
performing  division  by  logarithms,  we  may  either  subtract  the  logarithm  of  the  divisor  or  add  the  arith- 
metical complement  of  that  logarithm.  As  the  addition  of  a  number  of  quantities  can  be  performed 
in  a  single  operation,  while  in  subtraction  the  difference  between  only  two  quantities  can  be  taken  at  a 
time,  it  is  frequently  a  convenience  to  deal  with  the  arithmetical  complements  rather  than  with  the 
logarithms  themselves. 


Example  III. 

„.      ,.-    ^,  .        40.32X .00815 

Simplify  the  expression,    92  4y  0025  ' 

40.32 : Log.  1.60552 

.00815 Log.  7.91116 

22.4 Log.  1.35025.... Colog.  8.64975 

.0025 Log.  7.39794. . .  .Colog.  2. 60206 


Example  I. 
Divide  875  by  25. 

875 Log.  2.94201 

25 Log.  1.39794.. ..Colog.  8.60206 

Quotient,  35 Log.  1.54407 

Example  II. 

Divide  0.00075  by  0.025. 

0.00075 Log.  6.87506 

0.026.... Log.  8.39794.... Colog.  1.  60206 

Quotient,  0.03 Log.  8.47712 

To  perform  involution  by  logarithms,  multiply  the  logarithm  of  the  given  number  by  the  index  of  the 
power  to  which  the  quantity  is  to  be  raised;  the  product  will  be  the  logarithm  of  the  power  sought. 


Result,  5.868 ....Log.  0.76849 


Example  I. 

Required  the  square  of  18. 

18 Log.  1.25527 

2 


Answer,  324 Log.  2.51054 

Example  II. 

Required  the  square  of  6.4. 

6.4 Log.  0.80618 

2 


AuBwer,  40.96 Log.  L  61236 


Example  III. 

Required  the  cube  of  13. 

13 Log.  1.11394 

3 


Answer,  2197 Log.  3.34182 

Example  IV. 

Required  the  cube  of  0.25. 

0.25 Log.  9.39794 

3 


Answer,  0.015625 Log.  8.19382 


In  the  last  example,  the  full  product  of  the  multiplication  of  9.39794—10  by  3  is  28.19382—30,  which 
is  equivalent  to  8.19382—10. 

To  perform  evolution  by  logarithms  divide  the  logarithm  of  the  number  by  the  index  of  the  power; 
the  quotient  will  be  the  logarithm  of  the  root  sought.  If  the  number  whose  root  is  to  be  extracted  is  a 
decimal  fraction  less  than  unity,  increase  the  index  of  its  logarithm  by  adding  a  number  of  tens  which 
shall  be  less  by  one  than  the  index  of  the  power  before  making  the  division. 


Example  I. 
Required  the  square  root  of  324. 

324 Log.  2)2.51055 

Answer.  18 Log.      L  25527 

Example  II. 
Required  the  cube  root  of  2197. 

2197 Log.  3)3. 34183 

Answer,  13 Log.      L  11394 


Example  III. 

Required  the  square  root  of  40.96. 

40.96 Log.  2)1.61236 

Answer,  6.4 Log.      0.80618 

Example  IV. 

Required  the  cube  root  of  0.015625. 

0.015625 Log.        8.19382 

Add  20  to  the  index 3)28.19382 


Answer,  0.25 Log. 


9. 39794 


In  the  last  example  the  logarithm  8. 19382—10  was  converted  into  its  equivalent  form  of  28. 19382—30, 
which,  divided  by  3,  gives  9.39794—10. 

To  find  the  logarithm  of  any  furtction  of  an  angle,  Table  44  must  be  ena ployed.  This  table  is  so 
arranged  that  on  every  page  there  appear  the  logarithms  of  all  the  functions  of  a  certain  angle  A, 


RULES  AND   PRINCIPLES   OF   MATHEMATICS.  275 

together  with  those  of  the  angles  90°— A,  90°+ A,  and  180°— A;  thus  on  each  page  may  be  found  the 
logarithms  of  the  functions  of  four  different  auglee.  The  number  of  degrees  in  the  respective  angles 
are  printed  in  bold-faced  type,  one  in  each  corner  of  the  page;  the  number  of  minutes  corresponding 
appear  in  one  column  at  the  left  of  the  page  and  in  anothei  at  the  right;  the  names  of  the  functions 
to  which  the  various  logarithms  correspond  are  printed  at  the  top  and  bottom  of  the  columns.  The 
invariable  rule  must  be  to  take  the  name  of  the  function  from  the  top  or  the  bottom  of  the  page, 
according  aa  the  number  of  degrees  of  the  given  angle  is  found  at  the  top  or  bottom;  and  to  take  the 
minutes  from  the  right  or  left  hand  column,  according  as  the  number  of  degrees  is  found  at  the  right 
or  left  hand  side  of  the  page;  or,  more  briefly,  take  names  of  functions  and  number  of  minutes, 
respectively,  from  the  line  and  column  nearest  in  position  to  the  number  of  degrees. 

Taking,  as  an  example,  the  thirty-first  page  of  the  table,  it  will  be  found  that  30°  appears  at  the 
upper  left-hand  corner,  149°  at  the  upper  ri^ht-nand,  59°  at  the  lower  right-hand,  and  120°  at  the  lower 
left-hand  corner.  Suppose  that  it  is  desired  to  find  the  log.  sine  of  30°  10^;  following  the  rule  given,  we 
find  lO''  in  the  left-hand  column  and  Sine  at  the  top  ot  the  page,  and  abreast  one  and  below  the  other  is 
the  required  logarithm,  9.70115.  But  if  the  log.  sine  of  59°  10'  were  sought,  as  59°  appears  below  and  at 
the  right  of  the  page,  the  logarithm  9.93382  would  be  taken  from  the  column  markea  Sine  at  the  bottoni 
and  abreast  10'  on  the  rignt.  It  may  also  be  seen  that  log.  sin  30°  10'=log.  cos  59°  50''=log.  cos 
120°  10'=log.  sin  149°  50'=9.70115,  the  equality  of  the  functions  agreeing  with  trigonometrical 
deductions;  (in  this  statement  numerical  A-alues  only  are  regarded,  and  not  signs;  the  latter  must,  of 
course,  be  taken  into  account  in  all  operations) . 

ExAMPLK  I.  '  Example  II. 


Required  the  log.  sine,  cosecant,  tangent,  cotan- 
gent, secant,  and  cosine  of  28°  37'. 

Log.  sin        9.  68029        Log.  cot   10.  26313 
Log.  cosec  10.  31971         Log.  sec  10.  05658 


Required  the  log.  sine,  cosecant,  tangent,  cotaO' 
gent,  secant,  and  cosine  of  75°  42'. 

Log.  sin        9. 98633        Log.  cot    9. 40636- 
Log.  cosec  10. 01367        Log.  sec  10. 60730 


Log.  tan       9. 73G87        Log.  cos     9. 94342  I  Log.  tan      10. 59364        Log.  cos    9. 39270 

When  the  angle  of  which  the  logarithmic  function  is  required  is  given  to  seconds,  it  becomes 
necessary  to  interpolate  between  the  logarithms  given  for  the  even  minutes  next  below  and  next  above^ 
this  may  be  done  either  by  computation  or  (except  in  a  few  cases)  by  inspection  of  the  table. 

To  mterpolate  by  computation,  let  n  represent  the  number  of  seconds,  D  the  difference  between  the' 
logarithms  of  the  next  lesser  and  next  greater  even  minute,  and  d  the  difference  between  the  logarithia 
of  the  next  lesser  even  minute  and  that  of  the  required  angle.     Then, 

It  should  be  noted  when  the  number  of  seconds  is  30,  20,  15,  or  some  similar  number,  permitting^ 

the  reduction  of  the  fraction  ^  to  a  simple  value,  such  aa  i,  i,  \,  aa  the  interpolation  by  this  method 

60 

may  thus  be  made  with  greater  facility. 

Haviuj?  obtained  the  difference  of  the  logarithm  from  that  of  the  next  lower  even  minute,  it  most 
be  applied  in  the  proper  direction — that  is,  if  the  function  is  such  that  its  logarithm  increases  aa  the 
angle  increases,  the  logarithmic  difference  must  be  added;  but  if  it  decreases,  then  that  difference  must 
be  subtracted. 

For  example,  let  it  be  required  to  find  the  log.  sin  and  log.  cosec  of  30°  ICX  19".  The  log.  sin  of 
30°  10'  is  9.70115;  the  difference  between  this  logarithm  and  that  of  the  sine  of  30°  11'  (9.70137)  is  +  22^ 
which  is  D.     Hence, 

<i=^X(+22)=+7; 

and  the  required  logarithm  is  9.70122.     The  log.  cosec  of  30°  10'  is  10.29885;  the  difference,  D,  between 
that  and  log.  cosec  30°  11'  (10.29863)  is  -22.     In  this  case 

rf=^X(-22)  =  -7; 

therefore,  log.  cosec  30°  10'  19"= 10. 29878. 

The  method  of  interpolating  by  inspection  consists  in  entering  that  column  marked  "  Diff."  which 
is  adjacent  to  the  one  from  which  the  logarithmic  function  for  the  next  lower  minute  is  taken,  and 
finding,  abreast  the  number  in  the  left-hand  minute  column  which  corresponds  to  the  seconds,  the 
required  logarithmic  difference;  and  the  latter  is  to  be  added  or  subtracted  according  as  the  logarithms' 
increase  or  decrease  with  an  increased  angle.  Thus,  if  it  be  required  to  find  log.  sin  30°  10'  19",  find  as 
before  log.  sin  30°  10'=9. 70115,  then,  in  the  adjacent  column  headed  "Diff."  and  abreast  the  number 
of  seconds,  19,  in  the  left-hand  minute  column  will  be  found  7,  the  logarithmic  difference;  add  this,  as 
the  function  is  increasing,  and  we  have  the  required  logarithm  9.70122.  If  log.  cosec  30°  10'  19"  be 
sought,  find  log.  cosec  30°  10'=10.29885;  then  in  the  adjacent  difference  column,  which  is  the  same  as^ 
was  used  for  the  sines,  find  as  before  the  logarithmic  difference,  7;  and  since  this  function  decreases  as 
the  angle  increases,  this  must  be  subtracted;  therefore,  log.  cosec  30°  10'  19"= 10. 29878. 

This  method  of  interpolation  by  inspection  is  not  available  in  that  portion  of  the  table  where  the 
logarithmic  differences  vary  so  rapidly  that  no  values  will  apply  alike  to  all  the  angles  on  the  same- 
page;  on  such  pages  the  difference  for  one  minute  is  given  in  a  column  headed  "Diff.  1',"  instead  of 
the  usual  difference  for  each  second;  in  this  case  the  interpolation  must  be  made  by  computation,  the 
given  difference  for  one  minute  being  D.  In  other  parts  of  the  table  the  interpolation  by  inspection 
may  be  liable  to  slight  error  because  of  the  variation  in  logarithmic  difference  for  different  angles  on. 
the' same  page;  but  the  tabulated  values  are  suflBciently  accurate  for  the  usual  calculations  in  navigation,- 


276 


RULES  AND  PRINCIPLES   OF   MATHEMATICS. 


It  will  be  evident  that  while  the  methods  explained  have  contemplated  entering  the  tables  with  a 
smaller  angle  and  interpolating  ahead,  it  would  be  equally  correct  to  enter  with  a  greater  angle  and 
nterpolate  back  for  the  proper  number  of  minutes,  making  the  requisite  change  in  the  sign  of  the 
icorrection. 

Example  I.  Example  II. 


Required  the  log.  sine,  cosine,  and  tangent  of 
42°  57^  06'^ 


For  42°  57' 


Log.  sin 
Log.  cos 
Log.  tan 


9. 83338 
9. 86448 
9.96890 


d 


+1 
-1 

+3 


For  42°  67'  06' 


9. 83339 
9.86447 
9. 96893 


Required  the  log.  secant,  cosecant,  and  cotangent 
of  175°  32'  36^'. 


For  175°  32' 


Log.  sec 
Log.  cosec 
Log.  cot 


10. 00132 
11. 10858 
11. 10726 


d 


—  1 
+97 
+98 


For  175°  32'  36" 


10. 00131 

11. 10955 
11. 10824 


It  should  be  observed  that,  for  uniformity  and  convenience,  all  logarithms  given  in  Table  44  have 
been  increased  by  10  in  the  index,  and  it  is  understood  that  —10  ought  properly  to  be  written  after 
each;  thus  all  logarithms  under  10.00000  represent  functions  whose  value  is  less  than  unity,  and  all 
over  10.00000  those  greater  than  unity;  for  example,  11.10726  is  the  logarithm  of  a  number  in  which 
the  decimal  point  should  be  placed  after  the  second  figure  from  the  left. 

To  find  ilie  angle  corresponding  to  any  logarithmic  function,  the  process  is  the  reverse  of  the  one  just 
described.  Find,  in  the  column  marked  with  the  name  of  the  function,  either  at  top  or  bottom,  the 
two  logarithms  between  which  the  given  one  falls;  write  down  the  degrees  and  minutes  of  the  lesser  of 
the  two  corresponding  angles,  which  will  be  the  degrees  and  minutes  of  the  angle  required.  Call  the 
difference  between  the  two  tabulated  logarithms  D,  and  the  difference  between  the  given  logarithm  and 
that  which  corresponds  to  the  lesser  angle,  d;  then  if  n  represents  the  number  of  seconds,  we  have: 

d 
n=^X60. 

Or,  the  same  may  be  obtained  by  inspection  (except  where,  as  before  explained,  the  differences 
for  seconds  are  not  tabulated )  by  finding,  in  the  ' '  Diff. ' '  column  adjacent  to  that  from  which  the  logarithm 
was  taken,  the  logarithmic  difference,  d,  and  noting  the  number  of  seconds  abreast  which  it  stands  in 
the  left-hand  minute  column. 

Interpolation  may  be  also  made  in  the  reverse  direction  from  the  next  greater  even  minute. 

Thus,  if  it  be  required  to  find  the  angle  corresponding  to  log.  sin  9.61^0,  we  find  log.  sin  24°  16', 
9.61382,  and  log.  sin  24°  17',  9.61411;  hence  D=29,  and  d=18; 

18 
n=29X  60=37; 

and  the  angle  is  24°  16'  37".  Or,  in  adjacent  column  headed  "Diff.,"  18  would  be  found  abreast  38, 
39,  or  40  (seconds)  in  the  left-hand  minute  column — a  correspondence  sufficiently  close  for  navigation 
work. 

If  the  angle  were  known  to  be  in  the  second  quadrant,  we  find  log.  sin  155°  43',  9.61411,  and  log. 
sin  155°  44',  9.61382;  here  D=29,  and  d=ll; 

n=^X60=23; 
therefore,  the  angle  is  155°  43'  23".     Or,  in  adjacent  "Diff."  column  find,  abreast  11,  23  or  24  seconds. 


Example  I. 

Find  angles  less  than  90°  corresponding  to  log. 
cot  10.33621,  log.  sec  10.11579,  and  log.  cos  8.70542. 


Log.  cot  10.33621 
Log.  sec  10.11579 
Log.  cos     8.  70542 


o 

' 

d 

n 

24 

45 

8 

15 

40 

00 

4 

22 

87 

05 

116 

28 

Example  II. 

Find  angles  in  second  quadrant  corresponding  to 
log.  tan  10.15593,  log.  sin  8.87926,  and  log.  cosec 
10.04944. 


o 

' 

d 

" 

124 

55 

19 

42 

175 

39 

69 

25 

116 

49 

3 

27 

Log.  tan  10. 15593 
Log.  sin  8. 87926 
Log.  cosec  10. 04944 

The  Hour  Columns  in  Table  44  give  the  measure  in  time  corresponding  to  twice  the  angular  distance 
given  in  arc.  Thus,  abreast  the  angle  13°  00'  stands  in  the  P.  M.  column  1'^  44™  00*,  corresponding  in 
time  to  2X13°  00';  and  in  the  A.  M.  column  lO''  16™  00',  which  is  the  same  subtracted  from  12^.  These 
columns  are  of  use  in  working  the  various  formulae  which  involve  functions  of  half  the  hour  angle. 
Interpolation  for  values  intermediate  to  those  given  in  the  tables  is  made  on  the  same  principle  as  for 
the  angular  measure;  this  operation  may  be  performed  by  inspection  by  the  use  of  the  small  tables  at 
the  bottom  of  each  page,  where  n,  the  number  of  seconds  of  time,  is  given  in  bold-faced  type,  and  d,  the 
logarithmic  difference  for  the  respective  columns,  appears  below. 


Example  I. 
Given  1=1^  48"  44»,  find  log.  cot  ^  t. 


For  V  48™  40*, 
Diff.  for  4%  Col.  B 

For  1"  48"  44», 


log.  cot.  ^  t 


10. 61687 
28 


Example  II. 

Given  log.  sin  i  t,  9.91394,  find  the  Hour  A.  M. 
corresponding. 

For  9.91389,  4»'39™12» 

Diff.  for  5,  Col.  C  -  5 


log.  cot  i  t      10. 61659 


For  9.91394, 


4  39  07 


RULES  AND   PRINCIPLES   OF   MATHEMATICS.  277 

MISCELLANEOUS    USEFUL    DATA. 


Earth's  Polar  radiu8=6,356,583.8  meters. 
Earth's  Equatorial  radiu8=6,378,206.4  meters. 

Earth's  Compres8ion=2C)3  ^^- 

Earth's  Eccentricity=0.0822719 log  8.  9152513. 

Number  of  feet  in  one  statute  mile=5280 log  3.  7226339. 

Number  of  feet  in  one  nautical  mile=6080.27 log  3.  7839229. 

Sine  of  1'''= 0.00000485 log  4.  6855749. 

Sine  of  1^=0.00029089 _ log  6.  4637261. 

The  Napierian  base  £ =2. 7182818 log  0.  4342945. 

The  modulus  of  common  logarithms =0.4342945 log  9.  6377843. 

French  meter  in  English  feet,  3.2808333 log  0.  5159842. 

French  meter  in  English  statute  miles,  0.000621370 log  6.  7933503. 

French  meter  in  nautical  miles,  0.000539568 log  6.  7320613. 

1  pound  Avoirdupois=7,000  grains  Troy. 

French  gramme =0.00220606  Imperial  pound  Troy. 

French  kilogramme=0.0196969  English  cwts. 

Cubic  inch  of  distilled  water,  in  grains=252.458. 

Cubic  foot  of  water,  in  ounces  Troy=908.8488. 

Cubic  foot  of  water,  in*pound8  Troy =75. 7374. 

Cubic  foot  of  water,  in  ounces  Avoirdupois=997. 1369691. 

Cubic  foot  of  water,  in  pounds  Avoirdupois=62.3210606. 

Length  of  pendulum  which  vibrates  second  at  Greenwich,  39.1393  inches. 


)■  Bar.  30.00  in.;  ther.  62°  F. 


APPENDIX  IV. 

MAEITIME  POSITIONS  AND  TIDAL  DATA. 


The  following  table  contains  the  latitude  and  longitude  of  a  large  number  of  places,  together  with 
lunitidal  intervals  and  tidal  ranges  at  the  more  important  ones.  It  is  arranged  geographically  and  followed 
by  an  alphabetical  index. 

The  geographical  position  generally  relates  to  some  specified  exact  location,  and  is  based  upon  the 
best  available  authority.  The  tidal  data  relate  to  the  waters  adjacent  to  the  point  whose  latitude  and 
longitude  are  given,  being  abstracted  from  the  Tide  Tables  published  by  the  United  States  Coast  and 
Geodetic  Survey. 

The  high-water  and  low-water  limitidal  intervals  represent  the  mean  intervals  between  the  moon's 
transit  and  the  time  of  next  succeeding  high  and  low  waters  throughout  a  lunar  month.  The  spring 
and  neap  ranges  are  the  differences  in  height  between  high  water  and  low  water  at  spring  and  at  neap 
tides.  For  those  places  where  the  tide  is  chiefly  of  a  diurnal  type,  and  where  there  is  usually  but  one 
high  and  one  low  water  during  a  lunar  day,  the  tidal  values  are  bracketed;  in  such  cases  the  lunitidal 
intervals  are  for  the  semidiurnal  part  of  the  tide  (which,  however,  is  only  appreciable  for  a  few  days 
when  the  moon  is  near  the  equator),  and  the  range  given  in  the  column  headed  "Spg."  does  not,  as  m. 
other  cases,  apply  to  the  spring  tide,  but  to  the  greatest  periodic  daily  range,  which  usually  occurs  a  day 
or  two  after  the  moon  attams  its  extreme  of  declination,  and  is  therefore  near  one  of  the  tropics.  As  those 
places  where  the  diurnal  type  jpredominates  seldom  experience  large  tidal  effects,  the  general  data 
iumidied  regarding  such  tides  will  suffice  for  the  ordinary  purpose  of  the  navigator.  The  method  of 
finding  the  time  of  high  or  low  water  from  thia  table  ia  illustrated  in  article  504,  Chapter  XX. 

278 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OP  NORTH  AMEBICA. 


[Page  279 


Place. 


Salisbury  Island:  E.  pt 

Nottingham  Island:  S.  pt. . 
Digges  Island:  W.  extreme. 

Cape  Wostenholme 

Charles  Island:  E.  pt 

W.  pt 


Cape  Wegsp 

Prince  of  Wales  Sound:  Center  of  ent 

Cape  of  Hopes  Advance 

Akpatok  Island:  E.  pt 

Green  Island:  NE.  pt 

Button  Islands:  N .  pt 

Cape  Chidleigh , 

Resolution  Island:  S.  pt.,  Hutton h'dl'd. . 
E.  pt.,  C.  Resolution. , 

Black  Head 

Eclipse  Harbor:  E.  side 

Nachvack  Bay:  Islands  off  entrance 

Saddle  Island 

Port  Manvers:  Entrance 

Nain:  Church 

Hopedale  Harbor:  Hill  to  E'd 

Aillick  Harbor:  Cape  Mokkivik 

Cape  Harrison:  N.  extreme 

Indian  Harbor:  Obsy 

Outer  Gannet  Island:  Summit 

Gready  Harbor 

Cartwright  Harbor:  Caribou  Castle 

Indian  Tickle:  Summit 

Rouudhill  Island:  Summit 

Occasional  Harbor:  E.  summit  of  Twin  I 

Cape  St.  Lewis:  SE.  pt 

Battle  Islands:  NE.  extreme,  SE.  I. . . . 
Table  Head 


Belle  Isle:  Lighthouse. 


Cape  Bauld:  Lighthouse 

Bell  Island:  S.  end 

Cape  St.  John:  Gull  Island  light 

Tilt  Cove,  Union  Copper 

Mine 

Funk  Island:  Summit 

Offer  Wadham:  Lighthouse 

Toulinguet  Islands:  I>ighthouse 

Seldom-come-by  Harbor:  Ship  Hill 

CapeFreels:  Gull  I 

Greenspond  Island 

Cape  Bona  vista:  Lighthouse 

Catalina  Harbor:  Green  I.  lighthouse 

Bonaventure  Head 

Hearts  Content:  Lighthouse 

Baccalieu  Island :  Lighthouse 

Harbor  Grace:  Lighthouse  on  beach. ... 

Cape  St.  Francis:  Lighthouse 

St.  Johns  Harbor:  Chain  Rock  Battery. . 

Cape  Race:  Lighthouse 

Cape  Pine:  Lighthouse 

Trepassey  Harbor:  Shingle  Neck 

Cape  St. 'Mary:  Lighthouse 

Little  Placentia  Harbor:  W.  side  Coopers 

Cove 

Burin  Island:  Lighthouse 

Laun:  Gr.  Laun  R.  C.  Church 


Lat.  N. 


63  27  00 
63  06  00 
62  37  00 
62  35  00 
62  48  00 
62  50  00 
62  30  00 
62  07  00 
61  18  00 
60  10  00 
60  40  00 
60  52  00 

60  33  00 

61  21  00 
61  40  00 
60  00  00 
59  48  00 
59  07  00 
57  35  00 
57  00  00 
56  32  45 
55  27  04 
55  13  33 
54  55  50 
54  26  55 
54  00  05 
53  50  00 
53  42  37 
53  34  25 
53  26  00 
52  40  07 
52  21  16 
52  15  36 
52  06  00 

51  53  00 

51  38  48 
50  42  10 
49  59  54 

49  53  00 
49  45  29 
49  35  40 
49  41  20 
49  36  50 
49  15  20 
49  04  20 
48  42  01 
48  30  15 
48  16  55 

47  53  10 

48  08  58 
47  42  45 
47  48  30 
47  34  02 
46  39  24 
46  37  04 
46  43  20 

46  49  34 

47  17  55 
47  00  26 
46  56  30 


Long.  W. 


Lun.  Int. 


H.W. 


76  30  00 

77  50  00 

78  08  00 
77  33  00 

74  00  00 

75  20  00 
74  03  00 
72  25  00 
70  02  00 
67  05  00 
67  50  00 
64  40  00 

64  12  00 

65  00  00 
64  30  00 
64  28  00 
64  07  15 
63  20  00 

61  20  00 

62  07  00 
61  40  13 
60  12  34 
59  08  01 
57  56  40 
57  12  40 
56  31  31 
56  23  00 
56  59  50 
55  58  39 
55  35  48 
55  44  29 
55  38  08 
55  32  20 
55  41  00 

55  22  10 

55  25  12 
55  35  30 
55  21  33 

55  37  17 
53  10  56 

53  45  00 

54  47  35 
54  12  00 
53  25  12 
53  37  45 
53  04  42 
53  02  40 
53  23  35 
53  23  20 

52  47  42 

53  08  11 
52  47  20 

52  40  54 

53  04  30 
53  31  55 

53  22  10 

54  11  42 

53  58  43 

55  08  49 
55  32  00 


A.  m. 

"shs 


8  00 
7  00 


7  00 
5  30 


6  10 


6  27 


6  38 
6  30 


L.W. 


7  23 


7  15 


7  12 
6  50 


6  50 
8  20 


8  05 


K   m. 
"'2'46 


1  48 
0  48 


0  48 
11  43 


12  23 


0  15 


0  26 
0  18 


Range. 


13.5 


5.0 
5.2 


6.5 
6.9 


7.0 


6.0 


5.0 
3.5 


1  11   4. 1 
"i  03'  '*3."3 


1  01 
0  38 


0  38 
2  08 


1  53 


3.3 
6.5 


6.6 
7.2 


7.0 


Neap. 


ft. 


2.0 
2.1 


3.0 
3.2 


3.2 


2.8 


2.3 

L6 


L9 


L5 


L5 
3.0 


3.1 
3.3 


3.2 


Page  280]  APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST   COAST  OF  NORTH  AMERICA— Continued. 


I  M 


Place. 


St.  Pierre:  U.  S.  Coast  Survey  Station... 
Brunet  Island:  Mercers  Hd.  lighthouse.. 

Boar  Islands:  Burgeo  I.  lighthouse 

La  Poile  Bay:  Gr.  Espic  Church 

Cape  Ray:  Lighthouse. . . : 

Codroy  Island:  S.  side  Boat  Harbor 

Cape  St.  George:  Red  I.,  SE.pt 

Cow  Head:  NW.  extreme 

Port  Saunders:  Two  Hills  Pt 

Rich  Point:  Lighthouse 

F^roUe  Pena:  New  FeroUe  Pt 

Flower  Cove:  Capstan  Pt 

Green  Island:  150  fms.  from  NE.  end. . . 
Cape  Norman :  Lighthouse 

Chateau  Bay:  S.  pt.  Castle  I 

Amour  Point:  Lighthouse 

Wood  Island:  S.  pt 

Greenly  Island:  Lighthouse 

Bradore  Bay:  Obs.  Spot,  Jones  Pt 

Old  Fort  Island:  Center 

Great  Mekattina  Island :  SE.  pt 

Mekattina  Harbor:  S.  point  of  Dead  Cove 
Little  Mekattina  I.:  S.  pt.  C.  McKinnon 

St.  Mary  Reefs 

South  Makers  I^edge 

Cape  Whittle 

Natashquan  Point:  S.  edge 

Clearwater  Point:  SW.  extreme 

Carousel  Island :  Lighthouse 

Point  de  Monts:  Lighthouse 

Quebec:  Mann's  Bastion,  Citadel 

Quebec:  Bonner's  Hill  Obsy 

Montreal:  St.  James  Cathedral 

Ottawa:  Dominion  Observatory 

Father  Point:  Lighthouse 

Cape  Chatte:  Extreme 

Cape  Magdalen :  Lighthouse 

Cape  Rosier:  Lighthouse 

Cape  Gasp4:  Lighthouse 

Anticosti  Island:  Heath  Pt.  lighthouse. . 
SW.  pt.  lighthouse.  .  . 

Bonaventure  Island :  E.  pt 

Leander  Shoal 

Macquereau  Point 

Chaleur  Bay:  Carlisle 

Dalhousie  I 

Miscou  Island:  Birch  Pt.  lighthouse 

Miramichi  Bay:  Portage  I.,  N.  pt 

Point  Escumenac:  Lighthouse 

North  Point:  Lighthouse 

Malpeque  Baj^:  Royalty  Pt 

East  Point:  Lighthouse 

Charlottetown:  Blackhouse  Pt.  light.... 

Gt.  Bird  Rock:  Lighthouse 

East  Island:  E.  extreme 

Entry  Island :  Lighthouse 

Amherst  Hbr.:  N.  side  of  entrance 

Deadman  Rock:  W.  pt 


Lat.  N. 


46  46  51 

47  15  30 
47  35  13 
47  39  50 
47  37  00 

47  52  30 

48  33  48 

49  55  20 

50  38  30 

50  41  50 

51  02  00 
51  17  25 
51  24  10 
51  38  00 

51  58  00 
51  27  35 
51  22  45 
51  22  26 
51  27  22 
51  21  40 
50  47  30 
50  46  44 
50  31  10 
50  14  00 
50  09  30 

50  11  00 
50  06  00 
50  12  27 
50  05  40 
49  19  35 
46  48  23 

46  47  59 
45  29  57 

45  23  30 

48  31  25 

49  06  00 
49  15  40 
48  51  37 

48  45  15 

49  05  20 
49  23  45 

48  29  30 
48  24  00 
48  12  00 
48  01  00 
48  04  24 
48  01  07 

47  14  00 
47  05  00 

47  03  46 

46  33  56 
46  27  15 

46  11  36 

47  50  40 
47  37  40 
47  16  30 
47  14  23 
47  16  03 


Long.  W. 


56  10  36 

55  51  40 

57  36  52 

58  24  10 

59  18  00 
59  23  40 
59  13  10 
57  50  00 
57  17  07 
57  25  00 
57  03  50 

56  44  45 
56  33  40 
55  53  52 

55  50  20 

56  51  05 

57  08  00 
57  10  04 
57  13  21 

57  46  00 

58  51  30 

58  59  20 

59  20  25 
59  45  00 

59  57  00 

60  08  00 

61  44  00 

63  27  03 

66  22  44 

67  21  55 
71  12  19 
71  13  10 
73  34  08 
75  42  59 

68  27  40 
66  46  00 
65  19  30 

64  12  00 
64  09  35 
61  42  30 

63  35  46 

64  08  00 
64  18  00 

64  46  30 

65  19  00 

66  22  10 

64  29  20 

65  02  00 
64  47  33 

63  58  49 
63  41  35 
61  57  35 
63  06  58 

61  08  32 
61  24  30 
61  41  20 

61  49  38 

62  12  25 


Lun.  Int. 


Range. 


H.W. 


h.  m. 
8  23 
8  53 
8  22 
8  50 


8  50 


9  40 


1  25 


1  43 
1  48 
6  07 


1  52 
1  46 
1  33 
1  25 


1  20 
1  25 


4  20 

5  15 
8  17 

11  07 


L.W. 


Spg. 


h.  m. 
2  11 
2  41 
2  10 
2  38 


ft. 

6.6 

6.5 

6.2 

6.0 


2  32 


4.3 


3  13 


4.9 


6  45 


4.0 


7  05 
7  18 
0  54 


8.1 
10.8 
14.6 


7  33 
7  13 
6  50 
6  40 


12.0 

10.5 

6.4 

5.5 


6  35 
6  40 


3.6 
4.9 


7  33 

8  07 

9  10 
8  25 

10  59 


4.7 
4.8 
8.1 
4.0 
2.3 


11  00 

11  55 

2  20 

4  23 


2.4 
1.8 
1.4 
6.4 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST   COAST  OP  NORTH  AMERICA— Continued. 


[Page  281 


Place. 


Lat.  N. 


Long.  W, 


Lun.  Int. 


Range. 


H.  W.         L.W 


Neap. 


St.  Paul  Island:  Lighthou.se,  NE.  end. 
Lighthouse,  SW.  end. 


Cape  North :  Lighthouse 

St.  Anns  Harbor:  E.  pt.  entrance.. . 

Sydney  Harbor:  Lighthouse 

Scatan  Island:  Lighthouse,  NE.  pt . 

Louisburg:  Lighthouse,  NE.  pt 

Madame  Island:  S.  pt 

Port  Hood :  Just-au-corps  I 


Sable  Island:  Lighthouse,  E.  end. 


Pictou:  Customhouse 

Cape  St.  George 

North  Canso:  Lighthouse,  NW.  entrance. 

Arichat  Harbor:  R.  C.  Church  steeple 

Cape  Canso:  Cranberry  I.,  lighthouse. . . , 

White  Head  Island :  Lighthouse , 

Green  Island :  Lighthouse 

Wedge  Island :  Lighthouse 

Halifax:  Dockyard  observatory 

Sambro  Island :  Lighthouse 

Margaret  Bay:  Shut-in  I 

Tancook  Island 

Lunenburg :  Battery  Pt.  light 

Cape  La  Have :  Black  Rock 

CoflBn  Island :  Lighthouse 

Little  Hope  Island:  Lighthouse 

Shelburne  Hbr.:  Two  lights,  McNutts  I. 

Cape  Sable:  Lighthouse 

Seal  Island :  Lighthouse 

Yarmouth :  Cape  Fourchu  light 

Cape  St.  Mary 

Bryer  Island :  Lighthouse 

Annapolis  Harbor:  Prim  Pt.  light 

Haute  Island :  Lighthouse 

Cape  Chignecto 

Bumtcoat  Head:  Lighthouse 


Cape  Enrag^:  Lighthouse 

Cape  Quaco:  Lighthouse 

St.  Johns:  Partridge  I.  light 

Cape  Lepreau :  Lighthouse 

L'Etang  Harbor:  S.  pt.  tower 

St.  Andrew:  S.  pt.  li^t 

Campo  Bello  Island:  Lighthouse,  N.  pt. . 
Grand  Manan  Island:  Lighthouse,  NE.  pt. 

Gannet  Rock:  Lighthouse,  NE.  pt 

Machias  Island :  Lighthouse 


Calais:  Astronomical  station 

Eastport:  Cong.  Church 

Quoddy  Head :  Lighthouse 

Machias:  Town  Hall 

Petit  Manan  Island:  Lighthouse. 

Bakers  Island :  Lighthouse 

Mount  Desert  Rock:  Lighthouse. 

Bangor:  Thomas  Hill 

Belfast:  Methodist  Church 

Rockland :  Episcopal  Church 

Matinicus  Rock :  Lighthouse 

Monhegan  Island:  Lighthouse. . . 
Seguin  Island :  Lighthouse 


47  13  50 
47  11  20 

47  01  45 
46  21  00 
46  12  25 
46  02  15 
45  54  34 

45  28  00 

46  00  00 

43  58  14 

45  40  50 
45  52  00 
45  41  42 
45  30  48 
45  19  49 
45  11  58 
45  06  15 
45  00  35 

44  39  38 
44  26  10 
44  34  00 
44  29  00 
44  21  45 
44  12  00 
44  02  00 
43  48  30 
43  37  15 
43  23  19 
43  23  34 

43  47  28 

44  05  20 
44  14  57 

44  41  34 

45  14  55 
45  19  00 
45  18  40 

45  35  34 
45  19  30 
45  14  20 
45  03  40 
45  04  00 
45  04  06 
44  57  40 
44  45  52 
44  30  38 

44  30  07 

45  11  05 
44  54  15 

44  48  55 

44  43  01 

44  22  03 

44  14  29 

I  43  58  08 

'  44  48  23 

!  44  25  29 

!  44  06  06 

i  43  47  03 

43  45  53 

I  43  42  26 


60  08  32 
60  09  50 

60  23  27 
60  27  00 

60  12  50 
59  40  25 
59  59.26 

61  03  00 

61  36  00 

59  44  15 

62  42  10 
61  52  00 
61  29  10 
61  01  47 

60  55  41 

61  08  14 
61  32  40 
61  62  45 

63  35  22 
63  33  30 

63  54  00 

64  06  00 
64  17  35 
64  18  00 
64  37  30 

64  47  15 

65  15  45 

65  37  11 

66  00  52 
66  09  21 
66  12  40 
66  23  38 
65  47  20 
65  00  45 
64  57  00 

63  48  30 

64  46  55 

65  32  00 

66  03  20 
66  27  40 

66  49  00 

67  02  52 
66  54  10 
66  44  00 

66  47  00 

67  06  13 

67  16  50 
66  59  14 

66  57  04 

67  27  22 

67  51  51 

68  11  58 
68  07  44 

68  46  59 

69  00  19 
69  06  52 

68  51  28 

69  18  59 
69  45  32 


8  30 


8  35 
8  25 
8  10 


7  45 
7  55 
9  05 


9  34 
9  20 
9  26 

7  55 
7  43 
7  45 


7  34 
"7'32 
"7'39 


8  17 

9  35 
10  00 


10  29 

10  49 

11  07 


0  27 


11  21 
11  07 
11  04 
11  09 
11  00 


11  02 

io'Si 


11  36 
11  09 


11  02 


0  23 
11  35 
11  09 
10  45 


h.    tn. 
2  12 


ft. 

2.7 


2  17 
2  13 
2  05 


3.1 
6.0 
5.0 


1  35 

1  47 

2  47 


5.0 
5.0 
3.5 


13 
00 
10 

47 
36 
38 


3.9 
2.8 
3.1 
5.0 
6.5 


1  46 
'i'36" 
"i"36" 


5.2 
"7.*i" 


2  05 

3  23 
3  41 


8.5 
12.8 
16.0 


4  36 

4  41 

5  27 


20.8 
27.5 
33.0 


7  27 


50.5 


30.0 
23.9 
24.5 
23.3 
24.9 


5  21 


22.5 


4  56 

5  40 
5  05 


18.0 

23.3 
20.9 


4  59 


15.5 


6  47 
5  22 
4  55 
4  31 


15.1 
11.7 
11.0 
10.2 


ft. 
1.4 


1.6 
3.7 
3.1 


L8 


2.0 
L4 
L6 
3.1 
4.0 
4.1 


3.2 
'4.'4 
T3 


5.2 

9.5 

1L8 


15.4 
20.4 
24.4 


37.4 


22.2 

17.7 
18.2 
17.1 
18.2 


16.7 


13.2 

17.1 
15.2 


n.3 


n.o 

8.6 
8.1 
7.5 


Page  282]  APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OP  NORTH  AMERICA— Continued. 


Place. 


Lat.  N. 


Long.  W. 


Lun.  Int. 


Range. 


H.W. 


L.W. 


Spg. 


Bath:  Winter  St.  Church 

Brunswick :  College  spire 

Augusta:  Baptist  Church 

Portland:  Customhouse 

Portland  Head  lighthouse .  . . 

Cape  Elizabeth :  Lighthouse  (west) 

Wood  Island :  Lighthouse 

Boon  Island :  Lighthouse 

Whale  Back;  Lighthouse 

Portsmouth:  Navy-yard  flagstaff 

Fort  Constitution 

Hampton:  Baptist  Church 

Isles  of  Shoals:  White  I.  lighthouse 

Newburyport:  Academy 

Plum  I.  lighthouse 

Ipswich:  Lighthouse  (rear) 

Annisquam  Harbor:  Lighthouse 

Cape  Ann:  Thatchers  I.  lighthouse  (N.) 

Gloucester:  Universalist  Church 

Ten-pound  I.  lighthouse... 

Beverly:  Hospital  Pt.  lighthouse 

Salem:  Derbys  WTiarf  lighthouse 

Marblehead:  Lighthouse 

Cambridge:  Harvard  Observatory 

Boston:  Navy-yard  flagstaff 

State  House 

Little  Brewster  I.  lighthouse. . 

Minots  Ledge:  Lighthouse 

Plymouth:  Pierhead 

Gurnet  lighthouse 

Barnstable :  Lighthouse 

Cape  Cod :  Highlands  lighthouse 

Chatham:  Lighthouse  (south) 

Monomoy  Point :  Lighthouse 

Nantucket:  South  Church 

Nantucket  Shoals:  Lightship 

Sankaty  Head :  Lighthouse .' 

Tarpaulin  Cove:  Lighthouse 

Vineyard  Haven:  W.  Chop  lighthouse. 

Gay  Head:  Lighthouse 

Cuttyhunk:  Lighthouse 

New  Bedford :  Baptist  Church 

Sakonnet  Point :  Lighthouse 

Beaver  Tail :  Lighthouse 

Newport:  Flagstaff,  torpedo  station 

Bristol  Ferry:  Lighthouse 

Providence :  Brown  University  Obsy . . . 

Point  Judith:  Lighthouse 

Block  Island:  Lighthouse  (SE.) 

Watch  Hill  Point:  Lighthouse 

Montauk  Point:  Lighthouse 

Stonington:  Lighthouse 

New  London :  Groton  Monument 

Little  Gull  Island :  Lighthouse 

Gardners  Island:  Lighthouse,  N.  pt 

Plum  Island :  Lighthouse,  W.  pt 

Saybrook:  Lighthouse,  Lynde  Pt 

New  Haven:  Yale  University  Obsy 


43  54  55 

43  54  29 

44  18  52 
43  39  28 
43  37  23 
43  33  51 
43  27  24 
43  07  17 

43  03  32 
43  04  56 
43  04  16 
42  56  15 
42  58  02 

42  48  30 
42  48  55 
42  41  07 
42  39  43 
42  38  21 
42  36  46 
42  36  07 
42  32  48 
42  31  00 
42  30  20 
42  22  48 
42  22  22 
42  21  28 
42  19  41 
42  16  11 

41  58  44 

42  00  12 

41  43  20 

42  02  23 
41  40  17 
41  33  34 
41  16  55 

40  37  05 

41  17  01 
41  28  08 
41  25  51 
41  20  55 
41  24  52 
41  38  10 

41  26  30 
41  26  58 
41  29  07 
41  38  34 
41  50  21 
41  21  40 
41  09  10 
41  18  14 

41  04  16 
41  19  31 
41  21  16 
41  12  23 
41  08  29 
41  10  25 
41  16  17 
41  19  22 


69  49  00 
69  57  44 

69  46  37 

70  15  18 
70  12  30 
70  12  11 
70  19  46 
70  28  37 

70  41  49 
70  44  22 
70  42  34 
70  50  12 
70  37  25 

70  52  28 
70  49  10 
70  46  00 
70  40  55 
70  34  31 
70  39  59 
70  39  58 
70  51  23 
70  53  03 

70  50  03 

71  07  46 
71  03  05 
71  03  50 
70  53  26 
70  45  35 
70  39  12 
70  36  04 
70  16  52 
70  03  40 
69  57  01 

69  59  39 

70  05  57 
69  36  33 

69  57  57 

70  45  29 
70  36  01 
70  50  08 
70  57  01 

70  55  36 

71  13  30 
71  24  00 
71  19  40 
71  15  39 
71  23  59 
71  28  55 
71  33  08 
71  51  32 

71  51  27 

71  54  49 

72  04  47 
72  06  26 
72  08  44 
72  12  43 
72  20  37 
72  55  09 


h.    m. 
12  13 


2  54 
11  06 


11  12 


11  23 


11  19 
11  23 


11  17 
11  13 


11  02 


11  16 
11  09 


11  27 
'ii'69 


11  23 
11  36 


12  11 

12  00 

0  04 


7  51 
11  34 
7  31 
7  36 
7  57 

7  40 
7  40 
7  48 

7  53 

8  12 
7  32 

7  33 

8  49 

8  20 

9  09 
9  26 
9  26 
9  40 


10  29 

11  08 


h.    m. 
6  16 


10  18 
4  51 


4  51 


5  09 


4  58 

5  10 


5  04 
5  00 


4  49 


5  03 

4  57 


5  17 
'4  56 


5  11 
5  25 


5  57 

5  48 

6  00 


1  51 
4  33 
1  20 

0  59 

1  18 

1  05 
1  09 
1  00 
0  40 

0  57 

1  17 

1  25 

2  38 

2  03 

3  03 
3  32 
3  04 
3  35 


4  11 
4  54 


ft. 
7.9 


4.9 
10.1 


10.2 


10.5 


10.0 
9.1 


10.1 
10.1 


10.2 


10. 6 
10.6 


11.0 
16.9' 


10.8 
11.6 


4.6 
4.3 
3.8 


2.8 
2.0 
3.7 
4.3 
5.2 

4.5 
4.7 
4.4 
5.2 
5.4 
3.8 
3.7 
3.2 

2.3 
3.2 
2.9 
3.0 
2.5 


4.3 
7.0 


APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OP  NORTH  AMEBIC  A— Continued. 


[Page  283 


Place. 


Bri('geport  Harbor:  Lighthouse 

Norwalk  Island :  Lighthouse 

Shinnecock  Bay:  Lighthouse 

Fire  Island :  Lighthouse 

Albany :  New  Dud  ley  Observatory . 

New  York:  Nav>'-yard  flagstaff 

CityHall 

Fort  Wadeworth:  Lighthouse 


Sandy  Hook:  Lighthouse  (rear) 

Lightship 

Navesink  Highlands:  N.  lighthouse 

Bamegat  Inlet:  Lighthouse 

Tuckers  Beach :  Lighthouse 

Absecon  Inlet:  Lighthouse 

Five  Fathom  Bank:  Lightship 

Cape  May:  Lighthouse 

Philadelphia,  Pa.:  University  Obsy 

Navy-yard     fla^aff, 

League  I 

Wilmington,  Del. :  Town  Hall 

Cape  Henlopen :  Lighthouse 

Aesateague  Island :  Lighthouse 

Hog  Island:  Lighthouse 

Cape  Charles:  Lighthouse 

Baltimore:  Johns  Hopkins  Obsy 

Annapolis:  Naval  Academy  Observatory 

Point  Lookout:  Lighthouse 

Washington,  D.  C:  Navy-yard  flagstaff.. 

Naval  Observatory . . 

Capitol  dome 

Old  Point  Comfort:  Lighthouse 

Norfolk:  Navy-yard  flagstaff 

Richmond,  Va. :  Capitol 

Cape  Henry :  Lighthouse 


Elizabeth  City:  Courthouse... 

Eden  ton:  Courthouse 

Currituck  Beach:  Lighthouse., 

Bodie  Island:  Lighthouse 

Cape  Hatteras:  Lighthouse — 

Ocracoke :  Lighthouse 

Newbem :  Episcopal  spire 

Cape  Lookout:  Lighthouse — 
Beaufort,  N.  C:  Courthouse... 
Frying-Pan  Shoals:  Lightship. 


Georgetown :  Episcopal  Church 

Lighthouse,  North  I 

Cape  Romain:  Lighthouse 

Charleston:  Lighthouse,  Morris  I 

St.  Michael's  Church 

Beaufort,  S.  C:  Episcopal  Church 

Port  Royal:  Martins  Industry  lightship. 


Tybee  Island:  Lighthouse.. 
Savannah:  Exchange  spire. 
Sapelo  Island:  Lighthouse. 
Darien:  Winnowing  House. 

St.  Simon:  Lighthouse 

Brunswick:  Academy 


Lat.  N. 


41  09  24 

41  02  56 
40  51  03 
40  37  57 

42  39  13 
40  42  02 
40  42  44 
40  36  20 

40  27  42 
40  28  15 
40  23  48 
39  45  52 
39  30  22 
39  21  59 
38  47  20 

38  55  59 

39  58  02 

39  53  14 
39  44  27 

38  46  42 
37  54  40 
37  23  46 

37  07  22 

39  17  48 

38  58  53 
38  02  19 
38  52  30 
38  55  14 
38  53  20 
37  00  06 
36-49  33 
37  32  16 
36  55  35 

36  17  58 
36  03  24 
36  22  36 
35  49  07 
35  15  17 
35  06  32 
35  06  21 
34  37  22 
34  43  05 
33  34  26 

33  22  08 
33  13  21 
33  01  06 
32  41  43 
32  46  34 
32  26  02 
32  05  33 

32  01  20 
32  04  52 
31  23  28 
31  21  54 
31  08  02 
31  08  51 


Long.W. 


73  10  49 
73  25  11 

72  30  16 

73  13  08 
73  46  42 

73  58  51 

74  00  24 
74  03  15 

74  00  09 
73  50  09 

73  59  10 

74  06  24 
74  17  08 
74  24  52 
74  34  36 

74  57  39 

75  16  39 

75  10  32 
75  33  03 
75  05  03 
75  21  23 
75  41  59 

75  54  24 

76  36  30 
76  29  08 
76  19  20 

76  59  45 

77  03  57 
77  00  36 
76  18  24 

76  17  46 

77  26  04 
76  00  27 

76  13  23 

76  36  31 
75  49  51 
75  33  49 
75  31 .16 

75  59  11 

77  02  24 

76  31  29 

76  39  48 

77  49  12 

79  16  49 
79  10  55 
79  22  19 
79  52  54 

79  55  49 

80  40  27 
80  33  15 

80  50  37 

81  05  26 
81  17  01 
81  25  39 
81  23  30 
81  29  26 


Lun.  Int. 


H.  W. 


h.  m. 
11  09 
11  03 

7  48 

7  19 
5  13 

8  44 


7  41 
7  30 


7  50 
7  48 
9  59 


8J6 
1  28 

0  53 

12  00 

8  17 


8  03 

6  34 
4  39 
0  31 

7  42 


8.44 
9  05 
4  30 
7  53 


7  37 


7  00 


6  29 

7  21 


8  39 
"659 


7  20 

8  10 


7  10 

8  13 
7  30 
7  40 

7  30 

8  00 


Range. 


L.  W, 


5  04 
4  56 
1  38 

1  20 
0  46 

2  49 


1  38 
1  23 


1  43 
1  42 
3  57 


1  47 
8  58 

8  02 
6  40 
1  50 


2  19 

0  44 
10  53 

6«2 

1  56 


2  17 

2  47 

11  55 

1  43 


1  26 


0  45 


0  20 

1  08 


Spg. 


3  38 
056' 


1  10 

2  06 


1  04 
3  07 
1  24 
1  44 
1  27 
1  57 


ft. 

8.4 
8.2 
3.0 
2.2 
2.8 
5.3 


5.4 
5.6 


2.7 
4.2 
4.7 

"5.6' 
6.2 

7.0 
6.7 
5.4 


3.0 
L4 
LO 
1.7 
3.5 


3.0 
3.2 
4.3 
3.2 


3.4 


2.2 


4.4 
3.3 


4.3 
■5.'9" 


6.0 

8.5 


7.9 
7.6 
8.4 
7.5 
7.5 
7.8 


Neap. 


ft. 

5.9 

5.7 

2.0 

1.4 

1.8 

3.4 


3.5 
3.6 


L7 
2.7 
3.0 

'3*6 
4.4 

5.2 
4.9 
3.5 


2.0 
LO 
0.8 
LI 
2.5 


2.0 
2.1 
2.9 
2.1 


2.2 


L5 


3.0 
2.3 


2.9 
4.1 


4.2 
5.9 


5.5 
5.3 
5.8 
5.2 
5.3 
5.4 


Page  284]  APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST   COAST   OF  NORTH  AMERICA— Continued. 


Place. 


Amelia  Island :  Lighthouse 

Femandina:  Astronomical  station 

St.  Johns  River:  Lighthouse 

Jacksonville:  Methodist  Church 

St.  Augustine:  Presbyterian  Church. . . . 

Lighthouse 

Cape  Canaveral :  Lighthouse 

Jupiter  Inlet:  Lighthouse 

Fowey  Rocks:  Lighthouse 

Carysf ort  Reef :  Lighthouse 

Alligator  Reef :  Lighthouse 

Sombrero  Key :  Lighthouse 

Sand  Key:  Lighthouse 

Key  West:  Lighthouse 

Loggerhead  Key :  Lighthouse 

Sanibel  Island :  Lighthouse 

Gasparilla  Island :  Lighthouse 

Tampa  Bay:  Egmont  Key  light 

Cedar  Keys:  Ast.  station,  Depot  Key. .. 

Seahorse  Key  light 

St.  Marks:  Fort  St.  Marks 

Apalachicola:  Flagstaff 

Cape  St.  George:  Lighthouse 

Cape  San  Bias:  Lighthouse 

Pensacola:  Lighthouse 

Navy-yard  chimney 

Sand  Island :  Lighthouse  (front) 

Mobile  Point:  Lighthouse 

Mobile:  Episcopal  Church 

Horn  Island :  Lighthouse 

East  Pascagoula:  Coast  Survey  station. . . 
Mississippi  City :  Coast  Survey  station . . . 

Ship  Island:  Lighthouse 

Cat  Island :  Lighthouse 

Chandeleur :  Lighthouse 

Mouth  Mississippi  River:  Pass  a  1' Outre 
light 

S.  Pass  light 
(East  Jetty). 

SW.  Pass  light 

New  Orleans:  United  States  Mint 

Barataria  Bay:  Lighthouse 

Timbalier  Island:  Lighthouse 

Ship  Shoal :  Lighthouse 

Southwest  Reef :  Lighthouse 

Calcasieu  Pass :  Lighthouse 

Sabine  Pass:  Lighthouse 

Galveston :  Cathedral,  N .  spire 

Lighthouse,  Bolivar  Pt 

Matagorda:  Coast  Survey  station 

Lighthouse 

Indianola:  Coast  Survey  station 

Lavaca:  Coast  Survey  station 

Aransas  Pass :  Lighthouse 

Brazos  Santiago:  Light,  S.  end  Padre  I.. 

Point  Isabel :  Lighthouse 

Rio  Grande  del  Norte:  Obsy.  N.  side  of 
entrance 


Lat.  N. 


30  40  23 
30  40  18 
30  23  36 
30  19  43 
29  53  20 
29  53  07 

28  27  37 
26  56  54 
25  35  25 

25  13  17 
24  51  02 
24  37  36 
24  27  10 
24  32  58 

24  38  04 

26  27  11 

26  43  06 

27  36  04 

29  07  29 

29  05  49 

30  09  03 
29  43  32 
29  35  18 

29  40  00 

30  20  47 
30  20  49 

30  11  19 
30  13  44 
30  41  26 
30  13  23 
30  20  42 
30  22  54 
30  12  53 
30  13  57 
30  02  58 

29  11  30 

28  59  28 

28  58  22 

29  57  46 
29  16  30 
29  02  49 

28  54  56 

29  23  36 
29  46  55 
29  43  04 

29  18  17 
29  22  05 
28  41  29 
28  20  18 
28  32  28 
28  37  36 
27  51  53 
26  04  16 
26  04  36 

25  57  22 


Long.  W. 


81  26  26 
81  27  47 
81  25  27 
81  39  14 
81  18  41 
81  17  12 
80  32  30 
80  04  48 
80  05  41 
80  12  40 

80  37  08 

81  06  40 
81  52  40 

81  48  04 

82  55  42 
82  00  43 
82  15  34 

82  45  40 

83  01  57 

83  03  58 

84  12  42 

84  59  12 

85  02  54 
85  21  30 
87  18  32 

87  16  06 

88  03  02 
88  01  26 
88  02  28 
88  31  39 

88  32  45 

89  01  57 

88  57  56 

89  09  41 

88  52  19 

89  02  28 

89  08  08 

89  23  30 

90  03  28 

89  56  43 

90  .21  25 

91  04  15 
91  30  14 
93  20  43 

93  51  00 

94  47  26 

94  46  00 

95  57  26 

96  25  28 
96  31  01 

96  37  21 

97  03  23 
97  10  00 
97  12  28 

97  08  57 


Lun.  Int. 


H.  W.    L.  W 


ft.  m. 


7   39 
7  36 


8  12 
8  00 
8  00 
8  20 
8  21 
8  22 
8  24 

8  40 

9  20 
9  44 

12  17 
0  42 

11  32 
0  42 


2  00 

[12  10] 


[11  10] 

iii"28"] 


[11  25 
[1  35 

[12  00 
[0  20 


[0  23] 
[11  53] 

[11  15] 

[10  55] 
[10  54] 


[11  00 
[11  50 
[0  18 
[0  40] 

2  17 

3  17 

[4  18] 
[4  07] 


[4  35] 


[4  25] 


[155] 


ft.  m. 


1  31 
1  33 


00 
52 
00 
16 
08 
00 
05 
20 
36 
21 
6  10 

6  19 
5  07 

7  13 


8  30 
[5  35] 


[4  55] 

■i4"26i 


3  09 
6  50 
5  40 
5  45 


[6  35] 
[5  33] 


[5  00] 

[4  42] 
[4  4lj 


4  47 

5  38 

6  33 
6  56 

8  41 

9  36 

[10  33] 
[10  23] 


[10  47] 


[10  35] 


[8  03] 


Range. 


Spg.       Neap. 


6.9 
5.4 


5.3 
5.9 
L8 
2.6 
2.7 
2.6 
1.9 
L5 
1.6 
1.4 
2.3 
1.4 
L8 
3.1 


2.6 
[2.5] 


[2.1] 
iL7i 


[1-5] 
2.1] 
'2.0] 
'2.3] 


[2.1] 
[L8] 

[L6] 

[1.7] 
[L9] 


0.9 


[1.6] 


[1-6] 


[1.4] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  285 


Place. 


Lat.  N. 


Long.  W. 


Lun.  Int. 


H.W. 


Range. 


L.W, 


Neap. 


San  Fernando  River:  Entrance 

Santander  River:  Entrance 

Mount  Mecate:  Summit 

Tampico:  Lighthouse 

Cape  Roxo 

Lobos  Cav:  Lighthouse 

Tuxpam  Keefs:  Middle  islet 

Mexico:  Tacubaya  National  Obey 

Bemal  Chico:  Middle  of  islet 

Zempoala  Point :  Extreme 

Vera  Cruz :  San  Juan  d'UUoa  light 

Sacrificios  Island 

Orizaba  Mountain :  17,400  feet 

Cofre  de  Perote  Mount:  14,000  feet 

Alvarado :  E .  side  of  entrance 

Roca  Partida:  Summit 

Tuxtla,  volcano :  Summit 

Montepio :  Landing  place 

Zapotiilan  Point:  Lighthouse 

San  Juan  Point :  Lighthouse 

Puerto  Mexico:  Lighthouse 

Santa  Ana  Lagoon :  Entranpe 

Tupilco  River:  Entrance 

Tabasco  River:  Lighthouse 

Carmen  Island:  NE.  pt 

Laguna  de  Terminos:  Vigia  tower,  W. 
end  Carmen  I 


Paypoton  Mount:  Summit 

Lerma:  Church 

Campeche:  Lighthouse 

Fort  San  Josd 

Point  Palmas 

Sisal:  Fort  light 

Madagascar  Reef :  Center 

Progreso:  Lighthouse 

SUan:  Village 

Lagartoa:  Village 

Cape  Catoche:  Lighthouse 

Areas  Cays :  Lighthouse 

Obispo  Shoal :  16-foot  spot 

New  Bank :  Center 

Triangles,  E.  reef:  Beacon 

Triangles,  W.  reef:  Cay  at  SW.  end. 

Bajo  N'uevo  Reef:  Center 

Arenas  Cays:  NW.  Cay 

Alacran  Reef:  Perez  Cay 

Contoy  Island :  Lighthouse 

Mugeres  Island :  Lighthouse 

Canciin  IslanS :  Nisuc  Pt 

Cozumel  Island:  N.  pt.  lighthouse. . 
S.  pt.  lighthouse... 

Ascension  Bay:  Allen  Pt 

Chinchorro  Bank:  Cayo  Lobos  light. 

Half  moon  Cay:  Lighthouse 

Mauger  Cay,  NW.  end:  Lighthouse. 

Glover  Reef:  SW.  Cay 

English  Cay :  Lighthouse 

St.  Georges  Cay:  Center 


25  23  40 
23  46  20 
22  38  40 
22  15  50 
21  35  00 
21  28  12 
21  03  00 
19  24  18 
19  39  50 
19  27  26 
19  12  30 
19  10  10 
19  04  00 
19  29  30 
18  49  00 
18  44  00 
18  29  00 
18  40  00 
18  34  00 
18  19  45 
18  08  56 
18  18  49 
18  26  44 
18  39  30 
18  47  08 

18  38  44 

19  38  00 
19  48  24 
19  50  20 

19  51  36 
21  02  00 
21  10  06 
21  26  30 
21  17  00 
21  23  00 
21  36  30 
21  35  50 

20  12  45 
20  29  00 
20  32  00 
20  54  54 

20  58  00 

21  50  00 

22  07  10 
22  23  36 
21  33  00 
21  12  00 
21  03  00 
20  35  50 
20  16  20 
19  46  55 
18  23  20 

17  12  15 
17  36  15 

16  42  20 

17  19  30 
17  33  15 


97  21  25 

97  46  55 

98  04  55 
97  49  55 
97  22  00 
97  13  00 
97  13  35 

99  11  38 
96  24  39 
96  20  22 
96  07  57 

96  05  30 

97  15  55 
97  07  30 
95  44  48 
95  11  14 
95  08  00 
95  05  12 
94  50  00 
94  38  57 
94  24  47 
93  51  53 
93  25  25 
92  42  00 
91  30  50 

91  50  17 

90  43  27 
90  36  11 
90  32  20 
90  30  51 
90  22  00 
90  02  37 

90  18  27 
89  39  30 
88  54  27 

88  10  27 
87  04  10 

91  57  45 

92  13  27 

91  52  27 

92  12  47 
92  18  57 
92  04  26 
91  24  21 

89  41  45 
86  48  00 
86  43  39 
86  46  45 
86  43  55 

86  59  04 

87  28  27 
87  23  40 

87  32  30 
87  46  30 

87  50  .TO 

88  03  20 
88  04  45 


A.  m. 


A.  m. 


[106] 


[7  19] 


[1.3] 


[2  49] 


[8  38] 


[2.4] 


[12  16] 


[6  00] 


[1-6] 


2  59 


9  28 


2.1 


1.3 


10  20 


4  10 


1.8 


0.9 


9  30    3  19 
[12  06]  [5  50 


[12  00] 


9  20 


8  20 


L5 
[1-6] 


0.8 


[5  45] 


[1.6; 


3  08 


L6 


0.9 


2  08 


L5 


0.8 


Page  286]                                     APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST   COAST  OF  NORTH  AMERICA— Continued 

. 

1 

8 

Place. 

Lat.  N. 

Long.  W. 

Ltin 

Int. 

Range. 

H.W. 

L.  W. 

Spg. 

Neap. 

s 

i 

« 

h 

9 
V 

a 
e 
H 

ei 

s 
« 

% 

« 
0 

e 
■  ** 

s 

0" 
m 
0 

6 

Sand-Fly  Cays:  Hut,  S.  end 

16  57  50 

16  48  50 

17  29  20 
16  57  40 
16  47  45 
16  48  10 
16  30  54 
16  14  15 
15  54  00 

15  49  45 
15  38  00 
15  24  20 

15  52  20 

15  57  45 

16  08  00 
15  47  11 
15  48  45 
15  38  00 

15  55  45 

16  03  40 

15  58  00 

16  18  00 

16  24  20 

16  28  00 

18  44  00 

17  24  21 

15  53  00 

16  00  00 
15  51  50 
15  48  50 
15  23  40 

15  00  04 

16  03  30 
15  52  00 
15  51  00 
15  08  50 

15  07  00 

14  21  12 

16  54  00 

15  47  45 
14  21  33 
14  08  00 
14  30  00 
13  34  30 
13  22  54 
12  31  40 
12  24  00 
12  10  00 
12  22  35 
12  20  39 

11  59  00 

12  17  30 
12  09  17 
10  56  15 

10  02  00 
10  00  16 

O             /             If 

88  06  05 
88  05  36 
88  11  20 
88  13  48 
88  15  15 
88  37  40 
88  22  13 
88  35  51 
88  56  20 

88  46  22 

89  01  36 
89  09  15 

88  33  22 
88  38  50 
88  20  15 
88  04  31 
87  27  46 
86  55  00 

85  59  18 

86  59  15 
86  32  09 
86  34  27 

86  18  41 
85  55  00 

84  02  00 

83  56  25 

85  27  10 
85  03  00 

84  38  33 
84  17  10 
83  42  36 

83  09  22 
83  08  20 
82  23  27 
82  18  07 
82  42  08 
82  20  00 

82  45  57 
80  51  27 

79  50  53 

80  15  20 

81  08  21 
81  07  21 

80  05  05 

81  21  26 
8l  43  06 
81  27  53 

81  49  54 

83  23  10 
83  37  12 
83  41  57 

82  58  35 

83  03  35 
83  42  15 

83  48  30 

83  00  57 

ft.     TO. 

ft.    m. 

ft. 

ft. 

South  Water  Cay:  Center 

Belize:  Fort  George  light 

8  00 

1  50 

L5 

0.8 

North  Standing  Creek :  Entrance 

Sittee  Point:  Cay 

Cockscomb  Mount:  Summit,  4,000  feet... 
Placentia  Point:  Huts  on  point 

Icacos  Point:  S.  extreme 

Sarstoon  River:  Entrance 

Dulce  Ri  ver :  Entrance,  W .  side 

9  00 

2  60 

2.0 

1.1 

Dulce  Gulf:  Fort  St.  Philip 

Izabal 

Hospital  Bight:  Hut,  N.  pt.  of  entrance.. 

Cape  Three  Points:  NW.  extreme 

Seal  Cays:  S.  Cav 

1 

Omoa:  Entrance 

Cape  Triunfo :  Bluff  pt 

1 

Congrehoy  Peak:  Summit,  8,040 feet 

Truxillo:  Fort 

1 

Utilla  Island :  S.  Cay 

Hog  Islands:  Highest  hill  on  W.  islet 

Roatan:  Center  of  Coxen  Cay 

! 

7  35 

1  23 

3.5 

1.8 

Port  Royal,  NW.  pt.  of  Geoi^e 
Cay 

Bonacca  Island:  Summit,  1,200  feet 

Misteriosa  Bank:  S.  Point 

8  50 

2  38 

1.5 

0.8 

Swan  Islands:  Light  on  W.  pt.  of  west 
island 

Great  Rock  Head :  Bluff  extreme 

Cape  Camaron 

Brewers  Lagoon:  E. side  of  entrance. . . . 

Patuca  River:  E.  side  of  entrance 

Carataska  Lagoon:  E.  side  of  entrance 

Cape  Gracias-d-Dios:  Lighthouse 

10  20 

4  07 

2.0 

1.1 

Caxones  Reef:  Great  Hobby  Islet 

Gorda  Bank:  Gorda  Cay 

Farrall  Rock:  Center 

Half  moon  Cay:  Center 

Alargate  Reef:  E.  pt 

Mosquito  Cays:  S.  end 

Rosalind  Bank :  N W.  extreme 

Serranilla  Bank:  Beacon  Cay 

4  00 
4  00 

10  13 
10  13 

2.0 
2.0 

1.1 
1.1 

Serrana  Bank :  Little  Cay 

Quita  Sueno  Bank:  S.  extreme  of  reef 

Spit  at  NW.  end 

Roncador  Cay:  S.  pt 

Old  Providence:  Isabel  House 

4  00 

10  13 

LO 

0.5 

St.  Andrews  Island :  SW.  cove,  Entrance  I . 
Courtown  Cays:  Middle  Cay.. 

Albuquerque  Bank:  Smith  Cay 

Pearl  Cays:  Colombilla  Cay 

1  50 

8  03 

2.0 

LI 

Pearl  Cays  Lagoon:  Mosqui,to  Pt 

Bluefields:  Schooner  Pt 

1  40 

7  52 

2.0 

LI 

Little  Com  Island :  Gun  Pt 

Great  Corn  Island :  Wells  N.  of  Quin  Bluff. 
Grey  town :  Lighthouse 

1  35 
1  00 

7  47 
7  13 

2.0 
L5 

LI 
0.8 

Mount  Cartago:  Peak,  11,100  feet 

Port  Limon:  Monument,  Park,  opp.  P.  0. 

1  00 

7  13 

L6 

0.9 

APPENDIX   IV.                                     [Page  287 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— €ontinued. 

S 

8 

Place.                                           Lat.  N. 

Long.  W. 

Lun.  Int. 

Range. 

H.  W.         L.  W. 

Spg. 

Neap. 

i 

a 

0 

C&rrctsi  Point'  Extxeme                     

9      r        r 

9  38  30 
9  26  16 
9  25  00 
9  14  24 

9  20  17 
9  14  53 
9  17  00 
9  10  30 
9  06  00 
9  19  27 
9  22  39 
9  22  09 
9  33  20 
9  34  00 
8  53  52 
8  46  30 

82  39  06 
82  20  40 
82  19  28 
82  19  36 

82  14  29 

82  07  48 

83  03  00 
81  54  06 
81  33  57 
80  00  22 
79  57  13 
79  54  42 
79  39  13 
78  57  00 
77  40  53 
77  32  15 

h.    m.    ,     h.    m. 

//. 

ft. 

Almirante  Bay:  Tirbi  Pt.,  Extreme 

Columbus  I.,  Lime  Pt 

Shepherd  I.,  Summit 

Bocas  del  Toro,   Radio 
Tel  Sta 

i 

0  42 

Crawl  Cay  Channel:  Crawl  Cay 

Blanco  Peak:  Summit,  11,740  feet 

Chiriqui  Lagoon:  Valiente  Peak,  Summit. 
Escudo  de  Veragua:  NW.  Pt.  of  Island .  . . 
Chaeres'  San  Lorenzo  Castle 

i 

1 

Torn  Point  •  T.icrht.hniisp 

Colon :  Lighthouse 

0  06 

6  18 

LI 

0.6 

Porto  Belfo"  Ft  St  Geronimo 

Gulf  of  San  Bias  •  Cape  San  Bias 

Caledonia  Harbor:  Dobbin  Cay 

11  30 

5  17 

L5 

0.8 

Port  Carreto  •  Peak        

WEST  COAST  OF  NORTH  AMERICA. 

i 

s 

i 

■d 
s 
* 

M 

d 
£ 

Point  Barrow:  Highest  lat.  of  Alaska 

Icy  Cape*  Extreme 

71  23  30 
70  16  00 
68  52  00 
67  09  00 
66  14  30 
66  32  00 
65  35  30 
65  33  30 
65  16  40 
64  26  00 
63  26  00 
63  34  30 
61  40  00 
63  16  00 
60  18  00 
60  13  00 
60  25  22 
58  48  31 
57  30  24 

55  54  59 

56  34  23 

52  56  01 
51  59  04 
51  23  39 

51  49  18 

52  10  36 

57  07  19 

53  52  54 

54  13  30 

54  26  12 

55  20  45 
55  19  17 
55  07  36 
55  03  17 
54  58  25 
54  55  30 

156  27  00 
161  47  30 
166  06  00 
163  34  00 

161  45  00 
163  36  00 
168  40  00 
168  00  00 
166  46  30 

165  05  00 

162  02  30 
162  42  30 

166  15  00 

168  41  00 
172  02  00 

172  36  00 
166  08  30 
160  50  00 

157  58  30 
160  34  54 

169  39  50 

LongE. 

173  12  24 
177  30  00 
179  12  06 

Long  W. 
176  52  00 

174  15  18 

170  17  52 
166  31  44 
162  38  00 
162  18  00 
160  38  39 
160  31  14 
159  56  06 
159  23  05 
159  22  18 
159  15  03 

11  41 

5  33 

0.6 

0.2 

Cape  Lisbume'  849  feet 

Cape  Krusenstem  ■  Extreme 

ChamLsso  Island :  Summit 

7  45 

1  50 

2.0 

0.6 

Diomede  Island:  Fairway  Rock 

Cape  Prince  of  Wales*  W  pt 

Port  Clarence:  Point  Spencer 

6  10 
2  05] 
[8  05] 

1  10 
8  25] 
1  20' 

LI 

[2.1] 
[4.5] 

0.9 

Cape  Nome:  Extreme 

St  Michael :  Fort 

Stuart  Island  ■  W  pt 

Cape  Romanzof'  Extreme 

St  Lawrence  Island  ■  E  pt 

St  Matttiew  Island:  SE.  pt 

4  40 

11  00 

3.1 

L6 

Pinnacle  Islet*  Summit  930  feet 

Nunivak  Island'  Cape  Etolin 

Hafijenmeister  Islanc 

Port  Moller 

St  George  Island  *  S  side       

Attu  Island :  Chichagof  Harbor 

3  35 
3  30 

9  48 
9  43 

5.7 
5.2 

2.9 

2.7 

Kiska  Island:  Kiska  Harbor,  Ast.  sta 

Amchitka  Island:  Constantine  Harbor — 

Adakh  Island :  Bay  of  Islands 

3  25 

9  38 

5.0 

2.6 

Atka  Island :  Nazan  Bay  (church) 

Pribilof  Island:  St.  Paul  I.,  village 

Unalaska  Island:  C.  S.  station,  Iliuliuk. . 
Sannakh  Reefs:  S  edge 

4  17 

3  50 

12  13 

10  29 
9  58 
6  10 

2.7 
2.9 

5.7 

L4 
L5 

2.8 

Unga  Island 

2  40 

8  55 

8.2 

4.1 

NE  harbor 

Simeonof  Island:  Simeonof  Harbor 

2  20 

8  33 

7.5 

3.8 

Page  288]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMERICA— Continued. 


Place. 


Cape  Strogonof :  Extreme 

Chignik  Bay:  Anchorage 

Anowik  Island:  S.  end 

Lighthouse  Rocks 

Chirikof  Island 

Kodiak  Island,  St.  Paul  Harbor:  Cove 

NW.  of  village 

Port  Etches 

Middleton  Island 

Mount  St.  Elias:  Summit 

Yakutat  Bay:  Port  Mulgrave 

Lituya  Bay 

Sitka:  Middle  of  parade  ground 

Juneau 

Wrangell:  Ast.  station 

North  Island:  N.  pt , 

Cape  Knox:  Extreme 

Port  Kuper :  Sansum  I 

Forsyth  Point:  Extreme 

St.  James  Cape:  S.  extreme 

Cumshewa  Harbor:  N.  side  of  entrance.. 

Skidegate  Bay:  Rock  on  bar 

Rose  Spit  Point:  Extreme , 

Masset  Harbor:  Masset  village 

Cape  Edenshaw:  Extreme 

Hecate  Bay:  Observatory  Islet 

Stamp  Harbor:  Observatory  Islet 

Island  Harbor:  Observatory  Islet , 

Cape  Beale:  Lighthouse 

Hesquiat  Harbor:  Boat  Cove , 

Estevan  Point:  S.  extreme 

Nootka  Sound :  Friendly  Cove 

Port  Langf ord :  Colwood  Islet. ..'. 

Esperanza  Inlet:  Observatory  Rock , 

Kyuquot  Sound :  Shingle  Pomt 

Nasparti  Inlet:  Head  Beach 

Cook  Cape:  Solander  I 

North  Harbor:  Observatory  Rock 

Hecate  Cove:  Kitten  Islet 

Cape  Scott:  Summit 

Bull  Harbor,  Hope  Island :  N .  pt.  Indian  I 

Port  Alexander:  Islet  in  center 

Beaver  Harbor :  Shell  Islet 

Cormorant  I.:  Yellow  Bluff  in  Alert  Bay 

Baynes  Sound:  Beak  Pt 

Nanoose  Harbor:  Entrance  Rock 

Nanaimo:  Lighthouse 

Benson's  House 

Victoria:  Li^thouse 

Esquimau :  Fisgard  I .  light 

Race  Island :  Lighthouse 

Port  San  Juan :  Pinnacle  Rock 

Port  Simpson :  Methodist  Church  Spire . . 
Prince  Rupert  Hbr. :  Fairview  Obs.  Spot. 

Port  Harvey :  Tide  Pole  Islet 

Port  Neville:  Robber's  Nob 

Knox  Bay,  Thurlow  Island:  Stream  at 

head  of  bay 

Valdes  Island:  S.  pt 

Howe  Sound:  Plumper  Cove 


Lat.  N. 


56  48  00 
56  19  20 

56  05  13 
55  45  24 

55  48  22 

57  47  57 
60  20  43 

59  27  22 

60  20  45 
59  33  42 

58  36  57 

57  02  52 

58  18  00 

56  27  00 

54  15  25 
54  10  30 
52  56  31 

52  09  07 
51  54  00 

53  02  00 

53  22  20 

54  13  00 
54  02  14 
54  05  50 

49  15  22 
49  13  46 
48  54  41 

48  47  23 

49  27  31 
49  22  07 
49  35  31 
49  47  20 
49  52  45 

49  59  55 

50  11  21 
50  06  31 
50  29  25 
50  32  26 
50  46  41 
50  54  47 
50  50  49 
50  42  36 
50  35  02 
49  36  29 
49  15  43 
49  12  50 

49  10  15 
48  25  26 
48  25  50 
48  17  53 

48  33  30 

54  33  20 
54  17  17 

50  33  58 
50  31  09 

•50  24  15 
50  02  42 

49  24  39 


Long.  W. 


158  46  00 
158  24  24 

156  39  19 

157  27  04 
155  42  51 

152  21  21 
146  37  38 
146  18  45 
141  00  12 
139  46  16 
137  40  06 
135  19  31 
134  24  00 

132  23  00 

133  02  00 
133  05  10 
132  09  06 
131  03  20 
131  01  26 
131  31  00 
131  51  00 

131  37  00 

132  11  16 
132  26  10 

125  55  43 

124  50  07 

125  16  54 

125  13  14 

126  24  53 
126  31  58 
126  36  58 
126  56  31 

126  59  21 

127  08  56 
127  37  24 

127  56  46 

128  03  05 

127  35  44 

128  26  11 
127  55  29 
127  39  23 
127  24  33 
126  56  56 
124  50  44 
124  07  32 
123  48  11 
123  56  02 
123  23  31 
123  26  48 

123  31  47 

124  27  37 

130  26  09 
130  21  33 
126  16  06 
126  03  47 

125  38  26 
125  14  34 
123  28  46 


Lun.  Int. 


H.  W. 


A.  m. 


1  45 


0  16 
0  50 


0  34 


0  06 
0  45 
0  30 


0  00 


0  07 


12  15 
0  45 


12  20 
12  05 


12  05 


11  55 
11  50 
11  47 


0  10 
0  32 
0  30 
0  55 
4  45 
4  52 


4  40 
[2  17 
[2  00 


0  15 

0  50 

1  55 

2  30 

3  40 

4  45 

5  38 


L.W. 


h.    m. 


7  58 


6  24 

7  05 


6  41 


6  17 
6  56 
6  39 


6  12 


6  19 


6  08 

7  20 


6  15 
5  56 


5  55 


5  45 
5  38 
5  34 


6  22 

6  44 

6  42 

7  08 
11  00 
11  18 


11  05 
[8  311 
[8  14] 


8  10 
8  47 

10  00 

10  15 

11  58 


Range. 


Spg. 


ft. 


9.0 
10.1 


9.5 


9.9 
18.6 

17.7 


1L5 


12.8 


10.0 
12.4 


9.9 
10.3 


9.8 


9.7 
9.3 
9.3 


10.7 
1L6 
1L5 
12.8 
10.6 
10.2 


m 


20 

24,17 
14.1 
16.0 

15.7 
7.2 
9.0 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMEBIC  A— Continued. 


[Page  289 


Place. 


Atkinson  Point:  Lighthouse 

Vancouver,   Burrard   Inlet:   Govt.    Re- 
serve, English  Bay 

Eraser  River:  Garry  Pt 

New  Westminster:  Military  barracks 

Point  Roberts :  Parallel  station 

Semiamoo  Bay :  Parallel  station 

Admiralty  Head:  Lighthouse 

Steilacoom :  Methodist  Church 

Seattle:  C.  S.  aat.  station 

Port  Townsend :  C.  S.  ast.  station 

Smith  Island:  Lirfithouse 

New  Dungeness:  Lighthouse 

Port  Angeles :  Ediz  Hook  lighthouse 

Cape  Flattery:  Lighthouse 

Cape  Shoal  water :  Lighthouse 

Cape  Disappointment:  Lighthouse 

Bremerton :  Navy-yard  flagstaff 

Tacoma:  St.  Luke  s  Church 

Astoria:  FlagstafiP 

Yaquina  Head :  Lighthouse 

Cape  Arago,  or  Gregory :  Lighthouse 

Cape  Blanco:  Lighthouse 

Crescent  City :  Lighthouse 

Trinidad  Head :  Lighthouse 

Eureka:  Methodist  Church 

Humboldt:  Lighthouse 

Cape  Mendocino:  Lighthouse 

Pomt  Arena:  Lighthouse 

Point  Reyes:  Lighthouse 

San  Francisco:  Davidson  Observatory. . . 

Berkeley,  Univ.  Obsy . . . 

Mare  Island:  Chronom.  and  Time  Sta., 

Navy-yard 

Benicia:  Church 

Farallon  Islet:  Lighthouse 

Santa  Clara:  Catholic  Church 

Mount  Hamilton:  Obs.  peak 

San  Jose :  Spire 

Pigeon  Point:  Lighthouse 

Santa  Cruz :  Warehouse  flagstaff 

Monterey:  C.  S.  azimuth  station 

Point  Pinos:  Lighthouse 

Piedras  Blancas:  Lighthouse 

Point  Conception :  Lighthouse 

Santa  Barbara:  N.  tower,  Mission  Church 

San  Buenaventura:  C.  S.  ast.  station 

Pt.  Fermin,  San  Pedro  Bay:  Lighthouse. 

Los  Angeles:  Courthouse 

Point  Loma :  Lighthouse 

San  Diego:  C.  S.  ast.  station 

Mexican  Boundary:  Obelisk 

San  Miguel  Island :  Seal  Pt 

Santa  Rosa  Island :  E.  pt 

Santa  Cruz  Island:  NE.  pt 

Anacapa  Island :  E.  pt 

Santa  Barbara  Island:  Summit 

San  Nicolas  Island :  Summit 

Santa  Catalina  Island :  Catalina  Peak . . . 


Lat.  N. 


49  19  42 

49  16  18 
49  07  04 
49  13  01 
49  00  00 
49  00  00 

48  09  19 
47  10  20 

47  35  54 

48  06  56 
48  19  07 
48  10  52 
48  08  24 
48  23  30 
46  43  00 

46  16  29 

47  33  24 
47  15  32 

46  11  19 
44  40  35 
43  20  36 
42  50  22 

41  44  36 
41  03  01 
40  48  11 
40  41  37 
40  26  18 
38  57  12 
37  59  39 
37  47  28 

37  52  24 

38  05  56 
38  03  05 
37  41  51 
37  20  49 
37  21  03 
37  19  58 
37  10  49 
36  57  31 
36  35  21 
36  37  55 
35  39  50 
34  26  49 
34  26  10 
34  15  46 

33  42  14 

34  03  05 
32  39  48 
32  43  06 

32  31  58 
34  04  19 

33  56  30 

34  03  12 
34  00  25 
33  28  16 
33  14  55 
33  23  09 


LODR.  W. 


123  15  54 

123  11  26 
123  11  27 
123  53  52 
123  04  52 
122  44  56 

122  40  34 
122  35  51 
122  19  59 
122  44  58 

122  50  36 

123  06  31 

123  24  07 

124  44  06 
124  04  25 
124  03  11 
122  37  33 

122  26  26 

123  49  42 

124  04  40 
124  22  31 
124  33  30 

124  12  10 
124  09  03 
124  09  41 
124  16  26 
124  24  25 
123  44  27 
123  01  24 
122  25  43 
122  15  41 

122  16  24 

122  09  23 

123  00  07 
121  56  26 
121  36  40 

121  53  39 

122  23  39 
122  01  29 
121  52  59 
121  56  02 
121  17  06 
120  28  18 
119  42  42 

119  15  56 
118  17  41 

118  14  32 
117  14  37 
117  09  41 

117  07  32 

120  21  55 

119  58  29 
119  33  51 
119  23  04 
119  02  29 
119  31  19 

118  24  05 


Lun.  Int. 


H.W. 


5  20 

5  28 
5  11 


4  59 


0  08 


12  22 
4  27 
4  32 

0  15 
11  50 
11  55 


11  33 
11  27 
11  57 
11  33 
11  00 

10  36 

11  23 

12  07 
11  43 

1  05 

1  35 

10  40 


10  54 
10  43 


9  37 
9  53 
9  36 


9  29 
9  32 


9  23 
*9'29" 


9  20 
9  28 


L.  w. 


A.  m. 

11  35 

12  01 
11  23 


11  10 


11  04 
10  33 
9  32 
9  28 
8  34 
8  23 
6  16 


6  19 
10  35 
10  45 

6  42 
5  37 
5  49 


7  15 
7  48 
4  25 


4  27 
4  24 


3  15 
3  21 
3  13 


3  07 
3  20 


3  02 
'306 


3  04 
3  08 


Range. 


Spg. 


ft. 
7.8 

8.2 
7.0 


7.1 


ILO 
9.2 
6.2 
5.6 
5.0 
5.3 
7.1 


7.7 
9.4 
9.8 

7.8 
7.3 
6.0 


5.8 
5.7 

5.7 


5.1 
4.6 

5.6 
5.6 
4.5 


5.2 

4.8 


4.8 
49 
5.5 


5.2 
5.1 


4.9 


4.9 
5.1 


Neap. 

ft. 
4.9 

5.0 
4.4 


4.6 


7.2 
6.0 
4.0 
3.7 
3.3 
3.4 
4.1 


3.4 
3.3 
3.3 
3.1 
3.0 
2.6 
3.2 
3.2 
2.9 

3.7 
3.7 
2.9 


3.3 
3.1 


2.2 
2.2 
2.5 


2.3 
2.3 


2.2 
'2.*2 


2.2 
2.3 


21594°— 14- 


-19 


Page  290]  APPENDIX   IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OP  NORTH  AMERICA— Continued. 


Place. 


Ensenada  Harbor:  Head  of  bay,  close  to 

beach 

San  To  mas:  NW.  shore  of  cove 

Colnett  Bay:  Head  of  bay 

San  Martin  Island:  Hassler  Cove 

Port  San  Quentin:  Sextant  Pt 

San  Geronimo  Island:  Bight  at  E.  end. . . 

Canoas  Point:  High  bluff 

Guadeloupe:  North  pt 

La  Playa  Maria:  Mound  on  W.  side 

Santa  Rosalia  Bay:  Obs.  spot,  Cairn 

Lagoon  Head :  Highest  pt.  of  crater 

Cerros  Island:  SE.  extremity 

San  Benito  Island:  Summit  of  W.  island.. 

San  Bartolom^:  N.  side  of  entrance 

Asuncion  Island :  Summit  of  island 

San  Ignacio  Point:  Extreme 

Abreojos  Point:  Extreme  of  rocky  ledge. , 

San  Domingo  Point:  Edge  of  cliff 

San  Juanico  Point:  KnoU 

Alijos  Rocks:  South  Rock 

Cape  San  Lazaro:  Extreme 

Magdalena  Bay:  Obs.  spot  (post)  N.  of 

Port  Magdalena 

Cape  Tosco:  Extreme 

El  Conejo  Point:  Extreme 

Todos  Santos:  Foot  of  hill,  Lobos  Pt 

San  Lucas:  Steep  sand  beach,  NW.  pt.  of 

bay 

San  Jos6  del  Cabo:  NE.  side  of  entrance. 

Arena  Point:  Extreme , 

Arena  de  la  Ventana:  Extreme , 

Pichilinque  Bay:  SE.  pt.  of  San  Juan, 

Nepomezeino  I 

La  Paz:  Obs.  spot,  El  Mogote 

Lupona  Point:  Extreme 

San  Evaristo:  3  m.  S.  of  S.  Evaristo  Hd. 

San  Marcial  Point:  Extreme 

Salinas  Bay:  Beach,  NE.  pt.  of  bay 

Loreto:  Cathedral 

Pulpito  Point:  Summit 

Muleje:  Equipalito  Pt 

San  Marcos  Island:  S.  sand  spit 

Santa  Maria  Cove:  Beach  on  NW.  shore. 

San  Carlos  Point:  Extreme 

Santa  Teresa  Bay:  Beach  on  N.  side 

Las  Animas:  Low  pt 

Raza  Island:  Landing  place,  S.  side 

Angeles  Bay:  Bight  on  NW.  shore 

Remedies  Bay:  Beach  on  W,  shore 

Mejia  Island:  S.  side 

San  Luis  Island:  SE,  side 

San  Firmin:  Beach,  N.  of  bight 

San  Felipe  Point:  Peak,  1,000  feet 

Philips  Point:  Beacon 


Georges  Island:  NE.  shore 

Cape  Tepoca:  Hill,  300  feet 

Libertad!^  Anchorage:  Beach 

Patos  Island:  SE.  end 

Tibiu-on  Island:  SE.  end 

Kino  Point:  0.2  mile  N.  88°  W.  of  mound. 

San  Pedro:  N.  side  of  bay 

Guaymas:  Lighthouse 


Lat.  N. 


31  51  10 
31  33  04 
30  57  39 
30  28  58 
30  22  16 
29  47  20 
29  25  29 
29  10  50 
28  56  06 
28  40  16 
28  14  26 
28  03  52 
28  18  08 
27  39  35 
27  06  10 
26  45  45 
26  42  49 
26  18  56 
26  03  18 
24  58  00 
24  47  31 

24  38  23 
24  18  12 
24  20  17 
23  27  14 

22  53  07 

23  03  35 

23  32  48 

24  03  52 

24  15  31 
24  10  10 
24  24  10 

24  52  03 

25  29  23 

25  59  37 

26  00  41 
26  30  44 

26  53  37 

27  10  21 

27  26  06 

28  00  07 
28  25  04 
28  47  40 
28  49  11 

28  56  39 

29  13  52 
29  33  08 

29  57  27 

30  25  16 

31  02  57 
31  46  10 

31  00  54 
30  16  05 
29  54  12 
29  16  12 
28  45  55 
28  45  28 
28  03  22 
27  50  28 


Liin.  Int. 


Range. 


Long.  W. 


116  38  05 
116  40  51 
116  17  28 
116  06  46 
115  59  07 
115  48  12 
115  12  14 
118  18  30 
114  31  06 
114  14  15 

114  06  21 

115  11  32 
115  36  10 
114  54  27 

114  17  25 
113  16  25 
113  35  04 
112  41  44 
112  17  52 

115  51  54 
112  18  25 

112  08  54 
111  42  54 
111  30  21 
110  14  07 

109  54  50 
109  40  43 
109  28  57 

109  50  29 

110  20  34 
110  20  41 
110  20  35 

110  41  47 

111  01  43 
111  06  53 
111  21  03 
111  27  14 

111  58  04 

112  05  39 
112  19  56 
112  47  36 

112  51  59 

113  12  48 
113  00  05 
113  34  35 
113  40  00 

113  35  19 

114  25  49 
114  39  47 
114  52  10 
114  43  31 

113  16  30 
112  53  26 
112  45  04 
112  28  51 
112  21  46 
111  58  37 
111  16  00 
110  54  28 


H.  W. 


i.  m. 
9  28 


9  27 
"923 


9  15 


9  05 
"906 


9  00 
'8*29" 


8  25 


8  36 


9  40 


11  50 


11  30 


L.  W. 


Spg. 


h.    m. 
3  06 


ft. 
5.0 


3  05 

s'oo' 


5.8 


4.9 


2  53 


7.6 


2  42 
"2'37" 


7.8 
"8.'2' 


2  48 
'217" 


6.7 
"5.*7" 


2  12 


5.5 


2  20 


4.5 


3  34 


5.4 


5  47 


11.  2   2.  6 


5  26 


5.0 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMEBIC  A— Continued . 


[Page  291 


Place. 


Lat.  N. 


Long.  W. 


Lun.  Int. 


Range. 


H.W. 


L.W. 


Spg. 


Neap. 


Ciarifl  Island:  NW.  part 

Santa  Barbara:  NW.  side  of  bay 

Agiabampo:  SE.  side  of  entrance 

Topolobampo:  SE.  end  of  Santa  Maria  I. 

Navachista:  W.  side  of  creek 

Playa  Colorado:  N.  side  of  entrance. . . . 

Altata:  N.  side  of  entrance 

Mazatlan:  Lighthouse 

Palenita  Village:  Boca  Tecapan 

San  Bias:  Customhouse 

Maria  Madre  Island:  SE.  extreme 

Mita  Point:  Extreme 

Penas  Anchorage:  Mouth  of  Rio  Real 

Cape  Corrientes:  Extreme 

Perula  Bay:  Smooth  Rock 

San  Benedicto  Island:  S.  extreme 

Socorro  Island:  SE.  part 

Roca  Partida:  Summit 

Clarion  Island:  S.  end 

Clipperton  Island:  Summit 

Navidad  Bay:  W.  end  of  sandy  beach. . . 
Manzanilla  Bay:  Flagstaff,  U.S.  consulate 
Sacatula  River:  Beach,  W.  side  of  bay. . . 
Isla  Grande:  Tripod  on  NW.  summit — 

Sihuatanejo  Point:  Tree  on  beach 

Morro  Petatlan:  Junction  of  stony  and 

sandy  beaches 

Tequepa  Harbor:  Limekiln 

Acapulco:  Lighthouse 

Maldonado:  El  Recordo  Pt 

Port  Angeles:  Lighthouse 

Sacrificios  Point:  Highest  pt.  of  cape. . . 

Port  Guatulco:  Cross 

Morro  Ayuca:  Summit  of  N.  edge  of  cape 
Salina  Cruz:  Lighthouse 

Champerico:  Inshore  end  of  iron  wharf. . 

San  Jose  de  Guatemala:  Lighthouse 

Acajutla:  Lighthouse 

Libertad:  Lighthouse 

La  Union:  Lighthouse 

Chicarene  Point:  Extreme 

Corinto:  Lighthouse 

San  Juan  del  Sur:  Signal  station 

Salinas  Bay:  Salinas  Islet 

Port  Culebra:  Extremity  of  Mala  Pt 

Ballena  Bay:  N.  Estero  Toussa 

Parida  Anchorage:  S.  pt.  of  Deer  Id 

Port  Nuevo:  Entrada  Pt 

Bahia  Honda:  W.  end  of  Centinela  I. .  . 
Coiba  (Quibo)  Island:  Observation  pt. . . 
Cocos  Island:  Head  of  Chatham  Bay. . . 

Panama :  Cathedral,  S .  tower 

Taboga  Island:  Church 

Cape  Mala:  Extreme 

Malpelo  Island :  Summit 

Point  Cham6:  Extreme 

Flamenco  Island:  N.  Pt 

Chepillo  Island:  Center 

Rey  Island:  Cocas  Pt.  extreme 

Darien  Harbor:  Graham  Pt 


26  58  59 
26  41  09 
26  16  35 
25  33  56 
25  23  06 
25  11  42 
24  38  52 
23  10  40 
22  30  26 
21  32  30 
21  30  45 
20  45  50 
20  36  26 
20  25  00 
19  34  48 
19  17  15 
18  42  57 
18  59  41 

18  20  55 

10  17  00 

19  13  25 
19  03  15 
17  58  21 
17  40  15 
17  37  50 

17  31  28 
17  16  13 
16  49  10 
16  19  37 
15  39  09 
15  40  41 
15  44  58 

15  52  17 

16  09  36 

14  17  44 
13  55  15 
13  34  20 
13  28  50 
13  20  00 
13  17  09 
12  27  54 

11  14  45 
11  03  10 
10  36  46 

9  43  45 
8  10  13 
8  04  30 
7  43  32 

7  24  20 
5  32  57 

8  57  06 
8  47  45 

7  27  40 
4  03  00 

8  39  00 
8  54  30 
8  56  32 
8  12  30 
8  28  50 


109  57  17 
109  40  48 
109  17  30 

109  10  23 
108  49  00 

108  23  37 
107  59  37 
106  26  47 
105  44  25 

105  18  40 

106  33  14 
105  33  37 
105  16  00 
105  39  21 
105  08  54 

110  49  22 
110  56  53 
112  04  07 
114  44  17 

109  13  00 
104  43  26 
104  19  50 
102  07  06 
101  40  25 
101  33  23 

101  27  14 
101  04  32 
99  55  50 
98  35  05 
96  30  43 
96  15  04 
96  08  10 
95  46  43 
95  12  16 

91  55  36 
90  49  45 
89  50  26 
89  19  20 
87  51  00 
87  47  06 
87  12  31 
85  53  00 
85  43  38 
85  42  46 

85  00  46 
82  14  32 
81  43  30 
81  31  58 
81  41  51 

86  59  17 
79  32  09 
79  33  16 
79  59  25 
81  36  00 
79  41  45 
79  31  15 
79  07  55 
78  54  40 
78  05  35 


h.    m. 


10  07 
9  08 


9  08 


9  07 


9  07 


8  50 


2  50 
2  50 

2  55 

3  05 
3  15 


2  55 

3  00 
2  50 
2  45 


3  15 

's'io 


3  00 
3  00 
3  10 


3  30 


3  05 
3  00 


h.    m. 


3  59 
2  51 


5.8 
3.8 


2  52 


3.2 


2  53 


2.5 


2  54 


L9 


2  38 


2.0 


9  02 
9  02 
9  08 
9  18 
9  28 


8.5 

9.0 

9.5 

10.0 

10.5 


9  08 
9  12 
9  02 

8  58 


10.5 

10.0 

9.5 

9.0 


9  28 
'922' 


10.5 

'ii.'6" 


9  14 
9  13 
9  22 


16.0 
15.4 
13.0 


9  42 


15.0 


9  18 
9  13 


16.0 
15.7 


L4 
0.9 


LO 


1.1 


L3 


0.9 


4.6 
4.9 
5.1 
5.4 

5.7 


5.7 
5.4 
5.1 
4.9 


5.7 
"5.9 


8.7 
8.3 
7.0 


8.1 


8.7 
8.5 


Page  292] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  INDIA  ISLANDS. 


Place. 


Memory  Rock:  Center 

Bahama  Island :  W.  pt 

Abaco  Island :  Lighthouse 

Little  Guana  Cay:  Lighthouse 

Walker  Cay:  Highest  part 

Great  Isaac  Cay:  Lighthouse 

Gun  Cay:  Lighthouse 

Ginger  Cay:  Center 

Cay  Lobos:  Lighthouse 

St.  Domingo  Cay:  Center 

Cay  Verde:  Hill  at  S.  end 

Ragged  Island:  Gun  Pt 

Nairn  Cay:  E.  pt 

Nurse  Channel  Cay:  Beacon 

Long  Island:  S.  pt 

Great  Exuma  Island :  Beacon 

Clarence  Harbor:  Lighthouse 

Eleuthera  Island:  Lighthouse 

Royal  Island:  Eastern  Pass 

Nassau:  Lighthouse 

Androa  Island :  Lighthouse 

Great  Stirrup  Cay:  Lighthouse 

Little  Stirrup  Cay:  WT  end 

San  Salvador  (Cat  I.) :  Lighthouse 

Concepcion  Island :  W.  bay 

Watlings  Island:  Hinchinbroke  Rock  ... 

Rum  Cay:  Harbor  Pt 

Castle  Island:  Lighthouse 

Fortune  Island:  S.  end 

Crooked  Island:  Moss  flagstaff 

Bird  Island:  Lighthouse 

Samana  Cay:  W.  pt 

Plana  Cay:  NW.  pt 

Mariguana  Island:  SE.  pt 

Hogety  Reef:  NW.  Cay 

Inagua  Island:  Lighthouse 

Little  Inagua  Island :  NW.  pt 

W.  Caicos  Cay:  Hill,  SE.  end 

French  Cay:  W.  pt 

Fort  George  Cay :  Old  magazine 

Caicos  Island:  Parsons  Pt.,  S.  islet 

Turk  Island:  Lighthouse 

Square  Handkerchief  Bank:  NE.  breaker 

Silver  Bank:  E.  extreme 

Navidad  Bank:  Center  of  E.  side 

Cape  Maysi:  Lighthouse 

Port  Baraooa:  Lighthouse 

Port  Cayo  Moa:  Carenero  Pt 

Nipe  Bay:  Extremity  of  Carenero  Pt 

Lucrecia  Point:  Lighthouse 

Port  Sama:  E.  side  of  entrance 

Peak  of  Sama:  Summit,  885  feet 

Port  Naranjo:  E.  side  of  entrance 

Gibara:  Lighthouse 

Port  Padre:  Guinchos  Pt 

Port  Nuevitas:  NW.  corner  R.  R.  station 

Matemillos  Point:  Lighthouse 

Cay  Verde:  NW.  end 

Cay  Confites:  S.  pt 

Paredon  Grande  Cay:  Lighthouse 

San  Fernando:  NW,  corner  Old  Spanish 

Fort  No.  1 

Cayo  Frances:  Lighthouse 


Lat.  N. 


26  56  53 
26  41  18 

25  51  30 

26  31  10 

27  15  42 
26  02  00 
25  34  30 
22  45  10 
22  22  30 

21  42  00 

22  01  15 
22  14  02 
22  20  44 
22  31  15 

22  51  00 

23  32  15 

23  06  00 
25  00  00 
25  31  20 
25  05  37 

24  43  45 

25  49  40 
25  49  12 
24  06  15 
23  50  50 
23  56  40 
23  37  45 
22  06  40 
22  32  40 
22  47  30 

22  51  00 

23  05  30 
22  34  38 
22  16  30 
21  40  30 

20  56  00 

21  30  40 
21  37  30 
21  30  00 
21  54  00 
21  29  33 
21  30  55 
21  06  30 
20  35  00 
20  02  00 

20  15  00 
20  21  46 
20  41  41 

20  47  19 

21  04  24 
21  09  00 
21  07  00 
21  07  30 
21  07  15 
21  18  30 
21  32  44 

21  40  02 

22  08  45 
22  11  14 
22  29  10 

22  09  44 
22  38  41 


Long.  W. 


79  06  54 
79  00  38 

77  10  45 

76  57  36 

78  23  48 

79  06  00 
79  18  26 
78  06  02 

77  34  26 
75  44  39 
75  10  34 
75  45  17 
75  28  20 
75  51  41 

74  51  54 

75  46  24 

74  59  00 

76  13  00 

76  51  48 

77  21  58 
77  46  45 
77  53  55 
77  57  06 

75  26  00 
75  07  27 
74  28  20 
74  50  08 
74  20  37 
74  22  54 
74  20  21 
74  22  48 
73  49  15 
73  38  03 

72  47  03 

73  50  29 
73  40  17 

73  42  33 
72  28  18 
72  12  51 
72  07  14 
71  31  12 
71  07  29 
70  29  54 
69  21  24 
68  47  24 

74  08  01 
74  29  13 

74  53  44 

75  34  21 
75  36  59 
75  47  18 
75  47  40 

75  52  18 

76  06  27 

76  35  34 

77  15  18 
77  08  04 
77  37  33 

77  39  23 

78  09  11 

78  35  54 

79  13  44 


Lun.  Int. 


H.  W, 


A.  m. 
7  40 


20 


8  20 
7  00 


7  20 
7  40 


7  00 


7  20 


7  50 


7  30 


5  40 


6  20 


7  00 


7  20 


L.W. 


ft.   TO. 

1  28 


2  08 


2  08 
0  48 


1  08 
1  28 


0  48 


1  08 


1  38 


1  18 


11  53 


0  08 


0  48 


1  08 


Range. 


Spg. 


ft. 
3.2 


3.0 


4.1 
4.0 


4.0 
3.0 


4.0 


3.0 


3.5 


3.0 


2.8 


2.4 


2.2 


2.8 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  INDIA  ISLANDS— Continued, 


[Page  293 


Place. 


Isabella  deSagua:  SE.  corner  of  church  .. 

Cay  Sal:  Lighthouse 

Bahia  de  Cadiz  Cay :  Lighthouse 

Piedraa  Cay:  Lighthouse 

Cardenas:  Cross  on  Cathedral 

Matanzas:  Summit  of  peak 

Habana:  Morro  lighthouse 

Transit  pier,  Casa  Blanca  Ob- 
servatory   

Flagstaff,  Cabafias  Fortress 

Bahia  Honda :  SE.  comer  Morillo  Fort 

Gobemadora  Pt. :  Lighthouse 

Dimas :  N  W.  corner  of  warehouse 

Cape  San  Antonio :  Lighthouse 

Radio  tower 

La  Caloma:  SW.  comer  of  warehouse 

San  Felipe  Cays:  SW.  pt 

Isla  de  Pinos:  Port  Frances 

Batabano:  Lighthouse 

Piedraa  Cay:  Lighthouse 

Cienfuegoe:  Colorados  Pt.  light 

Cathedral  tower 

Flagstaff,  Punta  Gorda 

Casilda:  Observation  pier 

Jucaro:  Observation  pier 

Santa  Cruz  del  Sur:  Observation  pier 

Manzanillo:  Observation  pier 

Niquero:  Sugar  mill,  smokestack 

Cape  Cruz:  Lighthouse 

Pomt  Mota 

Chirivico:  Damas  Cay 

Santiago :  Lighthouse 

Guantanamo  Bay:  Fisherman  Pt 

Lighthouse 

Naval  Station  flagstaff. 

Port  Escondido :  Inner  Entrance  Pt 

Port  Baitiqueri:  Barlovento  Pt 

Cayman  Brae :  Ej)t 

Little  Cayman:  W.  pt 

Grand  Cayman:  Fort  George,  W.  end 

Formigas  Bank:  Shoal  spot 

Morant  Point:  Lighthouse 

Port  Antonio :  Folly  Pt.  Light 

Port  Maria:  NW.  wharf 

St.  Ann  Bay:  Long  wharf 

Falmouth:  Fort 

Montego  Bay:  Fort 

St.  Lucia:  Port 

Savanna-la-Mar:  Fort 

Kingston:  Port  Royal  flagstaff 

Port  Royal:  Fort  Charles,  flagstaff 


Morant  Cays:  NE.  Cay 

Pedro  Bank:  Portland  Rock,  E.  end. 
Baxo  Nuevo:  Sandy  Cay 


Cape  Engano:  Extreme 

SamanaTown:  Obs.  spot 

Cape  Cabron :  _  East  extreme . . . 

Port  Plata:  Lighthouse 

Monte  Cristi:  Cabra  Island. . . 

Manzanillo  Point 

CapeHaitien:  Town  fountain . 


Lat.  N. 


22 
23 
23 
23 
23 
23 
23 

23 
23 
22 
23 
22 
21 
21 
22 
21 
21 
22 
21 
22 
22 
22 
21 
21 
20 
20 
20 
19 
19 
19 
19 
19 
19 
19 
19 
20 
19 
19 
19 

18 
17 
18 
18 
18 
18 
18 
18 
18 
17 
17 


56  30 

56  30 
12  34 
14  10 
02  43 
01  54 
09  26 

09  04 
09  11 
59  11 

00  00 

29  32 

52  01 

53  55 
14  36 

55  00 
35  30 

41  09 

57  45 

01  49 
08  36 
06  52 
48  16 
37  24 

42  23 
20  26 

02  55 
50  32 

53  31 

56  57 

57  29 

54  42 

53  04 
57  00 

54  08 
01  01 
45  15 
39  10 
17  45 

33  00 

55  05 

11  31 
23  00 

26  24 

30  34 
29  25 

27  45 

12  20 
55  56 
55  56 


17  26  30 

17  06  20 
15  53  00 

18  35  52 

19  12  29 
19  22  12 
19  48  51 
19  54  00 
19  46  20 
19  46  19 


Long.  W. 


80  00  32 
80  27  51 

80  29  26 

81  07  20 
81  12  02 

81  43  18 

82  21  29 

82  20  38 

82  21  01 

83  09  13 

83  13  00 

84  14  17 
84  57  09 
84  56  16 
83  34  24 
83  31  18 
83  09  13 
82  17  42 
81  07  18 
80  26  32 
80  27  05 
80  27  11 
79  58  58 
78  51  13 
77  59  45 
77  07  33 
77  34  50 
77  43  33 


75  52  03 
75  09  28 
77  09  28 
75  07  33 
75  03  08 

74  50  49 

79  46  07 

80  07  17 

81  23  17 

75  44  24 

76  11  08 
76  26  31 

76  54  22 

77  12  52 
77  39  62 

77  56  16 

78  10  52 
78  08  64 
76  50  35 

76  50  38 

75  58  20 

77  26  28 

78  39  04 

68  18  50 

69  19  23 

69  12  12 

70  41  27 

71  40  15 

71  46  40 

72  12  07 


LuD.  Int. 


Range. 


H.W. 


L.W. 


Spg. 


Neap. 


ft.  m. 


ft.  m. 


ft. 


8  30 

8  18 


2  18 
1  56 


2.2 
L3 


8  30 


2.18 


L5 


4  47 


11  00 


2.0 


8  20 
7  50 


2  30 
2  00 


2.2 
2.6 


[1.3] 


[1.1] 
'[1:2] 


[1.1] 


9  00 


2  48 


3.0 


6  50 


0  39 


5.5 


1.2 
0.7 


0.9 


1.1 


LI 
1.3 


L5 


2.9 


Page  294] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  INDIA   ISLANDS— Continued. 


Place. 


PortPaix:  Wharf 

St.  Nicholas  Mole:  Fort  George,  flagstaff . . 

Gonaives:  Verreur  Pt 

Gonave  Island:  W.  pt 

Arcadins  Islands:  Lighthouse 

Port  au  Prince:  Fort  Islet  light 

Jeremie:  Fort 

Cape  Dame  Marie:  Extreme 

Navassa  Island:  NW.  extreme 

Aux  Cayes:  Tourterelle  Bat'y 

Jacmel:  Wharf 

False  Cape:  Extreme 

Beata  Island:  NW.  pt 

Fraile  Rock:  Center 

Alta  Vela:  Summit 

Avarena  Point:  Extreme 

Salinas  Point  (Caldera) :  Extreme 

Sto.  Domingo  City:  Lighthouse 

Saona  Island:  Pt.  Catuano 

Mona  Island:  Lighthouse 

Mayaguez :  Mouth  of  Mayaguez  R 

Aguadilla:  Columbus  Monument 

San  Juan:  Morro  lighthouse 

Cape  San  Juan :  Lighthouse 

Guanica:  Meseta  Pt.  lighthouse 

Culebrita  Island :  Lighthouse 

Vieques  (Crab)  Island:  Port  Ferro  light. 

St.  Thomas:  Fort  Christian,  SW.  bastion. 

St.  John  Island:  Ram  Head 

Tortola:  Fort  Burt 

Virgin  Gorda:  Vixen  Pt 

An^ada:  W.  pt 

E.  extreme  of  reefs 

St.  Croix,  Christiansted:  SW.  bastion  of 

fort.. 

St.  Croix,  Lang's  Observatory 

Sombrero:  Lighthouse 

Dog  Island :  Center 

Anguilla:  Customhouse 

St.  Martin:  Fort  Marigot  light 

St.  Bartiiolomew:  Fort  Oscar 

Saba:  Diamond  Rock 

St.  Eustatius:  Fort  flagstaff 

St.  Christopher:  Basseterre  Church 

Booby  Islajid:  Center 

Nevis:  Fort  Charles 

Barbuda:  Flagstaff,  Martello  Tower 

Antigua,  English  Harbor:  Flagstaff,  dock- 
yard  

Sandy  Island:  Lighthouse 

Redonda  Islet:  Center 

Montserrat:  Plymouth  Wharf. 

Guadeloupe,  Basseterre:  Light  on  mast. . 

Port  Louis:  Light  on  mast. 

Gozier  Islet:  Lighthouse. . . 

Manroux  Id. :  Lighthouse . . 

Point  a  Pitre:  Jarry  Mill. . . 

Desirade:  E.  pt 

Petite  Terre:  Lighthouse 

Marie  Galante:  Lighthouse 

Saintes  Islands:  Tower  on  Chameau  Hill . 


Lat.  N. 


19  57  06 
19  49  15 
19  27  12 
18  56  00 
18  48  50 
18  33  31 
18  39  15 
18  36  48 
18  25  00 
18  11  08 
18  13  25 
17  46  08 
17  36  55 
17  37  37 

17  28  22 

18  08  55 
18  12  13 
18  27  54 
18  11  57 

18  05  17 
18  12  37 
18  24  51 
18  28  23 
18  23  01 

17  57  10 

18  18  56 
18  05  54 

18  20  23 
18  18  08 
18  25  04 
18  30  39 
18  45  11 
18  36  30 

17  45  09 

17  44  43 

18  35  37 
18  16  42 
18  13  06 
18  04  07 
17  53  58 
17  39  10 
17  29  10 
17  18  12 
17  13  38 
17  07  52 
17  35  50 

17  00  00 
17  06  54 
16  55  18 
16  42  12 

15  59  50 

16  25  09 
16  11  57 
16  13  14 
16  13  56 
16  19  56 
16  10  17 
15  52  59 
15  51  32 


Long.  W. 


72  50  00 

73  23  07 

72  43  52 

73  18  20 
72  39  13 

72  21  00 

74  06  52 

74  25  50 

75  01  57 

73  44  08 
72  30  45 
71  41  06 
71  31  10 
71  41  10 
71  38  30 
71  02  25 
70  32  53 
69  52  59 
68  45  41 

67  50  50 
67  09  17 
67  09  42 
66  07  26 

65  37  07 

66  54  13 
65  13  40 
65  25  26 

64  55  47 
64  42  03 
64  36  47 
64  21  48 
64  24  58 
64  10  45 

64  42  16 
64  41  14 
63  28  13 
63  16  00 
63  04  39 
63  05  45 

62  51  30 

63  15  16 
62  59  09 
62  43  14 
62  35  25 
62  37  29 
61  49  54 

61  46  07 

61  55  11 

62  19  10 
62  13  24 
61  44  09 
61  32  15 
61  29  40 
61  32  05 
61  33  15 
61  00  44 
61  06  45 
61  19  15 
61  35  55 


Lun.  Int. 


Range. 


H.W.        L.W. 


Spg.       Neap. 


h.    m. 


h.    m. 


[1-2] 


[2.5] 


[2.2] 


7  04 


2  00 


2.0 


LO 


8  21 


2  20 


L3 


0.9 


[7  311 
[7  35] 

[7  11] 


[1  30] 
[140] 

[0  58] 


[LO 
LO' 

Li; 

[1-2] 


[1.5] 


[2.0] 


[1.3] 


APPENDIX   IV.                                     [Page  295 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST   INDIA  ISTiAUDS— Continued. 

1 

Place. 

Lat.  N. 

Long.  \V. 

Lun.  Int. 

Range.         1 

H.  W. 

L.  W. 

Spg. 

Neap. 

Dominica,  Prince   Ruperts  Bav:     Sand 

beach  W.  of  church 

Roseau:  Flagstaff ,  Fort  Young 
Aves  Island :  Center 

15  34  34 
15  17  27 
15  42  00 

14  35  44 

14  43  54 
14  46  13 
14  23  23 

61  28  14 
61  23  52 
63  37  46 

61  04  30 

61  11  09 
60  53  20 

60  52  33 

61  00  48 

59  37  16 
59  .SI  50 

h.    m. 
4  00 

h.    m. 
10  12 

ft. 
L5 

ft. 
0.8 

Martinique,  Fort  de  France:    Fort  St. 
Louis  light 

St.  Pierre:  Ste.  Marthe  Bat- 
tery  

Caravelle  Pen.:  Lighthouse. 
Cabrit  Islet:  Summit 

3  50 

10  02 

1.1 

0.6 

St.  Lucia,  Port  Castries:  Lighthouse 14  01  54 

Barbados,  Bridgetown:    Flagstaff,  Pick- 
ett's Battery 13  05  43 

S.  Point:  Lighthouse 13  02  45 

2  50 

9  02 

3.0 

L5 

Ragged  Point:  Lighthouse 13  09  40       59  26  04 

St.  Vincent,  Kingstown:  Lighthouse 13  09  19 

Bequia  Island,  Admiralty  Bay:  Church. .    13  00  25 

Grenada:  St.  George  Lighthouse 12  03  02 

Tobago,  Rocky  Bay:  Lighthouse 11  10  08 

Testigos  Islets:  Center  of  Testigo  Grande.    11  25  02 

Sola  Island:  Center 11  19  00 

Pampatar,  Margarita  I.:  San  Carlos  Castle.    10  59  43 
Tortugas  Island:  S.  end  of  W.  Tortugillo  i 

Islet 10  57  45 

Orchila  Island:  S.  side i  11  47  57 

61  14  34 
61  14  09 
61  45  06 
60  42  38 
63  05  48 
63  36  00 
63  48  00 

65  26  38 

66  12  31 
66  39  10 
68  14  10 
68  39  19 
68  55  48 
68  56  17 
70  02  34 

2  50 

9  05 

L6 

0.8 

2  30 

3  50 

8  42 
10  02 

1.5 
2.1 

6.8 
1.1 

Roques  Islands:  Pirate  Cay 

11  56  16 

Bonaire  Island :  Lighthouse 

12  02  06 

11  59  30 

12  06  58 
12  06  15 
12  31  05 

Little  Curasao  Island :  Lighthouse 

Curafao  Island :  Fort  Nassau 

Lighthouse 

Oruba  Island:  Lighthouse 

NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA.                                    1 

i 

s 

s 

© 
© 

s 
a 

Caribana  Point:  Extreme 

8  37  30 

9  24  00 
9  24  00 

10  25  50 

11  00  15 

10  07  00 

11  15  28 

11  33  30 

12  12  34 

76  52  55 
76  10  45 

Fuerte  Island:  N.  extreme 

Cispata  Port:  Zapote  Pt 

75  48  00 
75  32  50 
74  57  55 
74  49  51 
74  14  33 
72  54  50 
72  09  42 
71  45  42 

71  07  55 
71  37  00 
70  17  21 
70  04  55 
70  57  00 
69  34  20 
68  19  55 
68  22  54 
68  00  55 
66  56  06 
66  06  15 
66  04  13 
66  09  25 
64  44  00 
64  11  33 
64  17  55 

Cartagena:  Lighthouse 

Savanilla:  Lighthouse 

Magdalena  River:  NW.  pt.  of  Gomez  I. . . 
Santa  Marta:  Lighthouse 



Rio  de  la  Hacha:  Light  on  church 

Cape  La  Vela:  Sand  beach  inside  cape. . . 
Bahia  Honda:  E.  pt.,  S.  side 

12  23  09 

Espada  Point:  Extreme 

12  04  00 

10  57  30 

11  48  56 

12  11  00 
12  29  15 
11  27  56 

10  47  00 

11  10  00 
10  29  53 
10  36  57 
10  35  00 
10  34  06 
10  49  30 
10  13  30 
10  27  20 
10  40  00 
10  42  00 

Maracaibo:  Zapara  I.  light 

5  05 

11  17 

2.5 

1.5 

Estangues  Point:  500  ft.  from  extreme 

Cape  San  Roman :  Extreme 



Marjes  Islets:  N.  islet 

1 

Vela  de  Coro:  Lighthouse 

1 

Tucacas  Island :  Ore  house 

St.  Juan  Bay:  Cay 

Puerto  Cabello:  Lighthouse 

La  Guaira:  Lighthouse 

6  00       12  12 

2.8 

L7 

Cape  Codera:  Morro 

Corsarios  Bay:  W.  pt 

1 

Centinela  Islet:  Center 

\"'   ' 

Barcelona:  Morro 

Cumana:  Lighthouse 

Escarceo  Point;  Extreme    . 

Chacopata:  Morro 

63  50  25 



Page  296]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMEBIC  A— Continued. 


Place. 


Esmeralda  Islet:  Center 

Carupano:  Lighthouse 

Pt.  Herman  Vasc[uez 

Puerto  Santo  Bay:  Sand  spit  S.  of  Moito. 

Tres  Puntas  Cape:  Extreme 

Unare  Bay:  Obs.  spot,  200  yds.  S.  of  Morro. 

Pena  Point:  Extreme 

Pato  Island:  E.  pt 

Mocomoco  Pt. :  Extreme 


Port  of  Spain:  King's  Wharf  light 

Chacachacare  Island:  Rocks  off  SW.  pt. . 
Galera  Point:  NE.  extreme,  lighthouse... 

Icacos  Point:  Lighthouse 

San  Fernando:  Pierhead 


Demerara:  Georgetown  lighthouse. 

Nickerie  River:  Lighthouse 

Paramaribo:  Stone  steps 

Maroni  River:  W.  lighthouse 

Salut  Islands:  Lighthouse 

Enfant  Perdu  Islet:  Lighthouse. . . 

Cayenne:  Lighthouse 

Connetable  Islet:  Center 

Carimare  Mount:  Summit 


Orange  Cape:  Extreme... 
Maye  Mountain:  Summit. 
North  Cape:  Extreme 


Cape  Magoari:  Extreme 

Para:  Customhouse 

Atalaia  Point:  Lighthouse 

Itacolomi  Point:  Lighthouse 

Maranhao  Island:  Landing  place 

Santa  Anna  Island:  Lighthouse 

Tutoya:  Entrance 

Paranahiba  River:  Amargao  Village 

Ceara:  Lighthouse. 

Ja^uaribe  River:  Pilot  station 

Caigara:  Village 

Cape  St.  Roaue:  Extreme 

Rio  Grande  do  Norte:  Lighthouse 

Natal:  Cathedral 

Parahiba  River:  Lighthouse  at  entrance. 

Parahiba:  Cathedral 

Olinda:  Lighthouse 

Pemambuco:  Picao  lighthouse 

Cape  St.  Augustine:  Lighthouse 

Tamandare:  Village 

Maceio:  Lighthouse 

San  Francisco  River:  Lighthouse  at  en- 
trance   

Cotinguiba  River:  Lighthouse  at  entrance 

Vaza  Barris  River  :^  Semaphore  at  en- 
trance  

Real  River:  Lighthoiise 

Conde:  Village 

Garcia  d' Aviia:  Tower 

Bahia :  Santo  Antonio  lighthouse 

Itaparica:  Fort  on  N.  pt 

Morro  de  Sao  Paulo:  Lighthouse 

Camamu:  Village 

Contas:  Church 


Lat.  N. 


10  40  00 

10  40  15 
10  42  00 
10  43  27 
10  45  00 
10  44  19 
10  43  48 
10  38  15 
8  39  25 

10  38  37 
10  40  03 
10  50  02 
10  03  29 
10  16  59 


6  49  20 
5  58  30 
49  30 
44  50 
16  50 
02  40 
66  20 
49  30 
23  20 


4  20  45 
2  46  30 
1  40  17 
Lat.  8. 

0  17  00 

1  26  59 
0  35  03 

2  10  11 
31  48 
16  22 

41  55 
53  20 

42  05 
25  35 
03  15 
29  15 

45  05 

46  41 
56  30 
06  35 

8  00  50 
8  03  22 
8  20  45 

8  43  40 

9  39  35 

10  30  30 

10  58  20 

11  09  45 

11  27  40 

12  12  05 

12  33  40 

13  00  37 

12  52  48 

13  22  37 

13  56  42 

14  17  40 


Long.  W. 


63  31  55 
63  18  00 
63  14  00 
63  09  43 
62  41  55 
62  44  29 
61  50  50 
61  51  18 

60  10  15 

61  30  35 
61  45  54 

60  54  10 

61  55  41 
61  28  12 

58  11  30 
57  00  30 
55  08  48 
54  00  30 
52  34  53 
52  21  11 
52  20  26 
51  55  36 
51  50  36 

51  27  46 
50  54  46 
49  56  46  ! 

48  23  30 
48  30  01 
47  20  54 
44  25  56 
44  18  45 
43  37  30 
42  18  02 
41  40  35 
38  28  25 
37  44  55 
36  02  52 
35  15  52 
35  11  55 
35  12  43 
34  49  30 
34  53  04 
34  50  36 
34  51  57 

34  56  05 

35  05  06 

35  44  54 

36  21  51 

37  04  00 

37  12  36 
37  24  GO 

37  45  46 

38  02  16 
38  32  06 
38  41  28 

38  54  38 

39  07  05 
39  00  45 


Lun.  Int. 


H.  W.    L.  W 


h.    m. 


4  20 


4  18 


5  50 


4  27 


11  50 


6  50 
5  35 
5  05 


5  25 
5  50 


4  05 


4  33 


4  20 

4  17 


4  10 


3  50 
3  50 


h.    m. 


10  30 


9  50 


12  00 


10  30 


5  37 


0  38 
11  47 
11  17 


11  37 

12  00 


10  17 


10  50 


10  32 
10  29 


10  22 


10  00 
10  00 


Range. 


Spg.   Neap. 


3.2 


8.6 


9.5 


6.0 


n.o 


16.5 
13.1 
11.7 


8.2 
8.0 


7.0 


8.5 
7.8 


7.6 


6.0 
6.3 


APPENDIX  IV.                                   [Page  297 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OP  SOUTH  AMERICA— Continued. 

1 

Place. 

Lat.S. 

Long.  W. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

eg 
S 

Ilb606 :  Church 

tin 

14  47  40 

14  56  40 

15  13  27 

15  21  00 

16  17  20 

16  25  38 

17  21  40 
17  31  45 
17  43  30 

17  57  31 

18  06  15 
20  19  23 
20  38  25 
20  49  00 

20  57  35 

21  38  40 

22  02  00 
22  23  45 
22  26  00 
22  37  00 

22  46  00 

23  00  42 

22  53  15 

23  01  43 
22  54  46 

22  54  24 

23  03  40 

22  32  00 

23  03  40 
23  04  20 

22  57  20 

23  09  20 
23  00  30 
23  09  50 
23  12  20 
23  25  55 
23  32  57 
23  45  15 
23  58  30 

23  47  20 

24  03  06 

23  56  00 

24  06  30 
24  10  32 
24  28  45 

24  42  35 

25  06  40 
25  30  55 
25  31  20 
25  26  30 
25  44  10 

25  50  15 

26  14  17 

26  46  45 

27  01  35 
27  18  00 
27  25  30 
27  22  55 
27  50  27 
27  36  00 

27  56  40 

28  38  00 

29  20  20 
32  06  40 

39  03  25 
39  01  45 
39  01  15 
39  16  45 
39  02  05 
39  04  15 
39  13  15 
39  12  00 
.39  14  36 

38  41  46 

39  31  16 

40  16  36 
40  23  46 
40  40  45 

40  46  35 

41  02  21 

40  59  00 

41  47  35 
41  43  15 
41  59  45 

41  54  05 

42  00  00 
42  01  15 

42  54  05 

43  09  19 
43  10  21 
43  08  45 
43  11  01 
43  33  24 

43  59  26 

44  02  29 
44  08  24 
44  19  04 
44  05  45 

44  42  04 

45  04  04 
45  03  50 
45  00  39 
45  15  20 

45  21  04 

46  15  57 
46  19  09 

45  40  49 

46  47  44 

46  41  04 

47  32  54 

47  51  50 

48  19  53 
48  31  03 
48  43  14 
48  23  14 
48  25  51 
48  39  29 
48  36  59 
48  36  44 
48  22  20 
48  34  25 
48  26  09 
48  35  16 
48  34  14 
48  33  44 

48  49  45 

49  43  39 
52  07  44 

ft.    m. 
3  35 

A.    m. 
9  47 

It. 
6.4 

ft. 
3.1 

Oliven^a:  Center  of  village 

Una:  Center  of  village 

Comandatuba:  Center  of  village 

Santa  Cruz:  Church 

3  25 

9  37 

6.0 

2.9 

Porto  Seguro:  Matriz  Church 

Prado:  River  entrance 

Alcoba^a:  Center  of  village 

Caravellae:  Center  of  village 

3  10 
3  15 

9  23 
9  27 

6.4 
7.5 

3.1 
3.6 

AbrolhoB  Island :  LighthouBe 

Porto  Alegre:  Center  of  village 

Espiritu  Santo  Bay:  Lighthouse 

2  50 

9  00 

4.0 

L9 

Guarapiri  Islets:  E.  islet 

Benevente:  Village 

2  40 

8  52 

5.0 

2.4 

Itapemirim:  Moscaa  Islet 

Sao  Joao  da  Barra:  Lighthouse   

Cape  St.  Thoni6:  Extreme 

Macah6:  Fort  at  entrance 

2  20 

8  30 

9.2 

4.4 

Santa  Anna  Island :  Summit 

Barra  Sao  Jo3o:  Village 

Busios:  Church 

Cape  Frio:  Lighthouse 

Port  Frio:  Village 

2  30 

8  42 

4.9 

2.3 

Maricas  Islands:  S.  islet 

Rio  de  Janeiro:  Fort  Vill^;agnon  Light. . 

National  Observatory 

Raza  Island:  Lighthouse 

2  50 

9  00 

4.2 

2.0 

Petropolis:  Center  of  town 

Cape  Guaratiba:  Summit 

Msu^mbaya  Island:  Summit  of  SW.  end. . 
Mangaratiba:  Village 

Palmafl  Bay:  Beach  at  head  of  bay : . 

Angi"a  dos  Reis:  Landing  place 



Ilha  Grande:  Lighthouse 

Parati:  Fort 

1  35 

7  47 

5.3 

2.5 

Ubatuba:  Cathedral 

Porcos  Grande  Islet:  Summit 

Busios  Islets:  Summit 

St.  Sebastian  Island:  Boi  Pt.  light 

Villa  Nova  da  Princessa:  Center 

Santos:  Moela  I.  lighthouse 

Quay 

2  50 

9  00 

5.0 

2.8 

Alcatrazes  Island:  Summit,  880  ft 

Concei^ao:  Church 

Quemada  Grande  Island:  Summit,  623  ft. 
loruane:  Ouav 

Bom  Abrigo  .  [slet:  Lighthouse 

Ilha  do  Mel:  Lighthouse 

Paranagua:  Quay 

2  55 

9  05 

6.4 

3.1 

Antonina:  Quay 

Coral  Islet:  Center 

Itacolomi  Islet:  Center 

Sao  Francisco:  Center  of  town 

Itapacaroya:  Church 

Cambria:  Church. . .            

Arvoredo  Island :  Lighthouse 

- 

Anhatomirim:  Lighthouse    

Sta.  Catherina  Island :  Rapa  Pt 

2  35 

8  47 

5.9 

2.8 

Naufragados  light. 
Nossa  Senhora  do  Deeerto:  Quay 

Cape  St  Martha"  Lighthouse 

Torres  Point'  Extreme 

Rio  Grande  do  Sul :  Lighthouse 

4  00 

10  12 

1.8 

0.9 

Page  298]                                   APPENDIX  IV. 

MAKITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OF   SOUTH  AMERICA— Continued. 

1 
8 

Place. 

Lat.  S. 

Long.  W. 

Lun 

Int. 

Range.         1 

H.W. 

L.W. 

Spg. 

Neap. 

as 

S 

a 

a 

i 

a 
"S 
a 

9 
61 

h 
< 

i 

a 

0 

Castillos:  Beuna  Vista  Hill,  184  feet 

Cape  Santa  Maria :  Lighthouse 

34  21  19 

34  40  01 

35  01  39 
34  58  15 
34  56  55 
34  54  33 
34  28  20 

34  10  50 
34  36  30 

34  54  30 

35  15  45 

35  26  50 

36  18  24 
36  53  00 
38  05  30 
38  57  00 

38  43  50 

39  26  30 

39  57  30 

40  32  52 

40  36  10 

41  02  00 
41  11  00 

40  49  00 

41  41  10 

42  14  15 
42  46  15 
42  57  00 

42  45  40 

43  20  45 

44  30  40 

45  04  00 
45  03  00 
45  10  10 
47  06  20 
47  45  05 
47  57  15 

49  15  20 

50  08  30 

50  58  27 

51  33  21 

52  18  35 
54  40  35 

54  43  24 

54  45  16 

54  53  45 

54  48  02 

55  17  00 
55  19  00 
55  35  30 
55  48  54 
55  58  41 
55  51  20 
55  43  15 

55  52  30 

56  28  50 
55  24  50 
54  45  40 
54  24  48 

53  47  16 

54  09  14 
54  53  16 

54  57  10 

55  55  04 

56  12  15 

57  52  27 

58  15  40 
58  22  14 
57  54  15 
57  10  45 
57  05  28 
56  44  15 

56  38  54 

57  30  01 

61  59  15 

62  15  27 
62  03  22 
62  07  46 
62  09  30 
62  10  12 

62  45  11 

63  08  16 

64  54  41 

65  12  29 
64  27  56 

63  37  16 

64  28  20 

64  59  00 

65  03  36 
65  22  10 
65  36  01 

65  52  30 

66  32  36 
65  51  46 
65  54  45 
65  45  40 

67  42  30 

68  23  00 

69  09  47 
69  00  31 
68  22  12 
65  05  53 

63  47  00 

64  03  00 

64  45  45 

65  13  48 

66  49  00 

67  10  00 
67  19  00 

66  43  48 

67  16  15 

67  34  00 

68  04  40 

69  17  30 
68  41  30 

70  01  30 

71  36  10 

72  10  20 

h.    m. 
8  20 

h.    m. 
2  08 

ft. 
2.0 

ft. 
0.9 

Lobos  Island:  Center 

Maldonado:  Lighthouse 

Flores  Island :  Lighthouse 

Montevideo:  Cathedral,  SE.  tower 

Colonia:  Lighthouse 

2  00 
6  30 

8  12 
0  00 

3.5 

4.0 

2.3 

2.7 

Martin  Garcia  Island :  Lighthouse 

Buenos  Ayres:  Cupola  of  customhouse 

La  Plata:  National  University  Obsy 

Indio  Point:  Lighthouse 

6  43 

12  15 

2.1 

L4 

Piedras  Point:  Extreme 

Cape  San  Antonio:  Lighthouse 

9  50 

3  35 

5.3 

3.5 

Madanas  Point:  Lighthouse 

Cape  Corrientes:  E.  summit 

Port  Belgrano:  Anchor-Stock  Hill 

Argentina:  Fort 

6  00 

0  00 

15.8 

8.2 

Labyrinth  Head :  Summit 

Union  Bay:  Indian  Head 

San  Bias  Harbor:  SW.  end  of  Hog  Islet... 

San  Bias  Bay:  Summit  of  Rubia  Pt 

Rio  Negro:  Main  Pt 

10  50 

4  38 

14.7 

7.7 

Bermeja  Head :  E.  summit 

Port  San  Antonio:  Point  Villarino 

San  Antonio  Sierra:  Summit 

10  35 

4  23 

23.5 

12.3 

Port  San  Jose:  San  Quiroga  Pt 

Delgado  Point:  SE.  cliff 

Cracker  Bay:  Anchorage 

Port  Madryn:  Anchorage  off  cave  bluff. .. 
Chupat  River:  Entrance 

7  05 

0  52 

13.2 

6.9 

Port  St.  Elena:  St.  Elena  pen 

3  50 

10  03 

16.8 

8.8 

Leones  Island :  SE.  summit 

MeloPort:  W.  pt 

Port  Malaspina:  S.  pt 

Cape  Three  Points:  NE.  pitch 

Port  Desire:  Largest  ruin 

0  00 

6  12 

18.3 

9.6 

Sea  Bear  Bay:  Wells  Pt 

Port  San  Julian:  ShoU  Pt 

10  35 
9  20 
9  00 
8  40 
8  18 
4  20 

4  19 

4  23 
3  08 
2  47 
2  28 
2  06 
10  33 

10  32 

29.5 
39.6 
40.0 
45.6 
38.7 
9.9 

7.8 

15.4 
20.7 
20.9 
23.9 
20.2 
5.2 

6.0 

Port  Santa  Cruz :  Mount  at  entrance 

Coy  Inlet:  Height  S.  side  of  entrance 

Gallegos  River:  Observation  mound 

Cape  Virgins:  SE.  extreme 

Cape  San  Diego:  Extreme 

Staten  Island,  Cape    St.    John:    Light- 
hoiise,  W.  pt 

Port    Cork:    Observation 
mark,  summit 

Cape    St.    Bartholomew: 
Middle  pt 

Good  Success  Bay:  S.  end  of  beach 

Lennox  Cove:  Bluff,  N.  end  of  beach 

Goree  Road :  Guanaco  Pt 

3  50 

10  03 

6.7 

5.2 

Wollaston  Island :  Middle  Cove 

Bameveldt  Islands :  Center 

Cape  Horn:  South  summit,  500  ft 

Hermite  Island:  St.  Martin  Cove 

False  Cape  Horn:  S.  extreme 

4  07 

10  02 

4.8 

3.8 

Ildefonso  Islands:  Highest  summit 

Diego  Ramirez  Island:  Highest  summit. . 

York  Minster  Rock:  Summit,  800  ft 

Cape  Desolation:  S.  summit 

3  50 

10  03 

5.0 

3.9 

Mount  Skyring:  Summit,  3,000  ft 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF   SOUTH  AMEBIC  A. 


[Page  299 


Place. 


Lat.  S. 


Long.  W. 


Lun.  Int. 


Range. 


H.  W. 


L.W. 


Spg. 


Neap. 


Noir  Island:  SE.  extreme 

Landfall  Island:  Summit  of  Cape  Inman. 

Cape  Deseado :    Peaked  summit 

Apostle  Rocks:  W.  rocks 

Cape  Pillar:  N.  cliff 

Dungeness  Point:  Lighthouse 

CapeEspiritu Santo:  NE.  cliff 

Catharine  Point:  NE.  extreme 

Cape  Possession:  Lighthouse 

Cape  Orange:  N.  extreme 

Delgada  Point:  Lighthouse 

Cape  Gregory :  Lighthouse 

Cape  St.  Vincent:  W.  extreme 

Elizabeth  Island:  NE.  bluff 

Sandy  Point:  Lighthouse 

Cape  St.  Valentine:  Summit,  at  extreme. 

Port  Famine :  Observatory 

Cape  San  Isidro :  Extreme 

Cape  Fro  ward :  Summit  of  bluff 

Mount  Pond:  Summit 

Port  Gallant:  Wigwam  Pt 

Charles  Island :  White  rock  near  NW.  end . 

Rupertlsland:  Summit 

Mussel  Bay:  Entrance 

Tilly  Bay:  Sarah  I 

Borja  Bay:  Bluff  on  W.  shore 

Cape  Quod:  Extreme 

Barcelo  Bay.  Entrance 

Swallow  Bay:  Shag  I 

Cape  Notch:  Extreme 

Playa  Parda  Cove:  Summit  of  Shelter  I. . 

Pollard  Cove:  Entrance 

Port  Angosto:  Hay  Pt 

St.  Anne  Island:  Central  summit 

Half  Port  Bay:  Point 

Upright  Port:  Entrance 

Port  Tamar:  Mouat  Islet 

Port  Churruca:  Summit  of  Blanca  Pen. . . 
Valentine  Harbor:  Observation  mount. . . 

Cape  Parker:  W.  summit 

Mercy  Harbor:  Summit  of  Battle  I 

Mayne  Harbor:  Observation  spot 

Port  Grappler:  Observation  spot 

Port  Riofrio:  Vitalia  I 

Eden  Harbor:  Observation  spot 

Halt  Bay:  Observation  islet 

Westminster  Hall  Islet:  E.  summit 

Evangelistas  Island:  Lighthouse 

Cape  Victory:  Extreme 

Cape  Isabel:  W.  extreme 

Cape  Santiago:  Summit 

Molyneux  Sound :  Romalo  I 

Cape  Tres  Puntas:  Summit,  2,000  ft 

Port  Henry:  Observation  spot 

Mount  Corso:  SW.  summit 

Rock  of  Dundee:  Summit 

Santa  Barbara  Port:  N.  extreme  obs.  ;pt. . 
Guaineco  Islands:  Speedwell  Bay,  hill, 

NE.pt 

Port  Otway :  Observation  spot 

Cape  Tres  Montes:  Extreme 

Cape  Raper:  Rock  close  to  cape 

Christmas  Cove:  SE.  extreme 

Hellyer  Rocks:  Middle 


54  30  00 
53  18  30 
52  55  30 
52  46  15 
52  42  50 
52  23  55 
52  39  00 
52  32  00 
52  17  54 
52  28  40 
52  28  00 
52  38  18 
52  46  20 

52  49  18 

53  10  10 
53  33  30 
53  38  12 
53  47  00 
53  53  43 
53  51  45 
53  41  45 
53  43  57 
53  42  00 
53  37  10 
53  34  20 
53  31  45 
53  32  10 
53  30  50 
53  30  05 
53  25  00 
53  18  45 
53  15  30 
53  13  40 
53  06  30 
53  11  40 
53  06  35 

52  55  46 

53  01  00 
52  55  00 
52  42  00 
52  44  58 

51  18  29 
49  25  19 
49  12  40 

49  07  30 

48  54  20 

52  37  18 
52  24  00 
62  16  10 
51  51  50 

50  42  00 
50  17  20 
50  02  00 
50  00  18 

49  48  00 
48  06  15 
48  02  20 

47  39  30 
46  49  31 
46  58  57 
46  49  10 
46  35  00 
46  04  00 


73  00  00 

74  18  15 
74  36  30 
74  46  50 
74  42  20 
68  26  45 
68  34  00 
68  45  20 

68  57  10 

69  24  00 

69  33  00 

70  14  16 
70  25  25 
70  37  61 
70  64  24 
70  34  27 
70  58  31 

70  55  03 

71  17  16 
71  55  30 

71  59  41 

72  04  45 
72  10  42 
72  19  30 
72  27  10 
72  34  16 
72  32  26 
72  38  00 
72  47  30 

72  47  55 

73  00  30 
73  12  05 
73  21  30 
73  15  30 
73  17  45 
73  16  15 
73  44  28 

73  59  33 

74  17  45 
74  13  30 
74  38  14 
74  04  00 
74  17  39 
74  23  27 
74  25  10 
74  20  55 

74  23  10 

75  06  00 

74  55  00 

75  13  20 

75  27  45 

74  51  30 

76  22  00 

75  13  20 
75  34  00 
75  40  30 
75  28  20 

75  10  00 

76  18  20 
75  25  30 
75  37  55 
75  31  30 
75  12  00 


2  20 
1  60 


0.32 
8  19 
8  20 
8  24 
8  35 


8  47 

9  23 


10  24 

11  03 


11  58 

12  21 
0  28 


1  20 


1  64 


1  63 

"in 

'i'69 


0.55 


0  65 


0.30 


0  15 

o'io' 


33 
03 


ft. 

4.8 

4.7 


6  45 
2  07 
2  08 
2  12 
2  25 


4.0 
39.4 
39.0 
30.0 
39.0 


2  40 

3  20 


39.0 
21.0 


4  24 

5  03 


5  58 

6  21 
6  53 


7  40 


8  11 


8  08 
'7"44' 
"7'2i' 


7  07 


7  08 


6  45 


6.30 
"6'25' 


8.0 
6.0 


6.0 
8.0 
7.0 


8.0 


6.5 


6.0 


4.0 


6.0 


4.4 


4.6 


5.3 
'5.'3 


ft. 

3.7 

3.7 


3.1 
20.6 
20.4 
15.7 
20.4 


20.4 
ILO 


4.2 
2.6 


3.1 
4.2 
3.7 


4.2 


2.9 


3.9 


4.5   3.5 


3.1 


4.6 


3.4 


3.5 


4.1 
"4.'i 


Page  300]                                    APPENDIX   IV. 

MABITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  SOUTH  ATVTRItlC A— Continued. 

1 

Place. 

Lat.  S. 

Long.  W. 

Lun.  Int. 

Range.         1 

H.W, 

L.w. 

Spg. 

Neap. 

e 

a 

A 
Q 

Cape  Taytao:  W.  extreme 

0            t           « 

45  53  20 
44  55  50 
44  09  00 
43  49  15 
43  43  05 
43  19  30 
43  16  25 
43  11  30 

42  46  45 
42  29  15 
42  22  45 
42  11  15 
41  28  36 
41  46  20 
41  49  58 
40  46  19 
40  43  18 
40  35  52 
40  21  04 
40  11  47 
39  51  37 
39  23  00 
38  21  22 
37  35  20 
37  22  30 
37  05  20 
36  59  07 
36  42  00 
36  36  45 
34  46  02 
33  34  13 
33  38  30 
33  26  42 
33  01  08 
33  01  52 
32  46  00 
32  07  55 
31  51  45 
31  39  30 
31  17  05 
30  50  45 
30  14  00 
30  15  14 
29  56  15 
29  56  24 
29  55  10 
29  34  40 
29  15  45 
29  00  50 
28  27  20 
28  05  45 
28  04  30 
27  54  10 
27  39  20 
27  20  00 
27  03  15 
27  03  15 
26  51  05 
26  34  30 
26  20  00 
26  16  12 
26  09  15 

75  06  00 
75  08  45 
74  07  45 
74  00  30 
74  42  15 

73  42  25 

74  24  15 
72  48  30 

72  31  25 

73  45  05 
73  38  10 
72  35  55 

72  56  15 

73  07  65 
73  51  12 
73  51  00 
73  49  50 
73  45  00 
73  45  20 
73  41  50 
73  26  25 
73  14  00 
73  58  06 
73  39  55 
73  40  00 
73  11  13 
73  32  30 
73  07  27 
73  02  49 
72  06  12 
71  38  00 

69  56  30 

70  41  32 

71  38  52 
71  38  42 
71  32  56 
71  33  22 
71  34  51 
71  35  20 
71  39  21 
71  39  00 
71  39  00 
71  31  09 
71  21  00 
71  21  53 
71  22  21 
71  33  20 
71  34  38 
71  36  40 
71  15  45 
71  12  48 
71  11  32 
71  09  38 
71  03  26 
70  58  45 
70  52  54 
70  53  45 
70  51  55 
70  44  25 
70  37  25 
80  11  43 
70  43  57 

A.    m. 
0  00 

h.    m. 
6  13 

ft. 
4.4 

ft. 
3.4 

Socorro  Island :  S.  extreme 

Mayne  Mountain:  Summit,  2,080  ft 

Port  Low:  Huacanec  I.,  S.  end 

0  15 
12  10 

6  10 
6  00 

Guafo  Island :  S.  extreme 

6.1 

3.1 

Port  San  Pedro:  Cove  on  S.  shore 

Cape  Quilan :  SW.  extreme 

Corcovado  Volcano:  Summit,  7,527  ft 

Minchinmadiva   Volcano:     S.    summit, 
8,000  feet 

Castro:  Extreme  of  point 

0  01 

6  21 

18.0 

9.1 

Dalcahue:  Chapel 

Comau  Inlet:  Morro  Comau 

Port  Montt:  Lt.  on  end  of  pier 

0  31 

1  10 
0  04 

""7'35' 
6  20 

2L0 

14.8 

5.9 

14.5 
7.5 
3.0 

Port  Calbuco :  La  Picuta 

Ancud :  Ahui  Pt.  light 

Condor  Cove:  Landing 

Ranu  Cove :  Anchorage 

Muilcalpue  Cove :  Landing  place 

Milagro  Cove :  Landing  place 

Laruehuapi  Cove:  Landing  place 

Valdivia :  Niebla  Fort  light 

0  00 
10  25 
10  18 
10  20 
10  15 
10  10 
10  05 
10  10 
10  04 
10  05 
9  57 
9  44 

6  13 
4  13 

4  05 

5  07 
4  02 
3  55 
3  50 
3  55 
3  51 
3  53 
3  48 
3  34 

7.2 
5.6 
4.9 
3.3 
4.9 
5.3 
4.9 
6.0 
5.3 
5.0 
4.1 
4.0 

3.7 
2.8 
2.5 
L7 
2.5 
2.7 
2.5 
3.0 
2.7 
2.5 
2.1 
2.0 

Queule  Bay:  Choros  Pt 

Mocha  Island :  Lighthouse 

Lebu  River:  Tucapel  Head 

Yanez  Port:  Anchorage 

Lota:  Lighthouse 

Santa  Maria  Island :  Lighthouse 

Talcahuano:  Fort  Galvez 

Light  on  Quinquina  I 

Llico:  Village 

Port  San  Antonio :  Village 

Aconcagua  Mountain :  Summit 

Santiago :  Observatory 

Valparaiso :  Playa  Ancha  Pt.  light 

Site  of  old  Fort  San  Antonio. . 
Quintero  Point:  Summit 

9  37 

3  26 

3.9 

2.0 

9  35 
9  30 
9  26 

3  25 
3  20 
3  16 

4.1 
3.9 
4.2 

2.1 
2.0 
2.1 

Pichidangui:  SE.  pt.  of  island 

Tablas  Point:  SW.  extreme 

Chuapa  River:  S.  entrance  pt 

Maitencillo  Cove:  N.  head 

Talinay  Mount:  Summit 

Lengua  de  Vaca:  Lighthouse  . 

Port  Tongoi:  Obs.  spot.  W.  of  village 

Cnqiiinnbf^"  Tnrtnpn.  Pt    light 

9  15 
8  58 

3  05 

2  48 

4.1 
4.9 

2.1 

2.5 

Smeltmg  works,  N.  of  town. . 
N.  islet. 

Pajaros  Islets :  Lighthouse. . . . 

Choros  Islands:  SW.  pt.  of  Largest  island. . 
Chanaral  Island :  Lig  ithouse 

Huasco:  Light  on  mole 

8  23 
8  50 

2  10 

2  38 

4.9 
4.9 

2.5 
2.5 

Herradm^  de  Carrizal:  Landing  place. . . 
Port  Carrizal :  Middle  Point 

Matamoras  Cove:  Outer  pt.  S.  side 

Salado  Bay:  Summit  of  Caches  Pt 

Copiapo:  Landing  place 

8  21 
8  50 

2  08 
2  37 

5.0 
4.9 

2.5 
2.5 

Ca  dera:  Lighthouse 

Light  on  mole  head 

Cabeza  de  Vaca  Point:  Extreme 

Flamenco:  SE.  comer  of  bay 

9  00 
9  05 

2  47 
2  52 

5.0 

4.9 

2.5 
2.5 

Chanaral  Bay:  Observation  pt 

St.  Felix  I. :  Peterborough  Cathedral  Rock 
Pan  de  Azucar  Island  *  Summit 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OP  SOUTH  A -MTHRIC A— Continued. 

[Page 

301 

1 

Place. 

Lat.  S. 

Long.  W. 

Lun. 

Int. 

Range.         1 

H.W. 

L.W. 

Spg. 

Neap. 

1 

2 

Lavata:  Cove  near  SW.  pt 

25  39  30 
25  31  00 
25  25  20 
25  07  00 
25  05  25 
24  34  30 
24  15  00 
23  53  00 
23  38  50 
23  33  05 
23  28  30 
23  26  42 
23  06  30 
22  34  00 
22  06  00 
21  55  50 
21  28  00 
21  05  30 
20  57  40 
20  51  05 
20  12  30 
19  05  01 
19  36  30 
19  19  00 
18  45  40 
18  28  43 
17  58  35 

17  42  00 

17  37  00 

17  01  00 

17  00  00 

16  42  20 

16  23  50 

16  13  30 

15  48  00 

15  33  15 

15  20  56 

14  57  00 

14  41  00 

14  09  50 

13  50  00 

13  48  00 

13  45  00 

13  38  20 

13  01  00 

12  48  00 

12  31  00 

12  11  30 

12  04  03 

12  08  15 

11  47  10 

11  27  10 

10  49  45 

10  06  15 

9  38  35 

9  15  30 

9  04  40 

8  46  30 

8  34  50 

8  05  40 

7  42  40 

7  23  40 

70  44  03 
70  41  18 
70  34  10 
70  30  16 
70  29  50 
70  36  29 
70  33  00 
70  32  28 
70  25  18 
70  26  55 
70  34  56 
70  37  11 
70  31  39 
70  17  42 
70  13  40 
70  11  17 
70  02  45 
70  12  12 
70  10  26 
70  14  40 
70  11  20 
70  10  30 
70  15  21 
70  17  50 
70  21  50 
70  20  00 

70  52  31 

71  22  31 

71  20  01 

72  02  53 
72  07  16 

72  27  16 

73  16  41 

73  41  31 

74  27  16 

74  51  01 

75  09  36 
75  30  46 

75  49  56 

76  16  36 
76  27  31 
76  18  31 
76  10  00 
76  24  15 
76  31  06 
76  38  11 

76  48  56 

77  02  31 
77  15  44 
77  14  45 
77  16  11 
77  50  04 

77  43  42 

78  10  02 
78  21  33 
78  30  03 
78  35  57 
78  45  16 

78  56  53 

79  06  46 
79  26  00 
79  33  15 

ft.    m. 
9  10 

ft.    m. 
2  57 

ft. 
5.0 

ft. 
2.5 

San  Pedro  Point:  Summit 

Port  Taltal:  Lighthouse 

9  20 
9  35 
9  30 

3  07 
3  22 
3  17 

4.9 
5.0 
4.9 

2.5 
2.5 
2.5 

Grande  Point:  Outer  summit 

Paposo  Road:  Huanillo  Pt 

Reyes  Head :  Extreme  pitch ... 

Cobre  Bay:  Pt  W,  of  village  . 

Jara  Head :  Summit 

Antofagasta:  Lighthouse 

9  05 

2  52 

4.7 

2.4 

Chimba  Bay:  E.  pt.  of  laige  island 

Moreno  Mountain:  Summit... 

Constitution  Cove:  Shingle  pt.  of  island.. 
Mexillones  Mount:  Summit 

9  35 
9  44 
8  55 

3  22 
3  31 
2  42 

3.9 
4.0 
4.8 

2.0 
2.0 
2.4 

Port  Cobija:  Landing  place 

Tocopilla :  Extremity  Point 

San  Francisco  Head :  W.  pitch 

Loa  River:  Mouth 

Lobos  Point:  Outward  pitch 

9  00 

2  47 

4.9 

2.5 

Pabellon  de  Pica:  Summit 

Pa tache  Point:  Extreme..   .. 

Iquique:  Lighthouse 

8  35 

2  22 

5.0 

2.5 

Mexillon  Bay :  Landing  place 

Pisagua:  Pichalo  Pt.  extreme 

8  32 

2  20 

5.0 

2.5 

Gorda  Point:  W  low  extreme 

Lobos  Point:  Summit 

Arica:  Iron  chiirch 

7  49 

1  37 

5.6 

2.8 

Schama  Mount:  Highest  summit 

Coles  Point:  Extreme. 

Ilo:  Mouth  of  rivulet 

7  55 

1  43 

5.3 

2.7 

Port  Mollendo*  Lighthouse. 

Islay :  Customhouse 

7  39 

1  27 

6.2 

3.1 

QuiJica:  W.  head  of  cove 

Pescadores  Point*  SW  extreme 

Atico:  E.  cove 

Chala  Point:  Extreme 



Lomas:  Flagstaff  on  pt 



San  Juan  Port:  Needle  Hammock 

Nasca  Point:  Summit.  ... 

6  47 

0  35 

3.9 

2.0 

Mesa  de  Dona  Maria:  Central  summit 

Carre ta  Mount:  Summit 



San  Gullan  Island:  N  summit 

Paraca  Bay:  N.  extreme  of  W.  pt 

Pisco:  Lighthouse 

6  16 

0  04 

3.8 

L9 

Chincha  Islands:  Boat  slip,  E.  side  N.  id. . 
Frayles  Point:  Extreme 

Asia  Rock:  Summit 

Chilca  Point:  SW.  pitch 

Morro  Solar*  Summit     .   . 

San  Lorenzo  Island:  Lighthouse.  . 

Callao:  Palominos  Rock  Light 

5  47 

i2  '^ 

3.5 

L8 

Pescadores  Islands:  Summit  of  largest 

Pelado  Tslanrl :  Siinimit ,    , 

Sup6  *  W^  end  of  village          . 

Huarmey :  W.  end  of  sandy  beach 

floliTia  RfifloTifla.*  SiiTTimit, 

5  08 

11  21 

2.1 

1.1 

Samanco  Bay  Cross  Pt 

Chimbote:  Village,  N.  part 

4  50 

11  03 

2.0 

1.0 

Chao  Islet:  Center 

Guanape  Islands:  Summit  of  highest 

TTnanohflnn  Point*  SW   fffrPiTifi 

Malabrigo  Bay:  Rocks 

4  19 

10  32 

2.1 

LI 

Pacasmayo  ■  Lighthouse 

Page  302]                                     APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  SOUTH  AMERICA— Continued. 

1 

Place. 

Lat.  S. 

Long.  W. 

Lun.  Int. 

Kange. 

H.  W. 

L.  w. 

Spg. 

Neap, 

9 

0 

•e 

9 
w 

i 
a 

e 

0 

Eten  Head:  Lighthouse 

6  55  50 
6  46  00 
6  46  45 
6  26  45 
5  55  30 
5  05  02 
4  40  50 
4  16  40 
3  30  42 

3  10  40 
2  12  24 
2  44  30 
2  12  00 
1  16  55 
1  03  30 
0  56  50 
0  35  25 
0  21  30 

Lat  N. 
0  50  10 

0  40  00 

1  03  30 
1  36  00 

1  49  36 

2  37  10 

2  58  10 

3  49  27 

4  17  06 

5  28  46 

6  41  19 
6  49  45 

79  51  30 

79  57  55 

80  42  54 

80  51  56 

81  09  19 
81  07  17 
81  17  01 
81  12  01 
80  28  12 

80  25  29 
79  52  19 

79  53  45 

80  59  00 

81  03  55 
80  55  55 
80  42  50 
80  25  24 
80  30  37 

80  05  40 
80  07  55 

79  42  00 
79  03  30 

78  45  29 
78  24  24 
78  11  16 
77  11  45 
77  29  44 
77  33  28 
77  30  31 
77  40  55 

ft.      TO. 

4  04 

ft.    m. 
10  17 

ft. 
2.5 

ft. 
1.3 

Lambayeque:  Beach  opposite 

Lobos  de  Af uera  Island :  Cove  on  E.  side . . 
Lobos  de  Tierra  Island:  Central  summit. . 
Aguja  Point:  W.  cliff  summit 

1 

Paita  Cathedral             

Parinas  Point :  Extreme 

Cape  Blanco:  Under  middle  of  high  cliff. . 
Tumbez :  Malpelo  Pt 

Guayaquil  River:  Light  on  Santa  Clara  I. 

Guayaquil,  Concejo:  S.  pt.  of  city 

Puna:  llandinga  Pt.  light 

4  00 
7  00 

10  13 
1  00 

10.0 

n.o 

5.1 
5.6 

Point  Santa  Elena:  Veintemilla  light 

Plata  Isle:  E.  pt 

3  00 

•  9  13 

7.9 

4.0 

Cape  San  Lorenzo:  Marlinspike  Rock 

Manta  Bay:  Lighthouse 

3  10 

9  23 

7.5 

3.8 

Caraques  Bay:  Punta  Playa 

Cape  Pasado :  Extreme 

3  15 

9  28 

9.9 

5.0 

Point  Galera:  N.  extreme 

Cape  San  Francisco:  SW.  extreme 

Esmeralda  River:  Lighthouse 

Mangles  Point:  S.  pt.  of  creek  entrance. . . 
Tumaco:  S.  pt.  of  El  Morro  I 

3  35 

9  48 

13.2 

7.1 

Guascama  Point:  Extreme 

Gorgona  Island:  Watering  Bay 

Buenaventura:  Basin  Pt 

6  00 

12  13 

13.2 

7.1 

Chirambiri  Point:  N.  extreme 

Cape  Corrientes:  SW.  extreme 

3  40 
3  30 

9  53 
9  43 

13.1 
13.3 

7.0 
7.2 

Cupica  Bay:  Entrance  to  Cupica  River. . 
Cape  Marzo:  SE.  extreme 

ISLANDS  IN  THE  ATLANTIC  OCEAN. 

IB 

•0 

a 

s 

0 

Fseroe  Islands,  Strom  Islet:  Thorshaven 

Fort  flagstaff 

Halderoig    Islet:    Halde- 
roig  Chiu*ch 

62  02  26 

62  18  20 
61  23  00 
57  35  52 

39  40  07 
39  27  00 
38  32  09 
38  31  45 
38  34  30 
38  25  00 

38  40  30 

39  05  24 

38  38  20 

37  44  16 
37  49  20 

36  56  00 

37  16  44 

6  43  08 

7  00  36 
6  45  30 

13  42  21 

31  08  00 
31  08  49 
28  34  00 
28  37  39 
28  44  00 
28  28  12 
28  13  00 
28  00  45 

27  13  45 

25  40  40 
25  08  21 
25  10  00 
24  47  06 

Numiken  Rock 

Rockall  Islet:  Summit,  70  feet 

Corvo  Island:  S.  pt 

Flores  Island:  Santa  Cruz  Fort 

Fayal  Channel:  N.  Magdalen  Rock 

Fayal  Island,  Horta:  Castle  of  Santa  Cruz. 
Caldera:  Summit  3,351  ft. . . 
Pico  Island t  Summit..               .  . 

11  30 

5  18 

3.9 

1.8 

St.  George  Island :  Lighthouse 

Graciosa  Island:  Santo  Fort  light 

Terceira  Island:  Monte  del  Brazil,  near 
Angra 

0  20 

6  32 

4.4 

2.0 

St.  Michael  Island:  Customhouse,  Ponta 
Delgada 

Pt.  Amel  light 

Santa  Maria  Island:  Villa  do  Porto  light.. 
Formigae  Islands:  Highest  rock 

0  15 

6  27 

5.7 

2.6 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  IN  THE  ATIiANTIC  OC5E AN— Continued. 


[Page  803 


Si 


Place. 


Porto  Santo  Island :  Lighthouse 

Desertas:  Chao  I.,  Sail  Rock 

Madeira  Island :  Funchal  light 

Fora  I.  lighthouse 

Pico     Ruivo,    summit, 

6,056  ft 

Pargo  jW.)Pt 

Salvage  Islands:  Lightnouse,  Gran  Sal- 
vage I 

Al^ranza  Island:  Delgada  Pt.  light 

Lanzarote  Island:  Port  Naos  light 

Pechinguera  Pt.  light. 

Lobos  Island :  Martino  Pt.  light 

Fuerta  Ventura  Island :  Jandia  Pt.  light. 

Gran  Canaria :  Isleta  Pt.  light 

Palmas  light 

Teneriffe  Island:  Anga  Pt.  light ; 

Santa  Cruz,   Br.   con- 
sulate  

Summit  of  peak,  12,180 

ft 

Gomera  Island :  Port  Gomera 

Ferro  Island:  Port  HieiTo 

Palma  Island :  Light,  NE.pt 

San  Antonio  Island :  Bull  Pt.  light 

Summit,  7,400  ft.  .  , 
St.  Vincent  Island :  Porto  Grande  light. . 

St.  Lucia  Island:  N.  pt 

Raza  Island:  E.  pt 

St.  Nicholas  Island :  Lighthouse 

Sal  Island:  N.  pt.  light 

S.pt 

Boavista  Island :  NW.pt 

NE.pt 

Lighthouse 

Mayo  Island:  Engli&h  Road 

St.  Jago  Island:  Reta  Pt.  light 

Porto  Praya,  S.  light. . . 

Fogo  Island:  N.  S.  da  Luz,  village 

Brava  Island :  Lighthouse 

Ireland  Island:  Dock  yard  clock  tower.. 

Bastion  C 

Hamilton  Island:  Gibbs  Hill  light 

St.  Davids  Island :  Lighthouse 

St,  Paul  Rocks:  Summit,  64  ft 

Rocas  Reef:  NW.  sandy  islet 

Fernando  Noronha:  The  Pyramid 

Ascension  Island:  Fort  Thornton 

St.  Helena  Island:  Obs.  Ladder  Hill 

Martin  Vaz  Rocks:  Largest  islet 

Trinidad  Island:  SE.pt 

Inaccessible  Island :  Cfenter 

Tristan  da  Cunha  Islands:  NW.  pt 

Gough  Island:  Pengxiin  Islet 


Lat.  N. 


33  03  15 
32  35  45 
32  37  43 
32  43  14 

32  45  00 
32  48  07 

30  08  00 

29  23  50 
28  57  24 
28  50  56 
28  45  25 
28  03  00 
28  10  42 
28  07  06 
28  35  25 

28  28  12 

28  16  35 
28  08  00 

27  46  30 

28  50  06 

17  06  50 
17  04  00 
16  53  14 
16  49  00 
16  38  00 
16  34  00 
16  50  50 
16  34  00 
16  13  20 
16  11  00 
16  09  10 
15  07  30 
15  18  06 
14  53  40 
14  53  00 

14  50  30 

32  19  22 
32  19  37 
32  15  05 
32  21  40 

0  55  30 

Lat.  S. 
3  51  30 
3  50  30 
7  55  20 

15  55  00 
20  27  42 
20  30  32 
37  19  00 
37  02  48 
40  19  11 


Long.  W, 


16  16  20 
16  33  30 
16  54  53 
16  39  31 

16  57  30 

17  16  05 

15  54  00 

13  29  31 
13  33  07 
13  52  05 

13  49  13 

14  31  35 

15  25  11 

15  2:4  56 

16  08  11 

16  15  09 

16  38  02 

17  05  55 
17  54  22 
17  47  01 

24  59  15 

25  17  00 
24  59  30 
24  47  08 
24  38  08 
24  10  00 
22  54  55 
22  55  42 
22  55  44 
22  42  00 

22  57  20 

23  12  42 
23  47  06 

23  31  45 

24  30  38 
24  40  00 

64  49  35 
64  49  15 
64  49  40 
64  38  40 

29  22  28 


33  49  29 

32  25  29 

14  24  35 

5  43  03 

28  46  57 

29  14  56 
12  23  00 
11  18  39 

9  56  11 


Lun.  Int. 


Range. 


H.  W.    L.  W 


h.    m. 
0  40 


0  35 


0  50 


0  40 


1  15 


0  20 


5  50 


7  30 


5  50 


7  04 


12  50 


h.    m. 
6  52 


6  47 


7  00 


6  50 


7  27 


6  30 


12  00 


1  20 


12  00 


0  52 


Spg.   Neap. 


6.6 


6.6 


8.5 


9.3 


7.8 


3.3 


4.4 


4.8 


4.0 


11  18 

11  13 

11  30 

9  10 

9  48 

9  53 


10.0 
6.0 
2.0 
2.8 
3.5 
4.0 


5  40 


5.2 


ft. 
3.0 


3.0 


3.9 


4.3 


3.6 


4.0 


L5 


2.0 


2.2 


2.6 


4.6 
2.7 
0.9 
L3 
L6 
L8 


2.4 


Page  304]                                     APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  TN"  TTTR  ATLANTIC  OCEAN— Continued. 

o 

Place.- 

Lat.  S. 

Long.  W. 

Lun.  Int. 

Range.         1 

H.  W. 

L.  w. 

Spg. 

Neap. 

a- 

Port  Egmont;  Observation  spot 

51  21  26 
51  04  11 
51  32  20 
51  41  10 
51  40  40 

54  04  45 

53  48  00 

59  34  00 

55  57  00 

60  54  00 

60  46  00 
62  55  36 

54  16  00 

0            f            1/ 

60  04  52 
68  30  56 
58  08  04 
57  51  30 
57  41  48 

38  15  00 

43  25  00 
27  45  00 
26  33  00 

44  25  00 

45  53  00 
60  35  00 

Long.  E. 
6  14  00 

h.    m. 
7  20 

h.    m. 
1  08 

ft. 
10.7 

ft. 
5.6 

Maje  Hsjrbor:  Observation  spot  .  .      ... 

Port  Louis:  Flagstaff,  govt,  house 

Port  Stanley:  Governor's  bouse 

5  31 

11  27 

4.3 

2.2 

Cape  Pembroke:  Lighthouse 

South  Georgia  Island:  N.  cape.  • --• 

Shag  Rocks :  Center 

Sandwich  Islands:  S.  Thul6 

Traverse  I.  volcano. . . 

New  S.  Orkney  Is.:  E.  pt.  Laurie  I 

E.  summit  Corona- 
tion I.,  5,397  ft.... 
New  S.  Shetland  Islands,  Deception  Is- 
land ■  Port  Foster       

Bouvets  Island  (Circumcision):  Center. . . 

ATLANTIC  COAST  OF  EUKOPE. 

0 

Greenwich"  Observatory 

Lat.  N. 
51  28  38 

51  45  34 

52  12  52 
51  22  28 
51  08  23 
50  54  47 
50  44  15 

50  46  35 
50  48  03 
50  53  45 
50  42  07 
50  39  42 
50  34  30 
50  31  10 
50  13  18 
50  20  02 
50  10  49 
50  08  30 

49  57  40 

50  02  44 
50  04  10 

49  53  33 

50  33  00 

51  04  00 
51  12  05 
51  27  24 
51  27  48 
51  36  50 
51  37  52 
51  41  00 

51  43  15 

52  24  20 

52  45  00 

53  18  30 
53  18  54 

Long.  W. 

0  00  00 

1  15  06 

Long.  E. 

0  05  41 

1  26  48 
1  22  22 
0  58  18 

0  13  00 

Long.  W. 

1  05  15 
1  05  58 
1  24  00 
1  33  04 
1  35  25 

1  17  47 

2  27  30 

3  38  28 

4  09  27 

4  15  53 

5  01  00 
5  12  06 
5  39  18 

5  44  45 

6  20  38 
5  01  55 
4  12  30 
4  40  35 

2  35  55 

3  09  42 

3  56  00 

4  40  59 

5  10  30 
5  40  15 
4  05  40 
4  47  50 
4  42  00 
4  37  01 

1  10 

7  46 

18.8 

12.6 

North  Foreland :  Lighthouse 

11  24 
11  09 

10  35 

11  10 

5  53 

5  43 
4  23 
4  58 

16.8 
19.8 
215 
19.8 

8.4 
10.0 
11.0 
10.1 

South  Foreland:  Lighthouse 

Dungeness:  Lighthouse 

Beachy  Head:  Lighthouse 

Portsmouth:  Observatory 

11  31 

0  35 

11  05 

4  19 
6  48 
4  53 

13.2 
12.8 
12.2 

6.7 
6.5 
6.2 

Southampton*  Royal  Pier  light 

Hurst  Castle:  W.  light 

^Aarllpn  T?nplrs'   Oln  lifrlithoilfift 

Portland  •  Notch  Bill  fight 

6  29 
5  25 
5  20 

0  09 
11  38 
11  33 

6.7 
14.9 
15.3 

LO 
6.8 
7.0 

Start  Point:  Lighthouse 

Plymouth:  Breakwater  fight 

Falmouth-  St  Anthonv  Pt   fiffht 

Lizard  Point:  W.  fighthouse 

4  45 

10  58 

14.2 

6.5 

Porthcumow:  SE.  cor.  telegraph  co.'s  sta. 

Lands  End:  Longships  fighthouse 

Scilly  Islands:  St.  Agnes  fighthouse 

4  15 

10  28 

15.9 

7.3 

Bideford:  High  lighthouse 

5  45 

5  00 
7  00 

6  45 
5  45 
5  40 
5  41 
5  40 

7  25 
7  24 

11  58 

11  13 

0  48 

0  33 
11  58 
11  53 
11  54 
11  53 

1  13 
1  12 

22.7 
26.9 
3L3 
36.2 
27.1 
25.3 
24.0 
20.9 
14.2 
14.9 

11.4 
13.5 
15.7 
18.1 
13.6 
12.7 
12.0 
10.5 
7.1 
7.5 

Lundy  Island:  Lighthouse,  N.  pt 

Bristol:  Cathedral 

Cardiff:  Lighthouse,  W.  pier 

Swansea:  Lighthouse,  W.  pier 

Caldy  Island :  Lighthouse 

St.  Anns :  Upper  fighthouse 

Smalls  Rocks:  Lighthouse 

ABerystwith :  Lighthouse 

Bardsey  Island :  Lighthouse 

South  Stack:  Lighthouse  on  rocks 

Holyhead :  Lighthouse  on  old  pier 

10  00 

3  48 

15.8 

7.9 

APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  305 


Place. 


Skerries  Rocks:  Lighthouse,  highest  I  — 

Bidstone :  Lighthouse  on  hill 

Liverpool:  Rock  light 

Bidston  Observatory 

Morecambe  Bay:  Fleetwood  high  light. . . 

Calf  of  Man:  Upper  lighthouse 

Isle  of  Man :  Ayre  Pt.  lighthouse , 

St.  Bees:  Lighthouse 

White  Haven:  W.  pierhead  light 

Mull  of  Galloway:  Lighthouse 

Ayr,  Firth  of  Clyde:  Lighthotise,  N.side 
harbor 


Troon:  Lighthouse,  inner  pier., 
Ardrossan:  S.  breakwater  light. 


Pladda  Island :  Lighthouse 

Glasgow:  Observatory 1 

Can  tyre:  Lighthouse 

Rhynns  of  Islay :  Lighthouse 

Oban:  Lighthouse  on  N.  pier 

Skerryvore  Rocks:  Lighthouse 

Barra  Head:  Lighthouse 

Glas  Island:  Lighthouse,  Scalpay  I 

Stomoway :  Amish  Pt.  light 

Butt  of  Lewis:  Lighthouse 

Cape  Wrath:  Lighthouse 

Dunnet  Head:  Lighthouse 

Kirkwall  (Orkneys):  New  pierhead  light. 

Startpoint  (Orkneys):  Lighthouse 

North  Ronaldsay:  Lighthouse 

Fair  Isle  Skroo:  Lighthouse 

Sumburgh  Head:  Lighthouse 

Blackness     (Shetland     Is.):  Lighthouse 

pier 

Lerwick  (Shetland  Is.) :  Fort 

Hillswickne&s  (Shetland  Is.):  S.  extreme. 
Balta  I.  (Shetland  Is.):  Cairn  on  E.  side. . 

Pentland  Skerries:  Upper  lighthouse 

Tarbertness:  Lighthouse 

Buchanness:  Lighthouse 

Aberdeen  (Girdleness):  Lighthouse 

Buddonness:  Upper  lighthouse 

Bell  Rock:  Lighthouse 

May  Island :  Lighthouse 

Inch  Keith  Rock:  Lighthouse 

Edinburgh:  City  observatory 

Berwick:  Lighthouse 

Fam  Island:  NW.  lighthouse 

Coquet  Island:  Lighthouse 

Tynemouth:  Souter  Point  lighthouse 

North  Shields:  Lighthouse 

Sunderland:  N.  pier  light 

Hartlepool:  Lighthouse 

Flamborough:  New  lighthouse 

Humber     River:  Killingholme     middle 

light 


Lat.  N. 


Spurn  Head:  Upper  lighthouse . 

Lowestoft:  Lighthouse 

Orfordness:  N.  lighthouse 

Harwich:  Landguard  Pt.  light. 


53  25  15 
53  24  02 
53  26  38 
53  24  05 

53  55  03 

54  03  14 
54  24  56 
54  30  50 
54  33  00 

54  38  10 

55  28  10 
55  32  55 
55  38  27 
55  26  00 
55  52  43 
55  18  39 

55  40  20 

56  24  50 
56  19  22 

56  47  08 

57  51  25 

58  11  28 
58  30  40 
58  37  30 
58  40  16 

58  59  15 

59  16  45 
59  23  24 
59  33  00 

59  51  15 

60  08  02 
60  09  22 
60  27  20 
60  44  25 
58  41  22 
57  51  54 
57  28  15 
57  08  33 
56  28  07 
56  26  03 
56  11  00 
56  02  09 
55  57  23 
55  46  00 
55  37  00 
55  20  06 

54  58  10 

55  00  30 
54  55  07 
54  41  51 
54  07  00 

53  39  00 


53  34  45 
52  29  14 
52  05  00 
51  56  05 


Long.  W. 


36  20 
10  42 
02  27 
04  20 
00  20 
49  37 
22  01 

37  50 
36  00 
51  20 


4  38  10 
4  41  00 

4  49  28 

5  07  09 
4  17  38 

48  00 
30  46 
28  20 
06  32 
39  09 

6  38  28 
6  22  10 
6  16  01 
4  59  41 

22  25 
57  33 
22  25 
22  45 
36  30 
16  20 


1  16  02 
1  08  41 

1  29  50 
0  47  30 

2  55  25 
46  30 
46  22 
04  06 
44  53 
23  06 
33  22 
08  05 
10  47 
59  00 
39  00 
32  00 
21  30 
26  00 
21  30 
10  19 


0  05  00 
0  12  00 

Long.  £. 

0  07  10 

1  45  24 
1  34  30 
1  19  10 


Lun.  Int. 


H.W. 


h.    TO. 


11  08 
11  00 


10  55 


11  00 
11  05 

11  40 


11  35 


0  55 
10  20 


5  10 
"5"35 

'e'ss 


9  57 


10  50 
9  35 


10  20 


9  30 
10  00 


0  24 

0  50 

1  56 


1  58 

2  08 


Range. 


L.W. 


3  11 
3  12 

3  21 

4  20 


5  16 

9  47 

11  05 

11  56 


ft.  m. 


5  27 
4  48 


4  43 


4  48 

4  53 

5  28 


5  23 


7  08 
4  08 


11  22 
'ii"47 
"'6'22 


3  44 


4  37 
3  22 


4  17 


3  17 
3  47 


6  36 

7  02 

8  08 


8  11 
8  28 


9  31 

9  32 

9  43 

10  36 


11  29 

3  35 

4  53 

5  44 


Spg. 


27.6 
27.4 


19.7 


25.9 
14.8 

8.7 


8.8 


11.2 
4.0 


12.8 

ii.'i' 

13.' 4' 


9.8 


5.0 
5.2 


6.0 


6.4 
9.8 


11.2 
11.7 
15.5 


16.5 
15.0 


14.8 
14.5 
14.2 
15.8 


18.5 
6.2 
7.8 

n.2 


Neap. 


ft. 


14.0 
13.9 


10.0 


13.1 
8.9 

5.2 


5.3 


6.7 
2.4 


7.7 
'4.8 
'5.' 7 


4.2 


2.2 

2.2 


2.6 


2.7 
4.2 


6.1 
6.4 
8.5 


8.9 

7.5 


7.4 
7.3 
7.0 


10.2 
3.6 
4.5 
6.6 


21594°— 14- 


-20 


Page  306] 


APPENDIX  IV. 

MARITIME  POSITIONS   AND  TIDAL  DATA. 
ATLANTIC  COAST  OP  ETJBOPE— Continued. 


Place. 


Cape  Clear:  Old  lighthouse 

Fastnet  Rock :  Lighthouse 

Mount  Gabriel:  Ordnance  survey  station. 

Castlehaven :  Lighthouse 

Mizen  Hill:  Ordnance  survey  station. . . . 

Bantry  Bay :  Roancarrig  light 

Bull  Rock:  Lighthouse 

Skelligs  Rocks:  Lighthouse 

Valentia:  Lighthouse 

Port  Magee 

Dingle  Bay:  Light  at  entrance 

Blasket  Islands:  Westernmost  rock 

Smerwick:  Signal  tower 

Tralee  Bay:  Lighthouse 

Beeves  Rocks:  Lighthouse 

Limerick:  Cathedral 

Shannon  River:  Loop  Head  light 

Eeragh  Island:  Lighthouse 

Arran  Island:  Lighthouse 

Galway:  Mutton  I.  light 

Golam'Head:  Tower 

Slyne  Head:  N.  lighthouse 

Clifden  Bay:  Gortrumnagh  Hill 

TuUy  Mountain :  Ordnance  survey  station . 

Inishboffin :  Lyon  Head  light 

Inishturk  Island:  Tower 

Clew  Bay:  Inishgort  light 

Newport:  Church 

Clare  Island:  Lighthouse 

Blacksod  Point:  Lighthouse 

Eagle  Island :  W.  lighthouse 

Broadhaven:  Guba  Cashel  light 

Dounpatrick    Head:    Ordnance    survey 
station 

Anghris  Head:  Ordnance  survey  station.. 

Knocknarea:  Tumulus 

Sligo  Bay:  Black  Rock  light 

Knocklane:  Ordnance  survey  station.  . . . 

Killybegs  (Donegal  Bay):  St.  Johns  Pt. 
light 

Rathlin  O'Bime  Islet:  Lighthouse 

Aran  Island :  Rinrawros  light 

Bloody  Foreland:  Ordnance  survey  sta- 
tion  

Tory  Island:  Lighthouse 

Horn  Head:  Ordnance  survey  station 

Melmore  Head:  Tower 

Fanad  Point:  Lighthouse 

Glashedy  Island:  Ordnance  survey  station 

Malin  Head :  Tower 

InishtrahuU :  Lighthouse 

Inishowen  Head :  E.  lighthouse 

Moville:  New  Pier 

Londonderry:  Cathedral 

Scalp  Mountain :  Ordnance  survey  station . 

Benbane  Head:  Summit 

Rathlin  Island :  Altacarry  lighthouse 

Maiden  Rocks:  W.  lighthouse 

Lough  Lame:  Farres  Pt.  lighthouse 

Belfast  Bay:  Light,  east  side 

Mew  Islands:  Lighthouse 

Donaghadee:  Lighthouse 

South  Rock:  Light  vessel 


Lat.  N. 


51  26  02 
51  23  18 
51  33  24 
51  31  00 
51  27  41 
51  39  10 
51  35  30 
51  46  14 
51  56  00 

51  53  08 

52  07  15 
52  04  30 
52  13  46 
52  16  14 
52  39  00 
52  40  04 

52  33  38 

53  08  55 
53  07  38 
53  15  13 
53  13  46 
53  23  58 
53  29  47 
53  35  00 
53  36  40 
53  42  27 
53  49  34 
53  53  06 

53  49  30 

54  05  45 
54  17  00 
54  16  00 

54  19  36 
54  16  33 
54  15  30 
54  18  00 
54  20  50 

54  34  08 

54  39  47 

55  00  52 

55  08  13 
55  16  26 
55  12  31 
55  15  14 
55  16  33 
55  19  07 
55  22  50 
55  25  55 
55  13  38 
55  10  20 

54  59  40 

55  05  23 
55  15  03 
55  18  05 
54  55  47 
54  51  07 
54  40  20 
54  41  50 
54  38  45 
54  24  04 


Long.  W 


9  29  03 

9  36  25 

9  32  44 

9  10  20 

9  48  19 

9  44  49 

10  18  03 

10  32  45 

10  19  16 

10  23  17 

10  15  30 

10  40  00 

10  21  40 

9  52  53 

9  01  18 

8  37  23 

9  55  54 
9  51  30 
9  42  06 
9  03  10 
9  46  03 

10  14  01 

10  03  54 

10  00  15 

10  09  40 

10  06  41 

9  40  12 

9  32  56 

9  59  00 

10  03  34 

10  05  31 

9  53  00 

9  20  41 
8  46  02 
8  34  25 
8  37  00 
8  40  14 

8*27  33 
8  49  52 
8  33  48 


8  15  38 
8  15  00 
7  57  15 
47  12 
37  53 
23  51 
22  22 
13  37 


Lun.  Int. 


7 
7 
7 
7 
7 
6  55  38 


02  20 
19  25 

21  51 
28  45 
10  45 
44  18 
47  21 
49  30 

31  30 

32  01 

22  20 


H.  W, 


h.    m. 
3  50 


4  10 


3  30 


3  40 


3  40 
3  50 


6  00 


4  15 
4  19 


4  16 
'4"26' 


4  50 


5  10 


5  03 


L.  W. 


6  55 

7  48 


10  30 


10  42 

ii  66" 


h.      TO. 

10  03 


10  23 


9  43 


9  53 


9  53 
10  03 


0  13 


10  28 
10  19 


10  29 
"i6'33' 


11  03 


11  23 


11  16 


Range. 


10.6 


10.8 


10.7 


10.7 
12.3 


18.7 


13.4 
15.1 


13.2 

ii'i' 


10.4 


11.4 


11.2 


5  28  I  11  41  I  11.  6 


0  43 

1  35 


4  18 


4  06 
'4"48' 


7.5 
8.0 


6.7 


9.3 

ii.'i" 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EXJBOPE— Continued. 


[Page  307 


Place. 


Lat.  X. 


Long.  W. 


Lun.  Int. 


H.W. 


L.W. 


Range. 


Spg. 


Neap. 


Dundrum  Bay:  St.  John  Pt.  light 

Carlingford  Lough:  Haulbowline  Rk.  It. . 

Drogheda:  Lighthouse 

Rockabill:  Lighthouse 

Howth  Peninsula:  Bailey  light 

Dublin:  Observatory 

N.  wall  light 

Poolbeg:  Lighthouse 

Kingstown:  E.  pier  light 

Killiney  Hill:  Mapae  obelisk 

Bray  BLead:  Ordnance  survey  station 

Wicklow:  Upper  light 

Tara  Hill:  Summit 

Black  Stairs  Mountain:  Ordnance  survey 
station 

Tory  Hill:  Ordnance  survey  station 

Wexford:  College 

Forth  Mount:  Ordnance  survey  station.., 

Tuskar  Rock:  Lighthouse 

Great  Saltee:  S.  end 

Waterford:  Hoop  Pt.  light 

Waterford:  Cathedral 

Great  Newton  Head:  Metal  Man  Tower.. 

Dungarvan:  Ballinacourty  light 

Knockmealdown  Mount:  Ordnance  sur- 
vey station 

Helvick  Head:  Ordnance  siu-vey  station. 

Mine  Head:  Lighthouse 

Youghal:  Lighthouse 

Capel  Island:  Tower 

Ballycottin:  Lighthouse 

Cork  Harbor:  Haulbowline  Coal  Wharf.. 

Queenstown:  Roches  Pt.  light 

Kinsale:  Lighthouse,  S.  pt 

Seven  Heads:  Tower 

Galley  Head:  Light  on  summit 

Stag  Rocke:  Largest 

Alderney  Harbor:  Old  pier  light 

St.  Heliers:  Light  on  Victoria  Pier 


Vardo:  Fortress 

Vadso:  Lighthouse 

North  Cape:  Extreme 

Fruholm:  Lighthouse 

Hammerfest:  Lighthouse 

Tromso:  Observatory 

Hekkingen :  Lighthouse 

Andenes:  Lighthouse 

Lodingen  (Hjertholm):  Lighthouse. 
Lofoten  Island:  Skraaven  I.  light. . 

Glopen  light 

Gryto:  Lighthouse 

Stot:  Lighthouse 

Traenen:  Soe  Islet  light 

Bronnosund:  Lighthouse 

Villa:  Lighthouse 

Halten  Island:  Lighthouse 

Koppem 

Agdenes:  Lighthouse 

Trondheim:  Mumkholmen  flagstaff. 

Grip:  Chiu-ch 

Chnstiansund:  Storvaden 

Freikallen 


54  13  30 
54  01  10 
53  43  00 
53  35  47 
53  21  40 
53  23  13 
53  20  47 
53  20  30 
53  18  10 
53  15  52 
53  10  39 
52  57  54 
52  41  55 

52  32  55 
52  20  53 
52  20  04 
52  18  57 
52  12  09 
52  06  41 
52  07  25 
52  15  33 
52  08  13 
52  04  27 

52  13  39 
52  03  00 
51  59  33 
51  56  34 
51  52  54 
51  49  30 
51  50  33 
51  47  33 
51  36  11 
51  34  14 
51  31  50 
51  28  05 
49  43  00 
49  10  29 


70  22  00 

70  04  00 

71  11  00 
71  06  00 
70  40  15 
69  39  12 
69  36  05 
69  19  30 
68  24  40 
68  09  20 
67  53  15 
67  23  15 
66  56  35 
66  25  50 
65  28  40 
64  32  55 
64  10  25 
63  48  25 
63  38  45 
63  27  04 
63  13  11 
63  07  01 
63  03  04 


5  39  30 

6  04  45 
6  15  00 
6  00  20 
6  03  06 
6  20  17 
6  13  33 
6  09  00 
6  07  30 
6  06  37 
6  04  55 
6  00  08 
6  13  01 

6  48  17 

7  07  31 
6  28  15 
6  33  41 
6  12  35 
6  37  15 

6  55  53 

7  06  24 
7  10  15 
7  33  05 


54  54 
32  39 
35  08 

50  34 

51  10 
59  00 

8  18  20 
8  15  14 
8  31  58 
8  42  51 

8  57  10 

9  13  27 
2  12  00 
2  06  44 

Long.  E. 
31  07  30 
29  45  00 
25  40  00 
23  59  00 
23  40  00 
18  57  00 
17  50  15 
16  08  00 
16  02  30 
14  40  40 
13  04  30 
13  52  30 
13  28  50 

11  59  50 

12  13  30 
10  42  10 

9  24  50 
9  44  45 
9  45  20 
10  23  30 
7  36  05 
7  43  35 
7  46  04 


10  45 
10  45 


10  55 


11  00 
10  52 


10  30 
10  10 


7  05 


5  30 
5  05 


5  00 


5  02 


4  33 
4  30 
4  20 


6  21 
6  09 

5  40 


2  20 
1  35 


0  42 


11  35 


11  18 


11  00 


ft. 


4  33 
4  33 


15.8 

n.6 


4  43 


12.7 


4  48 
4  27 


13.0 
10.9 


4  18 
3  58 


11.8 
8.7 


0  53 


4.9 


11  43 

ii'is 


8.8 
i2.'3' 


11  13 


11  15 


4  40   10  53 


10  59 
10  43 
10  33 


0  16 
0  00 


11  57 


8  40 
7  48 


6  55 


5  23 


5  04 


4  48 


12.4 


12.6 


n.8 


n.6 

11.4 
10.7 


17.2 
3L2 


9.0 


8.3 

7.8 


7.0 


6.9 


8.4 


5.0 


ft. 


9.2 
6.8 


7.5 


7.6 
6.4 


6.9 
5.1 


2.9 


5.1 
"6.2 


6.2 


6.3 


5.9 


5.8 
5.7 
5.3 


7.6 
13.6 


5.1 


4.7 
4.4 


4.0 


3.3 


4.1 


2.9 


Page  308]                                   APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATTiANTIC  COAST  OF  EUROPE— Continued. 

3 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

« 

1 

Hestfikjaer:  Lighthouse 

63  05  00 

62  58  49 
62  48  20 
62  19  38 
62  11  12 
61  51  21 
61  38  40 
61  33  35 
61  19  16 
60  45  05 
60  23  54 
60  21  39 
60  07  50 
59  57  44 
59  18  20 
59  03  10 
58  58  30 
58  39  25 
58  36  56 
58  25  51 
58  06  25 
57  58  55 

57  58  00 

58  07  50 
58  04  15 
58  15  02 
58  24  40 
58  51  50 

58  59  25 

59  00  01 
58  59  34 

58  58  05 

59  01  35 
59  10  30 
59  23  10 
59  25  34 
59  29  23 
59  39  52 
59  40  21 
59  54  44 
59  09  00 
59  07  08 
58  59  45 
58  54  05 

58  56  24 
58  54  12 
58  32  45 
58  20  12 
57  53  49 
57  40  58 
57  18  15 
57  06  26 
56  54  08 
56  40  21 
56  14  40 
56  18  06 
56  02  37 
55  52  00 
55  41  52 
55  36  47 
55  23  00 

7  29  55 
7  12  32 
6  36  10 
5  16  25 
5  07  59 
5  15  11 
4  47  38 
4  46  45 
4  47  14 

4  42  55 

5  18  11 
5  19  35 
5  01  00 
5  03  30 

4  52  35 

5  24  20 
5  45  20 
5  33  35 
5  49  08 

5  58  49 

6  34  20 

7  03  10 

7  29  50 

8  00  30 
8  03  30 
8  31  36 

8  47  55 

9  36  15 
9  45  50 
9  45  14 

10  03  28 
10  09  26 
10  31  55 
10  36  25 
10  32  45 
10  29  52 
10  19  15 
10  38  08 
10  36  55 
10  43  23 

10  50  15 

11  24  09 

10  47  20 

11  00  45 

11  10  28 
11  00  36 
11  02  16 
11  13  24 
11  28  04 
11  53  54 

11  54  16 

12  14  32 
12  29  48 
12  51  38 
12  51  47 
12  27  11 
12  41  30 

12  49  48 

13  11  15 
12  59  49 
12  49  02 

h.    TO. 

h.    m. 

ft. 

ft. 

Stemshesten 

Jilrstenen:  Lighthouse 

Svinoen  Islet 

Hjoerringa  Mountain:  Summit 

Hornelen  Mountain:  Summit 

Batalden  Island:  Store 

Kinnsund:  Lighthouse 

Alden , 

Helliso:  Lighthouse 

Bergen:  Naval  School  Obsy 

10  15 

3  55 

4.1 

2.1 

Lorstakken  Mountain:  Summit 

Marstenen  Islet :  Lighthouse 

Furen  Islet 

Ulsire :  Lighthouse - 

Hvidingso :  Lighthouse 

Port  Stavanger  ■  Lighthouse 

9  43 

3  40 

1.9 

0.8 

Obristadbroekke :  Lighthouse 

Synesvarde  Mountain:  Summit 

Kompas  Mountain:  Summit 

Lister:  Lighthouse 

Lindesnes:  Lighthouse 

Ryvingen  Island:  Lighthouse 

Christianssand  ■  Odderoen  light 

4  16 

10  15 

LI 

0.5 

Okso :  Lighthouse 

Hamberg:  Mill 

Arendal  Inlet:  Inner  Torungerne  light. . . 
Jomfruland :  Lighthouse 

4  17 

10  10 

LO 

0.7 

Langotangen:  Lighthouse 

Langesund :  Church 

Frederiksvsern:   Lookout  tower 

4  34 

10  00 

1.3 

1.0 

Svenor:  Lighthouse 

Foerder  Islet:  Lighthouse 

Fulehuk:  Lighthouse 

Ilorten:  Church 

Holmestrand :  Church 

Drobak :  Church 

Oscarsberg:  Fort  flagstaff 

Christiania :  Observatory 

5  22 

10  37 

1.2 

0.9 

Stromtangen  (Torgauten):  Lighthouse — 
Fredriksten:  Fort  clock  tower 

Torbjomskjaer :  Lighthouse 

Koster:  Lighthouse 

Stromstad:  Steeple 

Nord  Koster  Islands:  Lighthouse 

Wadero  Island :  Lighthouse 

Hollo  Island :  Lighthouse 

Paternoster  Rocks:  Lighthouse 

Gottenbiu-g:  Signal  station 

Nidingen  Islet:  Lighthouse 

Warberg:  Castle  tower 

Falkenberg:  Church 

Halmstad :  Palace 

Engelholm:  Church 

Kullen  Point:  Lighthouse 

Helsingborg :  Lighthouse 

Landskrona :  Lighthouse 

Lund :  Royal  Observatory 

Malmo:  Lighthouse 

Falsterbo :  Lighthouse 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  309 


Place. 


Trelleborg:  Lighthouse 

Ystad :  Lighthouse. 

Sandhammaren :  Lighthouse 

Hano  Island :  Lighthouse 

Karlshamn:  Lighthouse 

Karlskrona:  Stumholm  Tower 

Oland  Island :  Light  on  S.  pt 

Gottland  Island:  Hoburg  light,  S.  pt. 

Ostergarns  light 

Faro  Island :  Holmadden  light 

Sparo  Vestervik :  Granso  light 

Haradsskar  Islet:  Lighthouse 

Norrkopings  Inlopp:  Lighthouse 

Landsort:  Lighthouse 

Stockholm:  Observatory 

Upsala:  Observatory 

Norrtelge:  Inn 

Soderarm:  Lighthouse 

S vartklubben :  Lighthouse 

Osthammar:  Church 

Oregrund:  Clock  tower 

Djursten:  Lighthouse 

Foremark:  Church 

Orskar  Rock:  Lighthouse 

Gefle:  Church 

Eggegrund  Islet:  Lighthouse 

Hamrange:  Church 

Soderhamm:  Courthouse 

Enanger:  Church 

Hudiksvalls:  Courthouse 

Gnarp:  Church 

Sundsvall:  Church 

Lungo:  Lighthouse 

Skags  Head:  Lighthouse 

Holmogadd :  Lighthouse 

Umea:  Bredekar  Light 

Bjuroklubb :  Lighthouse 

Pi  tea 

Rodkallen:  Lighthouse 

Maloren:  Lighthouse 


Tomea:  Lighthouse 

Uleaborg :  Karlo  I .  light 

Ulko  Kalla  Rock:  Lighthouse. 

Norrsher  Islet:  Kvarken  light.. 

Kaske:  Shelgrund  I.  light 

Biemeborg:  Sebsher  light 

Nuistad:  Ensher  light 

Abo:  Observatory 

Aland  Island:  Shelsher  light... 

Ekkere  Light 

Logsher  light... 

Bogsher:  Beacon 

Ute  Islet :  Lighthouse 

Gauge :  Gauge  I.  light 

Rensher :  Lighthouse 

Helsingfors :  Observatory 

Soder  Skars :  Lighthouse 

Kalboden  Island :  Light  vessel . 

Rodsher  Island:  Lighthouse... 

Hogland  Island:  Lower  light... 
Upper  light. . . 


Lat.  N. 


22  00 

25  42 
22  58 
00  54 

10  04 

09  45 

11  50 
55  18 

26  29 

57  24 
45  38 

08  52 

17  55 

44  26 
20  33 
61  29 

45  24 

45  15 

10  35 
15  19 
20  26 
22  15 

22  26 

31  41 
40  29 
43  48 

55  57 

18  22 

32  54 
43  57 
02  51 

23  30 

38  35 

11  55 
35  34 

39  33 
28  50 

19  10 
18  53 
31  30 

48  30 
02  20 

20  05 
14  08 
20  06 
28  29 
43  10 
26  57 

24  45 
13  20 
50  50 
31  11 

46  30 
46  00 

56  10 

09  43 
06  40 

58  45 
58  08 
00  40 
06  22 


Long.  E. 


13  09  20 

13  49  38 

14  11  10 
14  50  57 

14  52  02 

15  36  05 

16  24  04 
18  11  06 

18  59  27 

19  22  36 
16  40  36 
16  59  22 

16  11  28 

17  52  09 

18  03  30 

17  37  32 

18  41  34 

19  24  34 
18  49  49 
18  22  36 
18  26  33 
18  24  21 
18  09  49 
18  22  38 
17  08  29 
17  33  50 
17  02  57 
17  04  18 
17  01  51 
17  07  37 
17  16  22 

17  19  05 

18  05  05 

19  02  50 

20  45  35 

20  18  35 

21  34  45 

21  30  00 

22  21  55 

23  34  00 

24  12  00 
24  34  00 

23  27  00 

20  37-40 

21  11  24 
21  22  34 

21  01  00 

22  17  03 
19  34  00 
19  31  20 

19  54  05 

20  25  50 

21  22  00 

22  58  08 

24  24  43 

24  67  17 

25  25  51 

25  37  30 

26  41  05 

27  01  40 
26  58  44 


Lun.  Int. 


Range. 


H.  W.    L.W. 


h.    m. 


Spg.   Neap. 


ft. 


Page  310]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Sommer  Island :  Lighthouse 

Vieborg  Bay:  Nelva  I.  light 

Stirsudden:  Lighthouse 

Kronstadt:  Light  on  Frederikstadt  bas 

tion 

Cathedral 

St.  Petersburg:  Observatory 

Pulkowa:  Observatory 

Peterhof :  Pier-head  light 

Oranienbaum:  Lighthouse 

Seskar  Islet:  Lighthouse 

Narva:  Light  S.  pt.  of  entrance 

Stensher  Rock:  Lighthouse 

Ekholm  Islet:  Lighthouse 

Koksher:  Lighthouse 

Revel:  Light  N.  end  of  W.  mole 

Cathedral 

Nargen  Island:  Lighthouse 

Surop:  W.  light 

Baltic  Port:  Lighthouse 

Odenskholm  Island:  Lighthouse 

Takhkona  Point:  Lighthouse 

Dago  Island :  Dagerort  light 

Filzand  Island:  Lighthouse 

S valf erort  Tzerel :  Lighthouse 

Kuino:  Lighthouse 

Pemau:  Light  at  S.  entrance 

Riga:  Ust  Dyinski  light 

Cathedral  of  St.  Peter 

Runo  Island:  Lighthouse 

Domesnes:  Lighthouse 

Windau:  Light  on  S.  jetty 

Libau:  Light  at  entrance  of  port 

Memel:  Lighthouse 

HeiUgen  Creutz:  Church  tower 

Brusterort:  Lighthouse 

Pillau:  Lighthouse 

Fischausen:  City  Hall  tower 

Konigsberg:  Observatory 

Tolkemit:  Church  tower 

Elbing:  Church  tower 

Tiegenort:  Church  tower 

Dantzig:  Observatory 

Neufahrwasser  light 

Weichselmunde:  Fortress  tower 

Putziger  Heistemest:  Church  tower.  .  . , 

Oxhoft:  Lighthouse 

Hela:  Lighthouse 

Rixhoft:  Lighthouse 

Leba:  Church  tower 

Stopelmunde:  Church 

Jershoft:  Lighthouse 

Rugenwalde:  St.  Mary's  Church 

Coslin:  St.  Mary's  Church 

Funkenhagen:  Lighthouse 

Colbem:  St.  Mary's  Church 

Gross-Horst:  Lighthouse 

Cammin:  Cathedral  tower 

Wollin:  Church  tower 

Stettin:  N.  Castle  tower 

Swinemunde:  Lighthouse 


Lat.  N. 


Long.  E. 


60  12  31 

27  33  46 

60  14  43 

27  58  36 

60  11  05 

29  03  01 

59  58  14 

29  47  12 

59  59  44 

29  46  07 

59  56  30 

30  19  22 

59  46  19 

30  19  40 

59  53  26 

29  54  54 

59  55  40 

29  46  38 

60  02  08 

28  23  01 

59  28  04 

28  03  31 

59  49  10 

26  23  00 

59  41  06 

25  48  58 

59  42  00 

25  02  37 

59  27  05 

24  46  10 

59  26  28 

24  44  45 

59  36  22 

24  31  57 

59  27  55 

24  24  05 

59  21  30 

24  04  30 

59  18  06 

23  23  15 

59  05  25 

22  36  15 

58  55  02 

22  11  36 

58  23  02 

21  49  56 

57  54  37 

22  04  15 

58  05  50 

23  59  34 

58  23  10 

24  49  25 

57  03  38 

24  01  27 

56  57  01 

24  06  38 

57  48  02 

23  15  00 

57  48  10 

22  39  15 

57  24  00 

21  34  00 

56  31  01 

20  59  40 

55  43  45 

21  06  06 

54  53  47 

20  01  25 

54  57  40 

19  59  06 

54  38  25 

19  53  55 

54  43  49 

20  00  39 

54  42  50 

20  29  46 

54  19  19 

19  31  58 

54  09  44 

19  23  58 

54  16  30 

19  08  37 

54  21  18 

18  39  54 

54  24  28 

18  39  59 

54  23  51 

18  41  03 

54  12  16 

18  40  35 

54  33  09 

18  33  46 

54  36  06 

18  49  04 

54  49  55 

18  20  29 

54  45  29 

17  33  38 

54  35  16 

16  51  35 

54  32  29 

16  32  50 

54  25  27 

16  24  52 

54  11  28 

16  11  05 

54  14  40 

15  52  39 

51  10  40 

15  34  44 

54  05  47 

15  04  06 

53  58  29 

14  46  36 

53  50  41 

14  37  12 

53  25  41 

14  33  52 

53  55  03 

14  17  19 

Lun.  Int. 


Range. 


H.W. 


L.W. 


Neap. 


ft.     TO. 


h.    m. 


ft. 


/.'. 


APPENDIX  IV.                                     [Page  311 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EITROPE— Continued. 

3 

5 

Place. 

Lat.  N. 

Long.  E. 

Liin.  Int. 

Range. 

H.W. 

L.AV. 

Spg. 

Neap, 

a 

a 

1 

Streckelsberg:  Survey  station  near  beacon 
Usedom :  Church  tower 

54  03  08 
53  52  17 

53  56  59 

54  03  18 
54  05  49 
54  15  02 
54  22  56 
54  25  08 
54  40  53 
54  18  42 
54  28  28 
54  20  47 
54  14  42 
54  10  42 
54  05  27 
54  06  32 
54  08  00 
53  53  50 
53  58  54 

53  57  44 

54  26  16 
54  29  43 
54  28  54 
54  19  47 
54  23  52 
54  27  25 
54  20  28 
54  28  25 
54  30  55 
54  39  48 
54  47  05 
54  54  28 
54  40  23 
54  56  48 

54  58  05 

55  02  46 
55  03  52 
55  05  31 
55  03  04 
54  54  13 
54  41  51 
54  41  21 
54  28  43 
54  19  08 
54  07  52 
54  10  57 
53  57  15 
53  55  01 
53  52  25 
53  36  12 
53  33  43 
53  32  45 
53  33  07 
53  32  52 
52  31  31 

52  29  07 

53  28  30 
53  42  50 
53  36  20 
53  32  52 
53  46  57 
53  42  21 

o           /           * 

14  01  17 
13  55  26 
13  51  13 
13  46  51 
13  22  53 
13  55  42 
13  37  54 
13  26  11 
13  26  12 
13  05  30 
12  30  23 
12  24  02 
12  26  04 
12  05  19 

12  08  10 
11  46  04 
11  41  54 
11  28  09 
11  05  54 

10  52  59 

11  11  59 
11  14  29 
11  04  18 
10  32  59 
10  22  24 
10  12  04 
10  08  53 

9  50  23 
9  34  23 
9  56  13 
9  26  20 
9  45  35 
10  02  23 
9  52  20 
9  58  41 
9  25  18 
9  23  35 
8  39  41 
8  26  50 
8  22  03 
8  33  13 

8  33  58 

9  03  21 
8  56  38 
8  51  53 

7  53  11 

8  24  35 
8  29  58 

8  42  43 

9  28  48 
9  36  40 
9  56  35 
9  58  27 
9  58  21 

13  21  52 
13  28  33 

9  59  37 
8  14  48 
8  18  30 
8  34  25 
8  04  47 
8  01  43 

h.      TO. 

A.    m. 

ft. 

ft. 

Lassau :  Church  tower 

Wolgast:  Church  tower 

Griefswald:  St.  Nicholas  Church 

Griefswalder  Oie:  Lighthouse 

Granitz:  Castle  tower 

Bergen :  Church  tower 

Arkona:  Lighthouse 

Stralsund:  St.  Mary's  Church 

Darsserort:  Lighthouse 

Wustrow:  Church 

Ribnitz :  Church  tower 

Wameraunde:  Church 

Rostock:  St.  Jacob's  Church 

Diedrichshagen :  Survey  station 

Basdorf :  Survey  station 

Wismar :  St  Nicholas  Church 

Hohenschonbei^:  Survey  station 

Travemunde :  Lighthouse 

Burg:  Church  tower 

Manenleuchte :  Lighthouse 

Petersdorf :  Church  tower 

Hessenstein:  Flagstaff  of  lookout  tower... 
Schonberg:  Church 

Bulk :  Lighthouse 

Kiel:  Observatory 

Eckemforde:  Church 

Schleswig:  Cathedral 

Kappeln :  Church 

Flensberg:  Church 

Duppel:  Survey  station 

Schleimunde:  Lighthouse 

Augustenbui^:  C  lurch 

Hugeberg:  Survey  station 

Apenrade:  Church 

Skoorgaarde:  Survey  station 

Ballum:  Church 

List:  E.  lighthouse 

0  20 

6  33 

5.2 

3.0 

Keitum:  Church 

Fohr:  St.  Nicholas  Church 

1  35 

7  47 

7.8 

4.5 

Galgenberg:  Survey  station 

Husum:  Church 

2  10 

1  45 

1  11 

11  29 

8  23 
7  57 
7  24 
5  17 

10.8 

ILO 

1L7 

8.1 

6.2 
6.4 
6.8 
4.7 

Tonning:  Church 

Busum :  Church 

Helgoland :  Lighthouse 

Scharhom :  Beacon 

Neuwerk:  Lighthouse 

Cuxhaven:  Lighthouse 

0  39 

6  51 

10.1 

5.8 

Stade:  Church  steeple 

Steinkirchen :  Church 

4  00 

10  13 

8.5 

4.9 

Altona:  Observatory 

Hambui^:  Old  Observatory 

5  00 

11  12 

6.1 

3.5 

Imperial  Marine  Observatory . 
Berlin :  Urania  Observatory 

Treptow  Observatory 

Harburg:  Lighthouse     

Hohe  Weg:  Lighthouse 

0  25 

6  38 

10.1 

5.7 

Langwarden :  Church            

Bremerhaven:  New  harbor  light 

Minsener  Sand:  Light  vessel 

0  54 
0  10 

7  07 
6  23 

10.4 
9.5 

5.8 
5.3 

Schillighom:  Lighthouse 

Page  312] 


APPENDIX  IV. 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC   COAST   OF  EUHOPE— Continued. 


Place. 


WiUaelmsliaven :  Observatory 

Wangeroog:  Lighthouse 

Spikeroog:  Church 

Langeoog:  Belvedere 

Balstriun:  Church 

Nordemey :  Lighthouse 

Juist:  Church 

Emden:  City  Hall  tower 

Falster:  Gjedser  light 

Moen  Island:  Stege  Church  spire 

Moen  light,  SE.  pt 

Prceste:  Church  spire 

Kjorge:  Church  tower 

Amager  Island:  HoUcenderby  Ch.  spire.. 

Nordse  Rase  light 

Copenhagen:  University  Observatory 

Bomholm:  Ronne  light 

Christianso  Island:  Great  tower 

Kronberg:  High  spire 

Nakkehooed:  Upper  light 

Hesselo  leland :  Lighthouse 

Anholt  Island:  Lighthouse 

Spodsbjerg:  Lighthouse 

Roeskilde:  Cathedral 

Nykjobing:  Church  tower 

Oddensby :  Church  tower 

Sejro  Island:  Sejro  Point  light 

Kallundborg:  Church 

Omo  Island:  Church 

Vordingborg:  Waldemar's  tower 

Veiro  Island :  Lighthouse 

Langeland  Island:  Fakkebjerg  light 

Mro  Island:  Church  spire 

Lyo  Island:  Church  tower 

Assens:  Church  tower 

Baago  Island:  Lighthouse 

Kolding:  Castle  tower 

Bogense:  Church  spire 

Nyborg:  Church  spire 

Turo  Island:  Church  spire 

Svendborg:  Frue  Church 

Endelave  Island :  Church  tower 

Samso  Island:  Koldby  Church  tower.  . . . 

Horsens:  Frelser  Chiirch  spire 

Tuno  Island:  Lighthouse 

Samsoe  Island:  Nordby  Church  tower. . . 

Aarhus:  Cathedral  spire 

Hjelm  Islet:  Lighthouse 

Fomaes:  Lighthouse 

Hals:  Church  tower 

Aalborg:  St.  Rudolph's  Church 

Cape  Skaw,  or  Skagen:  Old  lighthouse. . . 

Hirtshals:  Lighthouse 

Haustholm:  Lighthouse 

Boobjerg:  Lighthouse 

Ringkjobing:  Church  spire 

Loune:  Church  tower 

Blaabjerg:  Summit,  100  ft 

Guldager:  Church 

Fano  Island:  Nordby  Church 

Mano  Island:  Church  spire 


Lat.  N. 


53  31  52 
53  47  25 
53  46  19 
53  45  06 
63  43  46 
53  42  39 
53  40  45 
53  22  06 


33  50 
59  03 

56  46 
07  24 
29  44 
35  45 
38  10 
41  13 

05  40 
19  19 
02  20 

07  10 
11  50 
44  16 

58  36 
38  34 
55  30 

57  52 

55  09 
40  50 
09  48 
00  26 
02  19 

44  23 
51  14 

02  34 

16  09 

17  44 

29  31 

34  03 

18  41 

03  00 
03  37 

45  32 
48  02 
51  44 

56  58 

57  06 
09  26 

08  00 
26  36 

59  54 
02  54 

43  46 

35  06 

06  50 

30  48 
05  27 
47  17 

44  50 

31  52 
26  26 
16  11 


Long.  E. 


8  08  47 


54  09 
41  45 
35  41 
22  03 
13  58 

6  59  53 

7  12  25 


11  58  03 

12  17  16 
12  32  40 
12  03  07 
12  07  36 
12  38  24 
12  41  26 
12  34  41 

14  42  00 

15  11  39 
12  32  02 
12  20  50 
11  42  50 
11  39  15 

11  51  36 

12  05  02 
11  40  29 
11  24  06 
11  05  07 
11  05  04 
11  09  32 
11  54  59 
11  22  23 
10  42  13 
10  24  11 
10  09  16 

9  53  50 

9  48  09 

9  28  40 

10  05  29 

10  47  47 

10  40  02 

10  36  48 

10  16  20 

10  33  37 

9  51  19 

10  26  51 

10  33  00 

10  12  50 

10  48  32 

10  57  40 

10  18  53 

9  55  22 

10  36  38 

9  56  44 

8  36  10 

8  07  23 

8  14  52 

8  14  36 

8  14  43 

8  24  12 

8  24  03 

8  32  38 


Lun.  Int. 


H.  W.    L.  W 


ft.  m. 
0  04 

11  27 


11  05 


0  24 


9  33 


5  46 
4  18 


2  35 


2  35 
2  34 


Range. 


Spg.   Neap. 


h.  m. 
6  17 
5  15 


ft. 

13.2 

8.0 


ft. 

7.4 

4.5 


4  53 


7.3 


4.1 


6  36 


8.9 


5.0 


3  21 


0.6 


0.3 


11  58 
10  30 


LO 
L2 


.05 
.07 


8  47 


2.1 


L2 


47 
46 


4.5 
4.7 


2.6 
2.7 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  313 


Place. 


Lat.N. 


Long.  £. 


Lun.  Int. 


Range. 


H.W. 


L.W. 


Neap. 


ft. 
2.0 


Niewe  Diep:  Time-ball  station 

Amsterdam :  W.  church  tower 

Utrecht:  Observatory 

Leyden:  Observatory 

The  Hague:  Church  tower 

Scheveningen :  Lighthouse 

Brielle:  Lighthouse 

Rotterdam :  Time-ball  station 

Ilellevoetsluis:  Time-ball  station 

Willemstadt:  Lighthouse 

Goedereede:  Light  on  church  tower. . . . 

Flushing:  Time-ball  station 

Light,  Westhaven  bastion 

Brussels:  New  observatory 

Antwerp:  Observatory 

Notre  Dame  Cathedral 

Blankenberghe:  Fort  lighthouse 

Ostend:  Lighthouse 

Church  tower 

Nieuport:  Templars  tower 

Paris:  Observatory 

Dunkerque:  Tower 

GraveUnes:  Light  on  N.  breakwater.  . . . 

Calais:  Light  on  old  fort 

Cape  Oris  Nez :  Lighthouse 

Boulogne,  C.  Alprech:  Lighthouse 

Abbeville:  Tower 

Cayeux:  Lighthouse 

Dieppe:  W.  jetty  light 

Ailly  Point:  Lighthouse 

St.  Valery  en  Caux:  Light  on  W.  break- 
water  

Fecamp:  N.  jetty  light 

Cape  La  Heve:  S.  light 

Havre:  S.  jetty  light 

Honfleur :  Hospital  jetty  light 

Caen:  Church  tower 

Port  CorseuUes:  W.  jetty  light 

Point  De  Ver :  Ligh&ouse 

Cape  La  Hougue:  Lighthouse 

Cape  Barfleur:  Lighthouse 

Cherbourg:  Light,  W.  head  of  breakwater 

Naval  Observatory 

Cape  La  Hague :  Lighthouse 

Casqueta  Rocks:  Light  on  NW.  rock. . . . 
Port  St.  Peter,  Guernsey :  Light  on  Castle 

Coonet  Breakwater 

Douvres  Rocks:  Lighthouse 

Cape  Carteret :  Lighthouse 

Coutances:  Cathedral  tower 

Granville:  L^hthouse 

Chausey  Is . :  Light  on  S  E .  end  of  large  id . 

St.  Malo:  Rochebourne  light 

Cape  Frehel :  Lighthouse 

Heau  de  Brehat:  Lighthouse 

Morlaix,  He  Noire:  Lighthouse 

De  Bas  Islet:  Lighthoiise 

Abervrach :  Light  on  Vrach  Islet 

Ushant:  Stiff  Point  light 


52  57  50 
52  22  30 
52  05  10 
52  09  20 
52  04  40 
52  06  16 
51  54  29 
51  54  30 
51  49  19 
51  41  48 
51  49  08 
51  26  33 
51  26  24 

50  47  66 
61  12  28 

51  13  17 
51  18  47 
51  14  13 
51  13  50 
61  07  63 

48  60  11 
61  02  09 
61  00  18 
50  57  45 
50  52  10 
50  41  57 
50  07  05 
50  11  42 

49  56  06 
49  55  04 

49  52  28 
49  46  05 
49  30  04 
49  29  01 
49  25  32 

49  11  14 
49  20  18 
49  20  28 
49  34  19 
49  41  50 
49  40  29 
49  38  54 
49  43  22 
49  43  17 

49  27  13 
49  06  28 
49  22  27 
49  02  54 
48  50  07 
48  62  13 
48  40  18 
48  41  05 
48  54  33 
48  40  23 
48  44  45 
48  36  57 
48  28  31 


46  36 
53  01 
07  45 

29  03 
18  30 
15  10 
10  46 
28  50 
07  40 
26  26 
58  35 
35  48 

34  32 

21  44 
24  44 
24  12 
06  54 
55  51 
55  22 
45  34 

20  15 

22  31 
06  34 
51  07 

35  02 
33  47 
49  56 

30  46 
05  01 

0  57  35 

0  42  34 
0  22  12 
0  04  08 
0  06  22 
0  13  43 

Long.  W. 
0  21  10 
0  27  24 
0  31  08 


16  21 
15  56 
43  44 
38  08 

57  15 
22  41 

31  31 

48  49 

48  25 
26  39 
36  46 

49  20 

58  41 
19  08 
05  11 
52  33 
01  38 
34  34 
03  26 


h.    m. 
7   17 


2  50 

3  35 

2  20 

3  20 


0  44 


4  15 


0  05 
0  02 


0  10 


11  58 
11  59 
11  39 
11  17 
11  18 


10  54 


10  29 
10  06 


9  03 


8  13 
8  14 


7  30 


6  20 
6  12 
6  67' 


6  50 

5  55 

6  43 


5  35 
5  00 
4  35 
4  00 
3  36 


h.    m. 
1  06 


ft. 
3.9 


9  02 

9  47 

8  32 

9  32 


4.8 
6.7 

5.2 
9.8 


6  66 


14.7 


10  27 


14.8 


6  17 
6  32 


12.5 
16.1 


6  22 


15.7 


5  58 

6  16 
6  13 

5  51 

6  62 


16.8 
19.0 
2L0 
21.6 
26.2 


6  48 


27.3 


6  33 
5  02 


26.8 
23.3 


4  14 


22.6 


2  46 
2  37 


18.6 
17.0 


1  44 


0  16 
0  07 


17.6 

'is.' 5' 

26.0 


0  15 


30.8 


0  09 
0  04 
0  04 


36.7 
34.7 
36.0 


12  00 
11  25 
11  00 
10  25 
10  00 


30.4 
23.1 
22.0 
20.6 
18.9 


2.5 
3.6 
2.8 
6.2 


7.8 


7.8 


6.7 
8.4 


8.4 


8.5 

9.6 

10.7 

ILO 

12.8 


13.3 


13.1 
1L4 


ILO 


8.2 
7.6 


6.9 
1L6 


13.6 


16.0 
15.2 
15.7 


13.3 

10.6 

10.1 

9.5 

8.7 


Page  314] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Lat.  N. 


Long.  W. 


Lun.  Int. 


Range. 


H.W. 


L.W. 


Spg. 


Brest:  Observatory 

Brest  (approach) :  Quelern  light 

De  Sein  Islet:  Lighthouse 

Bee  du  Raz:  Lighthouse 

Audierne :  Pierhead  light 

Penmarch  Rocks:  Lighthouse 

Glenan  Islands:  Light,  Penfret  I 

De  Groix  Island :  Lighthouse 

Lorient :  Church-tower  light 

Belle  Isle:  Lighthouse 

Port  Haliguen :  Light  on  N .  jetty 

Haedic  Island :  Lighthouse 

Port  Navalo:  Lighthouse 

Vannes:  St.  Pierre  Church 

Le  Four  Rock:  Lighthouse 

Croisic :  End  of  breakwater 

Guerande:  Steeple 

Port  St.  Nazaire :  Lighthouse 

Paimboeuf :  Steeple 

Nantes :  Cathedral 

Noir  Moutier  Island :  Lighthouse 

Le  Pilier  Island :  Lighthouse 

D' Yeu  Island :  Lighthouse 

La  Chaume:  Lighthouse 

Point  de  Grouin  du  Cou:  Lighthouse 

R6  Island:  Light,  NW.  pt 

Rochelle:  E.  Quay  l%ht 

Aix  Island :  Lighmouse 

Rochefort:  Hospital 

Oleron  Island :  Light,  NW.  pt 

Point  de  la  Coubre:  Lighthouse 

Point  Cordouan :  Lighthouse 

Point  de  Grave :  Lighthouse 

Bordeaux:  University  Obsy.,  Moirac 

Bayonne :  Cathedral 

Biarritz :  Lighthouse 

St.  Jean  deXuz:  St.  Barbe  Point  light.. 
Hendaye:  Abbadia  Observatory 

Fuenterrabia:  Light  on  Cape  Higuera... 

Port  Pasages:  Light  at  entrance 

San  Sebastian:  Monte  Igueldo  light 

Bilbao:  Light  on  Galea  Castle 

Castro  Urdiales:  Santa  Ana  Castle  light.. 

Santona :  Pescador  Point  light 

Santander :  Cape  Mayor  light 

San  Martin  de  la  Arena:  Lighthouse 

San  Vincent  de  la  Barquera:  End  of  new 

mole 

Rivadesella:  Mount  Somos  light 

Gijon :  Santa  Catalina  light 

Aviles:  Lighthouse 

Rivadeo:  Lighthouse 

Estaca  Point:  Lighthouse 

Port  Cedeira:  Lighthouse 

Ferrol:  Old  naval  observatory 

Priorino  Chico  light 

Coruna :  Hercules  Tower  light 

Cape  Finisterre :  Lighthouse 

Vigo:  Cres  I.  light 

Oporto:  Light,  N.  S.  de  Luz 


48  23  32 
48  19  10 
48  02  40 
48  02  28 
48  00  47 
47  47  52 
47  43  17 
47  38  51 
47  44  53 
47  18  42 
47  29  10 
47  19  18 
47  32  53 
47  39  30 
47  17  63 
47  18  30 
47  19  44 
47  16  18 
47  17  17 
47  13  08 
47  00  41 
47  02  35 
46  43  04 
46  29  38 
46  20  41 
46  14  40 
46  09  25 
46  00  36 

45  56  37 

46  02  49 
45  41  39 
45  35  14 
45  34  10 
44  50  07 
43  29  29 
43  29  38 
43  23  58 
43  22  52 

43  23  30 
43  20  05 
43  19  22 
43  22  36 
43  24  20 
43  28  36 
43  29  30 
43  26  50 

43  23  35 
43  31  00 
43  32  48 
43  38  05 
43  34  40 
43  47  20 
43  39  00 
43  29  30 
43  27  30 
43  23  10 
42  52  45 
42  12  30 
41  09  10 


29  36 
34  28 
52  03 
45  25 
32  50 
22  30 
57  15 

30  35 
21  31 
13  38 
06  09 
50  07 
55  08 
45  28 
38  05 

31  25 
25  48 
11  50 
02  09 

32  59 
13  16 

21  37 

22  56 
47  45 
27  49 

33  40 
08  57 
10  40 

0  57  50 

1  24  37 
1  15  16 
1  10  24 
1  04  27 

0  31  23 

1  28  43 
1  33  16 
1  39  53 
1  45  02 


47  30 
56  05 
01  40 
04  06 
16  10 
28  06 
47  40 
01  00 


24  55 

07  10 

40  11 

56  00 

03  00 

42  00 

8  05  30 

8  13  29 

8  20  20 

8  24  26 

9  15  28 
8  54  00 
8  40  35 


ft.  m. 
3  23 


3  25 


3  04 
3  05 
3  00 


3  25 


3  35 

4  18 

5  50 
3  05 


3  18 
3  20 


3  27 
3  27 
3  45 


3  35 


6  30 


3  00 


2  50 
2  45 
2  45 


2  43 

2  44 


2  43 
2  42 


2  25 


9  45 
9*53' 


ft. 
19.5 


17.2 


9  31 
9  34 
9  27 


ILl 
13.3 
13.0 


9  36 
9  50 
9  58 
9  46 
10  08 
12  11 


13.8 
16.6 
16.9 
16.7 
16.6 
15.8 


9  47 


16.7 


9  56 
10  39 

12  28 
9  26 


16.6 
17.0 
16.5 
16.7 


9  40 
9  44 


14.7 
12.7 


9  22 
9  22 
9  55 


16.6 
16.6 
16.7 


9  53 


16.8 


0  12 
'914 


15.3 

ii's" 


9  05 
9  03 
9  03 
9  07 
9  18 
9  14 

9  14 


n.7 
12.7 

n.8 

12.3 
14.8 

n.7 

10.4 


9  03 

8  58 
8  58 


13.5 
12.0 
14.4 


8  56 
8  57 


14.8 
14.9 


8  56 
8  55 


14.8 
10.0 


8  38 


10.0 


APPENDIX  IV.                                   [Page  315 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST   OF  EU HOPE— Continued. 

s 

A 
fl 

Place. 

Lat.  N. 

Long.  W. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

40  12  25 
40  10  47 
39  24  49 
39  21  00 
38  46  49 
38  42  31 
38  29  15 
37  01  20 
37  07  48 

36  58  23 

37  11  00 
37  15  08 
36  43  58 
36  27  42 
36  31  30 
36  10  50 

35  59  53 

36  07  19 
36  07  10 
36  06  25 

8  25  47 

8  54  15 

9  30  29 
9  22  30 
9  29  46 
9  11  10 
8  56  00 
8  58  00 
8  39  53 
7  51  48 
7  24  00 
6  57  12 
6  26  30 
6  12  18 
6  19  00 
6  02  08 
5  36  31 
5  26  12 
5  21  17 
5  20  42 

h.    m. 

h.    m. 

ft. 

ft. 

Cape  Mondego :  Lighthouse 

2  20 

8  35 

7.0 

3.0 

'Rorlnnof'i  Tqlnnrl  •   T/ifhthotiaft 

Peniche  ■  Lighthouse 

2  05 

8  15 

7.8 

3.4 

Lisbon:  Royal  Observatory,  Tapada 

Setubal  *  Lighthouse 

2  20 
2  10 

8  05 
8  20 

n.i 

1L6 

4.8 
5.0 

Lagos'  Church 

1  55 

8  08 

13.0 

5.6 

P.ono  Sta    Marin*  Liphthoiise 

San  Lucar  ■  Chipiona  light 

1  15 

7  28 

12.3 

5.6 

Cadiz :  Observatory  of  San  Fernando 

San  Sebastian  light 

1  45 

7  58 

n.8 

5.4 

Pa-no  Trsifdlofar*  T.ichthniisfi 

Tarifa"  Lighthouse 

1  32 

7  52 

5.6 

2.6 

Europa  Pt.  light 

1  35 

7  55 

3.7 

L7 

COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS. 

Malaga*  Lighthouse 

36  42  39 
36  50  12 

36  42  57 

37  33  28 
37  35  50 
37  33  22 

37  34  38 

38  12  30 
38  20  12 
38  30  00 
38  30  57 
38  33  30 

38  38  36 
38  40  51 
38  48  06 

38  51  00 

39  12  15 
39  28  05 
39  27  50 

39  53  57 

40  04  53 
40  27  48 
40  33  30 

40  43  10 

41  06  00 
41  25  18 

41  50  04 

42  16  15 
42  19  10 

4  24  38 
2  27  50 
2  11  12 
1  15  12 
0  59  09 
0  57  58 
0  50  20 
0  30  12 
0  28  48 
0  11  42 
0  10  06 
0  04  02 

Long.  E. 
0  02  52 
0  09  17 
0  12  02 
0  07  30 

Long.W. 
0  13  37 
0  19  48 
0  18  50 

Long.  E. 
0  41  19 
0  08  56 
0  28  48 
0  39  45 

0  53  55 

1  14  42 

2  07  00 

3  08  28 
3  17  10 
3  18  55 

2  15 

8  35 

2.9 

L5 

riartairPTia*  Arspnal  patft 

Escombrera  light 

Ranta  Pnla.  Rav*  Tii&hthouse 

Alicante  *  N  mole  light        

Villaioyose*  Lighthouse.. 

Benidonne*  Tower.  ..........  . 

Altea:  Lighthouse 

Calpe '  Church  tower. , 

Jarea"  Cape  San  Antonio  light 

Deniac  Mole-head  light 

Cape  Cullera'  Lighthouse 

Valenciai  Lighthouse 

Mole-end  light 

5  00 

11  30 

L5 

0.8 

Columbretes  Islands*  Lighthouse 

Oropesa  Cape  ■  Lighthouse 

Vinaroz  ■  Mole-head  light 

Port  Alfapues*  Bana  light 

Cape  Tortosa*  Lio'hthouse 

1 

Tarragona*  E  mole  light 

1 

Barcelona :  Royal  Academy  Obsy 

Palamos  Bay*  Molino  Pt  light 

CaHaniipa"  Cloclc  towpr 

Canft  Crwnt  •  TjichthonHP 

Page  316]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE   MEDITERRANEAN,  ADRIATIC,  AND*  BLACK   SEAS— Continued. 


Place. 


Lat.  N. 


Cape  Bear:  Lighthouse 

Port  Vendres:  Fort  Fanal  light 

Port  Nouvelle:  S.  jetty  light 

Cette:  Light,  St.  Louis  mole 

Aigues  Mortes:  Espignette  Pt.  light 

Planier  Rock :  Lighthouse 

Marseilles:  Janet  Cliff  light 

National  observatory 

Ciotat:  Berouard  mole  light 

Toulon:  St.  Mandrien  light 

Grand  Riband  Island:  Lighthouse 

Cannes:  Lighthouse 

Antibes:  Garoupe  light 

Nice:  Lighthouse 

Villefranche:  Mole-head  light 

Cape  Ferret  light 

Port  Ibiza:  Lighthouse 

Cabrera  Island :  Lighthouse , 

Pi  (Majorca) :  Lighthouse 

Port  Mahon  (Minorca) :  Lighthouse 

Carloforte:  Int.  Latitude  Obey 

Cape  Spartivento:  Lighthouse 

Cape  Sandalo:  Light  on  San  Pietro  I 

Porte  Conte:  Cape  Caccia  light 

Port  Torres:  Lighthouse 

Cape  Testa:  Lighthouse 

Razzoli  Island :  Lighthouse 

Caprera  Island :  Galera  Pt 

Cape  Figari:  Signal  station 

Cape  Tavolara :  Lighthouse 

Cape  Bella  vista :  Lighthouse 

Cape  Carbonera:  Cavoli  I.  light 

Cagliari:  Light  on  mole 

Bonifacio:  Mount  Pertusato  light 

Ajaccio:  Lighthoiise 

Corti:  Church  tower 

Calvi:  Lighthouse 

Cape  Corso :  Giraglia  I .  light 

Bastia:  Lighthouse 

Porto  Vecchio:  Chiape  Pt.  light 

Cape  Melle:  Lighthouse 

Genoa:  San  Benigno  light 

Hydro.  Institute  Obsy 

Spezzia:  Fort  Santa  Maria  light 

Florence:  Arcetri  Observatory 

Leghorn  (Livomo):  Light  on  S.  end  of 
curved  breakwater 

Capraia  Island:  Cape  Ferrajone  light 

Elba  Island,  Porto  Longone:  Cape  For- 
cado  light 

Pianosa  Island:  Light  on  battery,  W. 
side  of  fort 

Africa  Rock:  Lighthouse 

Monte  Christo  Islet:  Summit 

Giglio  Island,  Cape  Rosso:  Lighthouse. . 

Civita  Vecchia:  Light  N.  end  of  break- 
water  

Rome:  Royal  Observatory  at  Capitol 

Gaeta:  Orkndo  tower 


42  30  59 

42  31  18 

43  00  47 
43  23  50 
43  29  17 
43  11  57 
43  20  43 
43  18  18 
43  10  21 
43  05  10 
43  01  01 
43  32  51 
43  33  51 
43  41  32 
43  41  58 
43  40  30 

38  54  10 

39  06  34 
39  33  00 
39  51  53 

37  08  09 

38  52  34 

39  08  44 

40  33  50 

40  50  25 

41  14  36 
41  18  24 
41  14  15 
40  59  52 

40  54  55 
39  55  47 
39  05  15 
39  12  35 

41  22  10 

41  52  50 

42  18  14 

42  35  10 

43  01  45 

42  41  47 

41  35  45 

43  57  17 

44  24  15 
44  25  09 
44  04  00 
43  45  15 

43  32  36 
43  02  57 

42  45  14 

42  35  06 
42  21  28 
42  20  15 
42  19  13 

42  05  38 
41  53  34 
41  12  27 


Long.  E. 


07  30 
06  50 
04  08 
42  08 

08  32 
13  51 
20  46 
23  39 
36  42 

5  56  06 

6  08  39 


00  54 
08  02 

17  15 

18  42 

19  41 


1  27  25 

2  57  20 
2  37  00 
4  18  20 

8  18  44 
8  51  08 
8  13  29 
8  10  00 

8  23  56 

9  08  42 
9  20  28 
9  29  40 
9  39  14 
9  44  22 
9  42  52 
9  32  35 
9  07  20 

9  11  15 

8  35  45 

9  09  04 

8  43  25 

9  24  10 
9  27  00 
9  22  05 

8  10  22 
8  54  19 

8  55  20 

9  50  48 
11  15  20 

10  17  45 
9  51  07 

10  24  38 

10  05  50 
10  03  54 
10  18  39 

10  55  24 

11  46  50 

12  29  06 

13  35  15 


Lun.  Int. 


H.  \V.    L.  W. 


h.    m. 


7   31 


8  22 


h.    m. 


2  00 


2  24 


Range. 


Spg.   Neap. 


0.6 


0.6 


0.3 


0.2 


APPENDIX  IV.  [Page  317 

MARITIME   POSITIONS   AND  TIDAL  DATA. 
COASTS  OF  THE   MEDITEBBANEAN,  ADBIATIC,  AOTJ  BLACK   SEAS— Continued. 


Place. 


Lat.  N. 


Long.  E. 


Lun.  Int. 


n.  W.        L.  W 


Range. 


Spg.       Neap. 


Ponza  Islet:  Pun  to  della  Guardia  light. . . 
Naples;  Observatory,  Capo  di  Monte 

Light  on  elbow  of  mole 

Capri  Island :  Carena  Pt.  light 

Lipari  Island:  Casa  Bianca  light 

Ustica  Island:  NE.  point  light , 

Faro  of  Messina:  Capo  di  Faro  light. . . . . 

Milazzo:  Lighthouse 

Palermo :  Royal  Observatory , 

lAsht  on  mole  head 

Trapani :  Palumbo  Rock  light 

Maritimo  Island :  Light  on  SW.  pt 

Marsala:  W.  mole  light 

Girgenti:  Port  Empedoche  light 

Gozo  Island:  Lighten  NW.  pt 

Malta  Island,  Valetta  Harbor:  Lighthouse. 

Linosa  Island :  J^^anding  Cove 

Lampedusa  Island:  Carallo  Bianco  light. 

Cape  Passaro:  Lighthouse 

Syracuse:  Maniace  Castle  light 

Augusta  Port:  Torre  d'Avola  light 

Catania:  Sciari  Biscari  light 

Royal  University  Observatory . 

Cape  Taormma:  Semaphore 

Mes.sina:  San  Ranieri  light 

Cape  Peloro:  Lighthouse 

Cape  Spartivento :  Lighthouse 

Cape  Colonna:  Lighthouse 

Cotrone:  Mole-head  light 

Taranto:  Cape  St.  Vito  light 

Gallipoli:  St.  Andrea  light 

Cape  Sta.  Maria  di  I>euca:  Lighthouse. . . 

Cape  Otranto:  Lighthouse 

Port  Otranto:  Castle 

Brindisi:  Lighthouse 

Bari:  St.  Catalolo  light 

Viesti:  Light  on  St.  Croce  Rock 

Manfredonia:  Lighthouse 

Tremiti  Islands:  Caprara  I.  light 

Ancona:  Monte  Cappucini  light 

Makmocco :  Rocchetta  Mole  light 

Venice:  Site  of  tower  of  St.  Mark 

Nautical  Institute  Observatory. 

Grado:  Church  tower 

Monfalcone:  Church  tower 

Trieste:  Imperial  Maritime  Observatory. 

Theresa  Mole  light 

Capo  d'Istria:  Lighthouse 

Isola:  Lighthouse 

Pirano:  Lighthouse 

Salvore  Point:  Lighthouse 

Citta  Nuova:  Lighthouse 

Parenzo :  Cathedral  tower 

Rovigno:  St.  Eufemia  light 

Pola:  Imperial  Hydro.  Office  Obsy 

Promontore  Point:  Porer  Rock  light 

Nera  Point:  Lighthouse 

Finme:  Cathedral  tower 

Porto  Re:  Lighthouse 

Veglia:  Mole  nead 

Prestenizza  Point:  Lighthouse 

Cherso :  Kimen  Point  light 


40  52  38 
40  51  46 
40  50  20 
40  32  07 
38  28  43 
38  42  40 
38  16  02 
38  16  10 
38  06  44 
38  07  56 
38  00  39 
37  57  13 
37  47  10 
37  16  55 
36  04  10 
35  54  00 
35  51  50 

35  29  37 

36  41  03 

37  03  04 
37  12  39 
37  29  35 
37  30  13 

37  50  25 

38  11  32 

38  16  03 
37  55  27 

39  01  29 

39  04  38 

40  24  41 
40  02  48 

39  47  43 

40  06  23 
40  09  06 

40  39  36 

41  08  19 
41  53  17 

41  37  39 

42  08  14 

43  37  14 
45  20  30 
45  26  02 
45  26  11 

45  41  06 
45  48  33 
45  38  45 
45  38  54 
45  33  00 
45  32  34 
45  31  54 
45  29  24 
45  19  16 
45  13  45 
45  05  00 

44  51  49 
44  45  30 

44  57  24 

45  19  36 
45  16  18 
45  01  30 
45  07  12 
44  57  36 


12  57  17 
14  15  26 
14  15  37 
14  11  40 

14  51  40 

13  12  00 

15  39  11 
15  13  42 
13  21  29 
13  22  29 
12  29  50 
12  02  55 

12  25  59 

13  32  27 

14  12  55 

14  31  80 
12  52  09 

12  36  12 

15  07  45 
15  17  37 
15  13  20 
15  05  19 
15  m  00 
15  18  30 
15  34  33 

15  39  15 

16  03  45 

17  12  09 
17  08  07 
17  12  23 

17  56  55 

18  22  17 
18  31  25 
18  28  45 
17  59  37 
16  50  52 
16  11  13 
15  55  34 
15  31  36 

13  31  18 
12  19  09 
12  20  24 

12  20  32 

13  22  54 
13  32  10 
13  45  44 
13  45  14 
13  43  18 
13  39  32 
13  33  48 
13  29  30 
13  33  42 
13  35  39 
13  38  00 
13  50  43 

13  53  36 

14  08  42 
14  26  41 
14  33  42 
14  34  36 
14  16  30 
14  23  30 


ft.  m. 


ft.  m. 


4  00 


10  13 


0.7 


0.2 


3  12 


9  25 


0.7 


0.2 


3  00 


9  13 


0.9 


0.3 


3  30 


9  43 


L8 


0.5 


10  15 


4  45 


3.3 


0.9 


9  20 


3  50 


2.0 


0.6 


9  00 


8  15 


3  25 


2  35 


3.4 


L2 


0.9 

'o.'s 


Page  318]                                     APPENDIX   IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK   SEAS— Continued. 

8 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range. 

H.W. 

L.W, 

Spg. 

Neap. 

i 

ta 

Galiola  Rock:  Lighthouse 

0           t          « 

44  43  36 
44  37  20 
44  32  11 
44  27  42 
44  24  42 
44  59  24 
44  40  06 
44  31  30 
44  07  05 
44  09  06 
43  56  16 
43  51  15 
43  37  36 
43  45  08 
43  31  00 

43  27  00 
43  31  02 
43  30  07 
43  23  50 
43  19  12 
43  17  46 
43  05  28 
43  01  43 
43  04  30 
43  09  24 
43  09  50 
43  07  30 

43  02  50 

42  57  42 
42  54  19 

42  57  37 
42  45  54 
42  45  05 
42  45  05 
42  23  30 
42  47  06 
42  45  30 
42  39  00 
42  35  08 
42  27  04 
42  23  36 
42  25  30 
42  16  42 
42  11  43 

42  05  15 
41  55  47 

41  35  10 
41  23  31 
41  18  40 
41  08  44 
41  02  12 
40  47  00 
40  36  14 
40  25  30 
40  25  17 
40  12  00 
40  02  57 
39  54  29 

14  10  36 
14  14  06 
14  28  06 
14  33  28 
14  34  06 
14  53  48 

14  34  42 

15  04  24 
15  14  05 

14  49  24 

15  26  21 
15  12  06 
15  34  24 
15  58  07 

15  55  00 

16  08  51 
16  15  09 
16  26  06 
16  11  10 

16  24  30 

17  01  36 
15  27  30 

15  45  29 

16  12  28 
16  27  14 

16  41  55 

17  12  00 

17  00  19 
17  12  44 
16  51  32 

16  43  07 

17  08  54 
16  51  45 
16  29  29 

16  15  12 

17  22  51 

17  46  48 

18  03  08 
18  10  49 
18  25  36 
18  32  00 
18  46  12 
18  50  36 

18  56  25 

19  04  19 
19  12  29 

19  27  15 
19  24  54 
19  27  14 
19  26  47 
19  26  30 
19  20  14 
19  19  14 
19  27  55 
19  17  45 
19  38  33 
19  47  53 
19  54  55 

A.     TO. 

h.    m. 

ft. 

ft. 

Unie  Island:  Netak  Point  light 

Lussin  Piccolo:  Manora  Observatory 

St.  Pietro  di  Nembo  Island :  Health  office. 
Gruizza  Rock:  Lighthouse 

8  10 

2  25 

LI 

0.3 

Zengg:  Mole-head  light 

Terstenik  Rock:  Lighthouse 

Carlobago:  Lighthouse 

Zara:  Church  tower 

Blanche  Point:  Lighthouse 

Zara  Vecchia :  Church  tpwer 

Port  Tajer:  Lestrice  I.  light 

Lucrietta  Island :  Lighthouse 

Sebenico:  Mount  Tartaro 

6  10 

0  20 

LO 

0.3 

Rogosnizza  Port:  Mulo  Rock  light 

Zirona     Gitinde     Island:     St.     George 
Chiirch  tower 

Trani:  Cathedral  tower 

...... 

Port  Spalato:  Cathedral  tower 

Solta  I.,  Port  OHvetto:  St.  Nicholas  tower 
Spalato  Passage :  Spec  Pt.  light 

Makarska;  Chturch  tower 

Porno  Rock :  Center 

St.  Andrea  Rock:  Summit 

Lissa  Island :  Hoste  Rock  light 

4  00 

10  30 

2.4 

0.7 

Pakon jidol  Rock :  Lighthouse 

Lesina  Island :  Port  Gelsa  light 

St.  Giorgio  Pt.  light 

Sabioncello    Peninsula:    Cape    Gomena 
light 

Sorelle  Rocks:  Lighthouse 

Curzola  Island:  Porto  Bema  mole  head. 
Porto    Valle      Grande, 
church  tower 

Lagostini  Island:  Glavat  Rock  light 

T/flgosta  Island :  St.  George  Chapel 

Cazza  Island :  Lighthouse 

Pelagosa  Rock :  Lighthouse 

Meleda  Island :  Port  Palazzo  Ruin 

Olipa  Rock :  Lighthouse 

Pettini  di  Ragusa  Rocks:  Lighthouse 

Bobara  Rock :  Summit 

Molonta  Peninsula:  Summit 

Ostro  Point:  Lighthouse 

Cattaro:  Health  office 

Budua:  Mole-head  light 

Katie  Rock:  St.  Domenica  Chapel 

Antivari:  Pt.  Valovica  light 

Dulcigno:  W.  windmill 

Cape  Rodoni:  Guardhouse 

Cape  Pali:  Guardhouse 

Durazzo :  Lighthouse 

Cape  Laghi:  Ruin 

Skumbi  River :  Pyramid  at  mouth 

Semeny  River:  Samana  Pt.  light 

Vojazza  River:  Pyramid  at  mouth 

Avlona:  Lighthouse 

CapeLinguelta:  Extreme 

Mount  Cica:  Pyramid 

Port  Palermo:  Pyramid 

Cape  Kiefali:  Pyramid 

' 

il 


APPENDIX   IV.                                     [Page  319 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITEKBANEAN,  ADBIATIC,  AND  BLACK   SEAS— Continued. 

1 

Place. 

I.at.  N. 

Long.  E. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

0 

Saseno  Island :  Lighthouse 

t           1           K 

40  30  12 
39  51  53 
39  39  27 
39  29  50 
39  16  32 
39  39  54 
39  37  05 
39  11  30 
38  56  30 
38  47  25 
38  40  40 
38  22  04 
38  11  36 
38  15  00 
37  38  20 
37  47  10 

37  15  12 
37  03  38 
36  54  10 
36  48  40 
36  47  50 
36  57  20 
35  28  55 

35  20  30 

36  29  40 

36  34  25 
36  15  20 
36  40  27 

36  59  12 

37  06  32 
37  00  01 

37  08  38 
37  26  12 
37  07  36 
37  25  55 
37  38  00 
37  39  28 
37  44  00 
37  57  30 

36  47  05 

37  18  42 
37  31  45 
37  44  30 
37  56  14 
37  58  21 
37  38  45 

37  52  48 

38  01  28 

38  28  15 

39  10  48 

40  37  28 
39  52  10 
39  50  52 
39  31  58 
39  12  35 

39  06  10 
39  03  20 
38  32  00 

9         t        n 

19  16  15 

19  26  06 

20  07  12 
20  17  09 
20  24  55 
19  43  09 

19  56  30 

20  12  34 
20  45  40 
20  44  16 
20  42  44 
20  43  37 

20  29  30 

21  43  50 
21  18  55 

20  55  26 

21  01  14 
21  34  35 
21  40  29 
21  42  40 
21  58  00 

21  56  42 

24  09  39 

25  09  44 

26  59  25 

26  24  28 
25  13  00 
24  23  15 

24  40  30 

25  23  00 
25  14  21 

25  14  08 
24  56  14 
24  32  23 
24  23  35 
24  44  32 
24  19  44 
24  04  12 
24  42  30 
23  05  40 
23  08  53 
23  25  45 
23  25  30 
23  38  10 

23  43  14 

24  02  15 
24  03  00 

24  16  42 
23  36  45 

23  27  07 

22  58  00 

25  03  20 

25  14  14 

24  59  13 

25  50  00 

26  34  54 

26  31  39 
25  35  00 

A.     TO. 

ft.      TO. 

n. 

ft. 

Fano  Island :  Pt.  Kastri  light 

Port  Pagonia:  Ruin 

Port  Gomenitza:  Well  Dogana 

Port  Parga:  Madonna  I 

Port  St.  Spiridione:  Convent 

Corfu:  Lighthouse 

Paxo  Island:  Madonna  I.  light 

Prevesa;  Fort  Nuovo  minaret 

Port  Drepano:  Observation  island 

Port  Vliko:  Customhouse 

Port  Vathi:  Lazaretto  light 

Port  Argostoli:  St.  Theodore  light 

Patras:  Lighthouse 

3  40 

9  53 

LO 

0.3 

Katakolo:  Lighthouse 

Zante:  Mole  light 

Strovathi,  or  Strivali  Island:  Stamphani 
I.  light 

Proti  Passage:  Marathon  Pt 

Navarin :  Lighthouse 

Mothoni :  Rotmd  tower 

Koroni  Anchorage:  Mole  light 

Petalidi  Bay:  Petalidi  Pt 

Candia  Island,   Port  Suda:  Lighthouse. . . 

Megalo    Kastron:    Mole 

&ht 

Kandeliusa  Island :  Lighthouse 

Stampali  Island,  Maltezana  Port:  Agios 
loanes 

Christiana  Islands:  N.  pt 

Milo  Island:  Summit,  Mt.  St.  Elias 

Siphano  Island:  Lighthouse 

Naxos  Island,  Naxia:  Gate  on  Bacchus  I. 
Pares  Island,  Port  Trio:  Trio  Pt 

Port    Nausea:    St.    Yanni 
Church 

Syra:  Mole  light 

Sermo  Island:  Amyno  Pt 

Thermia  Island:  Ruins  of  Cythnus 

Jura  Island :  North  pt 

Port  St.  Nikolo:  Lighthouse 

St.  Nikalao  Island:  Port  Mandri 

Andros  Island,  Cape  Fasse:  Lighthouse... 
leraka:  Acropolis 

Port  Kheli:  Lighthouse 

Poros  Island :  Lighthouse 

^gina:  Lighthouse 

Pira>us :  Lighthouse 

Athens:  National  Observatory 

Cape  Colonna:  Extreme 

Port  Raphti:  Statue  I 

Petali  Island:  Trago  I.  peak 

Skiathos  Island:  Moimt  Stavros 

Salonika:  S.  bastion 

IjCmnos  Island :  Kastro  Castle 

Port  Moudros:  Sangrada  Pt 

Strati  Island:  St.  Strati  Church 

Mi tyleni  Island,     PortSigri:  Lighthouse. 
Mityleni :  Light  on  Mit- 
yleni  Pt 

Portlero:  Sidero  Islet. 
Psara  Island*  Fort 

_ 

Page  320]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE   MEDITEBRANEAN,  ADBIATIC,  AND    BLACK   SEAS— Continued. 


Place. 


Port  Baklar:  Cape  Xeros 

Port  Isene:  Tower 

Samoa  Island:  Fonia  Pt.  light 

Tchesm^:  C.  Kecil  light 

Kos:  Lighthouse 

Marmorice  Harbor:  Adassi  Pt.  light. 

Makry  Harbor:  Kasil  I 

Rhodes  Port:  Arab's  Tower  light 

Port  Lindo:  Tower 

Dardanelles:  Hellas  Pt.  light 

Gallipoli:  Lighthouse 

Bosphorus :  Tofana  Pt.  light 

Scutari:  Leander  Tower  light 

Constantinople:  Seraglio  Pt.  light.. 

St.  Sophia  Mosque. 

Cape  Kara  Bumu :  Lighthouse 

Yuiada  Road :  Fort  Tersana 

Burghaz :  Lighthouse 

Varna  Bay :  Lighthouse 

Kusterjeh:  Cape  Kusterjeh  light.  . . 

Danube  River:  Salina  light 

Fidonisi  Island :  Lighthouse 

Odessa:  University  Observatory 

Nikolaieff :  Naval  Observatory 

Dnieper  Bay:  Fort  Nikolaeo  light. . 

Sebastopol :  E.  lidithouse 

Balaklava  Bay :  Hospital 

Kertch :  Lighthouse 

Berdiansk:  Breakwater  light 

Saukhoum :  Lighthouse 

Batoum:  Lighthouse 

Trebizond :  Lighthouse 

Sinope:  Lighthouse 

Bender  Erekli :  Lighthouse 

Marmora  Island :  Light  off  E.  pt 

Artaki  Bay:  Zeitijn  Adasi  Islet 

Tenedos  Island:  Ponente  Pt.  light. 

Port  Ajano:  Nikolo  Rock 

Port  Ali-Agha:  W.  pt.  of  entrance.. 
Smyrna:  English  consulate  flagstaff 

Vourlah:  Customhouse 

Sighajik  Harbor:  Beacon  on  islet. . 

Budrum :  Lighthouse 

Adalia:  Lighthouse 

Alexandretta:  Lighthouse 

Latakia:  Lighthouse 

Tripoli  Roadstead :  Bluff  Islet  light 

Ruad  Island :  Lighthouse 

Beirut:  Lighthouse 

Saida  (ancient  Sidon) :  Lighthouse. 
S<ir  (ancient  Tyre):  Lighthouse. . . 

Acre :  Lighthouse 

Haifa :  Lighthouse 

Famagusta:  Lighthouse 

C.  Gata:  Light 

Lamaka:  Lighthouse 

Port  Said :  High  lighthouse 

River  N  ile :  Damietta  Mouth 

Rosetta  Mouth  light.  . . 

Aboukir  Bay:  Nelson  I.  peak 

Alexandria:  Eunostoa  Pt.  light 


Lat.  N. 


32  40 
16  33 
41  24 
19  55 
55  00 
48  00 
39  33 

26  00 
05  53 
02  30 

24  27 
01  20 
01  02 
00  35 

00  16 
21  15 

52  04 

27  52 
10  00 
10  20 
09  47 
16  00 

28  37 
58  22 

34  27 
36  55 

29  50 
21  03 
45  00 
58  00 

39  30 

01  00 
01  20 
18  03 
38  10 
23  30 
50  00 

01  21 
50  10 

25  40 
21  48 
12  21 

02  00 
52  00 

35  30 

30  30 
29  25 
52  00 
54  10 
34  20 
16  30 
54  35 
47  40 


35  07  10 
34  33  45 
34  54  00 

31  15  41 
31  31  40 
31  29  30 
31  21  23 
31  11  43 


Long.  E. 


26  45  00 

27  36  55 
26  58  42 

26  17  45 

27  18  25 

28  18  00 

29  06  13 
28  16  24 

28  08  10 
26  10  54 

26  41  24 

29  01  00 
29  00  29 
29  01  14 
28  58  59 
28  42  14 

27  58  45 
27  35  54 

27  58  35 

28  39  14 

29  41  14 

30  14  14 

30  45  32 

31  58  27 
31  33  36 
33  36  26 
33  36  25 
36  28  30 
36  46  40 

40  55  10 

41  38  15 
39  46  25 

35  13  20 

31  25  49 
27  46  09 
27  47  30 

25  58  34 

26  47  57 

26  57  20 

27  09  10 
26  47  00 

26  47  32 

27  27  05 

30  45  34 

36  10  20 
35  46  30 
35  44  24 
35  51  00 
35  28  25 
35  21  30 
35  14  40 
35  08  00 
35  05  00 

33  57  22 
33  01  30 
33  38  59 

32  18  45 

31  51  00 
30  19  10 
30  06  00 
29  51  40 


Lun.  Int. 


H.  AV.    L.  W 


Jl.      TO. 


9  15 


9  45 


9  40 


9  40 


9  45 


3  15 


3  35 


3  30 


3  30 


3  15 


Range. 


Spg.   Neap, 


2.5 


1.2 


1.4 


1.0 


1.1 


0.7 


0.3 


0.4 


0.3 


0.3 


I 


APPENDIX  IV.                                   [Page  321 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE   MEDITBBBANEAJf,  ADBIATIC,  AND  BLACK   SEAS— Continued. 

1 

Place. 

Lat.  N. 

Long.  E. 

Lim.  Int. 

Range. 

n.  W. 

L.  W. 

Spg. 

Neap. 

i 

a 

9 

H 
i 

0 

t 

0 
h 

e 
g 

Ben  Ghazi'  Castle 

32  06  51 
32  54  03 

34  39  01 

35  30  24 

35  45  24 

36  23  20 

36  50  12 

37  04  45 

36  48  19 

37  10  42 
37  16  38 
37  31  16 
36  57  15 

36  54  29 

37  05  17 
36  46  41 
36  47  16 
36  47  50 
36  33  07 

35  44  21 
35  43  22 

35  11  05 
35  58  00 
35  53  44 
35  47  00 

20  02  40 
13  10  50 

10  41  17 

11  05  15 
10  50  42 

10  37  10 

11  07  00 
11  03  15 
10  18  31 

10  17  30 
9  53  21 
8  56  12 
7  46  40 
6  53  11 
6  28  37 
5  06  22 
3  04  13 
3  02  08 
1  20  36 

Long.W. 

0  41  38 

1  07  57 

2  25  45 

3  03  29 
5  16  46 
5  48  31 

h.    m. 

9  55 

10  00 

3  35 

ft.    m. 
3  45 
3  50 

9  57 

ft. 

1.2 

1.9 

4.2 

ft. 
0.3 
0.5 

LI 

Tripoli  Harbor:  Lighthouse 

Sfax  •  Has  Tina  light 

Mphpdiah  •  Sidi  .lubber    .                  .... 

Mouastir"  Burj  el  Kelb  battery 

Hamraamet  Bay:  Castle  flagstaff 

T^nlihia  Tinnd  *  Tjipfhthouse 

Cape  Bon*  Lighthouse 

Tunis :  Goletta  light 

3  33 

9  55 

3.0 

0.8 

Cape  Farina  ■  Extreme 

Bona  •  Fort  Genois  licrht 

Stnra'  SiTifre  T    licht        .    .        

Cape  Carbon  ■  Lighthouse 

Algiers:  Lighthouse  near  Admiralty 

Bouzareah  Observatory 

2  46 

8  58 

2.6 

L3 

Cape  Tenez :  Lighthouse 

Oran  *  Mprs  p1  TCehip  licht 

TTahihsis  Tslflnd  •  T^ifi'ht.noiifle 

Zafarin  Islands:  Light  Isabel  Segunda  I.. 

Ceuta :  Lighthouse 

1  55 
1  30 

8  07 
7  40 

3.3 
8.0 

L5 
3.7 

Tangier:  Casbah  tower 

Cape  Spartel  ■  Lighthouse    .    . .       

35  47  14         5  55  41 

WEST  COAST  OF  AFBICA. 

El  Araish"  S  pt  of  entrance 

35  12  50 
34  04  10 
33  36  00 
33  08  00 
31  30  30 
30  38  00 
28  45  00 
27  56  00 
26  07  57 
25  07  06 
23  36  03 
22  12  37 
20  46  27 
18  18  45 
16  01  31 
14  44  45 
14  43  20 
14  40  30 
14  38  55 
14  39  55 
13  39  45 
13  28  00 
12  35  00 
10  36  37 
M)  03  15 
9  30  30 
9  16  10 
8  57  05 

6  09  13 

6  48  00 

7  33  00 

8  35  05 

9  43  30 
9  50  00 

11  02  00 

12  56  00 
14  29  00 

14  50  44 

15  58  00 

16  48  11 

17  05  40 
16  02  00 

16  30  22 

17  32  25 
17  30  55 
17  25  28 
17  26  47 
17  24  30 
16  40  30 
16  35  00 
16  44  00 
14  42  00 
14  04  30 

13  44  00 
13  26  20 
13  18  25 

Sali:  Fort 

1  35 

7  45 

10.4 

4.8 

Cape  Dar  el  Beida*  Lighthouse 

Cape  Blanco  North*  Extreme 

Mogador  Harbor:  English  consulate 

Cape  Ghir*  Extreme 

1  05 

7  17 

10.9 

5.0 

Cape  Noim  *  Extreme 

Cape  Juby :  Extreme 

11  55 
11  50 

5  43 
5  38 

8.5 
7.3 

3.9 
3.4 

Cape  Bojador:  Extreme 

Ouro  River  entrance :  Dumford  Pt 

Cape  Blanco*  Extreme 

11  35 

5  23 

5.5 

2.5 

Rirrl  Island*  Flagstaff 

Bathurst:  Flagstaff 

9  00 

2  50 

5.9 

2.7 

Ponga  River  entrance:  Observation  Pt 

7  30 

1  20 

11.4 

5.2 

Scarcies  River:  W.  end  of  Yellaboi  I 

1 

i 

21594°— 14- 


-21 


Page  322] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  AFRICA— Continued. 


Place. 


Sierra  Leone:  Light  on  cape 

N.  battery 

Sherbro  Island:  N.  island 

Sherbro  River:  Manna  Pt 

Gallinas  River:  W.  elbow  of  Kamasoun  I. 

Cape  Mount:  W.  peak 

Cape  Mesurado:  Lighthouse 

Monrovia:  Lighthouse 

Marshall:  Agent's  house 

Grand  Bassa:  Agent's  house 

Cestos:  Factory 

Sangwin  River:  Sangwin  Pt 

Sinon:  Bloobarra  Pt 

Cape  Palmas:  Lighthouse 

Tabou  River:  Tabou  Pt 

Axim  Bay:  Ft.  St.  Anthony 

Cape  Three  Points:  Lighthouse 

Dix  Cove:  Fort 

Tacorady  Bay:  Tacorady  Pt 

Chama  Bay:  Dutch  Fort 

ElMinaBay:  Ft.  St.  George 

Cape  Coast  Castle :  Lighthouse 

Accra:  Lighthouse 


Volta  River  entrance:  Dolbens  Pt 

Lagos  River:  Lighthouse 

Benin  River  entrance :  N .  pt 

Brass  River:  Entrance  (approx.) 

Calebar  River  (New):  Rough  Comer 

Opobo  River:  W.  pt.  beacon  (approx.).. . 

Quaebo  River:  Bluff  Pt 

Calebar  River  (Old):  Judicial  Ho.  flagstaff 

(Duke  Town) 

Fernando  Po  Island :  Lighthouse 

San  Bento  River:  Joho  Pt.  (approx.) 

Princes  Island:  Diamond  Rocks,  center 

of  largest 

St.  Thomas  Island:  Ft.  San  Sebastian 

light 


Anno  Bon  Island :  Tiu-tle  Islet 

Cape  Lopez:  Lighthouse 

Mayumba  Bay :  Lighthouse 

Loango  Bay :  Indian  Pt.  light 

Black  Point  Bay:  Sandy  Pt , 

Malemba  Bay :  Landing  Cove 

Kabenda  Bay:  Kabenda  Pt.  light 

Congo  River  entrance:  Shark  Pt 

Mai-gate  Head:  Summit 

St.  Paul  de  Loando:  Flagstaff,  Ft.  San 

Miguel 

Lobito  Point:  Extreme 

Benguela :  Telegraph  office 

Elephant  Bay :  Fnar  Rocks 

St.  Mary  Bay:  Bay  I 

Little  Ush  Bay:  Lighthouse 

Port  Alexander:  Bateman  Pt 

Great  Fish  Bay:  Tiger  Pt 

Cape  Frio:  Extreme 

Walfisch  Bay :  Lighthouse 

Ichabo  Island 

Angra  Pequena:  Diaz  Pt 

Elizabeth  Bay:  S.  pt.  of  Possession  I 


Lat.  N. 


8  30  00 

8  29  57 

7  40  36 

7  22  45 

7  00  08 

6  44  30 

6  19  10 

6  19  00 

6  08  06 

5  54  08 

26  25 

12  42 

59  15 

22  10 

24  47 

52  18 
4  45  00 
4  47  45 

53  00 
01  00 
04  48 
06  20 
31  50 


5  46  00 

6  25  15 
5  46  01 
4  16  40 
4  23  07 
4  27  00 
4  30  40 


4  57  53 
3  46  10 
1  35  00 

1  40  42 

0  20  30 

Lat.  S. 

1  24  18 
0  36  25 

3  23  00 

4  40  00 

4  49  00 

5  18  30 

5  32  30 

6  04  36 
6  31  50 

8  48  24 
12  20  00 

12  34  43 

13  12  30 
13  26  05 
15  09  00 

15  47  30 

16  30  00 
18  23  00 
22  57  00 
26  17  00 
26  37  52 
26  58  30 


Long.  W, 


13  18  30 
13  14  30 
13  04  30 
12  31  55 
11  38  45 
11  22  51 
10  49  25 
10  50  00 
10  22  45 
10  04  05 
9  34  45 

20  16 
02  05 

44  15 

21  30 
14  45 
05  45 
56  40 

45  00 
38  00 
21  05 
13  50 


0  11  30 

Long.  E. 
0  41  00 
3  25  15 

5  03  05 

6  15  00 

7  07  00 
7  40  00 

7  59  00 

8  18  57 

8  47  05 

9  39  00 

7  27  56 
6  42  45 

5  38  12 

8  43  10 

10  38  00 

11  46  30 

11  45  00 

12  08  00 
12  11  00 

12  15  00 
•12  25  25 

13  13  20 
13  32  00 

13  23  45 
12  48  55 
12  36  00 
12  12  00 
11  52  40 
11  42  00 
11  57  12 

14  30  00 

14  57  20 

15  07  02 
15  12  22 


Lun.  Int. 


Range. 


H.  W. 


h.    m. 
7   40 


5  50 


5  40 


L.  w. 


ft.  m. 
1  30 


ft. 
1L6 


12  00 


10.4 


11  54 


4  50   11  05 
4  30   10  43 


4  00   10  13 


4  20 


4  25 
4  13 


4  10 


3  40 

's'so" 


2  35 


10  32 


4  20   10  33 
4  50   11  05 


10  38 
10  26 


10  25 


9  53 
'9'43' 


3  00    9  12 


8  47 


6.0 


4.8 
4.3 


4.7 


6.0 


4.2 
3.3 


7.0 
6.5 


6.0 


4.8 
'5.5' 


5.7 


5.5 


APPENDIX   IV.                                     [Page  323 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
WJSST  COAST  OF  AFRICA— Continued. 

^ 

Place. 

Lat.S. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.W. 

L.W. 

Spg. 

Neap. 

North  Nolloth :  Magistrate's  house 

Hondeklip  Bay 

0        r        » 

29  15  12 

30  18  33 
30  33  07 
33  07  51 
33  48  52 

33  56  04 

34  21  12 

16  52  02 

17  16  20 

17  27  30. 

18  01  21 
18  22  33 
18  28  41 
18  29  26 

ft.    m. 

2  25 

ft.    m. 
8  38 

ft. 
5.3 

ft. 
2.2 

Roodewaf  Bay 

Saldanha  Bay:  Constable  Hill 

2  20 

8  33 

5.1 

2.1 

Table  Bay:  Robben  I.  light 

Cape  Town ;  Royal  Observatory 

1  36 

7  47 

4.6 

2.0 

Cape  of  Good  Hope :  Lighthouse 

EAST  COAST  OF  AFRICA  AND  TITR  RED  SEA. 

Simons  Bay :  Lighthouse 

34  10  45 
34  23  48 
34  46  45 
34  49  45 
34  23  47 
34  11  10 
34  04  35 
34  06  15 
34  12  30 
34  01  41 
33  57  43 
33  50  27 
33  36  09 
33  28  00 
33  23  10 
33  05  10 
33  01  45 
32  42  00 
32  02  30 
31  48  15 
31  38  06 
31  26  15 
29  52  40 
29  50  47 
29  00  12 
28  32  30 
28  09  36 

25  58  30 
24  05  30 
23  45  30 
22  05  00 
21  31  00 
20  38  10 
20  10  42 
18  52  50 
18  01  24 
17  51  50 
17  15  00 
17  06  30 
16  33  24 
16  20  30 
15  08  00 
15  02  12 
15  00  45 
14  58  20 
14  53  00 
13  23  40 
12  55  45 
12  19  30 
11  09  18 

18  27  30 

18  50  20 

19  38  17 

20  00  37 
20  48  40 

22  09  31 

23  03  38 

23  24  23 

24  50  20 

25  42  12 

25  37  21 

26  17  13 

26  54  10 

27  03  00 
27  20  48 
27  49  12 

27  55  02 

28  22  36 

2  35 

8  48 

5.2 

2.2 

Cape  Hangklip :  Extreme 

Quoin  Point:  Extreme 

Cape  Agulhas:  I/ighthouse 

2  40 

8  53 

5.2 

2.2 

Port  Beaufort:  Flagstaff 

St.  Blaize:  Lighthouse 

3  18 

9  31 

5.6 

2.0 

Knysna  Harbor :  Fountain  beacon 

Plettenberg  Bay:  Summit  of  Seal  Pt 

St.  Francis:  Lighthouse 

Cape  Recife:  Lighthouse 

Port  Elizabeth:  Lighthouse 

3  21 

9  33 

5.4 

L9 

Bird  Islands:  Lighthouse 

Port  Alfred :  Signal  staff 

Waterloo  Bay:  Maitland  Signal  Hill 

Madagascar  Reef :  Center 

Cove  Rock :  Center         

East  London:  Lighthouse 

3  37 

9  50 

5.0 

L8 

Cape  Morgan:  Extreme 

Hole-in-the-Wall           

29  06  40 
29  21  15 
29  33  16 

29  48  40 

31  03  41 

30  00  18 

31  51  39 

32  27  39 

32  38  10 

32  35  55 
35  29  45 
35  31  41 
35  29  00 

Rame  Head :  Extreme.           

Cape  Hermes:  Extreme 

Waterfall  Bluff 

Port  Natal  (Durban) :  Lighthouse 

3  58 

10  11 

5.6 

L6 

Govt.  Observatory 

Dimiford  Point:  Extreme 

Cape  St.  Lucia:  Extreme 

Cape  Vidal :  Extreme 

Delagoa  Bay:  Pta.  Vermelha  (Reuben 
Pt.)  light 

5  10 

11  22 

n.9 

3.4 

Cape  Corrientes:  Small  rock 

Innamban  Bay:  Barrow  Hill  light 

Cape  St.  Sebastian:  Extreme 

4  30 

10  42 

n.o 

3.2 

Bazaruto  Island:  N.  pt.  light 

35  29  30 
34  53  30 
34  46  00 

36  11  47 

36  58  30 

37  01  09 

38  04  00 

Chuluwan  Island :  Lighthouse  

Sofala:  Fort  on  N.  side  of  entrance 

Zambesi  River:  Kangoni  Mouth 

4  15 

10  27 

13.5 

3.9 

Kiliman  River:  Lighthouse 

Kiliman :  Town 

« 

Mazemba  River:  Entrance 

Premeira  Islands:  Center  of  Casuarina  I.. 

Angoxa  Islands:  Center  of  Hurd  I 

Mafamale  Island:  Center 

39  06  27 

39  49  57 

40  03  57 
40  36  12 
40  48  45 
40  45  06 
40  45  10 

Port  Mokambo:  Mokambo  Pt 

Port  Mozambique:  St.  George  I.  light 

San  Sebastian  fight. . . 
Cape  Cabeceira:  Lighthouse 

4  00 

10  12 

n.8 

3.4 

Port  Conducia:  Bar  Pt 

40  40  00 
40  46  00 
40  31  15 
40  40  09 
40  43  21 

Lurio  Bay:  Pando  Pt 

PembaBay:  N  pt.  light                  

Querimba  Islands:  Ibo  I.  light     

Numba  Island:  E.  pt  

Page  324]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  AFRICA  AND  THE  BED  SEA— Continued. 


Place. 


Cape  Delgado:  Lighthouse 

Msimbati :  Has  Matunda 

Mikindini  Harbor:  Kinizi 

Mgan  Mwania:  Madjori  Rock 

Lindi  River:  Fort  flagstaff 

Mchinga  Bay:  Observation  spot 

Easwere  Harbor:  Rustmigi 

Kilwa  Kisiwani :  Fort 

Mafia  Island:  Moresby  Pt 

Dar-Es-Salaam:  Flagstaff 

Bagamoyo:  French  Mission 

Zanzibar:  English  consulate 

Tanga  Bay:  Lighthouse 

Mombasa:  Lighthouse 

Port  Melinda:  Vasco  de  Gama's  Pillar — 

Lamo  Bay:  Lamo  Castle 

Manda  Roads:  E.  side  of  Manda  To  to  I. . 

Port  Dumford:  Foot  Pt 

Kisimayu  Bay:  S.  pt.  of  Kisimayu  I 

Brava:  Well 

Meurka  Anchorage:  S.  pt.  of  town 

Magadoxa:  Tower 

Murat  Hill :  Peak 

Ras  Hafun:  E.  extreme  of  Africa 

Cape  Guardafui:  E.  pt 

Kal  Farun  Islet:  Center 

Abd-al-Kuri  Island:  NE.  pt 

Sokotra  Island:  Tamarida,  mosque 

Ras  Antareh:  Extreme  of  rocky  pt 

Mait  Island:  Center 

Port  Berbera:  Lighthouse 

Zeyla:  Mosque 

Perim  Island:  Lighthouse 

Hanfelah  Bay:  Hanfelah  Pt 

Disei  Island:  Village  Bay 

Massaua  Harbor:  N.  pt.  of  entrance 

Kh6r  Nowarat:  Shatireh  Islet 

Suakin:  Lighthouse 

Makaua  Island:  S.  pt 

St.  Johns  Island:  Peak 

Daedalus  Shoal:  Lighthouse 

Kosair  Anchorage:  SW.  angle  of  fort 

Brothers  Island :  Lighthouse 

Safajah  Island:  N.  summit 

Ashrafi  Island :  Lighthouse 

Ras  Gharib:  Lighthouse 

Zafarana:  Lighthouse 

Suez :  Newport  Rock 

Tor:  Ruined  fort 

Sherm  Yahar:  Entrance 

Sherm  Joobbah:  Entrance 

Sherm  Wej :  Lighthouse 

Sherm  Hassey :  Anchorage 

Yemb6:  Anchorage 

Sherm  Rab^h:  Anchorage 

Jiddah:  Jezirah  el  Mifsaka  I 

Lith:  Agha  Islet 

Jelalil :  Anchorage 

Kunfidah :  Islet 

Khor  Nohud:  Entrance 


Lat.  s. 


41  20 
19  22 
16  31 
06  43 
59  30 
44  22 

25  36 
57  15 
38  10 
49  41 

26  10 
09  43 
00  35 
04  30 

12  48 
15  42 

13  35 
13  00 
22  35 


Lat.  N. 
1  06  48 

1  42  06 

2  01  48 
2  30  00 

10  26  30 

11  50  30 

12  26  00 
12  11  15 
12  39  00 
11  27  30 
11  13  00 

10  25  00 

11  22  00 

12  39  00 


44  00 
28  10 

37  12 
15  12 
07  00 

44  00 
36  20 
56  30 
06  24 
18  50 

45  48 
47  21 
20  52 

06  29 
53  05 
13  47 
35  45 
33  00 
13  00 

38  35 
05  15 
43  50 
28  00 
09  00 
55  30 

07  40 
15  50 


Long.  E. 


40  38  35 
40  26  34 
40  10  33 
40  02  14 
39  46  41 
39  47  07 
39  39  31 
39  30  42 
39  54  42 
39  17  05 

38  54  27 

39  11  08 
39  10  20 

39  41  13 

40  11  21 
40  56  21 

40  59  40 

41  54  15 

42  33  57 


44  03  27 

44  53  49 

45  24  39 

46  07  00 
51  22  55 

51  16  45 

52  09  35 

52  25  35 

53  59  31 
49  35  40 

47  17  00 
44  59  35 
43  29  35 
43  25  35 

40  52  00 
39  45  30 
39  27  23 
38  19  30 
37  19  09 
37  15  30 
36  10  15 
35  51  00 
34  17  03 

34  50  45 
33  59  43 
33  42  28 
33  06  31 
32  39  43 

32  32  50 

33  36  56 

35  30  30 

35  32  30 

36  27  00 

37  17  45 

38  02  45 

39  00  30 

39  10  38 

40  12  00 

40  30  00 

41  03  20 
41  27  30 


Lim.  Int. 


Range. 


H.  W. 


ft.  m. 
3  59 


3  55 


4  05 


4  30 


4  15 


6  00 


7  30 
7  50 


0  45 

2  io 


6  40 


10  35 
10  40 
10  45 


3  30 


L.W, 


Spg. 


ft.  m. 
10  11 


ft. 
11.3 


10  08 


10.9 


10  17 


14.5 


4  00   10  13 


12.1 


10  42 


n.7 


10  27 


7.5 


12  12 


6.1 


7.5 


1  18 
1  38 


8.5 

7.2 


6  57 
'8"22" 


4.0 

'i.'?" 


0  28 


2.0 


4  23 

4  28 
4  32 


L5 
5.5 
6.8 


9  42 


2.0 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  AFBICA  AND  THE  RED  SEA— Continued. 


[Page  325 


Place. 


Farisan  I.  Anchorage:  Jebel  Mandhakh 

Gizau :  Fort 

Ivbheiya:  Hill  Fort 

Kamardn  Bay:  Harbor 

Hodeida  Road 

Jebel  Zukur  Island:  N.  pt 

Mokha:  N.  Fort 


Lat.  N. 

o    /    » 

16  50  15 
16  53  00 
15  42  00 
15  20  30 
14  47  00 
14  03  53 
13  19  43 

Long.  E. 


41  58  15 

42  29  00 
42  38  45 
42  34  00 
42  56  00 

42  45  28 

43  13  36 


Lun.  Int. 


Range. 


H.  W.        L.  W 


h.   m. 


1  15 


11  45 


Spg.       Neap. 


h.   m. 


ft. 


7  27 


2.9 


ft. 
"i.'2 


5  33 


4.5 


1.9 


ISULNDS  OF  THE  INDIAN  OCEAN. 


Chitlac  Islet:  S.  end 

Betrapar  lelet:  N.  Island 

Kittan  Islet:  S.  end 

Cardamum  Islet:  Center 

Ameni  Islet:  N.  end 

Underut  Islet:  Center 

Cabrut  Islet:  E.  end 

Seuheli  Par:  N.  islet 

Kalpeni  Islet:  S.  end 

Mimkoi  Island:  Lighthouse 

Heawandu  Island:  S.  end 

Kee-lah  Island :  N.  end 

Mah  Kundu  Island:  NE.  extreme 

Nar  Force  Island 

Hee-tah-doo  Island 

To-du  Island:  Center 

Gafor  Island :  Center 

Mal6,  or  Kings  Island :  Flagstaff 

Pha-li-du  Island:  Northern  end 

Moluk  Island :  Center 

Himmittee  Island 

Kimbeedso  Island:  S.  end 

Esdu  Island:  NE.pt 

Wahdu  Island:  E.  end 

Addu  Atoll:  Gung  I 

Amirante  Islands:  He   des   Roches,    N. 

beach 

African  Islands 

Seychelles,  Platte  I. :  S.  end 

Port  Victoria:  EndofHodoul 

Jetty 

Bird  Island:  Tree 

Chagos  Archipelago,  Peros  Banhos:  Dia- 
mond Islet 

Diego  Garcia:  N.  end 

of  Middle  I 

Cargados  Carajos:  Establishment  I.,  flag- 
staff  

Rodriguez  Island:  Mathxirina  Bay,  Point 
Venus 

Flat  Island:  Lighthouse 

Cannonier  Point:  Lighthouse 

Port  Louis:  Martello  tower,  Ft.  George... 

Royal  Alfred  Obsy 

Grand  Port:  Fouquet  I.  light 


11  40  45 
11  35  00 
11  27  30 
11  13  00 
11  06  00 
10  47  00 
10  32  00 
10  06  00 
10  03  00 
8  16  00 


6  55  00 
6  59  00 
6  25  00 
5  26  30 
01  30 
25  45 
44  00 
10  15 
41  00 
57  00 
16  00 
10  30 
07  00 


5 
4 
4 
4 
3 
2 
3 
2 
2 
0  14  30 


Lat.S. 
0  41  30 


5  40  56 

4  52  26 

5  53  00 

4  37  15 
3  43  06 

5  15  00 
7  13  37 

16  25  12 
19  40  22 

19  52  36 

19  59  45 

20  08  46 
20  05  39 
20  24  20 


72  42  54 
72  09  54 
72  59  00 
72  44  00 

72  41  00 

73  40  00 
72  37  40 

72  15  10 

73  35  54 
73  01  15 

72  55  54 

73  12  54 

72  41  54 

73  20  00 
72  53  00 

72  57  24 

73  28  00 
73  30  24 
73  24  54 
73  34  24 

72  48  00 

73  03  00 
73  35  54 
73  13  00 

73  06  54 


53  41  03 
53  23  38 
55  27  10 

55  27  23 
55  12  19 

71  43  47 

72  23  50 

59  46  40 

63  25  38 

57  39  14 
57  32  35 
57  29  26 
57  33  09 
57  47  14 


10  20 


11  27 


0.20 


4  22 


1  30 
1  50 
0  20 


0  48 


4  00 


6.3 


3.0 


5  15 


2.5 


L2 


6  25 


2.9 


L4 


10  35 


4.3 


L2 


7  43 

8  03 
6  32 


5.8 
4.0 
5.5 


L7 
L2 
1.6 


7  00 


L6 


0.3 


Page  326]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  INDIAN  OCEAN— Continued. 


Place. 


Reunion  Island :  St.  Denis  light 

Bel-Air  light 

St.  Paul  light 

St.  Pierre  light 

Tromelin  Island:  N.  end 

Agalegas  Island:  NW.  pt 

Farquhar  Islands:  Hall's  house 

Alphonse  Island:  SE.  part  (Trees) 

Coetivy  Island :  N.  end 

Cape  St.  Mary:  S.  extreme 

Leven  Island:  Center 

Port  Machikora:  Barracouta  I 

St.  Augustine  Bay:  Nosi  Vei  I 

Murderers  Bay:  Center  of  Murder  I 

Cape  St.  Vincent:  Extreme 

Mourondava:  Village 

Tsmano:  Village 

Kovra  Rythi  Point:  Extreme 

Coffin  Island :  Nosi  Vao 

Cape  St.  Andrew:  Extreme 

Boyanna  Bay:  Barabata  Pt 

Cape  Tauzon:  Extreme 

Majunga  (Mojanga) :  Lighthouse 

Majamba  Bay:  W.  pt 

Narendri  Bay:  Moormora  Pt 

Port  Radama:  Pt.  Blair '. 

Radama  Islands:  N.  pt.  Nossuvee  I. . . . . 

Baratoube  Bay:  Ambubuka  Pt 

Nosi  Be:  Hellville  Jetty 

Minow  Islands:  N.  pt.  Great  I 

Cape  San  Sebastian:  Extreme 

Port  Liverpool:  N.  pt.  of  entrance 

Cape  Amber:  NE.  extreme 

Port  Lady  Frances:  Sunson  Pt 

Port  Looke:  Pt.  Bathurst 

Port  Leven:  S.  pt.  Nosi  Hau  I 

Andrava  Bay:  Berry  Head 

Vohemar:  Flagstaff 

Cape  East:  Ugoncy  I 

Venangue  Be  Bay :  Entrance 

PortChoiseul:  Maran  Seelzy  Village. ... 

Cape  Bellone:  Extreme 

St.  Marys  Island :  Light  on  Madame  I 

Port  Tantang:  Flagstaff 

Fenerive  Pomt:  Flagstaff 

Tamatave:  Pt.  Hastie 

Mahanuru:  Town 

Matatane:  Village 

Santa  Lucia:  N.  end  of  town,  Obs.  Rock. 

Point  Ytapere:  Extreme 

Ytapere  Bay:  N.  pt 

Fort  Dauphin:  Flagstaff 

Europa  Island:  Center 

Bassaa  da  India:  E.  pt 

Geyser  Reef:  SE.  extreme 

Mayotta Island:  Zaoudzi 

Johanna  Island:  Landing  place,  Pomoni 

Harbor 

Mohilla  Island:  Numa  Choa Harbor 

Glorioso  Islands:  W.  islet 

Comoro  Island :  Islet  in  Mauroni  Bay 

Assumption  Island:  Hummock 


Lat.  S. 


20  51  38 
20  53  11 

20  59  45 

21  19  47 

15  51  37 
10  21  30 

10  06  45 
7  00  30 
7  06  00 

25  39  10 
25  12  30 
25  03  00 

23  38  25 

22  05  18 
21  54  24 

20  18  18 
19  49  30 
17  53  00 
17  29  00 

16  12  10 
16  07  00 
15  46  30 
15  43  45 
15  11  42 

14  40  18 
13  59  00 
13  55  40 
13  27  15 
13  23  38 
12  49  30 
12  27  20 
12  03  18 

11  57  30 

12  23  20 
12  44  02 
12  49  00 

12  56  48 

13  81  15 

15  15  48 
15  54  50 

15  27  55 

16  14  00 

17  00  05 

16  42  30 

17  23  16 

18  09  47 

19  55  00 

21  58  10 

24  46  25 
24  59  42 

24  58  50 

25  01  30 

22  22  30 
21  29  00 
12  26  30 
12  47  02 

12  16  20 
12  25  00 
11  34  48 
11  40  44 
9  46  20 


Long.  E. 


55  26  59 
55  36  18 
55  16  18 

55  28  58 
54  28  46 

56  32  00 

51  10  21 

52  44  57 
56  22  00 

45  06  50 
44  17  57 
44  07  20 
43  38  20 
43  15  20 

43  20  21 

44  19  21 
44  31  30 
44  02  20 

43  45  18 

44  29  05 

45  17  09 

45  43  09 

46  18  45 

46  57  29 

47  24  36 
47  58  21 
47  48  05 

47  59  30 

48  17  34 
48  38  57 

48  45  45 

49  11  21 
49  17  25 
49  35  56 
49  45  06 
49  54  00 

49  56  25 

50  01  59 
50  31  21 
50  16  05 
49  49  11 
49  50  59 
49  50  59 
49  56  15 
49  32  04 
49  25  31 
48  52  10 
48  14  50 
47  10  34 
47  07  20 
47  04  24 
46  59  11 

40  24  10 
39  40  39 

46  32  35 

45  16  27 

44  24  54 
43  47  00 

47  24  09 
43  19  15 

46  31  07 


Lun.  Int. 


Range. 


H.  W.    L.  W. 


Spg.   Neap. 


h.    m. 


ft. 


ft. 


11  50 


5  38 


3.5 


0.6 


5  40 


11  52 


9.8 


2.9 


4  15 


11  28 


10.9 


3.2 


3  45 


9  57 


5.1 


L5 


4  00 


10  12 


7.3 


2.1 


4  15 


10  27 


4.7 


L3 


4  00 


10  13 


n.9 


2.0 


4  45 


10  58 


10.0 


1.7  I 


APPENDIX  IV.                                     [Page  327 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OP  THE  INDIAN  OCEAN— Continued. 

« 

M 
h 

g 

i 

m 

e 
1 

h 

e 
M 

Place. 

Lat.  S. 

Long.  £. 

Lun.  Int. 

1 

Range.         1 

H.W. 

L.W. 

Spg. 

Neap. 

Aldabra  Island:  West  I.,  E.  side  entrance 

Cosmoledo  Islands:  Observation  islet 

Prince  Edwards  Islands:  Marion  I.,  Obs. 
spot,  NE.  side 

o            /            # 

9  22  35 
9  41  20 

46  49  30 

46  36  00 
46  22  00 
46  01  00 
46  28  18 
46  10  40 
46  26  00 

48  40  00 

48  26  45 

49  42  00 

49  21  22 
49  41  00 
49  29  00 

53  02  45 
53  13  00 
53  02  50 
38  42  51 
37  50  00 
12  06  22 
10  25  19 

•      f      » 

46  14  52 

47  32  25 

37  49  15 

50  41  30 

51  30  15 

50  40  00 

51  50  00 
50  35  00 

52  13  00 

69  04  00 
68  48  20 
68  54  00 

70  04  31 
70  15  00 
70  29  50 

73  15  30 
73  52  00 
72  31  45 
77  31  53 
77  29  15 
96  53  02 
105  45  57 

h.    m. 

ft.    m. 

ft. 

ft. 

Penguin  Islands  Center  of  SW.  islet 

Possession  Island:  NW.  pt.  .  » 

Twelve  Islands:  Summit  NE.  I 

Navire  Bay 

Hog  Island:  Summit 

East  Island :  Center 

Christmas  Harbor 

Blighs  Cape 

Cape  Bourbon 

Molloy,  Port  Royal  Sound:  U.  S.  Tr.  of 
Venus  Obs  ,  1874 

0  14 

6  36 

4.6 

L3 

Cape  Challenger 

Balfour  Rock 

Heard  Island:  Cape  Laurens,  NW.  end. . . 
Sealing  station 

McDonald  Island,  Sumpiit 

St.  Pauls  Island:  Ninepin  Rock 

Amsterdam  Island:  Summit,  2,750  feet. . . 

Keeling  or  Cocos  Islands :  Direction  I 

Christmas  Island :  Flying  Fish  Cove 

10  40 

10  50 

5  20 

7  10 

4  28 

4  38 

11  32 

1  00 

3.0 
3.3 
5.1 
4  5 

0.9 
LO 
L5 
L3 

SOUTH  COAST  OF  ASIA. 

5 

Aden:  Telegraph  station 

Lat.  N. 

12  47  16 

13  22  00 
13  24  50 

13  28  45 

14  20  10 
14  31  15 
14  43  50 
14  49  00 

14  54  40 

15  12  00 

15  38  00 

16  30  00 

16  59  00 

17  32  45 
17  53  15 

19  00  25 

20  10  00 
20  31  30 

22  32  40 

23  38  00 
23  52  00 

23  51  30 

24  21  50 

25  21  00 

26  24  13 
26  30  00 
25  21  34 

24  29  02 

25  17  24 

26  10  55 
26  13  56 
30  32  00 
29  22  56 

44  59  07 

45  40  50 

46  26  35 

46  39  00 

48  56  45 

49  07  35 
49  35  05 

49  57  05 

50  16  35 

51  10  30 

52  14  20 
52  48  00 

54  43  29 
56  03  05 

56  20  35 

57  51  35 

58  38  35 

58  58  35 

59  48  35 
58  30  50 
58  08  00 
57  26  00 
56  46  12 
56  22  56 
56  32  22 
56  31  29 

55  24  12 
54  22  14 
51  33  32 
51  13  46 
50  31  18 

47  51  23 

48  00  55 

7  49 

1  41 

4.9 

2.0 

Sughra:  Sheik's  house 

Mokatein:  Black  ruin 

Howaiyuh:  Sheik's  house 

Banderburimi:  SE.  house  of  town 

Makalleh  Bay:  Flagstaff 

8  20 

2  07 

6.8 

2.8 

Shahah  Roads:  Customhouse 

Sharmoh :  Single  house 

Kosair:  High  house 

Sihut:  Center  of  town 

Ras  Fartak :  Extreme  pt 

Damghot:  Town 

Merbat:  Towti 

8  50 

2  38 

7.0 

2.9 

Kuria  Maria  Is.,  Hullaniyeh  I. :  NE.  bluff 
Ras  Sherbedat:  Point 

Cape  Isolette:  Islet 

Masirah  Island :  Point  Abu-Rasas 

Point  Ras  Ye 

9  45 
9  15 
9  30 

3  32 
3  03 
3  20 

9.6 
8.9 
6.0 

4.4 

4.1 
2.8 

Ras-al-Hed :  Extreme  pt 

Maskat  (Muscat) :  Maskat  Pt 

Deimaniyeh  Islands:  E.  islet 

Sueik:  Fort 

Sohar:  SE.  tower  of  town  hall 

Khor  Fakan  Bay:  W.  end  of  village 

Ras  Musendom:  N.  end  of  island 

Great  Quoin  Islet:  Center 

Sharjah :  High  tower  with  flagstaff 

Abu-Thabi:  Fort  flagstaff 

Al  Beda'a  Harbor:  Nessah  Pt.,  N.  extreme 
RasRakkin:  NW.  pt 

Bahrein  Harbor:  Portuguese  fort 

5  15 

11  30 

6.4 

3.7 

Basrah :  Customhouse  fla^'staff 

Kuweit  Harbor:  N.  end  of  town 

0  05 

6  17 

8.3 

4.8 

Page  328] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
SOUTH  COAST  OF  ASIA— Continued. 


Place. 


K^rig  Islet:  Fort  flagstaff 

Abu  Snahr:  Residency  flagstaff. . . 

Shaikh  Shu'aib  Islet:  E.  end 

Kais  Islet:  NE.pt 

B^idil:  Chapel 

Hanjam  Islet:  Ruined  mosque 

Kasm:  Fort 

Jask  Bay :  Telegraph  office 

Kub  Kalat:  High  peak,  1,680  feet.. 

Chahbar  Bay :  Telegraph  office 

Gwatar  Bay:  Islet 

Gwadar  Bay:  Tel^raph  office 

Pasni:  Telegraph  office 

Ormarah :  Telegraph  office 

Sunmiyani:  Jam's  house 

Cape  Monze:  Peak 

Elarachi:  Manora  light 

Observatory 

Mandavi:  Lighthouse 

Beyt  (Bet) :  Lighthoiise 

Dwarka:  L^hthouse 

Temple  spire 

Porbandar:  Lighthouse 

Mangarol:  Lighthouse 

Diu  Head :  Lighthouse 

Kutpur:  Lighthouse 

Bhaunagar :  Lighthouse 

Perim  Island:  Lighthouse 

Cambay :  Flagstaff 

Surat  River:  Tapti  light 

Surat:  Minaret  Adrusah 

Bassein:  Center  of  town 

Bombay:  Colaba  Observatory 

Kenery  Island  light 

Bankot:  Fort  Victoria 

Ratnagherry :  Fort 

Viziaorug:  Fort  Flagstaff 

Cape  Ramas:  W.  bastion  of  fort 

Goa:  St.  Denis  Chiu-ch 

Aguada  li^ht 

Vingorla:  Signal-station  light 

Vingorla  Rocks:  Lighthouse 

Sedashigar  Bay:  Oyster  Rock  light 

Kumpta:  Lighthouse 

Hin^war:  Monument 

Kundapur:  Lighthouse 

Mangalore:  Lighthouse 

Kannanur:  Lighthouse 

Tellicherri:  Flagstaff 

Mahfe:  Lighthouse 

Calicut:  Lighthouse 

Cochin:  Lighthouse 

Alipee:  Lighthouse 

Quilon:  Tangacherri  Point  light 

Trivandrum:  Observatory 

Tiruchendore:  Pagoda  on  pt 

Cape  Comorin :  Lighthouse 

Tuticorin:  Lighthouse 

Pamban  Pass:  Lighthouse 


Lat.  N. 


15  25 
59  07 
47  40 
33  37 

39  12 

40  49 
57  27 
38  19 
29  45 

16  43 
03  17 


25  07  19 
25  15  52 
25  11  55 
25  25  19 
24  50  03 


47  37 

49  50 

50  00 
29  20 
14  00 

14  00 
38  00 
06  00 

41  20 
02  21 
47  00 
35  54 
17  00 
05  20 
12  19 

20  10 
53  45 

42  08 

58  00 

59  30 
33  26 
05  12 

21  24 

29  25 

51  10 
53  20 
49  00 
25  00 
17  28 
38  15 

52  17 
51  10 
45  00 
42  00 

15  10 
58  00 

30  00 

53  20 
30  47 
29  55 
04  00 
47  10 
17  20 


Long.  E. 


50  21  11 
50  50  35 

53  23  36 

54  02  21 

55  16  47 

55  54  25 

56  17  37 

57  45  57 

59  40  32 

60  37  40 

61  26  24 

62  19  42 

63  28  37 

64  37  02 
66  35  39 
66  39  58 

66  58  06 

67  01  33 
69  20  15 
69  05  15 

68  57  06 

68  58  54 

69  36  00 

70  06  32 

70  50  45 

71  49  35 

72  14  00 
72  21  08 
72  35  10 
72  38  40 
72  49  27 
72  48  44 
72  48  56 

72  48  49 

73  02  40 
73  15  56 
73  19  39 
73  54  50 
73  54  00 
73  46  10 
73  37  00 

73  27  15 

74  03  40 
74  22  30 
74  26  40 
74  39  50 

74  50  40 

75  21  51 
75  29  40 
75  31  10 

75  46  40 

76  14  40 
76  20  40 
76  34  00 

76  56  45 
78  07  47 

77  32  35 

78  11  26 

79  12  50 


Lun.  Int. 


Ran^je. 


H.  W.    L.  W. 


Spg. 


A.  m. 


7   12 


0  30 


10  50 
9  20 


9  20 


8  50 
10  15 
i2  05* 


4  27 


11  26 


10  34 


10  34 


10  50 


11  21 
11  33 


0  18 


1  52 
1  37 


A.  m. 


1  13 


6  40 


ft. 
'2.6' 

'e.'e 


4  35 
3  05 


n.6 

7.8 


3  05 


8.1 


2  35 
4  00 


8.1 
7.3 

io.s" 


11  18 


29.8 


5  08 


12.0 


4  10 


5.2 


4  11 


5.0 


4  28 


6.5 


4  59 

5  06 


2.7 
2.1 


6  16 


2.5 


7  51 
7  36 


3.  0   0.  8 
2.  0   0.  5 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
SOUTH  COAST  OF  ASIA— Continued. 


[Page  329 


Place. 


Manaar:  Center  of  town 

Colombo:  Lighthouse 

Dondra  Head:  Lighthouse 

Point  de  Galle:  Lighthouse 

Great  Bassas  Rocks:  Lighthouse. 
Little  Bassas  Rocks:  Lighthouse. 

Batticaloa:  Lighthouse 

Trincomali:  Dock-yard  flagstaff.. 


Caljmere  Point:  Lighthouse 

Negapatam:  Lighthouse 

Pondicherri:  Lighthouse 

Madras:  Observatory 

Lighthouse 

Pulicat:  Lighthouse 

Anneghon:  Lighthouse 

Kistna:  Lighthouse 

Masulipatam:  Flagstaff 

Coconada:  Lighthouse 

Vizagapatam:  Fort  flagstaff 

Kalingapatam:  Lighthouse 

Gopalpur:  Lighthouse 

Gaujam:  Fort 

Juggernath:  Great  temple 

False  Point:  Lighthouse 

Balasor  River:  Chandipur  light. . . 

Saugor  Island:  L'ghthouse 

Diamond  Harbor:  Flagstaff 

Calcutta:  Ft.  William  semaphore. 


Chittagong  River:  Lighthouse 

Akyab:  Oyster  Reef  light 

Old  temple 

Ramree  Island:  S.  pt 

Chedubah  Island:  N W.  peak 

Cape  Negrais:  Extreme 

Bassein  River:  Alguada  Reef  light 

Bassein:  Port  Dalhousie 

Andaman  Is.:  Table  Id.,  Lighthouse 

Port  Comwallis,  Rock  in 

entrance 

Port  Blair,  Lighthouse 

Little   Andaman    Island, 
SE.pt 

Krishna  Shoal :  Light  vessel 

Rangoon  River:  Grove  Pt.  light 

Rangoon :  Great  Dagon  pagoda 

Moulmein:  Docks 

Moulmein  River:  Amherst  Pt.  light 

Double  Island:  Lighthouse 

Tavoy  River:  Lighthouse 

Mergui:  Courthouse 

Tenasserim 

St.  Matthew  Island:  Hastings  Harbor... 

Pak  Chan  River:  Lighthouse 


Tongka     Harbor,     Junkseylon     Island: 

Lighthouse 

Pulo  Penang:  Fort  Comwallis 

Dinding  Channel:  Hospital  Rock 

One  Fathom  Bank:  Lighthouse 


Lat.  N. 


8  59  00 
6  55  40 

5  55  30 

6  01  25 
6  10  10 

6  25  00 

7  45  00 

8  33  30 

10  18  00 

10  45  28 

11  55  40 
13  04  08 
13  05  15 
13  25  15 

13  53  08 

15  47  00 

16  09  45 

16  56  21 

17  41  34 

18  19  00 

19  13  00 
19  22  30 

19  48  17 

20  20  20 

21  27  15 

21  38  40 

22  11  10 
22  33  25 

22  11  00 
20  05  00 
20  08  53 
18  51  00 
18  50  30 
16  01  30 

15  42  14 

16  01  30 

14  12  30 

13  18  40 

11  40  40 

10  27  00 

15  37  26 

16  30  01 
16  46  00 
16  26  00 
16  04  45 
15  52  00 
13  36  40 

12  26  15 
12  06  00 
10  05  05 

9  58  00 


7  50  00 
5  24  45 
4  13  05 
2  52  10 


Long.  E. 


79  53  52 

79  50  40 

80  34  12 

80  13  04 

81  28  15 
81  44  00 
81  41  00 
81  13  42 

79  51  30 
79  50  47 

79  50  10 

80  14  55 
80  17  27 
80  19  12 
80  12  30 

80  59  00 

81  11  00 

82  15  05 

83  17  42 

84  07  30 

84  52  06 

85  03  29 

85  49  09 

86  44  00 

87  02  20 

88  02  00 
88  11  07 
88  20  12 

91  49  00 

92  39  00 

92  52  40 

93  56  30 

93  31  00 

94  13  16 
94  12  00 

94  23  00 
93  22  30 

92  57  10 
92  45  15 

92  31  10 

95  37  32 

96  23  00 

96  07  30 

97  38  00 
97  33  05 

97  35  00 

98  13  00 

98  35  59 

99  03  00 
98  10  15 
97  35  00 


98  25  30 
100  21  44 
100  34  15 
100  59  12 


Lun.  Int. 


II.  W 


h.    m. 

"i'bb 

2  02 


8  10 


8  37 


8  42 
8  48 


9  21 


1  25 
1  02 


9  40 


3  05 


9  50 
9  40 


4  26 
3  07 
2  12 


10  50 
10  40 


11  50 


5  50 


L.  W. 


A.  m. 

"lid 

"807 


1  44 


2  37 
"2'26 


2  35 
2  34 


3  00 


9  06 
7  56 


3  28 


9  55 


3  37 
3  27 


Kange. 


Spg.   Neap. 


ft. 


2.0 
1.9 


2.0 


2.1 
3.1 


4.5 
4.4 


6.8 


11.2 
13.1 


7.6 


18.7 


8.6 
6.3 


11  15 

10  49 

8  49 


16.9 
11.7 
19.2 


4  20 
4  10 


15.6 
18.0 


5  40 


8.8 


12  00 


14.4 


ft. 


0.4 
6.'4 


0.5 


0.9 
'i.2 


L9 

L8 


2.6 


4.4 
5.6 


3.0 


7.8 


2.9 
2.1 


7.0 
5.0 
7.4 


5.9 
6.9 


3.8 


6.2 


Page  330]                                    APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
SOUTH  COAST  OF  ASIA— Continued. 

i 

Place. 

Lat.  N. 

Long.  E. 

Lun 

.Int. 

Range. 

H.  W. 

L.w. 

Spg. 

Neap. 

i 

s 

Cape  Rachado:  Lighthouse. . . ; 

2  24  08 
2  11  30 
1  09  57 
1  17  33 
1  19  57 

1  04  20 
1  03  13 
0  57  10 
0  44  30 
0  55  50 
0  36  52 
0  36  30 

Lat.  S. 
0  12  34 
0  26  13 
0  57  51 

Lat.  N. 
9  15  40 

8  02  10 

6  46  20 

5  45  00 
5  34  40 
5  15  58 

Lat.  S. 

0  00  32 

1  00  55 
1  23  13 

1  35  33 

2  59  26 
5  27  00 
5  55  02 
5  11  24 
5  18  50 
4  48  35 

3  59  25 
3  47  22 
2  44  54 
2  10  35 
0  59  56 
0  57  53 
0  53  58 
0  07  41 
0  03  13 
0  02  56 

Lat.  N. 
0  11  41 
0  33  11 

0  34  47 

1  17  36 
1  24  16 

1  44  24 

2  16  47 
2  02  32 

2  51  30 

3  14  59 

4  08  14 
4  38  21 

101  51  02 

102  15  00 

103  44  47 

103  51  11 

104  24  08 

104  27  21 
104  10  30 
104  19  52 
104  21  19 
104  25  43 
104  04  42 
104  11  31 

104  36  14 

104  30  15 

105  38  20 

92  48  00 

93  29  42 

93  49  20 

95  04  33 
95  19  00 

97  30  11 

103  47  58 

104  21  30 
103  59  14 

103  36  41 

104  45  34 

105  15  58 
104  32  36 
103  55  42 

102  07  28 

103  20  18 

101  00  58 

102  14  50 
101  17  25 
100  50  06 
100  19  28 
100  20  19 

98  53  58 

99  45  20 
98  05  55 

98  16  43 

99  22  09 
99  06  33 
97  43  43 
97  36  46 

97  12  28 

98  46  08 
97  45  06 
97  06  53 

95  56  02 
97  10  13 

96  07  23 
95  34  29 

ft.    m. 

ft.    m. 

ft. 

ft. 

Malakka:  Stat.  St.  Pauls  Hill 

7  20 

1  08 

10.5 

4.5 

Singapore  Strait:  Coney  Island  light 

Singapore :  Cathedral  tower 

10  18 

4  02 

7.6 

3.2 

Singapore  Strait:  Pedra  Branca  light. . . . 
Summit  Bintang  great 

hill,  1,253  feet 

Rhio  Straits,  Pulo  Sauh:  Lighthouse 

Terkolei:  Lighthouse 

Little  Garras:  Lighthouse... 
Rhio,  Bintang  Island :  Residency  flagstaff  . 
Pitong  Island:  Peak 

9  40 

3  14 

7.1 

3.1 

Abang  Besar  Island:  N.  pt 

Linga  Island:  Flagstaff 

6  00 

12  13 

1L5 

4.9 

Singkep  Island:  Mountain  summit 

Menali  Island:  N.  pt 

Nicobar  Islands,  Car  Nicobar:  N.  pt 

Nicobar  Islands,  Nancowry  Harbor:  Na- 
val Pt 

9  05 

2  52 

8.3 

2.8 

Great  Nicobar:  W.  pt. 
Galathea  Bay 

Acheen  (Acheh)  Head:  Pulo  Bras  light... 

N.  extreme 

Diamond  Point :  Lighthouse 

10  00 

11  50 

3  44 
5  34 

5.2 

8.7 

2.3 
3.7 

Point  Baru  or  Datu:  Extreme 

Point  Bon  or  Djabon:  Extreme 

Moeara-Kompehi:  Fort 

Djambi:  Flagstaff  of  fort 

Palembang:  Residency  flagstaff 

Lampong  Bay:  Telok  Betong  light 

Blimbing  Bay 

5  40 

11  52 

2.6 

0.7 

Kroe:  Village 

Engano  Island :  Barioe  anchorage 

Bintoean:  River  mouth 

Mega  Island:  N.  pt 

Benkulen :  Light  louse 

5  50 

12  03 

4.0 

LI 

Bantal:  Village 

Indrapura  Point:  Extreme 

Pisang:  Lighthouse 

Padang:  Lighthouse 

5  35 

11  48 

5.5 

L4 

Siberoet  Island:  Sigeb  Pt 

Katiagam :  Village 

Batoe  Islands:  N.  point  of  Simoe  Islet. . . 
Summit  of  Tello 

' 

Ayer  Bangis :  Fort  flagstaff 

5  29 

11  42 

2.8 

0.7 

Natal:  Fort  flagstaff 

Niaa  Island:  Lagoendi  Bay 

Sitoli ." 

Lapan 

Siboga:  Flagstaff 

Singkel :  Post  oflice 

Bangkaru  Islands:  Bay 

Simaloe  Island :  NW.  pt 

Tampat  Toewon:  Flagstaff 

Analaboe 

Batoe  Toetong:  Lauding  place 



APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA. 


[Page  331 


Place. 


Lat.  S. 


Long.  E. 


Lun.  Int. 


H.W.         L.W 


Range. 


Spg.       Neap. 


099 


Java  Head:  First  Pt.  light 

Sunda  Strait:  Krakatoa  I.  peak — 
North  Watcher  Island:  Lighthouse 

Lucipara  I . :  Beacon 

Banka  Island:  Tobol  Ali  Fort 

Berikat,  summit. . . 

Nanka  I . :  Lighthouse 

Banka  Island :  Mintok  light 

Blinyu 

Crassok  Pt 

Shoal  water  Inland:  Lighthouse 

Pulo  Lepar:  Lighthouse 

Pulo  Jelaka :  Lighthouse 

Billiton  Island :  Tanjong  Pandan 

Langkuks  I .  light 

Gaspar  Island :  Peak 

Carimata  Island :  Sharp  peak 

Pulo  Eu :  Center 

PuloAor:  S.  peak,  1,805  feet 

St.  Barbe  Island :  Center  of  W.  side 

Direction  Island:  S.  pt 

Dato  Island :  Summit 

St.  Julian  Island:  Summit 

Tambelan  Island:  S.  pt 

Tamban  I.  obs.  station 

Victory  Island :  S.  pt 

Anamba  Islands :  White  rock 

Pulo  Repon 

Pulo  Domar 

St.  Pierre  Rock:  S.  pt 

Natuna  Islands:  Pyramidal  rocks 

Semione  I 

Anjer :  Fourth  Pt.  light 

Bantam:  Flagstaff 

Batavia:  Observatory 

Buitenzorg:  Palace  tower 

Boompjeo  Island:  Racket  I.  light 

Cheribon:  Lighthouse 

Tegal:  Flagstaff 

Pekalongan:  Light  W.  of  entrance 

Samarang:  Lighthouse 

Rembang:  Residency  flagstaff 

Siu-abaya :  Time-ball  station 

Pasuruan:  Lighthouse 

Madura  Island :  Lighthouse 

Soemenep  flagstaff 

Besuki:  Lighthouse 

Cape  Sedano:  NE.  pt.  of  Java 

Banjuwangi:  Fort 

Bantenan:  S.  pt.  of  Java 

Barung  Island:  S.  pt 

Kambangan  Island :  Lighthouse 

Cape  Anjoe:  Extreme 


6  44  30 
6  08  46 
5  12  17 
13  05 
00  48 
34  18 
23  20 
04  03 
38  26 
29  00 


19  10 
56  52 
52  05 
44  40 
32  12 
24  30 


1  33  24 

2  07  00 
2  26  30 

Lat.  N. 
0  07  26 
0  14  19 
0  06  37 
0  55  00 
0  56  52 


00  27 
34  41 
18  10 
25  00 
44  31 
51  42 
03  00 
31  00 


Lat.  S. 
6  04  15 
6  01  20 
6  07  40 
6  35  45 

5  56  15 

6  43  00 
6  51  09 
6  51  29 
6  57  09 

6  42  18 
12  10 
37  30 
02  00 
02  30 
43  25 
49  00 

8  12  30 
8  47  00 
8  32  00 

7  46  30 
7  25  00 


105  11  48 

105  26  58 

106  27  33 
106  13  02 
106  27  22 
106  50  36 
105  44  30 
105  09  45 

105  46  28 

106  57  30 


107  12  42 

106  54  38 

107  00  43 
107  38  46 
107  37  15 
107  03  33 


108  55  13 
104  17  00 
104  34  06 


107  13  00 

108  01  47 
108  37  05 

106  45  00 

107  32  57 
106  24  10 

106  18  27 
105  35  58 
105  52  00 
105  22  57 

108  38  55 

107  21  40 

107  42  30 

105  53  05 

106  08  20 
106  48  37 
106  49  11 

108  22  37 

108  34  00 

109  08  07 

109  41  08 

110  25  03 

111  20  32 

112  43  58 
112  55  00 

112  41  09 

113  53  45 

113  41  10 

114  26  53 
114  22  55 
114  25  13 
113  15  00 
109  02  12 
106  24  30 


5  30 

6  50 


h.    m. 

11  42 

0  37 


ft. 

2.5 

3.8 


ft. 

0.7 

LI 


[9  05] 


[2  52] 


[10.1] 


[6  50] 


[0  38] 


[9.3] 


[2  08] 


[8  21] 


[5.6] 


[3  17] 


[9  29] 


[6.6] 


7  11 


0  58 


2.4 


0.7 


[11  58] 


[5  46] 


[3.0] 


[6  00] 


[12  13] 


[4.0] 


12  07 
11  44 


5  54 
5  31 


4.9 
6.2 


1.7 
2.3 


10  00 


3  45 


7.8 


2.6 


8  33 


2  21 


5.2 


Page  332] 


APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Place. 


Karimon  Djawa  Island:  Flagstaff 

Rawean  Island:  Sangkapura flagstaff 

Great  Solombo  Island :  NW.  pt 

Arentes  Island :  S.  pt 

Bali  Island :  Buleleng  lighthouse 

Peak,  11,326  ft 

Badong  Bay,  Kotta  village. 

Lombok  Island :  Peak,  12,379  ft 

Ampenam  light 

Sumbawa  I. :  Sumbawa  village 

Tambora  Volcano,  summit 

E.  side  of  crater , 

Bima,  flagstaff 

Postilion  Islands:  N.  island 

Maria  Reigersbergen  I 

Ardassier  Islands:  S.  id 

Brill  Reef:  Lighthouse 

Hegadis  Island 

Token  Bessi  I. :  Wangi-Wingi,  NW.  pt . . 

Binongko,  S.  pt 

Gunong  Api:  Volcano 

Lucipari  Islands:  N.  islet 

Flores  Island:  Reo  village 

Ende  village 

Flores  Head,  extreme. . .  . 

Komba  Island:  Peak,  S.  part 

Adenara Island:  Summit,  Mount Woka. . 

Lombata  Island:  Mount  Lamararap 

Pan  tar  Island:  S.  peak  of  saddle  on  S.  pt 

Ombay  Island :  Dololo  anchorage 

Timor  Island:  Deli,  customhouse 

Atapopa 

Koupang,  Fort  Concordia. 

Rotti  Island:  W.  pt 

Saru  Island:  Seba  Bay,  on  NW.  side 

Sandalwood  Island:  Nangamessie 

Wetta  Island:  Ilwaki  road 

Roma  Island:  W.  pt 

Moa  Island:  Buffalo  Peak,  4,100  ft 

Sermata  Island:  NE.  pt 

Damma  Island:  Kulewatta  Harbor,  N.  pt 

Nila  Island:  Center 

Mano  or  Bird  Island:  NW.  extremity. . . 
Timor  Laut  Island:  Olilet,  on  E.  coast. . 

Vordate  Island:  S.  pt 

Mulu  Island :  N.  pt 

Am  Islands:  S.  island 

N.pt 

Great  Ki  Island:  S.  pt 

Tello  Islands:  S.  island,  summit 

Tehor  Island:  NE.  pt 

Matabella  Islands:  Kukur 

Goram  Islands:  Goram  Mosque 

Banda  Island:  Mole 

Bouro  Island,  Kajeli:  Fort  Defense 

Ceram  Island:  Kawa 

Amboina  Island:  Lighthouse 

Sula  Islands,  Taliabo  Island:  NW.  pt. . . 

Mangola  Island:  E.  pt. . . . 

Besi  Island:  E.  pt 

Obi  Major  Island:  W.  pt 

Popa  Island :  Outer  Extremity  Bay .... 
Mysole  Island :  Ef be  Harbor 


Lat.  S. 

o   /    » 

5  52  57 

5  51  18 

5  32  28 

5  05  46 

8  05  30 

8  21  00 

8  42  30 

8  23  00 

8  34  15 

8  32  00 

8  12  30 

8  27  00 

6  31  00 

7  30  00 

7  35  00 

6  05  50 

6  07  00 

5  15  00 

6  17  00 

6  43  00 

5  28  30 

8  16  15 

8  50  55 

8  04  45 

7  48  00 

8  20  30 

8  33  00 

8  34  00 

8  12  00 

8  34  00 

9  00  00 

10  09  54 

10  46  00 

10  29  00 

9  35  03 

7  53  00 

7  38  00 

8  12  00 

8  14  00 

7  03  00 

6  44  00 

5  32  50 

7  55  00 

7  04  00 

6  35  00 

7  05  00 

5  20  00 

5  56  00 

5  20  00 

4  44  00 

4  33  00 

4  03  05 

4  31  53 

3  22  48 

2  55  52 

3  41  00 

1  44  00 

1  48  12 

2  28  00 

1  30  00 

1  11  21 

2  04  00 

Long.  E. 


110  25  29 
112  39  10 
114  23  42 

114  35  00 

115  03  48 
115  28  00 

115  08  47 

116  27  30 

116  04  09 

117  20  33 

117  57  00 

118  43  55 
118  43  00 
117  56  00 

117  22  00 

118  56  50 

122  40  00 

123  32  00 
123  59  00 

126  43  30 

127  30  00 

120  29  55 

121  38  40 

122  52  00 

123  31  00 
123  15  00 

123  22  00 

124  06  00 

124  23  00 

125  33  57 
124  52  00 
123  33  57 
122  52  00 
121  46  00 
120  14  30 


126  22 

127  19 

128  01 

129  00 

128  28 

129  29 

130  17 

131  23 
131  55 

131  34 
134  31 
134  40 

132  54 
131  58 
131  47 
131  50 
131  25 
129  53 

127  06 

128  07 

128  10 
122  20 
126  21 

126  01 

127  18 

129  55 

130  12 


Lun.  Int. 


H.  W.    L.  W. 


Bange. 


Spg.   Neap. 


ft.  m. 


h.   m. 


ft. 


10  50 


4  38 


8.7 


3.0 


7  50 


1  37 


5.8 


2.0 


0  00 


6  12 


5.7 


2.0 


0  45 


6  58 


5.7 


2.0 


10  50 
ii  20 


4  37 

5  07" 


8.5 
16.5' 


2.9 
"5.6 


1  45 
1  20 


7  57 
7  32 


9.0 

4.2 


6.6 
3.1 


2  20 


8  32 


7.5 


5.5 


I 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 


[Page  333 


Place. 


Gebey  Island:  NW.  pt 

Halmahera  I.,  Cape  Tabo:  E.  extreme. 

(Gillolo  I.)   Cape  Salawag:  N.  E.  pt 

Derrick   Point:    N.   ex 

treme 

Makkian  or  Makjan  I.:  Fort  Reeburgh.. 
Temate  Island:  Residency  flagstaff 

Batian  Island:  Church 

Tanjong  Data 

Sarawak  River:  Po  Pt.  light 

Sardwak:  Fort 

Cape  Sirik:  Lighthouse 

Tanjong  Barram 

Bruni  River:  Lighthouse. 

Labuan  I.,  Victoria  Hbr.:  Lighthouse. . 

Sandakan  Harlwr:  Flagstaff 

Unsang:  Anchorage 

Tanjong  Mangkalihat  E.  pt.  of  Borneo. . 


E.  pt.  delta  River  Koetei. 
S.  pt.  Koengit  Islet. 


Pamaroong  I 

Pulo  Laut 

Selatan  Point: "Extreme  of  Sita  Pt 

Bandjermasin:  Residency  flagstaff 

Sampit  Bay:  Bandaran  Pt 

Kottaringin  Bay:  Samadra  I 

Succadana:  Town 

Padang  Tikar:  Point. 


Port  Laykan:  SW.  pt.  of  Celebes. 

Makassar:  Fort  light 

Palos  Bay:  Village  at  head 


Cape  Rivers:  NE.  Cape,  Slime  Islet... 

Gorontalo:  Lighthouse 

Manado  Bay:  Lighthouse 

Bajuren  Island :  Summit 

Tagulanda  Island:  Peak 

Seao  Island:  Conical  peak 

Sauguir  Island:  S.  pt.  Cape  Palumbatu. 
Taluat  Island:  Kabruang  I.,  SE.  pt  — 
Cape  Flesko:  Extreme 


Cape  Talabo:  E.  end.. 
Wowoni  Island:  N.  pt. 
Bouton  Island:  N.  pt. 

E.  pt.. 

Fort.. 
Cape  Lassa:  Extreme. 
Salavar  Island:  N.  pt. 

S.  pt.. 


Balabac   Island,  Cape  Melville:  Light- 
house  ». . . 

Palawan  Island,  Cape  Buliluyan:  S.  ex- 
treme  

Victoria  Peak,  5,680  ft. . 
Port  Royalist:  Tide  Pole 

Pt.  Light 

TavtayPort 


Lat.  S. 


0  02  02 

0  11  00 

1  26  00 

2  12  00 
0  24  00 
0  47  13 

Lat.  8. 
0  38  03 

Lat.  N. 

2  05  15 
43  50 
33  55 
45  20 
36  15 
02  00 

15  25 
50  24 

16  30 
01  12 


Lat.  S. 
0  45  00 
4  05  42 
10  40 
18  55 
16  00 
54  00 
14  00 


0  40  00 

5  36  00 
5  08  09 

0  57  00 

Lat.  N. 

1  20  00 
0  29  41 


31  00 
07  00 
22  00 
44  00 
21  00 
49  00 


0  27  00 

Lat.  S. 
0  46  00 
3  58  00 
23  30 
15  00 
29  15 
35  00 
47  00 


4 
5 
5 
5 
5 
6  26  00 


Lat.  N. 

7  49  25 

8  20  25 

9  22  30 

9  43  43 
10  50  00 


Long.  £. 


129  17  30 
128  52  00 
128  37  00 

128  03  30 
127  21  00 
127  22  39 


127  28  21 

109  39  07 

110  30  30 
109  20  40 

111  21  20 

113  58  57 
115  03  00 

115  16  05 
lis  07  12 
119  16  00 
119  00  00 

117  37  00 

116  01  40 

114  42  18 
114  34  56 
113  08  00 
111  24  00 
109  58  00 
109  16  00 

119  26  00 
119  23  55 
119  47  30 


120  43  30 

123  03  08 

124  50  00 

125  22  00 
125  24  30 
125  26  00 
125  39  00 
127  02  30 
124  26  00 


123  27  00 
123  00  00 
123  04  00 
123  16  00 
122  36  41 
120  29  00 
120  30  00 
120  28  30 


117  00  00 

117  09  35 

118  17  30 

118  43  03 

119  31  10 


Lun.  Int. 


H.W. 


h.    m. 


5  00 


4  00 

5  20 


9  35 
12  00 


[7  45] 


7  00 


4  40 


6  00 


L.W. 


h.   m. 


11  10 


10  12 

11  35 


3  23 
5  50 


[133] 


0  47 


10  55 


12  15 


Range. 


Spg. 


Neap. 


3.9 


2.9 


9.0 
14.1 


3.9 
6.1 


5.5 
6.8 


2.4 
lto4 


[7.0] 


7.2 


3.1 


3.9 


2.9 


4.3 


3.1 


[11  30]   [5  20] 


[6.5] 


Page  334] 


APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Ck)ntinued. 


Place. 


Palawan  Island,  Port  Barton:  BubonPt. 
Kabuli  I.:  Summit,  N. 

extreme 

Cuyo  Island:  Obs.  spot 

Agutaya  Islet:  Summit  of  Mt.  Aguade — 

Quiniluban  Islet:  Summit 

Culion  Island:  Fort 

Busuanga  Island:  Mt.  Tundalara 

Apo  Islet:  Summit 

Caluya  Island:  Summit 

Semerara  Island:  N.  extremity 

Mindoro  Island:  Mangarin  Pt.,  SE.  ex- 
tremity  

Sablayan  Pt. ,  Vantay . . . 

Monte  Calavite 

Escarceo  Pt 

Pt.  Dumaly 

Ylin  Island 

Lubang    Island,     Port 

Tulig 

Luzon  Island,  Batangas:  Ast.  station. . . . 

Balayan:  Plaza  Rizal 

LoroPeak:  Summit,  3,985 

feet 

Caballo  I . :  Lighthouse 

Corregidor  Island:  Light- 
house  

Cavite:  Sangley  Pt.  light.. 
Manila:  Pasig lighthouse.. 

Manila:  Cathedral 

Subic:  Town 

Capones  Islet:  Lighthouse. 

Iba:  Ast.  station 

Port  Masinloc:  Bani  Pt. . . 

Santa  Cruz :  Plaza 

Sual:  Army  Hospital 

Silaqui  Islet:  Summit 

Port  San  Fernando:  Main 

street 

Candon:  Ast.  station 

Port  Santiago:  Remarkable 

tree  S.  of  port 

Vigan:  Race  track 

Salomague  Island:     Port 

Salomague  flagstaff 

Currimao:  Town 

Cape     Bojeador:     Light- 
house  

Mairaira  Pt. :  Semaphore. . . 

Aparri :  Plaza 

Port    San    Vicente:    San 

Vicente  Islet 

Cape  Engano:  Rona  Islet.. 

Camiguin  I . :  Summit 

Fuga  Island:  W.  summit. . 
Dalupiri  Island:  Peak. . . . 

Calayan  Island:  NE.  pt 

Babayan  Claro  Island :  W.  pt 

Balingtang  Islands 

Batan  Island :  Mount  Irada 

Ibayat  Island:  Mount  Santa  Rosa 

Yami  Island:  Islet  off  SW.  part 

Luzon  Island,   Port  Dimasalasan:    En- 
trance  


Lat.  N. 


10  29  19 

11  26  25 

10  51  26 

11  09  09 
11  25  47 

11  53  53 

12  02  09 
12  39  46 

11  54  28 

12  06  45 

12  20  03 

12  50  15 

13  28  40 
13  31  35 
13  06  05 

12  17  15 

13  49  30 
13  45  22 

13  56  17 

14  12  20 
14  21  48 

14  22  27 
14  29  57 
14  35  49 
]4  35  31 
14  52  36 

14  55  33 

15  19  30 
15  34  48 

15  45  43 

16  04  06 
16  27  15 

16  37  15 

17  11  43 

17  16  55 
17  33  56 

17  47  17 

18  01  09 

18  31  08 
18  39  02 
18  21  43 

18  28  32 
18  32  02 
18  50  26 

18  52  54 

19  03  03 
19  22  00 
19  30  00 

19  58  30 

20  28  30 

20  48  00 

21  04  56 

17  20  17 


Long.  E. 


119  05  36 

119  29  55 
121  00  25 

120  56  26 
120  45  38 
120  00  48 
120  12  56 

120  27  18 

121  30  24 
121  20  10 

121  03  33 
120  44  42 
120  22  33 

120  59  17 

121  29  20 
121  01  53 

120  09  58 

121  02  56 
120  43  37 

120  38  10 
120  36  40 

120  33  48 
120  54  43 
120  57  19 
120  58  06 
120  13  52 
120  00  15 
119  57  11 
119  54  16 

119  54  00 

120  06  01 

119  56  10 

120  18  25 
120  26  14 

120  25  07 
120  22  51 

120  25  04 
120  28  44 

120  35  35 

120  50  53 

121  37  27 

122  04  14 
122  05  49 
121  48  26 
121  15  42 
121  11  28 
121  32  00 

121  52  00 

122  14  00 
122  01  20 
121  52  30 

121  58  24 

122  19  20 


Lun.  Int. 


Range. 


H.W. 


/».    m. 


[11  07] 


[10  22] 


10  44 
"i9"42i 


[10  20 
[10  21 

[9  40] 


5  43 


6  00 


L.w. 


Neap. 


A.    m. 


ft. 


[4  50] 


[4.9] 


[3  56] 


[4.4] 


[4  10] 
■i4'33i 


[4.6] 

[s's] 


[3  33] 
[3  44] 

[3  29] 


[2.4] 
[2.3] 

[2.6] 


-0  02 


3.2 


L9 


-0  12 


6.0 


2.7 


APPENDIX  IV.                                     [Page  336 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OP  ASIA— Continued. 

1 
8 

Place. 

Lat.  N. 

Long.  £. 

Lun.  Int. 

Range.         1 

H.W. 

L.W. 

Spg. 

Neap. 

m 

V 

a 

M 
C 

e 
a. 

a 

a 

Luzo«  Island,  Polillo  I:  PortPolillo.... 
Tabaco:  Church  belfry .. . 
Catanduanes  Islands:  N. 
islet 

0            /            JP 

14  51  00 

13  21  33 

14  09  00 

13  28  30 
12  31  20 

12  52  20 
12  22  10 
12  36  00 

12  10  03 

11  56  09 

13  07  40 
13  18  10 

12  54  03 
12  56  56 
12  38  42 
12  33  44 
12  03  15 
12  36  00 
12  35  33 
12  24  55 
11  01  30 
11  46  44 
11  47  30 
11  15  08 
11  00  17 
11  02  37 
10  07  39 
10  03  22 
10  17  30 

9  15  17 

9  03  37 
9  18  25 

10  24  35 
10  40  21 
10  26  38 
10  41  27 

10  44  08 

11  16  47 
11  28  20 
11  45  30 
11  35  40 
11  35  06 
10  11  26 

9  53  00 
9  41  34 
9  47  53 

6  14  30 

7  01  22 

5  22  30 

6  28  50 

7  21  15 

6  52  15 
6  54  03 

0        f        tr 

121  54  48 

123  43  53 

124  06  48 

124  04  48 

124  04  18 

123  49  22 
123  35  58 
123  14  36 
123  12  47 
123  07  34 

123  02  45 
121  54  33 

121  43  08 

122  04  48 
122  08  38 
121  58  32 

121  53  53 

122  17  08 
122  16  26 

122  33  23 

125  43  14 

124  51  37 
124  18  15 
124  59  56 
124  36  20 
124  22  07 
124  50  15 

124  32  35 

123  54  18 

123  34  26 

123  06  09 
123  18  43 

123  07  05 
122  55  42 
122  40  20 
122  34  26 

121  54  27 

122  09  09 
121  52  36 

121  58  59 

122  28  50 

122  45  03 

126  02  53 

125  31  17 
125  58  22 
125  28  30 
125  47  48 
125  34  35 

125  13  48 

123  57  37 

124  11  42 

122  04  00 
122  04  52 

ft.    m. 

A.     7R. 

ft. 

ft. 

6  08 

0  00 

5.2 

2.8 

Catanduanes  Islands:  S. 
extreme 

, 

Point  Calaan:  S.  extreme. 
Port   Sorsogon,   Tinacos 
Islet 

Masbate  Island,  Palanog:  Pier 

Bugui  Pt.  lighthouse 

Camasusu  I.:  Summit. . . 

Tin tolo  Point:  Extreme. 

Burias  Island :  Busainga 

[4  30] 

[10  20] 

[5.5] 

Marinduque  I. :  Summit  of  Mount  Catala. . 
Maestro  de  Campo  Island,  Port  Concep- 
cion :  Point  Fernandez 

Banton  Island:  Ban  ton  Mountain 

Tablas  Island:  Tablas  Head 

Sanguilan  Pt 

Carabao  Island :  W.  pt 

Romblon  Island:  Sabang  Pt.  light 

Summit  over  port 

Sibuyan  Island :  Summit 

Samar  Island,  Guiuan :  Pier 

Catbalogan :  Fort 

Maripipi  Island :  Summit 

Leyte  Tacloban  .  .        

6  53 

1  25 

1.5 

1.1 

Ormoc :  Ast.  station 

Palompon :  Church 

Maasin 

11  47 

4  50 

2.8 

2.0 

Bohol  I . ,  Lapiniu  I . :  Mount  Basiao 

Cebu  Island,  Cebu:  Plaza 

Siquijor  Island,  Port  Canoan:  S.  pt.  of 
entrance 

Negros  Island,  Port  Bunbonon;  E.  pt.  of 
entrance 

Dumaguete:  Town 

Volcano     of     Malaspina, 
8,192  ft 

Bacalod :  Town 

Guimaras  I.,  Inampulugan  I.,  SW.  pt 

Panay  Island,  Iloilo :  Fort 

11  06 

5  22 

4.2 

1.9 

San  Jos6 

Pan  de  Azucar 

Batbatan  Island:  Summit. 

Pucio  Point:  Extreme 

Port  Batan:  Village 

Capiz :  Town 

Siargao  Island,  Port  Sapao:  Semaphore. . . 
Gibdo  Island :  Semaphore 

Bucas  Island:  E.  pt.  of  Port  Sibanga 

Mindanao  Island :  Surigao 

[ii  40] 

[6  15] 

[6.5] 

Cape  St.  Augustin 

Davao:   Mole 

6  00 

-0  13 

6.9 

5.1 

Saranguni  Islets:   W. 
islet 

Basianang  Bay:  N.  pt. 

of  Donauang  I 

PoUoc:  Small  hill  back 

of  town 

Santa    Cruz    Islands: 
SE.  islet 

Zamboanga:  Fort 

6  50 

0  42 

3.8 

2.8 

Page  336]                                    APPENDIX  IV. 

MAKITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 

1 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

i 

a 

c 

M 
« 

a 
a. 

a 

a 
a 
tk 

S 

0 
w 

S 

i 
C 

S 

d 
S 

V 

0 
0 

Mindanao  Islands  Sibuco  Bay:  Hill  S.  of 
beach  

7  18  05 

7  45  41 

8  40  15 

8  08  29 

9  10  19 
10  43  00 

10  27  00 

9  35  30 
7  43  00 
7  00  38 
4  54  10 
4  49  30 

4  55  30 

5  50  00 
5  00  30 
5  13  00 
5  25  15 
5  27  10 
5  32  35 
5  41  30 
5  44  30 

5  54  45 

6  02  30 
6  03  30 

5  52  30 

6  15  15 
6  42  43 

3  17  00 

4  53  00 

5  21  40 

5  44  21 

6  13  25 

6  57  01 

7  13  54 

8  24  47 
13  44  32 
12  31  00 

12  27  43 
12  01  55 

11  33  00 
11  06  25 
10  13  45 

9  18  14 
8  25  20 

10  46  47 
10  21  16 

10  19  51 

11  21  00 

12  53  40 

13  45  23 
15  23  34 

15  57  10 

16  07  00 

19  22  14 

20  25  30 
20  40  03 
20  51  44 

20  56  29 

21  01  57 

O           t          It 

122  03  18 

122  04  58 

123  23  13 

123  50  44 

124  42  50 
121  33  00 
121  03  00 

121  23  30 
118  27  00 

118  26  06 

119  22  45 
119  48  00 
119  46  45 

118  11  00 

119  44  15 

120  40  45 
120  35  00 
120  11  30 
120  48  51 
120  49  45 

120  55  00 

121  00  40 

121  18  20 
120  59  52 

119  55  55 

120  29  30 

121  56  50 

103  40  00 
103  38  00 
103  08  00 
103  01  45 
102  10  30 

101  17  39 
100  36  12 
100  45  27 
100  29  29 
100  57  30 

102  04  19 
102  15  47 
102  57  14 
102  47  49 

102  52  45 

103  27  14 

104  48  30 
106  42  12 

106  20  38 

107  04  55 

108  58  00 

109  23  42 
109  14  52 
109  05  35 
108  32  47 
108  11  30 

105  55  22 

106  08  41 
106  47  10 
106  40  54 
106  17  56 
105  48  40 

ft.    m. 

ft.     771. 

ft. 

ft. 

Port  Sta,  Maria:  Fort. 

Dapitan :  Village 

Misamis:  Fort 

Camiguin  Island :  Mount  Camiguin 

Sombrero  Rock :  Center 

[10  48] 

[4  50] 

[5.1] 

Piedra  Blanca :  Center 

Cagayanes  Islands:  Rocky  islet  between 

two  larger  islands 

San  Miguel  Isles:  E.pt.of  ManukManukan. 
Cagayan  Jolo  Island:  Middle  of  W.  coast. 
Omapui  Island:  NW.  extreme 

Sibutu  Island :  Hill  on  E.  coast 

Simonor  Island :  NW.  pt 

Bahaltolis  Island:  Sandakan  Harlx>r 

Bongao  Island :  S.  pt 

Keenapoussan  Island :  Center 

Bubuan  Island:  Lagoon  entrance 

Cuad  Basang  Island :  SW.  pt 

Siassi:  Town,  center  of  old  fort 

5  54 

-0  18 

8.6 

6.4 

Bulipongpong  Island:  Center  hill 

Tapul  Island:  Center  hill,  1,676  ft 

Jolo  Islands:  Maimbun  Anchorage,  dry 
bank 

Dalrymple  Harbor,  Tulyan 
Islet 

Jolo  lighthouse 

[9  38] 

[3  10] 

[5.0] 

Doc  Can  Islet:  W.  extreme 

Pangituran  Island :  SW.  pt 

Basilan  Island :  La  Isabe  a 



Pulo  Varella :  Center 

Pulo  Brala:  Center 

Tringano  River:  N .  pt 

8  00 

1  48 

5.8 

2.5 

Great  Redang  Harbor:  Bukit  Mara 

Kelantan  R. :  Lighthouse 

Tanjong  Patani:  NE.  pt 

Singora  (Sungkla):  SW.  pt.  of  Koh  Ngu. . 
Koh  Krah  Islet:  SE.pt 

8  20 

2  08 

2.8 

L2 

Bangkok:  Wat  Cheng 

8  00 

2  00 

7.3 

3.1 

Cape  Liant:  Koh  Chuen  Lighthouse 

Chentabun  River:  Entrance,  Bar  I 

Koh  Chang:  Obsy .  I.  on  W.  side 

10  00 

3  50 

4.5 

2.1 

Koh  Kong  R.:  S.  pt.  of  entrance 

Kusrovie  Rock:  Center 

Koh  Tang  Rocks:  Veer  Islet 

Panjang  Island :  West  Pt 

Obi  Islands:  Lighthouse 

Saigon:  Observatory 

5  00 

11  20 

9.8 

4.2 

Mitho:  S.  gate  of  citadel 

Cape  St.  James:  Lighthouse 

Cape  Padaran:  Extreme 

Cape  Varella:  Extreme 

Quin  Hon :  Battery  flagstaff 

Canton  Pulo:  Lighthouse 

Cham-Callao  Islet:  Watering  place 

Tourane  Bay :  Ligbihouse 

Hon-M6 :  Summit 

Nam-Dinh :  Citadel  tower 

Hon  Dau  Island :  Lighthouse 

9  00 

2  48 

4.3 

2.1 

Haif ong :  Observation  pagoda 

Haiduong:  Citadel  tower 

Hanoi:  Citadel  tower 

APPENDIX   IV.                                     [Page  337 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 

8 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

«  . 

i 

a 
a 

Condore  Islands :  Lighthouse 

9        r       It 

8  40  06 

9  58  23 
10  32  36 

2  02  55 

3  00  00 

21  29  00 
18  09  00 
18  11  30 
20  01  15 

15  46  30 

16  36  00 
16  40  07 
16  49  55 

20  42  03 

21  22  30 
21  24  15 
21  31  00 
21  34  00 

21  28  00 

22  11  40 

22  11  24 

23  06  35 
22  02  00 

21  48  50 

22  16  52 
22  16  23 
22  03  40 
22  15  45 
22  27  06 
22  24  06 
22  30  42 
22  32  54 
22  18  30 
22  48  14 
22  48  07 

22  56  24 

23  14  00 
23  20  43 
23  15  43 
23  32  30 

23  47  15 

24  09  49 
24  23  16 
24  25  44 
24  49  13 
24  52  12 

24  59  36 

25  02  18 
25  12  00 
25  16  30 
25  26  10 
25  58  10 

25  59  00 

26  08  26 
26  09  29 
26  22  37 
26  30  00 
26  36  06 
26  42  30 
26  51  25 

26  58  52 

27  09  20 
27  09  42 

106  41  42 
109  06  00 

108  56  27 

109  06  10 

107  48  00 

109  06  00 
109  35  00 

109  41  30 

110  16  10 

111  14  30 

111  40  30 

112  43  32 
112  20  44 
116  43  07 
111  10  30 
111  15  25 
111  38  30 

111  46  43 

112  21  30 

113  34  00 
113  33  25 
113  16  30 
113  47  00 

113  56  20 

114  09  31 
114  10  02 
114  19  25 
114  22  07 
114  36  45 
114  39  12 

114  50  00 

115  01  00 
115  06  54 

115  47  56 

116  04  26 
116  29  44 
116  47  00 

116  40  22 

117  17  04 
117  42  00 

117  36  48 

118  13  30 
118  10  00 
118  30  11 
118  41  00 

118  58  00 

119  27  07 
119  10  36 
119  35  00 
119  45  00 
119  56  07 
119  59  02 
119  27  16 

119  37  35 

120  24  06 
120  29  40 
120  10  00 
120  11  12 
120  22  42 
120  32  33 
120  42  34 
120  25  50 
120  32  42 

h.    m. 

h.    m. 

ft. 

ft- 

Safatu  Island:  Summit 

Ceicer  de  Mer  Island:  SW.  hill 

Natuna  Islands:  Murundum  I.,  SE.  pt... 
Low  I 

Pakhoi :  Customhouse  flagstaff 

5  00 

11  12 

14.0 

6.6 

Hainan  Island :  Cape  Bastion,  extreme. . . 
Gaalong  Bay,  E.  Brother. 
Ligh  thouse .... 

Paracel  Islands:  Triton  I 

Observation  bank 

Lincoln  I 

Woody  I 

Pratas  Island:  NE  part 

Ty-fung-kyoh  Islanc  :  Center 

Tien-pak  Harbor:  Pauk  PyaJi  Islet 

Song-yui  Point:  Extreme 

11  50 

5  37 

8.2 

3.8 

Hui-lang-san  Harbor:  Mamechow  Islet. . . 
Mandarins  Cap :  Summet,  200  ft 

Macao :  Fort  Guia  light 

9  50 

3  38 

6.3 

3.0 

Fort  San  Francisco 

Canton:  Dutch  Folly  light 

2  00 

800 

5.1 

2.4 

Raleigh  Rock:  Center 

Gap  Rock"  Lighthouse      .    ...... 

Hongkong:  Cathedral 

Wellington  Battery 

9  20 

2  52 

4.4 

2.0 

Lema  Island:  Lema  Head 

Nine-pin  Rock:  Center.... 

T|ini-5».Tig  TslHTid  -  SlimTnit 

Single  Island:  E  summit  .... 

Mendoza  Island:  Summit 

Pank  Piah  Rock:  Summit 

Pedra  Blanca  Rock:  Summit,  130  ft 

Chino  Bay:  Obs.  spot 

Cupchi  Point:  Hil    

Breaker  Point :  Lighthouse ^ 

Cape  of  Good  Hope :  Lighthouse 

Swatow:  British  consulate 

2  50 

9  00 

7.5 

3.5 

Lamock  Island  ■  Lio'hthouse 

Brothers  Islets:  SE.  Islet 

Tong-sang  Harbor :  Fall  Peak 

11  20. 

5  08 

12.0 

7.6 

Chapel  Island :  Lighthouse 

Amoy:  Taitan  I.  light 

0  05 

6  13 

15.5 

9.9 

Dodd  Island :  Lio'h thouse    .... 

Chinchin  Harbor:  Pisai  Islet 

Pyramid  Point:  Extreme    . 

Ockseu  Island  ■  Lighthouse  . 

Sorrel  Rock :  Summit 

Lamyit  Island:  High  Cone  Peak 

Hungwha  Channel :  Sentry  I 

Turnabout  Island :  Lighthouse 

East  Dog  Island :  Lighthouse 

Min  River:  Pagoda,  Losing  I 

0  30 

9  45 

7  00 
3  33 

19.3 
19.0 

12.2 
12.0 

Temple  Pt 

Alligator  Island:  Summit 

Tung-yung  Islands:  Peak,  N.  end 

Coney  Island :  Summit        .       . 

Double  Peak  Island :  Highest  peak 

Pih-seang  Island  ■  Town  I 

DaTippiriiis  Rook  ■  SumiTnit 

Tae  Islands*  Summit 

Nam-quan  Harbor:  Bate  I 

9  50 

3  38 

17.2 

10.9 

Pinp-fnTig  Tslflnd  •  PuTI'Tn't 

21594°— 14- 


-22 


Page  338] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 


(3  C9 

la 


m 

Is 


Place. 


Pih-quan  Peak:  Summit 

Port  Namki:  E.  horn 

Pih-ki-shan  Island :  Summit. 

Pe-ehan  Islands:  Summit,  SW.  end 

Tung-chuh  Island :  Summit 

Kweshan  Islands:  Patahecock 

Nimrod  Sound :  Middle  islet 

Tong-ting  Islet:  Summit 

Chin-liai:  Citadel 

Ning-po:  Square  I.  light 

Chusan  Islands:  Ting-hai  Harbor 

Video  Island :  Summit 

West  Volcano  Island :  Lighthouse , 

Chapu:  Battery 

Gutzlaff  Island:  Lighthouse , 

Saddle  Islands:  N.  Saddle  light. , 

West  Barren  Island:  Summit. 

Shanghai:  Eng.  consulate  flagstaff 

Woosung:  Lighthouse 

Shaweishan  Island :  Lighthouse 

Wang-kia-tia  Bay:  Langwang  temple 

Kiaochow  Bay:  Yunui  San  light 

Staunton  Island:  Landing  place,  N.  side.. 

Shantung  Promontory :  Lighthouse 

Weihaiwei:  Light,  S.  side  harbor 

Chifoo:  Lighthouse 

Fort  flagstaff 

Miautao  Island:  Peak  of  N.  Island 

Pei  Ho:  S.  Taku  Fort,  S.  Cavalier 

Tientsin:  Shore  opp.  NE.  angle  of  wall. . . 

Shaluitien  Island :  Lighthouse 

Newchwang:  Lightship 

Hulu-shan  Bay:  N.  side 

Port  Adams:  Entry 

Liao-ti-shan  Promontory:   SW.  pt.  light. , 

Ryojun  Ko  (P.  Arthur):  Obs.  spot 

Dairen  Wan:  Isthmus  on  S.  Sanshan  I. . . 

Round  Island :  Summit , 

Thornton   Haven,    Hai-yun-tan   Island: 
Beach  opposite  Temple  Point , 

Pescadores  Islands:  Fisher  I.  light 

Second  pt.  on  N.  side 
Makung  Harbor. . . 

South  Cape:  Lighthouse 

Takau:  Saracen  Head 

Port  Heongsan 

Tamsui  Harbor:  White  Fort 

Kiirun  Ko  (Kelung  Hbr.):  Li§:hthouse  . . 

Soo  (Sauo)  Bay:  Beach  near  village. 

Botel  Tobago  Sima:  S.  extreme 

Sakishima  Gun  to,  Kumi  I.:  N.  beach... 

(Meiaco  Sima  Is.)  Broughton  Bay:  Land- 
ing place  

Port  Haddington: 

Hamilton  pt 

Tai-pin-san:  Ilirara, 
Karimata  Anch 

Raleigh  Rock:  Summit,  270  ft 

Ti-ao-usu  Island:  Summit,  600  ft 

Hoa-pin-su  Island:  N.  face 


Lat.  N. 


27  19  18 
27  26  18 

27  37  36 

28  05  07 

28  43  45 

29  22  45 
29  34  20 
29  51  53 
29  57  08 

29  59  21 

30  04  30 
30  08  04 
30  20  50 
30  36  00 
30  48  37 
30  51  41 

30  44  07 

31  14  41 
31  23  18 
31  25  27 

35  39  00 

36  02  50 

36  45  29 

37  24  00 
37  27  41 
37  34  10 

37  32  51 

38  23  37 

38  58  16 

39  09  00 

38  56  00 

40  35  00 

39  30  46 
39  16  00 
38  43  17 
38  47  50 
38  52  38 

38  40  00 

39  04  00 
23  32  53 

23  32  54 

21  55  00 

22  36  14 

24  46  00 

25  10  24 
25  09  12 
24  35  28 
22  01  40 

24  26  00 

24  21  30 

24  25  00 

24  48  18 

25  55  00 
25  58  30 
25  47  07 


Long.  E. 


120  27  14 

121  06  36 
121  12  09 
121  30  04 

121  55  21 

122  13  16 

121  43  15 

122  35  24 
121  43  06 

121  45  22 

122  03  47 
122  45  48 
121  51  25 

121  03  00 

122  10  12 

122  40  17 

123  08  27 
121  28  55 

121  29  36 

122  14  12 

119  51  30 

120  17  30 
122  16  48 
122  42  00 
122  15  05 

121  31  09 

121  21  27 

120  55  00 
117  42  48 

117  11  44 

118  31  00 

122  00  00 

121  18  03 
121  35  59 
121  08  26 
121  15  54 

121  51  59 

122  11  30 

123  10  34 

119  28  05 

119  30  12 

120  51  00 
120  15  54 

120  55  00 

121  25  00 
121  44  28 
121  49  20 

121  39  45 

122  56  00 

124  17  40 

124  06  40 

125  17  57 
124  35  00 

123  40  00 
123  30  31 


Lun.  Int. 


H.W. 


ft.  m. 


1  00 


0  12 


4  50 


4  00 

9  20 

10  25 


6  50 


4  30 


10  05 


9  45 


10  00 

10  15 

6  00 


7  27 


L.  W. 


Spg. 


ft.  m. 


ft. 


7   12 


06 


9.1 


11  03 


114 


10  12 

3  08 

4  13 


6.8 
9.0 
8.1 


1  00 


4.5 


10  50 


11.7 


3  53 


7.5 


3  32 


4.0 


3  47 

4  03 
12  13 


8.0 
3.0 
5.8 


1  14 


4.9 


2.1 


APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OP  ASIA— Continued, 


[Page  339 


Place. 


Nansei  Shoto,  Great  Nansei:  Nafa-Kiang. 

Yori-sima,  413  ft 

Yerabu-sima  peak,  687  ft.. 
Kakirouma:  Summit, 

2,207  ft 

Iwo-sima:    Volcano, 

541ft 

Oho-sima:  N.  extreme 

Kikai-jima:   Summit, 

867  ft 

Kusakaki  Jima:  IngersoU  Rocks,  530  ft. . . 

Kuro  Sima:  2,160ft 

Iwo  Shima:  Peak,  2,469  ft 

Yakuno  Shima:  Mount  Matomi,  6,252  ft. . 

P"'ira8e  Rocks:  Highest,  92  ft 

Kuchino  Shima:  Summit,  2,230  ft 

Guaja  Shima:  Summit,  1,687  ft 

Naka  no  Shima:  Peak,  3,400  ft 

Suwanose  Jima:  Volcano,  2,706  ft 

Tokara  Jima:  Summit,  860 ift 

Yoko  Shima:  Summit,  1,700  ft 

Choda  Island:  S.  pt 

Sir  James  Hall  Islands:  N.  island 

(Chemulpo:  So  Wolmi 

Marjoribanks  Harbor:  Manzoc  Islet 

Tasdefoin Islet:  Center 

Guerin  Island :  Summit,  969  ft 

Kokoun-tau  Islands:  Camp  Islet 

Barren  Island :  Center,  600  ft 

Sea  Rock:  Center,  160  ft 

Modeste  Island:  N.  peak.  1,228  ft 

Ross  Island:  Peak,  1,920ft 

Kuper  Harbor:  NE.  extreme  of  Josling  I . . 

Port  Hamilton:  W.  pt.  of  Obs.  Island 

Bate  Islands:  Summit  Tliornton  Islet. . . . 

Montravel  Island:  Center,  1,041  feet 

Quelpart  Island:  Beaufort  I.,  middle   of 

W.  side 

Observation  Island :  Point  of  \V.  arm 

Sentinel  Island :  Summit ,  400  feet 

Broughton  Head :  Extreme 

Tsau-ling-hai  Harbor:  Lighthouse 

Cape  Clonard :  Extreme 

Ping-hai  Harbor 

Liancourt  Rocks:  Summit,  410  ft 

MatuSima:  Peak,  4,000  ft 

Port  Lazaref :  S.  IJ  miles  from  the  S.  end 

of  Bontenef  I 

Tsu  Sima:  Observation  rock 

Iki  Sima:  Summit,  S.  end  of  island 

Oro  No  Sima:  Summit,  277ft 

Kosime  No  Osima:  Summit  Wilson  I 

Yeboshi  Sima:  Lighthouse 

Yobuko  Harbor :  Blu ff  opposite  Nicoya . . . 

Hirado  No  Seto:  Taske light 

Goto  Island :  Ose  Saki  light 

Pallas  Rocks:  S.  rock 

Meiaco Sima:  EarsPeak 

Nagasaki:  U.  S.  Transit  Venus  Station 

Nezumi  Jima:  Obs.  spot 

Kuchinotsu:  Lighthouse 


Lat.  N. 


26  12  25 

27  02  00 
27  21  00 

27  44  00 

27  53  00 

28  31  40 

28  18  00 

30  51  00 
30  50  00 
30  47  00 
30  17  00 
30  05  00 

29  59  00 
29  54  00 
29  52  00 
29  38  00 
29  08  00 
28  47  30 

38  27  00 
37  58  00 
37  27  40 
36  26  45 
36  24  30 
36  07  00 
35  48  08 
35  21  00 
34  42  00 
34  42  30 
34  06  00 
34  17  20 
34  01  23 
33  57  00 
33  59  00 

33  29  40 

34  39  00 
34  33  00 

34  48  00 

35  07  15 

36  05  45 

36  36  00 

37  09  30 
37  30  00 

39  19  12 


18  55 
44  30 

52  10 

53  50 
41  30 
32  30 
23  31 
36  45 
13  12 
03  00 
43  21 
43  15 
36  05 


Long.  E. 


127  40  10 

128  25  24 
128  33  10 

128  59  00 

128  14  30 

129  42  30 

129  59  00 

129  28  00 

129  55  30 

130  18  00 
130  32  00 

130  03  00 
129  5<)  00 
129  33  00 
129  52  30 
129  42  00 
129  13  30 
129  01  30 

124  34  40 

124  34  30 
126  36  27 
126  28  00 
126  24  00 
126  01  09 
126  31  00 

125  58  00 

126  19  45 
125  16  00 

125  07  00 

126  35  28 

127  18  34 
126  18  00 
126  55  00 

126  58  25 

128  14  00 
128  40  00 

128  44  00 

129  02  10 
129  33  30 

129  20  00 

131  55  00 

130  53  00 

127  32  48 

129  13  06 

129  42  30 

130  02  00 
130  25  20 
129  58  50 
129  52  43 
129  33  21 

128  36  10 
128  04  39 

128  25  00 

129  52  25 

129  49  55 

130  13  40 


Lun.  Int. 


H.W.    L.  W, 


Range. 


Spg.   Neap. 


6  30 


h.    m. 
0  15 


ft. 
5.8 


ft. 
2.5 


4  19 


10  31 


28.8 


11.6 


9  05 


2  52 


10.5 


4.2 


7  35 


1  23 


7.0 


3.0 


8  56 


2  44 


6.7 


2.4 


9  23 


3  10 


6.4 


2.5 


7  54 

8  14 


1  41 


8.4 

n.2 


3.5 

7.2 


Page  340] 


APPENDIX   IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Place. 


Lat.  N. 


Long.  E. 


Lirn.  Int. 


H.W. 


L.  W. 


Range. 


Spg. 


Kagoshima:  Breakwater  light 

Tsukarase  Rocks:  Summit,  96  ft 

Uji  Shima:  High  Peak,  1,097  ft 

Yamagawa  Harbor :  Spit  N .  of  town 

Satano  Misaki :  Lighthouse 

Shimonoseki  Strait:  MejiZaki,  extreme. 

Rokuren  Island :  Lighthouse 

Shirasu  Reef:  Lighthouse 

Susaki:  SW.  battery 

Tomo  Roads:  Tamatau  Sima 

Port  Okayama:  Take  Sima  temple 

Wusimado  Pt. :  Wusimado  Peak,  548  ft. . 

Akashi-no-seto :  Maico  Fort 

Hiogo:  Wada  Misaki  light 

Kobe:  Lighthouse 

Osaka:  Fort  Temposan  light 

Sakai:  Pier-head  light 

Osaki  Bay:  Tree  Islet,  S.  pt 

Yura  No  Uchi:  Pier 

Tanabe  Bay:  Fossil  pt 

Oo-sima  Hbr.:  Kashmosaki  light,  E.  pt. 

Uragami  Harbor:  Village  pt 

Owashi  Bay :  Hikimoto 

Mura  Harbor:  Osima  Islet 

Matoya  Harbor:  Anori-saki  light 

OmoiSaki:  Lighthouse 

Shimizu  Bay:  Mound  on  pt 

Mikomoto  Island :  Light  house 

Simoda  Harbor:  Center  I 

Yokosuka  Harbor:  Eyi  Yania  pt 

Yokohama:  Time-ball  station 

Tokio:  University  Observatory 

No  Sima  Saki:  L^hthouse 

Vriea  Island  (O Sima)  Volcano:  Summit, 

2,512  ft 

Kozu  Shima  Volcano:  Summit,  2,000  ft. 

Mikake  Jima:  Summit,  2,690  ft 

Redfield  Rocks:  S.  rock 

Mikura  Jima :  Summit 

Broughton  Rock:  Summit,  60  ft 

Fatsizio  Island :  Observation  spot 

Aoga  Shima:  Center 

Bayonnaise  Island:  Summit,  26  ft 

Smith  Island :  Summit,  250  ft 

Ponafidin  Island:  Summit,  1,328  ft 

Lots  Wife  Rock :  Summit,  300  ft 

Inaboye  Saki:  Lighthouse 

Kinkwosan  Island:  Lighthouse 

Kamaishi  Harbor:  SE.  end  of  village  — 

Yaraada  Harbor:  Ko  Sima,  90  ft 

Siriya  Saki:  Lighthouse 

Tonwi  Saki:  Center  of  Low  Islet  off 

Aomori:  Lighthouse 

TatsupiSaki:  N.  side 

Bittern  Rocks:  SW.  rock 

Tobi  Shima:  Takamori  Yama 

Awa  Sima:  NE.  extreme 

Sado  Island :  Ya  Saki 

Fushiki  Harbor:  Lighthouse 

Cape  Rokugo:  Extreme 

Niigata:  Buddhist  temple 

Mana  Sima:  Summit,  200  ft 

Manao  Harbor:  Sorenjo  Pt 

Tsuruga:  Town 


31  35  39 
31  20  00 
31  12  00 

31  12  43 

30  59  30 
33  57  46 
33  58  53 
33  59  11 

33  23  19 

34  22  37 
34  35  58 
34  37  27 
34  38  05 
34  39  20 
34  41  18 
34  39  45 
34  35  12 
34  07  42 
33  57  34 
33  41  14 
33  28  15 

33  33  37 

34  06  10 
34  13  52 
34  21  57 

34  35  52 

35  00  51 
34  34  25 

34  39  49 

35  17  30 
35  26  41 
35  39  18 
34  54  17 

34  43  30 
34  13  15 

34  05  00 
33  56  50 
33  52  00 
33  39  00 
33  04  24 

32  29  00 
32  00  40 

31  27  00 
30  28  26 
29  46  28 

35  42  13 

38  16  57 

39  16  30 

39  27  17 
41  25  58 
41  33  34 

40  50  00 

41  16  17 
40  31  00 
39  12  02 
38  29  23 
38  19  55 

36  47  47 

37  31  45 
37  55  14 
37  35  00 
37  02  37 
35  40  24 


130  33  49 
129  46  20 

129  29  00 

130  37  00 
130  39  30 
130  57  50 
130  52  07 
130  47  36 
133  17  00 
133  23  23 

133  59  24 

134  09  21 

135  01  51 
135  10  56 
135  11  34 
135  26  00 
135  27  44 
135  08  19 
135  07  21 
135  23  04 
135  51  59 

135  54  25 

136  14  35 
136  48  51 

136  54  09 
138  13  49 
138  31  19 
138  56  30 

138  57  30 

139  39  43 
139  39  00 
139  44  30 
139  53  24 

139  23  00 
139  08  00 
139  31  00 

138  48  15 

139  34  00 
139  17  45 
139  50  24 

139  43  31 

140  00  00 
140  02  00 
140  14  02 
140  19  40 

140  52  22 

141  35  33 
141  52  50 
141  59  00 
141  27  32 
140  56  36 
140  44  40 
140  22  37 
139  31  00 
139  32  58 
139  15  31 

138  27  09 

137  03  15 
137  19  00 

139  03  01 
136  54  00 
136  58  24 
136  01  22 


ft.  in. 
6  40 


7  20 


8  30 


5  55 
11  16 


7  30 


6  23 
5  52 


5  52 


5  25 


5  04 


4  30 


2  30 


ft.  m. 
1  00 


ft. 
10.5 


1  08 


9.5 


2  20 


6.7 


12  08 
5  04 


5.0 
10.2 


1  25 


4.7 


0  10 
12  04 


4.7 
4.3 


12  04 


3.9 


11  30 


4.9 


11  17 


3.7 


10  45 


3.4 


8  42   0.  6   0. 4 


APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— ContiBued. 


[Page  341 


Place. 


Oki  Islands:  N.  pt 

Taka  Yama  (Cape  Louisa):  Extreme. 

Ai  Sima:  Summit,  300  ft 

Mino  Sima:  Summit,  492  ft 

Kado  Sima:  Tsuno  Shima  light 

Hakodate:  Lightship 

Endermo  Harbor:  Hluff  on  E.  side. . . 

Okishi  Bay :_  Lighthouse 

Noshiaf  Saki:  Lighthouse 

Nemuro :  Benten  Sima  light 

Notsuke  Anchorage:  Village 

Noshiaf  Misaki:  Lighthouse 

Rifiiri  Islet:  Peak,  5,713  ft 


Kunashir  Island :  St.  Anthonys  Peak . 

Iturup  Island:  NE.  pt 

Urup  Island :  Cape  Vanderlind 

Broughton  Island :  Siunmit 

Simusir  Island :  Prevost  Peak 

Ketoy  Island :  S.  pt 

Matana  Island :  Peak ' 

Shiash-Kotan  Island :  Center 

Kharim-Kotan  Island :  Peak 

Oune-Kotan  Island:  SW.  pt 

Moukon  rushi  Island :  Center 

Pore  musir  Island :  Fool's  Peak 

Soumshu  Island :  Center 


Karafuto 


(S.  Sakhalin): 

C.  Nortoro  (Nifihi  Notoro  Mi- 
saki) Light 

C.  Shiretoko  (Nata  Shiretoko 
Misaki) 


Sakhalin  I.,  Cape  Elizabeth:  N.  pt 

Wawoda  Rock:  Summit,  12  ft 

Expedition  Bay :  Lighthouse 

Port  Novogoroa :  Lighthouse 

Vladivostok:  Cape  Goldobin  light 

Cape  Povorotnyi :  Lighthouse 

Port  Olga:  Lighthouse 

St.  Vladimir  Bay :  Orekhera  Pt 

Shelter  Bay 

SybilloBay 

Rque  Bay 

Bullock  Bay 

Luke  Point:  Extreme 

Cape  Disappointment:  Extreme 

Cape  Suffren:  Extreme 

Cape  St.  Nikolaia:  Lighthouse 

De  Kastri:  Lighthouse 

Nikolaevsk:  Cathedral 

Great  Shantar  Island :  N .  pt 

Port  Aian :  Cape  Vneshni 

St.  Jona  Island:  Summit,  1,200  ft 

Okhotsk:  Battery 

Cape  Lopatka:  Extreme 

Petropavlovsk :  Rakof  light 

Cape  Shipunski:  Extreme 

Bering  Island:  Cape  Khitroff 

Mednoi,  or  Copper  Island:  SE.  extreme. 

Cape  Kamchatka:  Extreme 

Karajinski  Island:  S.  pt 

Cape  Oliutorski:  Extreme,  2,480  ft 

Cape  Navarin:  Extreme,  2,512  ft 


Lat.  N. 


36  30  00 
34  40  00 
34  32  00 
34  48  00 
34  21  12 

41  47  36 

42  19  54 

42  56  52 

43  22  56 
43  20  22 

43  33  11 
45  26  30 
45  11  00 

44  20  00 

45  38  30 

45  37  00 

46  42  30 

47  02  50 

47  17  30 

48  06  00 

48  52  00 

49  08  00 
49  19  00 

49  51  00 

50  15  36 
50  46  00 


45  53  10 

46  01  20 

54  24  30 
42  14  30 
42  38  05 

42  33  40 

43  05  13 

42  41  00 

43  22  00 

43  53  40 

44  30  00 
44  43  45 

44  46  15 

45  05  00 
45  19  30 
45  41  30 

47  20  00 

48  59  30 
51  28  00 
53  08  05 

55  11  00 

56  25  28 
56  22  30 
59  19  45 

51  02  00 

52  52  37 

53  04  30 

54  56  00 
54  32  24 
56  10  00 

58  26  00 

59  55  GO 
62  14  30 


Long.  E. 


133  23  00 
131  30  00 
131  18  00 
131  09  00 
130  50  29 
140  41  49 

140  59  33 

144  52  38 

145  49  10 
145  34  40 

145  18  00 

141  38  40 
141  19  00 

146  15  00 
149  14  00 

149  34  00 

150  28  30 

151  52  50 

152  24  00 

153  12  30 

154  08  00 
154  39  00 
154  44  00 
154  32  00 
156  15  20 
156  26  00 


142  04  51 

143  26  30 

142  46  30 
137  17  00 

130  48  45 

131  10  00 
131  52  46 
133  02  00 
135  15  00 

135  27  19 

136  02  00 
136  22  30 
136  27  15 

136  44  00 

137  10  15 

137  38  15 

138  58  00 
140  23  40 
140  48  00 
140  42  58 

137  40  00 

138  25  50 

143  15  45 
143  07  14 
156  46  00 
158  46  42 
160  04  00 
166  43  00 
168  09  00 
163  24  00 
163  34  00 
170  22  00 
179  04  30 


Lun.  Int. 


H.W, 


h.    m. 


11  41 


11  20 


2  45 


9  50 
10  45 


0  10 


3  55 
3  30 


6  00 


L.  W, 


h.    m. 


5  28 


10  00 
9  45 
9  53 

10  00 
9  46 

11  05 


5  08 


9  00 


3  40 

4  40 


Range. 


10  08 
9  45 


Spg. 
ft. 

i.i' 


12  15 


3.0 
3.5 
3.0 
3.1 
2.1 
3.7 


4.2 


L9 


2.7 
6.3 


7  30   8.4 


4.6 
5.1 


4.5 


Neap. 

ft. 
'6.5 


1.2 
1.5 
L4 
L4 
0.5 
L8 


1.7 


0.8 


LI 
2.6 


3.4 


1.9 

2.1 


L8 


Page  342]                                    APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 

1 

Place. 

Lat.  N. 

Long.  \V. 

Lun 

Int. 

Range.         1 

n.  w. 

L.  ^\'. 

Spg. 

Neap. 

i 
£ 

St.  Matthew  Island:  Cape  Upright,  SE.  pt. 
St.  Lawrence  Island:  N.  pt 

60  18  00 

63  12  00 

64  16  00 
64  25  55 
64  24  30 
64  46  00 

64  50  00 

65  00  30 

66  02  00 

172  04  00 
159  50  00 

173  10  00 
173  07  15 
172  12  30 
172  07  00 

Long.  E. 
178  40  00 

Long.  W. 
175  54  00 
169  32  30 

h.    m. 

h.    m. 

ft. 

ft. 

Cape  Tchoukotskio :  Extreme 

Port  Providence:  Emma  Harbor 

Cape  Indian:  Extreme 

Arakam  Island:  Cape  Kiguinin 

Anadir  River:  Mouth 

Cape  Bering:  Extreme 

East  Cape :  Extreme 

ISLANDS  OF  THE  PACIFIC. 

a 

H 
« 

0 

u 

el 
0, 

X 

•0 

fl 

4 
a 

M 
h 

.a 
0 

Malpelo  Island:  Summit,  1,200  ft 

Cocos  Island:  Head  of  Chatham  Bay 

Redondo  Rock:  Summit,  85  ft 

4  03  00 

5  32  57 

0  13  30 
0  20  00 
0  18  50 

0  34  25 

1  22  55 
0  59  00 
0  31  00 
0  15  20 
0  25  00 
0  36  30 
0  33  25 

0  50  30 

1  19  00 

1  25  00 

0  44  15 

1  57  17 

3  51  26 

4  41  10 

5  52  15 
0  13  30 

0  49  00 

Lat.  S. 

2  40  54 
2  35  00 

1  50  00 
1  29  14 
1  23  42 
1  17  14 
0  36  00 

Lat.  N. 
0  11  10 

0  20  54 

0  51  30 

1  38  45 

1  44  15 

2  03  00 

3  01  30 

81  36  00 
86  59  17 

91  03  00 

89  58  43 

90  30  08 

90  44  23 

91  49  43 
91  29  12 
91  36  00 
90  52  53 
90  43  30 
90  41  00 
90  33  58 
90  06  13 
90  28  13 

89  40  08 
89  16  58 

157  27  45 

159  21  50 

160  24  30 
162  05  00 
176  32  39 

176  43  09 

Long.  E. 

177  01  13 
176  07  00 
175  39  00 

175  12  20 

176  31  33 
175  57  09 
174  24  00 

173  32  40 

173  51  14 
173  03  30 
173  03  00 
173  07  00 
173  25  30 
172  45  40 

Towers  Island :  W.  cliff 

Bindloe  Island:  S.  summit 

Abingdon  Island:  Summit,  1,950  ft 

Wenman  Island:  Summit,  550  ft 

Albemarle  Island:  Iguana  Cove 

2  00 

8  13 

6.2 

3.1 

Marlborough  Island:  Cape  Hammond 

James  Island:  Sugarloaf,  1,200  ft 

2  45 

8  58 

5.2 

2.6 

Jervis  Island:  Summit 

Duncan  Island :  Center  hill .... 

Indefatigable  Island :  NW.  bay 

2  00 

8  13 

6.2 

3.1 

Barrington  Island:  W.  summit,  900  ft 

Charles  Island:  Summit,  1,780  ft 

2  10 

8  23 

6.0 

3.0 

Fatu  Iluku  or  Hood  Island:  E.  summit, 
640  ft 

Chatham  Island:  Mount  Pitt,  800  ft 

Christmas  Island:  N.  pt.  of  Cook  Islet — 
Fanning  Island:  Flagstaff,   entrance  to 
English  Hbr 

2  20 
4  25 
6  00 

8  33 
10  38 
12  15 

6.5 

2.4 

2.4 

3.3 
1.4 
1.4 

Washington  Island 

Palmyra  Island 

5  25 

11  40 

L5 

O.^Q 

Baker  Islet :  Center      

Howland  Islands :  Center  island 

7  10 

1  00 

6.2 

3.6 

Arorai  or  Hurds  Island :  S.  pt 

Tamana  Island :  Center 

Onoatoa  Island:  Center 

Taputeuea  or  Drummond  Island:  SE.pt.. 

Nukunau  or  Byron  Island:  SE.  pt 

Peru  or  Francis  Island :  N  W.  pt 

Nonuti  or  Sydenham  Island 

Aranuka  or  Henderville  Island:  W.  pt. 
of  W  isliind 

Apamama  or  Hoppers  Island:  Entrance 
ialet 

4  30 

10  45 

4.7 

2.7 

Maiana  Island'  S  pt... 

Tarawa  Island  ■  NE  pt 

4  45 

11  00 

4.7 

2.7 

Taritari  Island '  S   t)t     

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS   OP  THE   PACIFIC— Continued. 


[Page  343 


Place. 


Ebon  Atoll:  Rube  Pt 

Jaluit  or  Bonham  Islands:  Jarbor  Pier 

Burrh  Island:  Port  Rhin,  N.  pt.  of  en- 
trance  

Majuro  or  Arrowsmith  Islands:  Anchor- 
age Djarrit  I 

Amo  Atoll:  NE.pt 

Odia  Islands :  S.  islet 

Namu  Island :  S.  pt 

Jabwat  Island :  Center 

Aurh  or  Ibbetson  Island:  NE.  end,  an- 
chorage  

Maloclab  Islands:  NW.  end  Karen  Islet.. 

Wotje  or  Romanzov  Islands:  Christmas 
Harbor 

Litkieh  Island:  NW.  pt 

Ailuk  Islands:  Capeniur  Islet 

Bigar  Islet:  Center 

Kongelab  or  Pescadores  Islands:  Center 
of  group 

Rongerik  or  Radakala  Islands:  Observa- 
tion spot 

Ailinginae  Island :  Easternmost  Islet 

Bikini  or  Eschholtz  Islands:  W.  ex- 
treme  

Wottho  or  Schanz  Island :  Center 

Eniwetok  Islands:  North  or  Engibi  I. . . 

Ujelang  or  Providence  Island:  Center  of 
atoll 

Greenwich  Island :  Northern  islet 


Lat.  N. 


Eaatemmost  of  the  S. 


Matelotas  group 
islands 

Yap  Island :  Light  in  Tomil  Bay 

Eau  Island :  Center 

Uluthi  or  Mackenzie  Islands:  Mogmog 

Islet 

Feys  or  Tromelin  Island:  E.  extreme 

Sorol  or  Philip  Island :  Center 

Eauripik  or  Kama  Islands:  E.  islet 

Oleai  group:  Raur  Islet,  N.  pt 

Ifalik  or  Wilson  Islets:  N.  end 

Faraulep  Island :  S.  end 

W.  Faiu  Islet:  Center 

Olimarao  Islet:  Center , 

Toass  Island :  Center 

Satawal  Island :  Center 

Coquille  or  Pikelot  Island:  Center 

Suk  or  Polusuk  Island :  S.  end 

Los  Martires:  OUap  Islet,  N.  pt 

Namonuito  Islands:  Magur  Islet 

Hall  Island:  Nam  nine  Islet 

Hogolu  (Hogulu)  Group:  N.  end  of  Tsis 

Islet 

Namoluk  Islands:  NW.  islet 

Mortlock   Islands:  Lukanor,    Port   Cha- 

misso 

Nukuor  or  Monteverde  Islands:  E.  pt — 
Oraluk  or  Bordelaise  Island:  Center. . . . 
Ngatik  or  Valientes  Islands:  E.  extreme.. 

Ponapi  Island :  Ponapi  Harbor 

Mokil  or  Duperrey  Islands:  Aoura,  NE.  pt 
Pingelasp  or  MacAskill  Islands:  E.  end 

of  island 

XJalan  or  Strong  Island :  Chabrol  Harbor. 


4  35  25 

5  55  07 

6  14  00 

7  05  30 
7  09  17 

7  15  00 

8  14  00 
8  27  00 

8  19  00 
8  54  21 


Long.  E. 


168  41  31 

169  39  31 

171  46  00 

171  24  30 
171  55  51 
168  46  00 
168  03  00 
168  26  00 

171  09  00 

170  49  00 


9  28  09  170  16  05 

10  03  40  169  01  57 

10  17  25  169  59  20 

11  48  00  170  07  00 


11  19  21 

11  24  00 
11  07  00 

11  40  00 

10  05  00 

11  40  00 

9  39  00 
1  04  00 


8  18  30 

9  29  00 
9  52  30 

10  06  00 
9  46  00 
8  06  00 

6  40  00 

7  21  45 

7  15  00 

8  35  00 
8  03  00 
7  43  30 
7  29  30 

7  22  00 

8  09  00 

6  40  00 

7  38  00 

8  59  45 
8  25  30 

7  18  30 
5  55  00 


29  18 
51  00 
39  00 
48  00 
00  35 


6  41  45 

6  14  00 
5  20  06 


167  24  57 

167  35  00 
166  35  00 

166  24  25 
166  04  00 
162  15  00 

161  08  30 
154  47  55 


137  33  30 

138  04  00 

139  42  00 

139  46  00 

140  35  00 
140  52  00 
143  11  00 

143  57  30 

144  31  00 

144  36  00 

146  50  00 

145  55  45 

146  24  30 

147  06  48 

147  42  00 
149  21  00 

149  27  30 

150  14  30 

151  49  15 

151  56  30 
153  13  30 

153  58  00 
155  00  54 
155  05  00 

157  31  30 

158  17  35 

159  50  00 

160  38  43 
163  00  45 


Lun.  Int. 


H.W.    L.  W 


h.  m. 
4  45 


5  00 


4  50 


Range. 


Spg.   Neap. 


h.    m. 
11  00 


ft. 

4.7 


ft. 

2.7 


11  15 


5.0 


2.8 


11  00 


6.2 


3.6 


7  15 


1  00 


3.4 


4  00 


6  00 


10  15 


4.3 


2.4 


12  15 


3.5 


2.0 


Page  344]                                   APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS   OF  THE   PACIFIC— Continued. 

4^ 

6 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range.         1 

H.W. 

L.W. 

Spg. 

Neap. 

i 

V 

s 

t 
I 

£ 

M 

e 

fl 

2 

•s 
« 

» 

d 
« 

a 
£ 

V 
G 
si 
» 

M 

fl 
« 

B 

Angaur  Island:  SW.  pt 

o         /           9 

6  53  55 

7  02  00 
7  08  00 

7  19  00 

7  40  30 

8  08  00 

4  20  00 
3  02  00 

5  20  00 

13  26  22 

14  07  30 

14  59  22 

15  08  30 

15  17  10 

16  20  00 

16  41  00 

17  17  00 

17  36  00 

18  04  00 

18  46  20 

19  45  00 

20  00  00 
20  32  54 
19  15  00 
14  41  00 

16  44  48 
10  17  00 

19  46  14 

20  03  00 
19  28  00 

19  38  26 

20  33  39 
20  36  00 

20  52  00 

21  06  17 
21  18  16 
21  15  08 
21  17  57 

21  17  55 

22  12  51 
21  57  17 

23  05  50 
23  35  18 

23  46  00 
25  00  40 
25  31  00 

25  48  00 

26  00  00 

27  56  30 

28  13  15 
28  24  45 

24  14  00 

134  05  24 

133  18  03 

134  27  00 

134  32  30 
134  39  30 
134  17  00 

132  21  00 

131  11  00 

132  16  00 

144  39  42 

145  13  04 
145  36  20 
145  43  55 
145  42  50 
145  39  00 
145  47  00 
145  57  00 
145  55  00 
145  52  00 
145  41  45 
145  30  00 
145  21  00 
144  54  00 
166  31  30 

168  54  28 

Long.  W. 

169  32  24 
109  13  00 

155  05  31 
155  48  00 

155  55  00 

156  00  15 
156  35  04 
156  26  00 

156  35  00 

157  18  32 
157  39  07 
157  48  44 
157  51  34 
157  51  54 
159  30  47 
159  40  08 

161  58  17 
164  40  47 
166  17  57 
168  00  52 

170  39  20 

171  44  00 
173  57  00 
175  46  00 

177  21  30 

178  27  45 

Long.  E. 
154  00  00 

! 
A.    7n.    1     h,    7n. 

ft- 

ft. 

Pililu  Island :  S.  pt 

1 

Earakong  or  Akamokan  Islands:  Center.. 
Korro  Islands:  Korror  Harbor,  Malakal 
pier 



Baubeltaub  Island:  Cape  Artingal 

Kyangle  Islets:  Center  of  largest 

Warren  Hastings  Island:  Center 

Nevil  or  Lord  North  Island:  Center 

Sonserol  Island:  Approx. 

Guam:  Fort  Sta.  Cruz,  Harbor  of  Apra.. . 
Rota  Island:  Summit 

7  20 

1  20 

2.6 

L5 

Tinian  Island:  Sunharon  village 

Saipan  Island:  Magicienne  Bay,  landing. 

Tanapag  Hbr.,  Garapag... 

Anataxan  Island:  Center 

7  00 

0  50 

2.0 

LI 

Sariguan  Island:  Center 

Guguan  Island:  Center 

Alamaguan  Island:  Center 

Pagan  Island:  SW.  pt 

Agrigan  Island:  SE.  pt 

Asuncion  Island:  Crater,  2,600  ft 

Urracas  Islands:  Largest  islet 

Farralon  de  Pajaros:  S.  end 

Wake  Island:  Obs.  spot 

Gaspar  Rico  Reef:  N.  clump  of  rocks .... 

Johnston  or  Comwallis  Islands:  Flagstaff 
on  W.  island 

Clipperton  Island :  Center 

Hawaii  Island:  Hilo,  Kanaha  Pt.  light 

Kawaihae  light 

3  09 

9  08 

2.3 

L3 

Kealakeakua  Bay  light. 

Kailua,  stone  chiirch. . . 

Kahoolawe  Island:  Summit 

2  20 

8  10 

L6 

0.9 

Maui  Island :  Kanahena  Pt.  light 

Lahaina  light 

3  32 
2  38 

9  58 
8  56 

2.2 
2.1 

L2 
LI 

Molokai  Island:  Lighthouse 

Oahu  Island:  E.  pt  Makapuu  station .... 
Diamond  Head 

Honolulu,  Tr.  of  V.  Obs. . . . 

Honolulu,  Reef  light 

Kauai  Island:  Hanalei,  Black  Head 

Waimea,  stone  church .... 

Bird  Island:  Center 

3  46 

9  59 

L5 

0.8 

4  00 

10  20 

2.0 

LI 

Necker  Island:  Center 

French  Frigate  Shoal:  Islet  (120  ft.) 

Gardiner  Island:  Center 

Marc  Reef:  NW.  pt 

Laysan  Island:  Lighthouse 

Lisiansky  Island:  Lighthouse 

Pearl  and  Hermes  Reef:  NE.  extreme 

Midway  Islands:  Lighthouse,  Sand  I 

Ocean  Island:  Sand  Islet 

3  30 

9  45 

LI 

0.6 

Marcus  Island :  Center 

I 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS   OF  THE   PACIPIC— Continued. 


[Page  345 


Place. 


Ogasawara  Is.  (Benin  Is.),  Parrys Group: 

N.  rock 

Kater  Island: 

N.  rock 

Peel     Island: 
Port  Lloyd, 
observatory 
Volcano  Is.,  San  Alessandro  or  North  Is- 
land: Center 

Sulphur  Island 

San  Augustine  Island :  Center 

Rosario  Island :  Center,  148  ft 

Douglass  Rocks:  Center 

Borodino  Islands:  Center  of  N.  island.. 

Center  of  S.  island.. 

Rasa  Island:  Center 


Fatu  Hiva  Island:  S.  pt 

Motane  Island:  SSE.  pt 

Tahuata  Island:  Port  Resolution,  water- 
ing place 

Hiva-Oa  Island:  C.  Balguerie 

Fatu  Huku  Island:  Center 

Roa  Poua  Island:  Obelisk  Islet 

Nuka-Hiva  Island:  Port  Tai-o-hae  light. 

Iliaou  Island:  S.  pt 

Motu-ili  Island:  Summit,  130  ft 

Ua-Huka  or  Ua-Una  Island:  N.  pt 

Fetouhouhou  Island:  NE.  pt 


Caroline  Islands:  Solar  Eclipse  Transit 
Pier 

Voetok  Island:  Center 

Flint  Island:  S.  extremity 

Maiden  Island:  Flagstaff,  W.  side 

Starbuck  Island:  Flagstaff,  W.  side 

Penfhyn  or  Tongarewa  Island:  NNW.  pt 

Jarvis  Island:  Center 

Reirson  Island:  Church 

Humphrey  Island:  N.  pt 

Union  or  Tokelau  Islands:  Spot  N.  of 

Fakaofu  or  Bowditch  Islet 

Union  or  Tokelau  Islands:  Nuku-nono, 

or  SE.  island,  Duke  of  Clarence  I 

Union  or  Tokelau  Islands:  Clump  on  S. 

island,  Oatafu  or  Duke  of  York  I 


Canton  or  Mary  Island:  N.  pt. 

Enderbury  Island:  W.  pt 

Phoenix  Island,  N.  pt 

Bimeys  Island:  S.  pt 

Gardners  Island :  Center 

McKean  Island:  Center 

Hulls  Island:  W.  pt 


Mukulaelae  or  Mitchells  Island:  S.  pt 

Fimafuti  or  EUice  Island:  E.  pt , 

Nukufetau  or  De  Peysters  Island:  S.  pt. , 

Vaitupu  Island:  S.  end 

Nui  or  Netherland  Island:  S.  pt 

Nauomaga  Island:  Center 

Niutao  Island:  Church 

Nanomea  Island :  Center 


Lat.  N. 


Long.  E. 


27  45  00     142  06  53 


27  31  00 


27  05  37 

25  14  00 
24  48  00 

24  14  00 
27  15  32 
20  30  00 

25  59  38 
25  52  45 
24  27  00 

Lat.  S. 
10  32  00 
10  01  40 

9  56  00 
9  45  00 
9  27  30 
9  29  30 
8  55  13 
8  03  30 
8  44  00 
8  54  00 
7  55  00 


10  00  01 

10  06  00 

11  25  23 

4  03  00 

5  37  00 

8  55  15 
0  22  33 

10  02  00 
10  20  30 

9  23  02 
9  13  06 

8  39  40 


44  25 
08  30 
42  28 

34  15 
37  42 

35  10 
30  95 


9  18  00 
8  25  19 
8  04  02 
7  32  00 
7  15  45 
6  12  00 
6  06  00 
5  39  00 


142  11  53 


142  11  23 

141  11  00 
141  13  00 
141  20  00 
140  50  28 
136  10  00 
131  19  30 
131  12  17 
131  01  50 

Long.  W . 
138  39  20 

138  48  30 

139  09  00 
138  47  40 

138  55  10 

140  04  45 
140  04  00 
140  44  00 
140  38  30 

139  33  30 

140  34  40 


150  14  30 
152  23  00 

151  48  34 
155  01  00 
155  56  00 

158  07  00 

159  54  11 
161  05  30 
161  01  12 

171  14  46 

171  44  40 

172  28  10 

171  45  29 
171  10  00 

170  42  37 

171  32  07 
174  40  18 
174  17  26 

172  13  28 

Long.  E. 
179  50  00 
179  07  25 
178  28  51 
178  41  01 
177  16  50 

176  16  30 

177  20  01 
176  06  15 


Lun.  Int. 


H.W.    L.W. 


Range. 


Spg.   Neap. 


h,    m.        h.    tn. 


6  10 


0  00 


2.4 


L4 


2  30 


8  45 


3.1 


L9 


3  50 


10  05 


3.5 


2.1 


4  00 


10  14 


LI 


0.7 


0  00 


12  15 


L5 


0.9 


6  00 


12  13 


2.4 


L4 


5  00 


11  15 


4.6 


2.7 


Page  346] 


APPENDIX  IV. 

MARITIME  POSITIONS   AND  TIDAL  DATA. 
ISLANDS   OF  THE   PACIFIC— Continued. 


Place. 


Ocean  or  Paanopa  ^sland:  Center  (appx.) 

Pleasant  Island :  Center 

Indispensable  Reefs:  S.  pt.  of  S.  reef 

Rennel  Island:  SE.  extreme 

W.  end 

San  Cristoval  Island :  Point  Wangalaha. . 
Guadalcanal    Island:      Wanderer    Bay, 

mouth  of  Boyd  Creek , 

Florida  Island:  Mboli  Harbor,  Tree  Islet. 
Malaita  Island:  Village,   Mary  I.,    Port 

Adam 

Stewart  Islands:  Largest  islet 

Isabel  Island:  N.  side  of  Cockatoo  Islet. . , 

Gizo  or  Shark  Island:  N.  point  village 

Choiseul  Island:   Choiseul  Bay  entrance 

Treasury  Islands:  Observation  Islet 

Bougainville  Island:  Husker  Pt.,  Gazelle 

Harbor 

Buka  Island :  Cape  North 

Lord  Howe  Group:    Center,    small    SW. 

islet 

Center,    small    NE. 

islet 

NW.    pt.    of   Ham- 
mond I 

Neu  Pommem  (New  Britain),  Blanche 

Bay:  Matupil.  N.pt 

Duke  of  York  Island:  Makada  Harbor, 

SpitPt 

Neu  Mecklenburg  (New  Ireland):  Car- 
teret Harbor,  Cocoa- 
nut  I 

Katharine  Haven 

Holz  Haven,  E.  side.  . 
New  Hanover  Island:  Water  Haven, 
creek  mouth . .  . 
North  Haven  an- 
chorage  

St.  Matthias  Island:  SW.  extreme 

Admiralty   Island:  Nares    Harbor,   obs. 
islet 

St.  Andrew  Island:  Violet  Islet,  60  ft 

Jesus  Maria  Island :  SE.  pt 

Commerson  Island :  Center  of  largest  islet . 

Anchorite  Island:  N.  pt 

Hermit  or  Loaf  Island :  Peme  Islet 

Purdy  Island:  Mole  Islet 

Point  d'Urville:  extreme 

Drei  Cap  Peninsula:  Wass  Islet 

Triton  Bay:  Fort  Dubus,  Dubus  Haven. . 

Cape  Walsche:  Extreme 

Fly  River:  Free  Islet,  S.  pt 

Port  Moresby:  N.  end  of  Jane  I 

Cape  Rodney:  Extreme 

South  Cape:  S.  pt.  Su  Au  I 

Hayter  Island:  W.  end 

Cape  Cretin:  Cretin  Islets 


0  52  00 

0  25  00 

12  50  15 

11  52  15 

11  33  45 

10  17  32 

9  41  47 
9  01  30 

9  30  00 
8  23  00 
8  30  50 
8  05  40 

6  42  40 

7  24  30 

6  35  00 
5  00  00 

5  38  00 

5  18  00 

5  18  GO 

4  14  12 
4  06  25 


41  26 
11  00 
47  30 


2  33  43 


26  30 
35  00 


1  55  10 

2  25  40 
2  22  00 
0  45  00 

0  53  15 

1  28  00 

2  51  00 

1  25  40 

2  44  00 

3  47  00 
8  22  00 

8  41  00 

9  25  30 
10  14  30 
10  43  35 
10  37  00 

6  43  00 


Long.  E. 


169  35  00 
167  05  00 
160  26  00 

160  40  15 
159  55  00 

161  33  30 

159  39  30 

160  27  20 

161  27  40 

162  58  15 
159  38  20 
156  50  15 
156  23  16 
155  34  00 

155  05  00 
154  35  00 

159  21  00 

159  34  00 

159  17  00 

152  11  35 
152  06  15 


152  42  25 
151  35  30 
150  57  35 

150  04  33 

149  55  36 
149  37  00 


146  40  56 

147  28  35 
147  55  00 
145  17  00 
145  33  04 

145  08  00 

146  15  00 

135  28  12 
132  04  00 
134  06  00 
137  40  00 
143  36  04 

147  07  04 

148  30  30 
150  14  20 
150  40  34 
147  53  20 


Lun.  Int. 


H.  W.    L.  W. 


6  45 


5  00 


12  00 


9  00 


2  50 


2  30 


0  55 


8  50 


9  15 

8  25 


Spg.   Neap. 


ft.  m. 


ft. 


0  33 


11  15 


5  47 


2  45 


9  03 


8  43 


7  08 


2  38 


3  00 
2  12 


3.3 


3.5 


2.7 


2.1 


2.4 


2.4 


7.3 


8.0 


8.1 
5.8 


APPENDIX  IV. 

MARITIME   POSITIONS   AND  TIDAL  DATA. 
ISLAHUS   OF  THE   PACIFIC— Continued. 


[Page  347 


is 


N 

s  , 


Place. 


Trobriand  Islands:  NE.  pt.  Cape  Denis. . 

Woodlark  Islands:  N.  pt 

D'Entrecasteaux  Is.:   Ferj^uson   I.,   S\V. 
extreme 

Well  Island,  E.  pt. 

Normanby  I.,ob8. 

islet 

St.  Aignan  Island:  Summit 

Renard  Islands:  W.  pt 

Rossel  Island:  E.  pt 

Adele  Island:  S.  extreme 


Coringa  Islands:  Chilcott  Islet. 

Herald  Cays:  NE.  Cay 

Tregosse  Islands:  S.  islet 

Lhou  Reef:  Observation  Cay. . 

Mellish  Reef:  Cay  beacon 

Bampton  Island 

Renard  Island:  Center 

Wreck  Reef:  Bird  Islet 

i  Cato  Island:  Center 


Duff  or  Wilson  Group:  N .  island 

Matema  or  Sw^low  Group:  Nimanu  Islet . 

Tinakula  Island:  Summit,  2,200  ft 

Nitendi  Island:  NE.  pt.,  Cape  Byron 

Tapua  Island:  Basilislc  Harbor,  S.  pt.  of 

entrance 

Vanikoro:  Ocili  village 


i 


Torres  or  Ababa  island:  Hayter  Bay, 
Middlel 

Vanua  Lava  Island:  Port  Patterson, 
NusaPt 

Santa  Maria  Island:  Lasolara  Anchorage. 

Aurora  Island :  Laka-rere 

MallicoUo  Island:  Port  Sandwich,  pt.  on 
E .  side 

Vate  or  Sandwich  Island:  Havannah 
Harbor,  Matapou  Bay  flagstaff 

Erromaugo  Island:  Dillon  Bay,  Pt.  Wil- 
liams  

Tanna  Island:  Port  Resolution,  Mission. 

Erronan  or  Futuna  Island:  NW.  pt 

Aneityum  Island:  Port  Anatom,  Sand 
Islet 

Matthew  Island:  Peak,  465  feet 

Hunter  Island:  Peak,  974  feet 

Walpole  Island:  S.  pt 


Mitre  Island :  Center 

Rotumah  Island:  Epipigi  Peak. 


Kandavu  Island:  N.  rock  Astrolabe  Reef 

light 

Mt.     Washington,     N. 

peak 

Ngaloa    Harbor,    outer 

beacon 

Vatu  Lele  Island:  S.  pt 

Ovalau  Island:  Levuka  lighthouse 


Lat.  s. 


8  24  00 

9  03  30 

9  38  00 
9  41  00 

9  43  53 
10  42  00 

10  52  40 

11  23  25 
11  29  10 

16  50  00 

16  55  50 

17  43  00 
17  07  20 
17  24  39 
19  08  00 
19  14  00 

22  10  30 

23  15  02 

9  48  00 
10  21  00 
10  23  30 

10  40  00 

11  17  30 
11  40  24 


13  15  00 

13  48  00 

14  11  00 
14  58  00 

16  26  00 

17  44  58 

18  47  30 

19  31  17 

19  31  20 

20  15  17 
22  20  12 
22  24  02 
22  38  07 

11  55  00 

12  30  10 

18  38  15 

19  07  09 

19  05  30 
18  36  00 
17  40  45 


Long.  E. 


151  01  24 

152  47  00 

150  30  00 
150  58  00 

150  44  43 
152  42  04 
152  47  12 
154  08  00 

154  25  14 

149  58  00 

149  11  54 

150  42  04 
152  06  20 

155  52  24 

158  40  00 

159  00  00 
155  28  24 
155  33  04 

166  53  15 
166  17  15 

165  47  30 

166  00  30 

166  32  14 
166  57  45 


166  33  00 

167  30  31 

167  30  00 

168  02  00 

167  47  15 

168  18  50 

168  58  00 

169  27  30 

170  11  15 

169  44  45 

171  20  30 

172  05  15 
168  56  45 

170  10  00 
177  07  15 


178  32  15 

177  57  09 

178  10  24 

177  38  00 

178  49  00 


Lim.  Int. 


H.W.    L.  W 


ft.  m. 
4  45 
7  05 


4  50 


6  40 


4  38 

5  15 


5  10 


6  15 


6  40 


ft.  tn. 

10  58 

0  53 


11  05 


0  30 


10  50 

11  27 


11  23 


0  00 


0  25 


Range. 


Spg.   Neap. 


ft. 
3.0 

4.2 


ft. 

L8 

2.5 


3.8 


2  3 


3.8 


2.3 


3.8 
3.0 


L9 
L8 


3.1 


L9 


4.2 


2.5 


4.0 


2.4 


Page  348]                                   APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  TTTF.   PACIFIC— Continued. 

1 

Place. 

Lat.  S. 

Long.  E. 

Lun.  Int. 

Range.         1 

H.  W. 

h.    m. 

L.  W. 

Spg. 

Neap. 

i 

•0 

H 

S 

<£ 

M 
« 

9 

a 

ei 

Viti  Levu  Island:  Summit  of  Malolo  Islet. 
Suva  Harbor,  low  light . 
Mbega  or  Mbengha  Island:  Swan  Harbor, 
Leaven  Pt 

17  44  45 

18  06  50 

18  22  00 

19  09  38 
18  32  49 
17  59  32 
17  37  11 
17  27  14 
17  15  21 
16  42  01 

16  57  53 

16  49  19 

16  08  00 

16  46  00 
15  44  45 

17  03  00 
17  25  33 
17  17  20 
17  10  00 
17  25  26 
17  44  12 
17  39  33 

17  59  00 

18  14  10 
18  25  46 
18  38  56 
18  46  00 
18  56  15 

18  58  57 

19  03  00 
19  04  00 

19  49  11 

20  39  10 

21  00  09 
21  01  39 

14  14  20 
13  23  35 

15  34  00 
15  52  00 

15  58  00 

13  45  00 

13  48  56 

14  18  06 
14  19  00 

14  32  00 

19  10  00 
10  52  47 

13  14  30 
18  05  50 

16  28  00 

15  48  00 

16  52  00 

177  09  00 

178  24  40 

178  06  53 

179  44  27 
179  56  25 
179  14  08 
178  59  29 

178  57  46 

179  20  44 
178  54  15 

178  48  32 

179  16  08 
Long.  W. 

179  58  46 
179  51  00 
179  54  26 
179  17  00 
179  32  17 
179  10  00 
179  05  45 
179  10  33 
179  19  49 

178  50  27 

179  04  00 
178  52  00 
178  27  04 
178  30  54 
178  44  00 

178  59  05 

179  52  58 
178  47  25 
178  33  25 
178  13  38 
178  43  27 
178  44  03 
178  49  47 

178  06  45 
176  11  47 

175  40  40 
173  52  00 
173  52  00 

172  17  00 
171  44  56 
170  42  14 
169  32  00 

168  09  00 

169  50  00 
165  51  30 

163  04  10 
163  10  00 
154  30  00 
154  31  00 
154  OOOO 

h.    m. 

ft. 

ft. 

6  30 

0  15 

3.6 

2.2 

Matuku  Island:  N.  side  of  Matuku  en- 
trance  

Moala  Island:  Rocks  off  N.  pt 

Ngau  Island:  Herald  Bay,  E.  side 

Wakaya  Island :  Rocky  Peak 

Makongai  Island:  Dilliendreti  Peak 

Goro  Island:  NW.  pt 

Vanua  Levu  Island:  Mount  Dana 

Nandi,  observation 
islet 

Savu  Savu  Pt.,  ex- 
treme  

6  00 

12  13 

4.3 

2.6 

NE.Pt 

Taoiuni  Island:  Somu-Somu  town 

Thikombia  Island:  E.  hummock 

Naitamba  Island :  Center 

Vatu  Vara  Island:  N.  end,  summit 

Kanathea  Island :  S.  pt 

Vanua  Mbalavu  Island :  NW.  pt 

...« 

Mango  Island :  Pier  end 

6  10 

0  00 

3.1 

L9 

Thithia  Island :  Highest  peak 

Tuvutha  Island :  Peak 

Naian  Island :  Summit,  580  ft. 

Oneata  Island :  Summit  of  Loa  I 

Mothe  Island :  Summit 

Mamuka  Island:  Center,  260  feet 

Kambara  Island :  Highest  peak 

Totoya  Island:  Black  Rock  Bay,  W.  side. 
Fulanga  Island:  W.  bluff 

6  35 

0  20 

3.5 

2.1 

Ongea  Levu  Island :  Center 

Vatoa  or  Turtle  Island:  Hummock 

Ono  Islands:  Peak 

6  10 

0  00 

3.1 

L9 

Michaeloff  Island :  Center 

Simonoff  Island :  Center 

Fatuna  or  Home  Island:  Mt.  Schouten. . . 

Uea  or  Wallis  Island:  Fenua-fu  Islet 

Niua-fu  or  Good  Hope  Island:    NW.  ex- 
treme  

6  40 

0  28 

4.4 

2.7 

Keppel  Island :  Center 

Boscawen  Island :  Center 

Savaii  Island :  Paluale  village 

IJpulo  Is. :  Apia  Harbor,  obs.  spot 

Tutuila  Island:  Pago-Pago,  obs.  pt 

Manua  Island:  Village,  NW.  side 

Rose  Island:  Center 

Niue  or  Savage  Island :  S.  pt 

6  25 

7  00 
6  00 

0  13 

0  45 

12  13 

3.1 

2.7 
4.6 

L9 
L6 
2.7 

Danger,  or  Bernardo,  Is.:  Middle  rock... 
Suwarrow  or  Souwaroff  Island:  Cocoanut 
Islet 

3  10 

9  23 

2.4 

1.4 

Palmerston  Islands :  W.  islet 

Scilly  Islands:  E.  islet 

:::  1 

Bellingshausen  Island:  Center 

1 

Mopelia  (Lord  Howe)  Island:  Center 

1 

I 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 


[Page  349 


Place. 


Maitea  Island :  Summit 

Tahiti  Island :  Lighthouse 

Tubuai-Manu  or  Maia-iti  I.:  NW. 
Eimeo  Island:  Talu  Hbr.,  Vincennes  Pt.. 

Huaheine  Island :  Lighthouse 

Ulietea  Island :  Regent  Pt 

Tahoa  Island:  Center 

Bola-Bola  Island:  Otea-Vanua  village.. 
Tubai  or  Motu-iti  Island:  N.  pt.  of  reef. 
Marua  or  Maupili  Island :  Center 


Ducie  Island:  NE.  entrance 

Pitcaim  Island :  Village 

Henderson  or  Elizabeth  Island:  Center. . 

Oeno  Island:  N.  pt 

Mangareva  or  Gambier  Island:  Flagstaff.. 

Marutea  or  Lord  Hood  Island:  Center 

Maria  or  Moerenhout  Island :  Center 

Vahanga  Island:  W.  pt 

Morane  or  Cadmus  Island:  Center 

Tureia  or  Carysfort  Island:  E.  pt 

Miu-uroa  or  Osnabrug  Island:  Obs.  spot. . 

Tematangi  or  Bligh  Island:  N.  pt 

Nukutipipi:  SW.  pt 

Hereheretue  or  St.  Paul  Island:  Center.. 

Vanavana  or  Barrow  Island:  Center 

Nukutavake  or  Queen  Charlotte  I. :  N.  pt 
Reao  or  Clermont  Tonnere  Island:  NW. 

point 

Puka-ruha  or  Series  Island:  NW.  pt. 

Vahitahi  Island:  W.  pt 

Ahunui  or  Byam  Martin  Island:  NW.  pt. 

Pinaki  or  Whitsunday  Island:  E.  pt 

Tatakoto  or  Gierke  Island:  Flagstaff  on 

western  coast 

Hao  or  La  Harpe  Island:  NW.  pass 

Paraoa  or  Gloucester  Island:  Center 

Ravahere  Island:  S.  pt 

Reitoru  or  Bird  Island :  N .  beach 

Hikueru  or  Melville  Island:  E.  pt 

Tauere  Island:  NW^t 

Puka-puka  Island:  E.  pt 

Napuka  Island:  W.  pt 

Angatau  or  Araktcherf  Island:  W.  pt.  .  . 
Tukume  or  Wolkonsky  Island:  NW.  pt. . 

Tuanske  Island:  NW.  pt 

Nihiru  Island  (Tuanake):  SW.  pt 

Anaa  Island:  Islet  in  N.  pass 

Tepoto  Island:  N.  pt 

Haraiki  or  Crocker  Island:  SW.  pt 

Makemo  or  Phillips  Island:  W.  pass. . . . 
Fakarana  or  Wittgenstein   Island:  SE. 

pass 

Taiaro  or  Kings  I.:  Middle  of  W.  shore. . 

Aratika  Island:  E.  pt 

Toaii  or  Elizabeth  Island:  Amyot  Bay. . 

Takapoto  Island:  S.  pt 

Aheu  Island :  Lagoon  Entrance 

Rangiroa  Island :  E.  pt 

Makatea  Island :  W.  pt 

Matahiva  Island:  W.  pt 


Lat.  S. 


17  53  00 
17  29  10 
17  36  39 

17  29  23 
16  42  30 
16  50  00 
16  35  00 
16  31  35 
16  11  00 

16  26  00 

24  40  20 

25  03  50 
24  21  20 
24  01  20 
23  07  36 

21  31  30 

22  01  00 
21  20  00 

23  07  50 

20  46  20 

21  50  00 
21  38  00 
20  43  00 

19  53  17 

20  46  07 
19  16  30 

18  00  29 
18  16  00 

18  43  30 

19  37  00 
19  25  00 

17  19  30 

18  05  20 

19  08  45 
18  18  30 
17  49  35 
17  35  28 
17  20  30 
14  49  00 

14  12  00 

15  50  00 

15  44  20 

16  39  10 

16  44  29 

17  20  20 

16  47  49 

17  28  41 
16  26  09 

16  31  00 
15  43  15 
15  30  00 
15  50  00 
14  43  00 

14  29  10 

15  14  30 
15  50  30 
14  53  00 


Long.  W. 


148  05  00 

149  29  00 

150  36  56 
149  50  30 

151  01  28 
151  27  21 
151  35  00 
151  46  00 

151  48  00 

152  12  00 

124  48  00 
130  08  30 
128  19  00 
130  41  00 

134  57  54 

135  33  05 

136  10  15 

136  38  53 

137  06  15 

138  27  45 

138  56  30 
140  38  45 

143  03  15 

144  57  00 

139  08  45 
138  48  30 

136  26  30 

137  03  30 

138  53  15 

140  15  45 
138  40  45 

138  26  26 

140  59  30 

141  41  10 

142  11  31 

143  05  23 
142  35  16 
141  29  43 
138  46  45 

141  15  37 
140  53  35 

142  08  40 

144  14  45 

142  53  34 

145  30  54 

144  17  18 

143  31  17 

143  57  59 

145  22  45 

144  38  34 

145  24  45 

146  02  45 

145  11  00 

146  20  00 

147  11  00 

148  15  00 
148  39  45 


Lun.  Int. 


Range. 


H.W.    L.W. 


Spg.   Neap. 


A.  m. 


h.    m. 


ft. 


12  00 


5  48 


LO 


0.6 


12  10 


6  00 


L4 


0.8 


1  50 


8  03 


2.4 


L4 


2  40 


8  55 


2.4 


L4 


4  30 


10  43 


2.1 


L3 


Page  360] 


APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE   PACIFIC— Continued. 


9t« 


Place. 


Juan  Fernandez  Island:  Fort  S.  Juan 
Batista 

Mas  Afuera  Island :  Summit,  4,000  ft 

St.  Ambrose  Island :  N.  part  creek 

St.  Felix  Island:    Center 

Sala  y  Gomez:  N\V.  pt 

Easter  Island:  Cooks  Bay,  mission 

Rapa  or  Oparo  Island:  Tauna  Islet 

Bass  Islets  (Morotiri):  SE.  islet,  344  ft. . . 
Tubuai  or  Austral  Is.,  Vavitoal.:  Center. 

Tubuai    I.:   Flag- 
staff, N,  side 

Rurutu  I.:  N.  pt.. 

Rimitara  I. :  Center. 

Hull  Island:  NW.  pt 

Mangaia  Island:  Center 

Rarotonga  Island:  NW.  pt 

Mauki  or  Parry  Island:  Center 

Mitiero  Island:  Center 

Vatiu  or  Atiu  Island:  Center 

Hervey  Islets:  Center 

Aitutaki  Island:  Center 

Vavau  Island:  Port  Valdes,  Sandy  Pt 

Kao  Island:  Summit,  5,000  ft 

Tofua  Island:  Summit,  2,800  ft 

Tongatabu  Island:  Lighthouse 

Minerva  Reefs,  N.  Minerva:  NE.  side 

S.  Minerva:  S.  side  of  en- 
trance   

Kermadec  Is.,  Raoul  or  Sunday  I.:  Den- 
ham  B.  flagstaff 

Macauley  I. :  Center 

CiurtisL:  Center 

Conway  Reef:  Center • 

Loyalty  Is.,  Uvea  or  Halgan  I.:    Uvea 

Church 

Lifu  I.:  Wreck  Bay,   NW. 

shore 

Mare  or  Britannia  I. :  S.  pt . . . 

Port  Kanala:  Observatory 

St.  Vincent  Bay:  Marceau  I 

Noumea:  Lighthouse 

Balari  Pass:  Amed6e  I.  light 

Port  Alcmeme:  Alcmene  I 

Norfolk  Island:  Inner  end  of  jetty 

Elizabeth  Reef:  Center 

Lord  Howe  Island :  S.  end  of  middle  beach 

Balls  Pyramid:  Summit,  1,816  ft 

Macquarie  Island:  N.  pt 

Auckland  Is.:  Port  Ross,  Terror  Cove 

Campbell  Island:  S.  harbor.  Shoal  Pt 

Antipodes  Island:  Summit,  600  ft 

Bounty  Islands:  Anchorage  N.  I.,  West 
Group 

Chatham  Island,  Whare-Kauri  Island: 
Port  Waitangi,  Pt.  Hanson 

Chatham  Island,  Whare-Kauri  Island: 
Port  Hutt,  Gordon  Pt 


Lat.  S. 


33  37  36 
33  46  00 
26  18  07 
26  16  00 

26  27  41 

27  10  00 
27  35  46 
27  55  30 
23  55  00 

23  21  45 
22  29  00 

22  45  00 

21  47  00 
21  49  00 
21  11  35 
20  17  00 
20  01  00 

20  04  00 
19  18  00 
18  54  00 

18  39  02 

19  41  35 

19  45  00 

21  08  00 

23  37  06 
23  55  00 

29  15  30 

30  15  00 

30  35  00 

21  44  45 

20  27  06 

20  46  00 

21  42  00 

21  29  12 

22  00  10 
22  16  22 
22  28  44 
22  42  30 

29  03  45 
29  56  00 

31  31  38 
31  45  10 
54  19  00 
50  32  15 
52  33  26 
49  42  00 

47  43  00 

43  57  24 
43  49  03 


Long.  W. 


78  50  02 
80  46  00 

79  54  56 

80  06  56 
105  28  00 
109  26  00 
144  17  20 
143  28  21 
147  48  00 

149  35  35 

151  23  41 

152  55  00 

154  51  00 
157  56  00 
159  47  00 
157  23  00 

157  34  00 

158  08  00 

158  54  00 

159  32  00 

174  01  00 

174  59  50 

175  03  00 

175  12  00 

178  55  45 

179  07  45 

177  55  40 

178  31  45 
178  37  00 

Long.  E. 
174  37  45 

166  35  25 

167  02  30 

168  00  00 

165  58  50 

166  03  30 
166  25  52 

166  28  51 

167  27  55 

167  58  06 
159  04  30 
159  05  58 
159  16  10 
158  56  00 
166  13  20 

169  08  41 

178  43  05 

179  00  27 

Long.  W. 

176  32  15 

176  42  00 


Lun.  Int. 


Range. 


H.  W. 


ft.  m. 


4  00 
0  40 
0  10 


3  00 


6  00 


6  20 


6  20 

7  50 


6  00 


6  30 


5  40 
8  25 


7  55 
7  30 
"8'26 


11  50 

11  45 

3  20 


5  22 


L.  W. 


ft.  m. 


10  15 
6  53 
6  25 


9  13 


12  15 


0  10 


0  10 

1  35 


12  13 


0  18 


11  52 
2  13 


1  45 
1  17 
'2'68' 


5  38 
5  33 
9  30 


Spg. 


0  23 


ft. 


3.3 

2.8 
2.4 


2.4 


2.7 


3.8 


3.8 
5.5 


3.3 


4.2 


3.3 
3.1 


3.6 

4.7 
'5.4' 


3.2 
3.5 
5.3 


2.5 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATJSTRAUA. 


[Page  351 


Place. 


Groate  Eylandt:  SE.  pt 

Bickerton  Island:  Summit 

Cape  Arnheim:  Extreme 

Cape  Wilberiorce:  E.  extreme 

Cape  Wessel:  Extreme 

Dale  Point:  Extreme 

Cape  Stewart:  Extreme 

Liverpool  River:  W.  pt.  entrance. . 

Cape  Croker:  Extreme 

Port  Essington:  Govermnent  house . 
Melville  Island:  Cape  Van  Diemen. . 

Bathurst  Island :  CapeFourcroy 

Adelaide  River:  E.  entrance  pt 

Port  Darwin:  Charles  Pt.  light 

Port  Patterson:  Quail  Islet 

Port  Keate:  Tree  Pt 

Pearce  Point;  Extreme 

Victoria  River:  Water  Valley 


Cape  Dussejour:  Rock  off  cape 

Cape  Londonderry:  Extreme 

Cape  Bougainville:  Extreme 

Caseini  Island:  S.  pt 

Cape  Voltaire:  Flat  Hill 

Barker  Islets:  Center 

Montalivet  Islands:  W.  islet 

Maret  Islets:  N.  islet 

Colbert  Islet:  Center 

Prince  Regent  River:  Mount  Trafalgar. . 

Port  Nelson :  Careening  beach 

De  Freycinet  Islets:  Beacon  on  summit. . . 

Red  Islet:  Center 

Cockell  Islet:  W.  pt 

MacLeay  Islets:  Rock  off  N.  end 

Port  Usbome:  S.  pt 

Fitz  Roy  River:  Escape  Pt 

Cape  L'Ev^nue:  Extreme 

Lacepede  Island:  N\V.  islet 

Cape  Baskerville:  Extreme 

Cape  Latouche  Tr^ville:  Extreme 

Turtle  Isles:  Center  of  N.  isle 

Cape  Lamljert:  Extreme 

Legendre  Island:  NW.  extreme , 

Rosemary  Island:  W.  summit 

Enderby  Island:  Rocky  Head 

Monte bello  Island :  N .  extreme  of  reef 

Barrow  Island:  N.  pt 

Northwest  Cape:  Extreme 

Cape  Cuvier:  Extreme 

Cape  Inscription:  Extreme 

Houtman  Rocks:  N.  islet 

Port  Gregory 

Cape  Leschenault:  Extreme 

Rottnest  Island :  Lighthouse 

Perth  (Frenxantle) :  Arthur  Head  light. . . 
State  Observatory . . . 

Peel:  Robert  Pt 

Cape  Naturaliste:  Extreme 

Cape  Leeuwin :  Lighthouse 

D'Entrecasteaux  Point:  Extreme 

Nuyts  Point:  Extreme 

West  Cape  Howe:  Extreme 

Eclipse  Islets:  Summit  of  largest 

King  George  Sound:  Commissariat  house 
near  Albany  jetty 


Lat.  s. 


14  16  00 
13  45  00 
12  14  00 
11  53  00 

10  59  00 

11  36  00 
11  57  00 
11  54  00 

10  57  00 

11  22  02 
11  08  00 

11  51  00 

12  13  20 
12  23  20 

12  30  58 

13  59  00 

14  25  50 

15  13  45 

14  42  00 
13  44  00 
13  52  00 

13  57  07 

14  15  00 

13  55  00 

14  14  00 
14  23  00 

14  51  00 

15  16  36 
15  06  00 

14  59  20 

15  13  15 
15  46  00 
15  52  00 

15  39  25 
17  24  25 

16  23  00 

16  50  00 

17  09  00 

18  29  00- 

19  54  00 

20  36  00 
20  19  00 
20  27  00 
20  35  00 
20  16  45 

20  40  40 

21  46  41 

24  00  00 

25  29  19 
28  18  05 
28  12  00 

31  18  00 

32  00  20 
32  03  12 

31  57  09 

32  27  00 

33  31  45 

34  21  55 

34  52  00 

35  05  00 
35  09  00 
35  11  54 

35  02  20 


Long.  E. 


136  58  00 

136  15  00 

137  00  00 
136  34  00 
136  46  00 
136  07  00 
134  45  00 
134  12  00 
132  36  30 
132  09  18 

130  19  00 

129  58  00 

131  16  30 

130  37  00 
130  27  00 
129  37  00 
129  20  42 
129  48  14 

128  10  00 
126  57  00 
126  12  00 
125  38  45 
125  39  00 

124  55  00 

125  12  00 
125  00  00 

124  42  00 

125  07  00 
125  01  00 
124  32  11 
124  14  00 
124  04  00 
123  45  00 
123  36  27 
123  39  47 
122  55  45 
122  05  30 
122  15  00 
121  54  00 
118  48  00 
117  11  00 
116  45  00 
116  30  00 
116  23  00 
115  22  00 
115  27  45 
114  10  08 
113  21  00 

112  57  09 

113  35  33 

114  14  30 

115  30  00 
115  30  12 
115  43  48 
115  50  26 
115  44  00 
115  00  15 

115  08  00 

116  01  00 

116  38  00 

117  40  00 
117  53  45 

117  54  04 


Lun.  Int. 


H.W. 


h.    m. 


8  00 


6  17 


5  15 

4  57 
3  50 

5  45 

6  45 


11  30 


L.W. 


ft.  m. 


1  48 


0  05 


11  27 
11  18 

10  00 

11  58 
0  27 


[10  16] 


[10  53] 


Range. 


8pg. 


Neap. 


ft. 


ft. 


9.8 


5.8 


12.0 


7.1 


16.8 
17.0 
16.7 
21.9 
23.0 


9.9 
10.0 

9.9 
12.9 
13.6 


5  10 


17.6 


10.4 


[3  43] 


[2.1] 


[4  40] 


[2.6] 


Page  362] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
AUSTRALIA— Continued. 


Place. 


Bald  Isle:  Center 

Hood  Point:  Doubtful  Isles 

Recherche     Archipelago:     Termination 

Isle 

Culver  Point:  Extreme 

Dover  Point:  Extreme 


Fowler  Point:  Extreme 

Streaker  Bay:  Port  Blanche 

Coffin  Bay:  Mount  Dutton 

Cape  Catastrophe:  W.  pt 

Neptune  Isles:  SE.  islet 

Port  Lincoln:  English  Church 

Franklin  Harbor:  Observation  spot 

Port  Augusta:  Flagstaff 

Port  Victoria:  Wardang  Island  hut 

Cape  Spencer:  S.  pt 

Investigator  Strait:  Troubridge  light.. . 

Port  Wakefield:  Lighthouse 

Port  Adelaide :  Wonga  Shoal  light 

Observatory 

Cape  Jervis:  Lighthouse 

Cape  Borda:  Lighthouse 

Cape  Willoughby :  Lighthouse 

Port  Victor:  Flagstaff 

Cape  Jaffa:  Margaret  Brock  lighthouse. 
Cape  Northumberland:  Lighthouse 


Cape  Nelson:  S.  extreme 

Portland  Bay:  Lawrence  Rock 

Port  Fairy:  Griffith  Island  summit 

Cape  Otway :  Lighthouse 

King  Island:  Cape  Wickham  light 

Port  Phillip:  Point  Lonsdale  light 

Geelong:  Customhouse 

Melbourne:  Observatory 

Cape  Schanck:  Lighthouse 

Port  Western:  Extreme  of  W.  head 

Wilson  Promontory:  Light,  SE.  pt 

Kent  Island :  Deal  Island  light 

Flinders  Is.:  Strzelecki  Peaks,  SE.  peak 

Groose  Island :  Light  on  S.  end 

Banks  Strait:  Swan  Island  light 

Port  Albert:  Lighthouse 

Gabo  Island:  Lighthouse 

Cape  Howe:  East  extreme 


Cape  Green:  SE.  pt 

Twofold  Bay:  Lookout  Pt.  light 

Dromedary  Mountain:  Summit 

Montagu  Island :  Lighthouse 

Bateman  Bay:  Observation  head 

UUaduUa :  Inner  end  of  pier 

Jervis  Bay:  Lighthouse 

Kiama  Harbor:  Outer  extreme  of  S.  head 

Wollongong :  Summit  of  head 

Sydney:  Observatory 

Port  Jackson:  Outer  S.  Head  light 

Broken  Bay:  Baranjo  Head  light 

Newcastle :  Nobb jr  Head  light 

Port  Stephens :  Lighthouse 

Sugar  Loaf  Point:  Lighthouse 

Port  Macquarie :  Entrance. 

Solitary  Islands:  S.  Isle  light 

Clarence  River:  S.  Head  light 


Lat.  S. 


34  55  00 
34  24  00 

34  30  00 
32  57  00 
32  34  00 

32  01  30 

32  48  00 

34  29  29 

35  00  15 
35  20  15 

34  43  22 

33  44  08 

32  29  42 

34  28  25 

35  18  21 

35  07  31 
34  12  00 
34  50  25 

34  55  38 

35  36  45 
35  45  30 
35  51  00 

35  34  06 

36  57  00 
38  04  18 

38  26  00 
38  24  39 
38  23  47 

38  51  45 

39  35  38 
38  18  00 
38  08  52 

37  49  53 

38  29  42 

38  29  15 

39  08  00 

39  25  45 

40  11  45 
40  18  40 
40  43  40 
38  45  06 
37  34  15 
37  30  10 

37  15  40 
37  04  18 
36  18  30 
36  14  30 
35  43  58 
35  21  41 
35  09  15 
34  40  25 
34  25  30 

33  51  41 
33  51  30 
33  35  00 
32  55  15 
32  45  10 
32  26  20 
31  25  30 
30  12  00 
29  25  30 


Long.  E. 


118  27  00 

119  34  00 

121  58  00 

124  39  00 

125  30  00 

132  33  00 

134  13  40 

135  24  56 

135  56  09 

136  06  24 

135  51  03 

136  57  22 

137  45  24 
137  22  21 

136  53  30 

137  49  39 

138  09  00 
138  26  58 
138  35  05 
138  05  29 
136  34  39 
138  07  45 

138  37  09 

139  39  39 

140  39  40 

141  32  39 

141  40  02 

142  14  37 

143  30  39 

143  57  03 

144  37  00 
144  21  47 
144  58  35 

144  52  51 

145  01  34 

146  25  16 

147  18  39 

148  04  00 

147  47  39 

148  07  24 
146  37  43 

149  55  10 

149  58  39 

150  03  04 

149  54  45 

150  01  34 
150  13  34 
150  12  34 
150  29  29 
150  46  26 
150  52  19 

150  55  14 

151  12  23 
151  18  15 
151  20  30 

151  48  19 

152  13  20 
152  33  40 

152  55  19 

153  17  00 
153  23  10 


Lun.  Int. 


Range. 


H.W. 


h.    TO. 


11  50 


0  35 


20 


4  31 
4  04 


4  00 


11  52 
" '6'26 


10  43 
2  02 
2  19 


10  38 


8  40 


8  05 


8  20 

'8'26 


8  40 


8  35 
8  15 


9  00 

's'is 


L.w. 


Spg. 


h.    m. 


9  35 


5.1 


6  55 


5.5 


2  15 


11.4 


10  45 
10  22 


10.2 
6.3 


10  15 


5  40 
'635 


4  30 
8  20 
8  41 


4  25 


2  27 


1  52 


2  07 

'2'67' 


2  27 


2  23 
2  00 


2  46 

'2  bo' 


5.8 


4.2 


2.5 
3.0 
1.9 


8.1 


4.5 


5.2 


5.3 

'5.'4' 


4.2 


4.7 
5.8 


4.1 
'4.'6" 


APPENDIX  IV.                                     [Page  353 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
AUSTRALIA— Continued . 

8 

Place. 

Lat.  s. 

Long.  E. 

Liuulnt. 

Range. 

H.W. 

L.  w. 

Spg. 

Neap. 

•6 

a 

« 

a 

S 

9 
9 

Richmond  River:  N.  Head  light 

28  51  30 
27  23  22 
27  28  00 
27  26  20 
27  02  10 
25  56  00 
25  00  15 
24  43  20 
24  45  00 
24  07  00 
24  01  20 
24  01  20 
23  53  00 
23  29  30 
22  31  40 
21  39  00 

21  19  15 
21  32  00 
20  32  20 
20  18  50 

20  15  30 

20  00  50 
19  57  30 
19  41  50 
19  19  20 
19  11  25 
18  45  30 
18  09  30 
17  40  40 
17  09  45 

16  04  20 
15  45  00 
15  29  45 
15  16  30 
14  37  15 
14  10  00 
14  07  45 
14  00  30 
13  24  45 
12  51  00 
11  58  15 

11  55  00 
11  46  30 
11  36  30 
10  41  30 
10  37  45 
10  22  00 

10  46  00 
10  36  05 

17  36  40 
17  35  10 
17  06  50 

153  35  55 
153  10  31 
153  01  36 
153  33  50 
153  28  04 
153  13  00 
153  23  00 
153  13  40 
152  25  00 
152  45  15 
151  41  04 
151  37  15 
151  23  50 
151  14  04 
150  45  44 
150  14  00 

149  43  30 
149  31  04 
148  58  00 

148  53  15 

149  00  00 

148  16  54 
148  27  34 
148  23  00 
147  27  40 
147  01  10 
146  42  50 
146  11  04 
146  11  00 
146  02  30 
145  29  34 
145  28  30 
145  17  30 
145  23  15 
144  57  30 
144  32  34 
144  15  19 
143  42  15 
143  36  19 
143  34  00 
143  15  15 

143  29  00 
143  06  00 
142  56  19 
142  32  24 
142  39  20 
142  21  19 

142  10  50 
141  53  49 
140  37  06 
139  45  56 
139  38  36 

ft.    tn. 

ft.    m. 

ft. 

ft. 

Brisbane:  Signal  station,  Fisherman  la... 
Observatory 

10  45 

4  30 

6.4 

3.9 

Lookout  Point:  Extreme 

Cape  Moreton:  Lighthouse 

■ 

Double  Island  Point :  Lighthouse 

Indian  Head :  Extreme 

Sandy  Cape:  Lighthouse 

Burnett  River:  S.  Head  light 

Lady  Elliot  Islet:  Lighthouse 

Bustard  Head:  Lighthouse 

Rodd  Bay:  Spit  end 

Port  Curtis:  Gatcombe  Head  light 

Cape  Capricorn:  Lighthouse 

Port  Bo  wen:  Observation  rock 

Percy  Isles:  Pine  I.  light 

Northumberland  Isles:  Summit  of  Prud- 
hoe  I 

Cape  Palmeraton:  N.  extreme 

Cape  Conway:  SE.  pt : . . . 

Port  Molle:  S.  side  of  entrance 

Cumberland  Island:  Whitsunday  I.,  sum- 
mit on  W.  side 

Port  Denison:  Obs.  pt.,  W.  side  of  Stone 
Isle '. 

10  05 

3  53 

9.0 

5.4 

Gloucester  Island:  Summit  near  N.  end.. 
Holbome  Islet:  Center 

Cape  Bowling  Green:  Lighthouse 

Cape  Cleveland:  Lighthouse 

Palm  Islands:  SE.  point  of  SE.  island. . . 

Rockingham  Bay:  Peak  of  Goold  Isle 

Barnard  Island:  Lighthouse 

Frankland  Island:  High  islet 

Cape  Tribulation:  Extreme 

Hope  Island:  S.  islet 

Cook  Mountain:  Summit 

8  55 

2  43 

7.5 

4,5 

Cape  Bedford:  SE.  extreme 

Murdock  Point:  Extreme 

Cape  Melville:  NE.  extreme 

Flinders  Island:  N.  extreme  of  N.  island. 
Claremont  Point:  Extreme 

Cape  Sidmouth:  Extreme 

9  00 

2  47 

9.6 

5.8 

Cape  Direction:  NE.  extreme 

Cape  Grenville:  Extreme 

Sir  Charles  Hardy  Island:  N.  extreme  of 
SE.  isle 

Bird  Island:  NW.  isle 

Hannibal  Isles:  E.  isle 

Cape  York:  Sextant  Rock 

i  66  1     7  in 

8.0 

4.7 

Mount  Adolphus:  Summit 

Travers  Isles:  Center 

Prince  of  Wales  Island:  Cape  Cornwall, 
extreme 

Booby  Island:  Center 

4  20 

10  30 

7.8 

4.7 

Flinders  River:  Entrance 

Albert  River:  Kangaroo  Pt 

Sweers  Island:  Inscription  Pt 

21594°— 14- 


-23 


Page  354] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
TASMANIA. 


Place. 


Cape  Portland:  NW.  pt 

Port  Dalrymple:  Low  Head  light 

Port  Sorrell:  NW.  entrance  head 

Port  Frederick:  Entrance 

Leven  River:  W.  entrance  head 

Emu  Bay:  Blackman  Pt 

Hunter  Island:  N.  pt 

Cape  Grim:  Outer  Doughboy  Islet .... 

Albatross  Islet:  N.  pt 

Arthur  River:  Entrance 

Pieman  River:  Rocks  close  to  entrance 

Macquarie  Harbor:  Entrance  Islet 

Cape  Sorrell :  Lighthouse 

Port  Davey :  Pollard  Head 

Southwest  Cape:  Extreme  pt 

Mewetone  Rock:  Center 

Cape  Bruny :  Lighthouse 

Bruny  Island:  Penguin  Islet 

HobartTown:  Transit  of  Venus  station. 

Cape  Pillar:  Tasman  Islet 

Cape  Frederik  Hendrik:  Extreme 

Freycinet  Peninsula:  Summit 

St.  Patrick  Head:  N.  pt 

Eddystone  Point:  Extreme 


Lat.  S. 

40  44  15 

41  03  25 

41  07  05 

41  10  00 

41  08  30 

41  02  50 

40  23  40 

40  40  10 

40  22  00 

41  04  00 

41  41  00 

42  11  37 

42  11  00 

43  19  00 

43  33  30 

43  44  30 

43  29  40 

43  21  00 

42  53  25 

43  14  00 

42  52  00 

42  13  00 

41  34  00 

40  59  40 

Long.  E. 


147  56  09 
146  47  54 
146  33  30 
146  24  30 
146  12  00 
145  56  39 
144  47  45 
144  39  44 
144  39  19 
144  44  00 

144  57  00 

145  12  34 
145  10  30 

145  53  00 

146  01  04 

146  22  04 

147  08  49 
147  23  40 

147  20  07 

148  02  00 
148  00  00 
148  18  04 
148  19  30 
148  20  50 


Lun.  Int. 


Range. 


n.  W.         L. W 


h.     TO. 


11  10 


7  20 


8  05 


Spg. 


h,    TO. 


5  00 


1  07 


1  52 


ft. 


9.0 


2.7 


4.2 


NEW  ZEALAND. 


Three  Kings  Islands:  NE.  extreme  of  NE. 
island 

North  Cape:  Cape  Islet 

Parenga-renga  Harbor:  Kohan  Pt 

Maunganui  Harbor:  White  Pt 

Wangaroa  Harbor:  Peach  Islet 

Bay  of  Islands:  Motu  Mea  Islet 

Wangaruru  Harbor:  Grove  Pt 

Wangari  Harbor:  Loot  Pt 

Great  Barrier  Island :  Needles  Pt 

Auckland  Harbor:  Lighthouse 

Coromandel  Harbor:  Tulinia  I 

Cape  Colville:  N.  pt 

Cuvier  Island:  Lighthouse 

Tauranga  Harbor:  Mount  Maunganui, 
860  ft 

White  Island:  Summit,  863  ft 

Cape  Runaway:  Extreme 

East  Cape:  Islet,  420  ft 

Tolaga  Bay:  Matu-heka  Islet 

Mahia  Peninsula:  S.  extreme  of  Port- 
land I 

Ahuriri  Harbor:  Lighthouse 

Kidnappers  Cape:  Extreme 

Cape  Palliser:  Lighthouse 

Port  Nicholson:  Pencarrow  light 

Wellington:  Queens  Wharf  light 

New  Observatory 

Mana-watu  River:  Lighthouse 

Wanganui  River:  N,  head 

Egmont  Mountain:  Summit,  8,270  ft 

New  Plymouth:  Flagstaff 

Kawhia  Harbor:  S.  head 


34  06  20 
34  25  07 

34  31  00 

35  00  20 
35  01  44 
35  17  00 
35  23  48 

35  51  09 

36  01  15 
36  50  06 
36  48  35 
36  28  20 

36  26  20 

37  36  25 
37  30  00 
37  30  45 

37  40  00 

38  20  50 

39  18  00 
39  28  30 

39  38  00 
41  36  45 
41  21  40 
41  17  17 
41  17  04 

40  27  10 
39  57  00 
39  18  00 
39  03  35 
38  04  50 


172  08  49 

173  03  34 
173  00  54 
173  32  39 

173  45  48 

174  06  06 
174  21  24 

174  31  14 

175  25  34 

174  51  00 

175  24  34 
175  21  04 

175  49  00 

176  10  14 

177  10  49 

177  59  34 

178  35  09 
178  20  14 

177  53  15 

176  54  14 

177  06  44 
175  18  45 
174  51  04 
174  47  25 

174  46  04 

175  14  40 
174  59  44 
174  03  59 
174  04  35 
174  48  04 


7  40 
7  26 
7  15 
7  05 


7  20 
7  05 


7  05 


8  10 
8  00 


6  05 


4  40 

'4'52' 

9  40 


9  15 
9  10 


1  30 
1  55 
1  05 
0  55 


6.4 
5.9 
6.5 
6.7 


1  10 
0  55 


10.8 
10.7 


0  55 


6.1 


2  00 
1  50 


6.6 


12  15 


3.5 


10  50 

1654' 

3  30 


5.7 
3.6' 


6.3 


3  05 
3  00 


n.  6 

IL  9 


APPENDIX  IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
NEW  ZEALAND— Continued. 


[Page  366 


22 


Place. 


Aotea  llarbor:  S.  head 

Whaingaroa  Harbor:  S.  entrance  pt 

Manukau  Harbor:  Paratutai  flagstaff 

Kaipara  Harbor:  Lighthouse 

Hokianga  River:  Flagstaff  at  entrance 

Cape  Campbell :  Lighthouse 

Port  Cooper:  Lyttleton  customhouse 

Akaroa  Island :  Lighthouse 

Ashburton  River:  N.  entrance  pt 

Waitangi  River:  N.  entrance  head 

Otago  Harbor:  Taivoa  Head  light 

Molyneux  Bay:  Landing  place 

Nugget  Point:  Lighthouse 

Bluff  Harbor:  Lighthouse 

Tewaewae  Bay:  Pahia  Pt 

Solander  Islands:  Summit,  1,100  ft 

Preservation  Inlet:  Lighthouse 

West  Cape:  Extreme 

Queenetown:  U.  S.  Tr.  of  Venus  station . . . 

Milford  Sound :  Freshwater  Basin 

Cascade  Point:  N.  extreme 

Grey  River:  Entrance 

Hokitika:  Entrance  light 

Cape  Foulwind:  Lighthouse 

Ca|)e  Farewell:  Extreme 

Nelson:  Bowlder  Bank  liglit 

D'Urville  Island:  Port  Hardy 

Port  Gore:  Head  of  Melville  Cove 

Port  Underwood :  Flag  Pt 

Port  William:  HoweU's  house 

Paterson  Inlet:  Glory  Cove 

Port  Adventure:  White  Beach,  S.  end 

Port  Pegasus:  Cove  abreast  Anchorage  I . . 
Codfish  Island:  NW.  extreme 

Snares  Islands:  SW.  islet 


Lat.  S. 

Long.  E. 

Liin. 

Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap. 

37  59  35 
37  46  22 
37  03  00 
36  23  00 
35  32  05 

41  44  00 
43  46  40 

43  54  00 

44  04  50 

44  54  50 

45  46  55 

46  24  05 
46  27  10 
46  37  00 
46  20  40 
46  36  00 
46  10  00 
45  54  50 

45  02  07 
44  40  20 
44  00  30 

42  26  20 
42  42  20 
41  45  40 

40  29  50 

41  16  05 

40  46  35 

41  01  55 
41  20  28 

46  50  30 

46  58  30 

47  03  52 

47  11  40 
46  45  45 

48  06  43 

174  50  04 
174  52  19 
174  31  14 
174  08  00 

173  21  59 

174  17  14 

172  44  17 

173  00  20 
171  48  34 
171  11  14 

170  44  02 
169  47  53 

169  50  04 
168  23  00 

167  42  19 
166  54  04 
166  38  15 

166  25  49 

168  40  06 

167  54  45 

168  21  34 

171  11  54 

170  59  30 

171  27  44 

172  41  04 

173  17  30 

173  54  04 

174  11  22 
174  08  24 

168  05  34 
168  09  54 
168  10  57 
167  40  51 
167  36  49 

166  27  44 

A.  m. 

h.    m. 

ft. 

ft. 

9  08 
9  05 
9  00 
8  40 

4  45 
3  45 

2  55 
2  50 
2  50 
2  30 

11  00 
10  00 

12.3 

12.6 

10.0 

9.2 

7.5 
7.4 

8.7 
9.0 
7.1 
6.5 

6.5 
5.8 

3  31 

9  39 

5.6 

4.4 

1  05 

7  15 

7.8 

6.2 

11  10 

5  00 

7.5 

5.9 

"* 

10  10 
10  20 

4  00 
4  10 

9.8 
9.5 

7.7 
7.5 

L. 

9  55 
9  45 

3  45 
3  36 

12.0 
11.6 

9.4 
9.2 

6  00 

12  15 

7.6 

6.6 

1  00 

9  15 

7.8 

6.2 

11  45 

5  40 

7.9 

6.2 

THE  ARCTIC  REGIONS. 


Cape  Walsingham:  Extreme 

Mile  Island:  N.pt 

Marble  Island:  E.  end 

Cape  Kendall:  Extreme 

Iglooik  Island :  E.  pt 

Victoria  Harbor:  N.  shore 

Elizabeth  Harbor:  Entrance.  . . . 

Magnetic  Pole,  1831 

PortNeill:  N.  pt.  of  entrance... 

Port  Bowen:  N.  cove 

Batty  Bay:  S.  pt.  of  entrance... 

Port  Leopold:  Whaler  Pt 

Careys  Islands 

Discovery  Harbor 

Alert's  Winter  Quarters 

Cape  Joseph  Henry:  N.  extreme 

Cape  Hecla:  N.  extreme 

Cape  Columbia:  Extreme 

Melville  Island:  Winter  Harbor. 
North  Cape 


00  00 

04  00 

33  00 

42  00 

21  00 

09  17 

38  14 

05  00 

09  13 

13  39 

13  00 

50  05 

49  00 

04  40 

27  00 

40  00 

54  00 

07  00 

47  10 

55  00 

69  28 
77  50 
91  06 

87  15 
81  31 

91  30 

92  10 
96  47 

89  00 

88  54 
91  08 

90  12 
73  10 
64  45 
61  18 

63  38 

64  45 

70  20 
110  48 
179  57 


4  00 

'o"56' 


11  38 


10  35 


1  20 


10  15 


0  40 


5  29 


4  20 


7  40 


12.0 


8.0 


5.5 


2.6 


3.8 


5.1 


4.2 


2.9 


1.0 


L9 


Page  356] 


APPENDIX   IV. 

MARITIME   POSITIONS  AND  TIDAL  DATA. 
THE  ARCTIC  REGIONS— Continued. 


Place. 


Liakhov  Islands:  E.  pt.  of  New  Siberia. . . 

Cape  Tscheljuskin:  E.  pt 

Nova  Zembia:  Vaigats  I.,  N.  pt 

Cape  Costin  (Kostina) 

NE.  pt.,  Cape  Desire 

Franz  Josef  Land:  Wilczek  I 

Mezen:  Epiphany  Church 

Morjovetz  Island:  Lighthouse 

Archangel:  Trinity  Church 

Jighinsk  Island :  Lighthouse 

Onega:  St.  Michael's  Church 

Salovetski:  Lighthouse 

Cape  Sviatoi  Nos:  Lighthouse 

Bear  Island 

Spitzbergen  Island :  S .  cape 

Cloven  Cliff 

Danes  I.,  Robbe  Bay 


Cape  Morris  Jesup 

Thank  God  Harbor 

Cape  York:  Extreme 

Upemivik:  Flagstaff 

Proven:  Village 

Omenak  Island :  Village 

Godhavn:  Village 

Jacobshavn :  Village 

Claushavn :  Village 

Christianshaab :  Village 

Egedesmunde:  Village 

Whalefish  Island:  Boat  Inlet. 

Holsteinberg :  Village 

Kangamint 

Ny  Sukkertop:  Village 

Godthaab :  Flagstaff 

Sermelik  Fjord :  Kasuk  Peak. 

Fiskemaes:  Village 

Jensen  Nunatak:  Peak 

Ravn  Storo:  Peak 

Frederikshaab:  Church. 

Kangarssuk  Havn :  Village 

Arsuk:  Pingo  Beacon 

Kajartalik  Island:  Summit... 

Ivigtuk:  House 

Bangs  Havn :  Anchorage 

Aurora  Harbor 

Julianshaab :  Village 

Neunortalik:  Village 

Frederiksthal:  Village 

Cape  Farewell:  Statenlluk.. 

Aleuk  Islands:  Center 

Cape  Tordenskjold:  Extreme. 

Cape  Bille:  Extreme , 

CapeJuul:  Extreme 

Cape  Lowenorn:  Extreme 

Dannesbrog  Island :  Beacon . . 

Ingolsfjeld 

Rigny  Mount:  Summit 

Pendulum  Islands 

Cape  Philipp  Broke 

Cape  Bismarck:  Extreme 


Lat.  S. 


75  10  00 
77  41  00 
70  25  00 
70  55  00 

76  58  00 
79  55  00 

65  50  18 

66  45  50 

64  32  06 

65  12  17 

63  53  36 

65  07  00 

68  08  51 

74  30  00 
76  35  00 
79  50  00 
79  42  00 

Lat.  N. 
83  39  00 
81  38  00 

75  55  00 
72  47  48 
72  20  42 
70  40  00 

69  14  04 
69  13  12 
69  07  30 
68  49  06 
68  42  30 

68  58  30 

66  55  54 
65  48  42 
65  24  30 

64  10  36 
63  29  12 
63  05  12 
62  50  00 
62  42  36 
61  59  36 
61  28  20 
61  10  24 
61  09  42 
61  12  12 
60  47  30 
60  48  36 
60  43  07 
60  08  12 
60  00  00 

59  49  00 

60  09  00 

61  25  00 

62  01  00 

63  14  00 

64  30  00 

65  18  00 

66  19  02 

69  00  12 
74  40  00 
74  55  00 

76  47  00 


Long.  E. 


150  30  00 
104  01  00 
59  10  00 
53  01  50 
65  40  00 
58  45  00 

44  17  00 
42  30  00 
40  33  30 
36  51  30 

38  08  30 
35  37  00 

39  48  54 
20  00  00 

17  23  00 
11  40  30 
11  07  00 

Long.  W. 
30  40  00 
61  44  00 
65  30  00 
55  53  42 
55  20  00 
51  59  00 
53  24  07 
50  56  30 

50  55  30 

51  00  00 

52  46  00 

53  27  00 
53  40  18 
53  23  00 
52  54  00 
51  45  48 
51  10  48 
50  43  36 

48  57  00 
50  20  48 

49  44  00 
48  51  00 
48  26  00 
48  30  42 
48  10  30 
47  52  00 
47  46  48 
46  01  00 

45  16  00 
44  40  00 
44  01  42 
42  55  00 
42  15  00 
42  00  00 

40  50  00 
39  30  00 
38  30  00 
35  11  00 
26  10  24 

18  17  00 

17  33  00 

18  40  00 


Lun.  Int. 


n.  W.   L.  W 


10  00 


7  18 
5  05 
9  02 


9  05 


0  14 


(approx) 
12  14 


10  50 


8  05 
6  20 


6  40 


6  12 


6  15 


4  56 

5  33 
2  55 
4  00 


11  05 
11  10 


h.    m. 


3  50 


2  00 
11  30 

3  10 


2  55 


6  25 


5  58 


4  38 


1  52 
0  07 


0  27 


Range. 


g.  Neap. 


ft- 


7.0 


2.2 
3.8 
9.1 


13.9 


5.3 


5.4 


8.0 


7.5 
10.0 


12.5 


0  00 


9.0 


0  03 


12.0 


11  09 

11  46 

9  10 

10  13 


7.0 
8.6 
9.4 

7.5 


4  53 

4  58 


6.7 
3.7 


APPENDIX   IV.                                     [Page  357 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
TTTK  ARCTIC  REGIONS— Continued. 

Place. 

Lat.  S. 

Long.  W. 

Lun.  Int. 

Range. 

H.W. 

L.W. 

Spg. 

Neap.  1 

a 

ed 
g 

M 

Jan  Mayen  Island:  Mt.  Beerenberg,  6,870 
ft 

Youngs  Foreland,  or 
Cape  Northeast 

Mary  Muss  Bay 

Langanaes  Point 

71  04  00 

71  08  00 
71  00  00 

66  22  45 
66  32  40 
66  33  42 
66  07  30 
66  27  29 
66  26  30 
65  30  15 
64  48  04 
64  08  40 
64  04  09 
63  48  06 

63  48  19 

64  35  42 

64  55  27 

65  16  14 
65  45  00 

n        r       0 

7  36  00 

7  26  00 

8  28  00 

14  30  46 

16  10  24 

17  57  36 

20  05  26 

22  23  04 

23  08  00 

24  31  26 
23  45  08 

21  55  00 

22  39  04 
22  39  00 
16  36  13 
14  08  31 
13  41  10 

13  32  22 

14  23  35 

ft.      TO. 

A.    m. 

/'.            ft. 

11  21 

5  06 

3.8 

2.2 

Rissnaes  Point 

Grimsey  Norddranger:  Tr.  Station 

Skagataaa  Point 

North  Cape :  Kalfatindr 

Straumness  Point 

Fugle  or  Staabierg  Huk:  Point 

Snaefells  Yokul :  Tiw  Station 

Reykiavik:  Observatory 

6  io     ii  25 

14.5 

8.4 

Cape  Skagi :  Lighthouse 

Reykianaes:  Lighthouse 

1 

Ingolfshofde:  Tr.  Station 

) 

Papey  Island :  Tr.  Station 

i 

Rev thur  Fjeld :  Tr.  Station 

1 

Balatangi:  Lighthouse 

1 

Dia  Fjefd:  Tr.  Station 

1 

1 

Page  358] 


INDEX  TO  APPENDIX  IV. 


Page. 

Admiralty  Islands 346 

Adriatic  Sea 315-321 

Africa,  east  coast 323-325 

north  coast 320,  321 

west  coast 321-323 

Alabama 284 

Alaska 287,288 

Albania 318 

Aleutian  Islands 287 

Algeria 321 

Arabia 327 

Arctic  regions 355-357 

Argentina 298 

Asia,  east  coast 331-342 

islands. 332 

south  coast 327-330 

Atlantic  Ocean,  islands  302-304 

Australia 351-353 

Austria 317,318 

Azores  Islands 302 

Bahama  Islands 292 

Balearic  Islands 316 

Baluchistan 328 

Banka  Strait 331 

Belgium 313 

Belize 285,286 

Bermuda  Islands 303 

Black  Sea 315-321 

Borneo 333 

Brazil 295,297 

British  Columbia 288, 289 

Burma 329 

California 289 

Canary  Islands 303 

Cape  Breton  Island 281 

Verde  Islands 303 

Caroline  Islands 343 

Celebes  Island 333 

Central  America,  east 

coast 285-287 

west  coast 291 

Ceylon 329 

Chile 298-801 

China 337,338 

Sea 337 

Entrance 331 

Chosen 339 

Cochin  China 336 

Colombia,  north  coast. .  295, 302 

west  coast 

Connecticut 282, 283 

Cook  Islands 350 

Coral  Sea  Archipelago 347 

Corsica 316 

Costa  Rica 280 

Crozet  Islands 327 

Cuba 292,293 

Cyprus 320 

Delaware 283 

Denmark 312 


REGIONS  AND   COASTS. 

Page. 
East    Indian    Is.,    smaller 

Dutch 332 

Ecuador 302 

E,^ypt 320 

Eliice  Islands 345 

Europe,  Atlantic  coast.   304-315 

Falkland  Islands 304 

Fiji  Islands 347,348 

Florida 284 

Formosa  Island 338 

France,     north     and     west 

coasta 313,314 

France,  south  coast 316 

Galapagos  Islands 342 

Gaspar  Strait 331 

Georgia 283 

Germany 310-312 

Gilbert  Islands 342 

Great  Britain 304-307 

Greece 319 

Greenland 356 

Guatemala 286 

Guiana 296 

Haiti,  island  of 293, 294 

Hawaiian  Islands 344 

Holland 313 

Honduras 286 

Iceland 357 

India 328,329 

Indian  Ocean,  islands..  325-327 
Italy 316,317 

Jamaica 293 

Japan 339-341 

Java 331 

Kergueleii  Islands 327 

Korea 339 

Kuril  Islands 341 

Labrador 279, 280 

Laccadive  Islands 325 

Ladrone  Islands 344 

Louisiade  Archipelago 347 

Louisiana 284 

Lower  California 290 

Mad£^ascar 326 

Madeira  Islands 303 

Magdalen  Islands 280 

Maine 281,  282 

Malaysia 329, 330 

Maldive  Islands 325 

Mariana  Islands 344 

Marquesas  Islands 345 

Marshall  Islands 343 

Maryland 283 

Massachusetts 282 

Mauritius  Island 325 


Mediterranean  Sea.  .  . .  315-321 

Mexico,  east  coast 285 

west  coast 290,  291 

Mississippi 284 

Molukka  Islands 332,  333 

Morocco 321 

Mosquito  Coast 286 

New  Brunswick 280,  281 

Caledonia 350 

Newfoundland 279,  280 

New  Guinea  Island 346 

Hampshire 282 

Hebrides  Islands 347 

Jersey 283 

South  Wales 352 

York 282,  283 

Zealand 354,  355 

Nicaragua 286 

North  America, east  coast  279-287 

west  coast. . . .  287-291 

Australia 351 

Carolina 283 

l8land,NewZealand  354,  355 

Norway 307, 308 

Nova  Scotia 281 

Oregon 289 

Pacific  Ocean,  Lilands. .  342-350 

Panama 287 

Pelew  Islands 344 

Pennsylvania 283 

Persia 328 

Peru 301,302 

Philippine  Islands 333-336 

Phoenix  Islands 345 

Porto  Rico 294 

Portugal 314,315 

Prince  Edward  Island 280 

Queen  Charlotte  Islands 288 

Queensland 353 

Red  Sea 324,325 

Rhode  Island 282 

Russia,  south  coast 320 

west  coast 309, 310 

St.    Lawrence,    River   and 

Gulf 280 

Samoan  Islands 348 

Santa  Cruz  Islands 347 

Sardinia 316 

Siam,  Gulf 336 

Siberia 341,342 

Society  Islands 349 

Solomon  Islands 346 

South  America,   north   and 

east  coasts 295-298 

South  America,  W.coast  298-302 

Australia 352 

Carolina  283 


INDEX  TO  APPENDIX   IV. 


[Page  359 


Page. 
South  Island,  New  Zealand  355 

S.  AV.  Is.  of  Japan 338,  339 

Spain,    north   and    west 

coasta 314,315 

south  and  east  coasts. .  315 

Stewart  Island 355 

Sumatra 330 

Sweden 308,  300 

Taiwan  ( Formosa) 338 

A.alborg 312 

Aarhus 312 

Ababa  Island 347 

Abaco  Island 292 

A  bang  Besar  Island 330 

Abbeville 313 

Abd-al-Kuri  Island 324 

Aberdeen 305 

Abervrach 313 

Aberystwith 304 

Abingdon  Island 342 

Abo 309 

AboukirBav 320 

Abreojos  Point 290 

Abrolhos  Island 297 

Absecon  Inlet 283 

Acajutla 291 

Acapulco 291 

Accra 322 

AcheenHead 330 

Aconcagua  Mountain 300 

Acre 320 

Adakh  Island 287 

Adalia 320 

Adams,  Port 338 

Addu  Atoll 325 

Adelaide,  Port 352 

River 351 

Ad^le  Island 347 

Aden 327 

Adenara  Island 332 

Admiralty  Head 289 

Islands 346 

Adolphus  Mountain. ... 353 

Adventure,  Port 355 

Mgina....- 319 

Aero  Island 312 

iErstenen 308 

Africa  Rock 316 

Agalegaa  Island 326 

Agdenes • 307 

Agiabampo 291 

Agrigan  Island 344 

AguadillaBay 294 

Aguia  Point 302 

Agulhaa,  Cape 323 

Agutaya  Islet 334 

Aheu  Island 349 

Ahunui  Island 349 

Ahuriri 354 

Ai  Sima 341 

Aian 341 

Aignan,  St.,  Island 347 

Aigues  Alortes 316 

Ailinginae  Islands 343 

Aillick  Harbor 279 

AiUy  Point 313 


REGIONS  AND  COASTS — Continued. 

Page. 

Tasmania 354 

Texas 284 

Tokara  Islands 339 

Tonga  Islands 350 

Trinidad 296 

Tuamotu  Archipels^o 349 

Tunis 321 

Turkey 320 

Uruguay 298 

PLACES. 

Ailuk  Islands 343 

Aitutaki  Island 350 

Aix  Island 314 

Aiaccio 316 

Aiano 320 

Akamokan  Island 344 

Akaroa  Island 355 

Akashi-no-seto 340 

Akpatok  Island 279 

Akyab 329 

Alacran  Reef 285 

Alamaguan  Island 344 

Aland  Island 309 

Alargate  Reef 286 

Albany 283 

Albatross  Islet 354 

Albemarle  Island 342 

Albert,  Port 352 

River 353 

Alboran  Island 321 

Albuquerque  Bank 286 

Alcatrazes  Island 297 

Alcmene 350 

Alcobaga 297 

Aldabra  Island 327 

Alden 308 

Alderney  Harbor 307 

Alegranza  Island 303 

Alegre,  Porto 297 

Alert 's  Winter  Quarters 355 

Alessandro,  San,  Island 345 

Aleuk  Islands 356 

Alexander,  Port 322 

Vancouver 288 

Alexandretta 320 

Alexandria 320 

Alfaques,  Port 315 

Alfred,  Port 323 

Algeciras 315 

Algiers 321 

AH-Agha,  Port 320 

Alicante 315 

Alijos  Rocks 290 

Alipee 328 

Alligator  Island 337 

Reef 284 

Almadie  Point 321 

Almeria 315 

Almirante  Bay 287 

Alphonse  Island 325 

AltaVela 294 

Altata 291 

Altea 315 

Altona 311 

Alvarado 285 

Amager  Island 312 

Amber,  Cape 326 


Page. 

Vancouver  Island 288 

Venezuela 295,296 

Victoria 352 

Virginia 283 

Washington 289 

Western  Aiistralia 351,352 

West  India  Islands 292-295 

Yucatan 285 

Amboina  Island 332 

Ambrose,  St.,  Island 350 

Amchitka  Island 287 

Amelia  Island 284 

Ameni  Islet 325 

Amherst  Harbor 280 

Amirante  Islands 325 

Amour  Point 280 

Amoy 337 

Amsterdam 313 

Island 327 

Ana,  Sta.,  Lagoon 285 

Anaa  Island 349 

Anacapa  Island 289 

Anadir  River 342 

Analaboe 330 

Anamba  Islands 331 

Anataxan  Island 344 

Anchorite  Island 346 

Ancona 317 

Ancud 300 

Andaman  Islands 329 

Andenes 307 

AndravaBay 326 

Andrea,  St.,  Rock 318 

Andrew,  St 281 

Cape 326 

Island 346 

Andrews,  St.,  Island 286 

Androa  Island,  Bahamas. . .  292 

Grecian  Arch ....  319 

Ane^da 294 

Aneityum  Island 347 

Angatau 349 

Angaur  Island 344 

Angeles  Bay 290 

Los 289 

Port,  Mexico 291 

,  Washington 289 

AnghrisHead 306 

Angosto,  Port 299 

Angoxa  Island 323 

Angra  dos  Reis 297 

Pequena 322 

Anguilla 294 

Anhatomirim 297 

Anholt  Island 312 

Animas,  Las 290 

Anjer 331 

Anjoe,  Cape 331 

Ann,  Cape 282 

St.,  Bay 293 

Anna,  Sta.,  Island,  N.  Brazil  297 

S.  Brazil. . . .  296 

Annapolis,  Maryland 283 

Nova  Scotia 281 

Anne,  St.,  Island 299 


Page  360] 


INDEX  TO  APPENDIX  IV. 


Page. 

Annisquam 282 

Anno  Bon  Island 322 

Anns,  St.,  C.  Breton  1 281 

England 304 

Anowik  Island 288 

Antareh,  Eas 324 

Antibes 316 

Anticosti  Island 280 

Antigua 294 

Antipodes  Island 350 

Antivari 318 

Antofagasta 301 

Antonina 297 

Antonio,  Port 293 

San,  Cape,  Argentina. .  298 

Cuba 293 

Mt.  and  Island...  303 

Port,  Argentina. .  298 

—-Chile 300 

Sierra 

Antwerp 313 

Aoga  Shima 340 

Aomori 340 

Aor,  Pulo 331 

Aotea 355 

Apaiang  Island 342 

Apalachicola 284 

Apamama 342 

Aparri 334 

Apenrade 311 

Apo  Islet 334 

Apostle^Rocks 299 

Arago  Cape 289 

Araish,  El 321 

Arakam  Island 342 

Araktcheff  Island 349 

Aran  Island 306 

Aransas  Pass 284 

Aranuka  Island 342 

Aratika  Island 349 

Arcadins  Islands 294 

Areas  Cays 285 

Archangel 356 

Ardassier  Islands 332 

Ardrossan 305 

Arena  de  la  Ventana 290 

Point,  California 289 

L.  California 290 

Arenas  Cay 285 

Arendal  Inlet 308 

Arentes  Island 332 

Argentina 298 

Aigostoli,  Port 319 

Anca 301 

Arichat  Harbor 281 

Arkona 311 

Armeghon 329 

Amheim,  Cape 351 

Amo  Atoll 343 

Arorai  Island 342 

Arran  Island 306 

Arrowsmith  Islands 343 

Arsuk 356 

ArtakiBay 320 

Arthur  River 354 

Port 338 

Am  Islands 332 

Arvoredo  Island 297 

Ascension  Bay 285 

Island 303 


PLACES — continued. 

Page. 

Ashburton  River 355 

Ashrafi  Island 324 

Asia  Rock 301 

Assateague  Island 283 

Assens 312 

Assumption  Island 326 

Astoria 289 

Asuncion  Island,  Ladroues.  344 

L.  Caliiomia 290 

Atalaia  Point 296 

Athens 319 

Atico 301 

Atiu  Island 350 

Atka  Island 287 

Atkinson  Point 289 

Attu  Island 287 

Auckland 354 

Islands 350 

Audieme 314 

Augusta 282 

Port,  Australia 352 

Sicily 317 

Augustenberg 311 

Augustin,  St.,  Cape,  Brazil.  296 

Philippines .  335 

Augustine,  San,  Island 345 

St.,  Bay 326 

Harbor 284 

Aurh  Island 343 

Aurora  Harbor 356 

Island 347 

Austral  Islands 350 

Aux  Cayes 294 

Avarena  Point 294 

Aves  Island 295 

Aviles 314 

Avlona 318 

AximBay 322 

Awa  Sima 340 

Ayamonte 315 

Ayer  Bangis 330 

Ayr 305 

Baago  Island 312 

Babayan  Claro  Island 334 

Baccalieu  Island 279 

Bagamoyo 324 

Bahaltolis  Island 336 

Bahama  Island 292 

Bahia,  Brazil 296 

Colombia 295 

de  Cadiz  Cay 293 

Honda,  C.  Ainerica 291 

Honda 293,295 

Bahrein  Harbor 327 

Baitiqueri,  Port 293 

Bajo  Nuevo 285 

Baiuren  Island 333 

Baker  Islet 342 

Bakers  Island 281 

Baklar 320 

Balilbac  Island 333 

Balaklava  Bay 320 

BalariPass 350 

Balasor  River 329 

Balatangi 357 

Balayan 334 

Bald  Isle 352 


Balfour  Rock 327 

Bali  Island 332 

Balingtang  Islands 334 

Ballena  Bay 291 

Balls  Pyramid 350 

Ballum 311 

Ballycottin 307 

Balstrum 312 

Balta  Island 305 

Baltic  Port 310 

Baltimore 283 

Bampton  Island 347 

Banda  Island 332 

Banderburum 327 

Bandjermasin 333 

Bangkaru  Islands 330 

Bangkok 336 

Bangor 281 

Bangs  Havn 356 

Banjuwangi 331 

Banka  Island 331 

Strait 331 

Bankot 328 

Banks  Strait 352 

Bantal 330 

Bantam 331 

Bantenan 331 

Banton  Island 335 

Bantry  Bay 306 

Baracoa 292 

Barataria  Bay 284 

Baratoube  Bay 326 

Barbados  Island 295 

Barbara,  Santa,  California. .  289 

Island 289 

Mexico 291 

Port  299 

Barbe,  St.,  Island . ' .'. .'.' .' .' '.  331 

Barbuda 294 

BarceloBay 299 

Barcelona,  Spain 315 

Venezuela 295 

Bardsey  Island 304 

Barfleur,  Cape 313 

Bari 317 

Barker  Islets 351 

Barnard  Island 353 

Bamegat  Inlet 283 

Bameveldt  Islands 298 

Barnstable 282 

Barrallead 305 

SaoJoao 297 

Barren  Island 339 

West 338 

Barrier,  Great,  Island 354 

Barrington  Island 342 

Barrow  Island,  Australia. . .  351 

Tuamotu  Arch. . .  349 

Point 287 

Bartholomew,  St 294 

Cape 298 

Bartolom^,  San 290 

Barton,  Port 334 

Baru,  Point 330 

Barung  Island 331 

Bas,  De,  Island 313 

Basdorf 311 

Basianang  Bay 335 

Bdsidu 328 

Basilan  Island 336 


INDEX  TO  APPENDIX  IV. 


[Page  361 


Page. 

Baskerville,  Cape 351 

Basrah 327 

Bass  Islets. . .- 350 

Bassa,  Grand 322 

Bassas  Rocks 329 

da  India 326 

Bassein,  Burma 329 

India 328 

River 329 

Basseterre 294 

Bastia 316 

Bastion,  Cape 337 

Basto 308 

Batabano 293 

Batalden  Island 308 

Batan  Island 334 

Port 335 

Batangas 334 

Batavia 331 

Batbatan  Island 335 

Bate  Islands 339 

BatemanBay 352 

Bath 282 

Bathurst 321 

Island 351 

Batian  Island 333 

Batoe  Islands 330 

BatoeToetong 330 

Batoiim 320 

Batticaloa 329 

Battle  Islands 279 

Batty  Bay 355 

Baubeltaub  Island 344 

Bauld  Cape 279 

BaxoNuevo 293 

Bay  of  Islands 354 

Baynes  Sound 288 

Bayonnaise  Islajid 340 

Bayonne 314 

Bazanito  Island 323 

Beachy  Head 304 

BealeCape 298 

Bear  Island 356 

Cape 316 

Beata  Island 294 

Beaufort,  N.  Carolina 283 

S.  Carolina 283 

Port 323 

Beaver  Harbor 288 

Beaver-tail  Light 282 

BecduRaz 314 

Beda'a,  Al 327 

Bedford,  Cape 353 

Bees,  St 305 

BeevesRocks 306 

Beirut 320 

Bel  Air 326 

Belfast 281 

Bay 306 

Belgrano 298 

Belize 286 

BeUIsland 279 

Rock,  Scotland 305 

Bellavista  Cape 316 

Belle  Isle,  France 314 

Belle  Isle,  Labrador 279 

Bellingshausen  Island 348 

Bellone,  Cape 326 

BenGhazi 321 

Benbane  Head 306 


PLACES — continued. 

Page. 

Bender  Erekli 320 

Benedict©,  San,  Island 291 

Benevente 297 

Benguela 322 

Benicia 289 

Benidonne 315 

Benia  River 322 

Benito,  San,  Island 290 

Benkulen 330 

Bento,  San,  River 322 

Benzert 321 

Bequia  Island 295 

Berbera 324 

Berdiansk 320 

Bergen,  Germany 311 

•^i Norway 308 

Berikat 331 

Bering,  Cape 342 

Island 341 

Berlanga  Island 315 

Berlin 311 

Bermejallead 298 

Bermudas 303 

BemalChico 285 

Bernardo  Islands 348 

Berwick 305 

Besuki 331 

Betrapar  Islet 325 

Beverly 282 

Beyt. 328 

Bhaunagar 328 

Blanche  Point 318 

Biarritz 314 

Bickerton  Island 351 

Bideford 304 

Bidstone 305 

Bierneborg 309 

Bigar  Islet. 343 

Bikini  Islands 343 

Bilbao 314 

Bille,  Cape 356 

Billiton  Island 331 

Bindloe  Island 342 

BintangHill 330 

Bintoean 330 

Bird  Island,  Australia 353 

Bahamas 292 

BandaSea 332 

N.Pacific 344 

Seychelle  Islands.  325 

Tuamotu  Arch . . .  349 

W.  Africa 321 

Islands 323 

Bimeys  Island 345 

Bismarck,  Cape 356 

Bittern  Rocks 340 

Bjuroklubb 309 

Blaabjerg 312 

Black  Head 279 

Point  Bay 322 

Stairs  Motmtain 307 

Blackness 305 

Blacksod  Point 306 

Blair,  Port 

Blaize,  St 323 

Blanco  Cape,  N.,  Africa 321 

Oregon 289 

Peru 302 

Africa 321 

Peak 287 


Page. 

Blankenbei^he 313 

Blaa,  San,  Argentina 298 

Cape,  Florida 284 

Mexico 291 

Blasket  Islands 306 

Bligh  Island 349 

BlighsCape 327 

Blimbing  Bay 330 

Blinyu 331 

Block  Island 282 

Bloody  Foreland 306 

Bluefields 286 

Bluff  Harbor 355 

Boar  Islands 280 

Boavista  Island 303 

Bobara  Rock 318 

Bocas  del  Tore 287 

Bodie  Island 283 

Bogense 312 

Bc^sher 309 

Bohol  Island 335 

Bojador,  Cape 321 

Boieador,  Cape 334 

Bola-Bola  Island 349 

Bom  Abrigo  Islet 297 

Bombay 328 

Bon,  Cape 321 

Pomt 330 

Bona 321 

Bonacca  Island 286 

Bonaire  Island 295 

Bonaventure  Head 279 

Island 280 

Bonaviflta  Cape 279 

Bongao  Island 336 

Bonham  Islands 343 

Bonifacio 316 

Bonin  Islands 345 

Boobjerg 312 

Booby  Island,  Leeward  Is. .  294 

Queensland 353 

Boompjeo  Island 331 

Boon  Island 282 

Borda,  Cape 352 

Bordeaux 314 

Bordelaise  Island 343 

BorjaBay 299 

Bomholm 312 

Borodino  Islands 345 

Boscawen  Island 348 

Bosphorus 320 

Boston 282 

Botel  Tobago  Sima 338 

Bougainville,  Cape 351 

Island 346 

Bougaroni,  Cape 321 

Boulogne 313 

Bounty  Islands 350 

Bourbon,  Cape 327 

Bouro  Island 332 

Bouton  Island 333 

Bouvets  Island 304 

Bowditch  Islet 345 

Bowen,  Port,  Australia 353 

-BaflBnsBay 355 

Bowling  Green,  Cape 353 

Boyanna  Bay 326 

BradoreBay 280 

Brala,  Pulo 336 

Bras,  Pulo 330 


Page  362] 


INDEX  TO  APPENDIX  IV. 


Brass  River 322 

Brava  Island,  C.  Verde  Is. .  303 

E.Africa 324 

Brazos  Santiago 284 

Bray  Head 307 

Breaker  Point 337 

Bremerhaven 311 

Bremerton 289 

Brest 314 

Brewers  Lagoon 286 

Brid£;eport 283 

Brieile 313 

Brill  Reef 332 

Brindisi 317 

Brisbane 353 

Bristol,  England 304 

Rhode  Island 282 

Britannia  Island 350 

Broadhaven 306 

Broken  Bay 352 

Bronnosimd 307 

Brothers  Island,  Red  Sea. .  324 

Islets,  China 337 

Broughton  Bay 338 

Head 339 

Island 341 

Rock 340 

Brunet  Island 280 

Bruni  River 333 

Brunswick,  Georgia 283 

Maine 282 

Bruny,  Cape 354 

Island 354 

Brussels 313 

Brusterort 310 

Bryer  Island 281 

Bubuan  Island 336 

-Bucaa  Island 335 

Buchanness 305 

Buddonness 305 

Budrum 320 

Buliluyan,  Cape 333 

Budua 318 

Buenaventura 302 

San :....  289 

Buenos  Ayres 298 

Bu|:ui  Point 335 

Buitenzorg 331 

Bukalsland 346 

Bulipongj)ong  Island 336 

Bulk 311 

BuU  Harbor 288 

Rock 306 

Bullock  Bay 341 

Burg 311 

Burghaz 320 

Bunas  Island 335 

Burin  Harbor 279 

Burnett  River 353 

Burntcoat  Head 281 

Burrh  Island 343 

Busios 297 

Islets 297 

Bustard  Head 353 

Busuanga  Island 334 

Biisum 311 

Butt  of  Lewis 305 

Button  Islands 279 

Byam  Martin  Island 349 

Byron  Island 342 


PLACES — continued. 

Page. 

Caballo  Island 334 

Cabeceira,  Cape 323 

Cabeza  de  Vaca 300 

Cabrera  Island 316 

Cabron  Cape 293 

Cabrut  Islet 325 

Cadaques 315 

Cadiz 315 

Cadmus  Island 349 

Caen 313 

Cagayan  Jolo  Island 336 

Cagayanes  Islands 336 

Cagliari 316 

Caigara 296 

Caicos  Island 292 

West,  Cay 292 

Calaan,  Point 335 

Calais,  France 313 

Maine 281 

Calavite,  Monte 334 

Calayan  Island 334 

Calbuco 300 

Calcasieu  Pass 284 

Calcutta 329 

Caldera 300 

Caldy  Island 304 

Calebar  River,  New 322 

Old 322 

Caledonia  Har1x)r 287 

Calf  of  Man 305 

Calicut 328 

Calimere  Point 329 

Callao 301 

Calpe 315 

Caluya  Island 334 

Calvi 316 

Camamu 296 

Camaron  Cape 286 

Camasusu  Island 335 

Cambay 328 

Cambria 297 

Cambridge,  England 304 

United  States 282 

Camiguin  Island,  Luzon 334 

Mindanao 336 

Cammin 310 

Campbell,  Cape 355 

Island 350 

Campeche 285 

Campobello  Island 281 

Canaria,  Gran,  Island 303 

Canaveral  Cape 284 

Cancun  Island 285 

Candia  Island 319 

Candon 334 

Cannes. 316 

Cannonier  Point 325 

Canoas  Point 290 

Canso,  Cape 281 

North 281 

Canton 337 

Island 345 

Pulo 336 

Cantyre 305 

CapeHaitien 293 

Cape  Town 323 

Cape  Verde  Islands 303 

Capel  Island 307 

Caped'Istria 317 

Capones  Islet 334 


Page. 

Capraia  Island 316 

Caprera  Island 316 

Capri  Island 317 

Capricorn,  Cape 353 

CarNicobar 330 

Carabane 321 

Carabao  Island 335 

Caraques  Bay 302 

Carataska  Lagoon 286 

Caravellas 297 

Carbon,  Cape 321 

Carbon  era  Cape 316 

Cardamum  Islet 325 

Cardenas 293 

Cardiff 304 

Careys  Islands 355 

Cargados  Carajos 325 

Caribana  Point 295 

Carimare  Moimtain 296 

Carimata  Island 331 

Carlingford  Lough 307 

Carlobago 318 

Carloforte 316 

Carlos,  San £00 

Point 290 

Carmen  Island 285 

Caroline  Islands,  N.  Pacific.  343 

S.  Pacific 345 

Carousel  Island 280 

Carre ta  Mountain 301 

Point 287 

Carreto,  Port 287 

Carrizal,  Port 300 

Carta^na,  Colombia 295 

Spain 315 

Cartage  Mountain 286 

Carteret  Cape 313 

Harbor 346 

Car twright  Harbor 279 

Carupano 295 

Carysf ort  Island 349 

Reef 284 

Cascade  Point 355 

Casilda 293 

Casqueta  Rocks 313 

Cassmi  Island 351 

Castilloa 298 

Castle  Island 292 

Castlehaven 306 

Castro 300 

Urdiales 314 

Cat  Island 284 

Catalina  Harbor 279 

Sta.,  Island 289 

Catanduanes  Islands 335 

Catania 317 

Catastrophe,  Capo 352 

Catbalogan 335 

Catharine  Point 299 

St 304 

Catherina,  Sta. ,  Island 297 

Cato  Island 347 

Catoche  Cape 285 

Cattaro 318 

Cavite 334 

Caxones 286 

Cayenne 296 

Cayeux 313 

Caymans 293 

Cazza  Island 318 


INDEX  TO  APPENDIX  IV. 


[Page  363 


Page. 

Ceard 296 

Cebu  Island 335 

Cedar  Keys 284 

Cedeira 314 

Ceicer  de  Mer  Islar.d 337 

Celebes 333 

Centinela  Islet 295 

Ceram  Island 332 

Cerros  Island 290 

Cestos 322 

Cette 316 

Ceuta 321 

Ceylon 329 

Chacachacare  Island 296 

Chacopata 295 

Chagos  Arch 325 

Chagres 287 

Chahbar  Bay 328 

Chala  Point 301 

ChaleurBay 280 

Challenger,  Cape 327 

Chama  Bay 322 

Cham-Callao  Island 336 

Cham6,  Point 291 

Chamisso  Island 287 

Champerico 291 

Chunaral  Bav. 300 

Island." 300 

Chandeleur  Islands 284 

Chao  Islet 301 

Chapel  Island 337 

Chapu 338 

Charles  Cape 283 

Island,  Chile 299 

Galapagos  Group .  342 

Hudson  Strait 279 

Charleston 283 

Charlottetown 280 

Chateau  Bay 280 

Chatham  Harbor 282 

Island,    Galapagos 

Group 342 

S.Pacific 350 

ChatteCape 280 

Chaume,  La 314 

Chausey  Islands 313 

Chedubah  Island 329 

Chemulpo 339 

Chentabun  River 336 

Chepillo  Island 291 

Cherbourg 313 

Cheribon 331 

Cherso 317 

Chicarene  Point 291 

Chidleigh  Cape 279 

Chifoo 338 

Chignecto  Cape 281 

Chignik  Bay 288 

Chilca  Point 301 

ChimbaBay 301 

Chimbote 301 

Chincha  Islands 301 

Chinchin  Harbor 337 

Chinchorro  Bank 285 

Chin-hai 338 

ChinoBay 337 

Chirambiri  Point 302 

Chirikof  Island 288 

Chiriqui  Lagoon 287 

Chirivico 293 


PLACES — continued. 

Page. 

Chitlac  Islet 325 

Chittagong  River 329 

Choda  Island 339 

Choiseul  Island 346 

Port 326 

ChoroB  Islands 300 

Christiana  Islands 319 

Christiania 308 

Christianshaab 356 

Christianso  Island 372 

Christianssand 308 

Christiansund 307 

Christmas  Cove 299 

Harbor 327 

I . ,  Indian  Ocean 327 

N.  Pacific 342 

Christopher,  St 294 

Chuapa  River 300 

Chuluwan  Island 323 

Chupat  River 298 

Churruca,  Port 299 

Chusan  Islands 338 

Claris  Island...: 201 

Cica,  Mount 318 

Cienfuegos 293 

Ciotat 316 

Cispata,  Port 295 

CittaNuova 317 

Civita  Vecchia 316 

Clara,  Sta 289 

Clare  Island 306 

Claremont  Point 353 

Clarence  Harbor,  Bahamas.  292 

Port,  Alaska 287 

River 352 

Clarion  Island 291 

Claushavn 356 

Clear  Cape 306 

Clearwater  Point 280 

Clerke  Island 349 

Clermont  Tonnere  Island...  349 

Cleveland,  Cape 353 

Clew  Bay 306 

ClifdenBay 306 

Clipperton  Island,  Mexico. .  291 

N.Pacific 344 

Clonard,  Cape 339 

Coast  Castle,  Cape 322 

Cobija 301 

CobreBay 301 

Cochin 328 

Cockell  Islet 351 

Cockscomb  Mountain 286 

Coconada 329 

Cocos  Island,  C.  America. . .  291 

N.Pacific 342 

Cod,  Cape 282 

CoderaCape 295 

Codfish  Island 355 

Codroy  Island 280 

Coetivy  Island 326 

Coffin  Bay 362 

Island,  Madagascar 326 

Nova  Scotia 281 

Cofre  de  Perote  Mt 285 

Coiba  Island 291 

Coimbra 315 

Colberg 310 

Colbert  Islet 351 

Coles  Point 301 


Page. 

Colina  Redonda 301 

Colnett  Bay 290 

Colombo 329 

Colon 287 

Colonia 298 

Colonna,  Cape,  Greece 319 

Italy 317 

Columbia,  Cape 355 

Columbretes  Islands 315 

Coliunbus  Island 287 

Colville,  Cape 354 

Comau  Inlet 300 

Comandatuba 297 

Commerson  Island 346 

Comorin,  Cape 328 

Comoro  Island 326 

Concei^-ao 297 

Conception  Island 292 

Point 289 

Conde 296 

Condor  Cove 300 

Condore  Islands 337 

Conducia 323 

Conejo,  El,  Point 290 

Coney  Island 337 

ConfitesCay 292 

Congo  River 322 

Congrehoy  Peak 286 

Conn^table  Islet 296 

Constantinople 320 

Constitution  Cove 301 

Contas 296 

Conte,  Port 316 

Contoy  Island 285 

Conway,  Cape 353 

Reef 350 

Cook  Cape 288 

Mountain 353 

Cooper,  Port 355 

Copenhagen 312 

Copiapo 300 

Copper  Island 341 

Coquet  Island 305 

Coquille  Island 343 

Coquimbo 300 

Coral  Island 297 

Islet 297 

Corcovado  Volcano 300 

Cordouan,  Point 314 

Corfu 319 

Coringa  Islands 347 

Corinto 291 

Cork,  Ireland 307 

Port,  Staten  Island.  . .  298 

Cormorant  Island 288 

Com  Islands 286 

Comwallis  Islands 344 

Port 329 

Coro,  Velade 295 

Coromandel  Harbor 354 

Coronation  Island 304 

Corregidor  Island 334 

Corrientes,  Cape,  Argentina.  298 

Colombia 302 

Mexico 291 

S.  Africa 323 

Corsarios  Bay 295 

Corseulles,  Port 313 

Corso,  Cape 316 

Mountain 299 


Page  364] 


INDEX  TO  APPENDIX  IV. 


Page. 

Corti 316 

Corufia 314 

Corvo  Island 302 

Coslin 310 

Cosmoledo  Island 327 

Cotinguiba 296 

Cotrone 317 

Coubre,  Point  de  la 314 

Courtown  Cays 286 

Coutances 313 

Cove  Rock 323 

Cow  Head 280 

Coy  Inlet 298 

Cozumel  Island 285 

Cracker  Bay 298 

Crassok  Point 331 

Crawl  Cay 287 

Crescent  City 289 

Cretin,  Cape 346 

Creux,  Cape 315 

Cristoval,  San,  Island 346 

Crocker  Island 349 

Croisic 314 

Croix,  St 294 

Croker,  Cape 351 

Crooked  Island 292 

Crozet  Islands 327 

Cruz  Cape 293 

Sta.,  Brazil 297 

California 289 

Island 289 

Islands,      Philip- 
pines   335 

S.  Pacific...  347 

Luzon 334 

Port 298 

Cuad  Basang  Island 336 

Cuba 

Culebra 291 

Culebrita  Island 294 

Culion  Island 334 

Cullera,  Cape 315 

Culver  Point 352 

Cumana 295 

Cumberland  Island 353 

Cumshewa  Harbor 288 

Cupchi  Point 337 

Cupica  Bay 302 

Cwcagao  Island 295 

Little 295 

Currimao 334 

Currituck  Beach 283 

Curtis  Island 353 

Port 353 

Curzola  Island 318 

Cuttyhunk  Light 282 

Cuvier,  Cape 351 

Island 354 

Cuxhaven 311 

Cuyo  Island 334 

Cyprus 320 

Daedalus  Shoal 324 

Dago  Island 310 

Dairen  Wan 338 

Dakar,  Port 321 

Dalcahue 300 

Dale  Point 351 

Dalrymple  Harbor 336 

Port 354 


PLACES — continued. 

Page. 

Dalupiri  Island 334 

Dame  Marie,  Cape 294 

Damghot 327 

Damma  Island 332 

Danger  Islands 348 

Dangerous  Rock 337 

Dannesbrog  Island 356 

Danube  River 320 

Dantzig 310 

Dapitan 336 

Dardanelles 320 

Dar  el  Beida,  Cape 321 

Dar-es-Salaam 324 

Darien  Harbor 291 

Georgia,  U.  S 283 

Darsserort 311 

Darwin,  Port 351 

Dato  Island 331 

Datu,  Point 330 

Dauphin,  Fort 326 

Davao 335 

Davey,  Port 354 

Davids,  St.,  Island 303 

De  Freycinet  Islets 351 

De  Kastri 341 

De  Peysters  Island 345 

Deadman  Rock 280 

Deception  Island 304 

Deimaniyeh 327 

Delagoa  Bay 323 

Delgada  Point 299 

Delgado,  Cape 324 

Point 298 

Demerara 296 

Denia 315 

Denis,  St 326 

Denison,  Port 353 

D'Entrecasteaux  Islands. . .  347 

Point 351 

D'Urville  Island 355 

—  Point 346 

Deseado,  Cape 299 

Desert,  Mt.,  Rock 281 

Desertas 303 

Desirade 294 

Desire,  Port 298 

Desolation,  Cape 298 

DiaFjeld 357 

Diamond  Harbor 329 

—;- Point 330 

Diedrichshagen 311 

Diego  Garcia 325 

Ramirez  Island 298 

San 289 

Cape 298 

Dieppe 313 

Digges  Islands 279 

Dimas 293 

Dimasalasan,  Port 334 

Dinding  Channel 329 

Dingle  Bay 306 

Diomede  Island 287 

Direction,  Cape 353 

Island 331 

Disappointment,  Cape,  Sib.  341 

— ; Washington. .....  289 

Discovery  Harbor 355 

Diseilsland 324 

DiuHead 328 

DixCove 322 


Page. 

Djabon,  Point 330 

Djambi 330 

Djursten 309 

Dnieper  Bay 320 

Doc  Can  Islet 336 

Dodd  Island 337 

Dog  Island 294 

Domar,  Pulo 331 

Demesnes 310 

Domingo,  San,  Point 290 

St.,  Cay 292 

Dominica 295 

Donaghadee 306 

Dondra  Head 329 

Donegal  Bay 306 

Double  Island 329 

Point 353 

Peak  Island 337 

Douglass  Rocks 345 

Dounpatrick  Head 306 

Douvres  Rocks 313 

Dover  Point.. 352 

Drei  Cap  Peninsula 346 

Drepano,  Port 319 

Drobak 308 

Drogheda 307 

Dromedary  Mountain 352 

Drummond  Island 342 

Dublin 307 

Ducie  Island 349 

Duff  Islands 347 

Duke  of  Clarence  Island 345 

York  I., N.Britain.  346 

— S.Pac.  346 

DulceGulf 286 

River 286 

Dulcigno 318 

Dumaguete 335 

Dumaly  Point 334 

Dumford  Poiat 323 

Duncan  Island 342 

Dundee,  Rock  of 299 

DundrumBay 307 

Dungarvan 307 

Dungeness 304 

New 289 

Point 299 

Dunkerque 313 

Dunnet  Head 305 

Duperrey  Islands 343 

Duppel 311 

Durazzo 318 

Dumford,  Port 324 

Dussejour,  Cape 351 

Dwarka 328 

Eagle  Island 306 

Earakong  Island 344 

East  Cape,  Madagascar 326 

New  Zealand 354 

Siberia 342 

Dog  Island 337 

Island,  Crozet  Is 327 

Magdalen  Is 280 

Easter  Island 350 

Eastport 281 

Eau  Island 343 

Eauripik  Islands 343 

Ebon  Atoll 343 


INDEX  TO  APPENDIX  IV. 


[Page  365 


Page. 

Eckemforde 311 

Eclipse  Harbor 279 

Islands 351 

Eddystone 304 

Point 354 

Eden  Harbor 299 

Edenshaw  Cape 288 

Edenton 283 

Edinburgh 305 

Eeragh  Island 306 

Egedesmunde 356 

Eggegrund  Islet 309 

Egmont  Mountain 354 

Port 303 

Eimeo  Island 349 

Ekholra  Islet 310 

Elba  Island 316 

Elbing 310 

Elena,  St.,  Port 298 

Sta.,  Point 302 

Elephant  Bay 322 

Eleuthera  Island 292 

Eliaa,  St.,  Mount 288 

Elizabeth  Bay 322 

Cape 282 

City 283 

Harbor 355 

Island,  Chile 299 

Tuamotu  Arch  . . .  349 

Port 323 

Elizabeth  Reef 350 

Ellice  Islands 345 

Emden 312 

Emu  Bay 354 

Endnger 309 

Endelave  Island 312 

Enderbury  Island 345 

Enderby  Island   351 

Endermo 341 

Enfant  Perdu  Island 296 

Engano,  Cape 293 

Engano,  Cape 334 

Engano  Island 330 

Engelholm 308 

English  Cay 285 

Eniwetok  Islands 343 

Enrag^,  Cape 281 

Ensenada 290 

Entry  Island 280 

Erromango  Island 347 

Erronan  Island 347 

Escarceo  Point,  Phil.  Is...  334 

,  Venezuela 295 

Eschholtz  Islands 343 

Escondido,  Port 293 

Escudo  de  Veragua 287 

Escumenac  Point 280 

Esdu  Island 325 

Esmeralda  Islet 296 

River 302 

Espada  Point,  Colombia. . .  295 

Espenberg,  Cape 287 

Esperanza  Inlet 288 

Espiritu  Santo  Bay 297 

Cape 299 

Esc^uimalt 288 

Eaemgton,  Port 351 

Estaca  Point 314 

Estangues  Point 295 

Estevan  Point 288 

Etches,  Port 288 


PLACES — continued. 

Page. 

EtenHead 302 

Eu,  Pulo 331 

Eureka 289 

Euripo  Strait 319 

Europa  Island 326 

Eustatius,  St 294 

Evangelistas  Island 299 

Evaristo,  San 290 

Expedition  Bay 341 

Exuma,  Great,  Island 292 

Faero  Islands 302 

Fair  Isle  Skroo 305 

Fairy,  Port 352 

Faiu,  W.,  Met 343 

Fakaofu  Islet 345 

Fakarana  Island 349 

Falkenberg 308 

Falkland  Islands 304 

Falmouth,  England 304 

Jamaica 293 

False,  Cape 294 

False  Cape  Horn 298 

Point 329 

Falster  Island 312 

Falsterbo 308 

Famagusta 320 

Famine,  Port 299 

Fanad  Point 306 

Fanning  Island 342 

Fano  Island,  Adriatic 319 

Denmark 312 

Farallon  Islet 289 

Faraulep  Island 343 

Farewell,  Cape,  Greenland.  356 

New  Zealand 355 

Farina,  Cape 321 

Farisan  Island 325 

Earn  Island 305 

Faro  Island,  Sweden 309 

of  Messina 317 

Farquhar  Islands 326 

FarrallRock 286 

Farralon  de  Pajaros 344 

Fartak,  Ras 327 

Fastnet  Rock 306 

Father  Point 280 

Fataizio  Island 340 

Fatu  Hiva  Island 345 

Huku  Island,Galapagos  342 

Marquesas . .  345 

Fatuna  Island 348 

Fayal  Channel 302 

Island 302 

Fecamp 313 

Felipe,  San,  Cays 293 

Point 290 

Felix,  St.,  Island,  Chile....  300 

S.  Pacific...  350 

Fenerive  Point 326 

Fermin  Point 289 

Femandina 284 

Fernando  Noronha 303 

Po  Island 322 

San,  Cuba 292 

River 285 

Port,  P.  1 334 

Trinidad 296 

F^roUe  Pena. ,  New 280 

Ferro  Island 303 

Ferrol 314 


Page. 

Fetouhouhou  Island 345 

Feys  Island 343 

Fidonisi  Island 320 

Figari  Cape 316 

Filzand  Island 310 

Finisterre,  Cape 314 

Firase  Rocks 339 

Fire  Island 283 

Firmin,  San 290 

Fischausen 310 

Fish,  Great,  Bay 322 

Little,  Bay 322 

Fiskemaes 356 

Fitz  Roy  River 351 

Fiume 317 

Five  Fathom  Bank 283 

Flamborough 305 

Flamenco 300 

Island 291 

Fiat  Island 325 

Flattery,  Cape 289 

Flensberg 311 

Flesko,  Cape 333 

Flinders  Island 352 

Islands 353 

River 353 

Flint  Island 345 

Florence 316 

Flores  Island,  Azores 302 

Indian  Arch 332 

Uruguay 298 

Florida  Island 346 

Flower  Cove 280 

Flushing 313 

Fly  River 346 

Foerder  Islet 308 

Fogo  Island 303 

Fohr 311 

Foreland,  North 304 

South 304 

Formigaa  Islands 302 

Shoal 293 

Formosa  Island 338 

Fomaes 312 

Forsmark 309 

Forsyth  Point 288 

Forth  Mountain 307 

Fortune  Island 292 

Foulwind,  Cape 355 

Four,  Le,  Rock 314 

Fowey  Rocks 284 

Fowler  Point 352 

Frances,  Cayo 292 

Francis  Island 342 

St.,  Cape,  C.  Colony...  323 

; Newf'drd...  279 

Francisco,  San 289 

Cape 302 

Head 301 

River 296 

Sao 297 

Frankland  Island 353 

Franklin  Harbor 352 

Franz  Josef  Land 356 

Eraser  River 289 

FraileRock i 294 

Frayles  Point 301 

Frederick,  Port 354 

Frederik  Hendrik,  Cape. . .  354 

Frederikshaab 356 

Frederiksthal 356 


Page  366] 


INDEX  TO  APPENDIX  IV. 


Page. 

Frederiksvaem 308 

Fredriksten 308 

FreelaCape 279 

Frehel,  Cape 313 

Freikallen 307 

Fremantle 351 

French  Cay 292 

Frigate  Shoal 344 

Freycinet,  De,  Islets 351 

Peninsula 354 

Frio,  Cape,  Brazil 297 

W.Africa 322 

Port 297 

Froward  Cape 299 

Fruholm 307 

Frying  Pan  Shoals 283 

Fuenterrabia 314 

Fuerta  Ventura  Island 303 

Fiierte  Island 295 

Fuga  Island 334 

Fugle  Huk 357 

Fuianga  Island 348 

Fulehuk 308 

Funafuti  Island 345 

Funk  Island 279 

Funkenhagen 310 

Furen  Islet 308 

Fushiki 340 

Futuna  Island 347 

GaalongBay 337 

Gabo  Island 352 

Gabriel  Mountain 306 

Gaeta 31G 

Gafor  Island 325 

Galapagos  Islands 342 

Galera  Point,  Ecuador 302 

Trinidad 296 

Galgenbeig 311 

GaliolaRock 318 

Galita  Island 321 

Gallant,  Port 299 

Galle,  Point  de 329 

Gallegos  River 298 

Galley  Head 307 

Gallinas  River 322 

Gallipoli,  Italy 317 

Turkey 320 

Galloway,  Mull  of 305 

Galveston 284 

Galway 306 

Gambler  Island 349 

Gauge 309 

Gannet,  Outer,  Island 279 

Rock 281 

Gap  Rock 337 

Garcia  d'Avila 296 

Gardiner  Island 344 

Gardners  I.,  Long  Island...  282 

S.Pacific 345 

Garrafi,  Little 330 

Caspar,  Island  and  Strait. .  331 

Rico  Reef 344 

Gasparilla  Island 284 

Gasp6  Cape 280 

Gata,  Cape,  Cyprus 320 

de,  Spain 315 

Gaujam 329 

Gay  Head 282 

Gebey  Islands 333 


PLACES — continued. 

Page. 

Geelong 352 

Gefle 309 

Genoa 316 

George,  Fort,  Cay 2J2 

St.,  Cape,  Florida 234 

Newf'dl'd...  280 

Nova  Scotia.  281 

Island,  Alaska. . .  287 

Azores 302 

Georges  Island 290 

St.,  Cay 285 

Geoi^etown 283 

Georgia,  South,  Island 304 

Geronimo,  San,  Island 290 

Geyser  Reef 326 

Gharib,  Ras 324 

Ghir,  Cape 321 

Gibara 292 

Gibdo  Island 335 

Gibraltar 315 

Giglio  Island 316 

Gijon 314 

Gilbert  Islands 342 

Gillolo  Island 333 

Ginger  Cay 292 

Giigenti 317 

Gizau 325 

Gizo  Island 346 

Glas  Island 305 

Glasgow 305 

Glashedy  Island 306 

Glenan  Islands 314 

Glorioso  Islands 326 

Gloucester  Island,  Aus 353 

TuamotuArch...  349 

Massachusetts 282 

Glover  Reef 285 

Gnarp 309 

Goa 328 

Grobernadora 293 

Godhavn 356 

Godthaab 356 

Goedereede 313 

GolamHead 306 

Gomenitza 319 

Gomera  Island 303 

Gonaives 294 

Gonave  Island 294 

Good  Hope,  Cape,  Africa...  323 

China 337 

Island 348 

Success  Bay 298 

Goose  Island 352 

Gopalpur 329 

Coram  Islands 332 

Gorda  Cay 286 

Point 331 

Gore,  Port 355 

Goree  Island 321 

Road 298 

Goi^ona  Island 302 

Goro  Island 348 

Gorontalo 333 

Goto  Island 339 

Gottenburg 308 

Gottland  Island 309 

Gough  Island 303 

Cozier  Islet 294 

Gozo  Island 317 

Graciaa  d  Dios,  Cape 286 


Graciosa  Island 302 

Grade 317 

Grand  Manan  Island 281 

Port 325 

Riband  Island 316 

Grande  Point 301 

Granitz 311 

Granville 313 

Crappler,  Port 299 

Grave,  Point  de 314 

Gravelines 313 

Gready  Harbor 279 

Great  Bird  Rock 280 

Rock  Head 286 

Green,  Cape 352 

Island,  Labrador 279 

Newfoundland...  280 

Nova  Scotia 281 

Greenly  Island 280 

Greenspond  Island 279 

Greenwich 304 

Island 343 

Gregory,  Cape 299 

Port 351 

Grenada 295 

Grenville,  Cape 353 

Grey  River 355 

Greytown 286 

Griefswald 311 

Griefswalder  Oie 311 

Grim,  Cape 354 

Grimsey  Norddranger. 357 

Grip 307 

GrisNezCape 313 

Groate  Evlandt 351 

Groix,  Island  de 314 

Gross-Horst 310 

Grouin  du  Cou,  Point  de. . .  314 

Gruizza  Rock 318 

Gryto 307 

Guadalcanal  Island 346 

Guadeloupe,  L.  California..  290 

West  Indies 294 

Guafo  1 300 

Guaineco  Islands 299 

Guaira,  La 295 

Guaja  Shima 339 

Guam  Island 344 

Guana,  Little,  Cay 292 

Guanape  Islands 301 

Guanica 294 

Guantanamo 293 

Guarapiri  Islets 297 

Guaratiba,  Cape 297 

Guardafui,  Cape 324 

Guascama  Point 302 

Guatulco,  Port 291 

Guayaquil 302 

Guaymas 290 

Guerande 314 

Guerin  Island 339 

Guguan  Island 344 

Guimaras  Island 335 

Guiuan 335 

Guldager 312 

Gull  Island,  Little 282 

Gullan,  San,  Island 301 

Gun  Cay 292 

Gunong  Api  Island 332 

GutzlaS  Island 338 


INDEX  TO  APPENDIX  IV. 


[Page  367 


Page. 

GwadarBay 328 

GwatarBay 328 

Habana 293 

Habibas  Island 321 

Hacha,  Rio  de  la 295 

Haddington,  Port 338 

Haedic  Island 314 

Hafun,  Rae 324 

Hagenmeister  Island 287 

Hague,  Cape  la 313 

The 313 

Haiduong 336 

Haifong 336 

Haifa 320 

Hainan  Island 337 

Hai-yun-tan  Island 338 

Hakodate 341 

Half  Port  Bay 299 

Halfmoon  Cay,  Belize 285 

Nicaragua 286 

Halgan  Island 350 

HalSax 281 

Haliguen,  Port 314 

Hall  Island 343 

Islands,  Sir  James.  . . .  339 

Halmahera  1 333 

Halmstad 308 

Hals 312 

Halt  Bay 299 

Halten  Island 307 

Hamberg 308 

Hamburg 311 

Hamilton  Island 303 

Mountain 289 

Port 339 

Hammamet  Bay 321 

Hammerfest 307 

Hampton 282 

Hamrange 309 

Hanalei 344 

Hanfelah  Bay 324 

Hangklip,  Cape 323 

Hanjam  Islet 328 

Hannibal  Isles 353 

Hano  Island 309 

Hanoi 336 

Hao  Island 349 

Haradsskar  Islet 309 

Haraiki  Island 349 

HarborGrace 279 

Harburg 311 

Hardy,  Sir  C,  Island 353 

Harpe,  La,  Island 349 

Harrison  Cape 279 

Hartlepool 305 

Harvey,  Port 288 

Harwich 305 

Hatteras  Cape 283 

Haustholm 312 

Haute  Island 281 

Have,  Cape  la 281 

Havre 313 

Hawaii 344 

Hayter  Island 346 

Heard  Island 327 

Hearts  Content 279 

HeaudeBrehat 313 

Heawandu  Island 325 

Hecate  Bay 288 


PLACES — continued. 

Page. 

Hecate  Cove 288 

Hecla.Cape 355 

Hed,  Kaaal 327 

Hee-tah-doo  Island 325 

Hegadis  Island 332 

Heili^en  Creutz 310 

Hekkingen 307 

Hela 310 

Helena,  St.,  Island 303 

Helgoland 311 

Hehers,  St 307 

Hellevoetsluis 313 

Helliso 308 

Hellyer  Rocks 299 

Helsmborg 308 

Helsingfors 309 

Helvick  Head 307 

Hendaye 314 

Hend  erson  Island 349 

Henderville  Island 342 

Henlopen  Cape 283 

Henry  Cape 283 

Port 299 

Ileongsan,  Port 338 

Herald  Cays 347 

Hereheretue  Island 349 

Hermes,  Cape 323 

Hermit  Island 346 

Hermite  Island 298 

Herradura  de  Carrizal 300 

Hervey  Islets 350 

Hesquiat  Harbor 288 

HesselS  Island 312 

Hessenstein 311 

Hestskjaer 308 

Heve,  Cape  La 313 

Hiaou  Island 345 

Hikueru  Island 349 

Hillswickness 305 

Hilo 344 

Himmittee  Island 325 

Hindwar 328 

Hiogo 340 

HiradoNoSeto 339 

Hirtshala 312 

Hiva-Oa  Island 345 

Hielm  Islet 312 

Hjertholm 307 

Hjoerringa  Mountain 307 

Hoa-pin-su  Island 338 

HobartTown 354 

Hodeidah  Road 325 

Hog  Island,  Indian  Ocean. .  327 

Virginia 283 

Islands 286 

Hogland  Island 309 

Hogolu  Islands 343 

Hogsty  Reef 292 

Hogulu  Islands 343 

HoheWeg 311 

Hohenschonberg 311 

Hokianga  River 355 

Hokitika 355 

Holbome  Islet 353 

Hole-in-the-Wall 323 

Hollo  Island' 308 

Holmestrand 308 

Holmogadd 309 

Holsteinberg 356 

Holyhead 304 


Page. 

Hon  Dau  Island 336 

Hondeklip  Bay 323 

Honfleur 313 

Hongkong 337 

Hon-M6 336 

Honolulu 344 

Hood  Island 342 

Lord,  Island. 349 

Point,  Australia 352 

Port,  Cape  Breton  I...  281 

Hope  Island 353 

Hopedale  Harbor 279 

Hopes  Advance,  Cape 279 

Hoppers  Island 342 

Horn,  Cape 298 

False  Cape 298 

Head 306 

Island 284 

Home  Island 348 

Hornelen  Mountain 308 

Horsens 312 

Horten 308 

Hospital  Bight 286 

Hougue,  Cape  La 313 

Houtman  Rocks 351 

Howaiyuh 327 

Howe,  Cape,  East 352 

West 351 

Lord,  Island 348,  350 

Islands 346 

Sound 288 

Howland  Islands 342 

Howth  Peninsula 307 

Huaheine  Island 349 

Huanchaco  Point 301 

Huarmey 301 

Huasco 300 

Hudiksvalls 309 

Huelva 315 

Iliigeberg 311 

Hui-Iang-san 337 

Hull  Island 360 

Hulls  Island 345 

Ilulu-shan  Bay. . .-. 338 

Humber  River 305 

Humboldt 289 

Humphrey  Island 345 

Hungwha  Channel 337 

Hunter  Island,  N.  Hebrides  347 

Tasmania 354 

Hurds  Island 342 

Hurst  Castle 304 

Husum 311 

Hvidingso 308 

Iba 334 

Ibayat  Island 334 

Ibbetson  Island 343 

Ibiza,  Port 316 

Icacos  Point,  Belize 286 

Trinidad 296 

Ichabo  Island 322 

Icy  Cape 287 

leraka 319 

Ifalik  Islands 343 

Iglooik  Island 355 

Ignacio,  San,  Point 290 

Iguape 297 

IkiSima 339 

Ildefonso  Islands 298 


Page  368] 


INDEX  TO  APPENDIX  IV. 


Page. 

Ilha  Grande 297 

Ilheos 297 

Ilo 301 

Iloilo 335 

InaboyeSaki 340 

Inaccessible  Island 303 

I  nagua  Islands 292 

Inch  Keith  Kocks 305 

Indefatigable  Island 342 

Indian,  Cape 342 

Harbor 279 

Head 353 

Tickle 279 

Indianola 284 

Indio  Point 298 

Indispensable  Keefs 346 

Indrapura  Point 330 

Ingolfshofde 357 

IngoMjeld 356 

ImshboffiQ 306 

Inishowen  Head 306 

InishrahuU 306 

Inishturk  Island 306 

Iniue  Island 

Innamban  Bay 323 

Inscription,  Cape 351 

Investigator  Strait 352 

Ipswich 282 

Iquape 297 

Iquique 301 

Ireland  Island 803 

Isaac,  Great,  Cay 291 

Isabel,  Cape 299 

Island 346 

Point 284 

Isabella  de  Sagua 293 

Isene 320 

Isidro,  San,  Cape 299 

Isla  Grande 291 

Island  Harbor 288 

Islay 301 

IsleofMan 305 

Isola 317 

Isolette,  Cape 327 

Istria,  Cape  d' 317 

Itacolomi  Islet 297 

Point 296 

Itapacaroya  Point 297 

Itaparica 296 

Itapemirim 297 

Iturup  Island 341 

Ivigtuk 356 

IwoShima 339 

Iwo-sima 339 

Jabwat  Island 343 

Jackson,  Port 352 

Jacksonville 284 

Jacmel 294 

Jacobshavn 356 

Jaffa,  Cape 352 

Jago,  St.,  Island 303 

Jaguaribe  River 296 

Jaluit  Island 343 

Jamaica 293 

James  Island 342 

St.,  Cape,  0.  China....  336 

Vancouver  I.  288 

Jan  Mayen  Island 357 

JaraHead 301 


PLACES — continued. 

Page. 

Jarea 315 

Jarvis  Island 345 

Jask  Bay 328 

Java 331 

Head 331 

Jean,  St.,  de  Luz 314 

Jebel  Zukur  Island 325 

Jelaka,  Pulo 331 

JelaUl 324 

Jensen  Nunatak 356 

Jeremie 294 

Jershoft 310 

Jervis  Bay 352 

Cape 352 

Island 342 

Jesus  Maria  Island 346 

Jiddah 324 

Jighinsk  Island 356 

Johanna  Island 326 

John,  St.,  Cape,  Newf'dl'd.  279 

Staten  Island  298 

Island 294 

Johns,  St.,  Island,  Red  Sea.  324 

New  Brunswick. .  281 

Newfoundland...  279 

River 284 

Johnston  Islands 344 

Jolo  Islands 336 

Jomfruland 308 

Jona,  St.,  Island 341 

Jos6,  San,  California 289 

de  Guatemala 291 

delCabo 290 

Port 298 

Joseph  Henry,  Cape 355 

Juan  Fernandez  Island 350 

San 294 

Cape 294 

delSur 291 

Point 285 

Port,  Peru 301 

Vancouver  I.  288 

St.,  Bay 295 

Juanico,  San,  Point 290 

Juby,  Cape 321 

Jucaro 293 

Judith  Point 282 

Juggemath 329 

Juist 312 

Julian,  San,  Port 298 

St.,  Island 331 

Julianshaab 356 

Juneau 288 

Jupiter  Inlet t 284 

Jura  Island 319 

Juul,  Cape 356 

Kabenda  Bay 322 

ICabuli  Island 334 

ICadoSima 341 

Kagoshima ^ 340 

Kaiioolawe  Island 344 

Kahrig  Islet 328 

Kaipara  Harbor 355 

Kais  Islet 328 

KaiartaUk  Island 356 

Kaldrouma 339 

Kal  Farun  Islet 324 

Kalboden  Island 309 

KaHbia 321 


Page. 

Kalingapatam 329 

Kallundborg 312 

Kalpeni  Islet 325 

ICama  Islands 343 

Kamaishi 340 

Kamardn  Bay 325 

Kambangan  Island 331 

Kambara  Island 348 

Kamchatka,  Cape 341 

Kanala,  Port 350 

Kanathea  Island 348 

Kandavu 347 

KandeUusa  Island 319 

Kangamint 356 

Kangarssuk  Ha vn 356 

Kannanur 328 

Kao  Island 350 

Kappeln , 311 

Kara  Bumu,  Cape 320 

Karachi 328 

Karafuto 341 

Karajinski  Island 341 

Karimon  Djawa  Island 332 

Karlshamn 309 

Karlskrona 309 

Kaske 309 

Kasm 328 

KatakoloBay 319 

Kater  Island 345 

Katiagam 330 

Katie  Rock 318 

Kauai  Island 344 

Kawhia  Harbor 354 

Keats,  Port 351 

Kee-lah  Island 325 

Keeling  Islands 327 

Keenapoussan  Island 336 

Keitum 311 

Kelantan  River 336 

Kendall,  Cape 355 

Kent  Island 352 

Keppel  Island 348 

Kermadec  Islands 350 

Kertch 320 

Ketoy  Island 341 

Key  West 284 

Kharig  Islet 328 

Kharim-Kotan  Island 341 

Kheli t319 

Khor  Nohud 324 

Nowarat 324 

Fakan  Bay 327 

Ki  Islands 332 

Kiaochow  Bay 338 

Kiama  Harbor 352 

IGdnappers  Cape 354 

Kiefali,  Cape 318 

Kiel 311 

Kiirun  Ko .• 338 

Kikai-jima 339 

Kiliman 323 

KillineyHUl 307 

Killybegs 306 

Kilwa  Kisiwani 323 

Kimbeedso  Island 325 

King  George  Sound 351 

Island,  Australia 352 

Kings  Island 349 

Kingston 293 

Kingstown 307 

Kinkwosan  Island 340 


INDEX  TO  APPENDIX  IV. 


[Page  369 


Page. 

Kinnstind 308 

Kino  Point 290 

Kinsale 307 

Kirkwall 305 

KisimayuBay 324 

Kiska  Island 287 

Kietna 329 

Kiflwere 324 

Kittan  Islet 325 

Kjorge 312 

Knocklane 306 

Knockmealdown  Mountain.  307 

Kjiocknarea 306 

Knox  Bay 288 

Cape 288 

Knysna 323 

Kobe 340 

Kodiak  Island 288 

Koh  Chang 336 

Kong  River 336 

Krah  Islet 336 

Tang  Rocks 336 

Kokoun-tan  Islands 339 

Koksher 310 

Kolding 312 

Komba  Island... 332 

Kompaa  Mountain 308 

Kongelab  Islands 343 

Konigsbere 310 

Koniushi  tslajad 287 

Koppem 307 

Koroni  Anchorage 319 

Korror  Islands 344 

Koa 320 

Koeair,  Arabia 327 

Red  Sea 324 

Koeime  No  Osima 339 

Koster 308 

Kottaringin  Bay 333 

Kovra  Ry thi  Point 326 

Kozu  Shima  Mountain 340 

Krakatoa  Island 331 

Krishna  Shoal 329 

Kroe 330 

Kronberg 312 

Kronstadt 310 

Kxusenstem  Cape 287 

Kub  Kalat 328 

Kuchino  Shima 339 

Kuchinotsu 339 

Kuino 310 

Kullen  Point 308 

Kumi  Island 338 

Kumpta 328 

Kunashir  Island 341 

Kundapur 328 

Kunfidah 324 

Kuper  Harbor 339 

Port 288 

Kiuia  Maria  Islands 327 

KuroSima 339 

Kusakaki  Jima 339 

Kusrovie  Rock 336 

Kusterjeh 320 

Kutpur 328 

Kuweit 327 

Kweshan  Islands 338 

Kyangle  Islets 344 

Kyuquot  Sound 288 


PLACES — continued. 

Pago. 

Labuan  Island 333 

Labyrinth  Head 298 

LaCaloma 293 

Laccadive  Islands 325 

Lacepede  Island 351 

Lady  Elliot  Island 353 

Frances,  Port 326 

Lagartos 285 

Laghi,  Cape 318 

Lagoon  Head 290 

Lagos 315 

River 322 

Lagosta  Island 318 

Lagostini  Island 318 

Laiemba  Island 348 

Lamaka 320 

Lambayeque 302 

Lambert,  Cape 351 

LamoBay 324 

Lamock  Island 337 

Lampedusa  Island 317 

Lampong  Bay 330 

Lamyit  Island 337 

Landfall  Island 299 

Lands  End 304 

Landskrona 308 

Landsort 309 

Langanaes  Point 357 

Langeland  Island 312 

Langeoog 312 

Langesund 308 

Langford,  Port 288 

Langkuas  Island 331 

Langotangen 308 

Langwarden 311 

Lanzarote  Island 303 

LaPaz 290 

La  Plata 298 

Laruehuapi  Cove 300 

Lassa,  Cape 333 

Laesau 311 

Latakia 320 

Latouche  Tr^ville,  Cape —  351 

Laun 279 

Laurie  Island 304 

Laut,  Pulo 333 

Lavaca 284 

Lavata 301 

Lawrence,      St.,      Island, 

Alaska 287 

Siberia 342 

Laykan,  Port 333 

Laysan  Island 344 

Lazaref,  Port 339 

Lazaro,  San,  Cape 290 

Leander  Shoal 280 

Leba 310 

Lebu  River 300 

Leeuwin,  Cape 351 

Legendre  Island 351 

Leghorn 316 

Lema  Island 337 

Lemnos  Island 319 

Lengua  de  Vaca  Point 300 

Lennox  Cove 298 

Leones  Island 298 

Leopold,  Port 355 

Lepar,  Pulo 331 

Le  Pilier  Island 314 


Page. 

Lepreau  Cape 281 

Lerma 285 

Lerwick 305 

Leschenault,  Cape 351 

Lesina  Island 318 

L'Etang  Harbor 281 

Leven  Island 326 

Port 326 

River 354 

L'Evdque,  Cape 351 

Lewis,  St.,  Cape 279 

Leyden 312 

Leyte  Island 335 

LhouReef 347 

Liakhov  Islands 356 

Liancourt  Rocks 339 

Liant,  Cape 336 

Liao-ti-shan 338 

Libau 310 

Libertad,  C.  America 291 

Mexico 290 

Lifu  Island 350 

Lighthouse  Rocks 288 

Limerick 306 

Limon,  Port 286 

Lincoln  Island 337 

Port 352 

Lindesnes 308 

Lindi  River 324 

Lindo,  Port 320 

Linga  Island 330 

Linguelta,  Cape 318 

Linosa  Island 317 

Lipari  Island 317 

Lisbon 315 

Lisbume  Cape 287 

Lisiansky  Island 344 

Lissa  Island 318 

List 311 

Lister 308 

Lith 324 

Litkieh  Island 343 

Little  Hope  Island 281 

Lituya  Bay 288 

Liverpool 305 

Port 326 

River 351 

Livomo 316 

Lizard  Point 304 

LUco 300 

Loa  River 301 

Loaf  Island 346 

Loango  Bay 322 

Lobito  Point 322 

Lobos  Cay,  Bahamas 292 

Mexico 285 

de  Afuera  Island 302 

Tierra 302 

Island,  Canaries 303 

Uruguay 298 

Point,  N.  Chile 301 

S.Chile 301 

Lodingen 307 

Lofoten  Island 307 

Loggerhead  Key 284 

Loheiyah 325  ^ 

Loma  Point 289 

Lomaa  Point 301 

Lombata  Island 332 


21594°— 14- 


-24 


Page  370] 


INDEX  TO  APPENDIX  IV. 


Lombok  Island 332 

London,  East 323 

Londonderry 306 

Cape 351 

Long  Island,  Bahamas 292 

United  States 282 

Look6,  Port 326 

Lookout  Cape,  N .  CaroHna. .  283 

Point,  Australia 353 

Maryland 283 

Lopatka,  Cape 341 

Lopez,  Cape 322 

Lorenzo,  San,  Cape 302 

Island 301 

Loreto 290 

Lorient 314 

Loro,  Mount 334 

Lorstakken  Mountain 308 

Los,  Isles  do 321 

Lota 300 

Lots  Wife  Rock 340 

Lough  Larne 306 

Louis,  Port,  Falkland  Is 304 

Guadeloupe 294 

Mauritius  Island .  325 

St 321 

Louisburg 281 

Louisiade  Archipelago 347 

Loune 312 

Low  Island 337 

Port 300 

Lowenom,  Cape 356 

Lowestoft 305 

Loyalty  Islands 350 

Lubang  Island 334 

Lucar,  San 315 

Lucas,  San 290 

Lucia,  Santa 326 

St 293 

Cape 323 

I.,  C.  Verde  Is. . .  303 

Windward  Is.  295 

Lucipara  Island 332 

Lucipari  Islands 331 

Lucrecia  Point 292 

Lucrietta  Island 318 

Ltiis,  San,  Island 290 

Luk6  Point 341 

Lund 308 

Lundy  Island 304 

Lunenburg 281 

Lungo 309 

Lupona  Point 290 

LurioBay 323 

Lussin  Piccolo 318 

Luzon  Island 334 

Lyo  Island 312 

Maasin 335 

Macah6 297 

Macao 337 

MacAskill  Islands 343 

Macauley  Island 350 

Maceio 296 

Machias 281 

—  Island 281 

Machikora 326 

Mackenzie  Islands 343 

MacLeay  Islets 351 

Macquarie  Harbor 354 

Island 350 


PLACES — continued . 

Page. 

Macquarie,  Port 352 

Macquereau  Point 280 

Madagascar 323 

Eeef ,  Africa 323 

■ •  Yucatan 285 

Madame  Island 281 

Madanas  Point 298 

Madeira  Island 303 

Madras 329 

Madryn,  Port 298 

Madura  Island 331 

Maestro  de  Campo  Island. .  335 

Mafamale  Island 323 

Mafialsland 324 

Magadoxa 324 

Magdalen  Cape 280 

Islands 280 

Magdalena  Bay 290 

River 295 

Magnetic  Pole 355 

Magoari  Cape 296 

Mah  Kundu  Island 325 

Mahanuru 326 

Mah6 328 

Mahia  Peninsula 354 

Mahon,  Port 316 

Maiana  Island 342 

MaidenRocks 306 

Mairaira  Point 334 

Mdit  Island 324 

Maitea  Island 349 

Maitencillo  Cove 300 

Majamba  Bay 326 

Majorca 316 

Majunga 326 

Maiiu"o  Islands 343 

MakallehBay 327 

Makarska 318 

Makassar 333 

Makatea  Island 349 

Makaua  Island 324 

Makemo  Island 349 

Makers  Ledge,  South 280 

Makkian Island (Makjan I.).  333 

Makongai  Island 348 

Makry 320 

Mala  Cape 291 

MalabrigoBay 301 

Malaga 315 

Malaita  Island 346 

Malakka 330 

Malamocco 317 

Malaspina,  Port 298 

Maiden  Island 345 

Maldonado,  Mexico 291 

Uruguay 298 

Mal6  Island 325 

Malemba  Bay 322 

MalinHead 306 

Mallicollo  Island 347 

Malmo 308 

Malo,  St 313 

Maloclab  Islands 343 

Maloren 309 

Malpelo  Island,  Galapagos..  342 

Panama 291 

Malpeque  Bay 280 

Malta 317 

Mamuka  Island 348 

Manaar 329 

Mana  Sima 340 


Page. 

Manado  Bay 333 

Manao 340 

Mana-watu  River 354 

Manda  Roads 324 

Mandarins  Cap 337 

Mandavi 328 

Manfredonia,. 317 

Mangaia  Island 350 

Mangalore 328 

Mangaratiba 297 

Mangareva  Island 349 

Mangarin  Point 334 

Mangarol 328 

Mangles  Point 302 

Mango  Island 348 

Manila 334 

Mano  Island,  Asia 332 

— Denmark 312 

Manoel,  Cape 321 

Manroux  1 294 

Manta  Bay 302 

Manua  Island 348 

Manukau  Harbor 355 

Manvers,  Port 279 

Manzanillo,  Cuba 293 

Manzanillo  Bay,  Mexico 291 

■  Point,  Haiti 293 

Maracaibo 295 

Maraki  Island 342 

Marambaya  Island 297 

Maranliiio  Island 296 

Marble  Island 355 

Marblehead 282 

Marcial,  San,  Point 290 

Marcos,  San,  Island 290 

Marcus  Island 344 

Mare  Harbor 304 

•  Island,  CaUfomia 289 

—S.Pacific 350 

Maret  Islets 351 

Margaret  Bay 281 

Margate  Head 322 

Maria  Island 349 

Madre  Island 291 

Port 293 

■  Sta.,  Cape,  Portugal.. .  315 

— Uruguay...  298 

Cove 290 

di Leuca,  Cape. .  -  317 

Island,  Azores 302 

Chile 300 

S.  Pacific...  347 

■ Port 335 

Marianas 344 

Maricas  Islands 297 

Marie  Galante 294 

Marienleuchte 311 

Mariguana  Island 292 

Marinduque  Island 335 

Marion  Island 327 

Maripipi  Island 335 

Maritimo  Island 317 

Marjes  Islets 295 

Marjoribanks 339 

Mark8,St 284 

Marlborough  Island 342 

Mai-mora  Island 320 

Marmorice 320 

MaroReef 344 

Maroni  River 296 


INDEX  TO  APPENDIX  IV. 


[Page  371 


Page. 

Marsala 317 

Marseilles 316 

Marshall 322 

Islands 343 

Marstenen  Islet 308 

Marta.Sta 295 

Martha,  St.,  Cape 297 

Martin  de  la  Arena,  San ....  314 

Garcia  Island 298 

San,  Island,  L.  Cal. . . .  290 

St.,  I.,  Leeward  Is 294 

Vaz  Rocks 303 

Martinique 294 

Martires,  Los 343 

Mama  Island 349 

Marutea  Island 349 

Mary  Island 345 

St.,  Bay 322 

Cape,  Madagascar.  326 

Newfound- 
land.... 279 

Nova  Scotia.  281 

Reefs 280 

Marys,  St.,  Island 326 

Marzo  Cape 302 

Mas  Afuera  Island 350 

Masbate  Island 335 

Mafiinloc 334 

Masirah  Island 327 

Maskat 327 

Massaua  Harbor 324 

Masset  Harbor 288 

Masulipatam 329 

Matabella  Islands 332 

Matacong  Island 321 

Matagorda 284 

Matahiva  Island 349 

Matamoras  Cove 300 

Matana  Island 341 

Matanzas  Peak 293 

Matatane 326 

Matelotas  Islands 343 

Matema  Islands 347 

Maternillos  Point 292 

Matinicus  Rock 281 

Matova 340 

Matthew  Island 347 

■ St.,  Island,  Alaska  ...  287 

Burma 329 

Siberia 342 

Matthias,  St.,  Island 346 

Matu  Sima 339 

Matuku  Island 348 

Mauger  Cay 285 

Maui  Island 344 

Mauki  Island 350 

Maun^auui  Harbor 354 

Maupili  Island 349 

Mauritius 325 

May,  Cape 283 

Island 305 

Mayaguez 294 

May6  Mountain 296 

Mayne  Harbor 299 

Mountain 300 

Mayo  Island 303 

Mayotta  Island 326 

Maysi  Cape 292 

Mayumba  Bay 322 

Mazarron 315 


PLACES — continued . 

Page. 

Mazatlan 291 

Mazemba  River 323 

Mbega  Island 348 

MchingaBay 324 

McKean  Island 345 

Mecate  Mountain 285 

Mednoi  Island 341 

Mega  Island 330 

Megalo  Kaatron 319 

Mehediah 321 

Meiaco  Sima 338 

Meiaco-sima  Islands 339 

Mejia  Island 290 

Mekattina  Islands 280 

Mel,  Ilhado 297 

Melbourne 352 

Meleda  Island 318 

Melinda 324 

Melle,  Cape 316 

MellishReef 347 

Melmore  Head 306 

Melo,  Port 298 

Melville,  Cape,  BalAbac  I..  333 

Queensland 353 

Island,  Australia 351 

Barrows  Strait. . .  355 

Tuamotu  Arch...  349 

Memel 310 

Memory  Rock 292 

Menali  Island 330 

Menchikof  Cape 287 

Mendocino  Cape 289 

Mendoza  Island 337 

Merbat 327 

Mercy  Harbor 299 

Mergui 329 

Mesa  de  Dofia  Maria 301 

Messina 317 

Meeurado,  Cape 322 

Meurka 323 

Mew  Islands 306 

Mewstone  Rock 354 

Mexican  Boundary 289 

Mexico,  City  of 285 

MexillonBay 301 

Mexillones  Mountain 301 

Mezen 356 

Miautao  Island 338 

Michael,  St.,  Fort 287 

Island 302 

Michaeloff  Island 348 

Middleton  Island 288 

Midway  Islands 344 

Miguel,  San,  Island 289 

— ^ Islands 336 

Mikake  Jima 340 

Mikindini 324 

Mikomoto  Island 340 

Mikura  Jima 340 

Milagro  Cove 300 

Milazzo 317 

Mile  Island 355 

Milford  Sound 355 

Milo  Island 319 

Min  River 337 

MinaBay,  El 322 

Minchinmadiva  Mountain . .  300 

Mindanao  Island 335 

Mindoro  Island 334 

Mine  Head 307 


Page. 

Minerva  Reefs 350 

Minikoi  Island 325 

Mine  Sima 341 

Minorca 316 

Minots  Ledge 282 

Minow 326 

MinsenerSand 311 

Mintok 331 

Miramichi  Bay 280 

Misamis 336 

Miscou  Island 280 

Mississippi  River,  mouth. . .  284 

City 284 

Misteriosa  Bank 286 

Mita  Point 291 

Mitchells  Island 345 

Mitho 336 

Mitiero  Island 350 

Mitre  Island 347 

Mityleni  Island 319 

MizenHill 306 

MoaCayo,  Port 292 

Island 332 

Moala  Island 348 

Mobile 284 

Mocha  Island 300 

Mocomoco  Point 296 

Modeste  Island 339 

Moeara  Kompehi 330 

Moen  Island 312 

Moerenhout  Island 349 

Mogador 321 

Mohilla  Island 326 

Moianga 

Mokambo,  Port 823 

Mokatein 327 

Mokha 325 

Mokil  Islands 343 

MoUe,  Port 353 

Mollendo,  Port 301 

MollerPort 287 

Molloy 327 

Molokai  Islands 344 

Molonta  PeninsiUa 318 

Moluk  Island 325 

Molukka  Islands 333 

Molyneux  Bay 355 

Sound 299 

Mombasa 324 

Mona  Island 294 

Monastir 321 

Mondego,  Cape 315 

Monfalcone 317 

Monhegan  Island 281 

Monomoy  Point 282 

Monrovia 322 

Montagu  Island 352 

Montalivet  Islands 351 

Montauk  Point 282 

Monte  Christo  Islet 316 

Monte  Cristi 293 

Montebello  Island 351 

Montego  Bay 293 

Montepio 285 

Monterey 289 

Monteverde  Islands 343 

Montevideo 298 

Montravel  Island 339 

Montreal 280 

Monts,  Point  de 280 


Page  372] 


INDEX  TO  APPETNDIX  IV. 


Montserrat 249 

Montt,  Port 300 

Monze,  Cape 328 

Mopelia  Island 348 

Morane  Island 349 

MorantCaya 293 

Point 293 

Morayva 315 

Morecambe  Bay 305 

Moreno  Mountain 301 

Moresby,  Port 346 

Moreton,  Cape 353 

Morgan,  Cape 323 

Morjovetz  Island 356 

Morlaix 313 

Morotirilslands 350 

Morria  Jesup,  Cape 356 

Morro  Ayuca 291 

de  Sao  Paulo 296 

'Petatlan 291 

Solar 301 

Mortlock  Islands 343 

Mosquito  Cays 286 

Mota,  Point 293 

Motane  Island 345 

Mothe  Island 348 

Mothoni 319 

Motu-ili  Island 345 

Motu-iti  Island 349 

MoudroB 319 

Moukon  ruflhi  Island 341 

Moulmein 329 

River 329 

Mount,  Cape 322 

Mourondava 326 

Moville 306 

Mozambique 323 

Msimbati 324 

Mugan  Mwania 324 

Mugeres  Island 285 

Mmlcalpue  Cove 300 

Mukulaelae  Island 345 

Muleje 290 

Mulu  Island 332 

Mura  Harbor 340 

MuratHill 324 

Murderers  Bay 326 

Murdock  Point 353 

Murundum  Island 337 

Mururoa  Island 349 

Muscat 327 

Musendum,  Ras 327 

Mussel  Bay 299 

Mysole  Island 332 

NachvackBay 279 

Nafa-Kiang 339 

Nagai  Island 287 

Nagasaki 339 

Naian  Island 348 

Nain 279 

Nairn  Cay 292 

Naitamba  Island 348 

NakanoShima 339 

Nakkehooed 312 

Nam-Dinh 336 

Namki,  Port 338 

Namoluk  Islands 343 

Namonuito  Islands 343 

Nam-quan 337 


PLACES — continued. 

Page. 

Namu  Island 343 

Nanaimo 288 

Nancowry  Harbor 330 

Nanka  Island 331 

Nanomea  Island 345 

Nanoose  Harbor 288 

Nansei  Shoto 339 

Nantes 314 

Nantucket  Island 282 

Shoals 282 

Naples 317 

Napuka  Island 349 

Nar  Foree  Island 325 

Naranjo,  Port 292 

Narendri  Bay 326 

Nargen  Island 310 

Narva 310 

Nasca  Point 301 

Nasparti  Inlet 288 

Nassau 292 

Natal,  Brazil 296 

^  Port,  Africa 323 

-Sumatra 330 

Natashquan  Point 280 

Natuna  Islands 331,  337 

Naturaliflte,  Cape 351 

Nauomaga  Island 345 

Navachista 291 

Navalo,  Port 314 

Navarin 319 

Cape 341 

Navassa  Island 294 

Navesink  Highlands 283 

Na\idadBank 292 

Bay 291 

NavireBay 327 

Naxos  Island 319 

Nazaire,  St.,  Port 314 

Necker  Island 344 

Needles  Rocks 304 

N^apatam 329 

Negrais,  Cape 329 

Negro,  Rio 298 

Negros  Island 335 

Neill,  Port 355 

Nelson 355 

Cape 352 

Port 351 

Nemuro 341 

Neptune  Isles 352 

Nera  Point 317 

Netherland  Island 345 

Neunortalik 356 

Neuwerk 311 

Nevil  Island 344 

Neville,  Port 288 

Nevis 294 

New  Bank 285 

Bedford 282 

Britain 346 

Caledonia 350 

Guinea 346 

Hanover 346 

Haven 282 

Hebrides 347 

Ireland 346 

London 282 

Mecklenburg 346 

Orleans 284 

Plymouth 354 


Page. 

NewPommem 346 

South  Orkneys 304 

Shetland 304 

Westminster 289 

York 283 

Newbem 283 

Newburyport 282 

Newcastle 352 

Newchwang 338 

Newfoxindland 279 

Newport,  Ireland 306 

Rhode  Island 282 

Newton  Head,  Great 307 

Nezumi  Jima 339 

Ngatik  Islands 343 

Ngau  Island 348 

Nias  Island 330 

Nice 316 

Nicholas,  St.,  Island 303 

Nicholson,  Port 354 

Nickerie  River 296 

Nicobar,  Great,  Island 330 

Islands 330 

San,  Island 289 

Nidingen  Islet 308 

Nieuport 313 

NieweDiep 313 

Nihiru  Island 349 

Niigata 340 

Nikalao,  St.,  Island 319 

Nikolaevsk 341 

Nikolaia,  St.,  Cape 341 

Nikolaieff 320 

Nikolo,  St.,  Port 319 

Nila  Island 332 

Nile  River 320 

Nimrod  Sound 338 

Nine-pin  Rock 337 

Ning-po 338 

NipeBay 292 

Niquero 293 

Nitendi  Island 347 

Niua-fu 348 

Nine  Island 348 

Niutao  Island 345 

No  Sima  Saki 340 

Noir  Island....^ 299 

Noir  Moutier  Island 314 

NoUoth,  Port 323 

Nome  Cape 287 

Nonuti  Island 342 

Nootka  Sound 288 

Nord  Koster  Islands 308 

Nordemey 312 

Norfolk 283 

Island 350 

Norman  Cape 280 

Norrkopings  Inlopp 309 

Norrsher  Islet 309 

Norrtelge 309 

North  Cape,  Arctic  Amer. .  355 

Brazil 296 

C.  Breton  1 281 

Iceland 357 

New  Zealand 354 

Norway 307 

Harbor 288 

Island,  Vancouver 288 

Volcano  Islands. .  345 

Lord,  Island 344 


INDEX  TO  APPENDIX  IV. 


[Page  373 


Page. 

North  Standing  Creek 286 

Northumberland,  Cape 352 

Isles 353 

Northwest  Cape 351 

Norwalk  Island 283 

Noshiaf  Misaki 341 

Saki 341 

NosiB^ 326 

NossaSenhoradoDeserto...  297 

Notch  Cape 299 

Notsuke 341 

Nottingham  Island 279 

Noumea 350 

Noun,  Cape 321 

Nouvelle,  Port 316 

Nova  Zembla 356 

Novogorod,  Port 341 

Nuevitas,  Port 292 

Nuevo,  Port 291 

Nugget  Point 355 

Nui  Island 345 

Nuistad 309 

Nuka-Hivi 345 

Nukufetau  Island 345 

Nukunau  Island 342 

Nuku-nono 345 

Nukuor  Islands 343 

Nukutavake  Island 349 

Nukutipipi  Island 349 

Numbalsland 323 

Nunez  River 321 

Nunivak  Island 287 

Nurse  Channel  Cay 292 

Nuyte  Point 351 

Ny  Sukkertop 356 

Nybotg 312 

Nykjobing 312 

Oahu 344 

Oatafu  Island 345 

Oban 305 

Obi  Islands 336 

Obi  Major  Island 332 

Obispo  Shoal 285 

Obristadbroekke 308 

Observation  Island 339 

Occasional  Harbor 279 

Ocean  Island,  N.  Pacific. . .  344 

S.Pacific 346 

Ockseu  Island 337 

Ocracoke 283 

Oddensby 312 

Odenskholm 310 

Odessa 320 

Odia  Islands 343 

Oeno  Island 349 

Offer  Wadham 279 

Ogasawara  Islands 345 

Oho-sima 339 

Okayama,  Port 340 

Okhotsk 341 

Oki  Islands 341 

OkishiBay 341 

Okso 308 

Oland  Island 308 

Old  Fort  Island 280 

Point  Comfort 283 

ProvicTonce 286 

Olcai  Islands 343 

Oleron  Island 314 


I'LACES — continued . 

Page. 

Olga,  Port 341 

Olimarao  Islet 343 

Olinda 296 

OlipaRock 318 

Oliutorski,  Cape 341 

Olivenja 297 

Omapui  Island 336 

Omenak  Island 356 

Omo  Island 312 

Omoa 286 

OmoiSaki 340 

One  Fathom  Bank 329 

Oneata  Island 348 

Onega 356 

Ongea  Levu  Island 348 

One  Islands 348 

Onoatoa  Islands 342 

06-Sima  Harbor 340 

Oparo  Island 350 

Opobo  River 322 

Oporto 314 

Oraluk  Island 343 

Oran 321 

Orange  Cape,  Brazil 296 

Magellan  Strait. .  299 

Oranienbaum 310 

Orchila  Island 295 

Oregrund 309 

Orfordness 306 

Orizaba  Mountain 286 

Orkney  Islands 306 

Ormarah 328 

Ormoc 336 

Ombay  Island 332 

Ore  No  Sima 339 

OropesaCape 316 

OrskarRock 309 

Oruba  Island 295 

Osaka..... 340 

OsakiBay 340 

Oscarsberg 308 

Osnabrug 349 

Oetend 313 

Osthammar 309 

Ostro  Point 318 

Otago  Harbor 365 

Otranto,  Cape  and  Port 317 

Ottawa 280 

Otway,  Cape 352 

Port 299 

Oune-Kotan  Island 341 

Ouro  River 321 

Ovalau  Island 347 

Owaahi  Bay 340 

Oxford 304 

Oxhoft 310 

Paanopa  Island 346 

Pabellon  de  Pica 301 

Pacasmayo 301 

Padang 330 

Tikar 333 

Padaran,  Cape 336 

Padre,  Port 292 

Pagan  Island 344 

Pa^nia,  Port 319 

Paimboeuf 314 

Paix,  Port 294 

Pajaros  Islets 300 

Pak  Chan  River 329 


Pago. 

Pakhoi 337 

Pakonjidol  Rock 318 

PalamosBay 315 

Palanog 335 

Paldwan  Island 333 

Palembang 330 

Palenita 291 

Palermo 317 

Port 318 

Pali,  Cape 318 

Pallaa  Rocks 339 

Palliser,  Cape 354 

Palm  Islands 353 

Palma  Island 303 

PalmasBay 297 

Cape 322 

Point 285 

Palmerston,  Cape 353 

Islands 348 

Palmyra  Island 342 

Palompon 335 

PalosBay 333 

Pamaroong  Island 333 

Pamban  Pass 328 

Pampatar  Island 296 

Pan  de  Azucar  Island 300 

Panama -.  291 

Panay  Island ,  336, 

Pangituran 336 

Paniang  Island 336 

PankPiahRock 337, 

Pantar  Island 332 

Papey  Island 367 

Paposo  Road 301 

Para 296 

ParacaBay 301 

Paracel  Islands '337 

ParahibaRiver  and  Port...  296 

Paramaribo..... 296 

Paranagua 297 

Paranahiba  River 296 

Paraoa  Island 349 

Parati .Tr. 297 

Paredon  Grande  Cay 292 

Parenga-renga 354 

Parenzo 317 

Parga 319 

Panda T. 291 

Parinas  Point 302 

Paris 313 

Parker  Cape 299 

Pares  Island 319 

Parry  Island 360 

Parrys  Group 345 

PasadoCape 302 

Pasages,  Port 314 

Pascagoula,  East 284 

Pasni 328 

Passaro,  Cape 317 

Pasuruao 331 

Patache  Point 301 

Patani,  Tanjong 336 

Paternoster  Rocks 308 

Paterson  Inlet 355 

Pato  Island 296 

PatucaRiver 286 

Patoslsland 290 

Patras 319 

Patrick,  St.,  Head 354 

Patterson,  Port 351 


Page  374] 


INDEX  TO  APPENDIX  IV. 


Paul,  St.,  de  Loando 322 

Island,  N.  Amer.   281 

Tuamotu....  349 

K^union  Island..  326 

Rocks 303 

Paula,  St.,  Island 327 

Paxo  Island 319 

Paypoton  Mountain 285 

Pearce  Point 351 

Pearl  and  Hermes  Beef. . . .  344 

Cays 286 

Pedra  Blanca  Rock 337 

•Branca 330 

deGalha 321 

Pedro  Bank 293 

San 290 

Point 301 

ZZ^ort 300 

Peel.  .1?:^.r. 351 

■Island.- 345 

Pegasus,  Port,  .t: 355 

PeiHo..'.rrr...::. 338 

Pekalongan. 331 

IPelado  Island 301 

rPelagosaRock 318 

j  Peloro,  Cape 317 

[PembaBay..: 323 

I  Pembroke  Cape 304 

i  Pena  Point 296 

jPenang,  Pulo 329 

j  Pefias  Anchorage 291 

j  Pendulum  Islands 356 

Penguin  Islands 327 

iPenha Grande 321 

IPeniche 315 

Penmarch  Rocks 314 

iPenrhyn  Island 345 

Pensacola 284 

Pentland  Skerries 305 

Percy  Isles 353 

Perim  Island,  Africa 324 

■ India 328 

Pernambuco 296 

Pemau 310 

Peroa  Banhoa  Islands 325 

Perth 351 

Peru  Island 342 

PerulaBay 291 

Pescadores  Islands,  Asia,  E. 

coast 338 

^N.  Pacific 343 

Peru 301 

Point 301 

Pe-shan  Islands 338 

Petali  Island 319 

Petalidi  Bay 319 

Peter  St.,  Port 313 

Peterhof 310 

Petersburg,  St 310 

Petersdorf 311 

Petit  Manan  Island 281 

Petite  Terre 294 

Petropavlovsk 341 

Petropolis 297 

Pha-li-du  Island 325 

Philadelphia 283 

Philip  Island 343 

Philipp  Broke,  Cape 356 

Philips  Point 290 

Phmlp,  Port 352 


PLACES — continued . 

Page. 

Phillii>8  Island 349 

Phoenix  Island 345 

H 316 

Pianosa  Island 316 

Pichidanqui 300 

Pichilinque  Bay 290 

Pico  Island 302 

Pictou  Harbor 281 

PiedraBlanca 336 

Piedraa  Blancas 289 

Cay,  Cuba,  N.  coast. . .  293 

• S.  coast 293 

Point 298 

Pieman  River 354 

Pierre,  St.,  Newf'dl'd 280 

Reunion  1 326 

• Rock 331 

Pietro  di  Nembo,  St.,  Island  318 

Pigeon  Point 289 

Pih-ki-shan  Island 338 

Pih-quan  Peak 338 

Pih-seang  Island 337 

Pikelot  Island 343 

Pililu  Island 344 

Pillau 310 

Pillar,  Cape,  Chile 299 

Tasmania 354 

Pinaki  Island 349 

Pine,  Cape 279 

Pingelasp  Islands 343 

Ping-fonglsland 337 

Ping-hai  Harbor 339 

Pinnacle  Islet 287 

Pinos,  Isla  de 293 

Pinos  Point 289 

Pique  Bay 341 

Piraeus 319 

Pirano 317 

Pisagua 301 

Pisang 330 

Pisco 301 

Pitcairn  Island 349 

Pitea 309 

Pitong  Island 330 

Pitre  Point 294 

Placentia  Harbor 279 

Point 286 

Pladda  Island 305 

Plana  Cay 292 

PlanierRock 316 

Plata,  Isle 302 

Platte  Island 325 

Playa  Colorado 291 

Maria,  La 290 

■PardaCove 299 

Pleasant  Island 346 

Plettenburg  Bay 323 

Plum  Island 282 

Plymouth,  England 304 

U.S 282 

Poile,La,  Bay 280 

Pola 317 

Sta.,  Bay 315 

Polillo  Island 335 

Pollard  Cove 299 

Police 335 

Polusuk  Island 343 

PomoRock 318 

Ponafidin  Island 340 

Ponapi  Island 343 


Page. 

Pond  Mountain 299 

Pondicherri 329 

Ponga  River 321 

Ponza  Islet 317 

Poolbeg 307 

Popalsland 332 

Popof  Island 287 

Porcos  Grande  Islet 297 

Porbandar 328 

Porman 315 

Poro  musir  Island 341 

Poros  Island 319 

Portau  Prince 294 

Montt 300 

of  Spain 296 

Plata 293 

Royal,  Jamaica 293 

S.  Carolina 283 

Said 320 

Portendik 321 

Porthcumow 304 

Portland,  Bay 352 

Cape 354 

England 304 

Maine 282 

Porto  Bello 287 

R^ 317 

Rico 294 

Santo 303 

Seguro 297 

Vecchio 316 

Portsmouth,  England 304 

U.S 282 

Possession,  Cape 299 

Island 327 

Postilion  Islands 332 

Povorotnyi,  Cape 341 

Prado 297 

Prataa  Island 337 

Premeira  Islands 323 

Preservation  Inlet 355 

Prestenizza  Point 31 7 

Prevesa 319 

Pribilof  Islands 287 

Prince  Edward  Island 280 

Edwards  Islands 327 

Prince  of  Wales  Cape 287 

Island 353 

Sound 279 

Regent  River 351 

Rupert  Hbr 288 

Princes  Island 322 

Proeste 312 

Progreso 285 

Promontore  Point 317 

Proti  Passage 319 

Proven 356 

Providence 282 

Island 343 

Port 342 

Psara  Island 319 

Pucio  Point 335 

Puerto  Cabello 295 

Mexico 285 

Santo  Bay 295 

Puka-puka  Island 349 

Puka-ruha  Island 349 

Pulicat 329 

Pulkowa 310 

Pulpito  Point 290 


INDEX  TO  APPENDIX  IV. 


[Page  376 


t 


Page. 

Puna 302 

Purdy  Island 346 

Putziger  Heistemest 310 

Pyramid  Point 337 

Pyramidal  Rocks 331 

Quaco,  Cape 281 

Quaebo  River 322 

Quebec 280 

Queen  Charlotte  Island 349 

Queenstown,  Ireland 307 

N.Zealand 355 

Quelpart  Island 339 

Quemada  Grande  Island . . .  297 

Quentin,  San,  Port 290 

Querimba  Islands 323 

QueuleBay 300 

Quilan,  Cape 300 

Quilca 301 

Quilon 328 

QuinHon 336 

Quiniluban  Islet 334 

Quintero  Point 300 

Quita  Sueiio  Bank 286 

Quod,  Cape 299 

QuoddyHead 281 

Quoin  Great,  Island 327 

Point 323 

Race,  Cape 279 

Island 288 

Rachado,  Cape 330 

Radakala  Islands 343 

Radama  Islands 326 

Port 326 

Ragged  Island 292 

Ragiisa  Rocks,  Pettini  di. . .  318 

Rakkin,  Ras 327 

Raleigh  Rock,  China 337 

Formosa 338 

Ramas,  Cape 328 

RameHead 323 

Ramree  Island 329 

Rangiroa  Island 349 

Rangoon 329 

River 329 

RaiiuCove 300 

Raoul  Island 

Rapa  Island 350 

Raper  Cape 299 

Raphti,  Port 319 

Rarotonga  Island 350 

Rasa  Island 345 

Rathlin  Island 306 

O'Bime  Island 306 

Ratnagherry 328 

Ravahere  Island 349 

Ravn  Store 356 

Rawean  Island 332 

Ray  Cape 280 

Raza  Island,  Brazil 297 

C.  Verde  la 303 

L.  California 290 

Razzoli  Island 316 

Re  Island 314 

Real  River 296 

Reao  Island 349 

Recherche  Archipelago 352 

Recife  Cape 323 

Red  Islet 351 


FLACES — continued. 

Page. 

Redang,  Great,  Harbor 336 

Redfield  Rocks 340 

Redonda  Islet 294 

Redondo  Rock 342 

Reirson  Island 345 

Reitoru 349 

Rembang 331 

Remedies  Bay 290 

Renard  Island 347 

Islands 347 

Rennel  Island 346 

Rensher 309 

Repon,  Pulo 331 

Resolution  Island 279 

Reunion  Island 326 

Revel 310 

Rey  Island 291 

ReyesHead 301 

Point 289 

Reykianaes 357 

Reykiavik 357 

ReythurFjeld 357 

Rhio 330 

Rhodes,  Port 320 

Rhynns  of  Islay 305 

Ribnitz 311 

Rich  Point 280 

Richmond 283 

River 353 

Riga 310 

Rigny  Mount 356 

Rimitara  Island 350 

Ringkjobin 312 

Rio  Grande  del  Norte 284 

do  Norte 296 

Sul 297 

Janeiro 297 

Riofrio,  Port 299 

Risiri  Islet 341 

Rissnaes  Point 357 

Rivadeo 314 

Rivadesella 314 

Rivers,  Cape 333 

Rixhoft 310 

Roa  Poua  Island 345 

Roatan 286 

Roberts  Point 289 

Roca,  Cape 315 

Partida,     Mexico,     E. 

coast 285 

W.  coast 291 

Rocas  Reef 303 

Rochefort 314 

Rochelle 314 

Rockabill 307 

Rockall  Islet 302 

Rockingham  Bay 353 

Rockland 281 

Rodd  Bay. . .- 353 

Rodkallen... ;. 309 

Rodney,  Cape 346 

Rodoni,  Cape 318 

Rodriguez  Island 325 

Rodsher  Island 309 

Roeskilde 312 

Rogosnizza 318 

Rokugo,  Cape 340 

Rokuren  Island 340 

Roma  Island 332 

Romain,  Cape 283 


Page. 

Roman,  San,  Cape 295 

RomanzofCape 287 

Romanzov  Islands 343 

Romblon  Island 335 

Rome 316 

Ronaldsay,  North 305 

Roncador  Cay 286 

Rongerik  Islands 343 

Roodewal  Bay 323 

Roque,  St.,  Cape 296 

Roques  Islands 295 

Rosa,  Sta.,  Island 289 

Rosalia,  Sta.,  Bay 290 

Rosalind  Bank 286 

Rosario  Island 345 

Rose  Island 348 

Spit  Point 288 

Rosenoary  Island 351 

Rosier  Cape 280 

Ross  Island 339 

Rossel  Island 347 

Rostock 311 

Rota  Island 344 

Rotterdam 313 

Rotti  Island 332 

Rottnest  Island 351 

Rotumah  Island 347 

Round  Island 338 

Roundhill  Island 279 

Rovigno 317 

Roxo  Cape 285 

Royal  Island 292 

Royalist,  Port 333 

Ruad  Island 320 

Rugenwalde 310 

Rum  Cay 292 

Runaway,  Cape 354 

Runo  Island 310 

Rupert  Island 299 

Rurutu  Island 350 

Ry  vingen  Island 308 

Ryojun  Ko 338 

Saba 294 

Sabine  Pass 284 

Sabioncello  Peninsula 318 

Sablayan  Point 334 

Sable  Cape 281 

Island 281 

Sacatula  River 291 

Sacrificios  Island 285 

Point 291 

Saddle  Group 338 

Island 279 

Sado  Island 340 

Safajah  Island 324 

Safatu  Island 337 

Sagua,  Isabello  de 

Saida 320 

Saigon 336 

Saintes  Islands 294 

Saipan  Island 344 

Sakai 340 

Sakhalin  Island 341 

Sakishima  Gunto 338 

Sakonnet  Point 282 

Sal  Cay 293 

Island 303 

Sala  y  Gomez 350 

SaladoBay 300 


Page  876] 


INDEX  TO  APPENDIX  IV. 


»  Page. 

Salayar  Island 333 

Saldanha  Bay 323 

Salem 282 

Sail 321 

Salina  Cruz 291 

Salinas  Bay,  C.  America. . .  291 

L.  California 290 

Point 294 

Salisbury  Island 279 

Salomague  Island 334 

Salonika 319 

Salovetsld 356 

Saltee,  Great 307 

Salut  Islands 296 

Salvador,  San 292 

Salvage  Islands 303 

Salvore  Point 317 

Sama,  Port  and  Peak 292 

Samana 293 

Cay 292 

Samanco  Bay 301 

Samar  Islana 335 

Samarang 331 

Sambro  Island 281 

Samoa  Islands 

Samos  Island 320 

Sampit  Bay 333 

Samso  Island 312 

Samsoe  Island 312 

San  Bias,  Gulf 287 

Sand  Island 284 

Key 284 

Sandakan  Harbor 333 

Sandalo,  Cape 316 

Sandalwood  Island 332 

Sandfly  Cay 286 

Sandiiammaren 309 

Sandwich  Island 347 

Islands 304 

Sandy  Cape 353 

Hook 283 

Point 299 

Sangwin  River 322 

Sanibel  Island 284 

Sankaty  Head 282 

Sannakhlsland 287 

Santa  Cruz  del  Sur 293 

Santander 314 

River 285 

Santiago  Cape 299 

de  Chile 300 

Cuba 293 

Port 334 

Santo  Domingo  City 294 

Santona 314 

Santos 297 

Sao  JoSo  da  Barra 297 

Saona  Island 294 

Sapelo  Island 283 

Sarang^uni  Islands 335 

Sarawak 333 

River 333 

Sariguan  Island 344 

Sarstoon  River 286 

Sarulsland 332 

Saseno  Island 319 

Satano  Misaki 340 

Satawal  Island 343 

Saugor  Island 329 

Sauguir  Island 333 


PLACE  8 — continu  ed . 


Sauh,  Pulo 330 

Saukhoum 320 

Saunders,  Port 280 

SauoBay 338 

Savage  Island 348 

Savaii  Island 348 

SavanUla 295 

Savannah 283 

Savanna-la-Mar 293 

Saybrook 282 

Scalp  Mountain 306 

Scarcies  River 321 

Scatari  Island : 281 

Schama  Mountain 301 

Schanck,  Cape 352 

Schanz  Island 343 

Scharhom 311 

Scheveningen 313 

Schillighom 311 

Schleimunde 311 

Schleswig 311 

Schonberg 311 

Scilly  Islands,  England ....  304 

S.Pacific 348 

Scott  Cape 288 

Scutari 320 

Sea  Bear  Bay 298 

Rock 339 

Seal  Cays 286 

Island 281 

Seao  Island 333 

Seattle 289 

Seba8tian,San,Cape,M'g'8c'r  326 

Spain 314 

St.,  Cape,  S.  Africa. ...  323 

Island 297 

Sebastopol 320 

Sebenico 319 

Sedano,  Cape 331 

SedashigarBay 328 

Seguin  Island 281 

Sem,  I.  de 314 

Sejro  Island 312 

Selatan  Point 333 

Seldom-come-by  Harbor 279 

Semeny  River 318 

Semerara  Island 334 

Semiamoo  Bay 289 

Semione  Island 331 

Sentinel  Island 339 

Series  Island 349 

Sermata  Island 332 

Sermelik  Fjord 356 

Sermo  Island 319 

Serrana  Bank 286 

Serxanilla  Bank 286 

Seskar  Islet 310 

Setubal 315 

SeuheliPar 325 

Seven  Heads 307 

Seychelles 325 

Sfax 321 

Shag  Rocks 304 

Shahah 327 

Shahr,  Abu 328 

Shaikh  Shu'aib  Islet 328 

Shaluitien  Island 338 

Shanghai 338 

Shannon  River 306 

Shantar  Islands 341 


Shantung 338 

Sharjah 327 

Shark  Island 346 

Sharmoh 327 

Shaweishan  Island 338 

Shelbume  Harbor 281 

Shelter  Bay 341 

Shepherd  Island 287 

Sherbedat,  Ras 327 

Sherbro  Island 322 

River 322 

Sherm  Hassey 324 

Joobbah 324 

Rabegh 324 

Wej 324 

Yahar 324 

Shetland  Islands 305 

Shiash-Kotan  Island 341 

Shields,  North 305 

Shimizu  Bay 340 

Shimonoseki  Strait 340 

Shinnecock  Bay 283 

Ship  Island 284 

Shoal 284 

Shipunski,  Cape 341 

ShirasuReef 340 

Shoals,  Isles  of 282 

Shoalwater  Cape 289 

Island 331 

Siargao  Island 335 

Siassi 336 

Siberoet  Island 330 

Siboga 330 

SibucoBay 336 

Sibutu  Island 336 

Sibuyan  Island 335 

Sidmouth,  Cape 353 

Sierra  Leone 322 

Sighajik 320 

Sigri,  Port 319 

Sihuatanejo  Point 291 

Sihut 327 

Silan 285 

Silaqui  Islet 334 

Silver  Bank 292 

Simaloe  Island 330 

Simeonof  Island 287 

Simoda 340 

Simon,  St.,  Island 283 

Simonoff  Island 348 

Simonor  Island 336 

Simons  Bay 323 

Simpson,  Port 288 

Simusir  Island 341 

Singapore 330 

Singkel  Island 330 

Singkep  Island 330 

Single  Island 337 

Singora  (Sungkla) 336 

Sinon 322 

Sinope 320 

Siphano  Island 319 

Siquijor  Island 335 

Sink,  Cape 333 

SiriyaSaki 340 

Sisal 285 

Sitka 288 

Sittee  Point 286 

Skagataas  Point 357 

Skagi,  Cape 357 


INDEX  TO  APPENDIX  IV. 


[Page  377 


Page. 

SkagsHead 309 

Skaw,  Cape 312 

Skelligs  Rocks 306 

Skerries  Rocks 305 

Skerry vore  Rocks 305 

Skiathos  Island 319 

SkidegateBay 288 

Skoorgaarde 311 

Skumbi  River 318 

Skyring  Mountain 298 

SligoBay 306 

SlyneHead 306 

Smalls  Rocks 304 

Smerwick 306 

Smith  Island,  Japan 340 

Washington 289 

Smyrna 320 

Snaefells  Yokul 357 

Snares  Islands 355 

Socorro  Island ,  Chile 300 

Mexico 291 

SoderSkars 309 

Soderarm 309 

Soderhamm 309 

Sofala 323 

Sohar 327 

Sokotra  Island 324 

Sola  Island 295 

Solander  Islands 355 

Solitary  Islands 352 

Solombo,  Great,  Island 332 

Solomon  Islands 346 

Solta  Island 318 

Sombrero 294 

Key 284 

Rock 336 

Sommer  Island 310 

Song-yui  Point 337 

Sonserol  Island 344 

SooBay 338 

Sorelle  Rocks 318 

Sorol  Island 343 

Sorrel  Rock 337 

Sorrell,  Cape 354 

Port 354 

Sorsogon,  Port 335 

Soumshu  Island 341 

Souwaroff  Island 348 

South  Cape,  Formosa 338 

N.  Guinea 346 

Rock 306 

Water  Cay 286 

Southampton 304 

Southsea  Castle 304 

Southwest  Cape 354 

Reef 284 

Spalato  Passage 318 

Port 318 

Sparo  Vestervik 309 

Spartel,  Cape 321 

Spartivento  Cape,  Italy 317 

Sardinia 316 

Spencer,  Cape 352 

Spezzia 316 

Spikeroog 312 

Spiridione,  St.,  Port 319 

Spitzbergen 356 

Spodsbjei^ 312 

Spurn  Head 305 

Square  Handherchief  Bank.  292 


L 


PLACES — continued. 

Page. 

StaabiergHuk 357 

Stack,  South 304 

Stade 311 

Stag  Rocks 307 

Stamp  Harbor 288 

Stampali  Island 319 

Stanley,  Port 304 

Starbuck  Island 345 

Start  Point 304 

Startpoint 305 

Staten  Island 298 

Staunton  Island 338 

Stavanger 308 

Steilacoom 289 

Steinkirchen 311 

Stemshesten 308 

StensherRock 310 

Stephens,  Port 352 

Stettin 310 

Stewart,  Cape 351 

Stewart  Islands 346 

Stirrup  Cays 292 

Stirsudden 310 

Stockholm 309 

Stonington 282 

Stopelmiinde 310 

Stora 321 

Stomoway 305 

Stot 307 

Stralsund 311 

Strati  Island 319 

Straumness  Point 357 

Streaker  Bay 352 

Streckelsberg 311 

Strogonof  Cape 288 

Stromstad 308 

Stromtangen 308 

Strong  Island 343 

Strovathi  Island 319 

Stuart  Island 287 

Suakin 324 

Sual 334 

Subic 334 

Succadana 333 

Suda,  Port 319 

Sueik 327 

Suez 324 

Suffren,  Cape 341 

Sugar  Loaf  Point 352 

Sughrah 327 

Suk  Island 343 

Sula  Islands 332 

Sulphur  Island 345 

Sumbawa  Island 332 

Sumburgh  Head 305 

Sunda  Strait 331 

Sunday  Island 350 

Sunderland 305 

Sundsvall 309 

Sunmiyani 328 

Sup6 301 

Sur 320 

Surabaya 331 

Surat 328 

River 328 

Sxuigao 335 

Surop 310 

Susaki 340 

SuwanoseJima 339 

Suwarrow  Island 348 


Page. 

Svalferort  Tzerel 310 

Svartklubben 309 

Svendborg 312 

Svenor 308 

SviatoiNos 356 

Svinoen 308 

Swallow  Bay 299 

Islands 347 

Swan  Islands 286 

Swansea 304 

Swatow 337 

Sweers  Island 353 

Swinemunde 310 

SybilloBay 341 

Sydenham  Island 342 

Sydney,  Australia 352 

Harbor,  C.  Breton  I . . .  281 

Synesvarde  Mountain 308 

Syra 319 

Syracuse 317 

Tabaco 335 

Tabasco  River 285 

Tabertness. 305 

Tablaa  Island 335 

Point 300 

Table  Bay 323 

Head 279 

Island 329 

Taboga  Island 291 

Tabou  River 322 

Tacloban 335 

Tacoma 289 

TacoradyBay 322 

Tae  Islands 337 

Tagulanda  Island 333 

Tahiti 349 

Tahoa  Island 349 

Tahuata  Island 345 

Taiaro  Island 349 

Tai-pin-san 338 

Tajer,  Port 318 

Taka  Yama 341 

Takapoto  Island 349 

Takau 338 

Takhkona  Point 310 

Talabo,  Cape 333 

Talcahuano 300 

Talinay  Mountain 300 

Taltal,  Port 301 

Taluat  Island 333 

Tamana  Island 342 

Tamandar6 296 

TamarPort 299 

Tamatave 326 

Tambelan  Island 331 

Tampa  Bay 284 

Tampat  Toewon  Point 330 

Tampico 285 

TamsuiHarbof 338 

Tanabe  Bay 340 

Tancook  Island 281 

TangaBay 324 

Tangier 321 

Tanjong  Barram 333 

Datu 333 

Mangkalihat 333 

Pandan 331 

Patani 336 

Tanna  Island 347 


Page  378] 


INDEX  TO  APPENDIX  IV. 


Page. 

Tantang,  Port 326 

Taoiunu 348 

Taormina  Cape 317 

Tapua  Island 347 

Tapul  Island 336 

Taputeuea 342 

TaraHill 307 

Taranto 317 

Tarawa  Island 342 

Tarbertness 305 

Tarifa 315 

Taritari  Island 342 

Tarpaulin  Cove 282 

Tarragona 315 

Tas  de  Foin  Islet 339 

Tatakoto 349 

TatsupiSaki 340 

Tauere  Island 349 

Tauranga  Harbor 354 

Tauzon,  Cape 326 

Tavolara  Cape 316 

Tavoy  River 329 

TaytaoCape 300 

TaytayFort 333 

Tchesm6 320 

Tchoukotskoi,  Cape 342 

Tegal 331 

Tehor  Island 332 

Tellicherri 328 

Telle  Islands 332 

Tematangi  Island 349 

Tenasserim 329 

Tenedoa  Island 320 

Teneriff e  Island 303 

Tenez,  Cape 321 

TepocaCape 290 

Tepoto  Island 349 

Tequepa 291 

Terceira  Island 302 

Teresa,  Sta.,  Bay 290 

Terkolei 330 

Terminos  Lagoon 285 

Temate  Island 333 

Terstenik  Rock 318 

Testa,  Cape 316 

Testigos  Islets 295 

Tewaewae  Bay 355 

Thabi,  Abu 327 

Thank  God  Harbor 356 

Thermia  Island 319 

Thikombia  Island 348 

Thithia  Island 348 

Thomas,  St.,  I.,  B.  of  Biafra   322 

West  Indies.   294 

Thom^,  St.,  Cape 297 

Thorton  Haven 338 

Three  Kings  Islands 354 

Points  Cape,  Africa. . .  322 

Argentina . . .  298 

Honduras...  286 

Ti-ao-usu  Island 338 

Tiburon  Island 290 

Tiegenort 310 

Tien-pak 337 

Tientsin 338 

Tilly  Bay 299 

Timbalier  Island 284 

Timor  Island 332 

Laut  Island 332 

Tinakula  Island 347 

Tinian  Island 344 


PLACES — continued. 

Page. 

Tintolo  Point 335 

Tirby  Point 287 

Tiruchendore 328 

Toasa  Island 343 

Toau 349 

Tobago 295 

TobiShima 340 

TobolAli 331 

Tocopilla 301 

Todos  Santos 290 

To-du  Island 325 

Tofua  Island 350 

Tokara  Jima 339 

Tokelau  Islands 345 

Token  Bessi  Island 332 

Tokio 340 

Tolaga  Bay 354 

Tolkemit 310 

Tomas,  San 290 

Tomo  Roads 340 

Tongarewa  Island 345 

Tonga  tabu  Island 350 

Tongka  Harbor 329 

Tongoi 300 

Tong-sang  Harbor 337 

Tong-ting  Islet 338 

Tonning 311 

Topolobampo 291 

Tor 324 

Torbjomskjaer 308 

Tordenskjold,  Cape 356 

Torgauten 308 

TonwiSaki 340 

Tomea 309 

Toro  Point 287 

Torres  Island 347 

Point 297 

Port 316 

Tortola 294 

Tortosa,  Cape 315 

Tortugas  Island 295 

Tory  Hill 307 

Island 306 

Tosco  Cape 290 

Totoya  Island 348 

Toulinguet  Islands 279 

Toulon 316 

Tourane  Bay 336 

Towers  Island 342 

Townsend,  Port 289 

Trsenen 307 

Trafalgar,  Cape 315 

TraleeBay 306 

Trani 318 

Trapani 317 

Travemunde 311 

Travers  Islands 353 

Treasury  Islands 346 

Trebizond 320 

Tregosse  Islands 347 

Trelleborg 309 

Tremiti  Islands 317 

Trepassey  Harbor 279 

Trea  Montes  Cape 299 

Puntaa  Cape,  Chile. ...  299 

Venezuela...  296 

Trevose  Head 304 

Triangles 285 

Tribulation,  Cape 353 

Trieste 317 

Trincomali 329 


Page. 

Tringano  River 336 

Trinidad  Head 289 

Island 303 

Tripoli,  Africa 321 

Turkey 320 

Tristan  da  Cunha 303 

Triton  Bay 346 

Island 337 

Triunfo  Cape 286 

Trivandrum 328 

Trobriand  Islands 347 

Tromelin  Island, Caroline  Is.  343 

Indian  Ocean 326 

Tromso 307 

Trondheim 307 

Troon 305 

Truxillo 286 

Tsau-liang-hai 339 

Tscheljuskin,  Cape 356 

Tsmano 326 

Tsu  Sima 339 

Tsukarase  Rocks 340 

Tsuruga 340 

Tuanske  Island 349 

Tubailsland 349 

Tubuai  Islands 350 

Tubuai-Manu  Island 349 

Tucacas  Island 295 

Tuckers  Beach 283 

Tukume  Island 349 

TuUy  Mountain 306 

Tumaco 302 

Tumbez 302 

Tung-chuh  Island 338 

Tung-yung  Islands 337 

Tuni-ang  Island 337 

Tunis 321 

Tuno  Island 312 

Tupilco  River 285 

Tureia  Island 349 

Turk  Island 292 

Turnabout  Island 337 

Turo  Island 312 

Turtle  Island 348 

Isles 351 

Tuskar  Rock 307 

Tuticorin 328 

Tutoya 296 

Tutuila  Island 348 

Tuvutha  Island 348 

Tuxpam  Reefs 285 

Tuxtla  Volcano 285 

Twelve  Islands 327 

Twofold  Bay 352 

Tybee  Island 283 

Ty-fung-kyoh  Island 337 

Tynemouth 305 

Ua-Huka  Island 345 

Ualan  Island 343 

Ubatuba 297 

Uea  Island 348 

Ujelang  Island 343 

Uji  Shima 340 

Uleaborg 309 

Ulietea  Island 349 

IJlko  Kalla  Rock 309 

UlladuUa 352 

Ulsire 308 

Uluthi  Islands 343 

Umea 309 


INDEX  TO  APPENDIX  IV. 


[Page  379 


Page. 
Una 297 

Unalaska  Island 287 

UnareBay 296 

Underut  Islet 325 

Underwood,  Port 355 

Unga  Island 287 

Unie  Island 318 

Union  Bay 298 

Islands 345 

Portdela 291 

Unsan^ 333 

Upemivik 356 

Upright  Port 299 

Upsala 309 

Upulo  Islands 348 

Uragami 340 

Urracaa  Islands 344 

Urup  Island 341 

Usbome,  Port 351 

Usedom 311 

Ushant 313 

Ustica  Island 317 

Ute  Islet 309 

Utillalsland 286 

Utrecht 313 

Uvea  Island 350 

Vadao 307 

Vahanga  Island 349 

Vahitahi  Island 349 

Vaitupu  Island 345 

Valdea  Island 288 

Valdivia 300 

Valencia 315 

Valentia 306 

Valentine  Harbor 299 

St.,  Cape 299 

Valery  en  Caux,  St 313 

ValientePeak 287 

Valientes  Islands 343 

Valparaiso 300 

Vanavana  Island 349 

Vancouver 289 

Vanikoro 347 

Vannes 314 

Vanua  Lava  Island 347 

Levu  Island 348 

Mbalavu  Island 348 

Vardo 307 

VarellaCape 336 

Pulo 336 

Varna  Bay 320 

Vat6  Island 347 

Vathi,  Port 319 

Vatiu  Island 350 

Vatoa  Island 348 

Vatu  Lele  Island 347 

Vara  Island 348 

Vavau  Island 350 

Vavitoa  Island 350 

Vaza  Barria  River 296 

Veglia 317 

Veiro  Island 312 

Vela,  La,  Cape 295 

Venangue  B6  Bay 326 

Vendres,  Port 316 

Venice 317 

Ver,  Pointde 313 

Vera  Cruz 285 

Verde  Cape 321 


PLACES — continued. 


Page. 

Verd  Cay,  Bahamas 292 

Cuba 292 

Vicente,  San,  Cape 299 

Port 334 

Victor- Port 352 

Victoria 288 

Harbor 355 

Port,  Australia 352 

Sey chelle  Islands.  325 

River 351 

Victory  Cape 299 

Island 331 

Vidal,  Cape 323 

Video  Island 338 

VieborgBay 310 

Vieques  Island 294 

Vieste 317 

Vigan 334 

Vigo 314 

Villa 307 

Nova  da  Princessa. . . .  297 

Villajoyose 315 

Villefranche 316 

Vinaroz 315 

Vincent,  San,  de  la  Barquera  314 

St.  Cape,  Chili 299 

Madagascar .  326 

Portugal 315 

I.,  C.  Verde  Is  . . .  303 

Windward  Is.  295 

Bay,  S.  Pacific ...  350 

Vineyard  Haven 282 

Vingorla 328 

Rocks 328 

Virgin  Gorda 294 

Virgins,  Cape 298 

VitiLevu 348 

Vizagapatam 329 

Viziadiug 328 

Vladimir,  St.,  Bay 341 

Vladivostok 341 

Vliko,  Port 319 

Vohemar 326 

Voiazza  River 318 

Volcano  Island,  West 338 

Islands 345 

Volta  River 322 

Voltaire,  Cape 351 

Vordate  Island 332 

Vordingborg 312 

Vostok  Island 345 

Vourlah 320 

Vriea  Island 340 

Wadero  Island 308 

Wadsworth,  Fort 283 

Wahdu  Island 325 

Waimea 344 

Waitangi  River 355 

Wakaya  Island 348 

Wake  Island 344 

Wakefield,  Port 352 

WalfischBay 322 

Walker  Cay 292 

Wallis  Island 348 

Walpole  Island 347 

Walsche,  Cape 346 

Walsingham,  Cape 355 

Wanganui  River 354 

Wangari  Harbor 354 


Page. 

Wangajoa  Harbor 364 

Wangaruru 354 

Wangeroog 312 

Wang-kia-tia  Bay 338 

Warberg 308 

Wamemunde 311 

Warren  Hastings  Island 344 

Washingtoji 283 

Island 342 

Watch  Hill  Point 282 

Watcher,  North,  Island 331 

Waterfall  Bluff 323 

Waterford 307 

Waterloo  Bay 323 

Watlings  Island 292 

WawodaRock 341 

Wedge  Island 281 

Weggs  Cape 279 

Weichselmunde 310 

Weihaiwei 338 

Wellington 354 

Wenman  Island 342 

Wessel,  Cape 351 

West  Cape 355 

Western,  Port 352 

Westminster  Hall  Islet 299 

Wetta  Island 332 

Wexford 307 

Whaingaroa  Harbor 355 

WhaleBack 282 

Whalefiah  Island 356 

Wliare-Kauri 350 

White  Haven 305 

Head  Island 281 

Island 354 

Rock 

Wliitsunday  Island 349 

WHiittle  Cape 280 

Wicklow 307 

Wilberforce,  Cape 351 

Wilhelmsliaven 312 

Willemstadt 313 

William.  Port 355 

Willoughby,  Cape 352 

Wilmington 283 

Wilson  Islands 347 

Islets 343 

Promontory 352 

Windau 310 

Winter  Harbor 355 

Wismar 311 

Wittgenstein  Island 349 

Wolgast 311 

Wolkonsky  Island 349 

Wollaston  Island 298 

Wollin 310 

Wollongong 352 

Wood  Island,  Labrador. . . .  280 

Maine 282 

Woodlark  Islands 347 

Woody  Island 337 

Woosung 338 

Wostenholme  Cape 279 

Wotje  Islands 343 

Wottho  Island 343 

Wowoni  Island 333 

Wrangell 288 

Wrath,  Cape 305 

Wreck  Reef 347 

Wusimado  Point 340 

Wustrow 311 


Page  380] 


INDEX  TO  APPENDIX  IV. 


Page. 

Yakuno  Shima 339 

YakutatBay 288 

Yamada 340 

Yamagawa 340 

Yami  Island 334 

Yafiez 300 

Yap  Island 343 

Yaquina  Head 289 

Yarmouth 281 

Yeboshi  Sima 339 

Yemb6 324 

Yerabu-sLma 339 

Yeu,  Island  de 314 

Ylin  Island 334 


PLACES — continued. 


Yobuko 339 

Yoko  Shima 339 

Yokohaina 340 

Yokosuka 340 

Yori-eima 339 

York,  Cape,  Greenland. . . .  356 

Queensland 353 

Minister  Rock 298 

Youghal 307 

Ystad 309 

Ytapere  Bay 326 

Point 326 

Yuiada  Road 320 

Yura  No  Uchi 340 


Page. 

Zafarana 324 

Zafarin  Islands 321 

Zambesi  River 323 

Zamboanga 335 

Zante 319 

Zanzibar 324 

Zapotitlan  Point 285 

Zara 318 

Vecchia 318 

Zempoala  Point 285 

Zengg 318 

Zeyla 324 

Zirona  Grande  Island 318 


INDEX  TO  PART  T. 


Subject. 


Abbreviations 

Account.    {See  Dead  reckoning.) 

Adjustments,  horizon  mirror 

index  mirror 

plane  table 

sextant 


permanent. . . 
theodolite  or  transit. 


Afternoon  sights 

AguUias  Current 

Airy 'a  method  for  great  circle  sailing. . . 

Alidade,  plane  table 

Almanac,  Nautical,    (-Se«  Nautical  Al- 
manac.) 

Altitude  and  azimuth 

time  azimuth 

azimuth 

calculated,  method  of 

circle,  definition 

circum-meridian 

forms  for 

computed,  method  of 

definition 

ex-meridian 

forms  for 


meridian,  constant 

form  for. . . 

forms  for 

latitude  by 

observation  of 

reduction  to 

forms . 

observed,  how  corrected 

of  Polaris  for  latitude 

single,  for  chronometer  error  . . 

latitude 

longitude  ashore 

at  sea 

true,  definition 

Altitudes,  doubloj  for  chro.  error 

Amplitude,  definition 

determination  of 

Anchor^e,  position  to  be  plotted 

Angle,  danger.     (5ee  Danger  angle.) 
hour.    {See  Hour  angle.) ' 

to  repeat 

Angles,  between  three  known  objects. . 
horizon,  for  finding  distance. . . 

round  of 

sextant  and  theodolite  in  hy- 
drography  

vertical  terrestrial,  to  measure 

26i°-45°  on  bow 

Anticyclonic  regions,  features  of 

Apparent  day,  definition 

variation  in  length 

noon,  definition 

time,  conversion  to  mean  . . . 

definition 

inequab'ty  of 


Art. 


246 
245 
413 
244 
248 
410 
389 
544 
194 
412 


235 
356 
353 
371 
217 
326 


371 
220 
326 


325 


321 
322 
326 


294 
333 
316 
332 
340 
341 
294 
320 
224 
347 
166 


411 
152 
139 
411 

452 
139 
147 
476 
273 
273 
273 
292 
273 
273 


Page. 


93 

93 

192 

93 

94 

190 

171 

237 

82 

192 


90 

147 
147 
155 

88 
129 
257 
155 

88 
129 
257 
128 
257 
256 
126 
126 
129 
257 
115 
136 
123 
134 
141 
142 
115 
125 

89 
144 

71 


191 
62 
58 

191 

202 
58 
60 
214 
102 
102 
102 
110 
102 
102 


Subject. 


Art. 


Page. 


Apparent  time,  relation  to  mean 

Arctic  Current 

Aries,  first  point  of,  definition 

Arming  of  lead 

Artificial  horizon,  description 

method  of  use 

should  be  tested  — 
Ascension,  right.     {See  Right  ascen- 
sion.) 

Astronomical  base. 

bearing 

time 

transit  instruments 

work  of  survey 

Atlantic  Ocean,  currents 

storms 

Attraction,  local 

Australia  Current 

Axis  of  rotation,  definition 

Azimuth,  altitude 

and  altitude 

circle 

definition 

from  Sumner  line 

how  deterijained 

named 

of  body  determines  use 

terrestrial  object 

time  and  altitude 

determination 

dit^am 

for  compass  errors 

in  great  circle  sailing. . 

tables 

Barometer,  aneroid 

comparisons 

definition 

effect  of,  on  tides 

mercurial 


sea 

standard 

temperature  correction 

to  determine  height 

vernier 

Base,  astronomical 

line,  description 

Beam  compass,  description 

Bearing  and  angle,  position  by 

distance,  position  by 

danger 

method  of  observing  and  plot- 
ting  

of  terrestrial  object 

Bearings,  bow  and  beam 

cross 

sun,  for  compass  error 

two,  of  object,  with  run  be- 
tween  

Beaufort's  scale  for  wind 

Bench  mark,  definition 


288 
530 
226 
19 
256 
257 
258 


441 

359 

277 

427 

445 

523 

489 

76 

540 

6 

353 

235 

34 

223 

370 

345 

344 

395 

359 

356 

349 

351 

89 

191 

351 

56 

57 

48 

496 

49 

51 

51 

55 

58 

52 

441 

434 

430 

143 

138 

157 

134 
359 
146 
134 
89 

144 

68 

511 


109 
235 

89 
13 
97 
98 
98 


200 

148 

103 

196 

201 

233 

224 

36 

236 

9 

147 

90 

18 

88 

153 

144 

144 

174 

148 

147 

145 

145 

40 

82 

145 

27 

27 

24 

226 

24 

25 

26 

26 

28 

25 

200 

198 

197 

59 

57 

64 

56 
148 
60 
56 
40 

59 

33 

230 


381 


382 


INDEX    TO    PART    I. 


Subject. 


Binnacles,  description 

Bottom,  quality  of,  on  chart 

Boxing  the  compass 

Brazil  Cxirrent 

Buoys 

C  — W,  definition 

Calculated  Altitude  Method 

Cape  Horn  Current 

Celestial  coordinates 

equator,  definition 

horizon,  definition 

latitude  and  longitude 

definition 

meridian ,  definition 

sphere  or  concave,  definition . . 

Celo-Navigation,  definition 

Chart.     {See  also  Projection.) 

as  record  of  piloting 

employment  in  piloting 

general  features 

great  circle 

for  composite  sailing. 

isobaric 

measures  of  depth  on 

Mercator,  to  construct 

quality  of  bottom  on 

standard  meridians  on 

Chilean  Current 

Chronometer,  advantage  of  more  than 

one 

C— W,  definition 

care  on  shipboard 

comparison 

record 

correction.     {See  Chro- 
nometer error.) 

description 

error,  by  double  alts 

single  altitude . 

time  sight 

signals 

transits 

definition 

differs  from  corr. . . 

from  rate 

hack,  use  of 

max.    and    min.    ther- 
mometer  

minus  watch,  definition. 

second  difference 

eight .    {See  Time  eight . ) 

temperature  curve 

transportation  of 

winding 

Circle,  declination,  definition 

hour,  definition 

of  altitude,  definition 

equal  altitude 

illumination 

vertical  definition 

Circum-meridian  altitude 

forms 

Civil  time 

Clouds,  description  and  symbols 

Coefficients,  constant 

quadrantal 

semicircular 

value  and  relation 

Collimation,  line  of,  definition 

Comparing  watch,  use  of 


Art. 

Page. 

35 

18 

46 

23 

27 

14 

532 

235 

162 

66 

268 

100 

371 

155 

541 

236 

234 

90 

215 

88 

213 

87 

238 

90 

229 

89 

216 

88 

210 

87 

4 

9 

166 

71 

165 

68 

37 

20 

189 

80 

197 

83 

460 

270 

47 

24 

41 

21 

46 

23 

45 

23 

541 

236 

265 

100 

268 

100 

260 

98 

263 

99 

264 

99 

259 

98 

320 

125 

316 

123 

316 

123 

314 

121 

315 

122 

261 

98 

312 

121 

311 

121 

268 

100 

262 

99 

268 

100 

265 

100 

266 

100 

260 

98 

262 

99 

216 

88 

216 

88 

217 

88 

363 

150 

363 

150 

217 

88 

326 

129 

257 
103 

277 

71 

34 

111 

48 

107 

47 

103 

46 

114 

48 

410 

190 

268 

100 

Subject. 


Comparison,  barometer 

chronometer,  method 

record 

Compass,  beam,  description 

boxing 

compensation.      {See  Devia- 
tion.) 

declination 

definition 

deviation.     {See  Deviation.) 

divisions  on  card 

dry 

error.    {See  Error,  compass.) 

local  attraction 

Lord  Kelvin 

Navy  service,  7i-inch 

variation 

wet 

Compasses  (drawing) 

Compensation,  compass.     {See  Devia- 
tion.) 

Composite  sailing,  computation 

definition 

graphic  approxima- 
tion  

shortest  course  for. . 
terrestrial  globe . . . . 

Computed  altitude  method 

Concave,  celestial,  definition 

Constant  deviation.     {See  Deviation.) 

for  meridian  altitude 

form . .  . 
Conversion  of  time,  apparent  to  mean. . 

definition 

mean  to  apparent . 

sidereal. . . 

sidereal  to  mean. . . 

Coordinates,  celestial 

definition 

Correction,  chro.     {See  Chronometer.) 

index,  sertant 

of  observed  altitude 

Course,  definition 

to  lay 

Culmination,  definition 

Current,  Agulhas , 

allowance  for 

Arctic 

Australia 

Brazil 

Cape  Horn 

Chilean 

determined  at  noon 

effect  in  piloting 

equatorial,  Atlantic 

Indian 

Pacific 

Guinea 

Gulf  Stream 

Humboldt 

Japan  Stream 

Kamchatka 

Kuroshiwo 

Labrador 

ocean,  Atlantic 

cause  of 

definition 

determination  of 

drift,  definition 

of  Atlantic 


232 


INDEX   TO   PAET   I. 


383 


Subject. 


Art. 


Current,  ocean,  Indian 

Pacific 

fitream,  definition... 

Bubmarine 

Oyaehiwo 

Peruvian 

Rennells 

Rossel _ 

Southern  connecting 

tidal,  definitions 

description  of 

observation  of 

to  find 

Ourve,  temperature,  chronometer  — 
Cyclones  and  cyclonic  circulations... 

Cyclonic  regions,  features  of 

stormfl,  description 

maneuvering  in .  . . 
Bummary  of  rules. . . 

tropicJil 

character. . 

Danger  angle,  horizontal 

vertical 

bearing 

Data,  useful,  miscellaneous 

Day's  work,  routine 

Dead  reckoning,  always  kept 

definition 

form  for 

method  of  working. 

value  of 

Decimal  fractions 

Declination  and  hour  angle 

right  ascension 

circle,  definition 

definition 

of  compass 

Declinatoire,  plane  table 

Definitions,  nautical  astronomy 

navigation 

Departure,  definition 

on  beginning  voyj^e .... 

to  take 

Depth,  measures  of,  on  charts. ..... 

recorder,  sounding  machine. 

Deviation,  causes  of 

classes  of 

compensation  of 

constant,  coefficient 

definition 

definition 

heeling  error,  compensation 

definition 

Napier  diagram  for 

quadrantal,  coefficients 

definition 

recompensation 

semicircular,  coefficients — 

definition 

table 

theory  of 

to  apply 

find 

Diagram,  time  azimuth 

Difference,  second.    (See  Second  dif- 
ference.^ 

Dip  of  horizon,  definition 

how  applied 

none    with    artificial 

horizon 

variation  in 

when  land  intervenes. , 


542 
535 
516 
518 
538 
541 
531 
540 
533 
490 
500 
506 
207 
266 
475 
476 
477 
486 
487 
478 
481 
155 
156 
157 


Page. 


383 
882 
202 


205 
203 


236 

237 

216 

218 

75 

412 

209 

1 

6 

382 

204 

47 

23 

99 

100 

119 

112 

111 

77 

125 

116 

94 

107 

106 

128 

103 

101 

92 

96 

78 

84 

351 


300 
303 

294 
301 
302 


237 

235 

232 

232 

236 

236 

235 

236 

235 

225 

227 

230 

86 

100 

213 

214 

214 

221 

222 

214 

218 

64 

64 

64 

277 

169 

169 

84 

254 

84 

84 

266 

90 

90 

88 

88 

36 

192 

87 

10 

10 

169 

84 

24 

14 

44 

45 

49 

48 

48 

37 

53 

49 

41 

47 

47 

54 

46 

45 

40 

43 

37 

39 

145 


116 
117 

115 
117 
117 


Subject. 


Art. 


Page. 


Distance  and  \)earing 

by  horizon  angle 

definition 

of  objects  of  known  height. 

polar,  definition 

zenith.  (5ce  Zenith  distance.) 

Distant  object  for  comjjass  error 

Diurnal  inequality  of  tide 

type  of  tide 

Dividers,  description 

pntportional,  description . . . 

Doldrums 

Doubling  angle  on  bow 

Drift  currents,  Atlantic 

Earth,  definitions  relating  to 

Eccentricity,  sextant 

Ecliptic,  definition 

Elevated  pole 

Ephemeris.    (5ee  Nautical  Almanac.) 

Equation  of  time,  definition 

in  conversion  of  time 

Equator,  celestial,  definition 

earth's 

Equatorial  currents.    (See  Current.) 

Equiangular  spiral 

Equinoctial,  definition 

Equinox,  definition 

vernal.    (See  First  jwint  of 
Aries.) 
Error,  chro.    (See  Chronometer.) 

compass,  causes 

to  apply 

find 

heeling.    {See  Deviation.) 

index,  sextant,  description 

probable,     of     position,     how 

shown 

sextant.    (See  Sextant.) 

Establishment,  tidal,  definitions 

Ex-meridian  altitudes 

forms 

Extraordinary  refraction  near  horizon.. 

Extra- tropical  cj^clonic  storms 

First  point  of  Aries,  definition 

hour  angle  is  si- 
dereal time 

Flinders  bar,  definition 

to  place 

Fogs  and  fc^  signals 

Forms  for  sights,  etc 

notes  on 

use  recommended . 

Fractions,  decimal 

Gauges,  tide,  description 

Geodetic  surveying 

Geometry 

formulae  derived  from 

Geo-Navigation,  definition 

Gimbals,  compass 

chronometer 

Glasses,  shade.    (See  Shade  glasses.) 
Globe,  terrestrial,  for  comp.  sailing.  .  . 
gt.  circle  sailing. 

Graduation,  sextant,  error 

Great  circle  charts 

for  comp.  sailing . . . 

course 

sailing,  advantages 

Airy's  method 

computation 

definition 

graphic  approx — 


138 
139 
6 
139 
219 

91 
498 
498 

7 
431 
465 
145 
527 

6 
248 
225 
214 

275 

288 

215 

6 

6 
215 
226 


74 

78 
83 

250 

398 

492 
326 


301 
488 
226 

276 
105 
127 
163 


399 


513 
408 


4 

28 

259 

200 
193 
248 
189 
197 
6 
186 
194 
190 
183 
192 


57 
58 
9 
58 
88 

40 

227 

227 

11 

197 

209 

60 

234 

10 

94 

89 

87 

103 
109 

88 
9 

10 

88 
89 


36 
37 
39 

«5 

176 

226 
129 
257 
117 
223 


103 

47 

54 

66 

254 

265 

176 

266 

231 

189 

268 

269 

9 

17 

98 

83 
82 
94 
80 
83 
10 
80 
82 
81 
79 
82 


384 


INDEX   TO   PART   I. 


Subject. 


Great  circle  sailing  methods 

terrestrial  globe. . . 
time   azimuth 

methods 

Greenwich  adopted  as  prime  meridian. 

time,  to  find 

Guinea  Current 

Gulf  Stream,  description 

extraordinary  dip  in ... . 

Gyro-compaae 

Hack  chronometer,  use  of 

Heading,  magnetic,  determination  of. . 
Heeling  error.     {See  Deviation . ) 
Height,  determination  by  barometer. . . 

Hehograph,  use  in  surveying 

Heliotrope,  use  in  surveying 

Horizon  angle,  distance  by 

artificial,  description 

method  of  use 

no  dip  with 

should  be  tested — 

celestial,  definition 

dip  of,  definition 

how  applied 

none    with    artificial 

horizon 

variation  in 

when  land  intervenes. . 

mirror,  adjustment 

description 

prismatic 

visible  or  sea,  definition 

Horse  latitudes 

Hour  angle  and  declination 

time,  coavession 

definition 

how  measured 

circle,  definition 

Humboldt  Current 

Hydrographic  survey j  method  of 

surveying,  definition 

Hydrography  in  survey,  description. . . 

to  plot 

Ice  and  its  movements  in  the  North 

Atlantic  Ocean 

Identification  of  unknown  bodies 

Index  correction,  sextant,  to  find 

error,  sextant,  description 

minor,  adjustment 

description 

prismatic 

Indian  Ocean,  currents 

Induction,  magnetic 

Instruments,  astronomical  transit 

nautical  astronomy 

navigation 

surveying 

Interpolation,  Nautical  Almanac 

Intersection,  Sumner.    (See  Sumner.) 

Intervals,  lunitidal,  definitions 

list  of 

mean  and  sidereal  time 

Iron,  hard  and  soft. 

Isobars,  chart  showing 

Japan  Stream 

E[amchatka  Current 

Knot,  length  of 

Kuroshiwo  Current 

Labrador  Current 

Lagging  of  tide 

Land  and  sea  breezes 


Art. 


188 
193 

191 
336 
280 
529 
526 
301 
33 
268 
122 

58 
426 
426 
139 
256 
257 
294 
258 
213 
300 
303 

294 
301 
302 
246 
240 
248 
213 
466 
236 
293 
222 
278 
216 
541 
432 
408 
451 
452 


392 
250 
249 
245 
240 
248 
542 
97 
427 
239 
7 
409 
283 

492 


289 
97 
460 
436 
637 
6 
536 
530 
497 
469 


Page. 


80 
82 

82 
140 
104 
235 
233 
117 

18 
100 

50 

28 

195 

195 

58 

97 

98 

115 

98 

87 

116 

117 

115 

117 

117 

93 

91 

95 

87 

209 

90 

111 

88 

103 

88 

236 

197 

189 

202 

202 

238 

172 

95 

95 

93 

91 

94 

237 

44 

196 

91 

11 

189 

106 

226 
279 
109 

44 
270 
235 
236 

10 
235 
235 
227 
211 


Subject. 


Latitude,  by  meridian  altitude 

forms . . 

Polaris 

reduction  to  meridian 

reduction    to    meridian, 

forms 

single  altitude 

forms 

9/    g/^  method 

forms 

celestial,  definition 

definition 

difference,  of  definition 

horse 

Lead,  arming 

description 

line,  marking  of 

Level  of  bench  mark 

surveying,  use  of 

description 

Lights,  employment  in  piloting 

Line,  base,  description  of 

of  coUimation,  definition , 

position.  (-Sffi  Sumner  line.) 

sight,  definition 

Sumner.  (See  Sumner  line.) 

Local  attraction 

time,  to  find 

Log  book 

chip 

ground 

patent 

electric  registers. 

revolutions  as  substitute . . 

Logarithms,  explanation 

Longitude,  by  single  altitude  ashore. 

at  sea. . 

time  sights,  forms 

transit  observations. . . 

celestial,  definition 

definition 

difference  of 

of  secondary  meridians. . . 

tertiary  meridians 

Loxodromic  Curve 

Lubber's  line 

Lunitidal  intervals,  definitions 

Ustof 

Magnetic  observations  in  survey 

Magnetism,  acquired  in  building  vessel 

features  of  earth's 

subpermanent 

transient 

Main  triangulation 

Maneuvering,  cyclonic  storms 

.    summary  of  rules 

Marine  surveying 

Mean  day,  definition 

directive  force 

noon,  definition 

sun,  definition 

Mean  time,  conversion  to  apparent. . . 

sidereal 

definition 

intervals,  relation  to  side- 
real  

time,  relation  to  apparent 

sidereal 

Mercator  projection,  description 

to  construct 

sailing 


INDEX    TO    PABT    I. 


385 


Subject. 


Meridian  altitude,  constant 

forma  for 

latitude  by 

observation  of 

reduction  to 

celestial,  definition 

of  earth,  definition 

passage,  definition 

prime,  Greenwich  adopted... 

secondary,  definition 

determination  of.. 

standard,  on  charts 

tertiary,  definition 

determination  of 

Meridional  parts 

Method  of  Saint  Hilaire  or  of  the  com- 
puted altitudes 

Middle  latitude  sailing 

correction 

Mile,  nautical  or  sea,  length  of 

Mirror,  horizon.     (yiSec  Horizon  mirror.), 
index.     (See  Index  mirror.) 

sextant,  resilvering 

Monsoon  winds 

Moon,  correction  of  observed  altitude.. 

form  for  latitude  sights 

meridian  altitude 

time  sight 

planets,  and  stars,  use  of 

value  of  observations  of 

Morning  sights 

Nadir,  definition 

Napier  diagram 

Nautical  Almanac,  description 

for  1915,  extracts . . 
gives      horizontal 

parallax 

interpolation 

reduction  of  ele- 
ments  

second  differences. 

Astronomy,  definitions 

instnunents 

mile,  length  of 

Navigation,  definitions 

instrimients  and  accessories 

Neap  tides 

Noon  sights 

Notes  on  forms  for  sights,  etc 

Occupying  a  station 

Ocean  current.     (See  Current,  ocean.) 

Octant,  description 

Optical  principal  of  sextant 

Orient,  to,  a  plane  table 

Oyashiwo  current 

Parallax,  definition 

horizontal,  in  Nautical  Al- 
manac  

how  applied 

of  planet  or  star 

Parallel  of  latitude,  definition 

rulers,  description 

sailing,  description 

Passage,  meridian,  definition 

Pelorus,  description 

Peruvian  Current 

Piloting,  definition 

requisites 

Plane  of  reference,  tidal 

sailing..." 

table,  adjustments 

description 


Art.  Page. 


235 


321 
322 
326 
216 
6 
271 
336 
336 
337 

45 
336 
339 

40 

371 

175 

178 

6 


254 
468 
294 


391 
394 
384 
212 
94 
282 


305 
283 

283 

285 

209 

239 

6 

1 

7 

494 

386 


411 

255 
242 
414 
538 
304 

305 
306 
294 
6 
8 
173 
271 
36 
541 
130 
131 
509 
169 
413 
412 


128 
256 
126 
126 
129 

88 
9 
102 
140 
140 
140 

23 
140 
141 

20 

155 

75 
77 
10 


96 
210 
115 
259 
257 
256 
172 
174 
169 
87 
41 
105 
248 

118 
106 

106 

108 

87 

91 

10 

9 

11 

226 

170 

265 

190 

97 

92 

192 

236 
118 

118 

119 

115 

9 

11 

75 

102 

19 

236 

56 

56 

230 

72 

192 

191 


Subject. 


Plane  table,  to  improvise 

use  of. 

Planet,  correction  of  observed  altitude. 

form  for  latitude  sights 

meridian  altitude .... 

time  sight 

identification  of  unknown 

Planets,  stars,  and  moon,  use  of 

Polar  distance,  definition 

Polaris,  latitude  by 

Pole,  elevated 

star,  latitude  by 

Poles  of  earth 

Portable  transit 

Position  by  angles  between  3  objects. . 
26i°-45''  on  bow . . . 

bearing  and  angle 

distance 

bow  and  beam  bearings. . . 

cross  bearings 

doubling  angle  on  bow 

two  bearings  and  run 

methods  of  fixing 

of  anchorage  to  be  plotted 

body  determines  its  use 

soundings  in  survey 

probable  error  of  by  Sumner 

lines,  how  shown 

Pressure,  effect  in  wind 

progressive  areas  of 

seasonal  variations  in 

variation  of  atmospheric 

Prime  meridian,  Greenwich  adopted .  . 

vertical,  definition 

Priming  of  tide 

Projection,  gnomonic 

Mercator 

polyconic 

systems  in  use 

Proportional  dividers,  description 

Prosection  method,  plane  table 

Protractor,  ordinary 

three  armed,  description. . . 

substitute 

use  of 

Quadrantal  deviation.  (See  Deviation.) 

Quintant,  description 

Range  of  tide  at  various  places 

definitions 

Ranges  for  finding  compass  error 

in  piloting 

Rate,  chronometer.    (See  Chronometer 

rate.) 
Reciprocal  bearings  for  compass  error. . 
Reckoning,  dead.     (See  Dead  reckon- 
ing-) 

Record  of  astronomical  work 

chronometer  comparisons 

piloting 

tidal 

Red  Sea,  extraordinary  dip  in 

Reduction  to  meridian 

forms  for 

Reference,  planes  of,  tidal 

Refraction,  correction  for 

definition 

effect  on  dip 

extraordinary,  near  horizon 

how  applied 

Relative  humidity 

Rennells  Current 

Repeat,  to,  an  angle 


Art.  Page. 


416 
413 
294 


392 
391 
219 
333 
214 
333 
6 
427 
152 
147 
143 
138 
146 
134 
145 
144 
133 
166 
395 
452 

398 

460 

474 

461 

471 

336 

217 

497 

44 

39 

43 

38 

431 

414 

9 

428 

429 

152 

255 


493 

90 

158 


88 


399 
263 
166 
507 
301 
326 


509 
298 
296 
301 
301 
299 
63 
531 
411 


193 

193 

115 

258 

256 

255 

172 

172 

88 

136 

87 

136 

9 

196 

62 

60 

59 

57 

60 

66 

60 

59 

56 

71 

174 

202 

176 

207 

212 

207 

212 

140 

88 

227 

23 

20 

22 

20 

197 

192 

11 

196 

196 

62 

97 

279 

226 

40 

65 


39 


176 
99 
70 
230 
117 
129 
257 
230 
116 
115 
117 
117 
116 
30 
235 
191 


21594°— 14- 


-25 


386 


INDEX   TO   PAKT   I. 


Subject. 


Resection  method,  plane  table 

Residual  deviation 

Rhumb  line,  definition 

not  shortest  course 

Right  ascension  and  declination 

definition 

Roaring  forties 

Rossel  Current 

Round  of  angles 

Run,  calculation  of 

determined  at  noon 

Running  survejr,  description 

Sailing,  composite.    (See  Composite.) 
great  circle.  (See  Great  circle.) 

Mercator 

middle  latitude 

correction 

parallel 

plane 

spherical 

traverse 

Sailings,  definition 

kinds  of 

Saint  Hilaire's  method 

Sargasso  sea 

Sea  and  land  breezes 

mile,  length  of 

pymbols  for  state  of 

water  temperature 

Second  difference,  chronometer 

Nautical  Almanac . 

Secondary  meridian,  definition 

determination  of. 

triangulation 

Seconds,  employment  in  naut.  sights. . 

Semicircles,  storm 

Semicircular  deviation.     (See  Devia- 
tion. ) 

Semidiameter,  definition 

how  applied 

measured 

of  planet  or  star 

Semidiurnal  type  of  tide 

Seztant  adjustments 

permanent 

angles  for  plotting  soundings. . 

choice  of 

definition 

description 

eccentricity 

graduation  errors 

index  correction,  to  find 

error,  description ..'... 

method  of  use 

optical  principle 

prismatic  mirrors 

shade  glasses 

resilVering  mirrors 

surveying 

vernier 

Shade  glasses,  for  artificial  horizon . . . 
sextant,  description . . . 

prismatic 

Sidereal  day,  definition 

noon,  definition ! 

time,  conversion  to  mean 

definition 

intervals,    relation    to 

mean 

relation  to  mean 

Sight,  chronometer.   (See  Time  sight.) 
latitude.    (See  Latitude.) 


Art. 

Page. 

414 

192 

123 

52 

6 

10 

185 

80 

237 

90 

237 

90 

467 

210 

540 

236 

411 

191 

208 

86 

388 

171 

457 

204 

186 

80 

179 

78 

175 

75 

178 

77 

173 

75 

169 

72 

168 

72 

172 

74 

167 

72 

les 

72 

371 

155 

528 

235 

469 

211 

6 

10 

73 

35 

64 

30 

265 

100 

285 

108 

336 

140 

337 

140 

444 

201 

397 

179 

485 

221 

307 

119 

308 

120 

251 

96 

294 

115 

498 

227 

244 

93 

248 

94 

452 

202 

253 

96 

239 

91 

240 

91 

248 

94 

248 

94 

250 

95 

249 

95 

252 

96 

242 

92 

248 

94 

248 

94 

254 

96 

423 

195 

241 

92 

256 

97 

240 

91 

248 

94 

276 

103 

276 

103 

291 

110 

276 

103 

289 

109 

287 

108 

Subject. 


Sight,  line  of,  definition 

longitude.     (See  Longitude.) 
time.     (See  Time  sight.) 

Sights,  afternoon 

employment  of  various 

morning 

noon 

Signals,  surveying,  description 

time,  for  chronometer  error 

Silvering  sextant  mirrors 

Solar  time.     (See  Apparent  time.) 

Solstice,  definition 

Sound  J  velocity  of 

Sounding  machine,  barometric  corr 

depth  recorder .... 

description 

tubes 

Soundings,  surveying,  how  plotted 

use  in  piloting 

Southern  connecting  current 

Sphere,  celestial,  definition 

Spherical  sailing 

Spring  tides 

Stadia.    (See  Telemeter.) 

Star,  correction  of  observed  altitude. . . 

form  for  latitude  sights 

meridian  altitude 

time  sight 

identification 

observations  in  surveying 

Stars,  planets,  and  moon,  use  of 

Station  pointer.     (See  Protractor,  three 
armed.) 

Storm  center,  motion  of 

rate  of  ])rogres8 

to  avoid 

fix  bearing 

distance 

semicircles 

tables 

Storms,  along  transatlantic  routes 

cyclonic.  (See  Cyclonic  storms.) 

Submarine  ocean  currents 

Sumner  line,  always  recommended. . 

applications  of 

choice  of  bodies 

description 

determination 


uses 

lines,  intersection,  computation 
graphically, 
when  run  in- 
tervenes. 
Sun,  correction  of  observed  altitude. . 

form  for  latitude  sights 

meridian  altitude 

time  sight 

mean,  definition 

observations  in  surveying 

Survey,  astronomical  work  of 

hydrographic,  method  of 

running,  description 

to  plot  soundings  in 

Surveying,  hydrographic,  definition.. 

instruments 

marine,  definition 

topographic,  definition 

transit,  description 

Symbols  for  clouds 

sea .'.. 

weather 

Table,  plane.    (See  Plane  table.) 


INDEX    TO   PAST   I. 


387 


Subject. 


Table,  tide 

time  azimuth 

Telemeter,  description 

substitute  for 

use  of 

Telescope,  direct  and  reversed 

sextant,  adjustment 

description 

zenith 

Temperature  curve,  chronometer 

Terrestrial  object,  true  bearing  of 

Tertiary  meridian,  definition 

determination  of. . . 

Theodolite,  adjustments 

angles  for  plotting  sound- 
ings... 

description 

method  of  use 

Thermometer,  classes  of 

description 

dry  and  wet  bulb 

max.  and  min.,  chro 

Three-armed    protractor.      (See    Pro- 
tractor.) 

point  problem,  conditions 

explanation 

Tidal  current.    (See  Current,  tidal.) 

day,  definition 

establishment,  definitions 

observations  in  survey 

instructions  for 

record 

Tide,  bench  mark,  deSnition 

cause  of 

definitions  relating  to 

diurnal  inequality 

type 

effect  of,  in  piloting 

wind  and  barometer  on. 

gauges,  description 

observation  of 

planes  of  reference  of 

priming  and  lading  of 

range  of,  at  various  places 

definitions 

semidiurnal  type 

spring  and  neap 

tables 

time  of  high  and  low 

form  for 

tropic 

types  of 

Time  and  altitude  azimuth 

hour  angle,  conversion  of . . . 
apparent.     (See  Apparent  time.) 

astronomical 

at  different  meridians 

azimuth.     (See  Azimuth,  time.) 

civil 

conversion  of.    (See  Conversion.) 
equation  of.    (See  Equation  of 
time.) 

Greenwich,  to  find 

local,  to  find 

mean.    (See  Mean  time.) 

of  high  and  low  water 

form  for. . . 


Art. 


501 
351 
417 
422 
417 
411 
247 
240 
427 
266 
359 
336 
339 
410 

451 

409 

411 

59 

59 

61 

262 


153 
152 

497 
492 
503 
503 
507 
511 
491 
490 
498 
498 
164 
496 
513 
504 
509 
497 


493 
498 
494 
501 
501 


498 
498 
356 
293 

277 
279 

277 


280 
279 

501 


228 
145 
194 
195 
194 
191 
94 
91 
190 
100 
148 
140 
141 
190 

203 
189 
190 
28 
28 
28 
99 


63 
62 

227 
226 
229 
229 
230 
230 
225 
226 
227 
227 
67 
226 
231 
229 
230 
227 
279 
226 
227 
226 
228 
228 
259 
227 
227 
147 
111 

103 
103 

103 


104 
103 

228 
259 


Subject. 


Time  of  transit,  how  found 

sidereal.    (See  Sidereal  time.) 

signals  for  chronometer  error 

eight  for  chronometer  error 

longitude  ashore 

at  sea 

forms  for 

solar.    (See  Apparent  time.) 

Topographic  surveving,  definition 

Topojgraphy  in  hyarographic  survey. . . 

Tracing  paper  to  plot  soundings 

3-point  problem. 

Trade  wind 

Transit,  astronomical 

definition 

observations  for  chronometer 

error 

longitude . . . 

portable 

surveying.     (See  Theodolite.) 

time  of,  how  found 

Traverse  sailing 

tables,  use  of 

Triangulation,  main 

secondary 

Trigonometric  functions 

logarithms 

Tropic  tide 

Tropical  cyclonic  storms 

character 

Tubes,  sounding  machine 

Unknown  bodies,  identification  of 

Useful  data,  miscellaneous 

Variation  of  compass,  definition 

to  apply 

find 

Variations,  atmospheric 

nonperiodic . . . 

periodic 

Vernier,  barometer 

sextant 

theodolite 

Vertical  angles,  terrestial,  to  measure. . 

circle,  definition 

prime 

Visible  horizon,  definition 

Watch,  comparing,  use  of 

Weather  symbols 

Wind,  Beaufort's  scale 

causes  of 

definition 

doldrums 

effect  of,  on  tides 

land  and  sea  breezes 

monsoon 

normal  pressure 

prevailing 

westerly 

"Roaring  forties " 

storms.    (See  Cyclonic  storms.) 

Trade 

true  direction  and  force 

wire  drag 

Zenith,  definition 

distance,  definition 

how  named 

telescope 


Art. 


Page. 


323 

314 
316 
340 
341 


408 
450 
160 
429 
464 
427 
271 

315 
338 
427 

323 
172 
170 
443 
444 


498 
478 
481 
21 
392 


75 
78 
83 
471 
473 
472 
52 
241 
409 
139 
217 
217 
213 
268 
70 
68 
459 
458 
465 
496 
469 
468 
460 
462 
467 
467 

464 
69 
454 
212 
221 
321 
427 


127 

121 
123 
141 
142 
254 

189 
202 
65 
1&6 
209 
196 
102 

122 
140 
196 

127 

74 

73 

201 

201 

270 

271 

227 

214 

218 

13 

172 

277 

36 

37 

39 

212 

212 

212 

26 

92 

189 

58 

88 

88 

87 

100 

34 

33 

206 

206 

209 

226 

211 

210 

207 

207 

210 

210 

209 
33 

203 
87 
88 

126 

196 


I 


PA.RT    II. 


TABLES. 


601 


PREFACE. 

The  following  tables  comprise  Part  II  of  the  American  Phactical  Navioator,  by  the  late  Nathaniel 
Bowditch,  LL.  D.,  as  revised  in  1880  and  in  1903,  and  again  in  1914,  under  the  direction  of  the  Bureau 
of  Navigation,  Navy  Department. 

In  the  present  edition,  former  tables  28A,  28B,  28C  and  28D,  Latitude  by  Polaris;  37,  Logarithms  for 
Equal  Altitude  Sights;  37A,  Equation  of  Equal  Altitudes  near  Noon,  have  been  omitted,  but  the  former 
assignment  of  table  numbers  and  page  numbers  has  not  been  disturbed,  the  pages  on  which  these 
tables  were  printed  being  simply  dropped  from  the  book  and  the  tables  and  pages  not  renumbered 
consecutively. 

This  edition  has  been  extended  by  incorporating  Table  45,  Logarithmic  and  Natural  Haversines; 
Table  46,  Consolidated  Altitude  Corrections;  Table  47,  Longitude  Factor,  and  Table  48,  Altitude  Factor. 


Hydrographic  Office, 

WasMngUm,  D.  C,  19 U. 


503 


CONTENTS  OF  PART  11. 


Page. 

Explanation  of  the  Tables 507 

Table  1.  Traverse  Table,  Quarter  Points 515 

2.  Traverse  Table,  Degrees 531 

3.  Meridional  Parte 621 

4.  Length  of  Degrees  of  Latitude  and  Longitude 629 

5A.  Distance  of  an  Object  by  Two  Bearings,  Quarter  Points 631 

5B.  Distance  of  an  Object  by  Two  Bearings,  Degrees 634 

6.  Distance  of  Visibility  of  Objects  of  different  Heights 640 

7.  Conversion  of  Arc  and  Time 641 

8.  Conversion  of  Sidereal  into  Mean  Solar  Time 642 

9.  Conversion  of  Mean  Solar  into  Sidereal  Time 645 

10.  Local  mean  time  of  Sun's  visible  Rising  and  Setting 648 

11.  Reduction  of  Moon's  Meridian  Passage  for  Longitude 672 

12.  Reduction  of  Quantities  from  Nautical  Almanac 673 

13.  Change  of  Sun's  Right  Ascension : 683 

14.  Dip  of  Sea  Horizon 685 

15.  Dip  at  Distances  short  of  Horizon 685 

16.  Parallax  of  Sun 685 

17.  Parallax  of  Planet 686 

18.  Augmentation  of  Moon's  Semidiameter 687 

19.  Augmentation  of  Moon's  Horizontal  Parallax 687 

20A.  Mean  Refraction 688 

20B.  Mean  Refraction  and  Parallax  of  Sun 689 

21 .  Correction  of  Refraction  for  Barometer 690 

22.  Correction  of  Refraction  for  Thermometer 691 

23.  Mean  Refraction  and  Mean  Parallax  of  Moon 693 

24.  Mean  Refraction  and  Parallax  of  Moon 693 

25.  Variation  of  Altitude  due  to  change  of  Declination 702 

26.  Variation  of  Altitude  in  one  minute  from  Meridian 704 

27.  Variation  of  Altitude  in  given  time  from  Meridian 714 

28A.  1 

^g^-  [omitted. 

28D.  J 

29.  Nautical  and  Statute  Miles 725 

30.  Conversion  of  Metric  and  English  Linear  Measure 726 

31.  Fahrenheit,  Centigrade,  and  Reaumur  Temperatures 727 

32.  True  Force  and  Direction  of  Wind 728 

33.  Distance  by  Vertical  Angle 729 

34.  Distance  by  Horizon  Angle. 731 

35.  Speed  Table  for  Measured  Mile 732 

36.  Local  Mean  and  Standard  Meridian  Times 733 

fy-j^  jOmitted. 

38.  Error  in  Longitude  produced  by  Error  in  Latitude 739 

39.  Amplitudes 740 

40.  Correction  for  Amplitude  observed  in  Apparent  Horizon 745 

41.  Natural  Sines  and  Cosines 746 

42.  L^arithms  of  Numbers 755 

43.  Logarithms  of  Trigonometric  Fimctions,  Quarter  Points 771 

44.  Ix^arithms  of  Trigonometric  Functions,  Degrees 772 

45.  Logarithmic  and  Natural  Haversines 817 

46.  Consolidated  table  of  Altitude  Corrections 922 

47.  The  Longitude  Factor 938 

48.  The  Latitude  Factor 941 

505 


I 


EXPLANATION  OF  THE  TABLES. 


TABLES  1,  2:  TRAVERSE  TABLES. 

Tables  1  and  2  were  originally  calculated  by  the  natural  sinea  taken  from  the  fourth  edition  of 
Sherwin's  Logarithms,  which  were  previously  examined,  by  differences;  when  the  proof  sheets  of  the 
first  edition  were  examined  the  numbers  were  again  calculated  by  the  natural  sines  in  the  second  edition 
»f  Button's  Logarithms;  and  if  any  difference  was  found,  the  numbers  were  calculated  a  third  time  by 
Taylor's  Logarithms. 

The  first  table  contains  the  difference  of  latitude  and  departure  corresponding  to  distances  not 
exceeding  300  miles,  and  for  courses  to  every  quarter  point  of  the  compass.  Table  2  is  of  the  same 
nature,  but  for  courses  consisting  of  whole  degrees;  it  was  originally  of  the  same  extent  as  Table  1,  but 
has  been  extended  to  include  distances  up  to  600  miles.  The  manner  of  using  these  tables  is  particularly 
explained  under  the  different  problems  of  Plane,  Middle  Latitude,  and  Mercator  Sailing  in  Chapter  V. 

The  tables  may  be  employed  in  the  solution  of  any  right  triangle. 

TABLE  3:   MERIDIONAL  PARTS. 

Thia  table  contains  the  meridional  parts,  or  increased  latitudes,  for  every  degree  and  minute  to  80°, 
calculated  by  the  following  formula: 


m 
in  which 


=^  log  tan  ^45°  +  g^  J  —  a  (e*  sin  L  +  J  e*  sm*  L  +  ^  c«  sin*  L  -f     .     .     . 

10800'' 
the  Equatorial  radius  a  =      ^     =  3437'. 74677  (log  3.5362739); 

M,  the  modulus  of  common  logarithms  =  0.4342945; 

^=  2.3025851  ( log  0.3622157 ) ; 

C,  the  compression  or  meridional  eccentricity  of  the  earth 

according  to  Clarke  (1880)  =  ggg^  =  0.003407562  (log  7.5324437); 


from  which 


e=s/2c  —  c'  =0.0824846  (log  8.9163666); 

^    =  7915^7044558  (log  3.8984895) ; 

a«»   =      23^38871  (log  1.3690072); 
Jae*  =       0^053042  (log  8.7246192) ; 
|ae«=        0^000216523  (log  6.3355038). 

The  results  are  tabulated  to  one  decimal  place,  which  is  sufficient  for  the  ordinary  problems  of 
navigation. 

The  practical  application  of  this  table  is  illustrated  in  Chapters  II  and  V,  in  articles  treating  of  the 
Mercator  Chart  and  Mercator  Sailing. 

TABLE  4:   LENGTH  OF  DEGREES  OF  LATITTTDE  AND  LONGITXTDE. 

This  table  gives  the  length  of  a  degree  in  both  latitude  and  longitude  at  each  parallel  of  latitude  on 
the  earth's  surface,  in  nautical  and  statute  miles  and  in  meters,  based  upon  Clarke's  value  (1866)  of  the 

earth's  compression,  "SqqT^"     ^^  *^^®  ^^^^  ^^  latitude,  the  length  relates  to  an  arc  of  which  the  given 
degree  is  the  center. 

TABLES  5 A,  5B:   DISTANCE  BY  TWO  BEARINGS. 

These  tables  have  been  calculated  to  facilitate  the  operation  of  finding  the  distance  from  an  object  by 
two  bearings  from  a  given  distance  run  and  course.  In  Table  5A  the  arguments  are  given  in  points, 
in  Table  5B  in  degrees;  the  first  column  contains  the  multiplier  of  the  distance  run  to  give  the  distance 
of  observed  object  at  second  bearing;  the  second,  at  time  of  passing  abeam. 

The  method  is  explained  in  article  143,  Chapter  IV. 

507 


508 


EXPLANATION   OF   THE   TABLES. 


TABIiE  6:   DISTANCE  OF  VISIBrLITT  OF  OBJECTS. 

This  table  contains  the  distances,  in  nautical  and  statute  miles,  at  which  any  object  is  risible  at  sesL 
It  is  calculated  by  the  formulae:  _  _  *  . 

d  =  1, 15  ^x,  and  d'  =  1.32  x/a;, 
in  which  d  is  the  distance  in  nautical  miles,  d'  the  distance  in  statute  miles,  and  x  the  height  of  the  eye 
or  the  object  in  feet. 

To  find  the  distance  of  visibility  of  an  object,  the  distance  given  by  the  table  corresponding  to  its 
height  should  be  added  to  that  corresponding  to  the  height  of  the  observer's  eye. 

Example:  Required  the  distance  of  visibility  of  an  object  420  feet  high,  the  observer  being  at  an 
elevation  of  15  feet. 

Dist.  corresponding  to  420  feet,  23.5  naut.  miles. 
Dist.  corresponding  to    15  feet,    4.4  naut.  miles. 


Dist.  of  visibility. 


27.9  naut.  miles. 


TABLE  7:    CONVERSION  OF  ARC  AND  TIME. 

In  the  first  column  of  each  pair  in  this  table  are  contained  angular  measures  expressed  in  arc 
(degrees,  minutes,  or  seconds),  and  in  the  second  column  the  corresponding  angles  expressed  in  time 
(hours,  minutes,  or  seconds).  As  will  be  seen  from  the  headings  of  columns,  the  time  corresponding 
to  degrees  (")  is  given  in  hours  and  minutes;  to  minutes  of  arc  (''),  in  minutes  and  seconds  of  time; 
and  to  seconds  of  arc  (''''),  in  seconds  and  sixtieths  of  a  second  of  time. 

The  table  will  be  especially  convenient  in  dealing  with  longitude  and  hour  angle.  The  method  of 
ite  employment  is  best  illustrated  by  examples. 


Example  I. 
Required  the  time  corresponding  to  50°  31'  21''''. 

50°  00'  OO''  =  3"  20'°  00^ 
31    00    =         2    04 

21  =         m 


50    31    21    =3    22     05.4 


Example  II. 

Required  the  arc  corresponding  to  &"  33° 

6"  32"  00»    =  98°  00'  00" 
1    24     =         21    00 
2#S=  37.6 


26'.5. 


6    33    26.5  = 


21    37.5 


TABLES  8  AND  9:    SIDEREAL  AND  MEAN  SOLAR  TIMES. 

These  tables  give,  respectively,  the  reductions  necessary,  to  convert  intervals  of  sidereal  time  into 
those  of  mean  solar  time,  and  intervals  of  mean  solar  into  those  of  sidereal  time.  The  reduction  for  any 
interval  is  found  by  entering  with  the  number  of  hours  at  the  top  and  the  number  of  minutes  at  the  side, 
adding  the  reduction  for  seconds  aa  given  in  the  margin. 

The  relations  between  mean  solar  and  sidereal  time  intervals,  and  the  methods  of  conversion  of 
these  times,  are  given  in  articles  289-291,  Chapter  IX. 


TABLE  10:   SXTN'S  RISING  AND   SETTING. 

This  table  gives  the  local  mean  time  of  the  sun's  visible  rising  and  setting — that  is,  of  the  appearance 
and  disappearance  of  the  sun's  upper  limb  in  the  unobstructed  horizon  of  a  person  whose  eye  is  15  feet 
above  the  level  of  the  earth's  surface,  the  atmospheric  conditions  being  normal. 

The  local  apparent  times  of  rising  and  setting  were  determined  from  the  formula  for  a  time  sight, 
the  altitude  employed  being  —0°  56' 08",  made  up  of  the  following  terms:  Refraction,  —  36'  29";  semi- 
diameter,  -  16'  00";  dip,  —  3'  48";  and  parallax,  +  9". 

To  ascertain  the  time  of  rising  or  setting  for  any  given  date  and  place,  enter  the  table  with  the 
latitude  and  declination,  interpolating  if  the  degrees  are  not  even.  In  the  line  R  will  be  found  the  time 
of  rising;  in  the  line  S,  the  time  of  setting.  Be  careful  to  choose  the  page  in  which  the  latitude  is  of 
the  correct  name,  and  in  which  the  "approximate  date"  corresponds,  nearly  or  exactly,  with  the 
given  date. 

This  table  is  computed  with  the  intention  that,  if  accuracy  is  desired,  it  will  be  entered  with  the 
declination  as  an  argument — not  the  date — as  it  is  impossible  to  construct  anv  table  based  upon  dates 
whose  application  shall  be  general  to  all  years.  But  as  a  given  degree  of  declination  will,  in  the 
majority  of  years,  fall  upon  the  date  given  in  the  table  as  the  "approximate  date,"  and  as,  when  it 
dops  not  do  so,  it  can  never  be  more  than  one  day  removed  therefrom,  it  will  answer,  where  a  slight 
inaccuracy  may  be  admitted,  to  enter  the  table  with  the  date  as  an  argument,  thus  avoiding  the  neces- 
sity of  ascertaining  the  declination. 

Example:  Find  the  local  mean  time  of  sunset  at  Rio  de  Janeiro,  Brazil  (lat.  22°  54'  S.,  long. 
43°  10'  W.),  on  January  1,  1903  (dec.  23°  04'  S.). 


Eacact  method. 


Lat.  22°  \ 

Dec.  23°; 

Corr.  for  +  54'  lat . 
Corr.  for  -f  04'  dec. 


&"  48- 

+  02 
00 


Approximate  method. 

Lat.  22°.. -I 

January  2  j 

Corr.  for  +  64' lat +02 

Corr.  for  1  dav —  01 


gh    48m 


L.  M.  T.  sunset 6  50 


L.  M.  T.  sunset ,   6    49 


EXPLANATION   OF   THE    TABLES.  509 

TABLE  11:  REDUCTION  FOR  MOON'S  TRANSIT. 

This  table  was  calculated  by  proportioning  the  daily  variation  of  the  time  of  the  moon's  passing  the 
meridian. 

The  numbers  taken  from  the  table  are  to  be  added  to  the  Greenwich  time  of  moon's  txansit  in  west 
longitude,  but  subtracted  in  east  longitude. 

TABLE  12:  REDUCTIONS  FOR  NAUTICAL  ALMANAC. 

This  is  a  table  of  proportional  parts  for  finding  the  variation  of  the  sun' s  right  ascension  or  declination, 
or  of  the  equation  oftime,  in  any  number  of  minutes  of  time,  the  horary  motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column;  also  for  finding  the  variation 
of  the  moon's  declination  or  right  ascension  in  any  number  of  seconds  of  time,  the  motion  in  one  minute 
being  given  at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

TABLE  13:  CHANOE  OF  SUN'S  RIGHT  ASCENSION. 

This  is  a  table  that  may  be  employed  for  finding  the  change  of  the  sun's  right  ascension  for  any 
given  number  of  hours,  the  hourly  change,  as  taken  from  the  Nautical  Almanac,  being  gfiven  in  the 
marginal  columns. 

TABLE  14:  DIP  OF  SEA  HORIZON. 

This  table  contains  the  dip  of  the  sea  horizon,  calculated  by  the  formula: 

in  which  F  =  height  of  the  eye  above  the  level  of  the  sea  in  feet. 
It  is  explained  in  article  300,  Chapter  X. 

TABLE  16:  DIP  SHORT  OF  HORIZON. 

This  table  contains  the  dip  for  various  distances  and  heights,  calculated  by  the  formula: 

D  =  ?  d  -f  0.56514  X  K 
7  a 

in  which  D  represents  the  dip  in  miles  or  minutes,  d,  the  distance  of  the  land  in  sea  miles,  and  h,  the 
height  of  the  eye  of  the  observer  in  feet. 

TABLE  16:  PARALLAX  OF  SUN. 

This  table  contains  the  sun's  parallax  in  altitude  calculated  by  the  formula: 

par.  =  sin  z  X  8^.75, 

in  which  z  =  apparent  zenith  distance,  the  sun's  horizontal  parallax  being  S'^.TS. 
It  is  explained  in  article  304,  Chapter  X. 

TABLE  17:  PARALLAX  OF  PLANET. 

Parallax  in  altitude  of  a  planet  is  found  by  entering  at  the  top  with  the  planet's  horizontal  parallax, 
and  at  the  side  with  the  altitude. 

TABLE  18:  AUGMENTATION  OF  MOON'S  SEMIDIAMETER. 

This  table  gives  the  augmentation  of  the  moon's  semidiameter  calculated  by  the  formula: 

x  =  c  8*  siD.h-\-  ^  c^^  sin*  ^  -f  i  c*  »*, 

where  ?i  =  moon's  apparent  altitude; 

8  =  moon's  horizontal  semidiameter; 
X  =  augmentation  of  semidiameter  for  altitude  h;  and 
log  c  =  5.25021. 

TABLE  10:  AUGMENTATION  OF  MOON'S  HORIZONTAL  PARALLAX. 

This  table  contains  the  augmentation  of  the  moon's  horizontal  parallax,  or  the  correction  to  reduce 
the  moon's  equatorial  horizontal  parallax  to  ^hat  point  of  the  earth's  axis  which  lies  in  the  vertical  of 
the  observer  m  any  given  latitude;  it  is  computed  by  the  formulae: 

A'r  =  «r(6-1),  ^  =,^(1  -  e»8in«  L)' 

where    it  =  equatorial  horizontal  parallax; 
L=  latitude; 

e  =  eccentricity  of  the  meridian;  log  e*  =  7.81602;  and 
A  Jf  =  augmentation  of  the  horizontal  parallax  for  the  latitude  li. 


510  EXPLANATION    OF    THE    TABLES. 

TABLE  20 A:  MEAN  REFRACTION. 

This  table  gives  the  refraction,  reduced  from  Bessel's  tables,  for  a  mean  atmospheric  condition  in 
which  the  barometer  is  30.00  inches,  and  thermometer  50°  Fahr. 

TABLE  SOB:    MEAN  REFRACTION  AND  PARALLAX  OF  SUN. 

This  table  contains  the  correction  to  be  applied  to  the  sun's  apparent  altitude  for  mean  refraction 
and  parallax,  being  a  combination  of  the  quantities  for  the  altitudes  given  in  Tables  16  and  20A. 

TABLES  21,  22:    CORRECTIONS  OF  REFRACTION  FOR  BAROMETER  AND 

THERMOMETER. 

These  are  deduced  from  Bessel's  tables.     The  method  of  their  employment  will  be  evident. 

TABLE  23:    MEAN  REFRACTION  AND  MEAN  PARALLAX  OF  MOON. 

This  table  contains  the  correction  of  the  moon's  altitude  for  refraction  and  parallax  corresponding 
to  the  mean  refraction  (Table  20A),  and  a  horizontal  parallax  of  the  mean  value  of  57^  30^^. 

TABLE  24:   MEAN  REFRACTION  AND  PARALLAX  OF  MOON. 

This  table  contains  the  correction  to  be  applied  to  the  moon's  apparent  altitude  for  each  minute  of 
horizontal  parallax,  and  for  every  10''  of  altitude  from  5°,  with  height  of  barometer  30.00  inches,  and 
thermometer  50°  Fahr. 

For  seconds  of  parallax,  enter  the  table  abreast  the  approximate  correction  and  find  the  seconds  of 
horizontal  parallax,  the  tens  of  seconds  at  the  side  and  the  units  at  the  top.  Under  the  latter  and 
opposite  the  former  will  be  the  seconds  to  add  to  the  correction. 

For  minutes  of  altitude,  take  the  seconds  from  the  extreme  right  of  the  page,  and  apply  them  as 
there  directed. 

TABLE  26:   CHANGE  OF  ALTITUDE  DUE  TO  CHANGE  OF  DECLINATION. 

This  table  gives  the  variation  of  the  altitude  of  any  heavenly  body  arising  from  a  change  of  100'''  in 
the  declination.  It  is  useful  for  finding  the  equation  of  equal  altitudes  by  the  approximate  method 
explained  in  article  324,  Chapter  XI,  and  for  other  purposes. 

If  the  change  move  the  body  toward  the  elevated  pole,  apply  the  correction  to  the  altitude  with  the 
eigne  in  the  table;  otherwise  change  the  signs. 

TABLE  26:   CHANGE  OF  ALTITUDE  IN  ONE  MINUTE  FROM  MERIDIAN. 

This  table  gives  the  variation  of  the  altitude  of  any  heavenly  body,  for  one  minute  of  time  from 
meridian  passage,  for  latitudes  up  to  60°,  declinations  to  63°,  and  altitudes  between  6°  and  86°.  It  is 
based  upon  the  method  set  forth  in  article  334,  Chapter  XII,  and  the  values  may  be  computed  by  the 
formula: 

1^^9635  cos  L  cos  d 
~         sin  (L— d) 

where  a = variation  of  altitude  in  one  minute  from  meridian, 
L  =  latitude,  and 

d  =  declination — positive  for  same  name  and  negative  for  opposite  name  to  latitude  at  upper 
transit,  and  negative  for  same  name  at  lower  transit. 

The  limits  of  the  table  take  in  all  values  of  latitude,  declination,  and  altitude  which  are  likely  to 
be  required.  In  its  employment,  care  must  be  taken  to  enter  the  table  at  a  place  where  the  declination 
is  appropriately  named  (of  the  same  or  opposite  name  to  the  latitude) ;  it  should  also  be  noted  that  at 
the  bottom  of  the  last  three  pages  values  are  given  for  the  variation  of  a  body  at  lower  transit,  which  can 
only  be  observed  when  the  declination  and  latitude  are  of  the  same  name,  and  in  which  case  the  reduc- 
tion to  the  meridian  is  subtractive;  the  limitations  in  this  case  are  stated  at  the  foot  of  the  page,  and 
apply  to  all  values  below  the  heavy  rules. 

TABLE  27:    CHANGE  OF  ALTITUDE  IN  GIVEN  TIME  FROM  MERIDIAN. 

This  table  gives  the  product  of  the  variation  in  altitude  in  one  minute  of  a  heavenly  body  near  the 
meridian,  by  the  square  of  the  number  of  minutes.  Values  are  given  for  every  half  minute  between 
0"  30' and  26'"  0",  and  for  all  variations  likely  to  be  employed  in  the  method  of  "reduction  to  the 
meridian." 

The  formula  for  computing  is: 

Red.  =  a  X  f^_ 
where  a  —  variation  in  one  minute  (Table  26) ,  and 

t  —  number  of  minutes  (in  units  and  tenths)  from  time  of  meridian  passage. 

The  table  is  entered  in  the  column  of  the  nearest  interval  of  time  from  meridian,  and  the  value 
taken  out  corrresponding  to  the  value  of  a  found  from  Table  26.  The  units  and  tenths  are  picked  out 
separately  and  combined,  each  being  corrected  by  interpolation  for  intermediate  intervals  of  time. 

The  result  is  the  amount  to  be  applied  to  the  observed  altitude  to  reduce  it  to  the  meridian  altitude, 
which  is  always  to  be  added  for  upper  transits  and  subtracted  for  lower. 


EXPLANATION   OF   THE  TABLES.  511 

TABLE  28,  A,  B,  C,  D:  LATITUDE  BY  POLARIS. 


[Omitted.] 


TABLES  29,  30,  31:  CONVEBSION  TABLES. 

These  are  self-explanatory. 

TABLE  32:  TB-UE  FOBCE  AND  DIRECTION  OF  WIND. 

This  table  enables  an  observer  on  board  of  a  moving  vessel  to  determine  the  true  force  and  direction 
of  the  wind  from  its  apparent  force  and  direction.  Enter  the  table  with  the  apparent  direction  of  the 
wind  (number  of  points  on  the  bow)  and  force  (Beaufort  scale)  as  arguments,  and  pick  out  the  direc- 
tion relatively  to  the  ship's  head  and  the  force  corresponding  to  the  known  speed  of  the  ship. 

Example:  A  vessel  steaming  SE.  at  a  speed  of  15  knots  appears  to  have  a  wind  blowing  from  three 
points  on  the  starboard  bow  with  a  force  of  6,  Beaufort  scale.     What  is  the  true  direction  and  force? 

In  the  column  headed  3  (meaning  three  points  on  bow,  apparent  direction)  and  in  the  line  6 
(apparent  force,  Beaufort  scale),  we  find  abreast  15  (knots,  speed  of  vessel)  that  the  true  direction  is  5 
points  on  starboard  bow,  i.  c,  S.  by  W.,  and  true  force  4. 

TABLE  33:    VERTICAL  ANGLES. 

This  table  gives  the  distance  of  an  object  of  known  height  by  the  vertical  angle  that  it  subtends  at 
the  position  of  the  observer.     It  was  computed  by  the  formula: 

h 
tan  <^  =  ^> 

where  a  =  the  vertical  angle; 

h  =  the  height  of  the  observed  object  in  feet;  and 

d  =  the  distance  of  the  object,  also  converted  into  feet. 

The  employment  of  this  method  of  finding  distance  is  explained  in  article  139,  chapter  IV. 

TABLE  34:    HORIZON  ANGLES. 

This  shows  the  distance  in  yards  corresponding  to  any  observed  angle  between  an  object  and  the 
sea  horizon  beyond,  the  observer  being  at  a  known  height. 
The  method  of  use  is  explained  in  article  139,  chapter  IV. 

TABLE  35:    SPEED  TABLE. 


k 


This  table  shows  the  rate  of  speed,  in  nautical  miles  per  hour,  of  a  vessel  which  traverses  a  measured 
mile  in  any  given  number  of  minutes  and  seconds.  It  is  entered  with  the  number  of  minutes  at  the  top 
and  the  number  of  seconds  at  the  side;  under  one  and  abreast  the  other  is  the  number  of  knots  of  speed- 


512  EXPLANATION   OF   THE   TABLES. 

TABLE  36:  LOCAL  AND  STANDARD  TIMES. 

This  table  contains  the  reduction  to  be  applied  to  the  local  time  to  obtain  the  corresponding  time 
at  any  other  meridian  whose  time  is  adopted  as  a  standard.  The  results  are  given  to  the  nearest  minute 
of  time  only;  being  intended  for  the  reduction  of  such  approximate  quantities  as  the  time  of  high  water 
or  time  of  sunset.     More  exact  reductions,  when  required,  may  be  made  by  Table  7. 

TABLE  37:  LOGARITHMS  FOR  EQUAL  ALTITUDE  SIGHTS. 


[OlOTTBD.] 


TABLE  37A:  EQUATION  OF  EQUAL  ALTITUDES  NEAR  NOON. 


[Omitted.] 


I 


EXPLANATION    OF   THE    TABLES.  513 

TABLE  38:  EFFECT  UPON  LONGITUDE  OF  EBBOB  IN  LATITUDE. 

Table  38  shows,  approximately,  the  error  in  longitude  in  miles  and  tenths  of  a  mile,  occasioned  by 
an  error  of  one  mile  in  the  latitude. 

Thus,  when  the  sun's  altitude  is  30°,  the  latitude  30°,  and  the  polar  distance  100°,  the  error  is 
eight- tenths  of  a  mile. 

The  effect  of  an  increase  of  latitude  is  as  follows: 

In  West  longitude,  /  East  "1  of  meridian,  the  f  decreased  \  except  where  marked  f  increased  "1 
the  body  being    \  West )      longitude  is     \  increased  j  '      by  *,  when  it  is      \  decreased  )  ' 

In  East  longitude,  /  East  "I  of  meridian,  the  f  increased  )  except  where  marked  /  decreased  \ 
the  body  being    \  West  J      longitude  is     \  decreased  /  '      by  *,  when  it  is      \  increased  / " 

A  deo'ease  of  latitude  has  the  contrary  effect. 

The  direction  of  error  may  readily  be  seen  by  drawing  the  Sumner  line  in  a  direction  at  right  angles 
to  the  approximate  bearing  oi  the  body. 

TABLE  30:  AMPLITUDES. 

This  table  contains  amplitudes  of  heavenly  bodies,  at  rising  and  setting,  for  various  latitudes  and 
declinations,  computed  by  the  formula: 

sin  amp.=8ec  Lat  Xsin  dec. 

It  is  entered  with  the  declination  at  the  top  and  the  latitude  at  the  side. 
Its  use  is  explained  in  article  358,  Chapter  XIV. 

TABLE  40:  COBBECTION  FOB  AMPLITUDES. 

This  table  gives  a  correction  to  be  applied  to  the  observed  amplitude  to  counteract  the  vertical 
displacement  due  to  refraction,  parallax,  and  dip,  when  the  body  is  observed  with  its  center  in  the 
visible  horizon. 

The  correction  is  to  be  applied  for  the  sun,  a  planet,  or  a  star,  as  follows: 

"^^  tSginl.  ^t  }^PP»y  ^b«  '^o"^*^^"  t°  ^^«  "g^*- 

^^^ttlnl/nl:  i2t  }*ppiy  *h«  «*>"««««°  ^  *^«  i«^*- 

For  the  moon,  apply  half  the  correction  in  the  contrary  manner. 

TABLE  41:  NATUBAL  SINES  AND  COSINES. 

This  table  contains  the  natural  sine  and  cosine  for  every  minute  of  the  quadrant,  and  is  to  be 
entered  at  the  top  or  bottom  with  the  degrees,  and  at  the  side  marked  M.,  with  the  minutes;  the 
corresponding  numbers  will  be  the  natural  sine  and  cosine,  respectively,  observing  that  if  the  degrees 
are  found  at  the  top,  the  name  sine,  cosine,  and  M.  must  also  be  found  at  the  top,  and  the  contrary  if 
the  degrees  are  found  at  the  bottom.  It  should  be  understood  that  all  numbers  given  in  the  table 
should  be  divided  by  100,000 — that  is,  pointed  off  to  contain  five  decimal  places.  Thus,  .43366  is  the 
natural  sine  of  25°  42'',  or  the  cosine  of  64°  18'. 

In  the  outer  columns  of  the  margin  are  given  tables  of  proportional  parts,  for  the  purpose  of  finding, 
approximately,  by  inspection,  the  proportional  part  corresponding  to  any  number  of  seconds  in  the 
proposed  angle,  the  seconds  being  found  in  the  marginal  column  marked  M.,  and  the  correction  in 
the  adjoining  column.  Thus,  if  we  suppose  that  it  were  required  to  find  tlie  natural  sine  corresponding 
to  25°  42'  W^,  the  difference  of  the  sines  of  25°  42'  and  25°  43'  is  26,  being  the  same  as  at  the  top  of  the 
left-hand  column  of  the  table;  and  in  this  column,  and  opposite  19  in  the  column  M.,  is  the  correc- 
tion 8.  Adding  this  to  the  above  number  .43366,  because  the  numbers  are  increasing,  we  get  .43374  for 
the  sine  of  25°  42'  19".  In  like  manner,  we  find  the  cosine  of  the  same  angle  to  be  .90108— 4=. 90104, 
using  the  right-hand  columns,  and  subtracting  hecauae  the  numbers  are  decreasing;  observing,  however, 
that  the  number  14  at  the  top  of  this  column  varies  1  from  the  difference  between  the  cosines  of  25°  42' 
and  25°  43',  which  is  only  13;  so  that  the  table  may  give  in  some  cases  a  unit  too  much  between  the 
angles  25°  42' and  25°  43';  but  this  is,  in  general,  of  but  little  importance,  and  when  accuracy  is  required, 
the  usual  method  of  proportional  parts  is  to  be  resorted  to,  using  the  actual  tabular  difference. 

TABLE  42:  LOGABITHMS  OP  NUMBEBS. 

This  table,  containing  the  common  logarithms  of  numbers,  was  compared  with  Sherwin's,  Hutton's, 
and  Taylor's  logarithms;  its  use  is  explained  in  an  article  on  Logarithms  in  Appendix  III. 

TABLE  43:  LOGABITHMS  OF  TBIGONOMETBIC  FUNCTIONS,  QUABTEB  POINTS. 

This  table  contains  the  logarithms  of  the  sines,  tangents,  etc.,  corresponding  to  points  and  quarter 
points  of  the  compass.     This  was  compared  with  Sherwin's,  Hutton's,  and  Taylor's  logarithms. 

21594°— 14 26 


514  EXPLANATION   OF   THE   TABLES. 

TABLE  44:  LOaARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,  DEGREES. 

This  table  contains  the  common  logarithms  of  the  sines,  tangents,  secants,  etc.  It  was  compared 
with  Sherwin's,  Hutton's,  and  Taylor's  tables.  Two  additional  columns  are  given  in  this  table,  which 
are  very  convenient  in  finding  the  time  from  an  altitude  of  the  sun;  also,  three  columns  of  proportional 
parts  for  seconds  of  space,  and  a  small  table  at  the  bottom  of  each  page  for  finding  the  proportional  parts 
for  seconds  of  time.  The  degrees  are  marked  to  180°,  which  saves  the  trouble  of  subtracting  the  given 
angle  from  180°  when  it  exceeds  90°. 

The  use  of  this  table  is  fully  explained  in  Appendix  III  in  an  article  on  Logarithms. 

TABLE  45:  LOGARITHMIC  AND  NATURAL  HAVERSINES. 

The  haversine  is  defined  by  the  following  relation: 

hav.  A=^  vers.  A=K1— cos  A)=sin2  ^A. 

It  is  a  trigonometric  function  which  simplifies  the  solution  of  many  problems  in  nautical  astronomy 
as  well  as  in  plane  trigonometry.  To  afford  the  maximum  facility  in  carrying  out  the  processes  of 
solution,  the  values  of  the  natural  haversine  and  its  logarithm  are  set  down  together  in  a  single  table 
for  all  values  of  angle  ranging  from  0°  to  360°,  expressed  both  in  arc  and  in  time. 

TABLE  46:  CORRECTIONS  TO  BE  APPLIED  IN  ORDER  TO  FIND  THE  TRUE  ALTI- 
TUDE OF  A  STAR  AND  ALSO  OF  THE  SUN  FROM  THE  OBSERVED  ALTITUDE 
ABOVE  THE  HORIZON. 

This  is  a  consolidated  table  in  which  the  tabulated  correction  for  an  observed  altitude  of  a  star 
combines  the  mean  refraction  and  the  dip,  and  that  for  an  observed  altitude  of  the  sun's  lower  limb 
combines  the  mean  refraction,  the  dip,  the  parallax,  and  the  mean  semidiameter,  which  is  taken  as 
16''.  A  supplementary  table  at  the  foot  of  the  main  table  takes  account  of  the  variation  of  the  sun's 
semidiameter  in  the  different  months  of  the  year. 

TABLE  47:  THE  LONGITUDE  FACTOR. 

The  change  in  longitude  due  to  a  change  of  V  in  latitude,  called  the  longitude  factor,  F,  is  given  in 
this  table  at  suitable  intervals  of  latitude  and  azimuth.  The  quantities  tabulated  are  computed  from 
the  formula — 

F=sec.  Lat.  Xcot.  Az. 

When  a  time  sight  is  solved  with  a  dead-reckoning  latitude,  the  resulting  longitude  is  only  true 
if  the  latitude  be  correct.  This  table,  by  setting  forth  the  number  of  minutes  of  longitude  due  to  each 
minute  of  error  in  latitude,  gives  the  means  of  finding  the  correction  to  the  longitude  for  any  error  that 
may  subsequently  be  disclosed  in  the  latitude  used  in  the  calculation. 

Regarding  the  azimuth  of  the  observed  celestial  body  as  less  than  90°  and  as  measured  from  either 
the  North  or  the  South  point  of  the  horizon  towards  East  or  West,  the  rule  for  determining  whether  the 
correction  in  longitude  is  to  be  applied  to  the  eastward  or  to  the  westward  will  be  as  follows:  If  the 
change  in  latitude  is  of  the  same  name  as  the  first  letter  of  the  bearing,  the  change  in  longitude  is  of  the 
contrary  name  to  that  of  the  second  letter,  and  vice  versa. 

Thus,  if  the  body  bears  S.  45°  E.  and  the  change  in  latitude  is  to  the  southward,  the  change  in 
longitude  will  be  to  the  westward;  and,  if  the  change  in  latitude  is  to  the  northward,  the  change  in 
longitude  will  be  to  the  eastward. 

The  convenient  application  of  the  longitude  factor  in  finding  the  intersection  of  Sumner  lines  is 
explained  in  article  389. 

TABLE  48:  THE  LATITUDE  FACTOR. 

The  change  in  latitude  due  to  a  change  of  V  in  the  longitude,  called  the  latitude  factor,  f,  is  given 
in  this  table  at  suitable  intervals  of  latitude  and  azimuth.  The  quantities  tabulated,  being  the  reciprocals 
of  the  values  of  the  longitude  factor,  are  computed  from  the  formula — 

^=F=sec.  Lat.Xcot.Az.==^««-  Lat.Xtan.  Az. 

When  an  ex-meridian  sight  is  solved  with  a  longitude  afterwards  found  to  be  in  error,  this  table,  by 
setting  forth  the  number  of  minutes  of  latitude  due  to  each  V  of  error  in  longitude,  gives  the  means 
of  finding  the  correction  in  the  latitude  for  the  amount  of  error  in  the  longitude  used  in  the  calculation. 

Regarding  the  azimuth  of  the  observed  celestial  body  as  less  than  90°  and  as  measured  from  either 
tiie  North  or  the  South  point  of  the  horizon  towards  East  or  West,  the  rule  for  determining  whether  the 
correction  in  latitude  is  to  be  applied  to  the  northward  or  to  the  southward  is  as  follows:  If  the  change 
in  longitude  ia  of  the  same  name  as  the  second  letter  of  the  bearing,  the  change  in  latitude  is  of  the 
contrary  name  to  the  first  letter,  and  vice  versa.  Thus,  if  the  body  bears  S.  14°  E.  and  the  change  in 
longitude  ia  to  the  westward,  the  change  in  latitude  will  be  to  the  southward,  and,  if  the  change  in 
longitude  is  to  the  eastward,  the  change  in  latitude  will  be  to  the  northward. 

The  convenient  application  of  the  latitude  factor  in  finding  the  intersection  of  Sumner  lines  is 
explained  in  article  390. 


TABLE  1. 

[Page  516    | 

Difference  of  Latitude  and  Departure  for  J  Point. 

N.  JE. 

N.  i  W. 

S.  iE. 

S.  \W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61 

60.9 

3.0 

121 

120.9 

5.9 

181 

180,8 

8.9 

241 

240.7 

11,8 

2 

2.0 

0.1 

62 

61.9 

3.0 

22 

121.9 

6.0 

82 

181.8 

8.9 

42 

241.7 

11.9 

3 

3.0 

0.1 

63 

62.9 

3.1 

23 

122.9 

6.0 

83 

182.8 

9.0 

43 

242.7 

11.9 

4 

4.0 

0.2 

64 

63.9 

3.1 

24 

123.9 

6.1 

84 

183.8 

9.0 

44 

243.7 

12.0 

5 

5.0 

0.2 

65 

64.9 

3.2 

25 

124.8 

6.1 

85 

184.8 

9.1 

45 

244.7 

12.0 

6 

6,0 

0.3 

66 

65.9 

3.2 

26 

125.8 

6.2 

86 

185.8 

9.1 

46 

245.7 

12.1 

7 

7.0 

0.3 

67 

66.9 

3.3 

27 

126.8 

6.2 

87 

186.8 

9.2 

47 

246.7 

12.1 

8 

8.0 

0.4 

68 

67.9 

3.3 

28 

127.8 

6.3 

88 

187.8 

9.2 

48 

247.7 

12.2 

9 

9.0 

0.4 

69 

68.9 

3.4 

29 

128.8 

6.3 

89 

188.8 

9.3 

49 

248.7 

12.2 

10 

10.0 

0.5 

70 

69.9 

3.4 

30 

129.8 

6.4 

90 

189.8 

9.3 

50 

249.7 
250.7 

12.3 

11 

11.0 

0.5 

71 

70.9 

3.5 

131 

130.8 

6.4 

191 

190.8 

9.4 

251 

12.3 

12 

12.0 

0.6 

72 

71.9 

3.5 

32 

131.8 

6.5 

92 

191.8 

9.4 

52 

251.7 

12,4 

13 

13.0 

0.6 

73 

72.9 

3.6 

33 

132.8 

6,5 

93 

192.8 

9.5 

53 

252.7 

12,4 

14 

14.0 

0.7 

74 

73.9 

3.6 

34 

133.8 

6.6 

94 

193.8 

9.5 

54 

253.7 

12,5 

15 

15.0 

0.7 

75 

74.9 

3.7 

35 

134.8 

6.6 

95 

194.8 

9.6 

55 

254.7 

12.5 

16 

16.0 

0.8 

76 

75.9 

3.7 

36 

135.8 

6.7 

96 

195.8 

9.6 

56 

255.7 

12.6 

17 

17.0 

0.8 

77 

76.9 

3.8 

37 

136.8 

6.7 

97 

196.8 

9.7 

57 

256.7 

12.6 

18 

18.0 

0.9 

78 

77.9 

3.8 

38 

137.8 

6.8 

98 

197.8 

9.7 

58 

257.7 

12.7 

19 

19.0 

0.9 

79 

78.9 

3.9 

39 

138.8 

6.8 

99 

198.8 

9.8 

59 

258.7 

12.7 

20 

20.0 

1.0 

80 

79.9 
80.9 

3.9 
4.0 

40 
141 

139.8 

6.9 

200 

199.8 

9.8 

60 

259.7 
260.7 

12.8 
12.8 

21 

21.0 

1.0 

81 

140.8 

6.9 

201 

200.8 

y.9 

261 

22 

22.0 

1.1 

82 

81.9 

4.0 

42 

141.8 

7.0 

02 

201.8 

9.9 

62 

261.7 

12.9 

23 

23.0 

1.1 

83 

82.9 

4.1 

43 

142.8 

7.0 

03 

202.8 

10.0 

63 

262.7 

12.9 

24 

24.0 

1.2 

84 

83.9 

4.1 

44 

143.8 

7.1 

04 

20.3.8 

10.0 

64 

263.  7 

13.0 

25 

25.0 

1.2 

85 

84.9 

4.2 

45 

144.8 

7.1 

05 

204.8 

10.1 

65 

264.7 

13.0 

26 

26.0 

1.3 

86 

85.9 

4.2 

46 

145.8 

7.2 

06 

205.8 

10.1 

66 

265.7 

1.3.1 

27 

27.0 

1.3 

87 

86.9 

4.3 

47 

146.8 

7.2 

07 

206.8 

10.2 

67 

266.7 

13.1 

28 

28.0 

1.4 

88 

87.9 

4.3 

48 

147.8 

7.3 

08 

207.7 

10.2 

68 

267.7 

13.2 

29 

29.0 

1.4 

89 

88.9 

4.4 

49 

148.8 

7.3 

09 

208.7 

10.3 

69 

268.7 

13.2 

30 
31 

30.0 
31.0 

1.5 

90 

89.9 

4.4 

50 

149.8 

7.4 
7.4 

10 

209.7 

10.3 

70 

269.7 

13,2 

1.5 

91 

90.9 

4.5 

151 

150.8 

211 

210.7 

10.4 

271 

270.7 

13,3 

32 

32.0. 

1.6 

92 

91.9 

4.5 

52 

151.8 

7.5 

12 

211.7 

10.4 

72 

271.7 

13,3 

33 

33.0 

1.6 

93 

92.9 

4,6 

53 

152.8 

7.5 

13 

212.7 

10.5 

73 

272.7 

13,4 

34 

34.0 

1.7 

94 

93.9 

4.6 

54 

153.8 

7.6 

14 

213.7 

10.5 

74 

273.  7 

13.4 

35 

35.0 

1.7 

95 

94.9 

4.7 

55 

154.8 

7,6 

15 

214.7 

10.5 

75 

274.  7 

13.5 

36 

36.0 

1.8 

96 

95.9 

4,7 

56 

155.8 

7.7 

16 

215.7 

10.6 

76 

275.  7 

13.5 

37 

37.0 

1.8 

97 

96.9 

4,8 

57 

156.8 

7,7 

17 

216.7 

10.6 

77 

276.7 

13.6 

38 

38.0 

1.9 

98 

97.9 

4.8 

58 

157.8 

7,8 

18 

217.7 

10.7 

78 

277.7 

13.6 

39 

39.0 

1.9 

99 

98.9 

4.9 

59 

158.8 

7.8 

19 

218.7 

10.7 

79 

278.7 

13.7 

40 

40.0 

2.0 

100 

99.9 

4,9 

60 

159.8 

7.9 

20 

219.7 

10.8 

80 

279.7 
280.7 

13.7 

41 

41.0 

2.0 

101 

100.9 

5,0 

161 

160.8 

7.9 

221 

220.7 

10.8 

281 

13.8 

42 

41.9 

2.1 

02 

101.9 

5,0 

62 

161.8 

7.9 

22 

221.7 

10.9 

82 

281.7 

13.8 

43 

42.9 

2.1 

03 

102.9 

5,1 

63 

162.8 

8.0 

23 

222.7 

10.9 

83 

282.7 

13.9 

44 

43.9 

2.2 

04 

103.9 

5.1 

64 

163.8 

8.0 

24 

223.7 

11.0 

84 

283.7 

13.9 

45 

44.9 

2.2 

05 

104.9 

5.2 

65 

164.8 

8.1 

25 

224.7 

11.0 

85 

284.7 

14.0 

46 

45.9 

2.3 

06 

105.9 

5.2 

66 

165.8 

8.1 

26 

225.  7 

11.1 

86 

285.7 

14.0 

47 

46.9 

2.3 

07 

106.9 

5.3 

67 

166.8 

8.2 

27 

226.7 

11.1 

87 

286.7 

14.1 

48 

47.9 

2.4 

08 

107.9 

5.3 

68 

167.8 

8.2 

28 

227.7 

11.2 

88 

287.7 

14.1 

49 

48.9 

2.4 

09 

108.9 

5.3 

69 

168.8 

8.3 

29 

228.7 

11.2 

89 

288.7 

14.2 

50 

49.9 

2.5 

10 

109.9 

5.4 

70 

169.8 

8.3 

30 

229.7 

11.3 

90 

289.7 

14.2 

51 

50.9 

2.5 

111 

110.9 

5.4 

171 

170.8 

8.4 

231 

230.7 

11.3 

291 

290.6 

14.3 

52 

51.9 

2.6 

12 

111.9 

5.5 

72 

171.8 

8.4 

32 

231.  7 

11.4 

92 

291.6 

14.3 

53 

52.9 

2.6 

13 

112.9 

5.5 

73 

172.8 

8.5 

33 

232.7 

11.4 

93 

292.6 

14.4 

54 

53.9 

2.6 

14 

113.9 

5.6 

74 

173.8 

8.5 

34 

233.  7 

11.5 

94 

293.6 

14.4 

55 

54.9 

2.7 

15 

114.9 

5.6 

75 

174.8 

8.6 

35 

234.7 

11.5 

95 

294.6 

14.5 

56 

55.9 

2.7 

16 

115.9 

5.7 

76 

175.  8 

8.6 

36 

235.7 

11.6 

96 

295.  6 

14.5 

57 

56.9 

2.8 

17 

116.9 

5.7 

77 

176.8 

8.7 

37 

236,7 

11.6 

97 

296.6 

14.6 

58 

57.9 

2.8 

18 

117.9 

5.8 

78 

177.8 

8.7 

38 

237,7 

11.7 

98 

297.6 

14.6 

59 

58.9 

2.9 

19 

118.9 

5.8 

79 

178.8 

8.8 

39 

238,7 

11.7 

99 

298.6 

14.7 

60 

59.9 

2.9 

20 

119.9 

5.9 

80 

179.8 

8.8 

40 

239.7 

11.8 

300 

299.6 

14.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

I^t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E. 

iN. 

E.  iS 

W.  iN. 

W.  \  S, 

[Fc 

)r  7i  Po 

ints. 

Page  616] 

TABLE  1. 

Difference  of  Latitude  and 

Depart 

ure  for  J  Point. 

N.  JE. 

N.  ^W. 

S.  iE. 

S.  i  w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.7 

6.0 

121 

120.4 

11.9 

181 

180.1 

17.7 

241 

239.8 

23.6 

2 

2.0 

0.2 

62 

61.7 

6.1 

22 

121.4 

12.0 

82 

181.1 

17.8 

42 

240.8 

23.7 

3 

3.0 

0.3 

63 

62.7 

6.2 

23 

122.4 

12.1 

83 

182.1 

17.9 

43 

241.8 

23.8 

4 

-    4.0 

0.4 

64 

63.7 

6.3 

24 

123.4 

12.2 

84 

183.1 

18.0 

44 

242.8 

23.9 

5 

5.0 

0.5 

65 

64.7 

6.4 

25 

124.4 

12.3 

85 

184.1 

18.1 

45 

243.8 

24.0 

6 

6.0 

0.6 

66 

65.7 

6.5 

26 

125.4 

12.4 

86 

185.1 

18.2 

46 

244.8 

24.1 

7 

7.0 

0.7 

67 

66.7 

6.6 

27 

126.4 

12.4 

87 

186.1 

18.3 

47 

245.8 

24.2 

8 

8.0 

0.8 

68 

67.7 

6.7 

28 

127.4 

12.5 

88 

187.1 

18.4 

48 

246.8 

24.3 

9 

9.0 

0.9 

69 

68.7 

6.8 

29 

128.4 

12.6 

89 

188.1 

18.5 

49 

247.8 

24.4 

10 

10.0 

1.0 

1.1 

70 
71 

69.7 
70.7 

6.9 

30 

129.4 

12.7 

90 

189.1 

18.6 

50 

248.8 

24.5 

11 

10.9 

7.0 

131 

130.4 

12.8 

191 

190.1 

18.7 

251 

249.8 

24.6 

12 

11.9 

1.2 

72 

71.7 

7.1 

32 

131.4 

12.9 

92 

191.1 

18.8 

52 

250.8 

24.7 

13 

12.9 

1.3 

73 

72.6 

7.2 

33 

132.4 

13.0 

93 

192.1 

18.9 

53 

251. 8 

24.8 

14 

13.9 

1.4 

74 

73.6 

7.3 

34 

133.4 

13.1 

94 

193.1 

19.0 

54 

252.8 

24.9 

15 

14.9 

1.5 

75 

74.6 

7.4 

35 

134.3 

13.2 

95 

194.1 

19.1 

55 

253.8 

25.0 

16 

15.9 

1.6 

76 

75.6 

7.4 

36 

135.3 

13.3 

96 

195.1 

19.2 

56 

254.8 

25.1 

17 

16.9 

1.7 

77 

76.6 

7.5 

37 

136.3 

13.4 

97 

196.1 

19.3 

57 

255.8 

25.2 

18 

17.9 

1.8 

78 

77.6 

7.6 

38 

137.3 

13.5 

98 

197.0 

19.4 

58 

256.8 

25.3 

19 

18.9 

1.9 

79 

78.6 

7.7 

39 

138.3 

13.6 

99 

198.0 

19.5 

59 

257.8 

25.4 

20 

19.9 

2.0 

80 

79.6 

7.8 

40 

139.3 

13.7 

200 

199.0 

19.6 

60 

258.7 

25.5 

21 

20.9 

2.1 

81 

80.6 

7.9 

141 

140.3 

13.8 

201 

200.0 

19.7 

261 

259.7 

25.6 

22 

21.9 

2.2 

82 

81.6 

8.0 

42 

141.3 

13.9 

02 

201.0 

19.8 

62 

260.7 

25.7 

23 

22.9 

2.3 

83 

82.6 

8.1 

43 

142.3 

14.0 

03 

202.0 

19.9 

63 

261.7 

25.8 

24 

23.9 

2.4 

84 

83.6 

8.2 

44 

143.3 

14.1 

04 

203.0 

20.0 

64 

262.7 

25.9 

25 

24.9 

2.5 

85 

84.6 

8.3 

45 

144.3 

14.2 

05 

204.0 

20.1 

65 

263.7 

26.0 

26 

25.9 

2.5 

86 

85.6 

8.4 

46 

145.3 

14.3 

06 

205.0 

20.2 

66 

264.7 

26.1 

27 

26.9 

2.6 

87 

86.6 

8.5 

47 

146.3 

14.4 

07 

206.0 

20.3 

67 

265.7 

26.2 

28 

27.9 

2.7 

88 

87.6 

8.6 

48 

147.3 

14.5 

08 

207.0 

20.4 

68 

266.7 

26.3 

29 

28.9 

2.8 

89 

88.6 

8.7 

49 

148. 3 

14.6 

09 

208.0 

20.5 

69 

267.7 

26.4 

30 

29.9 

2.9 

90 

89.6 
90.6 

8.8 

50 

149.3 

14.7 

10 

209.0 

20.6 

70 

268.7 

26.5 

31 

30.9 

3.0 

91 

8.9 

151 

150.3 

14.8 

211 

210.0 

20.7 

271 

269.7 

26.6 

32 

31.8 

3.1 

92 

91.6 

9.0 

52 

151.3 

14.9 

12 

211.0 

20.8 

72 

270.7 

26.7 

33 

32.8 

3.2 

93 

92.6 

9.1 

53 

152.3 

15.0 

13 

212.0 

20.9 

73 

271.7 

26.8 

34 

33.8 

3.3 

94 

93.5 

9.2 

54 

153.3 

15.1 

14 

213.0 

21.0 

74 

272.7 

26.9 

35 

34.8 

3.4 

95 

94.5 

9.3 

55 

154.3 

15.2 

15 

214.0 

21.1 

75 

273.7 

27.0 

36 

35.8 

3.5 

96 

95.5 

9.4 

56 

155.2 

15.3 

16 

215.0 

21.2 

76 

274.7 

27.1 

37 

36.8 

3.6 

97 

96.5 

9.5 

57 

156.2 

15.4 

17 

216.0 

21.3 

77 

275.7 

27.2 

38 

37.8 

3.7 

98 

97.5 

9.6 

58 

157.2 

15.5 

18 

217.0 

21.4 

78 

276.7 

27.2 

39 

38.8 

3.8 

99 

98.5 

9.7 

59 

158.2 

15.6 

19 

217.9 

21.5 

79 

277.7 

27.3 

40 

39.8 

3.9 

100 

99.5 

9,8 

60 

159.2 

15.7 

20 

218.9 

21.6 

80 

278.7 

27.4 

41 

40.8 

4.0 

101 

100.5 

9.9 

161 

160.2 

15.8 

221 

219.9 

21.7 

281 

279.6 

27.5 

42 

41.8 

4.1 

02 

101.5 

10.0 

62 

161.2 

15.9 

22 

220.9 

21.8 

82 

280.6 

27.6 

43 

42.8 

4.2 

03 

102.5 

10.1 

63 

162.2 

16.0 

23 

221.9 

21.9 

83 

281.6 

27.7 

44 

43.8 

4.3 

04 

103.5 

10.2 

64 

163.2 

16.1 

24 

222.9 

22.0 

84 

282.6 

27.8 

45 

44.8 

4.4 

05 

104.5 

10.3 

65 

164.2 

16.2 

25 

223.9 

22.1 

85 

283.6 

27.9 

46 

45.8 

4.5 

06 

105.5 

10.4 

66 

165.2 

16.3 

26 

224.9 

22.2 

86 

284.6 

28.0 

47 

46.8 

4.6 

07 

106.5 

10.5 

67 

166.2 

16.4 

27 

225.9 

22.2 

87 

285.6 

28.1 

48 

47.8 

4.7 

08 

107.5 

10.6 

68 

167.2 

16.5 

28 

226.9 

22.3 

88 

286.6 

28.2 

49 

48.8 

4.8 

09. 

108.5 

10.7 

69 

168.2 

16.6 

29 

227.9 

22.4 

89 

287.6 

28.3 

50 

49.8 

4.9 

10 

109.5 

10.8 

70 

169.2 

16.7 

30 

228.9 

22.5 

90 

288.6 

28.4 
28.5 

51 

50.8 

5.0 

111 

110.5 

10.9 

171 

170.2 

16.8 

231 

229.9 

22.6 

291 

289.6 

52 

51.7 

5.1 

12 

111.5 

11.0 

72 

171.2 

16.9 

32 

230.9 

22.7 

92 

290.6 

28.6 

53 

52.7 

5.2 

13 

112.5 

11.1 

73 

172.2 

17.0 

33 

231.9 

22.8 

93 

291.6 

28.7 

54 

53.7 

5.3 

14 

113.5 

11.2 

74 

173.2 

17.1 

34 

232.9 

22.9 

94 

292.6 

28.8 

55 

54.7 

5.4 

15 

114.4 

11.3 

75 

174.2 

17.2 

35 

233.9 

23.0 

95 

293.6 

28.9 

56 

55.7 

5.5 

16 

115.4 

11.4 

76 

175.2 

17.3 

36 

234.9 

23.1 

96 

294.6 

29.0 

57 

56.7 

5.6 

17 

116.4 

11.5 

77 

176.1 

17.3 

37 

235.9 

23.2 

97 

295.6 

,29.1 

58 

57.7 

5.7 

18 

117.4 

11.6 

78 

177.1 

17.4 

38 

236.9 

23.3 

98 

296.6 

29.2 

59 

58.7 

5.8 

19 

118.4 

11.7 

79 

178.1 

17.5 

39 

237.8 

23.4 

99 

297.6 

29.3 

60 

59.7 

5.9 

20 

119.4 

11.8 

80 

179.1 

17.6 

40 

238.8 

23.5 

300 

298.6 

29.4 

Dist. 

Dep. 

Lat. 

Di8t. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  JN. 

E.  JS. 

W.  JN 

WJS. 

"liv 

)r  7i  Po 

nts. 

TABLE  1. 

[Page 

617 

Difference  of  Latitude  and  Departure  for  J  Point. 

^T.  }E. 

N.  |W 

• 

S.  1  E. 

S.  fW 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.3 

9.0 

121 

119.7 

17.8 

181 

179.0 

26.6 

241 

238.4 

35.4 

2 

2.0 

0.3 

62 

61.3 

9.1 

22 

120.7 

17.9 

82 

180.0 

26.7 

42 

239.4 

35.5 

3 

3.0 

0.4 

63 

62.3 

9.2 

23 

121.7 

18.0 

83 

181.0 

26.9 

43 

240.4 

35.7 

4 

4.0 

0.6 

64 

63.3 

9.4 

24 

122.7 

18.2 

84 

182.0 

27.0 

44 

241.4 

35.8 

5 

4.9 

0.7 

65 

64.3 

9.5 

25 

123.6 

18.3 

85 

183.0 

27.1 

45 

242.3 

35.9 

6 

5.9 

0.9 

66 

65.3 

9.7 

26 

124.6 

18.5 

86 

184.0 

27.3 

46 

243.3 

36.1 

7 

6.9 

1.0 

67 

66.3 

9.8 

27 

125.6 

18.6 

87 

185.0 

27.4 

47 

244.3 

36.2 

8 

7.9 

1.2 

68 

67.3 

10.0 

28 

126.6 

18.8 

88 

186.0 

27.6 

48 

245.3 

36.4 

9 

8.9 

1.3 

69 

68.3 

10.1 

29 

127.6 

18.9 

89 

187.0 

27.7 

49 

246.3 

36.5 

10 

9.9 

1.5 
1.6 

70 
71 

69.2 

10.3 

30 

128.6 

19.1 

90 

187.9 

27.9 

50 

247.3 

36.7 

11 

10.9 

70.2 

10.4 

131 

129.6 

19.2 

191 

188.9 

28.0 

251 

248.3 

36.8 

12 

11.9 

1.8 

72 

71.2 

10.6 

32 

130.6 

19.4 

92 

189.9 

28.2 

52 

249.3 

37.0 

13 

12.9 

1.9 

73 

72.2 

10.7 

33 

131.6 

19.5 

93 

190.9 

28.3 

53 

250.3 

37.1 

14 

13.8 

2.1 

74 

73.2 

10.9 

34 

132.5 

19.7 

94 

191.9 

28.5 

54 

251.3 

37.3 

15 

14.8 

2.2 

75 

74.2 

11.0 

35 

133.5 

19.8 

95 

192.9 

28.6 

55 

252.2 

37.4 

16 

15.8 

2.3 

76 

75.2 

11.2 

36 

134.5 

20.0 

96 

193.9 

28.8 

.16 

253.2 

37.6 

17 

16.8 

2.5 

77 

76.2 

11.3 

37 

135.5 

20.1 

97 

194.9 

28.9 

57 

254.2 

37.7 

18 

17.8 

2.6 

78 

77.2 

11.4 

38 

136.5 

20.2 

98 

195.9 

29.1 

58 

255.2 

37.9 

19 

18.8 

2.8 

79 

78.1 

11.6 

39 

137.  5 

20.4 

99 

196.8 

29.2 

59 

256.2 

38.0 

20 

19.8 

2.9 

80 

79.1 

11.7 

40 

138.5 

20.5 

200 

197.8 

29.3 

60 

257.2 

38.1 

21 

20.8 

3.1 

81 

80.1 

11.9 

"141 

139.5 

20.7 

201 

198.8 

29.5 

261 

258.2 

38.3 

22 

21.8 

3.2 

82 

81.1 

12.0 

42 

140.5 

20.8 

02 

199.8 

29.6 

62 

259.2 

38.4 

23 

22.8 

3.4 

83 

82.1 

12.2 

43 

141.5 

21.0 

03 

200.8 

29.8 

63 

260.2 

38.6 

24 

23.7 

3.5 

84 

83.1 

12.3 

44 

142.4 

21.1 

04 

201.8 

29.9 

64 

261.1 

38.7 

25 

24.7 

3.7 

85 

84.1 

12.5 

45 

143.4 

21.3 

05 

202.8 

30.1 

65 

262.1 

38.9 

26 

25.7 

3.8 

86 

85.1 

12.6 

46 

144.4 

21.4 

06 

203.8 

30.2 

66 

263.1 

39.0 

27 

26.7 

4.0 

87 

86.1 

12.8 

47 

145.4 

21.6 

07 

204.8 

30.4 

67 

264.1 

39.2 

28 

27.7 

4.1 

88 

87.0 

12.9 

48 

146.4 

21.7 

08 

205.7 

30.5 

68 

265.1 

39.3 

29 

28.7 

4.3 

89 

88.0 

13.1 

49 

147.4 

21.9 

09 

206.7 

30.7 

69 

266.1 

39.6 

30 

29.7 

4.4 
4.5 

90 
91 

89.0 

13.2 

50 

148.4 

22.0 

10 

207.7 

30.8 

70 

267.1 

39.6 
39.8 

31 

30.7 

90.0 

13.4 

151 

149.4 

22.2 

211 

208.7 

31.0 

271 

268.1 

32 

31.7 

4.7 

92 

91.0 

13.5 

52 

150.4 

22.3 

12 

209.7 

31.1 

72 

269.1 

39.9 

33 

32.6 

4.8 

93 

92.0 

13.6 

53 

151.3 

22.4 

13 

210.7 

31.3 

73 

270.0 

40.1 

34 

33.6 

5.0 

94 

93.0 

13.8 

54 

152.3 

22.6 

14 

211.7 

31.4 

74 

271.0 

40.2 

35 

34.6 

5.1 

95 

94.0 

13.9 

55 

153.3 

22.7 

15 

212.7 

31.5 

75 

272.0 

40.4 

36 

35.6 

5.3 

96 

95.0 

14.1 

56 

154.3 

22.9 

16 

213.7 

31.7 

76 

273.0 

40.5 

37 

36.6 

5.4 

97 

96.0 

14.2 

57 

155.3 

23.0 

17 

214.7 

31.8 

77 

274.0 

40.6 

38 

37.6 

5.6 

98 

96.9 

14.4 

58 

156.3 

23.2 

18 

215.6 

32.0 

78 

275. 0 

40.8 

39 

38.6 

5.7 

99 

97.9 

14.5 

59 

157.3 

23.3 

19 

216.6 

32.1 

79 

276.0 

40.9 

40 

39.6 

5.9 

100 

98.9 

14.7 

60 

158.3 

23.5 

20  1  217.6 

32.3 

80 

277.0 
278.0 

41.1 

41 

40.6 

6.0 

101 

99.9 

14.8 

161 

159.3 

23.6 

221 

218.6 

32.4 

281 

41.2 

42 

41.5 

6.2 

02 

100.9 

15.0 

62 

160.2 

23.8 

22 

219.6 

32.6 

82 

278.9 

41.4 

43 

42.5 

6.3 

03 

101.9 

15.1 

63 

161.2 

23.9 

23 

220.6 

32.7 

83 

279.9 

41.5 

44 

43.5 

6.5 

04 

102.9 

15.3 

64 

162.2 

24.1 

24 

221.6 

32.9 

84 

280.9 

41.7 

45 

44.5 

6.6 

05 

103.9 

15.4 

65 

163.2 

24.2 

25 

222.6 

33.0 

85 

281.9 

41.8 

46 

45.5 

6.7 

06 

104.9 

15.6 

66 

164.2 

24.4 

26 

223.6 

33.2 

86 

282.9 

42.0 

47 

46.5 

6.9 

07 

105.8 

15.7 

67 

165.2 

24.5 

27 

224.5 

33.3 

87 

283.9 

42,1 

48 

47.5 

7.0 

08 

106.8 

15.8 

68 

166.2 

24.7 

28 

225.5 

33.5 

88 

284.9 

42.3 

49 

48.5 

7.2 

09 

107.8 

16.0 

69 

167.2 

24.8 

29 

226.5 

33.6 

89 

285.9 

42.4 

50 

49.5 

7.3 

10 

108.8 

16.1 

70 

168.2 

24.9 

30 

227.5 

33.7 
33.9 

90 

286.9 

42.6 

51 

50.4 

7.5 

111 

109.8 

16.3 

171 

169.1 

25.1 

231 

228.5 

291 

287.9 

42.7 

52 

51.4 

7.6 

12 

110.8 

16.4 

72 

170.1 

25.2 

32 

229.5 

34.0 

92 

288.8 

42.8 

53 

52.4 

7.8 

13 

111.8 

16.6 

73 

171.1 

25.4 

33 

230.5 

34.2 

93 

289.8 

43.0 

54 

53.4 

7.9 

14 

112.8 

16.7 

74 

172.1 

25.5 

34 

231.5 

34.3 

94 

290.8 

43.1 

55 

54.4 

8.1 

15 

113.8 

16.9 

75 

173.1 

25.7 

35 

232.5 

34.5 

95 

291.8 

43.3 

56 

55.4 

8.2 

16 

114.7 

17.0 

76 

174.1 

25.8 

36 

233.4 

34.6 

96 

292.8 

43.4 

57 

56.4 

8.4 

17 

115.7 

17.2 

77 

175.1 

26.0 

37 

234.4 

34.8 

97 

293.8 

43.6 

58 

57.4 

8.5 

18 

116.7 

17.3 

78 

176.1 

26.1 

38 

235.4 

34.9 

98 

294.8 

43.7 

59 

58.4 

8.7 

19 

117.7 

17.5 

79 

177.1 

26.3 

39 

236. 4 

35.1 

99 

295.8 

43.9 

60 

59.4 

8.8 

20 

118.7 

17.6 

80 

178.1 

26.4 

40 

237.4 

35.2 

300 

296.8 

44.0 

Dist 

Dep. 

L«t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  JN 

E.  |S. 

W.  JN. 

W.  |S 

[For  7k  V 

ointa. 

Page  618] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  1  Point 

. 

N.  byE 

N.  by 

w. 

S.  by 

E. 

3.  by 

w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.8 

11.9 

121 

118.7 

23.6 

181 

177.5 

35.3 

241 

236.4 

47.0 

2 

2.0 

0.4 

62 

60.8 

12.1 

22 

119.7 

23.8 

82 

178.5 

35.5 

42 

237.4 

47.2 

3 

2.9 

0.6 

63 

61.8 

12.3 

23 

120.6 

24.0 

83 

179.5 

35.7 

43 

238.3 

47.4 

4 

3.9 

0.8 

64 

62.8 

12.5 

24 

121.6 

24.2 

84 

180.5 

35.9 

44 

239.3 

47.6 

5 

4.9 

1.0 

65 

63.8 

12.7 

25 

122.6 

24.4 

85 

181.4 

36.1 

45 

240.3 

47.8 

6 

5.9 

1.2 

66 

64.7 

12.9 

26 

123.6 

24.6 

86 

182.4 

36.3 

46 

241.3 

48.0 

7 

6.9 

1.4 

67 

65.7 

13.1 

27 

124.6 

24.8 

87 

183.4 

36.5 

47 

242.3 

48.2 

8 

7.8 

1.6 

68 

66.7 

13.3 

28 

125.5 

25.0 

88 

184.4 

36.7 

48 

243.2 

48.4 

9 

8.8 

1.8 

69 

67.7 

13.5 

29 

126.5 

25.2 

89 

185.4 

36.9 

49 

244.2 

48.6 

10 

9.8 

2.0 

70 

68.7 

13.7 

30 

127.5 

25.4 

90 

186.3 

37.1 

50 

245.2 

48.8 
49.0 

11 

10.8 

2.1 

71 

69.6 

13.9 

131 

128.5 

25.6 

191 

187.3 

37.3 

251 

246.2 

12 

11.8 

2.3 

72 

70.6 

14.0 

32 

129.5 

25.8 

92 

188.3 

37.5 

52 

247.2 

49.2 

13 

12.8 

2.5 

73 

71.6 

14.2 

33 

130.4 

25.9 

93 

189.3 

37.7 

53 

248.1 

49.4 

14 

13.7 

2.7 

74 

72.6 

14.4 

34 

131.4 

26.1 

94 

190.3 

37.8 

54 

249.1 

49.6 

15 

14.7 

2.9 

75 

73.6 

14.6 

35 

132.4 

26.3 

95 

191.3 

38.0 

55 

250.1 

49.7 

16 

15.7 

3.1 

76 

74.5 

14.8 

36 

133.4 

26.5 

96 

192.2 

38.2 

56 

251.1 

49.9 

17 

16.7 

3.3 

77 

75.5 

15.0 

37 

134.4 

26.7 

97 

193.2 

38.4 

57 

252.1 

50.1 

18 

17.7 

3.5 

78 

76.5 

15.2 

38 

135.3 

26.9 

98 

194.2 

38.6 

58 

253.0 

50.3 

19 

18.6 

3.7 

79 

77.5 

15.4 

39 

136.3 

27.1 

99 

195.2 

38.8 

59 

254.0 

50.5 

20 

19.6 

3.9 

80 

78.5 

15.6 

40 

137.3 

27.3 

200 

196.2 

39.0 

60 

255.0 

50.7 

21 

20.6 

4.1 

81 

79.4 

15.8 

141 

138.3 

27.5 

201 

197.1 

39.2 

261 

256.0 

50.9 

22 

21.6 

4.3 

82 

80.4 

16.0 

42 

139.3 

27.7 

02 

198.1 

39.4 

62 

257.0 

51.1 

23 

22.6 

4.5 

83 

81.4 

16.2 

43 

140.3 

27.9 

03 

199.1 

39.6 

63 

257.9 

51.3 

24 

23.5 

4.7 

84 

82.4 

16.4 

44 

141.2 

28.1 

04 

200.1 

39.8 

64 

258.9 

51.5 

25 

24.5 

4.9 

85 

83.4 

16.6 

45 

142.2 

28.3 

05 

201.1 

40.0 

65 

259.9 

51.7 

26 

25.5 

5.1 

86 

84.3 

16.8 

46 

143.2 

28.5 

06 

202.0 

40.2 

66 

260.9 

51.9 

27 

26.5 

5.3 

87 

85.3 

17.0 

47 

144.2 

28.7 

07 

203.0 

40.4 

67 

261.9 

52.1 

28 

27.5 

5.5 

88 

86.3 

17.2 

48 

145.2 

28.9 

08 

204.0 

40.6 

68 

262.9 

52.3 

29 

28.4 

5.7 

89 

87.3 

17.4 

49 

146.1 

29.1 

09 

205.0 

40.8 

69 

263.8 

52.5 

30 

29.4 

5.9 

90 

88.3 

17.6 

50 

147.1 

29.3 

10 

206.0 
206.9 

41.0 

70 

264.8 

52.7 

31 

30.4 

6.0 

91 

89.3 

17.8 

151 

148.1 

29.5 

211 

41,2 

271 

265.8 

52.9 

32 

31.4 

6.2 

92 

90.2 

17.9 

52 

149.1 

29.7 

12 

207.9 

41.4 

72 

266.8 

53.1 

33 

32.4 

6.4 

93 

91.2 

18.1 

53 

150.1 

29.8 

13 

208.9 

41.6 

73 

267.8 

53.3 

34 

33.3 

6.6 

94 

92.2 

18.3 

54 

151.0 

30.0 

14 

209.9 

41.7 

74 

268.7 

53.5 

35 

34.3 

6.8 

95 

93.2 

18.5 

55 

152.0 

30.2 

15 

210.9 

41.9 

75 

269.7 

53.6 

36 

35.3 

7.0 

96 

94.2 

18.7 

56 

153.0 

30.4 

16 

211.8 

42.1 

76 

270.7 

53.8 

37 

36.3 

7.2 

97 

95.1 

18.9 

57 

154.0 

30.6 

17 

212.8 

42.3 

77 

271.7 

54.0 

38 

37.3 

7.4 

98 

96.1 

19.1 

58 

155.0 

30.8 

18 

213.8 

42.5 

78 

272.7 

54.2 

39 

38.3 

7.6 

99 

97.1 

19.3 

59 

155.9 

31.0 

19 

214.8 

42.7 

79 

273.6 

54.4 

40 

39.2 

7.8 

100 

98.1 

19.5 

60 

156.9 

31.2 

20 

215.8 

42.9 

80 

274.6 
275.6 

54.6 

41 

40.2 

8.0 

101 

99.1 

19.7 

161 

157.9 

31.4 

221 

216.8 

43.1 

281 

54.8 

42 

41.2 

8.2 

02 

100.0 

19.9 

62 

158.9 

31.6 

22 

217.7 

43.3 

82 

276.6 

55.0 

43 

42.2 

8.4 

03 

101.0 

20.1 

63 

159.9 

31.8 

23 

218.7 

43.5 

83 

277.6 

55.2 

44 

43.2 

8.6 

04 

102.0 

20.3 

64 

160.8 

32.0 

24 

219.7 

43.7 

84 

278.5 

55.4 

45 

44.1 

8.8 

05 

103.0 

20.5 

65 

161.8 

32.2 

25 

220.7 

43.9 

85 

279.5 

55.6 

46 

45.1 

9.0 

06 

104.0 

20.7 

66 

162.8 

32.4 

26 

221.7 

44.1 

86 

280.5 

55.8 

47 

46.1 

9.2 

07 

104.9 

20.9 

67 

163.8 

32.6 

27 

222.6 

44.3 

87 

281.5 

56.0 

48 

47.1 

9.4 

08 

105.9 

21.1 

68 

164.8 

32.8 

28 

223.6 

44.5 

88 

282.5 

56.2 

49 

48.1 

9.6 

09 

106.9 

21.3 

69 

165.8 

33.0 

29 

224.6 

44.7 

89 

283.4 

56.4 

50 

49.0 

9.8 

10 

107.9 

21.5 

70 

166.7 

33.2 

30 

225.6 

44.9 

90 

284.4 

56.6 

51 

50.0 

9.9 

111 

108.9 

21.7 

171 

167.7 

33.4 

231 

226.6 

45.1 

291 

285.4 

56.8 

52 

51.0 

10.1 

12 

109.8 

21.9 

72 

168.7 

33.6 

32 

227.5 

45.3 

92 

286.4 

57.0 

53 

52.0 

10.3 

13 

110.8 

22.0 

73 

169.7 

33.8 

33 

228.5 

45.5 

93 

287.4 

57.2 

54 

53.0 

10.5 

14 

111.8 

22.2 

74 

170.7 

33.9 

34 

229.5 

45.7 

94 

288.4 

57.4 

55 

53.9 

10.7 

15 

112.8 

22.4 

75 

171.6 

34.1 

35 

230.5 

45.8 

95 

289.3 

57.6 

56 

54.9 

10.9 

16 

113.8 

22.6 

76 

172.6 

34.3 

36 

231.5 

46.0 

96 

290.3 

57.7 

57 

55.9 

11.1 

17 

114.8 

22.8 

77 

173.6 

34.5 

37 

232.4 

46.2 

97 

291.3 

57.9 

58 

56.9 

11.3 

18 

115.7 

23.0 

78 

174.6 

34.7 

38 

233.4 

46.4 

98 

292.3 

58.1 

59 

57.9 

11.5 

19 

116.7 

23.2 

79 

175.6 

34.9 

39 

234.4 

46.6 

99 

293.3 

58.3 

60 

58.8 

11.7 

20 

117.7 

23.4 

80 

176.5 

35.1 

40 

235.4 

46.8 

300 

294.2 

58.5 

DIst. 

|Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  by  N. 

E.  I 

)yS. 

W.  b> 

N. 

W.  byS 

3. 

1 

Tor  7  p 

oints. 

TABLE  1. 

[Page  619 

Difference  of  Latitude  and  Departure  for  li  Points. 

N. 

by  E.  i  E. 

N.  by  W.  i  W.               S.  by  E.  i  E.                S. 

by  W.  i  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.2 

14.8 

121 

117.4 

29.4 

181 

175.6 

44.0 

241 

233.8 

58.6 

2 

1.9 

0.5 

62 

60.1 

15.1 

22 

118.3 

29.6 

82 

176.5 

44.2 

42 

234.7 

58.8 

3 

2.9 

0.7 

63 

61.1 

15.3 

23 

119.3 

29.9 

83 

177.5 

44.5 

43 

235.7 

59.0 

4 

3.9 

1.0 

64 

62.1 

15.6 

24 

120.3 

30.1 

84 

178.5 

44.7 

44 

236.7 

59.3 

5 

4.9 

1.2 

65 

63.1 

15.8 

25 

121.3 

30.4 

85 

179.5 

45.0 

45 

237.7 

59.5 

6 

5.8 

1.5 

66 

64.0 

16.0 

26 

122.2 

30.6 

86 

180.4 

45.2 

46 

238.6 

59.8 

7 

6.8 

1.7 

67 

65.0 

16.3 

27 

123.2 

30.9 

87 

181.4 

45.4 

47 

239.6 

60.0 

8 

7.8 

1.9 

68 

66.0 

16.5 

28 

124.2 

31.1 

88 

182.4 

45.7 

48 

240.6 

60.3 

9 

8.7 

2.2 

69 

66.9 

16.8 

29 

125.1 

31.3 

89 

183.3 

45.9 

49 

241.5 

60.5 

10 
11" 

9.7 

2.4 

70 

67.9 

17.0 

30 

126.1 

31.6 

90 

184.3 

46.2 

50 

242.5 
243.5 

60.7 

10.7 

2.7 

71 

68.9 

17.3 

131 

127.1 

31.8 

191 

185.3 

46.4 

251 

61.0 

12 

11.6 

2.9 

72 

69.8 

17.5 

32 

128.0 

32.1 

92 

186.2 

46.7 

52 

244.4 

61.2 

13 

12.6 

3.2 

73 

70.8 

17.7 

33 

129.0 

32.3 

93 

187.2 

46.9 

53 

245.4 

61.5 

14 

13.6 

3.4 

74 

71.8 

18.0 

34 

130.0 

32.6 

94 

188.2 

47.1 

54 

246.4 

61.7 

15 

14.6 

3.6 

75 

72.8 

18.2 

35 

131.0 

32.8 

95 

189. 2 

47.4 

55 

247.4 

62.0 

16 

15.5 

3.9 

76 

73.7 

18.5 

36 

131.9 

33.0 

96 

190.1 

47.6 

56 

248.3 

62.2 

17 

16.5 

4.1 

77 

74.7 

18.7 

37 

132.9 

33.3 

97 

191.1 

47.9 

57 

249.3 

62.4 

18 

17.5 

4.4 

78 

75.7 

19.0 

38 

133.9 

33.5 

98 

192.1 

48.1 

58 

250.3 

62.7 

19 

18.4 

4.6 

79 

76.6 

19.2 

39 

134.8 

33.8 

99 

193.0 

48.4 

59 

251.2 

62.9 

20 

19.4 

4.9 

80 

77.6 

19.4 

40 

135.8 

34.0 

200 

194.0 

48.6 

60 
261 

252.2 

63.2 

21 

20.4 

5.1 

81 

78.6 

19.7 

141 

136.8 

34.3 

201 

195.0 

48.8 

253.2 

63.4 

22 

21.3 

5.3 

82 

79.5 

19.9 

42 

137.7 

34.5 

02 

195.9 

49.1 

62 

254.1 

63.7 

23 

22.3 

5.6 

83 

80.5 

20.2 

43 

138.7 

34.7 

03 

196.9 

49.3 

63 

255.1 

63.9 

24 

23.3 

5.8 

84 

81.5 

20.4 

44 

139.7 

35.0 

04 

197.9 

49.6 

64 

256.1 

64.1 

25 

24.3 

6.1 

85 

82.5 

20.7 

45 

140.7 

35.2 

05 

198.9 

49.8 

65 

257.1 

64.4 

26 

25.2 

6.3 

86 

83.4 

20.9 

46 

141.6 

35.5 

06 

199.8 

50.1 

66 

258.0 

64.6 

27 

26.2 

6.6 

87 

84.4 

21.1 

47 

142.6 

35.7 

07 

200.8 

50.3 

67 

259.0 

64.9 

28 

27.2 

6.8 

88 

85.4 

21.4 

48 

143.6 

36.0 

08 

201.8 

50.5 

68 

.260.0 

65.1 

29 

28.1 

7.0 

89 

86.3 

21.6 

49 

144.5 

36.2 

09 

202.7 

50.8 

69 

260.9 

65.4 

30 

29.1 

7.3 

90 

87.3 

21.9 

50 

145.5 

36.4 

10 

203.7 

51.0 

70 

261.9 

65.6 

31 

30.1 

7.5 

91 

88.3 

22.1 

151 

146.5 

36.7 

211 

204.7 

51.3 

271 

262.9 

65.8 

32 

31.0 

7.8 

92 

89.2 

22.4 

52 

147.4 

36.9 

12 

205.6 

51.5 

72 

263.8 

66.1 

33 

32.0 

8.0 

93 

90.2 

22.6 

53 

148.4 

37.2 

13 

206.6 

51.8 

73 

264.8 

66.3 

34 

33.0 

8.3 

94 

91.2 

22.8 

54 

149.4 

37.4 

14 

207.6 

52.0 

74 

265.8 

66.6 

36 

34.0 

8.5 

95 

92.2 

23.1 

55 

150.4 

37.7 

15 

208.6 

52.2 

75 

266.8 

66.8 

36 

34.9 

8.7 

96 

93.1 

23.3 

56 

151.3 

37.9 

16 

209.5 

52.5 

76 

267.7 

67.1 

37 

35.9 

9.0 

97 

94.1 

23.6 

57 

152.3 

38.1 

17 

210. 5 

52.7 

77 

268.7 

67.3 

38 

36.9 

9.2 

98 

95.1 

23.8 

58 

153. 3 

38.4 

18 

211.5 

53.0 

78 

269.7 

67.5 

39 

37.8 

9.5 

99 

96.0 

24.1 

59 

154.2 

38.6 

19 

212.4 

53.2 

79 

270.6 

67.8 

40 

38.8 

9.7 

100 

97.0 

24.3 

60 

155.2 

38.9 

20 

213.4 

53.5 

80 

271.6 

68.0 

41 

39.8 

10.0 

101 

98.0 

24.5 

161 

156.2 

39.1 

221 

214.4 

53.7 

281 

272.6 

68.3 

42 

40.7 

10.2 

02 

98.9 

24.8 

62 

157.1 

39.4 

22 

215.3 

63.9 

82 

273.5 

68.5 

43 

41.7 

10.4 

03 

99.9 

25.0 

63 

158.1 

39.6 

23 

216.3 

54.2 

83 

274.5 

68.8 

44 

42.7 

10.7 

04 

100.9 

25.3 

64 

159.1 

39.8 

24 

217.3 

54.4 

84 

275.5 

69.0 

45 

43.7 

10.9 

05 

101.9 

25.5 

65 

160.1 

40.1 

25 

218.3 

54.7 

85 

277.5 

69.2 

46 

44.6 

11.2 

06 

102.8 

25.8 

66 

161.0 

40.3 

26 

219.2 

54.9 

86 

277.4 

69.5 

47 

45.6 

11.4 

07 

103.8 

26.0 

67 

162.0 

40.6 

27 

220.2 

55.2 

87 

278.4 

69.7 

48 

46.6 

11.7 

08 

104.8 

26.2 

68 

163.0 

40.8 

28 

221.2 

56.4 

88 

279.4 

70.0 

49 

47.5 

11.9 

09 

105.7 

26.5 

69 

163.9 

41.1 

29 

222.1 

55.6 

89 

280.3 

70.2 

50 
51 

48.5 

12.1 

10 

106.7 

26.7 

70 

164.9 

41.3 

30 

223.1 

55.9 

90 

281.3 

70.5 

49.5 

»12.4 

111 

107.7 

27.0 

171 

165.9 

41.5 

231 

224.1 

56.1 

291 

282.3 

70.7 

52 

50.4 

12.6 

12 

108.6 

27.2 

72 

166.8 

41.8 

32 

225.0 

56.4 

92 

283.2 

71.0 

53 

51.4 

12.9 

13 

109.6 

27.5 

73 

167.8 

42.0 

33 

226.0 

56.6 

93 

284.2 

71.2 

54 

52.4 

13.1 

14 

110.6 

27.7 

74 

168.8 

42.3 

34 

227.0 

56.9 

94 

285.2 

71.4 

55 

53.4 

13.4 

15 

111.6 

27.9 

75 

169.8 

42.5 

35 

228.0 

57.1 

95 

286.2 

71.7 

56 

54.3 

13.6 

16 

112.5 

28.2 

76 

170.7 

42.8 

36 

228.9 

57.3 

96 

287.1 

71.9 

57 

55.3 

13.8 

17 

113.5 

28.4 

77 

171.7 

43.0 

37 

229.9 

57.6 

97 

288.1 

72.2 

58 

56.3 

14.1 

18 

114.5 

28.7 

78 

172.7 

43.3 

38 

230.9 

57.8 

98 

289.1 

72.4 

59 

57.2 

14.3 

19 

115.4 

28.9 

79 

173.6 

43.5 

39 

231.8 

58.1 

99 

290.9 

72.7 

60 

58.2 

14.6 

20 

116.4 

29.2 

80 

174.6 

43.7 

40 

232.8 

58.3 

300 

291.0 

72.9 

Dist. 

Dep. 

Lat. 

DLst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

DiHt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

B 

NE.  f  E 

Ee 

5E.  i  E. 

WNW.  i  W. 

WSW.  f  W. 

[For  6J  Points.    1 

Page  520] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  IJ  Points. 

N 

.  byE. 

iE. 

N.  by 

w.  ^  w. 

S.  by  E.  ^  E. 

S. 

by  W.  i  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.4 

17.7 

121 

115.8 

35.1 

181 

173.2 

52.5 

230.6 

70.0 

2 

1.9 

0.6 

62 

59.3 

18.0 

22 

116.7 

35.4 

82 

174.2 

52.8 

42 

231.6 

70.2 

3 

2.9 

0.9 

63 

60.3 

18.3 

23 

117.7 

35.7 

83 

175.1 

53.1 

43 

232.5 

70.5 

4 

8.8 

1.2 

64 

61.2 

18.6 

24 

118.7 

36.0 

84 

176.1 

53.4 

44 

233. 5 

70.8 

5 

4.8 

1.5 

65 

62.2 

18.9 

25 

119.6 

36.3 

85 

177.0 

53.7 

45 

234.5 

71.1 

6 

5.7 

1.7 

66 

63.2 

19.2 

26 

120.6 

36.6 

86 

178.0 

54.0 

46 

235.4 

71.4 

7 

6.7 

2.0 

67 

64.1 

19.4 

27 

121.5 

36.9 

87 

178.9 

54.3 

47 

236.4 

71.7 

8 

7.7 

2.3 

68 

65.1 

19.7 

28 

122.5 

37.2 

88 

179.9 

54.6 

48 

237.3 

72.0 

9 

8.6 

2.6 

69 

66.0 

20.0 

29 

123.4 

37.4 

89 

180.9 

54.9 

49 

238.3 

72.3 

10 
11 

9.6 

2.9 

70 

67.0 

20.3 
20.6 

30 

124.4 

37.7 

90 

181.8 
182.8 

55.2 

50 

239.2 

72.6 

10.5 

3.2 

71 

67.9 

131 

125.4 

38.0 

191 

55.4 

251 

240.2 

72.9 

12 

11.5 

3.5 

72 

68.9 

20.9 

32 

126.3 

38.3 

92 

183.7 

55.7 

52 

241.1 

73.2 

13 

12.4 

3.8 

73 

69.9 

21.2 

33 

127.3 

38.6 

93 

184.7 

56.0 

53 

242.1 

73.4 

14 

13.4 

4.1 

74 

70.8 

21.5 

34 

128.2 

38.9 

94 

185.6 

56.3 

54 

243.1 

73.7 

15 

14.4 

4.4 

75 

71.8 

21.8 

35 

129.2 

39.2 

95 

186.6 

56.6 

55 

244.0 

74.0 

16 

15.3 

4.6 

76 

72.7 

22.1 

36 

130.1 

39.5 

96 

187.6 

56.9 

56 

245.0 

74.3 

17 

16.3 

4.9 

77 

73.7 

22.4 

37 

131.1 

39.8 

97 

188.5 

57.2 

57 

245.9 

74.6 

18 

17.2 

5.2 

78 

74.6 

22.6 

38 

132.1 

40.1 

98 

189.5 

57.5 

58 

246.9 

74.9 

19 

18.2 

5.5 

79 

75.6 

22.9 

39 

133.0 

40.3 

99 

190.4 

57.8 

59 

247.8 

75.2 

20 

19.1 

5.8 

80 

76.6 

23.2 

40 

134. 0 

40.6 

200 

191.4 

58.1 

60 

248.8 

75.5 

21 

20.1 

6.1 

81 

77.5 

23.5 

141 

134.9 

40.9 

201 

192.3 

58.3 

261 

249.8 

75.8 

22 

21.1 

6.4 

82 

78.5 

23.8 

42 

135.9 

41.2 

02 

193.3 

58.6 

62 

250.7 

76.1 

23 

22.0 

6.7 

83 

79.4 

24.1 

43 

136.8 

41.5 

03 

194.  3 

58.9 

63 

251.7 

76.3 

24 

23.0 

7.0 

84 

80.4 

24.4 

44 

137.8 

41.8 

04 

195.2 

59.2 

64 

252.6 

76.6 

25 

23.9 

7.3 

85 

81.3 

24.7 

45 

138.8 

42.1 

05 

196.2 

59.5 

65 

253.6 

76.9 

26 

24.9 

7.5 

86 

82.3 

25.0 

46 

139.7 

42.4 

06 

197.1 

59.8 

66 

254.5 

77.2 

27 

25.8 

7.8 

87 

83.3 

25.3 

47 

140.7 

42.7 

07 

198.1 

60.1 

67 

255.5 

77.5 

28 

26.8 

8.1 

88 

84.2 

25.5 

48 

141.6 

43.0 

08 

199.0 

60.4 

68 

256.5 

77.8 

29 

27.8 

8.4 

89 

86.2 

25.8 

49 

142.6 

43.3 

09 

200.0 

60.7 

69 

257.4 

78.1 

30 

28.7 

8.7 

90 

86.1 

26.1 

50 

143.5 

43.5 

10 

201.0 
201.9 

61.0 

70 

258.4 

78.4 

31 

29.7 

9.0 

91 

87.1 

26.4 

151 

144.5 

43.8 

211 

61.3 

271 

259.3 

78.7 

32 

30.6 

9.3 

92 

88.0 

26.7 

52 

145.5 

44.1 

12 

202.9 

61.5 

72 

260.3 

79.0 

33 

31.6 

9.6 

93 

89.0 

27.0 

53 

146.4 

44.4 

13 

203.8 

61.8 

73 

261.2 

79.2 

34 

32.5 

9.9 

94 

90.0 

27.3 

54 

147.4 

44.7 

14 

204.8 

62.1 

74 

262.2 

79.5 

35 

33.5 

10.2 

95 

90.9 

27.6 

55 

148. 3 

45.0 

15 

205.7 

62.4 

75 

263.2 

79.8 

36 

34.4 

10.5 

96 

91.9 

27.9 

56 

149.3 

45.3 

16 

206.7 

62.7 

76 

264.1 

80.1 

37 

35.4 

10.7 

97 

92.8 

28.2 

57 

150.2 

45.6 

17 

207.7 

63.0 

77 

265.1 

80.4 

38 

36.4 

11.0 

98 

93.8 

28.4 

58 

151.2 

45.9 

18 

208.6 

63.3 

78 

266.0 

80.7 

39 

37.3 

11.3 

99 

94.7 

28.7 

59 

152.2 

46.2 

19     209. 6 

63.6 

79 

267.0 

81.0 

40 

38.3 

11.6 

100 

95.7 

29.0 

60 

153.1 

46.4 

20 

210.5 

63.9 

80 

267.9 

81.3 

41 

39.2 

11.9 

101 

96.7 

29.3 

161 

154.1 

46.7 

221 

211.5 

64.2 

281 

268.9 

81.6 

42 

40.2 

12.2 

02 

97.6 

29.6 

62 

155.0 

47.0 

22 

212.4 

64.4 

82 

269.9 

81.9 

43 

41.1 

12.5 

03 

98.6 

29.9 

63 

156.  0 

47.3 

23 

213.4 

64.7 

83 

270.8 

82.2 

44 

42.1 

12.8 

04 

99.5 

30.2 

64 

156.  9 

47.6 

24 

214.4 

65.0 

84 

271.8 

82.4 

45 

43.1 

13.1 

05 

100.5 

30.5 

65 

157.9 

47.9 

25 

215.3 

65.3 

85 

272.7 

82.7 

46 

44.0 

13.4 

06 

101.4 

30.8 

66 

158.9 

48.2 

26 

216.3 

65.6 

86 

273.7 

83.0 

47 

45.0 

13.6 

07 

102.4 

31.1 

67 

159.8 

48.5 

27 

217.2 

65.9 

87 

274.6 

83.3 

48 

45.9 

13.9 

08 

103.3 

31.4 

68 

160.8 

48.8 

28 

218.2 

66.2 

88 

275.6 

83.6 

49 

46.9 

14.2 

09 

104.3 

31.6 

69 

161.7 

49.1 

29 

219.1 

66.5 

89 

276.6 

83.9 

50 

47.8 

14.5 

10 

105.3 

31.9 

70 

162.7 

49.3 

30 

220.1 

66.8 

90 

277.5 

84.2 

51 

48.8 

14.8 

111 

106.2 

32.2 

171 

163.6 

49.6 

231 

221.1 

67.1 

291 

278.  5 

84.5 

52 

49.8 

15.1 

12 

107.2 

32.5 

72 

164.6 

49.9 

32 

222.0 

67.3 

92 

279.4 

84.8 

53 

50.7 

15.4 

13 

108.1 

32.8 

73 

165.6 

50.2 

33 

223.0 

67.6 

93 

280.4 

85.1 

54 

51.7 

15.7 

14 

109.1 

33. 1 

74 

166.5 

50.5 

34 

223.9 

67.9 

94 

281.3 

85.3 

55 

52.6 

16.0 

15 

110.0 

33.4 

75 

167.5 

50.8 

35 

224.9 

68.2 

95 

282.3 

85.6 

56 

53.6 

16.3 

16 

111.0 

33.7 

76 

168.  4 

51.1 

36 

225.  8 

68.5 

96 

283.3 

85.9 

57 

54.5 

16.5 

17 

112.0 

34.0 

77 

169.4 

51.4 

37 

226.8 

68.8 

97 

284.2 

86.2 

58 

55.5 

16.8 

18 

112.9 

34.3 

78 

170.3 

51.7 

38 

227.8 

69.1 

98 

285.2 

86.5 

59 

56.5 

17.1 

19 

113.9 

34.5 

79 

171.3 

52.0 

39 

228.7 

69.4 

99 

286.1 

86.8 

60 

57.4 

17.4 

20 

114.8 

34.8 

80 

172.2 

52.3 

40 

229.  7 

69.7 

300 

287.1 

87.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E> 

FE.  i  E. 

ES] 

E.  ^E. 

WN^ 

^V.  J  W 

WSW.  i  ^\ 

[For  6J  P< 

■)ints. 

TABLE  1. 

[Page  521    | 

Difference  of  Latitude  and  Departure  for  If  Points. 

N.  by 

E.  |E. 

N.  by 

w.  1 

W. 

S.  by  E.  f  E.            S.  by  W.  J  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.3 

61 

57.4 

20.6 

121 

113.9 

40.8 

181 

170.4 

61.0 

241 

226.9 

81.2 

2 

1.9 

0.7 

62 

58.4 

20.9 

22 

114.9 

41.1 

82 

171.4 

61.3 

42 

227.9 

81.5 

3 

2.8 

1.0 

63 

59.3 

21.2 

23 

115.8 

41.4 

83 

172.3 

61.7 

43 

228,8 

81.9 

4 

3.8 

1.3 

64 

60.3 

21.6 

24 

116.8 

41.8 

84 

173.2 

62.0 

44 

229.7 

82.2 

5 

4.7 

1.7 

65 

61.2 

21.9 

25 

117.7 

42.1 

85 

174.2 

62.3 

45 

230.7 

82.5 

6 

5.6 

2.0 

66 

62.1 

22.2 

26 

118.6 

42.4 

86 

175.1 

62.7 

46 

231.6 

82.9 

7 

6.6 

2.4 

67 

63.1 

22.6 

27 

119.6 

42.8 

87 

176.1 

63.0 

47 

232.6 

83.2 

8 

7.5 

2.7 

68 

64.0 

22.9 

28 

120.5 

43.1 

88 

177.0 

63.3 

48  1  233.5 

83.5 

9 

8.5 

3.0 

69 

65.0 

23.2 

29 

121.5 

43.5 

89 

178.0 

63.7 

49  i  234.4 

83.9 

10 

9.4 

3.4 

70 

65.9 

23.6 
23.9 

30 

122.4 
123.3 

43.8 

90 

178.9 

64.0 

50  !  235.4 

84.2 

11 

10.4 

3.7 

71 

66.8 

131 

44.1 

191 

179.8 

64.3 

251  !  236.3 

84.6 

12 

11.3 

4.0 

72 

67.8 

24.3 

32 

124.3 

44.5 

92 

180.8 

64.7 

52 

237.3 

84.9 

13 

12.2 

4.4 

73 

68.7 

24.6 

33 

125.2 

44.8 

93 

181.7 

65.0 

53 

238.2 

85.2 

14 

13.2 

4.7 

74 

69.7 

24.9 

34 

126.2 

45.1 

94 

182.7 

65.4 

54 

239.2 

85.6 

15 

14.1 

5.1 

75 

70.6 

25.3 

35 

127.1 

45.5 

95 

183.6 

65.7 

55 

240.1 

85.9 

16 

15.1 

5.4 

76 

71.6 

25.6 

36 

128.0 

45.8 

96 

184. 5 

66.0 

56 

241.0 

86.2 

17 

16.0 

5.7 

77 

72.5 

25.9 

37 

129.0 

46.2 

97 

185.5 

66.4 

57 

242.0 

86.6 

18 

16.9 

6.1 

78 

73.4 

26.3 

.38 

129.9 

46.5 

98 

186.4 

66.7 

58 

242.9 

86.9 

19 

17.9 

6.4 

79 

74.4 

26.6 

39 

130.9 

46.8 

99 

187.4 

67.0 

59 

243.9 

87.3 

20 

18.8 

6.7 

80 

75.3 

27.0 
27.3 

40 
141 

131.8 

47.2 

200 
201 

188.3 
189.3 

67.4 

60 

244.8 
245.7 

87.6 

21 

19.8 

7.1 

81 

76.3 

132.8 

47.5 

67.7 

261 

87.9 

22 

20.7 

7.4 

82 

77.2 

27.6 

42 

133.7 

47.8 

02 

190.2 

68.1 

62 

246.7 

88.3 

23 

21.7 

7.7 

83 

78.1 

28.0 

43 

134.6 

48.2 

03 

191.1 

68.4 

63 

247.6 

88.6 

24 

22.6 

8.1 

84 

79.1 

28.3 

44 

135.6 

48.5 

04 

192.1 

68.7 

64 

248.6 

88.9 

25 

23.5 

8.4 

85 

80.0 

28.6 

45 

136.5 

48.8 

05 

193.0 

69.1 

65 

249.5 

89.3 

26 

24.5 

8.8 

86 

81.0 

29.0 

46 

137.5 

49.2 

06 

194.0 

69.4 

66 

250.5 

89.6 

27 

25.4 

9.1 

87 

81.9 

29.3 

47 

138.4 

49.5 

07 

194.9 

69.7 

67 

251.4 

89.9 

28 

26.4 

9.4 

88 

82.9 

29.6 

48 

139.3 

49.9 

08 

195.8 

70.1 

68 

252.3 

90.3 

29 

27.3 

9.8 

89 

83.8 

30.0 

49 

140.3 

50.2 

09 

196.8 

70.4 

69  1  253.3 

90.6 

30 

28.2 

10.1 

90 

84.7 

30.3 

50 

141.2 

50.5 

10 

197.7 
198.7 

70.7 

70 

254.2 

91.0 

31 

29.2 

10.4 

91 

85.7 

30.7 

151 

142.2 

50.9 

211 

71.1 

271 

255.2 

91.3 

32 

30.1 

10.8 

92 

86.6 

31.0 

52 

143.1 

51.2 

12 

199.6 

71.4 

72 

256.1 

91.6 

33 

31.1 

11.1 

93 

87.6 

31.3 

53 

144.1 

51.5 

13 

200.5 

71.8 

73 

257.0 

92.0 

34 

32.0 

11.5 

94 

88.5 

31.7 

54 

145.0 

51.9 

14 

201.5 

72.1 

74 

258.0 

92.3 

35 

33.0 

11.8 

95 

89.4 

32.0 

55 

145.9 

52.2 

15 

202.4 

72.4 

75 

258.9 

92.6 

36 

33.9 

12.1 

96 

90.4 

32.3 

56 

146.9 

52.6 

16 

203.4 

72.8 

76 

259.9 

93.0 

37 

34.8 

12.5 

97 

91.3 

32.7 

57 

147.8 

52.9 

17 

204.3 

73.1 

77 

260.8 

93.3 

38 

35.8 

12.8 

98 

92.3 

33.0 

58 

148.8 

53.2 

18 

2a5.3 

73.4 

78 

261.7 

93.7 

39 

36.7 

13.1 

99 

93.2 

33.4 

59 

149.7 

53.6 

19 

206.2 

73.8 

79 

262.7 

94.0 

40 

37.7 

13.5 

100 

94.2 

33.7 

60 

150.6 

53.9 

20 

207.1 

74.1 

80 

26:^.6 
264.6 

94.3 
94.7 

41 

38.6 

13.8 

101 

95.1 

34.0 

161 

151.6 

54.2 

221 

208.1 

74.5 

281 

42 

39.5 

14.1 

02 

96.0 

34.4 

62 

152.5 

54.6 

22 

209.0 

74.8 

82 

265.5 

95.0 

43 

40.5 

14.5 

03 

97.0 

34.7 

63 

153.5 

54.9 

23 

210.0 

75.1 

83 

266.5 

95.3 

44 

41.4 

14.8 

04 

97.9 

35.0 

64 

154.4 

55.2 

24 

210.9 

75.5 

84 

267.4 

95.7 

45 

42.4 

15.2 

05 

98.9 

35.4 

65 

155.4 

55.6 

25 

211.8 

75.8 

85 

268.3 

96.0 

46 

43.3 

15.5 

06 

99.8 

35.7 

66 

156.3 

55.9 

26 

212.8 

76.1 

86 

269.3 

96.4 

47 

44.3 

15.8 

07 

100.7 

36.0 

67 

157.2 

56.3 

27 

213.7 

76.5 

87 

270.2 

96.7 

48 

45.2 

16.2 

08 

101.7 

36.4 

68 

158.2 

56.6 

28 

214.7 

76.8 

88 

271.2 

97.0 

49 

46.1 

16.5 

09 

102.6 

36.7 

69 

159.1 

56.9 

29 

215.6 

77.1 

89 

272.1 

97.4 

50 
51 

47.1 

48.0 

16.8 

10 

103.6 

37.1 

70 

160.1 

57.3 

30  I  216.6 

77.5 

90 

273.0 

97.7 

17.2 

111 

104.5 

37.4 

171 

161.0 

57.6 

231 

217.5 

77.8 

291     274. 0 

98.0 

52 

49.0 

17.5 

12 

105.5 

37.7 

72 

161.9 

57.9 

32 

218.4 

78.2 

92     274. 9 

98.4 

53 

49.9 

17.9 

13 

106.4 

38.1 

73 

162.9 

58.3 

33 

219.4 

78.5 

93 

275.9 

98.7 

54 

50.8 

18.2 

14 

107.3 

38.4 

74 

163.8 

58.6 

34 

220.3 

78.8 

94 

276.8 

99.0 

55 

51.8 

18.5 

15 

108.3 

38.7 

75 

164.8 

59.0 

35 

221.3 

79.2 

95 

277.8 

99.4 

56 

52.7 

18.9 

16 

109.2 

39.1 

76 

165.7 

59.3 

36 

222.2 

79.5 

96 

278.7 

99.7 

57 

53.7 

19.2 

17 

110.2 

39.4 

77 

166.7 

59.6 

37 

223.1 

79.8 

97 

279.6 

100.1 

58 

54.6 

19.5 

18 

111.1 

39.8 

78 

167.6 

60.0 

38 

224.1 

80.2 

98 

280.6 

100.4 

59 

55.6 

19.9 

19 

112.0 

40.1 

79 

168.5 

60.3 

39 

225.0 

80.5 

99 

281.5 

100.7 

60 

56.5 

20.2 

20 

113.0 

40.4 

80 

169.5 

60.6 

40 

226.0 

80.9 

300 

282.5 

101.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

ENE.  \ 

E. 

I 

:sE.  \  I 

]_ 

M 

^NW.  i 

W.               WSW.  i  W. 

[For  6k  Po 

ints. 

Page  622] 

TABLE  1. 

Differenca  of  Latitude  and  Departure  for  2  Points. 

NNE. 

NNW. 

SSE. 

ssw. 

DiBt. 

Lat. 

Dep. 

Dlfit. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.4 

23.3 

121 

111.8 

46.3 

181 

167.2 

69.3 

241 

222.7 

92.2 

2 

1.8 

0.8 

62 

57.3 

23.7 

22 

112.7 

46.7 

82 

168.1 

69.6 

42 

223.6 

92.6 

3 

2.8 

1.1 

63 

58.2 

24.1 

23 

113.6 

47.1 

83 

169.1 

70.0 

43 

224.5 

93.0 

4 

3.7 

1.5 

64 

59.1 

24.5 

24 

114.6 

47.5 

84 

170.0 

70.4 

44 

225.4 

93.4 

5 

4.6 

1.9 

65 

60.1 

24.9 

25 

115.5 

47.8 

85 

170.9 

70.8 

45 

226.4 

93.8 

6 

5.5 

2.3 

66 

61.0 

25.3 

26 

116.4 

48.2 

86 

171.8 

71.2 

46 

227.3 

94.1 

7 

6.5 

2.7 

67 

61.9 

25.6 

27 

117.3 

48.6 

87 

172.8 

71.6 

47 

228.2 

94.5 

8 

7.4 

3.1 

68 

62.8 

26.0 

28 

118.3 

49.0 

88 

173.7 

71.9 

48 

229.1 

94.9 

9 

8.3 

3.4 

69 

63.7 

26.4 

29 

119.2 

49.4 

89 

174.6 

72.3 

49 

230.0 

95.3 

10 

9.2 

3.8 

70 

64.7 

26.8 

30 

120.1 

49.7 

90 

175.5 

72.7 

50 

231.0 

95.7 

11 

10.2 

4.2 

71 

65.6 

27.2 

131 

121.0 

50.1 

191 

,  176. 5 

73.1 

251 

231.9 

96.1 

12 

11.1 

4.6 

72 

66.5 

27.6 

32 

122.0 

50.5 

92 

177.4 

73.5 

52 

232.8 

96.4 

13 

12.0 

5.0 

73 

67.4 

27.9 

33 

122.9 

50.9 

93 

178.3 

73.9 

53 

233.7 

96.8 

14 

12.9 

5.4 

74 

68.4 

28.3 

34 

123.8 

51.3 

94 

179.2 

74.2 

54 

234.7 

97.2 

15 

13.9 

5.7 

75 

69.3 

28.7 

35 

124.7 

51.7 

95 

180.2 

74.6 

55 

235.6 

97.6 

16 

14.8 

6.1 

76 

70.2 

29.1 

36 

125.6 

52.0 

96 

181.1 

75.0 

56 

236.5 

98.0 

17 

15.7 

6.5 

77 

71.1 

29.5 

37 

126.6 

52.4 

97 

182.0 

75.4 

57 

237.4 

98.3 

18 

16.6 

6.9 

78 

72.1 

29.8 

38 

127.5 

52.8 

98 

182.9 

75.8 

58 

238.4 

98.7 

19 

17.6 

7.3 

79 

73.0 

30.2 

39 

128.4 

53.2 

99 

183.9 

76.2 

59 

239.3 

99.1 

20 

18.6 

7.7 

80 

'    73.9 

30.6 
31.0 

40 

129.3 

53.6 

200 

184.8 

76.5 

60 

240.2 

99.5 

21 

19.4 

8.0 

81 

74.8 

141 

130.3 

54.0 

201 

185.7 

76.9 

261 

241.1 

99.9 

22 

20.3 

8.4 

82 

75.8 

31.4 

42 

131.2 

54.3 

02 

186.6 

77.3 

62 

242.1 

100.3 

23 

21.2 

8.8 

83 

76.7 

31.8 

43 

132.1 

54.7 

03 

187.5 

77.7 

63 

243.0 

100.6 

24 

22.2 

9.2 

84 

77.6 

32.1 

44 

133.0 

55.1 

04 

188.5 

78.1 

64 

243.9 

101.0 

25 

23.1 

9.6 

85 

78.5 

32.5 

45 

134.0 

55.5 

05 

189.4 

78.5 

65 

244.8 

101.4 

26 

24.0 

9.9 

86 

79.5 

32.9 

46 

134.9 

55.9 

06 

190.3 

78.8 

66 

245.8 

101.8 

27 

24.9 

10.3 

87 

80.4 

33.3 

47 

135.8 

56.3 

07 

191.2 

79.2 

67 

246.7 

102.2 

28 

25.9 

10.7 

88 

81.3 

33.7 

48 

136.7 

56.6 

08 

192.2 

79.6 

68 

247.6 

102.6 

29 

26.8 

11.1 

89 

82.2 

34.1 

49 

137.7 

57.0 

09 

193.1 

80.0 

69 

248.5 

102.9 

30 

27.7 

11.5 

90 

83.1 

34.4 

50 

138.6 
139.5 

57.4 

10 

194.0 

80.4 

70 

249.4 

103.3 

31 

28.6 

11.9 

91 

84.1 

34.8 

151 

57.8 

211 

194.9 

80.7 

271 

250.4 

103.7 

32 

29.6 

12.2 

92 

85.0 

35.2 

52 

140.4 

58.2 

12 

195.9 

81.1 

72 

251.3 

104.1 

33 

30.5 

12.6 

93 

85.9 

35.6 

53 

141.4 

58.6 

13 

196.8 

81.5 

73 

252.2 

104.5 

34 

31.4 

13.0 

94 

86.8 

36.0 

54 

142.3 

58.9 

14 

197.7 

81.9 

74 

253.1 

104.9 

35 

32.3 

13.4 

95 

87.8 

36.4 

55 

143.2 

59.3 

15 

198.6 

82.3 

75 

254.1 

105.2 

36 

33.3 

13.8 

96 

88.7 

36.7 

56 

144.1 

59.7 

16 

199.6 

82.7 

76 

255.0 

105.6 

37 

34.2 

14.2 

97 

89.6 

37.1 

57 

145.0 

60.1 

17 

200.5 

83.0 

77 

255.9 

106.0 

38 

35.1 

14.5 

98 

90.5 

37.5 

58 

146.0 

60.5 

18 

201.4 

83.4 

78 

256.8 

106.4 

39 

36.0 

14.9 

99 

91.5 

37.9 

59 

146.9 

60.8 

19 

202.3 

83.8 

79 

257.8 

106.8 

40 

37.0 

15.3 

100 

92.4 

38.3 

60 

147.8 

61.2 

20 

203.3 

84.2 

80 

258.7 

107.2 

41 

37.9 

15.7 

101 

93.3 

38.7 

161 

148.7 

61.6 

221 

204.2 

84.6 

281 

259.6 

107.5 

42 

38.8 

16.1 

02 

94.2 

39.0 

62 

149.7 

62.0 

22 

205.1 

85.0 

82 

260.5 

107.9 

43 

39.7 

16.5 

03 

95.2 

39.4 

63 

150.6 

62.4 

23 

206.0 

85.3 

83 

261.5 

108.3 

44 

40.7 

16.8 

04 

96.1 

39.8 

64 

151.5 

62.8 

24 

206.9 

85.7 

84 

262.4 

108.7 

45 

41.6 

17.2 

05 

97.0 

40.2 

65 

152.4 

63.1 

25 

207.9 

86.1 

85 

263.3 

109.1 

46 

42.5 

17.6 

06 

97.9 

40.6 

66 

153.4 

63.5 

26 

208.8 

86.5 

86 

264.2 

109.4 

47 

43.4 

18.0 

07 

98.9 

40.9 

67 

154.3 

63.9 

27 

209.7 

86.9 

87 

265.2 

109.8 

48 

44.3 

18.4 

08 

99.8 

41.3 

68 

155.2 

64.3 

28 

210.6 

87.3 

88 

266.1 

110.2 

49 

45.3 

18.8 

09 

100.7 

41.7 

69 

156.1 

64.7 

29 

211.6 

87.6 

89 

267.0 

110.6 

50 

46.2 

19.1 

10 

101.6 

42.1 

70 

157.1 

65.1 

30 

212.5 

88.0 

90 

267.9 

111.0 

51 

47.1 

19.5 

111 

102.6 

42.5 

171 

158.0 

65.4 

231 

213.4 

88.4 

291 

268.8 

111.4 

52 

48.0 

19.9 

12 

103.5 

42.9 

72 

158.9 

65.8 

32 

214.3 

88.8 

92 

269.8 

111.7 

63 

49.0 

20.3 

13 

104.4 

43.2 

73 

159.8 

66.2 

33 

215.3 

89.2 

93 

270.7 

112.1 

54 

49.9 

20.7 

14 

105.3 

43.6 

74 

160.8 

66.6 

34 

216.2 

89.5 

94 

271.6 

112.5 

55 

50.8 

21.0 

15 

106.2 

44.0 

75 

161.7 

67.0 

35 

217.1 

89.9 

95 

272.5 

112.9 

56 

51.7 

21.4 

16 

107.2 

44.4 

76 

162.6 

67.4 

36 

218.0 

90.3 

96 

273.5 

113.3 

57 

52.7 

21.8 

17 

108.1 

44.8 

77 

163.5 

67.7 

37 

219.0 

90.7 

97 

274.4 

113.7 

58 

53.6 

22.2 

18 

109.0 

45.2 

78 

164.5 

68.1 

38 

219.9 

91.1 

98 

275.3 

114.0 

59 

54.5 

22.6 

19 

109.9 

45.5 

79 

165.4 

68.5 

39 

220.8 

91.5 

99 

276.2 

114.4 

60 

55.4 

23.0 

20 

110.9 

45.9 

80 

166.3 

68.9 

40 

221.7 

91.8 

300 

277.2 

114.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

ENE. 

ESE. 

WNW 

WSW 

[F 

or  6  Poi] 

its. 

TABLE  1. 

[Page  623    j 

Difference  of  Latitude  and  Departure  for  2J-  Points. 

NNE. 

iE. 

NNW 

.  i  W.                SSE. 

iE. 

ssw. 

iW. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

55.1 

26.1 

121 

109.4 

51.7 

181 

163.6 

77.4 

241 

217.9 

103.0 

2 

1.8 

0.9 

62 

56.0 

26.5 

22 

110.3 

52.2 

82 

164.5 

77.8 

42 

218.8 

103.6 

3 

2.7 

1.3 

63 

57.0 

26.9 

23 

111.2 

52.6 

83 

165.4 

78.2 

43 

219.7 

103.9 

4 

3.6 

1.7 

64 

57.9 

27.4 

24 

112.1 

53.0 

84 

166.3 

78.7 

44 

220.6 

104.3 

5 

4.5 

2.1 

65 

58.8 

27.8 

25 

113.0 

53.4 

85 

167. 2' 

79.1 

45 

221.5 

104.8 

6 

5.4 

2.6 

66 

59.7 

28.2 

26 

113.9 

53.9 

86 

168.1 

79.5 

46 

222.4 

105.2 

7 

6.3 

3.0 

67 

60.6 

28.6 

27 

114.8 

54.3 

87 

169.0 

80.0 

47 

223.3 

105.6 

8 

7.2 

3.4 

68 

61.5 

29.1 

28 

115.7 

54.7 

88 

169.9 

80.4 

48 

224.2 

106.0 

9 

8.1 

3.8 

69 

62.4 

29.5 

29 

116.6 

55.2 

89 

170.9 

80.8 

49 

226.1 

106.5 

10 

9.0 

4.3 

70 

63.3 

29.9 

30 

117.5 
118.4 

55.6 

90 
191 

171.8 

81.2 

50 
261 

226.0 

106.9 

11 

9.9 

4.7 

71 

64.2 

30.4 

131 

56.0 

172.7 

81.7 

226.9 

107.3 

12 

10.8 

5.1 

72 

65.1 

30.8 

32 

119.3 

56.4 

92 

173.6 

82.1 

52 

227.8 

107.7 

13 

11.8 

5.6 

73 

66.0 

31.2 

33 

120.2 

56.9 

93 

174.5 

82.6 

53 

228.7 

108.2 

14 

12.7 

6.0 

74 

66.9 

31.6 

34 

121.1 

57.3 

94 

175.4 

82.9 

54 

229.6 

108.6 

15 

13.6 

6.4 

75 

67.8 

32.1 

35 

122.0 

57.7 

95 

176.3 

83.4 

65 

230.6 

109.0 

16 

14.5 

6.8 

76 

68.7 

32.5 

36 

122.9 

58.1 

96 

177.2 

83.8 

56 

231.4 

109.5 

17 

15.4 

7.3 

77 

69.6 

32.9 

37 

123.8 

58.6 

97 

178.1 

84.2 

57 

232. 3 

109.9 

18 

16.3 

7.7 

78 

70.5 

33.3 

38 

124.8 

59.0 

98 

179.0 

84.7 

58 

233.2 

110.3 

19 

17.2 

8.1 

79 

71.4 

33.8 

39 

125.7 

59.4 

99 

179.9 

85.1 

59 

234.1 

110.7 

20 

18.1 

8.6 

80 
81 

72.3 

34.2 

40 

126.6 

59.9 

200 

180.8 

85.6 

60 

235.0 
236.9 

111.2 

21 

19.0 

9.0 

73.2 

34.6 

141 

127.5 

60.3 

201 

181.7 

85.9 

261 

111.6 

22 

19.9 

9.4 

82 

74.1 

35.1 

42 

128.4 

60.7 

02 

182.6 

86.4 

62 

236.8 

112.0 

23 

20.8 

9.8 

83 

75.0 

35.5 

43 

129.3 

61.1 

03 

183.5 

86.8 

63 

237.7 

112.4 

24 

21.7 

10.3 

84 

75.9 

35.9 

44 

130.2 

61.6 

04 

184.4 

87.2 

64 

238.7 

112.9 

25 

22.6 

10.7 

85 

76.8 

36.3 

45 

131.1 

62.0 

05 

185.3 

87.6 

65 

239.6 

113.3 

26 

23.5 

11.1 

86 

77.7 

36.8 

46 

132.0 

62.4 

06 

186.2 

88.1 

66 

240.5 

113.7 

27 

24.4 

11.5 

87 

78.6 

37.2 

47 

132.9 

62.9 

07 

187.1 

88.5 

67 

241.4 

114.2 

28 

26.3 

12.0 

88 

79.6 

37.6 

48 

133.8 

63.3 

08 

188.0 

88.9 

68 

242. 3 

114.6 

29 

26.2 

12.4 

89 

80.5 

38.1 

49 

134.7 

63.7 

09 

188.9 

89.4 

69 

243.2 

115.0 

30 
31 

27.1 

12.8 

90 

81.4 

38.5 

50 

136.6 

64.1 

10 

189.8 

89.8 

70 

244.1 

115.4 

28.0 

13.3 

91 

82.3 

38.9 

151 

136.5 

64.6 

211 

190.7 

90.2 

271 

245.0 

116.9 

32 

28.9 

13.7 

92 

83.2 

39.3 

52 

137.4 

65.0 

12 

191.6 

90.6 

72 

246.9 

116.3 

33 

29.8 

14.1 

93 

84.1 

39.8 

53 

138.3 

65.4 

13 

192.5 

91.1 

73 

246.8 

116.7 

34 

30.7 

14.5 

94 

85.0 

40.2 

54 

139.2 

65.8 

14 

193.5 

91.5 

74 

247.7 

117.2 

35 

31.6 

15.0 

95 

85.9 

40.6 

55 

140.1 

66.3 

16 

194.4 

91.9 

76 

248.6 

117.6 

36 

32.5 

15.4 

96 

86.8 

41.0 

56 

141.0 

66.7 

16 

195.3 

92.4 

76 

249.6 

118.0 

37 

33.4 

15.8 

97 

87.7 

41.5 

57 

141.9 

67.1 

17 

196.2 

92.8 

77 

260.4 

118.4 

38 

34.4 

16.2 

98 

88.6 

41.9 

58 

142.8 

67.6 

18 

197.1 

93.2 

78 

261.3 

118.9 

39 

35.3 

16.7 

99 

89.5 

42.3 

59 

143.7 

68.0 

19 

198.0 

93.6 

79 

252.2 

119.3 

40 
41 

36.2 

17.1 

100 

90.4 

42.8 

60 

144.6 

68.4 

20 

198.9 

94.1 

80 

253.1 

119.7 

37.1 

17.5 

101 

91.3 

43.2 

161 

145.5 

68.8 

221 

199.8 

94.6 

281 

254.0 

120.1 

42 

38.0 

18.0 

02 

92.2 

43.6 

62 

146.4 

69.3 

22 

200.7 

94.9 

82 

254.9 

120.6 

43 

38.9 

18.4 

03 

93.1 

44.0 

63 

147.4 

69.7 

23 

201.6 

96.3 

83 

266.8 

121.0 

44 

39.8 

18.8 

04 

94.0 

44.5 

64 

148.3 

70.1 

24 

202.5 

95.8 

84 

256.7 

121.4 

45 

40.7 

19.2 

05 

94.9 

44.9 

65 

149.2 

70.5 

25 

203.4 

96.2 

86 

257.6 

121.9 

46 

41.6 

19.7 

06 

95.8 

45.3 

66 

150.1 

71.0 

26 

204.3 

96.6 

86 

268.6 

122.3 

47 

42.5 

20.1 

07 

96.7 

45.7 

67 

151.0 

71.4 

27 

205.2 

97.1 

87 

259.4 

122.7 

48 

43.4 

20.5 

08 

97.6 

46.2 

68 

151.9 

71.8 

28 

206.1 

97.5 

88 

260.3 

123.1 

49 

44.3 

21.0 

09 

98.5 

46.6 

69 

152.8 

72.3 

29 

207.0 

.97.9 

89 

261.3 

123.6 

50 

45.2 

21.4 

10 

99.4 
100. 3" 

47.0 

70 

153.7 
154.6 

72.7 
73.1 

30 
231 

207.9 

98.3 

90 
291 

262.2 

124.0 

51 

46.1 

21.8 

111 

47.5 

171 

208.8 

98.8 

263.1 

124.4 

52 

47.0 

22.2 

12 

101.2 

47.9 

72 

155.5 

73.5 

32 

209.7 

99.2 

92 

264.0 

124.8 

53 

47.9 

22.7 

13 

102.2 

48.3 

73 

156.4 

74.0 

33 

210.6 

99.6 

93 

264.9 

126.3 

54 

48.8 

23.1 

14 

103.1 

48.7 

74 

157.3 

74.4 

34 

211.5 

100.0 

94 

265.8 

126.7 

55 

49.7 

23.5 

15 

104.0 

49.2 

75 

158.2 

74.8 

35 

212.4 

100.5 

95 

266.7 

126.1 

56 

50.6 

23.9 

16 

104.9 

49.6 

76 

159.1 

75.2 

36 

213.3 

100.9 

96 

267.6 

126.6 

57 

51.5 

24.4 

17 

105.8 

50.0 

77 

160.0 

75.7 

37 

214.2 

101.3 

97 

268.5 

127.0 

58 

52.4 

24.8 

18 

106.7 

50.5 

78 

160.9 

76.1 

38 

215.1 

101.8 

98 

269.4 

127.4 

59 

53.3 

25.2 

19 

107.6 

50.9 

79 

161.8 

76.5 

39 

216.1 

102.2 

99 

270.3 

127.8 

60 

54.2 

25.7 

20 

108.5 

51.3 

80 

162.7 

77.0 

40 

217.0 

102.6 

300 

271.2 

128.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

m 

].  by  E. 

fE. 

SI 

:.  by  E.  1  E. 

NW.  by  AV.  1  W. 

SW 

.  by  W. 

|W. 

[For  6| P 

oints. 

Page  524] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  2J  Points. 

Diet. 

NNE 

.  iE. 

NNW.  i  W.                SSE 

i  E.                  SSW 

^  w. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

63.8 

28.8 

121 

106.7 

57.0 

181 

159.6 

86.3 

241 

212.5 

113.6 

2 

1.8 

0.9 

62 

54.7 

29.2 

22 

107.6 

57.5 

82 

160.  5 

86.8 

42 

213.4 

114.1 

3 

2.6 

1.4 

63 

66.6 

29.7 

23 

108.5 

58.0 

83 

161.4 

86.3 

43 

214.3 

114.5 

4 

3.5 

1.9 

64 

66.4 

30.2 

24 

109.4 

58.5 

84 

162.3 

86.7 

44 

216.2 

115.0 

5 

4.4 

2.4 

65 

67.3 

30.6 

26 

110.2 

58.9 

85 

163.  2 

87.2 

45 

216.1 

115.6 

6 

5.3 

2.8 

66 

58.2 

31.1 

26 

111.1 

59.4 

86 

164.0 

87.7 

46 

217.0 

116.0 

7 

6.2 

3.3 

67 

69.1 

31.6 

27 

112.0 

69.9 

87 

164.9 

88.2 

47 

217.8 

116.4 

8 

7.1 

3.8 

68 

60.0 

32.1 

28 

112.9 

60.3 

88 

165.8 

88.6 

48 

218.7 

116.9 

9 

7.9 

4.2 

69 

60.9 

32.6 

29 

113.8 

60.8 

89 

166.7 

89.1 

49 

219.6 

117.4 

10 

8.8 

4.7 

70 

61.7 

33.0 

30 

114.6 

61.3 

61.8 

90 
191 

167.6 

89.6 

50 

220.6 

117.8 

11 

9.7 

5.2 

71 

62.6 

33.6 

131 

116.6 

168.4 

90.0 

251 

221.4 

118.3 

12 

10.6 

5.7 

72 

63.5 

33.9 

32 

116.4 

62.2 

92 

169.3 

90.6 

52 

222.2 

118.8 

13 

11.5 

6.1 

73 

64.4 

34.4 

33 

117.3 

62.7 

93 

170.2 

91.0 

53 

223.1 

119.3 

14 

12.3 

6.6 

74 

65.3 

34.9 

34 

118.2 

63.2 

94 

171.1 

91.6 

64 

224.0 

119.7 

15 

13.2 

7.1 

76 

66.1 

36.4 

35 

119.1 

63.6 

96 

172.0 

91.9 

65 

224.9 

120.2 

16 

14.1 

7.5 

76 

67.0 

35.8 

36 

119.9 

64.1 

96 

172.9 

92.4 

56 

225.8 

120.7 

17 

15.0 

8.0 

77 

67.9 

36.3 

37 

120.8 

64.6 

97 

173.7 

92.9 

57 

226.7 

121.1 

18 

15.9 

8.5 

78 

68.8 

36.8 

38 

121.7 

65.1 

98 

174.6 

93.3 

58 

227.5 

121.6 

19 

16.8 

9.0 

79 

69.7 

37.2 

39 

122.6 

65.5 

99 

176.5 

93.8 

59 

228.4 

122.1 

20 

17.6 

9.4 

80 

70.6 

37.7 
38.2 

40 

123.5 

66.0 
66.6 

200 
201 

176.4 

94.3 

60 

229.3 

122.6 

21 

18.5 

9.9 

81 

71.4 

141 

124.4 

177.3 

94.8 

261 

330.2 

123.0 

22 

19.4 

10.4 

82 

72.3 

38.7 

42 

125.2  ;  66.9 

02 

178.1 

95.2 

62 

231.1 

123.5 

23 

20.3 

10.8 

83 

73.2 

39.1 

43 

126.1  ;  67.4 

03 

179.0 

95.7 

63 

231.9 

124.0 

24 

21.2 

11.3 

84 

74.1 

39.6 

44 

127.0 

67.9 

04 

179.9 

96.2 

64 

232.8 

124.4 

25 

22.0 

11.8 

85 

75.0 

40.1 

45 

127.9 

68.4 

06 

180.8 

96.6 

65 

233.7 

124.9 

26 

22.9 

12.3 

86 

75.8 

40.6 

46 

128.8 

68.8 

06 

181.7 

97.1 

66 

234.6 

125.4 

27 

23.8 

12.7 

87 

76.7 

41.0 

47 

129.6 

69.3 

07 

182.  6 

97.6 

67 

235.5 

125.9 

28 

24.7 

13.2 

88 

77.6 

41.6 

48 

130.5 

69.8 

08 

183.4 

98.1 

68 

236.4 

126.3 

29 

25.6 

13.7 

89 

78.5 

42.0 

49 

131.4 

70.2 

09 

184.3 

98.5 

69 

237.2 

126.8 

30 

26.5 

14.1 

90 

79.4 

42.4 

60 

132.3 

70.7 

10 

185.  2 

99.0 

70 

238.1 

127.3 
127.7 

31 

27.3 

14.6 

91 

80.3 

42.9 

151 

133.2 

71.2 

211 

186.1 

99.6 

271 

239.0 

32 

28.2 

15.1 

92 

81.1 

43.4 

52 

134.1 

71.7 

12 

187.0 

99.9 

72 

239.9 

128.2 

33 

29.1 

15.6 

93 

82.0 

43.8 

63 

134.9 

72.1 

13 

187.8 

100.4 

73 

240.8 

128.7 

34 

30.0 

16.0 

94 

82.9 

44.3 

54 

135.8 

72.6 

14 

188.7 

100.9 

74 

241.6 

129.2 

35 

30.9 

16.5 

95 

83.8 

44.8 

65 

136.7 

73.1 

15 

189.6 

101.4 

76 

242.5 

129.6 

36 

31.7 

17.0 

96 

84.7 

46.3 

56 

137.6 

73.5 

16 

190.5 

101.8 

76 

243.4 

130.1 

37 

32.6 

17.4 

97 

86.6 

46.7 

67 

138.5 

74.0 

17 

191.4 

102.3 

77 

244.3 

130.6 

38 

33.5 

17.9 

98 

86.4 

46.2 

68 

139.3 

74.5 

18 

192.3 

102.8 

78 

245.2 

131.0 

39 

34.4 

18.4 

99 

87.3 

46.7 

69 

140.2 

76.0 

19 

193.1 

103.2 

79 

246.1 

131.  5 

40 

36.3 

18.9 

100 

88.2 

47.1 

60 

141.1 

75.4 

20 

194.0 

103.7 

80 

246.9 

132.0 
132.6 

41 

36.2 

19.3 

101 

89.1 

47.6 

161 

142.0 

75.9 

221 

194.  9 

104.2 

281 

247.8 

42 

37.0 

19.8 

02 

90.0 

48.1 

62 

142.9 

76.4 

22 

195.8 

104.7 

82 

248.7 

132.9 

43 

37.9 

20.3 

03 

90.8 

48.6 

63 

143.8 

76.8 

23 

196.  7 

105.1 

83 

249.6 

133.4 

44 

38.8 

20.7 

04 

91.7 

49.0 

64 

144.6 

77.3 

24 

197.6 

105.6 

84 

260.5 

133.9 

45 

39.7 

21.2 

05 

92.6 

49.5 

65 

145.5 

77.8 

26 

198.4 

106.1 

86 

251.3 

134.3 

46 

40.6 

21.7 

06 

93.6 

50.0 

66 

146.4 

78.3 

26 

199.3 

106.5 

86 

252.2 

134.8 

47 

41.6 

22.2 

07 

94.4 

50.4 

67 

147.3 

78.7 

27 

200.2 

107.0 

87 

253.1 

135. 3 

48 

42.3 

22.6 

08 

96.2 

50.9 

68 

148.2 

79.2 

28 

201.1 

107.5 

88 

254.0 

135.8 

49 

43.2 

23.1 

09 

.  96.1 

61.4 

69 

149.0 

79.7 

29 

202.0 

107.9 

89 

264.9 

136.2 

50 

44.1 

23.6 
24.0 

10 

97.0 

61.9 

70 

149.9 

80.1 

30 

202.8 

108.4 

90 

255.8 

136.  7 

61 

46.0 

111 

97.9 

52.3 

171 

160.8 

80.6 

231 

203.7 

108.9 

291 

256.6 

137.2 

52 

46.9 

24.5 

12 

98.8 

52.8 

72 

151.7 

81.1 

32 

204.6 

109.4 

92 

267.5 

137. 6 

53 

46.7 

25.0 

13 

99.7 

63.3 

73 

152.6 

81.6 

33 

205.5 

109.8 

93 

268.4 

138. 1 

54 

47.6 

25.5 

14 

100.5 

63.7 

74 

153.5 

82.0 

34 

206.4 

110.3 

94 

259.  3 

138.6 

55 

48.5 

25.9 

16 

101.4 

54.2 

75 

164.3 

82.5 

36 

207.3 

110.8 

96 

260.2 

139.1 

56 

49.4 

26.4 

16 

102.3 

64.7 

76 

166.2 

83.0 

36 

208.1 

111.2 

96 

261.0 

139.6 

57 

50.3 

26.9 

17 

103.2 

55.2 

77 

166.1 

83.4 

37 

209.0 

111.7 

97 

261.9 

140.0 

58 

51.2 

27.3 

18 

104.1 

56.6 

78 

157.0 

83.9 

38 

209.9 

112.2 

98 

262.8 

140.5 

59 

52.0 

27.8 

19 

104.9 

56.1 

79 

157.9 

84.4 

39 

210.8 

112.7 

99 

263.7 

140.9 

60 

52.9 

28.3 

20 

105.8 

56.6 

80 

168.7 

84.9 

40 

211.7 

113.1 

300 

264.6 

141.4 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

NE 

.  by  E.  i  E. 

SE 

.  by  E.  i  E. 

NW.  by  W.  ^  W. 

SW.  by  W.  i  W. 

[For  5J  P( 

jintfi. 

TABLE  1. 

[Page  625 

Difference  of  Latitude  and  Departure  for  2J  Points. 

NNE.'  J  E. 

NNW. 

i  W.                    SSE.  1  E 

SSW.  f  w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Diat. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist.       Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.3 

31.4 

121 

103.8 

62.2 

181 

155.2 

93.1 

241  i  206.7 

123.9 

2 

1.7 

1.0 

62 

53.2 

31.9 

22 

104.6 

62.7 

82 

156.1 

93.6 

42     207.6 

124.4 

3 

2.6 

1.5 

63 

54.0 

32.4 

23 

105.5 

63.2 

83 

157.0 

94.1 

43     208.4 

124.9 

4 

3.4 

2.1 

64 

54.9 

32.9 

24 

106.4 

63.7 

84 

157.8 

94.6 

44 

209.3 

125.4 

5 

4.3 

2.6 

65 

55.8 

33.4 

25 

107.2 

64.3 

85 

158.7 

95.1 

45 

210.1 

126.0 

6 

5.1 

3.1 

66 

56.6 

33.9 

26 

108.1 

64.8 

86 

159.5 

95.6 

46 

211.0 

126.5 

7 

6.0 

3.6 

67 

57.5 

34.4 

27 

108.9 

65.3 

87 

160.4 

96.1 

47 

211.9 

127.0 

8 

6.9 

4.1 

68 

58.3 

35.0 

28 

109.8 

65.8 

88 

161.3 

96.7 

48 

212.7 

127.5 

9 

7.7 

4.6 

69 

59.2 

35.5 

29 

110.6 

66.3 

89 

162.1 

97.2 

49 

213.6 

128.0 

10 

8.6 

5.1 

70 

60.0 

36.0 

30 
131 

111.5 

66.8 

90 

163.0 

97.7 

50 

214.4 
215.3 

128.5 

11 

9.4 

5.7 

71 

60.9 

36.5 

112.4 

67.3 

191 

163.8 

98.2 

251 

129.0 

12 

10.3 

6.2 

72 

61.8 

37.0 

32 

113.2 

67.9 

92 

164.7 

98.7 

52 

216.1 

129.6 

13 

11.2 

6.7 

73 

62.6 

37.5 

33 

114.1 

68.4 

93 

165.5 

99.2 

53 

217.0 

130.1 

14 

12.0 

7.2 

74 

63.5 

38.0 

34 

114.9 

68.9 

94 

166.4 

99.7 

54 

217.9 

130.6 

15 

12.9 

7.7 

75 

64.3 

38.6 

35 

115.8 

69.4 

95 

167.3 

100.3 

55 

218.7 

131.1 

16 

13.7 

8.2 

76 

65.2 

39.1 

36 

116.7 

69.9 

96 

168.1 

100.8 

56  !  219.6 

131.6 

17 

14.6 

8.7 

77 

66.0 

39.6 

37 

117.5 

70.4 

97 

169.0 

101.3 

57  i  220.4 

132.1 

18 

15.4 

9.3 

78 

66.9 

40.1 

38 

118.4 

70.9 

98 

169.8 

101.8 

58 

221.3 

132.6 

19 

16.3 

9.8 

79 

67.8 

40.6 

39 

119.2 

71.5 

99 

170.7 

102.3 

59 

222.2 

133.2 

20 

17.2 

10.3 

80 

68.6 

41.1 

40 

120.1 
120.9 

72.0 

200 

171.5 

102.8 

60 

223.0 

133.7 

21 

18.0 

10.8 

81 

69.  S 

41.6 

141 

72.5 

201 

172.4 

103.3 

261 

223.9 

134.2 

22 

18.9 

11.3 

82 

70.3 

42.2 

42 

121.8 

73.0 

02 

173.3 

103.8 

62 

224.7 

134.7 

23 

19.7 

11.8 

83 

71.2 

42.7 

43 

122.7 

73.5 

03 

174.1 

104.4 

63 

225.6 

135.2 

24 

20.6 

12.3 

84 

72.0 

43.2 

44 

123.5 

74.0 

04 

175.0 

104.9 

64 

226.4 

135.7 

25 

21.4 

12.9 

85 

72.9 

43.7 

45 

124.4 

74.5 

05 

175.8 

105.4 

65 

227.3 

136.2 

26 

22.3 

13.4 

86 

73.8 

44.2 

46 

125.2 

75.1 

06 

176.7 

106.9 

66 

228.2 

136.8 

27 

23.2 

13.9 

87 

74.6 

44.7 

47 

126.1 

75.6 

07 

177.5 

106.4 

67 

229.0 

137.3 

28 

24.0 

14.4 

88 

75.5 

45.2 

48 

126.9 

76.1 

08 

178.4 

106.9 

68 

229.9 

137.8 

29 

24.9 

14.9 

89 

76.3 

45.8 

49 

127.8 

76.6 

09 

179.3 

107.4 

69 

230.7 

138.3 

30 
31 

25.7 

15.4 

90 

77.2 

46.3 

50 

128.7 

77.1 

10 

180.1 

108.0 

70 

231.6 

138.8 

26.6 

15.9 

91 

78.1 

46.8 

151 

129.5 

77.6 

211 

181.0 

108.5 

271 

232.4 

139.3 

32 

27.4 

16.5 

92 

78.9 

47.3 

52 

130.4 

78.1 

12 

181.8 

109.0 

72 

233.3 

139.8 

33 

28.3 

17.0 

93 

79.8 

47.8 

53 

131.2 

78.7 

13 

182.7 

109.5 

73 

234.2 

140.4 

34 

29.2 

17.5 

94 

80.6 

48.3 

54 

132.1 

79.2 

14 

183.6 

110.0 

74 

235.0 

140.9 

35 

30.0 

18.0 

95 

81.5 

48.8 

55 

132.9 

79.7 

15 

184.4 

110.5 

75 

235.9 

141.4 

36 

30.9 

18.5 

96 

82.3 

49.4 

56 

133.8 

80.2 

16 

185.3 

lll.O 

76 

236.7 

141.9 

37 

31.7 

19.0 

97 

83.2 

49.9 

57 

134.7 

80.7 

17 

186.1 

111.6 

77 

237.6 

142.4 

38 

32.6 

19.5 

98 

84.1 

50.4 

58 

135.5 

81.2 

18 

187.0 

112.1 

78 

238.4 

142.9 

39 

33.5 

20.1 

99 

84.9 

50.9 

59 

136.4 

81.7 

19 

187.8 

112.6 

79 

239.3 

143.4 

40 

34.3 

20.6 

100 

85.8 

51.4 

60 

137.2 

82.3 

20 

188.7 

113.1 

80 

240.2 

143.9 

41 

35.2 

21.1 

101 

86.6 

51.9 

161 

138.1 

82.8 

221 

189.6 

113.6 

281 

241.0 

144.5 

42 

36.0 

21.6 

02 

87.5 

52.4 

62 

139.0 

83.3 

22 

190.4 

114.1 

82 

241.9 

145.0 

43 

36.9 

22.1 

03 

88.3 

53.0 

63 

139.8 

83.8 

23 

191.3 

114.6 

83 

242.7 

145.5 

44 

37.7 

22.6 

04 

89.2 

53.5 

64 

140.7 

84.3 

24 

192.1 

115.2 

84 

243.6 

146.0 

45 

38.6 

23.1 

05 

90.1 

54.0 

65 

141.5 

84.8 

25 

193.0 

115.7 

85 

244.5 

146.5 

46 

39.5 

23.6 

06 

90.9 

54.5 

66 

142.4 

85.3 

26 

193.8 

116.2 

86 

245.3 

147.0 

47 

40.3 

24.2 

07 

91.8 

55.0 

67 

143.2 

85.9 

27 

194.7 

116.7 

87 

246.2 

147.5 

48 

41.2 

24.7 

08 

92.6 

55.5 

68 

144.1 

86.4 

28 

195.6 

117.2 

88 

247.0 

148.1 

49 

42.0 

25.2 

09 

93.5 

56.0 

69 

145.0 

86.9 

29 

196.4 

117.7 

89 

247.9 

148. 6 

50 

42.9 

25.7 

10 

94.4 

56.6 

70 
171 

145.8 
146.7 

87.4 

30 

197.3 

118.2 

90 

248.7 

149.1 

51 

43.7 

26.2 

111 

95.2 

57.1 

87.9 

231 

198.1 

118.8 

291 

249.6 

149.6 

52 

44.6 

26.7 

12 

96.1 

57.6 

72 

147.5 

88.4 

32 

199.0 

119.3 

92 

250.5 

150.1 

53 

45.5 

27.2 

13 

96.9 

58.1 

73 

148.4 

88.9 

33 

199.9 

119.8 

93 

251.3 

150.6 

54 

46.3 

27.8 

14 

97.8 

58.6 

74 

149.2 

89.5 

34 

200.7 

120.3 

94 

252.2 

151.1 

55 

47.2 

28.3 

15 

98.6 

59.1 

75 

150.1 

90.0 

35 

201.6 

120.8 

95 

253.0 

151.7 

56 

48.0 

28.8 

16 

99.5 

59.6 

76 

151.0 

90.5 

36 

202.4 

121.3 

96 

253.9 

152.2 

57 

48.9 

29.3 

17 

100.4 

60.2 

77 

151.8 

91.0 

37 

203.3 

121.8 

97 

254.7 

152.7 

58 

49.7 

29.8 

18 

101.2 

60.7 

78 

152.7 

91.5 

38 

204.1 

122.4 

98 

255.6 

153.2 

59 

50.6 

30.3 

19 

102.1 

61.2 

79 

153.5 

92.0 

39 

205.0 

122.9 

99 

256.5 

153.7 

60 

51.5 

30.8 

20 

102.9 

61.7 

80 

154.4 

92.5 

40 

205.9 

123.4 

300 

257.3 

154.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

N] 

E.  by  E.  i  E. 

SI 

5.  by  E.  t  E. 

NW.  by  W.  i  W. 

sw 

.  by  VV.  i  W. 

[For  5J^  PoL 

nt8. 

Page  526] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  3  Points. 

NE.  by 

N. 

NW. 

by  N.                      SE.  by  S. 

SW.  by  S. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.7 

33.9 

121 

100.6 

67.2 

181 

160.6 

100.6 

241 

200.4 

133.9 

2 

1.-7 

1.1 

62 

51.6 

34.4 

22 

101.4 

67.8 

82 

151.3 

101.1 

42 

201.2 

134.4 

3 

2.5 

1.7 

63 

62.4 

36.0 

23 

102.3 

68.3 

83 

152.2 

101.7 

43 

202.0 

135.0 

4 

3.3 

2.2 

64 

53.2 

35.6 

24 

103.1 

68.9 

84 

153.0 

102.2 

44 

202.9 

135.6 

5 

4.2 

2.8 

65 

54.0 

36.1 

25 

103.9 

69.4 

85 

163.8 

102.8 

46 

203.7 

136.1 

6 

5.0 

3.3 

66 

64.9 

36.7 

26 

104.8 

70.0 

86 

164.7 

103.3 

46 

204.5 

136.7 

7 

5.8 

3.9 

67 

55.7 

37.2 

27 

106.6 

70.6 

87 

155.5 

103. 9 

47 

206.4 

137.2 

8 

6.7 

4.4 

68 

66.6 

37.8 

28 

106.4 

71.1 

88 

156.  3 

104.4 

48 

206.2 

137.8 

9 

7.5 

5.0 

69 

67.4 

38.3 

29 

107.3 

71.7 

89 

157.1 

105.0 

49 

207.0 

138.3 

10 

8.3 

5.6 

70 

58.2 

38.9 

30 

108.1 

72.2 
72.8 

90 
191 

158.0 

105.6 

60 

207.9 

138.9 

11 

9.1 

6.1 

71 

59.0 

39.4 

131 

108.9 

158.8 

106.1 

251 

208.7 

139.4 

12 

10.0 

6.7 

72 

59.9 

40.0 

32 

109.8 

73.3 

92 

159.6 

106.7 

52 

209.6 

140.0 

13 

10.8 

7.2 

73 

60.7 

40.6 

33 

110.6 

73.9 

93 

160.5 

107.2 

63 

210.4 

140.6 

14 

11.6 

7.8 

74 

61.5 

41.1 

34 

111.4 

74.4 

94 

161.3 

107.8 

54 

211.2 

141.1 

15 

12.5 

8.3 

75 

62.4 

41.7 

35 

112.2 

75.0 

96 

162.1 

108.3 

55 

212.0 

141.7 

16 

13.3 

8.9 

76 

63.2 

42.2 

36 

113.1 

75.6 

96 

163.0 

108.9 

56 

212.9 

142.2 

17 

14.1 

9.4 

77 

64.0 

42.8 

37 

113.9 

76.1 

97 

163.8 

109.4 

57 

213.7 

142.8 

18 

15.0 

10.0 

78 

64.9 

43.3 

38 

114.7 

76.7 

98 

164.6 

110.0 

58 

214.5 

143.3 

19 

15.8 

10.6 

79 

65.7 

43.9 

39 

115.6 

77.2 

99 

166.5 

110.6 

59 

215.4 

143.9 

20 

16.6 

11.1 

80 

66.5 

44.4 

40 

116.4 

77.8 

200 

166.3 

111.1 

60 

216.2 

144.4 

21 

17.5 

11.7 

81 

67.3 

45.0 

141 

117.2 

78.3 

201 

167.1 

111.7 

261 

217.0 

145.0 

22 

18.3 

12.2 

82 

68.2 

45.6 

42 

118.1 

78.9 

02 

168.0 

112.2 

62 

217.8 

145.6 

23 

19.1 

12.8 

83 

69.0 

46.1 

43 

118.9 

79.4 

03 

168.8 

112.8 

63 

218.7 

146.1 

24 

20.0 

13.3 

84 

69.8 

46.7 

44 

119.7 

80.0 

04 

169.6 

113.3 

64 

219.6 

146.7 

26 

20.8 

13.9 

85 

70.7 

47.2 

45 

120.6 

80.6 

05 

170.6 

113.9 

65 

220.  3 

147.2 

26 

21.6 

14.4 

86 

71.5 

47.8 

46 

121.4 

81.1 

06 

171.3 

114.4 

66 

221.2 

147.8 

27 

22.4 

15.0 

87 

72.3 

48.3 

47 

122.2 

81.7 

07 

172.1 

116.0 

67 

222.0 

148.3 

28 

23.3 

15.6 

88 

73.2 

48.9 

48 

123.1 

82.2 

08 

172.9 

115.6 

68 

222.8 

148.9 

29 

24.1 

16.1 

89 

74.0 

49.4 

49 

123.9 

82.8 

09 

173.8 

116.1 

69 

223.7 

149.4 

30 

24.9 

16.7 

90 

74.8 

50.0 

60 

124.7 

83.3 

10 

174.6 

116.7 

70 

224.5 
225.3 

160.0 
160.6 

31 

25.8 

17.2 

91 

75.7 

50.6 

161 

126.6 

83.9 

211 

175.4 

117.2 

271 

32 

26.6 

17.8 

92 

76.5 

51.1 

52 

126. 4 

84.4 

12 

176.3 

117.8 

72 

226.2 

151.1 

33 

27.4 

18.3 

93 

77.3 

51.7 

53 

127.2 

85.0 

13 

177.1 

118.3 

73 

227.0 

161.7 

34 

28.3 

18.9 

94 

78.2 

52.2 

64 

128.0 

85.6 

14 

177.9 

118.9 

74 

227.8 

162.2 

35 

29.1 

19.4 

95 

79.0 

52'.  8 

65 

128.9 

86.1 

15 

178.8 

119.4 

75 

228.7 

152.8 

36 

29.9 

20.0 

96 

79.8 

53.3 

56 

129.7 

86.7 

16 

179.6 

120.0 

76 

229.5 

163.  3 

37 

30.8 

20.6 

97 

80.7 

53.9 

67 

130.5 

87.2 

17 

180.4 

120.6 

77 

230.3 

163.9 

38 

31.6 

21.1 

98 

81.5 

54.4 

68 

131.4 

87.8 

18 

181.3 

121.1 

78 

231.1 

164.4 

39 

32.4 

21.7 

99 

82.3 

65.0 

69 

132.2 

88.3 

19 

182.1 

121.7 

79 

232.0 

155.0 

40 

33.3 

22.2 

100 

83.1 

55.6 

60 

133.0 

88.9 

20 

182.9 

122.2 

80 

232.8 
233.6 

156.6 

41 

34.1 

22.8 

101 

84.0 

56.1 

161 

133.9 

89.4 

221 

183.8 

122.8 

281 

166.1 

42 

34.9 

23.3 

02 

84.8 

56.7 

62 

134.7 

90.0 

22 

184.6 

123.3 

82 

234.  5 

166.7 

43 

35.8 

23.9 

03 

85.6 

67.2 

63 

135.5 

90.6 

23 

185.4 

123.9 

83 

235.3 

167.2 

44 

36.6 

24.4 

04 

86.5 

57.8 

64 

136.4 

91.1 

24 

186.2 

124.4 

84 

236.1 

157.8 

45 

37.4 

25.0 

05 

87.3 

58.3 

65 

137.2 

91.7 

25 

187.1 

125.0 

85 

237.0 

158.3 

46 

38.2 

25.6 

06 

88.1 

68.9 

66 

138.0 

92.2 

26 

187.9 

125.6 

86 

237.8 

168.9 

47 

39.1 

26.1 

07 

89.0 

69.4 

67 

138.9 

92.8 

27 

188.7 

126.1 

87 

238.6 

159.4 

48 

39.9 

26.7 

08 

89.8 

60.0 

68 

139.7 

93.3 

28 

189.6 

126.7 

88 

239.5 

160.0 

49 

40.7 

27.2 

09 

90.6 

60.6 

69 

140.5 

93.9 

29 

190.4 

127.2 

89 

240.3 

160.6 

50 

41.6 

27.8 

10 

91.5 

61.1 

70 

141.3 

94.4 

30 

191.2 

127.8 

90 

241. 1 

161.1 

51 

42.4 

28.3 

111 

92.3 

61.7 

171 

142.2 

95.0 

231 

192.1 

128.3 

291 

242.0 

161.7 

52 

43.2 

28.9 

12 

93.1 

62.2 

72 

143.0 

95.6 

32 

192.9 

128.9 

92 

242.8 

162.2 

53 

44.1 

29.4 

13 

94.0 

62.8 

73 

143.8 

96.1 

33 

193.7 

129.4 

93 

243.6 

162.8 

54 

44.9 

30.0 

14 

94.8 

63.3 

74 

144.7 

96.7 

34 

194.6 

130.0 

94 

244.6 

163.3 

65 

45.7 

30.6 

15 

95.6 

63.9 

75 

146.5 

97.2 

36 

195.4 

130.6 

95 

246.3 

163.9 

56 

46.6 

31.1 

16 

96.5 

64.4 

76 

146.3 

97.8 

36 

196.2 

131. 1 

96 

246.1 

164.4 

57 

47.4 

31.7 

17 

97.3 

65.0 

77 

147.2 

98.3 

37 

197.1 

131.7 

97 

246.9 

165.0 

58 

48.2 

32.2 

18 

98.1 

65.6 

78 

148.0 

98.9 

38 

197.9 

132.2 

98 

247.8 

166.6 

59 

49.1 

32.8 

19 

98.9 

66.1 

79 

148.8 

99.4 

39 

198.7 

132.8 

99 

248.6 

166.1 

60 

49.9 

33.3 

20 

99.8 

66.7 

80 

149.7 

100.0 

40 

199.6 

133.3 

300 

249.4 

166.7 

Dlst 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist.       Eep. 

Lat 

NE.  by  E. 

g 

5E.  by  E. 

NW.  by  W. 

SW.  by  W. 

[For  5  Points.       1 

TABLE  1. 

[Page 

527  1 

Difference  of  Latitude  and  Departure  for  S\  Points. 

NE.  IN 

. 

NW. 

1  N.                          SE.  1  S. 

SW.  1  S. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep.  1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

49.0 

36.3 

121 

97.2 

72.1 

181 

145.4 

107.8 

241 

193.6 

143.6 

2 

1.6 

1.2 

62 

49.8 

36.9 

22 

98.0 

72.7 

82 

146.2 

108.4 

42 

194.4 

144.2 

3 

2,4 

1.8 

63 

50.6 

37.5 

23 

98.8 

73.3 

83 

147.0 

109.0 

43 

195.2 

144.8 

4 

3.2 

2.4 

64 

51.4 

38.1 

24 

99.6 

73.9 

84 

147.8 

109.6 

44 

196.0 

145.4 

5 

4.0 

3.0 

65 

52.2 

38.7 

25 

100.4 

74.5 

85 

148.6 

110.2 

45 

196.8 

145.9 

6 

4.8 

3.6 

66 

53.0 

39.3 

26 

101.2 

75.1 

86 

149.4 

110.8 

46 

197.6 

146.5 

7 

5.6 

4.2 

67 

53.8 

39.9 

27 

102.0 

75.7 

87 

150.2 

111.4 

47 

198.4 

147.1 

8 

6.4 

4.8 

68 

54.6 

40.5 

28 

102.8 

76.2 

88 

151.0 

112.0 

48 

199.2 

147.7 

9 

7.2 

5.4 

69 

55.4 

41.1 

29 

103.6 

76.8 

89 

151.8 

112.6 

49 

200.0 

148.3 

10 

8.0 

6.0 

70 

56.2 

41.7 

30 

104.4 

77.4 

90 

152.6 

113.2 

50 

200.8 

148.9 
149.5 

11 

8.8 

6.6 

71 

57.0 

42.3 

131 

105.2 

78.0 

191 

153.4 

113.8 

251 

201.6 

12 

9.6 

7.1 

72 

57.8 

42.9 

32 

106.0 

78.6 

92 

154.2 

114.4 

52 

202.4 

150. 1 

13 

10.4 

7.7 

73 

58.6 

43.5 

33 

106.8 

79.2 

93 

155.0 

115.0 

53 

203.2 

150.7 

14 

11.2 

8.3 

74 

59.4 

44.1 

34 

107.6 

79.8 

94 

155.8 

115.6 

54 

204.0 

151.3 

15 

12.0 

8.9 

75 

60.2 

44.7 

35 

108.4 

80.4 

95 

156.6 

116.2 

55 

204.8 

151.9 

16 

12.9 

9.5 

76 

61.0 

45.3 

36 

109.2 

81.0 

96 

157.4 

116.8 

56 

205.6 

152.5 

17 

13.7 

10.1 

77 

61.8 

45.9 

37 

110.0 

81.6 

97 

158.2 

117.4 

57 

206.4 

153.1 

18 

14.5 

10.7 

78 

62.7 

46.5 

38 

110.8 

82.2 

98 

159.0 

117.9 

58 

207.2 

153.7 

19 

15.3 

11.3 

79 

63.5 

47.1 

39 

111.6 

82.8 

99 

159. 8 

118.5 

59 

208.0 

154.3 

20 

16.1 

11.9 

80 

64.3 

47.7 

40 

112.4 

83.4 

200 

160.6 

119.1 

60 

208.8 

154.9 

21 

16.9 

12.5 

81 

65.1 

48.3 

141 

113.3 

84.0 

201 

161.4 

119.7 

261 

209.6 

155. 5 

22 

17.7 

13.1 

82 

65.9 

48.8 

42 

114.1 

84.6 

02 

162.2 

120.3 

62 

210.4 

156.1 

23 

18.5 

13.7 

83 

66.7 

49.4 

43 

114.9 

85.2 

03 

163.1 

120.9 

63 

211.2 

156.7 

24 

19.3 

14.3 

84 

67.5 

50.0 

44 

115.7 

85.8 

04 

163. 9 

121.5 

64 

212.0 

157. 3 

25 

20.1 

14.9 

85 

68.3 

50.6 

45 

116.5 

86.4 

05 

164.7 

122.1 

66 

212.8 

157.9 

26 

20.9 

15.5 

86 

69.1 

51.2 

46 

117.3 

87.0 

06 

165.5 

122.7 

66 

213.7 

158.5 

27 

21.7 

16.1 

87 

69.9 

51.8 

47 

118.1 

87.6 

07 

166.3 

123.3 

67 

214.5 

159.1 

28 

22.5 

16.7 

88 

70.7 

52.4 

48 

118.9 

88.2 

08 

167.1 

123.9 

68 

215.3 

159.6 

29 

23.3 

17.3 

89 

71.5 

53.0 

49 

119.7 

88.8 

09 

167.9 

124.5 

69 

216.1 

160.2 

30 

24.1 

17.9 

90 

72.3 

53.6 

50 

120,5 

89.4 

10 

168.7 

125.1 

70 

216.9 

160.8 

31 

24.9 

18.5 

91 

73.1 

54.2 

151 

121.3 

90.0 

211 

169.5 

125.7 

271 

217.7 

161.4 

32 

25.7 

19.1 

92 

73.9 

54.8 

52 

122.1 

90.5 

12 

170.3 

126.3 

72 

218.5 

162.0 

33 

26.5 

19.7 

93 

74.7 

55.4 

53 

122.9 

91.1 

13 

171.1 

126.9 

73 

219.3 

162.6 

34 

27.3 

20.3 

94 

75.5 

56.0 

54 

123.7 

91.7 

14 

171.9 

127.5 

74 

220.1 

163.2 

35 

28.1 

20.8 

95 

76.3 

56.6 

55 

124.5 

92.3 

15 

172.7 

128.1 

75 

220.9 

163.8 

36 

28.9 

21.4 

96 

77.1 

57.2 

56 

125.3 

92.9 

16 

173.5 

128.7 

76 

221.7 

164.4 

37 

29.7 

22.0 

97 

77.9 

57.8 

57 

126.1 

93.5 

17 

174.3 

129.3 

77 

222.5 

165.0 

38 

30.5 

22.6 

98 

78.7 

58.4 

58 

126. 9 

94.1 

18 

175.1 

129.9 

78 

223.3 

165.6 

39 

31.3 

23.2 

99 

79.5 

59.0 

59 

127.7 

94.7 

19 

175.9 

130.5 

79 

224.1 

166.2 

40 

32.1 

23.8 

100 

80.3 

59.6 

60 

128.5 

95.3 

20 

176.7 

131.1 

80 

224.9 

166.8 

41 

32.9 

24.4 

101 

81.1 

60.2 

161 

129.3 

95.9 

221 

177.5 

131.6 

281 

225.7 

167.4 

42 

33.7 

25.0 

02 

81.9 

60.8 

62 

130.1 

96.5 

22 

178.3 

132.2 

82 

226.5 

168.0 

43 

34.5 

25.6 

03 

82.7 

61.4 

63 

1.30.9 

97.1 

23 

179.1 

132.8 

83 

227.3 

168.6 

44 

35.3 

26.2 

04 

83.5 

62.0 

64 

131.7 

97.7 

24 

179.9 

133.4 

84 

228.1 

169.2 

45 

36.1 

26.8 

05 

84.3 

62.5 

65 

132.5 

98.3 

25 

180.7 

134.0 

85 

228.9 

169.8 

46 

36.9 

27.4 

06 

85.1 

63.1 

66 

133.3 

98.9 

26 

181.  5 

134.6 

86 

229.7 

170.4 

47 

37.8 

28.0 

07 

85.9 

63.7 

67 

134.1 

99.5 

27 

182.3 

135.2 

87 

230.5 

171.0 

48 

38.6 

28.6 

08 

86.7 

64.3 

68 

134.9 

100.1 

28 

183.1 

135.8 

88 

231.3 

171.6 

49 

39.4 

29.2 

09 

87.5 

64.9 

69 

135.7 

100.7 

29 

183.9 

136.4 

89 

232.1 

172.2 

50 

40.2 

29.8 

10 

88.4 

65.5 

70 

136.5 

101.3 

30 

184.7 

137.0 

90 

232.9 

172.8 

51 

41.0 

30.4 

111 

89.2 

66.1 

171 

137.3 

101.9 

231 

185.5 

137.6 

291 

233.7 

173.3 

52 

41.8 

31.0 

12 

90.0 

66.7 

72 

138.2 

102.5 

32 

186.3 

138.2 

92 

234.5 

173.9 

53 

42.6 

31.6 

13 

90.8 

67.3 

73 

139.0 

103.1 

33 

187.1 

138.8 

93 

235.3 

174.5 

54 

43.4 

32.2 

14 

91.6 

67.9 

74 

139.8 

103.7 

34 

188.0 

139.4 

94 

236.1 

175.1 

55 

44.2 

32.8 

15 

92.4 

68.5 

75 

140.6 

104.2 

35 

188.8 

140,0 

95 

236.9 

175.7 

56 

45.0 

33.4 

16 

93.2 

69.1 

76 

141.4 

104.8 

36 

189.6 

140.6 

96 

237.7 

176.3 

57 

45.8 

34.0 

17 

94.0 

69.7 

77 

142.2 

105.4 

37 

190.4 

141.2 

97 

238.6 

176.9 

68 

46.6 

34.6 

18 

94.8 

70.3 

78 

143.0 

106.0 

38 

191.2 

141.8 

98 

239.4 

177.5 

69 

47.4 

35.1 

19 

95.6 

70.9 

79 

143.8 

106.6 

39 

192.0 

142.4 

99 

240.2 

178.1 

60 

48.2 

35.7 

20 

96.4 

71.5 

80 

144.6 

107.2 

40 

192.8 

143.0 

300 

241.0 

178.7 

Wst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  ^ 

^E. 

SE.  1  E. 

NW.  1  W.               SW.  f  W. 

[For  4|  Points.      1 

Page  628] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  3J  Points. 

NE.  J  N. 

NW 

.  ^N. 

SE 

.  ^S. 

SW.  i  s.                     1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

47.2 

38.7 

121 

93.6 

76.8 

181 

139.9 

114.8 

241 

186.3 

152.9 

2 

1.5 

1.3 

62 

47.9 

39.3 

22 

94.3 

77.4 

82 

140.7 

116.6 

42 

187. 1 

163.5 

3 

2.3 

1.9 

63 

48.7 

40.0 

23 

95.1 

78.0 

83 

141.6 

116.1 

43 

187.8 

154.2 

4 

3.1 

2.5 

64 

49.6 

40.6 

24 

95.9 

78.7 

84 

142.2 

116.7 

44 

188.6 

164.8 

5 

3.9 

3.2 

65 

60.2 

41.2 

25 

96.6 

79.3 

85 

143.0 

117.4 

46 

189.4 

155.4 

6 

4.6 

3.8 

66 

51.0 

41.9 

26 

97.4 

79.9 

86 

143.8 

118.0 

46 

190.2 

166.1 

7 

5.4 

4.4 

67 

51.8 

42.5 

27 

98.2 

80.6 

87 

144.6 

118.6 

47 

190.9 

166.7 

8 

6.2 

5.1 

68 

62.6 

43.1 

28 

98.9 

81.2 

88 

145.3 

119.3 

48 

191.7 

157.3 

9 

7.0 

5.7 

69 

63.3 

43.8 

29 

99.7 

81.8 

89 

146.1 

119.9 

49 

192.  5 

158.0 

10 

7.7 

6.3 

70 

54.1 

44.4 

30 

100.5 

82.5 

90 

146.9 
147.6 

120.5 

50 

193.3 

168.6 

11 

8.5 

7.0 

71 

54.9 

45.0 

131 

101.3 

83.1 

191 

121.2 

261 

194.0 

159.2 

12 

9.3 

7.6 

72 

55.7 

45.7 

32 

102.0 

83.7 

92 

148.4 

121.8 

62 

194.8 

159.9 

13 

10.0 

8.2 

73 

56.4 

46.3 

33 

102.8 

84.4 

93 

149.2 

122.4 

53 

196.6 

160.5 

14 

10.8 

8.9 

74 

57.2 

46.9 

34 

103.6 

85.0 

94 

150.0 

123.1 

54 

196.3 

161.1 

15 

11.6 

9.5 

75 

58.0 

47.6 

35 

104.4 

85.6 

95 

150.7 

123.7 

56 

197.1 

161.8 

16 

12.4 

10.2 

76 

58.7 

48.2 

36 

105.1 

86.3 

96 

151.6 

124.3 

56 

197.9 

162.4 

17 

13.1 

10.8 

77 

59.6 

48.8 

37 

105.9 

86.9 

97 

162.3 

126.0 

67 

198.7 

163.0 

18 

13.9 

11.4 

78 

60.3 

49.5 

38 

106.7 

87.5 

98 

163.1 

125.6 

58 

199.4 

163.7 

19 

14.7 

12.1 

79 

61.1 

50.1 

39 

107.4 

88.2 

99 

153.8 

126.2 

69 

200.2 

164.3 

20 

15.5 

12.7 

80 

61.8 

60.8 

40 

108.2 
109.0 

88.8 
89.4 

200 
201 

154.6 

126.9 

60 

201.0 

164.9 

21 

16.2 

13.3 

81 

62.6 

61.4 

141 

156.4 

127.6 

261 

201.8 

165.6 

22 

17.0 

14.0 

82 

63.4 

52.0 

42 

109.8 

90.1 

02 

166.1 

128.1 

62 

202.6 

166.2 

23 

17.8 

14.6 

83 

64.2 

52.7 

43 

110.6 

90.7 

03 

166.9 

128.8 

63 

203.3 

166.8 

24 

18.6 

15.2 

84 

64.9 

63.3 

44 

111.3 

91.4 

04 

157.7 

129.4 

64 

204.1 

167.5 

25 

19.3 

15.9 

85 

65.7 

63.9 

45 

112.1 

92.0 

05 

168.5 

130.1 

66 

204.8 

168.1 

26 

20.1 

16.5 

86 

66.6 

64.6 

46 

112.9 

92.6 

06 

169.2 

130.7 

66 

206.6 

168.7 

27 

20.9 

17.1 

87 

67.3 

55.2 

47 

113.6 

93.3 

07 

160.0 

131.3 

67 

206.4 

169.4 

28 

21.6 

17.8 

88 

68.0 

56.8 

48 

114.4 

93.9 

08 

160.8 

132.0 

68 

207.2 

170.0 

29 

22.4 

18.4 

89 

68.8 

66.6 

49 

116.2 

94.5 

09 

161.6 

132.6 

69 

207.9 

170.7 

30 

23.2 

19.0 

90 

69.6 

57.1 

60 

116.0 

95.2 

10 

162.3 

133.2 

70 

208.7 

171.3 

31 

24.0 

19.7 

91 

70.3 

67.7 

151 

116.7 

96.8 

211 

163.1 

133.9 

271 

209.5 

171.9 

32 

24.7 

20.3 

92 

71.1 

58.4 

62 

117.5 

96.4 

12 

163.9 

134.5 

72 

210.3 

172.6 

33 

25.5 

20.9 

93 

71.9 

59.0 

63 

118.3 

97.1 

13 

164.7 

136.1 

73 

211.0 

173.2 

34 

26.3 

21.6 

94 

72.7 

59.6 

64 

119.0 

97.7 

14 

166.4 

136.8 

74 

211.8 

173.8 

36 

27.1 

22.2 

95 

73.4 

60.3 

55 

119.8 

98.3 

15 

166.2 

136.4 

75 

212.6 

174.5 

36 

27.8 

22.8 

96 

74.2 

60.9 

66 

120.6 

99.0 

16 

167.0 

137.0 

76 

213.4 

176.1 

37 

28.6 

23.5 

97 

75.0 

61.6 

57 

121.4 

99.6 

17 

167.7 

137.7 

77 

214.1 

176.7 

38 

29.4 

24.1 

98 

75.8 

62.2 

68 

122.1 

100.2 

18 

168.6 

138.3 

78 

214.9 

176.4 

39 

30.1 

24.7 

99 

76.5 

62.8 

59 

122.9 

100.9 

19 

169.3 

138.9 

79 

215.7 

177.0 

40 

30.9 

25.4 

100 

77.3 

63.4 

60 

123.7 

101.5 

20 

170.1 
170.8 

139.6 

80 

216.4 

177.6 

41 

31.7 

26.0 

101 

78.1 

64.1 

161 

124.5 

102. 1 

221 

140.2 

281 

217.2 

178.3 

42 

32.5 

26.6 

02 

78.8 

64.7 

62 

125.2 

102.8 

22 

171.6 

140.8 

82 

218.0 

178.9 

43 

33.2 

27.3 

03 

79.6 

66.3 

63 

126.0 

103.4 

23 

172.4 

141.5 

83 

218.8 

179.5 

44 

34.0 

27.9 

04 

80.4 

66.0 

64 

126.8 

104.0 

24 

173.2 

142.1 

84 

219.5 

180.2 

45 

34.8 

28.5 

05 

81.2 

66.6 

65 

127.5 

104.7 

25 

173.9 

142.7 

85 

220.3 

180.8 

46 

35.6 

29.2 

06 

81.9 

67.2 

66 

128.3 

105.3 

26 

174.7 

143.4 

86 

221.1 

181.4 

47 

36.3 

29.8 

07 

82.7 

67.9 

67 

129.1 

105.9 

27 

175.5 

144.0 

87 

221.9 

182.1 

48 

37.1 

30.5 

08 

83.5 

68.5 

68 

129.9 

106.6 

28 

176.2 

144.6 

88 

222.6 

182.7 

49 

37.9 

31.1 

09 

84.3 

69.1 

69 

130.6 

107.2 

29 

177.0 

145.3 

89 

223.4 

183.3 

50 

38.7 

31.7 

10 

85.0 

69.8 

70 

131.4 

107.8 

30 

177.8 

146.9 

90 

224.2 

184.0 

51 

39.4 

32.4 

111 

86.8 

70.4 

171 

132.2 

108.5 

231 

178.6 

146.6 

291 

224.9 

184.6 

52 

40.2 

33.0 

12 

86.6 

71.1 

72 

133.0 

109.1 

32 

179.3 

147.2 

92 

226.7 

186.2 

53 

41.0 

33.6 

13 

87.4 

71.7 

73 

133.7 

109.8 

33 

180.1 

147.8 

93 

226.5 

185.9 

54 

41.7 

34.3 

14 

88.1 

72.3 

74 

134.5 

110.4 

34 

180.9 

148.4 

94 

227.3 

186.6 

55 

42.5 

34.9 

15 

88.9 

73.0 

75 

135.3 

111.0 

35 

181.7 

149.1 

95 

228.0 

187.1 

56 

43.3 

35.5 

16 

89.7 

73.6 

76 

136.0 

111.7 

36 

182.4 

149.7 

96 

228.8 

187.8 

57 

44.1 

36.2 

17 

90.4 

74.2 

77 

136.8 

112.3 

37 

183.2 

160.4 

97 

229.6 

188.4 

58 

44.8 

36.8 

18 

91.2 

74.9 

78 

137.6 

112.9 

38 

184.0 

161.0 

98 

230.4 

189.0 

59 

45.6 

37.4 

19 

92.0 

75.6 

79 

138.4 

113.6 

39 

184.7 

161.6 

99 

231.1 

189.7 

60 

46.4 

38.1 

20 

92.8 

76.1 

80 

139.1 

114.2 

40 

186.5 

162.3 

300 

231.9 

190.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  i] 

E. 

SE.  JE 

N 

W.  JW. 

sw.  ^^ 

V. 

[For  4J  Points.      1 

i^  >• 

— =^ 1 

TABLE  1. 

[Page  629 

Difference  of  Latitude  and  Departure  for  3|  Points. 

NE.  i  N. 

NW. 

tN. 

SE.  }  S. 

8W.  i  8. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

45.2 

41.0 

121 

89.7 

81.3 

181 

134.1 

121.6 

178.6 

161.8 

2 

1.5 

1.3 

62 

45.9 

41.6 

22 

90.4 

81.9 

82 

134.9 

122.2 

42 

179.3 

162.5 

3 

2.2 

2.0 

63 

46.7 

42.3 

23 

91.1 

82.6 

83 

135.6 

122.9 

43 

180.1 

163.2 

4 

3.0 

2.7 

64 

47.4 

43.0 

24 

91.9 

83.3 

84 

136.3 

123.6 

44 

180.8 

163.9 

5 

3.7 

3.4 

65 

48.2 

43.7 

25 

92.6 

83.9 

85 

137.1 

124.2 

45 

181.5 

164.5 

6 

4.4 

4.0 

66 

48.9 

44.3 

26 

93.4 

84.6 

86 

137.8 

124.9 

46 

182.3 

165.2 

7 

5.2 

4.7 

67 

49.6 

45.0 

27 

94.1 

85.3 

87 

138.6 

125.6 

47 

183.0 

165.9 

8 

5.9 

5.4 

68 

50.4 

45.7 

28 

94.8 

86.0 

88 

139.3 

126.3 

48 

183.8 

166.5 

9 

6.7 

6.0 

69 

51.1 

46.3 

29 

95.6 

86.6 

89 

140.0 

126.9 

49 

184.5 

167.2 

10 

7.4 

6.7 

70 

51.9 

47.0 

30 

96.3 

87.3 

90 

140.8 

127.6 

50 
251 

185.2 

167.9 

11 

8.2 

7.4 

71 

52.6 

47.7 

131 

97.1 

88.0 

191 

141.5 

128.3 

186.0 

168.6 

12 

8.9 

8.1 

72 

53.3 

48.4 

32 

97.8 

88.6 

92 

142.8 

128.9 

52 

186.7 

169.2 

13 

9.6 

8.7 

73 

54.1 

49.0 

33 

98.5 

89.3 

93 

143.0 

129.6 

53 

187.5 

169.9 

14 

10.4 

9.4 

74 

54.8 

49.7 

34 

99.3 

90.0 

94 

143.7 

130.3 

54 

188.2 

170.6 

15 

11.1 

10.1 

75 

55.6 

50.4 

35 

100.0 

90.7 

95 

144.5 

131.0 

55 

188.9 

171.2 

16 

11.9 

10.7 

76 

56.3 

51.0 

36 

100.8 

91.3 

96 

145.2 

131.6 

56 

189.7 

171.9 

17 

12.6 

11.4 

77 

57.1 

51.7 

37 

101.5 

92.0 

97 

146.0 

132.3 

57 

190.4 

172.6 

18 

13.3 

12.1 

78 

57.8 

52.4 

38 

102.3 

92.7 

98 

146.7 

133.0 

58 

191.2 

173.3 

19 

14.1 

12.8 

79 

58.5 

53.1 

39 

103.0 

93.3 

99 

147.4 

133.6 

59 

191.9 

173.9 

20 

14.8 

13.4 

80 

59.3 

53.7 

40 

103.7 

94.0 

200 

148.2 
148.9 

134.3 

60 

192.6 

174.6 

21 

15.6 

14.1 

81 

60.0 

54.4 

141 

104.5 

94.7 

201 

135.0 

261 

193.4 

175.3 

22 

16.3 

14.8 

82 

60.8 

55.1 

42 

105.2 

95.4 

02 

149.7 

135.7 

62 

194.1 

175.9 

23 

17.0 

15.4 

83 

61.5 

55.7 

43 

106.0 

96.0 

03 

150.4 

136.3 

63 

194.9 

176.6 

24 

17.8 

16,1 

84 

62.2 

56.4 

44 

106.7 

96.7 

04 

151.2 

137.0 

64 

195.6 

177.3 

25 

18.5 

16.8 

85 

63.0 

57.1 

45 

107.4 

97.4 

05 

151.9 

137.7 

65 

196.4 

178.0 

26 

19.3 

17.5 

86 

63.7 

57.8 

46 

108.2 

98.0 

06 

152.6 

138.3 

66 

197.1 

178.6 

27 

20.0 

18.1 

87 

64.5 

58.4 

47 

108.9 

98.7 

07 

153.4 

139.0 

67 

197.8 

179.3 

28 

20.7 

18.8 

88 

65.2 

59.1 

48 

109.7 

99.4 

08 

154.1 

139.7 

68 

198.6 

180.0 

29 

21.5 

19.5 

89 

65.9 

59.8 

49 

110.4 

100.1 

09 

154.9 

140.4 

69 

199.3 

180.6 

30 

22.2 

20.1 

90 

66.7 

60.4 

50 

111.1 

100.7 

10 

155.6 

141,0 

70 

200.1 
200.8 

181.3 

31 

23.0 

20.8 

91 

67.4 

61.1 

151 

111.9 

101.4 

211 

156.3 

141.7 

271 

182.0 

32 

23.7 

21.5 

92 

.68.2 

61.8 

52 

112.6 

102.1 

12 

157.1 

142.4 

72 

201.5 

182.7 

33 

24.5 

22.2 

93 

68.9 

62.5 

53 

113.4 

102.7 

13 

157.8 

143.0 

73 

202.3 

183.3 

34 

25.2 

22.8 

94 

69.6 

63.1 

54 

114.1 

103.4 

14 

158.6 

143.7 

74 

203.0 

184.0 

35 

25.9 

23.5 

95 

70.4 

63.8 

55 

114.8 

104.1 

15 

159.3 

144.4 

75 

203.8 

184.7 

36 

26.7 

24.2 

96 

71.1 

64.5 

56 

115.6 

104.8 

16 

160.0 

145.1 

76 

204.5 

185.4 

37 

27.4 

24.8 

97 

71.9 

65.1 

57 

116.3 

105.4 

17 

160.8 

145.7 

77 

205.2 

186.0 

38 

28.2 

25.5 

98 

72.6 

65.8 

58 

117.1 

106.1 

18 

161.5 

146.4 

78 

206.0 

186.7 

39 

28.9 

26.2 

99 

73.4 

66.5 

59 

117.8 

106.8 

19 

162.3 

147.1 

79 

206.7 

187.4 

40 

29.6 

26.9 

100 
101 

74.1 

67.2 

60 

118.6 

107.4 

20 

163.0 

147.7 

80 

207.5 

188.0 

41 

30.4 

27.5 

74.8 

67.8 

161 

119.3 

108.1 

221 

163.8 

148.4 

281 

208.2 

188.7 

42 

31.1 

28.2 

02 

75.6 

68.5 

62 

120.0 

108.8 

22 

164.5 

149.1 

82 

208.9 

189.4 

43 

31.9 

28.9 

03 

76.3 

69.2 

63 

120.8 

109.5 

23 

165.2 

149.8 

83 

209.7 

190.1 

44 

32.6 

29.5 

04 

77.1 

69.8 

64 

121.5 

110.1 

24 

166.0 

150.4 

84 

210.4 

190.7 

45 

33.3 

30.2 

05 

77.8 

70.5 

65 

122.3 

110.8 

25 

166.7 

151.1 

85 

211.2 

191.4 

46 

34.1 

30.9 

06 

78.5 

71.2 

66 

123. 0 

111.5 

26 

167.5 

151.8 

86 

211.9 

192.1 

47 

34.8 

31.6 

07 

79.3 

71.9 

67 

123.7 

112.2 

27 

168.2 

152.4 

87 

212.7 

192.7 

48 

35.6 

32.2 

08 

80.0 

72.5 

68 

124.5 

112.8 

28 

168.9 

153.1 

88 

213.4 

193.4 

49 

36.3 

32.9 

09 

80.8 

73.2 

69 

125.2 

113.5 

29 

169.7 

153.8 

89 

214.1 

194.1 

50 

37.0 

33.6 

10 

81.5 

73.9 

70 

126.0 

114.2 

30 

170.4 

154. 5 

90 

214.9 
215.6 

194.8 

51 

37.8 

34.2 

111 

82.2 

74.5 

171 

126.7 

114.8 

231 

171.2 

155.1 

291 

195.4 

52 

38.5 

34.9 

12 

83.0 

75.2 

72 

127.4 

115.5 

32 

171.9 

155.  8 

92 

216.4 

196.1 

53 

39.3 

35.6 

13 

83.7 

75.9 

73 

128.2 

116.2 

33 

172.6 

156.5 

93 

217. 1 

196.8 

54 

40.0 

36.3 

14 

84.5 

76.6 

74 

128.9 

116.9 

34 

173.4 

157.1 

94 

217.8 

197.4 

55 

40.8 

36.9 

15 

85.2 

77.2 

75 

129.7 

117.5 

35 

174.1 

157.8 

95 

218.6 

198.1 

56 

41.5 

37.6 

16 

86.0 

77.9 

76 

130.4 

118.2 

36 

174.9 

158.5 

96 

219.3 

198.8 

57 

42.2 

38.3 

17 

86.7 

78.6 

77 

131.1 

118.9 

37 

175.6 

159.2 

97 

220.1 

199.5 

58 

43.0 

39.0 

18 

87.4 

79.2 

78 

131.9 

119.5 

38 

176.3 

159.8 

98 

220.8 

200.1 

59 

43.7 

39.6 

19 

88.2 

79.9 

79 

132.6 

120.2 

39 

177.1 

160.5 

99 

221.5 

200.8 

60 

44.5 

40.3 

20 

88.9 

80.6 

80 

133.4 

120.9 

40 

177.8 

161.2 

300 

222.3 

201.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  i  E. 

S 

E.  }  E. 

N^ 

W.  J  W. 

SW.  }  W. 

[For  4}  Points.      1 

21594°— 14- 


-27 


Page  630] 

TABLE  1. 

Difference  of  Latitude  and 

Depart 

are  for  4  Points. 

NE. 

NW. 

SE. 

SW. 

Diet. 

Lat. 

bep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

1.4 

1.4 

62 

43.8 

43.8 

22 

86.3 

86.3 

82 

128.7 

128.7 

42 

171.1 

171.1 

3 

2.1 

2.1 

63 

44.5 

44.5 

23 

87.0 

87.0 

83 

129.4 

129.4 

43 

171.8 

171.8 

4 

2.8 

2.8 

64 

45.3 

45.3 

24 

87.7 

87.7 

84 

130.1 

130.1 

44 

172.5 

172.5 

5 

3.5 

3.5 

65 

46.0 

46.0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

173.2 

173.2 

6 

4.2 

4.2 

66 

46.7 

46.7 

26 

89.1 

89.1 

86 

131.5 

131.5 

46 

173.9 

173.9 

7 

4.9 

4.9 

67 

47.4 

47.4 

27 

89.8 

89.8 

87 

132.2 

132.2 

47 

174.7 

174.7 

8 

5.7 

5.7 

68 

48.1 

48.1 

28 

90.5 

90.5 

88 

132.9 

132.9 

48 

175.4 

175.4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91.2 

89 

133.6 

133.6 

49 

176.1 

176.1 

10 

7.1 

7.1 

70 

49.5 

49.5 
50.2 

30 

91.9 

91.9 

90 

134.4 

134.4 

50 

176.8 

176.8 

11 

7.8 

7.8 

71 

50.2 

131 

92.6 

92.6 

191 

135.1 

135.1 

251 

177.5 

177.5 

12 

8.5 

8.5 

72 

50.9 

50.9 

32 

93.3 

93.3 

92 

135.8 

135.8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51.6 

51.6 

33 

94.0 

94.0 

93 

136.5 

136.5 

53 

178.9 

178.9 

14 

9.9 

9.9 

74 

52.3 

52.3 

34 

94.8 

94.8 

94 

137.2 

137.2 

54 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

36 

95.5 

95.5 

95 

137.9 

137.9 

55 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

36 

96.2 

96.2 

96 

138.6 

138.6 

56 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.4 

54.4 

37 

96.9 

96.9 

97 

139.3 

139.3 

57 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

38 

97.6 

97.6 

98 

140.0 

140.0 

58 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

39 

98.3 

98.3 

99 

140.7 

140.7 

59 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 

141.4 

141.4 

60 

183.8 

183.8 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

99.7 

99.7 

201 

142.1 

142.1 

261 

184.6 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

43 

101.1 

101.] 

03 

143.5 

143.5 

63 

186.0 

186.0 

24 

17.0 

17.0 

84 

59.4 

59.4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

45 

102.5 

102.5 

05 

145.0 

145.0 

65 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

46 

103.2 

103.2 

06 

145.7 

145.7 

66 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

48 

104.7 

104.7 

08 

147.1 

147.1 

68 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190.2 

190.2 

30 

21.2 

21.2 

90 

63.6 

63.6 

50 

106.1 

106.1 

10 

148.5 

148.5 

70 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.2 

149.2 

271 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8" 

65.8 

53 

108.2 

108.2 

13 

150.6 

150.6 

73 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

54 

108.9 

108.9 

14 

151.3 

151.3 

74 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109.6 

109.6 

15 

152.0 

152.0 

75 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

56 

110.3 

110.3 

16 

152.7 

152.7 

76 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

57 

111.0 

111.0 

17 

153.4 

153.4 

77 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

58 

111.7 

111.7 

18 

154.1 

154.1 

78 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

59 

112.4 

112.4 

19 

154.9 

154.9 

79 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

60 

113.1 
113.8 

113.1 

20 

155.6 

155.6 
156.3 

80 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

221 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

02 

72.1 

72.1 

62 

114.6 

114.6 

22 

157.0 

157.0 

82 

199.4 

199.4 

43 

30.4 

30.4 

03 

72.8 

72.8 

63 

115.3 

115.3 

23 

157.7 

157.7 

83 

200.1 

200.1 

44 

31.1 

31.1 

04 

73.5 

73.5 

64 

116.0 

116.0 

24 

158.4 

158.4 

84 

200.8 

200.8 

45 

31.8 

31.8 

05 

74.2 

74.2 

65 

116.7 

116.7 

25 

159.1 

159.1 

85 

201.5 

201.5 

46 

32.5 

32.5 

06 

75.0 

75.0 

66 

117.4 

117.4 

26 

159.8 

159.8 

86 

202.2 

202.2 

47 

33.2 

33.2 

07 

75.7 

75.7 

67 

118.1 

118.1 

27 

160.5 

160.5 

87 

202.9 

202.9 

48 

33.9 

33.9 

08 

76.4 

76.4 

68 

118.8 

118.8 

28 

161.2 

161.2 

88 

203.6 

203.6 

49 

34.6 

34.6 

09 

77.1 

77.1 

69 

119.5 

119.5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 

35.4 

35.4 

10 

77.8 

77.8 

70 

120.2 

120.2 

30 

162.6 

162.6 

90 

205.1 

205.1 

51 

36.1 

36.1 

111 

78.5 

78.5 

171 

]20.9 

120.9 

231 

163.3 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79.2 

79.2 

72 

121.6 

121.6 

32 

164.0 

164.0 

92 

206.5 

206.5 

53 

37.5 

37.5 

13 

79.9 

79.9 

73 

122.3 

122.3 

33 

164.8 

164.8 

93 

207.2 

207.2 

54 

38.2 

38.2 

14 

80.6 

80.6 

74 

123.0 

123.0 

34 

165.5 

165.5 

94 

207.9 

207.9 

55 

38.9 

38.9 

15 

81.3 

81.3 

75 

123.7 

123.7 

35 

166.2 

166.2 

95 

208.6 

208.6 

56 

39.6 

39.6 

16 

82.0 

82.0 

76 

124.5 

124.5 

36 

166.9 

166.9 

96 

209.3 

209.3 

57 

40.3 

40.3 

17 

82.7 

82.7 

77 

125.2 

125.2 

37 

167.6 

167.6 

97 

210.0 

210.0 

58 

41.0 

41.0 

18 

83.4 

83.4 

78 

125.9 

125.9 

38 

168. 3 

168.3 

98 

210.7 

210.7 

59 

41.7 

41.7 

19 

84.1 

84.1 

79 

126.6 

126.6 

39 

169.0 

169.0 

99 

211.4 

211.4 

60 

42.4 

42.4 

20 

84.9 

84.9 

80 

127.3 

127.3 

40 

169.7 

169.7 

300 

212.1 

212.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

.    NE. 

NW. 

] 

3E. 

SW. 

[For  4  Points.      1 

Page  632] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  1°  (179°,  181' 

',  359°] 

. 

Dist. 

Lat. 

Dep. 

Dist. 
61 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61.0 

1.1 

121 

121.0 

2.1 

181 

181.0 

3.2 

241 

241.0 

4.2 

2 

2.0 

0.0 

62 

62.0 

1.1 

22 

122.0 

2.1 

82 

182.0 

3.2 

42 

242.  0 

4.2 

3 

3.0 

0.1 

63 

63.0 

1.1 

23 

123.0 

2.1 

83 

183.0 

3.2 

43 

243.0 

4.2 

4 

4.0 

0.1 

64 

64.0 

1.1 

24 

124.0 

2.2 

84 

184.0 

S.2 

44 

244.0 

4.3 

5 

5.0 

0.1 

65 

65.0 

1.1 

25 

125.0 

2.2 

85 

185.0 

3  2 

45 

245.0 

4.3 

6 

6.0 

0.1 

66 

66.0 

1.2 

26 

126.0 

2.2 

86 

186.0 

3.2 

46 

246.0 

4.3 

7 

7.0 

0.1 

67 

67.0 

1.2 

27 

127.0 

2.2 

87 

187.0 

3.3 

47 

247.0 

4.3 

8 

8.0 

0.1 

68 

68.0 

1.2 

28 

128.0 

2.2 

88 

188.0 

3.3 

48 

248.0 

4.3 

9 

9.0 

0.2 

69 

69.0 

1.2 

29 

129.0 

2.3 

89 

189.0 

3.3 

49 

249.0 

4.3 

10 

10.0 

0.2 

70 

70.0 

1.2 

30 

130.0 

2.3 

90 

190.0 

3.3 

50 

250.0 

4.4 

11 

11.0 

0.2 

71 

71.0 

1.2 

131 

131.0 

2.3 

191 

191.0 

3.3 

251 

251.0 

4.4 

12 

12.0 

0.2 

72 

72.0 

1.3 

32 

132.0 

2.3 

92 

192.0 

3.4 

52 

252.0 

4.4 

13 

13.0 

0.2 

73 

73.0 

1.3 

33 

133.0 

2.3 

93 

193.0 

3.4 

53 

253.0 

4.4 

14 

14.0 

0.2 

74 

74.0 

1.3 

34 

134.0 

2.3 

94 

194.0 

3.4 

54 

254.0 

4.4 

15 

15.0 

0.3 

75 

75.0 

1.3 

35 

135.0 

2.4 

95 

195.0 

3.4 

55 

255. 0 

4.5 

16 

16.0 

0.3 

76 

76.0 

1.3 

36 

136.0 

2.4 

96 

196.0 

3.4 

56 

256.0 

4.5 

17 

17.0 

0.3 

77 

77.0 

1.3 

37 

137.0 

2.4 

97 

197.0 

3.4 

57 

257.0 

4.5 

18 

18..  0 

0.3 

78 

78.0 

1.4 

38 

138.0 

2.4 

98 

198.0 

3.5 

58 

258.0 

4.5 

19 

19.0 

0.3 

79 

79.0 

1.4 

39 

139.0 

2.4 

99 

199.0 

3.5 

59 

259.0 

4.5 

20 

20.0 

0.3 

80 

80.0 

1.4 

40 

140.0 

2.4 

200 

200.0 

3.5 

60 

260.0 

4.5 

21 

21.0 

0.4 

81 

81.0 

1.4 

141 

141.0 

2.5 

201 

201.0 

3.5 

261 

261.0 

4.6 

22 

22.0 

0.4 

82 

82.0 

1.4 

42 

142.0 

2.5 

02 

202.0 

3.5 

62 

262.0 

4.6 

23 

23.0 

0.4 

83 

83.0 

1.4 

43 

143.0 

2.5 

03 

203.0 

3.5 

63 

263.0 

4.6 

24 

24.0 

0.4 

84 

84.0 

1.5 

44 

144.0 

2.5 

04 

204.0 

3.6 

64 

264.0 

4.6 

25 

25.0 

0.4 

85 

85.0 

1.5 

45 

145.0 

2.5 

05 

205.0 

3.6 

65 

265.0 

4.6 

26 

26.0 

0.5 

86 

86.0 

1.5 

46 

146.0 

2.5 

06 

206.0 

3.6 

66 

266.0 

4.6 

27 

27.0 

0.5 

87 

87.0 

1.5 

47 

147.0 

2.6 

07 

207.0 

3.6 

67 

267.0 

4.7 

28 

28.0 

0.5 

88 

88.0 

1.5 

48 

148.0 

2.6 

08 

208.0 

3.6 

68 

268.0 

4.7 

29 

29.0 

0.5 

89 

89.0 

1.6 

49 

149.0 

2.6 

09 

209.0 

3.6 

69 

269.0 

4.7 

30 
31 

30.0 

0.5 

90 

90.0 

1.6 

50 

150.0 
151.0 

2.6 

10 

210.0 

3.7 

70 

270.0 

4.7 

31.0 

0.5 

91 

91.0 

1.6 

151 

2.6 

211 

211.0 

3.7 

271 

271.0 

4.7 

32 

32.0 

0.6 

92 

92.0 

1.6 

52 

152.0 

2.7 

12 

212.0 

3.7 

72 

272.0 

4.7 

33 

33.0 

0.6 

93 

93.0 

1.6 

53 

153.0 

2.7 

13 

213.0 

3.7 

73 

273.0 

4.8 

34 

34.0 

0.6 

94 

94.0 

1.6 

54 

154.0 

2.7 

14 

214.0 

3.7 

74 

274.0 

4.8 

35 

35.0 

0.6 

95 

95.0 

1.7 

55 

155.0 

2.7 

15 

215.0 

3.8 

75 

275. 0 

4.8 

36 

36.0 

0.6 

96 

96.0 

1.7 

56 

156.0 

2.7 

16 

216.0 

3.8 

76 

276.0 

4.8 

37 

37.0 

0.6 

97 

97.0 

1.7 

57 

157. 0 

2.7 

17 

217.0 

3.8 

77 

277.0 

4.8 

38 

38.0 

0.7 

98 

98.0 

1.7 

58 

158.0 

2.8 

18 

218.0 

3.8 

78 

278.0 

4.9 

39 

39.0 

0.7 

99 

99.0 

1.7 

59 

159.0 

2.8 

19 

219.0 

3.8 

79 

279.0 

4.9 

40 

40.0 

0.7 

100 

100.0 
101.0 

1.7 

60 

160.0 

2.8 

20 

220.0 

3.8 

80 

280.0 

4.9 

41 

41.0 

0.7 

101 

1.8 

161 

161.0 

2.8 

221 

221.0 

3.9 

281 

281.0 

4.9 

42 

42.0 

0.7 

02 

102.0 

1.8 

62 

162.0 

2.8 

22 

222.0 

3.9 

82 

282.0 

4.9 

43 

43.0 

0.8 

03 

103.0 

1.8 

63 

163.0 

2.8 

23 

223.0 

3.9 

83 

283.0 

4.9 

44 

44.0 

0.8 

04 

104.0 

1.8 

64 

164.0 

2.9 

24 

224.0 

3.9 

84 

284.0 

5.0 

45 

45.0 

0.8 

05 

105.0 

1.8 

65 

165.0 

2.9 

25 

225.0 

3.9 

85 

285.0 

5.0 

46 

46.0 

0.8 

06 

106.0 

1.8 

66 

166.0 

2.9 

26 

226.0 

3.9 

86 

286.0 

5.0 

47 

47.0 

0.8 

07 

107.0 

1.9 

67 

167.0 

2.9 

27 

227.0 

4.0 

87 

287.0 

5.0 

48 

48.0 

0.8 

08 

108.0 

1.9 

68 

168.0 

2.9 

28 

228.0 

4.0 

88 

288.0 

5.0 

49 

49.0 

0.9 

09 

109. 0 

1.9 

69 

169.0 

2.9 

29 

229.0 

4.0 

89 

289.0 

5.0 

50 

50.0 

0.9 

10 

110.0 

1.9 

70 

170.0 

3.0 

30 

230.0 

4.0 

90 

290.0 

5.1 

51 

51.0 

0.9 

111 

111.0 

1.9 

171 

171.0 

3.0 

231 

231.0 

4.0 

291 

291.0 

5.1 

52 

52.0 

0.9 

12 

112.0 

2.0 

72 

172.0 

3.0 

32 

232.0 

4.0 

92 

292.0 

5.1 

53 

53.0 

0.9 

13 

113.0 

2.0 

73 

173.0 

3.0 

33 

233.0 

4.1 

93 

293.0 

5.1 

54 

54.0 

0.9 

14 

114.0 

2.0 

74 

174.0 

3.0 

34 

234.0 

4.1 

94 

294.0 

5.1 

55 

55.0 

1.0 

15 

115.0 

2.0 

75 

175.0 

3.1 

35 

235.0 

4.1 

95 

295.0 

5.1 

56 

56.0 

1.0 

16 

116.0 

2.0 

76 

176.0 

3.1 

36 

236.0 

4.1 

96 

296.0 

5.2 

57 

57.0 

1.0 

17 

117.0 

2.0 

77 

177.0 

3.1 

37 

237.0 

4.1 

97 

297.0 

5.2 

58 

58.0 

1.0 

18 

118.0 

2.1 

78 

178.0 

3.1 

38 

238.0 

4.2 

98 

298.0 

5.2 

59 

59.0 

1.0 

19 

119.0 

2.1 

79 

179.0 

3.1 

39 

239.0 

4.2 

99 

299.0 

5.2 

60 

60.0 

1.0 

20 

120.0 

2.1 

80 

180.0 

3.1 

40 

240.0 

4.2 

300 

300.0 

5.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

89°  (( 

)1°,  269°,  271° 

)• 

1 

TABLE  2. 

[Page 

533 

Difference  of  Latitude  and  Departure  for  1°  (179°,  181°,  369° 

). 

Diet. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

DiBt 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

301.0 

5.3 

361 

360.9 

6.3 

421 

420.9 

7.3 

481 

480.9 

8.4 

541 

540.9 

9.6 

02 

302.0 

6.3 

62 

361.9 

6.3 

22 

421.9 

7.4 

82 

481.9 

8.4 

42 

541.9 

9.5 

03 

303.0 

5.3 

63 

362.  9 

6.3 

23 

422.9 

7.4 

83 

482.9 

8.6 

43 

542.9 

9.5 

04 

304.0 

5.3 

64 

363.9 

6.4 

24 

423.9 

7.4 

84 

483.9 

8.5 

44 

543.9 

9.5 

06 

305.0 

5.3 

66 

364.9 

6.4 

25 

424.9 

7.4 

85 

484.9 

8.5 

46 

544.9 

9.5 

06 

306.0 

5.3 

66 

365.9 

6.4 

26 

425.9 

7.4 

86 

485.9 

8.5 

46 

546.9 

9.6 

07 

307.0 

5.4 

67 

366.9 

6.4 

27 

426.9 

7.4 

87  1  486.9 

8.5 

47 

646.9 

9.6 

08 

308.0 

5.4 

68 

367.9 

6.4 

28 

427.9 

7.5 

88 

487.9 

8.6 

48 

547.9 

9.6 

09 

309.0 

5.4 

69 

868.9 

6.4 

29 

428.9 

7.6 

89 

488.9 

8.6 

49 

548.9 

9.6 

10 

310.0 

5.4 

70 

369.9 
370!  9 

6.5 

30 

429.9 

7.5 

90 

489.9 

8.6 

50 

549.9 

9.6 

311 

311.0 

5.4 

371 

6.6 

431 

430.9 

7.5 

491 

490.9 

8.6 

551 

550.9 

9.6 

12 

312.0 

6.4 

72 

371.9 

6.5 

32 

431.9 

7.6 

92 

491.9 

8.6 

62 

561.9 

9.6 

13 

313.0 

5.5 

73 

372.9 

6.5 

33 

432.9 

7.5 

93 

492.9 

8.7 

53 

652.9 

9.7 

14 

314.0 

5.5 

74 

373.9 

6.5 

34 

433.9 

7.6 

94 

493.9 

8.7 

64 

653.9 

9.7 

15 

315.0 

6.6 

75 

374.9 

6.5 

36 

434.9 

7.6 

95  1  494.9 

8.7 

55 

554.9 

9.7 

16 

316.0 

5.5 

76 

376.9 

6.6 

36 

435.9 

7.6 

96 

495.9 

8.7 

66 

566.9 

9.7 

17 

317.0 

5.5 

77 

376.9 

6.6 

37 

436.9 

7.6 

97 

496.9 

8.7 

67 

556.9 

9.7 

18 

318.0 

5.5 

78 

377.9 

6.6 

38 

437.9 

7.6 

98 

497.9 

8.7 

58 

557.9 

9.7 

19 

319.0 

5.6 

79 

378.9 

6.6 

39 

438.9 

7.7 

99 

498.9 

8.8 

69 

658.9 

9.8 

20 

320.0 

5.6 

80 

379.9 

6.6 

40 

439.9 

7.7 

500  i  499.9 

8.8 

60 

559. 9 

9.8 

321 

321.0 

5.6 

381 

380.9 

6.7 

441 

440.9 

7.7 

501 

500.9 

8.8 

661 

560.9 

9.8 

22 

322.0 

6.6 

82 

381.9 

6.7 

42 

441.9 

7.7 

02 

601.9 

8.8 

62 

561.9 

9.8 

23 

323.0 

5.6 

83 

382. 9 

6.7 

43 

442.9 

7.7 

03 

602.9 

8.8 

63 

662.9 

9.8 

24 

324.0 

5.6 

84 

383.9 

6.7 

44 

443.9 

7.7 

04 

503.9 

8.8 

64 

563.9 

9.8 

25 

325.0 

6.7 

85 

384.9 

6.7 

45 

444.9 

7.8 

05 

604.9 

8.8 

66 

564.9 

9.9 

26 

326.0 

6.7 

86 

385.9 

6.7 

46 

445.9 

7.8 

06 

505.9 

8.9 

66 

665.9 

9.9 

27 

327.0 

5.7 

87 

386.9 

6.8 

47 

446.9 

7.8 

07 

506.9 

8.9 

67 

666.9 

9.9 

28 

328.0 

5.7 

88 

387.9 

6.8 

48 

447.9 

7.8 

08 

607.9 

8.9 

68 

567.9 

9.9 

29 

329.0 

6.7 

89 

388.9 

6.8 

49 

448.9 

7.8 

09 

608.9 

8.9 

69 

668.9 

9.9 

30 

330.0 

5.8 

90 

389.9 

6.8 

50 

449.9 

7.8 

10 

609.9 

8.9 

70 

569.9 

9.9 

331 

331.0 

5.8 

391 

390.9 

6.8 

451 

450.9 

7.9 

611 

610.9 

9.0 

571 

570.9 

10.0 

32 

332.0 

5.8 

92 

391.9 

6.8 

52 

451.9 

7.9 

12 

511.9 

9.0 

72 

671.9 

10.0 

33 

333.0 

6.8 

93 

392.9 

6.9 

63 

452.9 

7.9 

13 

512.9 

9.0 

73 

572.9 

10.0 

34 

333.9 

5.8 

94 

393.9 

6.9 

54 

453.9 

7.9 

14 

513.9 

9.0 

74 

573.9 

10.0 

35 

334.9 

6.8 

95 

394.9 

6.9 

55 

464.9 

7.9 

15 

614.9 

9.0 

76 

674. 9 

10.0 

36 

335.9 

5.9 

96 

395.9 

6.9 

56 

466.9 

8.0 

16 

515.9 

9.0 

76 

576.9 

10.0 

37 

336.9 

6.9 

97 

396.9 

6.9 

57 

456.9 

8.0 

17 

516.9 

9.1 

77 

676.9 

10.1 

38 

337.9 

5.9 

98 

397.9 

6.9 

68 

457.9 

8.0 

18 

517.9 

9.1 

78 

577.9 

10.1 

39 

338.9 

6.9 

99 

398.9 

7.0 

69 

458.9 

8.0 

19 

618.9 

9.1 

79 

678.9 

10.1 

40 

339.9 

6.9 

400 

399.9 

7.0 

60 

459.9 

8.0 

20 

519.9 

9.1 

80 

679.9 

10.1 

341 

340.9 

6.0 

401 

400.9 

7.0 

461 

460.9 

8.0 

621 

520.9 

9.1 

581 

680.9 

10.1 

42 

341.9 

6.0 

02 

401.9 

7.0 

62 

461.9 

8.1 

22 

621.9 

9.1 

82 

581.9 

10.1 

43 

342. 9 

6.0 

03 

402.9 

7.0 

63 

402.9 

8.1 

23 

622.9 

9.2 

83 

582.9 

10.2 

44 

343.9 

6.0 

04 

403.9 

7.1 

64 

463.9 

8.1 

24 

523.9 

9.2 

84 

683.9 

10.2 

45 

344.9 

6.0 

05 

404.9 

7.1 

66 

464.9 

8.1 

26 

524. 9 

9.2 

85 

584.9 

10.2 

46 

345.9 

6.0 

06 

405.9 

7.1 

66 

465.9 

8.1 

26 

625.  9 

9.2 

86 

586.9 

10.2 

47 

346.9 

6.1 

07 

406.9 

7.1 

67 

466.9 

8.1 

27 

526.9 

9.2 

87 

586.9 

10.2 

48 

347.9 

6.1 

08 

407.9 

7.1 

68 

467.9 

8.2 

28 

527.9 

9.2 

88 

587.9 

10.2 

49 

348.9 

6.1 

09 

408.9 

7.1 

69 

468.9 

8.2 

29 

628.9 

9.3 

89 

688.9 

10.3 

50 

349.9 

6.1 

10 
411 

409.9 

7.2 

70 
471 

469.9 

8.2 

30 
631 

529.9 

9.3 

90 

589.9 
590.9 

10.3 

351 

350.9 

6.1 

410.9 

7.2 

470.9 

8.2 

630.9 

9.3 

591 

10.3 

52 

351.9 

6.1 

12 

411.9 

7.2 

72 

471.9 

8.2 

32 

531.9 

9.3 

92 

591.9 

10.3 

53 

352.9 

6.2 

13 

412.9 

7.2 

73 

472.9 

8.2 

33 

532.9 

9.3 

93 

692. 9 

10.3 

54 

353.9 

6.2 

14 

413.9 

7.2 

74 

473.9 

8.3 

34 

533.9 

9.3 

94 

693.9 

10.3 

55 

354.9 

6.2 

15 

414.9 

7.2 

76 

474.9 

8.3 

35 

534.9 

9.4 

95 

594.9 

10.4 

56 

355.9 

6.2 

16 

416.9 

7.3 

76 

475.9 

8.3 

36 

536.9 

9.4 

96 

595.9 

10.4 

57 

356.9 

6.2 

17 

416.9 

7.3 

77 

476.9 

8.3 

37 

636.9 

9.4 

97 

696.9 

10.4 

58 

357.9 

6.2 

18 

417.9 

7.3 

78 

477.9 

8.3 

38 

537.9 

9.4 

98 

697.9 

10.4 

69 

368.9 

6.3 

19 

418.9 

7.3 

79 

478.9 

8.4 

39 

638.9 

9.4 

99 

598.9 

10.4 

60 

369.9 

6.3 

20 

419.9 

7.3 

80 

479.9 

8.4 

40 

539.9 

9.4 

600 

599.9 

10.5 

Di8t. 

Dep. 

Lat. 

DSst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

89°  (9 

1°,  269° 

,  271°) 

Page  534] 

TABLE 

2. 

Difference  of  Latitude  and  Depart 

ure  for  2°  (178°,  182 

°,  358° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61 

61.0 

2.1 

121 

120.9 

4.2 

181 

180.9 

6.3 

241 

240.9 

8.4 

2 

2.0 

0.1 

62 

62.0 

2.2 

22 

121.9 

4.3 

82 

181.9 

6.4 

42 

241.9 

8.4 

3 

3.0 

0.1 

63 

63.0 

2.2 

23 

122.9 

4.3 

83 

182.9 

6.4 

43 

242.9 

8.5 

4 

4.0 

0.1 

64 

64.0 

2.2 

24 

123.9 

4.3 

84 

183.9 

6.4 

44 

243.9 

8.5 

5 

5.0 

0.2 

65 

65.0 

2.3 

25 

124.9 

4.4 

85 

184.9 

6.5 

45 

244.9 

8.6 

6 

6.0 

0.2 

66 

66.0 

2.3 

26 

125.9 

4.4 

86 

185.9 

6.5 

46 

245.9 

8.6 

7 

7.0 

0.2 

67 

67.0 

2.3 

27 

126.9 

4.4 

87 

186.9 

6.5 

47 

246.8 

8.6 

8 

8.0 

0.3 

68 

68.0 

2.4 

28 

127.9 

4.5 

88 

187.9 

6.6 

48 

247.8 

8.7 

9 

9.0 

0.3 

69 

69.0 

2.4 

29 

128.9 

4.5 

89 

188.9 

6.6 

49 

248.8 

8.7 

10 

10.0 

0.3 

70 

70.0 

2.4 

30 

129.9 

4.5 

90 

189.9 

6.6 

50 

249.8 

8.7 

11 

11.0 

0.4 

71 

71.0 

2.5 

131 

130.9 

4.6 

191 

190.9 

6.7 

251 

250.8 

8.8 

12 

12.0 

0.4 

72 

72.0 

2.5 

32 

131.9 

4.6 

92 

191.9 

6.7 

52 

251.8 

8.8 

13 

13.0 

0.5 

73 

73.0 

2.5 

33 

132.9 

4.6 

93 

192.9 

6.7 

53 

252.8 

8.8 

14 

14.0 

0.5 

74 

74.0 

2.6 

34 

133.9 

4.7 

94 

193.9 

6.8 

54 

253.8 

8.9 

15 

15.0 

0.5 

75 

75.0 

2.6 

35 

134.9 

4.7 

95 

194.9 

6.8 

55 

254.8 

8.9 

16 

16.0 

0.6 

76 

76.0 

2.7 

36 

135.9 

4.7 

96 

195.9 

6.8 

56 

255.8 

8.9 

17 

17.0 

0.6 

77 

77.0 

2.7 

37 

136.9 

4.8 

97 

196.9 

6.9 

57 

256.8 

9.0 

18 

18.0 

0.6 

78 

78.0 

2.7 

38 

137.9 

4.8 

98 

197.9 

6.9 

58 

257.8 

9.0 

19 

19.0 

0.7 

79 

79.0 

2.8 

39 

138.9 

4.9 

99 

198.9 

6.9 

59 

258.8 

9.0 

20 

20.0 

0.7 

80 

80.0 

2.8 

40 

139.9 

4.9 

200 

199.9 

7.0 

60 

259.8 

9.1 

21 

21.0 

0.7 

81 

81.0 

2.8 

141 

140.9 

4.9 

201 

200.9 

7.0 

261 

260.8 

9.1 

22 

22.0 

0.8 

82 

82.0 

2.9 

42 

141.9 

5.0 

02 

201.9 

7.0 

62 

261.8 

9.1 

23 

23.0 

0.8 

83 

82.9 

2.9 

43 

142.9 

5.0 

03 

202.9 

7.1 

63 

262.8 

9.2 

24 

24.0 

0.8 

84 

83.9 

2.9 

44 

143.9 

5.0 

04 

203.9 

7.1 

64 

263.8 

9.2 

25 

25.0 

0.9 

85 

84.9 

3.0 

45 

144.9 

5.1 

05 

204.9 

7.2 

65 

264.8 

9.2 

26 

26.0 

0.9 

86 

85.9 

.3.0 

46 

145.9 

5.1 

06 

205.9 

7.2 

66 

265.8 

9.3 

27 

27.0 

0.9 

87 

86.9 

3.0 

47 

146.9 

5.1 

07 

206.9 

7.2 

67 

266.8 

9.3 

28 

28.0 

1.0 

88 

87.9 

3.1 

48 

147.9 

5.2 

08 

207.9 

7.3 

68 

267.8 

9.4 

29 

29.0 

1.0 

89 

88.9 

3.1 

49 

148.9 

5.2 

09 

208.9 

7.3 

69 

268.8 

9.4 

30 

30.0 

1.0 

90 

89.9 

3.1 

50 

149.9 

5.2 

10 

211 

209.9 

7.3 

70 

269.8 

9.4 

31 

31.0 

1.1 

91 

90.9 

3.2 

151 

150.9 

5.3 

210.9 

7.4 

271 

270.8 

9.5 

32 

32.0 

1.1 

92 

91.9 

3.2 

52 

151.9 

5.3 

12 

211.9 

7.4 

72 

271.8 

9.5 

33 

33.0 

1.2 

93 

92.9 

3.2 

53 

152.9 

5.3 

13 

212.9 

7.4 

73 

272.8 

9.5 

34 

34.0 

1.2 

94 

93.9 

3.3 

54 

153.9 

5.4 

14 

213.9 

7.5 

74 

273.8 

9.6 

35 

35.0 

1.2 

95 

94.9 

3.3 

55 

154.9 

5.4 

15 

214.9 

7.5 

75 

274.8 

9.6 

36 

36.0 

1.3 

96 

95.9 

3.4 

56 

155.9 

5.4 

16 

215.9 

7.5 

76 

275.8 

9.6 

37 

37.0 

1.3 

97 

96.9 

3.4 

57 

156.9 

5.5 

17 

216.9 

7.6 

77 

276.8 

9.7 

38 

38.0 

1.3 

98 

97.9 

3.4 

58 

157.9 

5.5 

18 

217.9 

7.6 

78 

277.8 

9.7 

39 

39.0 

1.4 

99 

98.9 

3.5 

59 

158.9 

5.5 

19 

218.9 

7.6 

79 

278.8 

9.7 

40 

40.0 

1.4 

100 

99.9 

3.5 

60 

159.9 

5.6 

20 

219.9 

7.7 

80 

279.8 

9.8 

41 

41.0 

1.4 

101 

100.9 

3.5 

161 

160.9 

5.6 

221 

220.9 

7.7 

281 

280.8 

9.8 

42 

42.0 

1.5 

02 

101.9 

3.6 

62 

161.9 

5.7 

22 

221.9 

7.7 

82 

281.8 

9.8 

43 

43.0 

1.5 

03 

102.9 

3.6 

63 

162.9 

5.7 

23 

222.9 

7.8 

83 

282.8 

9.9 

44 

44.0 

1.5 

04 

103.9 

3.6 

64 

163.9 

5.7 

24 

223.9 

7.8 

84 

283.8 

9.9 

45 

45.0 

1.6 

05 

104.9 

3.7 

65 

164.9 

5.8 

25 

224.9 

7.9 

85 

284.8 

9.9 

46 

46.0 

1.6 

06 

105.9 

3.7 

66 

165.9 

5.8 

26 

225.9 

7.9 

86 

285.8 

10.0 

47 

47.0 

1.6 

07 

106.9 

3.7 

67 

166.9 

5.8 

27 

226.9 

7.9 

87 

286.8 

10.0 

48 

48.0 

1.7 

08 

107.9 

3.8 

68 

167.9 

5.9 

28 

227.9 

8.0 

88 

287.8 

10.1 

49 

49.0 

1.7 

09 

108.9 

3.8 

69 

168.9 

5.9 

29 

228.9 

8.0 

89 

288.8 

10.1 

50 

50.0 

1.7 

10 

109.9 

3.8 

70 

169.9 

5.9 

30 

229.9 

8.0 

90 

289.8 

10.1 
10.2 

51 

51.0 

1.8 

111 

110.9 

3.9 

171 

170.9 

6.0 

231 

230.9 

8.1 

291 

290.8 

52 

52.0 

1.8 

12 

111.9 

3.9 

72 

171.9 

6.0 

32 

231.9 

8.1 

92 

291.8 

10.2 

53 

53.0 

1.8 

13 

112.9 

3.9 

73 

172.9 

6.0 

33 

232.9 

8.1 

93 

292.8 

10.2 

54 

54.0 

1.9 

14 

113.9 

4.0 

74 

173.9 

6.1 

34 

233.9 

8.2 

94 

293.8 

10.3 

55 

55.0 

1.9 

15 

114.9 

4.0 

75 

174.9 

6.1 

35 

234.9 

8.2 

95 

294.8 

10.3 

56 

56.0 

2.0 

16 

115.9 

4.0 

76 

175.9 

6.1 

36 

235.9 

8.2 

96 

295.8 

10.3 

57 

57.0 

2.0 

17 

116.9 

4.1 

77 

176.9 

6.2 

37 

236.9 

8.3 

97 

296.8 

10.4 

58 

58.0 

2.0 

18 

117.9 

4.1 

78 

177.9 

6.2 

38 

237.9 

8.3 

98 

297.8 

10.4 

59 

59.0 

2.1 

19 

118.9 

4.2 

79 

178.9 

6.2 

39 

238.9 

8.3 

99 

298.8 

10.4 

60 

60.0 

2.1 

20 

119.9 

4.2 

80 

179.9 

6.3 

40 

239.9 

8.4 

300 

299.8 

10.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

88°  (92°,  268° 

,  272°) . 

TABLE 

2. 

[Page  535     [ 

Difference  of  Latitude  and  Departure  for  2°  (178°,  182°,  358°] 

. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep.  1 

Dist. 

Lat. 

Dep. 

301 

300.8 

10.5 

361 

360.8 

12.6 

421 

420.8 

14.7 

481 

480.7 

16.8 

541 

540.7 

18.9 

02 

301.8 

10.5 

62 

361.8 

12.6 

22 

421.8 

14.7 

82 

481.7 

16.8 

42 

541.7 

18.9 

03 

302.8 

10.6 

63 

362.8 

12.7 

23 

422.8 

14.7 

83 

482.7 

16.8 

43 

542.7 

18.9 

04 

303.8 

10.6 

64 

363.8 

12.7 

24 

423.8 

14.8 

84 

483.7 

16.9 

44 

543.7 

19.0 

05 

304.8 

10.6 

65 

364.8 

12.7 

25 

424.8 

14.8 

85 

484.7 

16.9 

45 

544.7 

19.0 

06 

305.8 

10.7 

66 

365.8 

12.8 

26 

425.7 

14.9 

86 

485.7 

16.9 

46 

545.7 

19.0 

07 

306.8 

10.7 

67 

366.8 

12.8 

27 

426.7 

14.9 

87 

486.7 

17.0 

47 

546.7 

19.1 

08 

307.8 

10.7 

68 

367.8 

12.8 

28 

427.7 

14.9 

88 

487.7 

17.0 

48 

547.7 

19.1 

09 

308.8 

10.8 

69 

368.8 

12.9 

29 

428.7 

15.0 

89 

488.7 

17.0 

49 

548.7 

19.1 

10 

309.8 

10.8 

70 

369.8 

12.9 

30 

429.7 

15.0 

90 

489.7 

17.1 

50 

549.7 

19.2 

311 

310.8 

10.8 

371 

370.8 

12.9 

431 

430.7 

15.0 

491 

490.7 

17.1 

551 

550.7 

19.2 

12 

311.8 

10.9 

72 

371.8 

13.0 

32 

431.7 

15.1 

92 

491.7 

17.1 

52 

551.7 

19.2 

13 

312.8 

10.9 

73 

372.8 

13.0 

33 

432.7 

15.1 

93 

492.7 

17.2 

53 

552.7 

19.3 

14 

313.8 

10.9 

74 

373.8 

13.0 

34 

433.7 

15.1 

94 

493.7 

17.2 

54 

553.7 

19.3 

15 

314.8 

11.0 

75 

374.8 

13.1 

35 

434.7 

15.2 

95 

494.7 

17.2 

55 

554.7 

19.3 

16 

315.8 

11.0 

76 

375.8 

13.1 

36 

435.7 

15.2 

96 

495.7 

17.3 

56 

555.7 

19.4 

17 

316.8 

11.0 

77 

376.8 

13.1 

37 

436.7 

15.2 

97 

496.7 

17.3 

57 

556.7 

19.4 

18 

317.8 

11.1 

78 

377.8 

13.2 

38 

437.7 

15.3 

98 

497.7 

17.3 

58 

557.7 

19.4 

19 

318.8 

11.1 

79 

378.8 

13.2 

39 

438.7 

15.3 

99 

498.7 

17.4 

59 

558.7 

19.5 

20 
321 

319.8 

11.2 

80 

379.8 

13.2 

40 

439.7 

15.3 

500 

499.7 

17.4 

60 

559.7 

19.5 

320.8 

11.2 

381 

380.8 

13.3 

441 

440.7 

15.4 

501 

500.7 

17.5 

561 

560.7 

19.5 

22 

321.8 

11.2 

82 

381.8 

13.3 

42 

441.7 

15.4 

02 

501.7 

17.5 

62 

561.7 

19.6 

23 

322.8 

11.3 

83 

382.8 

13.3 

43 

442.7 

15.4 

03 

502.7 

17.5 

63 

562.7 

19.6 

24 

323.8 

11.3 

84 

383.8 

13.4 

44 

443.7 

15.5 

04 

503.7 

17.6 

64 

563.7 

19.6 

25 

324.8 

11.3 

85 

384.8 

13.4 

45 

444.7 

15.5 

05 

504.7 

17.6 

65 

564.7 

19.7 

26 

325.8 

11.4 

86 

385.8 

13.5 

46 

445.7 

15.6 

06 

505.7 

17.6 

66 

565.7 

19.7 

27 

326.8 

11.4 

87 

386.8 

13.5 

47 

446.7 

15.6 

07 

506.7 

17.7 

67 

566.7 

19.7 

28 

327.8 

11.4 

88 

387.8 

13.5 

48 

447.7 

15.6 

08 

507.7 

17.7 

68 

567.7 

19.8 

29 

328.8 

11.5 

89 

388.8 

13.6 

49 

448.7 

15.7 

09 

508.7 

17.7 

69 

568.  7 

19.8 

30 

329.8 

11.5 

90 

389.8 

13.6 

50 

449.7 

15.7 

10 

509.7 

17.8 

70 

569.7 

19.9 

331 

330.8 

11.5 

391 

390.8 

13.6 

451 

450.7 

15.7 

511 

510.7 

17.8 

571 

570.7 

19.9 

32 

331.8 

11.6 

92 

391.8 

13.7 

52 

451.7 

15.8 

12 

511.7 

17.8 

72 

571.7 

19.9 

33 

332.8 

11.6 

93 

392.8 

13.7 

53 

452.7 

15.8 

13 

512.7 

17.9 

73 

572.7 

20.0 

34 

333.8 

11.6 

94 

393.8 

13.7 

54 

453.7 

15.8 

14 

513.7 

17.9 

74 

573.6 

20.0 

35 

334.8 

11.7 

95 

394.8 

13.8 

55 

454.7 

15.9 

15 

514.7 

17.9 

75 

574.6 

20.0 

36 

335.8 

11.7 

96 

395.8 

13.8 

56 

455.7 

15.9 

16 

515.7 

18.0 

76 

575.6 

20.1 

37 

336.8 

11.7 

97 

396.8 

13.8 

57 

456.7 

15.9 

17 

516.7 

18.0 

77 

576.6 

20.1 

38 

337.8 

11.8 

98 

397.8 

13.9 

58 

457.7 

16.0 

18 

517.7 

18.1 

78 

577.6 

20.1 

39 

338.8 

11.8 

99 

398.8 

13.9 

59 

458.7 

16.0 

19 

518.7 

18.1 

79 

578.6 

20.2 

40 

339.8 

11.9 

400 

399.8 

13.9 

60 

459.7 

16.0 

20 

519.7 

18.1 

80 

579.6 

20.2 

341 

340.8 

11.9 

401 

400.8 

14.0 

461 

460.7 

16.1 

521 

520.7 

18.2 

581 

580.6 

20.2 

42 

341.8 

11.9 

02 

401.8 

14.0 

62 

461.7 

16.1 

22 

521.7 

18.2 

82 

581.6 

20.3 

43 

342.8 

12.0 

03 

402.8 

14.0 

63 

462.7 

16.1 

23 

522.7 

18.2 

83 

582.6 

20.3 

44 

343.8 

12.0 

04 

403.8 

14.1 

64 

463.7 

16.2 

24 

523.7 

18.3 

84 

583.6 

20.3 

45 

344.8 

12.0 

05 

404.8 

14.1 

65 

464.7 

16.2 

25 

524.7 

18.3 

85 

584.6 

20.4 

46 

345.8 

12.1 

06 

405.8 

14.2 

66 

465.7 

16.2 

26 

525.7 

18.4 

86 

585.6 

20.4 

47 

346.8 

12.1 

07 

406.8 

14.2 

67 

466.7 

16.3 

27 

526.7 

18.4 

87 

586.6 

20.4 

48 

347.8 

12.1 

08 

407.8 

14.2 

68 

467.7 

16.3 

28 

527.7 

18.4 

88 

587.6 

20.5 

49 

348.8 

12.2 

09 

408.8 

14.3 

69 

468.7 

16.4 

29 

528.7 

18.5 

89 

588.6 

20.5 

50 
351 

349.8 

12.2 

10 

409.8 

14.3 

70 

469.7 

16.4 

30 

529.7 

18.5 

90 

589.6 

20.5 

350.8 

12.2 

411 

410.8 

14.3 

471 

470.7 

16.4 

531 

530.7 

18.5 

591 

590.6 

20.6 

52 

351.8 

12.3 

12 

411.8 

14.4 

72 

471.7 

16.5 

32 

531.7 

18.6 

92 

591.6 

20.6 

53 

352.8 

12.3 

13 

412.8 

14.4 

73 

472.7 

16.5 

33 

532.7 

18.6 

93 

592.6 

20.6 

54 

353.8 

12.3 

14 

413.8 

14.4 

74 

473.7 

16.5 

34 

533.7 

18.6 

94 

593.6 

20.7 

55 

354.8 

12.4 

15 

414.8 

14.5 

75 

474.7 

16.6 

35 

534.7 

18.7 

95 

594.6 

20.7 

56 

355. 8 

12.4 

16 

415.8 

14.5 

76 

475.7 

16.6 

36 

535.7 

18.7 

96 

595.6 

20.7 

57 

356.8 

12.4 

17 

416.8 

14.5 

77 

476.7 

16.6 

37 

536.7 

18.7 

97 

596.6 

20.8 

58 

357.8 

12.5 

18 

417.8 

14.6 

78 

477.7 

16.7 

38 

537.7 

18.8 

98 

597.6 

20.8 

59 

358.8 

12.5 

19 

418.8 

14.6 

79 

478.7 

16.7 

39 

538.7 

18.8 

99 

598.6 

20.8 

60 

359.8 

12.5 

20 

419.8 

14.6 

80 

479.7 

16.7 

40 

539.7 

18.8 

600 

599.6 

20.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

88°  (92°,  268 

^  272° 

). 

Page  636] 

TABLE  2. 

Difference  of  Latitude  and  Depart 

ure  for  3°  (177°,  183 

%  357° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.9 

3.2 

121 

120.8 

6.3 

181 

180.8 

9.6 

241 

240.7 

12.6 

2 

2.0 

0.1 

62 

61.9 

3.2 

22 

121.8 

6.4 

82 

181.8 

9.6 

42 

241.7 

12.7 

3 

3.0 

0.2 

63 

62.9 

3.3 

23 

122.8 

6.4 

83 

182.7 

9.6 

43 

242.7 

12.7 

4 

4.0 

0.2 

64 

63.9 

3.3 

24 

123.8 

6.5 

84 

183.7 

9.6 

44 

243.7 

12.8 

5 

5.0 

0.3 

65 

64.9 

3.4 

26 

124.8 

6.5 

85 

184.7 

9.7 

45 

244.7 

12.8 

6 

6.0 

0.3 

66 

65.9 

3.5 

26 

125.8 

6.6 

86 

185.7 

9.7 

46 

245.7 

12.9 

7 

7.0 

0.4 

67 

66.9 

3.5 

27 

126.8 

6.6 

87 

186.7 

9.8 

47 

246.7 

12.9 

8 

8.0 

0.4 

68 

67.9 

3.6 

28 

127.8 

6.7 

88 

187.7 

9.8 

48 

247.7 

13.0 

9 

9.0 

0.5 

69 

68.9 

3.6 

29 

128.8 

6.8 

89 

188.7 

9.9 

49 

248.7 

13.0 

10 

10.0 

0.5 

70 

69.9 

3.7 

30 

129.8 

6.8 

90 

189.7 

9.9 

60 

249.7 

13.1 

11 

11.0 

0.6 

71 

70.9 

3.7 

131 

130.8 

6.9 

191 

190.7 

10.0 

251 

260.7 

13.1 

12 

12.0 

0.6 

72 

71.9 

3.8 

32 

131.8 

6.9 

92 

191.7 

10.0 

52 

251.7 

13.2 

13 

13.0 

0.7 

73 

72.9 

3.8 

33 

132.8 

7.0 

93 

192.7 

10.1 

53 

262.7 

13.2 

14 

14.0 

0.7 

74 

73.9 

3.9 

34 

133.8 

7.0 

94 

193.7 

10.2 

54 

253.7 

13.3 

15 

15.0 

0.8 

75 

74.9 

3.9 

36 

134.8 

7.1 

95 

194.7 

10.2 

55 

254.7 

13.3 

16 

16.0 

0.8 

76 

75.9 

4.0 

36 

136.8 

7.1 

96 

195.7 

10.3 

56 

255.6 

13.4 

17 

17.0 

0.9 

77 

76.9 

4.0 

37 

136.8 

7.2 

97 

196.7 

10.3 

57 

256.6 

13.6 

18 

18.0 

0.9 

78 

77.9 

4.1 

38 

137.8 

7.2 

98 

197.7 

10.4 

58 

267.6 

13.5 

19 

19.0 

1.0 

79 

78.9 

4.1 

39 

138.8 

7.3 

99 

198.7 

10.4 

69 

268.6 

13.6 

20 

20.0 

1.0 

80 

79.9 

4.2 

40 

139.8 

7.3 

200 

199.7 

10.5 

60 

259.6 

13.6 

21 

21.0 

1.1 

81 

80.9 

4.2 

141 

140.8 

7.4 

201 

200.7 

10.5 

261 

260.6 

13.7 

22 

22.0 

1.2 

82 

81.9 

4.3 

42 

141.8 

7.4 

02 

201.7 

10.6 

62 

261.6 

13.7 

23 

23.0 

1.2 

83 

82.9 

4.3 

43 

142.8 

7.5 

03 

202.7 

10.6 

63 

262.6 

13.8 

24 

24.0 

1.3 

84 

83.9 

4.4 

44 

143.8 

7.5 

04 

203.7 

10.7 

64 

263.6 

13.8 

25 

26.0 

1.3 

85 

84.9 

4.4 

45 

144.8 

7.6 

05 

204.7 

10.7 

65 

264.6 

13.9 

26 

26.0 

1.4 

86 

85.9 

4.5 

46 

146.8 

7.6 

06 

206.7 

10.8 

66 

266.6 

13.9 

27 

27.0 

1.4 

87 

86.9 

4.6 

47 

146.8 

7.7 

07 

206.7 

10.8 

67 

266.6 

14.0 

28 

28.0 

1.5 

88 

87.9 

4.6 

48 

147.8 

7.7 

08 

207.7 

10.9 

68 

267.6 

14.0 

29 

29.0 

1.5 

89 

88.9 

4.7 

49 

148.8 

7.8 

09 

208.7 

10.9 

69 

268.6 

14.1 

30 

30.0 

1.6 

90 

89.9 

4.7 

60 

149.8 

7.9 

10 

209.7 

11.0 

70 

269.6 
270.6 

14.1 

31 

31.0 

1.6 

91 

90.9 

4.8 

161 

160.8 

7.9 

211 

210.7 

11.0 

271 

14.2 

32 

32.0 

1.7 

92 

91.9 

4.8 

62 

151.8 

8.0 

12 

211.7 

11.1 

72 

271.6 

14.2 

33 

33.0 

1.7 

93 

92.9 

4.9 

63 

152.8 

8.0 

13 

212.7 

11.1 

73 

272.6 

14.3 

34 

34.0 

1.8 

94 

93.9 

4.9 

54 

153.8 

8.1 

14 

213.7 

11.2 

74 

273.6 

14.3 

35 

36.0 

1.8 

95 

94.9 

5.0 

56 

164.8 

8.1 

15 

214.7 

11.3 

75 

274.6 

14.4 

36 

36.0 

1.9 

96 

95.9 

5.0 

66 

155.8 

8.2 

16 

215.7 

11.3 

76 

275.6 

14.4 

37 

36.9 

1.9 

97 

96.9 

5.1 

57 

166.8 

8.2 

17 

216.7 

11.4 

77 

276.6 

14.5 

38 

37.9 

2.0 

98 

97.9 

6.1 

58 

167.8 

8.3 

18 

217.7 

11.4 

78 

277.6 

14.5 

39 

38.9 

2.0 

99 

98.9 

5.2 

59 

168.8 

8.3 

19 

218.7 

11.5 

79 

278.6 

14.6 

40 

39.9 

2.1 

100 

99.9 

5.2 

60 

159.8 

8.4 

20 
221 

219.7 

11.5 

80 

279.6 

14.7 

41 

40.9 

2.1 

101 

100.9 

5.3 

161 

160.8 

8.4 

220.7 

11.6 

281 

280.6 

14.7 

42 

41.9 

2.2 

02 

101.9 

6.3 

62 

161.8 

8.6 

22 

221.7 

11.6 

82 

281.6 

14.8 

43 

42.9 

2.3 

03 

102.9 

5.4 

63 

162.8 

8.6 

23 

222.7 

11.7 

83 

282.6 

14.8 

44 

43.9 

2.3 

04 

103.9 

6.4 

64 

163.8 

8.6 

24 

223.7 

11.7 

84 

283.6 

14.9 

45 

44.9 

2.4 

05 

104.9 

6.5 

65 

164.8 

8.6 

26 

224.7 

11.8 

86 

284.6 

14.9 

46 

45.9 

2.4 

06 

105.9 

5.6 

66 

165.8 

8.7 

26 

225.7 

11.8 

86 

286.6 

15.0 

47 

46.9 

2.5 

07 

106.9 

5.6 

67 

166.8 

8.7 

27 

226.7 

11.9 

87 

286.6 

16.0 

48 

47.9 

2.5 

08 

107. 9 

5.7 

68 

167.8 

8.8 

28 

227.7 

11.9 

88 

287.6 

15.1 

49 

48.9 

2.6 

09 

108.9 

6.7 

69 

168.8 

8.8 

29 

228.7 

12.0 

89 

288.6 

15.1 

50 

49.9 

2.6 

10 

109.8 

5.8 

70 

169.8 

8.9 

30 

229.7 

12.0 

90 

289.6 

16.2 

51 

50.9 

2.7 

111 

110.8 

6.8 

171 

170.8 

8.9 

231 

230.7 

12.1 

291 

290.6 

16.2 

52 

51.9 

2.7 

12 

111.8 

6.9 

72 

171.8 

9.0 

32 

231.7 

12.1 

92 

291.6 

15.3 

53 

52.9 

2.8 

13 

112.8 

5.9 

73 

172.8 

9.1 

33 

232.7 

12.2 

93 

292.6 

16.3 

54 

53.9 

2.8 

14 

113.8 

6.0 

74 

173.8 

9.1 

34 

233.7 

12.2 

94 

293.6 

16.4 

55 

54.9 

2.9 

15 

114.8 

6.0 

75 

174.8 

9.2 

35 

234.7 

12.3 

95 

294.6 

16.4 

56 

55.9 

2.9 

16 

115.8 

6.1 

76 

175.8 

9.2 

36 

236.7 

12.4 

96 

296.6 

16.5 

67 

56.9 

3.0 

17 

116.8 

6.1 

77 

176.8 

9.3 

37 

236.7 

12.4 

97 

296.6 

15.6 

58 

57.9 

3.0 

18 

117.8 

6.2 

78 

177.8 

9.3 

38 

237.7 

12.5 

98 

297.6 

16.6 

59 

68.9 

3.1 

19 

118.8 

6.2 

79 

178.8 

9.4 

39 

238.7 

12.5 

99 

298.6 

15.6 

60 

59.9 

3.1 

20 

119.8 

6.3 

80 

179.8 

9.4 

40 

239.7 

12.6 

300 

299.6 

15.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

87°  ( 

93°,  267 

°,  273° 

)• 

TABLE  2.  . 

[Page  637     | 

Difference  of  Latitude  and  Departure  for  3°  (177°,  183°,  357° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

300.6 

15.7 

361 

360.5 

18.9 

421 

420.4 

22.0 

481 

480.3 

26.2 

641 

540.2 

28.3 

02 

301.6 

15.8 

62 

361.5 

19.0 

22 

421.4 

22.1 

82 

481.3 

25.2 

42 

641.2 

28.4 

03 

302.6 

15.9 

63 

362.5 

19.0 

23 

422.4 

22.2 

83 

482.3 

25.3 

43 

642.2 

28.4 

04 

303.5 

15.9 

64 

363.5 

19.1 

24 

423.4 

22.2 

84 

483.3  1  25.3 

44 

543.2 

28.6 

05 

304.5 

16.0 

65 

364.5 

19.1 

25     424. 4 

22.3 

85 

484.3  1  26.4 

45 

544.2 

28.6 

06 

305.5 

16.0 

66 

365.5 

19.2 

26     425. 4 

22.3 

86 

485.3 

26.4 

46 

546.2 

28.6 

07 

306.5 

16.1 

67 

366.5 

19.2 

27     426. 4 

22.4 

87 

486.3 

26.5 

47 

546.2 

28.6 

08 

307.5 

16.1 

68 

367.5 

19.3 

28  I  427.4 

22.4 

88 

487.3 

25.6 

48 

647.2 

28.7 

09 

308.5 

16.2 

69 

368.5 

19.3 

29  1  428.4 

22.5 

89 

488.3 

25.6 

49 

548.2 

28.7 

10 
311 

309.5 
310.5 

16.2 

70 

369.5 

19.4 

30 
431 

429.4 

22.5 

90 

489.3 

25.6 

50 

549.2 

28.8 

16.3 

371 

370.5 

19.4 

430.4 

22.6 

491 

490.3 

26.7 

551 

550.2 

28.8 

12 

311.5 

16.3 

72 

371.5 

19.5 

32 

431.4 

22.6 

92 

491.3 

26.7 

52 

561.2 

28.9 

13 

312.5 

16.4 

73 

372.5 

19.5 

33 

432.4 

22.7 

93 

492.3 

25.8 

53 

552.2 

28.9 

14 

313.5 

16.4 

74 

373.5 

19.6 

34 

433.4 

22.7 

94 

493.3 

25.9 

54 

553.2 

29.0 

15 

314.5 

16.5 

75 

374.5 

19.6 

36 

434.4 

22.8 

96 

494.3 

26.9 

55 

654.2 

29.1 

16 

315.5 

16.6 

76 

375.5 

19.7 

36 

435.4 

22.8 

96 

495.3 

26.0 

66 

665.2 

29.1 

17 

316.5 

16.6 

77 

376.5 

19.8 

37 

436.4 

22.9 

97 

496.3 

26.0 

67 

566.2 

29.2 

18 

317.5 

16.7 

78 

377.4 

19.8 

38 

437.4 

22.9 

98 

497.3 

26.1 

68 

667.2 

29.2 

19 

318.5 

16.7 

79 

378.4 

19.9 

39 

438.4 

23.0 

99 

498.3 

26.1 

59 

558.2 

29.3 

20 

319.5 

16.8 

80 

379.4 

19.9 

40 

439.4 

23.0 

500 
501 

499.3 
500.3 

26.2 
26.2 

60 
561 

559.2 

29.3 
29.4 

321 

320.5 

16.8 

381 

380.4 

20.0 

441 

440.4 

23.1 

560.2 

22 

321.5 

16.9 

82 

381.4 

20.0 

42 

441.4 

23.1 

02 

501.3 

26.3 

62 

561.2 

29.4 

23 

322.5 

16.9 

83 

382.4 

20.1 

43 

442.4 

23.2 

03 

502.3 

26.3 

63 

662.2 

29.6 

24 

323.5 

17.0 

84 

383.4 

20.1 

44 

443.4 

23.3 

04 

503.3 

26.4 

64 

563.2 

29.6 

25 

324.5 

17.0 

85 

384.4 

20.2 

45 

444.4 

23.3 

05 

604.3 

26.4 

65 

564.2 

29.6 

26 

325.  5 

17.1 

86 

385.4 

20.2 

46 

445.4 

23.4 

06 

605.3 

26.6 

66 

666.2 

29.6 

27 

326.5 

17.1 

87 

386.4 

20.3 

47 

446.4 

23.4 

07 

506.3 

26.6 

67 

666.2 

29.7 

28 

327.5 

17.2 

88 

387.4 

20.3 

48 

447.4 

23.5 

08 

507.3 

26.6 

68 

567.2 

29.7 

29 

328.5 

17.2 

89 

388.4 

20.4 

49 

448.4 

23.5 

09 

508.3 

26.6 

69 

568.2 

29.8 

30 

329.5 

17.3 

90 

389.4 

20.4 

50 

449.3 

23.6 

10 

509.3 

26.7 

70 

569.  2 

29.8 

331 

330.5 

17.3 

391 

390.4 

20.5 

451 

450.3 

23.6 

511 

510.3 

26.7 

571 

570.2 

29.9 

32 

331.5 

17.4 

92 

391.4 

20.5 

52 

461.3 

23.7 

12 

511.3 

26.8 

72 

571.2 

29.9 

33 

332.5 

17.5 

93 

392.4 

20.6 

53 

452.3 

23.7 

13 

612.3 

26.8 

73 

572.2 

30.0 

34 

333.5 

17.5 

94 

393.4 

20.6 

54 

453.3 

23.8 

14 

513.3 

26.9 

74 

573.2 

30.0 

35 

334.5 

17.6 

95 

394.4 

20.7 

55 

454.3 

23.8 

15 

514.3 

27.0 

76 

674.2 

30.1 

36 

335.5 

17.6 

96 

395.4 

20.7 

56 

455.3 

23.9 

16 

515.3 

27.0 

76 

575.2 

30.1 

37 

336.5 

17.7 

97 

396.4 

20.8 

57 

456.3 

23.9 

17 

516.3 

27.1 

77 

576.2 

30.2 

38 

337.5 

17.7 

98 

397.4 

20.8 

58 

457.3 

24.0 

18 

517.3 

27.1 

78 

677.2 

30.2 

39 

338.5 

17.8 

99 

398.4 

20.9 

59 

458.3 

24.0 

19 

618.3 

27.2 

79 

678.2 

30.3 

40 

339.5 

17.8 

400 

399.4 

20.9 

60 

459.3 

24.1 

20 

519.3 

27.2 

80 

679.2 

30.3 

341 

340.5 

17.9 

401 

400.4 

21.0 

461 

460.3 

24.1 

621 

520.3 

27.3 

681 

580.2 

30.4 

42 

341.5 

17.9 

02 

401.4 

21.1 

62 

461.3 

24.2 

22 

621.3 

27.3 

82 

581.2 

30.4 

43 

342.5 

18.0 

03 

402.4 

21.1 

63 

462.3 

24.2 

23 

522.3 

27.4 

83 

582.2 

30.5 

44 

343.5 

18.0 

04 

403.4 

21.2 

64 

463.3 

24.3 

24 

523. 3 

27.4 

84 

583.2 

30.5 

45 

344.5 

18.1 

05 

404.4 

21.2 

65 

464.3 

24.4 

26 

624.3 

27.6 

85 

584.2 

30.6 

46 

345.5 

18.1 

06 

405.4 

21.3 

66 

465.3 

24.4 

26 

626.3 

27.5 

86 

685.2 

30.6 

47 

346.5 

18.2 

07 

406.4 

21.3 

67 

466.3 

24.6 

27 

526.3 

27.6 

87 

586.2 

30.7 

48 

347.5 

18.2 

08 

407.4 

21.4 

68 

467.3 

24.5 

28 

527.3 

27.6 

88 

587.2 

30.7 

49 

348.5 

18.3 

09 

408.4 

21.4 

69 

468.3 

24.6 

29 

528.3 

27.7 

89 

588.2 

30.8 

50 

349.5 

18.3 
18.4 

10 
411 

409.4 

21.5 

70 

469.3 

24.6 

30 

529.3 

27.7 

90 

589.2 
590.2 

30.9 

351 

350.5 

410.4 

21.5 

471 

470.3 

24.7 

631 

630.3 

27.8 

591 

30.9 

52 

351.5 

18.4 

12 

411.4 

21.6 

72 

471.3 

24.7 

32 

631.3 

27.8 

92 

591.2 

31.0 

53 

352.5 

18.5 

13 

412.4 

21.6 

73 

472.3 

24.8 

33 

532.3 

27.9 

93 

592.2 

31.0 

54 

353.  5 

18.5 

14 

413.4 

21.7 

74 

473.3 

24.8 

34 

533.3 

27.9 

94 

593.2 

31.1 

55 

354.5 

18.6 

15 

414.4 

21.7 

75 

474.3 

24.9 

36 

534.3 

28.0 

95 

594.2 

31.1 

56 

355.5 

18.6 

16 

415.4 

21.8 

76 

476.3 

24.9 

36 

635.3 

28.1 

96 

696.2 

31.2 

57 

356.5 

18.7 

17 

416.4 

21.8 

77 

476.3 

25.0 

37 

536.3 

28.1 

97 

696.2 

31.2 

58 

357.5 

18.8 

18 

417.4 

21.9 

78 

477.3 

25.0 

38 

537.3 

28.2 

98 

697.2 

31.3 

59 

358.5 

18.8 

19 

418.4 

21.9 

79 

478.3 

25.1 

39 

538.3 

28.2 

99 

598.2 

31.3 

60 

359.5 

18.9 

20 

419.4 

22.0 

80 

479.3 

25.1 

40 

539.3 

28,3 

600 

599.2 

31.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

87°  (93*,  267°,  273°).                                                                       1 

Page  638] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for 

4°  (176°,  184 

°,  356° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.9 

4.3 

121 

120.7 

8.4 

181 

180.6 

12.6 

241 

240.4 

16.8 

2 

2.0 

0.1 

62 

61.8 

4.3 

22 

121.7 

8.5 

82 

181.6 

12.7 

42 

24J.4 

16.9 

3 

3.0 

0.2 

63 

62.8 

4.4 

23 

122.7 

8.6 

83 

182.6 

12.8 

43 

242.4 

17.0 

4 

4.0 

0.3 

64 

63.8 

4.5 

24 

123.7 

8.6 

84 

183.6 

12.8 

44 

243.4 

17.0 

5 

5.0 

0.3 

65 

64.8 

4.5 

25 

124.7 

8.7 

85 

184.5 

12.9 

45 

244.4 

17.1 

6 

6.0 

0.4 

66 

65.8 

4.6 

26 

125.7 

8.8 

86 

185.5 

13.0 

46 

245.4 

17.2 

7 

7.0 

0.5 

67 

66.8 

4.7 

27 

126.7 

8.9 

87 

186.5 

13.0 

47 

246.4 

17.2 

8 

8.0 

0.6 

68 

67.8 

4.7 

28 

127.7 

8.9 

88 

187.5 

13.1 

48 

247.4 

17.3 

9 

9.0 

0.6 

69 

68.8 

4.8 

29 

128.7 

9.0 

89 

188.5 

13.2 

49 

248.4 

17.4 

10 

10.0 

0.7 

70 

69.8 

4.9 

30 

129.7 

9.1 

90 

189.5 

13.3 

50 

249.4 

17.4 

11 

11.0 

0.8 

71 

70.8 

5.0 

131 

130.7 

9.1 

191 

190.5 

13.3 

251 

250.4 

17.5 

12 

12.0 

0.8 

72 

71.8 

5.0 

32 

131.7 

9.2 

92 

191.5 

13.4 

52 

251.4 

17.6 

13 

13.0 

0.9 

73 

72.8 

5.1 

33 

132.7 

9.3 

93 

192.5 

13.5 

53 

252.4 

17.6 

14 

14.0 

1.0 

74 

73.8 

5.2 

34 

133.7 

9.3 

94 

193.5 

13.5 

54 

253.4 

17.7 

15 

15.0 

1.0 

75 

74.8 

5.2 

35 

134.7 

9.4 

95 

194.5 

13.6 

55 

254.4 

17.8 

16 

16.0 

1.1 

76 

75.8 

5.3 

36 

135.7 

9.5 

96 

195.5 

13.7 

56 

255.4 

17.9 

17 

17.0 

1.2 

77 

76.8 

5.4 

37 

136.7 

9.6 

97 

196.5 

13.7 

57 

256.4 

17.9 

18 

18.0 

1.3 

78 

77.8 

5.4 

38 

137.7 

9.6 

98 

197.5 

13.8 

58 

257.4 

18.0 

19 

19.0 

1.3 

79 

78.8 

5.5 

39 

138.7 

9.7 

99 

198.5 

13.9 

59 

258.4 

18.1 

20 

20.0 

1.4 

80 

79.8 

5.6 

40 

139.7 

9.8 

200 

199.5 

14.0 

60 

259.4 

18.1 

21 

20.9 

1.5 

81 

80.8 

5.7 

141 

140.7 

9.8 

201 

200.5 

14.0 

261 

260.4 

18.2 

22 

21.9 

1.5 

82 

81.8 

5.7 

42 

141.7 

9.9 

02 

201.5 

14.1 

62 

261.4 

18.3 

23 

22.9 

1.6 

83 

82.8 

5.8 

43 

142.7  i  10.0 

03 

202.5 

14.2 

63 

262. 4 

18.3 

24 

23.9 

1.7 

84 

83.8 

5.9 

44 

143.6 

10.0 

04 

203.5 

14.2 

64 

263.4 

18.4 

25 

24.9 

1.7 

85 

84.8 

5.9 

45 

144.6 

10.1 

05 

204.5 

14.3 

65 

264.4 

18.5 

26 

25,9 

1.8 

86 

85.8 

6.0 

46 

145.6 

10.2 

06 

205.5 

14.4 

66 

265.4 

18.6 

27 

26.9 

1.9 

87 

86.8 

6.1 

47 

146.6 

10.3 

07 

206.5 

14.4 

67 

266.3 

18.6 

28 

27.9 

2.0 

88 

87.8 

6.1 

48 

147.6 

10.3 

08 

207.5 

14.5 

68 

267.3 

18.7 

29 

28.9 

2.0 

89 

88.8 

6.2 

49 

148.6 

10.4 

09 

208.5 

14.6 

69 

268.3 

18.8 

30 
31 

29.9 

2.1 

90 

89.8 
90.8 

6.3 
6.3 

50 

149.6 

10.5 

10 

209.5 

14.6 

70 

269.3 

18.8 

30.9 

2.2 

91 

151 

150.6 

10.5 

211 

210.5 

14.7 

271 

270.3 

18.9 

32 

31.9 

2.2 

92 

91.8 

6.4 

52 

151.6 

10.6 

12 

211.5 

14.8 

72 

271.3 

19.0 

33 

32.9 

2.3 

93 

92.8 

6.5 

53 

152.6 

10.7 

13 

212.5 

14.9 

73 

272.3 

19.0 

34 

33.9 

2.4 

94 

93.8 

6.6 

54 

153.6 

10.7 

14 

213.5 

14.9 

74 

273.3 

19.1 

35 

34.9 

2.4 

95 

94.8 

6.6 

55 

154.6 

10.8 

15 

214.5 

15.0 

75 

274.3 

19.2 

36 

35.9 

2.5 

96 

95.8 

6.7 

56 

155.6 

10.9 

16 

215.5 

15.1 

76 

275.3 

19.3 

37 

36.9 

2.6 

97 

96.8 

6.8 

57 

156.6 

11.0 

17 

216.5 

15.1 

77 

276.3 

19.3 

38 

37.9 

2.7 

98 

97.8 

6.8 

58 

157.6 

11.0 

18 

217.5 

15.2 

78 

277.3 

19.4 

39 

38.9 

2.7 

99 

98.8 

6.9 

59 

158.6 

11.1 

19 

218.5 

15.3 

79 

278.3 

19.5 

40 

39.9 

2.8 

100 

99.8 

7.0 

60 

159.6 
160.6 

11.2 

20 

219.5 

15.3 

80 

279.3 

19.5 

41 

40.9 

2.9 

101 

100.8 

7.0 

161 

11.2 

221 

220.5 

15.4 

281 

280.3 

19.6 

42 

41.9 

2.9 

02 

101.8 

7.1 

62 

161.6 

11.3 

22 

221.5 

15.5 

82 

281.3 

19.7 

43 

42.9 

3.0 

03 

102.7 

7.2 

63 

162.6 

11.4 

23 

222.5 

15.6 

83 

282.3 

19.7 

44 

43.9 

3.1 

04 

103.7 

7.3 

64 

163.6 

11.4 

24 

223.5 

15.6 

84 

283.3 

19.8 

45 

44.9 

3.1 

05 

104.7 

7.3 

65 

164.6 

11.5 

25 

224.5 

15.7 

85 

284.3 

19.9 

46 

45.9 

3.2 

06 

105.7 

7.4 

66 

165.6 

11.6 

26 

225.4 

15.8 

86 

285.3 

80.0 

47 

46.9 

3.3 

07 

106.7 

7.5 

67 

166.6 

11.6 

27 

226.4 

15.8 

87 

286.3 

20.0 

48 

47.9 

3.3 

08 

107.7 

7.5 

68 

167.6 

11.7 

28 

227.4 

15.9 

88 

287.3 

20.1 

49 

48.9 

3.4 

09 

108.7 

7.6 

69 

168.6 

11.8 

29 

228.4 

16.0 

89 

288.3 

20.2 

50 

49.9 

3.5 

10 

109.7 

7.7 

70 

169.6 

11.9 

30 

229.4 

16.0 

90 

289.3 

20.2 

51 

50.9 

3.6 

111 

110.7 

7.7 

171 

170.6 

11.9 

231 

230.4 

16.1 

291 

290.3 

20.3 

52 

51.9 

3.6 

12 

111.7 

7.8 

72 

171.6 

12.0 

32 

231.4 

16.2 

92 

291.3 

20.4 

53 

52.9 

3.7 

13 

112.7 

7.9 

73 

172.6 

12.1 

33 

232.4 

16.3 

93 

292.3 

20.4 

54 

53.9 

3.8 

14 

113.7 

8.0 

74 

173.6 

12.1 

34 

233.4 

16.3 

94 

293.3 

20.5 

55 

54.9 

3.8 

15 

114.7 

8.0 

75 

174.6 

12.2 

35 

234.4 

16.4 

95 

294.3 

20.6 

56 

55.9 

3.9 

16 

115.7 

8.1 

76 

175.6 

12.3 

36 

235.4 

16.5 

96 

295.3 

20.6 

57 

56.9 

4.0 

17 

116.7 

8.2 

77 

176.6 

12.3 

37 

236.4 

16.5 

97 

296.3 

20.7 

58 

57.9 

4.0 

18 

117.7 

8.2 

78 

177.6 

12.4 

38 

237.4 

16.6 

98 

297.3 

20.8 

59 

58.9 

4.1 

19 

118.7 

8.3 

79 

178.6 

12.5 

39 

238.4 

16.7 

99 

298.3 

20.9 

60 

69.9 

4.2 

20 

119.7 

8.4 

80 

179.6 

12.6 

40 

239.4 

16.7 

300 

299.3 

20.9 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

J 

!6°;  ( 

H°,  266°,  274° 

)• 

TABLE  2. 

[Page  639 

Difference  of  Latitude  and  Depart 

are  for  4°  (176°,  184°,  356° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

301 

300.3 

21.0 

361 

360.1 

25.2 

421 

420.0 

29.4 

481 

479.8 

33.5 

541 

539.7 

37.7 

02 

301.3 

21.1 

62 

361. 1 

25.2 

22 

421.0 

29.4 

82 

480.8 

33.6 

42 

540.7 

37.8 

03 

302.2 

21.1 

63 

362.1 

25.3 

23 

422.0 

29.5 

83 

481.8 

33.7 

43 

541.7 

37.9 

04 

303.2 

21.2 

64 

363.1 

25.4 

24 

423.0 

29.6 

84 

482.8 

33.7 

44 

542.7 

37.9 

05 

304.2 

21.3 

65 

364.1 

25.5 

25 

424.0 

29.6 

85 

483.8 

33.8 

45 

543.7 

38.0 

06 

305. 2 

21.3 

66 

365.1 

25.5 

26 

424.9 

29.7 

86 

484.8 

33.9 

46 

544.7 

38.1 

07 

306.2 

21.4 

67 

366.1 

25.6 

27 

425.9 

29.8 

87 

485.8 

33.9 

47 

545.7 

38.1 

08 

307.2 

21.5 

68 

367.1 

25.7 

28 

426.9 

29.9 

88 

486.8 

34.0 

48 

546.7 

38.2 

09 

308.2 

21.6 

69 

368.1 

25.7 

29 

427.9 

29.9 

89 

487.8 

34.1 

49 

547.7 

38.3 

10 

309.2 

21.6 

70 

369.1 

25.8 

30 

428.9 

30.0 

90 

488.8 

34.2 

50 

548.7 

38.3 

311 

310.2 

21.7 

371 

370.1 

25.9 

431 

429.9 

30.1 

491 

489.8 

34.2 

551 

549.7 

38.4 

12 

311.2 

21.8 

72 

371.1 

25.9 

32 

430.9 

30.1 

92 

490.8 

34.3 

52 

550.7 

38.5 

13 

312.2 

21.8 

73 

372.1 

26.0 

33 

431.9 

30.2 

93 

491.8 

34.4 

53 

551.7 

38.5 

14 

313.2 

21.9 

74 

373.1 

26.1 

34 

432.9 

30.3 

94 

492.8 

34.4 

54 

552.7 

38.6 

15 

314.2 

22.0 

75 

374.1 

26.2 

35 

433.9 

30.3 

95 

493.8 

34.5 

55 

553.6 

38.7 

16 

315.2 

22.1 

76 

375.1 

26.2 

36 

434.9 

30.4 

96 

494.8 

34.6 

56 

554.6 

38.7 

17 

316.2 

22.1 

77 

376.1 

26.3 

37 

435.9 

30.5 

97 

495.8 

34.6 

57 

555.6 

38.8 

18 

317.2 

22.2 

78 

377.1 

26.4 

38 

436.9 

30.6 

98 

496.8 

34.7 

58 

556.6 

38.9 

19 

318.2 

22.3 

79 

378.1 

26.4 

39 

^37.9 

30.6 

99 

497.8 

34.8 

59 

557.6 

38.9 

20 

319.2 

22.3 

80 

379.1 

26.5 

40 

438.9 

30.7 

500 

498.8 

34.8 

60 

558.6 

39.0 

321 

320.2 

22.4 

381 

380.1 

26.6 

441 

439.9 

30.8 

501 

499.8 

34.9 

561 

559.6 

39.1 

22 

321.2 

22.5 

82 

381.1 

26.6 

42 

440.9 

30.8 

02 

500.8 

35.0 

62 

560. 6 

39.2 

23 

322.2 

22.5 

83 

382.1 

26.7 

43 

441.9 

30.9 

03 

501.8 

35.0 

63 

561.6 

39.2 

24 

323.2 

22.6 

84 

383.1 

26.8 

44 

442.9 

31.0 

04 

502.8 

35.1 

64 

562.6 

39.3 

25 

324.2 

22.7 

85 

384.0 

26.9 

45 

443.9 

31.0 

05 

503.8 

35.2 

65 

563.6 

39.4 

26 

325.2 

22.7 

86 

385.0 

26.9 

46 

444.9 

31.1 

06 

504.8 

35.2 

66 

564.6 

39.4 

27 

326.2 

22.8 

87 

386.0 

27.0 

47 

445.9 

31.2 

07 

505.8 

35.3 

67 

565.6 

39.5 

28 

327.2 

22.9 

88 

387.0 

27.1 

48 

446.9 

31.2 

08 

506.8 

35.4 

68 

566.6 

39.6 

29 

328.2 

23.0 

89 

388.0 

27.1 

49 

447.9 

31.3 

09 

507.8 

35.5 

69 

567.6 

39.7 

30 

329.2 

23.0 

90 

389.0 

27.2 

50 

448.9 

31.4 

10 

508.8 

35.6 

70 

568.6 

39.8 

331 

330.2 

23.1 

391 

390.0 

27.3 

451 

449.9 

31.5 

511 

509.8 

35.6 

571 

569.6 

39.8 

32 

331.2 

23.2 

92 

391.0 

27.3 

52 

450.9 

31.5 

12 

510.8 

35.7 

72  1  570. 6 

39.9 

33 

332.2 

23.2 

93 

392.0 

27.4 

53 

451.9 

31.6 

13 

511.8 

35.8 

73  i  571.6 

40.0 

34 

333.2 

23.3 

94 

393.0 

27.5 

54 

452.9 

31.7 

14 

512.7 

35.8 

74  1  572.6 

40.0 

35 

334.2 

23.4 

95 

394.0 

27.6 

55 

453.9 

31.7 

15 

513.7 

36.9 

75 

573.6 

40.1 

36 

335.2 

23.4 

96 

395.0 

27.6 

56 

454.9 

31.8 

16 

514.7 

36.0 

76 

574.6 

40.2 

37 

336.2 

23.5 

97 

396.0 

27.7 

57 

455.9 

31.9 

17 

515.7 

36.0 

77 

575.6 

40.2 

38 

337.2 

23.6 

98 

397.0 

27.8 

58 

456.9 

31.9 

18 

516.7 

36.1 

78 

576.6 

40.3 

39 

338.2 

23.6 

99 

398.0 

27.8 

59 

457.9 

32.0 

19 

517.7 

36.2 

79 

577.6 

40.4 

40 

339.2 

23.7 

400 

399.0 

27.9 

60 

458.9 

32.1 

20 

518.7 

36.2 

80 

578.6 

40.5 

341 

340.2 

23.8 

401 

400.0 

28.0 

461 

459.9 

32.2 

521 

519.7 

36.3 

581 

579.6 

40.5 

42 

341.2 

23,9 

02 

401.0 

28.0 

62 

460.9 

32.2 

22 

520.7 

36.4 

82 

580.6 

40.6 

43 

342.2 

23.9 

03 

402.0 

28.1 

63 

461.9 

32.3 

23 

521.7 

36.4 

83 

581.6 

40.7 

44 

343.1 

24.0 

04 

403.0 

28.2 

64 

462.9 

32.4 

24 

522.7 

36.5 

84 

582.6 

40.7 

45 

344.1 

24.1 

05 

404.0 

28.2 

65 

463.9 

32.4 

25 

523.7 

36.6 

85 

583.6 

40.8 

46 

345.1 

24.1 

06 

405.0 

28.3 

66 

464.9 

32.5 

26 

524.7 

36.7 

86 

584.6 

40.9 

47 

346.1 

24.2 

07 

406.0 

28.4 

67 

465.8 

32.6 

27 

525.7 

36.8 

87 

585.6 

40.9 

48 

347.1 

24.3 

08 

407.0 

28.5 

68 

466.8 

32.6 

28 

526.7 

36.8 

88 

586.6 

41.0 

49 

348.1 

24.3 

09 

408.0 

28.5 

69 

467.8 

32.7 

29 

527.7 

36.9 

89 

587.6 

41.1 

50 

349.1 

24.4 

10 

409.0 

28.6 

70 

468.8 

32.8 

30 
531 

528.7 
529.7 

37.0 

90 

588.6 

41.2 

351 

350. 1 

24.5 

411 

410.0 

28.7 

471 

469.8 

32.9 

37.0 

591 

589.6 

41.3 

52 

a51. 1 

24.6 

12 

411.0 

28.7 

72 

470.8 

32.9 

32 

530.7 

37.1 

92 

590.6 

41.3 

53 

352.1 

24.6 

13 

412.0 

28.8 

73 

471.8 

33.0 

33 

531.7 

37.2 

93 

591.6 

41.4 

54 

353. 1 

24.7 

14 

413.0 

28.9 

74 

472.8 

33.1 

34 

532.7 

37.2 

94 

592.6 

41.5 

55 

354.1 

24.8 

15 

414.0 

28.9 

75 

473.8 

33.1 

35 

533.7 

37.3 

95 

593.6 

41.5 

56 

355.1 

24.8 

16 

415.0 

29.0 

76 

474.8 

33.2 

36 

534.7 

37.4 

96 

594.6 

41.6 

57 

356.1 

24.9 

17 

416.0 

29.1 

77 

475.8 

33.3 

37 

535.7 

37.5 

97 

595.6 

41.7 

58 

357.1 

25.0 

18 

417.0 

29.2 

78 

476.8 

33.3 

38 

536.7 

37.5 

98 

596.6 

41.7 

59 

358. 1 

25.0 

19 

418.0 

29.2 

79 

477.8 

33.4 

39 

537.7 

37.6 

99 

597.6 

41.8 

60 

359.1 

25.1 

20 

419.0 

29.3 

80 

478.8 

35.5 

40 

538.7 

37.7 

600 

598.6 

41.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

i 

}6»;  ( 

94°,  266 

%  274° 

. 

1 

Page  540] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  5°  (175°,  185 

°,  355° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.8 

5.3 

121 

120.5 

10.5 

181 

180.3 

15.8 

241 

240.1 

21.0 

2 

2.0 

0.2 

62 

61.8 

5.4 

22 

121.5 

10.6 

82 

181.3 

15.9 

42 

241.1 

21.1 

3 

3.0 

0.3 

63 

62.8 

5.5 

23 

122.5 

10.7 

83 

182.3 

15.9 

43 

242. 1 

21.2 

4j 

4.0 

0.3 

64 

63.8 

5.6 

24 

123.5 

10.8 

84 

183.3 

16.0 

44 

243. 1 

21.3 

5 

5.0 

0.4 

65 

64.8 

5.7 

25 

124.5 

10.9 

85 

184.3 

16.1 

45 

244.1 

21.4 

6 

6.0 

0.5 

66 

65.7 

5.8 

26 

125.5 

11.0 

86 

185.3 

16.2 

46 

245.1 

21.4 

7 

7.0 

0.6 

67 

66.7 

5.8 

27 

126.5 

11.1 

87 

186.3 

16.3 

47 

246.1 

21.5 

8 

8.0 

0.7 

68 

67.7 

5.9 

28 

127.5 

11.2 

88 

187.3 

16.4 

48 

247.1 

21.6 

9 

9.0 

0.8 

69 

68.7 

6.0 

29 

128.5 

11.2 

89 

188.3 

16.5 

49 

248.1 

21.7 

10 

10.0 

0.9 

70 

69.7 

6.1 

30 

129.5 

11.3 

90 

189.3 

16.6 

50 

249.0 
250.  0" 

21.8 
21.9 

11 

11.0 

1.0 

71 

70.7 

6.2 

131 

130.5 

11.4 

191 

190.3 

16.6 

251 

12 

12.0 

1.0 

72 

71.7 

6.3 

32 

131.5 

11.5 

92 

191.3 

16.7 

52 

251.0 

22.0 

13 

13.0 

1.1 

73 

72.7 

6.4 

33 

132.5 

11.6 

93 

192.3 

16.8 

53 

252.0 

22.1 

14 

13.9 

1.2 

74 

73.7 

•6.4 

34 

133. 5 

11.7 

94 

193.3 

16.9 

54 

253.0 

22.1 

15 

14.9 

1.3 

75 

74.7 

6.5 

35 

134.5 

11.8 

95 

194.3 

17.0 

55 

254.0 

22.2 

16 

15.9 

1.4 

76 

75.7 

6.6 

36 

135.5 

11.9 

96 

195.3 

17.1 

56 

255.0 

22.3 

17 

16.9 

1.5 

77 

76.7 

6.7 

37 

136.5 

11.9 

97 

196.3 

17.2 

57 

256.0 

22.4 

18 

17.9 

1.6 

78 

77.7 

6.8 

38 

137.5 

12.0 

98 

197.2 

17.3 

58 

257.0 

22.5 

19 

18.9 

1.7 

79 

78.7 

6.9 

39 

138.5 

.12.1 

99 

198. 2 

17.3 

59 

258.0 

22.6 

20 

19.9 

1.7 

80 

79.7 

7.0 

40 

139.5 

12.2 

200 

199.2 

17.4 

60 

259.0 

22.7 

21 

20.9 

1.8 

81 

80.7 

7.1 

141 

140.5 

12.3 

201 

200.2 

17.5 

261 

260.0 

22.7 

22 

21.9 

1.9 

82 

81.7 

7.1 

42 

141.5 

12.4 

02 

201.2 

17.6 

62 

261.0 

22.8 

23 

22.9 

2.0 

83 

82.7 

7.2 

43 

142.5 

12.5 

03 

202.2 

17.7 

63 

262.0 

22.9 

24 

23.9 

2.1 

84 

83.7 

7.3 

44 

143.5 

12.6 

04 

203.2 

17.8 

64 

263.0 

23.0 

25 

24.9 

2.2 

85 

84.7 

7.4 

45 

144.4 

12.6 

05 

204.2 

17.9 

65 

264.0 

23.1 

26 

25.9 

2.3 

86 

85.7 

7.5 

46 

145.4 

12.7 

06 

205.2 

18.0 

66 

265.0 

23.2 

27 

26.9 

2.4 

87 

86.7 

7.6 

47 

146.4 

12.8 

07 

206.2 

18.0 

67 

266.0 

23.3 

28 

27.9 

2.4 

88 

87.7 

7.7 

48 

147.4 

12.9 

08 

207.2 

18.1 

68 

267.0 

23.4 

29 

28.9 

2.5 

89 

88.7 

7.8 

49 

148.4 

13.0 

09 

208.2 

18.2 

69 

268.0 

23.4 

30 

29.9 

2.6 

90 

89.7 

7.8 

50 

149.4 

13.1 

10 

209.2 

18.3 
18.4 

70 
271 

269.0 
270.0 

23.5 

31 

30.9 

2.7 

91 

90.7 

7.9 

151 

150.4 

13.2 

211 

210.2 

23.6 

32 

31.9 

2.8 

92 

91.6 

8.0 

52 

151.4 

13.2 

12 

211.2 

18.5 

72 

271.0 

23.7 

33 

32.9 

2.9 

93 

92.6 

8.1 

53 

152.4 

13.3 

13 

212.2 

18.6 

73 

272.0 

23.8 

34 

33.9 

3.0 

94 

93.6 

8.2 

54 

153.4 

13.4 

14 

213.2 

18.7 

74 

273.0 

23.9 

35 

34.9 

3.1 

95 

94.6 

8.3 

55 

154.4 

13.5 

15 

214.2 

18.7 

75 

274.0 

24.0 

36 

35.9 

3.1 

96 

95.6 

8.4 

56 

155.4 

13.6 

16 

215.2 

18.8 

76 

274.9 

24.1 

37 

36.9 

3.2 

97 

96.6 

8.5 

57 

156. 4 

13.7 

17 

216.2 

18.9 

77 

275.9 

24.1 

38 

37.9 

3.3 

98 

97.6 

8.5 

58 

157.4 

13.8 

18 

217.2 

19.0 

78 

276.9 

24.2 

39 

38.9 

3.4 

99 

98.6 

8.6 

59 

158.4 

13.9 

19 

218.2 

19.1 

79 

277.9 

24.3 

40 

39.8 

3.5 

100 

99.6 

8.7 

60 

159.4 

13.9 

20 

219.2 

19.2 

80 

278.9 

24.4 

41 

40.8 

3.6 

101 

100.6 

8.8 

161 

160.4 

14.0 

221 

220.2 

19.3 

281 

279.9 

24.5 

42 

41.8 

3.7 

02 

101.6 

8.9 

62 

161.4 

14.1 

22 

221.2 

19.3 

82 

280.9 

24.6 

48 

42.8 

3.7 

03 

102.6 

9.0 

63 

162.4 

14.2 

23 

222.2 

19.4 

83 

281.9 

24.7 

44 

43.8 

3.8 

04 

103.6 

9.1 

64 

163.4 

14.3 

24 

223.1 

19.5 

84 

282.9 

24.8 

45 

44.8 

3.9 

05 

104.6 

9.2 

65 

164.4 

14.4 

25 

224.1 

19.6 

85 

283.9 

24.8 

46 

45.8 

4.0 

06 

105.6 

9.2 

66 

165.4 

14.5 

26 

225.1 

19.7 

86 

284.9 

24.9 

47 

46.8 

4.1 

07 

106.6 

9.3 

67 

166.4 

14.6 

27 

226.1 

19.8 

87 

285.9 

25.0 

48 

47.8 

4.2 

08 

107.6 

9.4 

68 

167.4 

14.6 

28 

227.1 

19.9 

88 

286.9 

25.1 

49 

48.8 

4.3 

09 

108.6 

9.5 

69 

168.4 

14.7 

29 

228.1 

20.0 

89 

287.9 

25.2 

50 

49.8 
50.8 

4.4 

10 

109.6 

9.6 

70 

169.4 

14.8 

30 
231 

229.1 

20.0 

90 

288.9 
289.9 

25.3 

51 

4.4 

111 

110.6 

9.7 

171 

170.3 

14.9 

230.1 

20.1 

291 

25.4 

52 

51.8 

4.5 

12 

111.6 

9.8 

72 

171.3 

15.0 

32 

231.1 

20.2 

92 

290.9 

25.4 

53 

52.8 

4.6 

13 

112.6 

9.8 

73 

172.3 

15.1 

.33 

232.1 

20.3 

93 

291.9 

25.5 

54 

53.8 

4.7 

14 

113.6 

9.9 

74 

173.3 

15.2 

34 

233.1 

20.4 

94 

292.9 

25.6 

55 

54.8 

4.8 

15 

114.6 

10.0 

75 

. 174.  3 

15.3 

35 

234.1 

20.5 

95 

293.9 

25.7 

56 

55.8 

4.9 

16 

115.6 

10.1 

76 

175.3 

15.3 

36 

235.1 

20.6 

96 

294.9 

25.8 

57 

56.8 

5.0 

17 

116.  6 

10.2 

77 

176.3 

15.4 

37 

236.1 

20.7 

97 

295.9 

25.9 

58 

57.8 

5.1 

18 

117.6 

10.3 

78 

177.3 

15.5 

38 

237.1 

20.7 

98 

296.9 

26.0 

59 

58.8 

5.1 

19 

118.5 

10.4 

79 

178.3 

15.6 

39 

238.1 

20.8 

99 

297.9 

26.1 

60 

59.8 

5.2 

20 

119.5 

10.5 

80 

179.3 

15.7 

40 

239.1 

20.9 

300 

298.9 

26.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

85°  (95°,  265°,  275°) 

1 

TABLE  2. 

[Page  641 

Difference  of  Latitude  and  Departure  for  5°  (175°,  185 

°,  356° 

)• 

Dist. 

Lat.     }   Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

299.9     26.2 

361 

359.6 

31.5 

421 

419.4 

36.7 

481 

479.2 

41.9 

641 

538.9 

47.2 

02 

300.8 

26.3 

62 

360.6 

31.6 

22 

420.4 

36.8 

82 

480.2 

42.0 

42 

539.9 

47.3 

03 

301.8 

26.4 

63 

361. 6 

31.6 

23 

421.4 

36.9 

83 

481.2 

42.1 

43 

540.9 

47.4 

04  1  302.8 

26.5 

64 

362. 6 

31.7 

24 

422.4 

37.0 

84 

482.2 

42.2 

44 

541.9 

47.5 

05 

303.8 

26.6 

65 

363.6 

31.8 

25 

423.4 

37.1 

86 

483.2 

42.3 

46 

542.9 

47.6 

06 

304.8 

26.7 

66 

364.6 

31.9 

26 

424.4 

37.1 

86 

484.1 

42.4 

46 

543.9 

47.7 

07 

305.  8 

26.8 

67 

365.6 

32.0 

27 

425.4 

37.2 

87 

485.1 

42.4 

47 

544.9 

47.7 

08 

306.8 

26.9 

68 

366.6 

32.1 

28 

426.4 

37.3 

88 

486.1 

42.5 

48 

545.9 

47.8 

09  i  307.  8 

26.9 

69 

367.6 

32.2 

29 

427.4 

37.4 

89 

487.1 

42.6 

49 

546.9 

47.9 

10  i  308.8 
311  !  309.8 

27.0 
27.1 

70 

368.6 
'369.6 

32.3 

30 

428.4 

37.5 

90 

488.1 
489.1 

42.7 

60 

647.9 

48.0 

371 

32.3 

431 

429.4 

37.6 

491 

42.8 

551 

548.9 

48.1 

12 

310.  8 

27.2 

72 

370.6 

32.4 

32 

430.4 

37.7 

92 

490.1 

42.9 

52 

549.9 

48.2 

13 

311.8 

27.3 

73 

371.6 

32.5 

.33 

431.3 

37.7 

93 

491.1 

43.0 

53 

650.9 

48.3 

14 

312.8 

27.4 

74 

372.6 

32.6 

34 

432.3 

37.8 

94 

492.1 

43.1 

54 

551.9 

48.4 

15 

313.8 

27.5 

75 

373.6 

32.7 

35 

433.3 

37.9 

95 

493.1 

43.1 

56 

552.9 

48.4 

16 

314.  8 

27.5 

76 

374.6 

32.8 

36 

434.3 

38.0 

96 

494.1 

43.2 

66 

653.9 

48.5 

17 

315.  8 

27.6 

77 

375.6 

32.9 

37 

436.3 

38.1 

97 

495.1 

43.3 

57 

554.9 

48.6 

18 

316. 8 

27.7 

78 

376.6 

33. 0 

38 

436.3 

38.2 

98 

496.1 

43.4 

68 

566.9 

48.7 

19 

317.  8 

27.8 

79 

377.6 

33.0 

39 

437. 3 

38.3 

99 

497.1 

43.5 

69 

556. 9 

48.8 

20 

318. 8 
319.  8 

27.9 

80 

378.6 

33.1 

40 

438.3 

38.4 

500 

498.1 

43.6 

60 

557.9 

48.8 

321 

28.0 

381 

379. 5 

33.2 

441 

439.3 

38.4 

501 

499.1 

43.7 

561 

568.8 

48.9 

22 

320.8 

28.1 

82 

380. 5 

33.3 

42 

440.3 

38.5 

02 

500.1 

43.8 

62 

559.8 

49.0 

23 

.321.8 

28.2 

83 

381.5 

33.4 

43 

441.3 

38.6 

03 

501.1 

43.8 

63 

560.8 

49.1 

24 

322.8 

28.2 

84 

382.5 

33.5 

44 

442.3 

38.7 

04 

502.1 

43.9 

64 

561.8 

49.2 

25 

323.  8 

28.3 

85 

383.5 

33.6 

45 

443.3 

38.8 

05 

503.1 

44.0 

65 

562.8 

49.3 

26 

324.8 

28.4 

86 

384.  5 

33.7 

46 

444.3 

38.9 

06 

504.1 

44.1 

66 

563.8 

49.4 

27 

325.8 

28.5 

87 

385.  5 

33.7 

47 

445.3 

39.0 

07 

605.1 

44.2 

67 

564.8 

49.5 

28 

326.7 

28.6 

88 

386.  5 

33.8 

48 

446.3 

39.1 

08 

606.1 

44.3 

68 

565.8 

49.6 

29 

327.7  1  28.7 

89 

387.5 

33.9 

49 

447.3 

39.1 

09 

507.1 

44.4 

69 

566.8 

49.7 

30 

328.  7  1  28. 8 

90 
391 

388.5 
389.5 

34.0 

50 

448.3 

39.2 

10 

508.1 

44.5 

70 
571 

667.8 

49.7 

331 

329.7     28.9 

34.1 

451 

449.3 

39.3 

511 

509.0 

44.5 

568.8 

49.8 

32 

330.7     28.9 

92 

390.5 

34.2 

52 

450.3 

39.4 

12 

510.0 

44.6 

72 

569.8 

49.9 

33 

331.  7     29. 0 

93 

391.  5 

34.3 

53 

451.3 

39.5 

13 

511.0 

44.7 

73 

570.8 

50.0 

34 

332.7 

29.1 

94 

392.5 

34.3 

54 

452.3 

39.6 

14 

512.0 

44.8 

74 

571.8 

50.1 

35 

333.  7 

29.2 

95 

393.5 

34.4 

55 

453.3 

39.7 

16 

513.0 

44.9 

75 

672.8 

50.2 

36 

334.7 

29.3 

96 

394.5 

34.5 

56 

454.3 

39.8 

16 

514.0 

46.0 

76 

573.8 

60.3 

37     335. 7 

29.4 

97 

395.5 

34.6 

57 

465.3 

39.8 

17 

515.0 

45.1 

77 

574.8 

50.4 

38 

336.  7 

29.5 

98 

396.5 

34.7 

58 

456.3 

39.9 

18 

516.0 

45.2 

78 

575.8 

50.4 

39 

337.7 

29.6 

99 

397.5 

34.8 

59 

457.3 

40.0 

19 

517.0 

45.2 

79 

676.8 

50.5 

40 

338.7 

29.6 

400 

398.5 

34.9 

60 

458.2 

40.1 

20 

518.0 
519.0 

46.3 

80 

577.8 

50.6 

341 

339.7 

29.7 

401 

399.5 

35.0 

461 

459.2 

40.2 

521 

46.4 

581 

578.8 

50.7 

42 

340.  7 

29.8 

02 

400.5 

35.0 

62 

460.2 

40.3 

22 

520.0 

46.5 

82 

579.8 

50.8 

43 

341.7 

29.9 

03 

401.5 

35.1 

63 

461.2 

40.4 

23 

521.0 

45.6 

83 

580.8 

50.9 

44 

342.  7 

30.0 

04 

402.5 

35.2 

64 

462.2 

40.4 

24 

622.0 

46.7 

84 

681.8 

60.9 

45 

343.7 

30.1 

05 

403.5 

35.3 

65 

463.2 

40.5 

25 

523.0 

46.8 

86 

582.8 

51.0 

46 

344.7 

30.2 

06 

404.5 

35.4 

66     464. 2 

40.6 

26 

524.0 

45.9 

86 

583. 8 

51.1 

47 

345.7 

30.3 

07 

405.4 

35.5 

67 

466.2 

40.7 

27 

625.0 

46.9 

87 

584.8 

61.2 

48 

;M6.7 

30.3 

08 

406.4 

35.6 

68 

466.2 

40.8 

28 

626.0 

46.0 

88 

585.8 

51.3 

49     347. 7 

30.4 

09 

407.4 

35.7 

69 

467.2 

40.9 

29 

527.0 

46.1 

89 

586.8 

51.4 

50 

348.7 
349.7 

30.5 

10 

408.4 

35.7 

70 

468.2 

41.0 

30 

528.0 
529.0 

46.2 

90 

587.8 

61.6 

351 

30.6 

411 

409.4 

35.8 

471 

469.2 

41.1 

531 

46.3 

591 

688.7 

51.6 

52     350. 7 

30.7 

12 

410.4 

35.9 

72 

470.2 

41.1 

32 

530.0 

46.4 

92 

589.7 

61.6 

53     351. 7 

30.8 

13 

411.4 

36.0 

73 

471.2 

41.2 

33 

531.0 

46.6 

93 

590.7 

51.7 

54 

352.  6 

30.9 

14 

412.4 

36.1 

74 

472.2 

41.3 

34 

532. 0 

46.6 

94 

591.7 

51.8 

55 

353.6 

30.9 

15 

413.4 

36.2 

75 

473.2 

41.4 

35 

533.0 

46.6 

95 

592.7 

51.9 

56 

354.6 

31.0 

16 

414.4 

36.3 

76 

474.2 

41.5 

36 

533.9 

46.7 

96 

693.7 

52.0 

57 

355.6 

31.1 

17 

415.4 

36.4 

77 

475.2 

41.6 

37 

534.9 

46.8 

97 

694.7 

62.1 

58 

356.6 

31.2 

18 

416.4 

36.4 

78 

476.2 

41.7 

38 

536. 9 

46.9 

98 

595.7 

52.2 

59 

357.6 

31.3 

19 

417.4 

36.5 

79 

477.2 

41.8 

39 

536.9 

47.0 

99 

596.7 

52.3 

60 

358.6 

31.4 

20 

418.4 

36.6 

80 

478.2 

41.8 

40 

537.9 

47.1 

600 

597.7 

52.3 

Diet. 

Dep. 

Lat. 

Diat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

85°  (95°,  265°,  275°).                                                                       1 

Page  542] 

TABLE  2. 

Difference  of  Latitude  anc 

Departure  for  6°  (174°,  186°,  354° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
25.2 

1 

1.0 

0.1 

61 

60.7 

6.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239.7 

2 

2.0 

0.2 

62 

61.7 

6.5 

22 

121.3 

12.8 

82 

181.0 

19.0 

42 

240.7 

25.3 

3 

3.0 

0.3 

63 

62.7 

6.6 

23 

122.3 

12.9 

83 

182.0 

19.1 

43 

241.7 

2.5.4 

4 

4.0 

0.4 

64 

63.6 

6.7 

24 

123.3 

13.0 

84 

183.0 

19.2 

44 

242.7 

25.5 

5 

5.0 

0.5 

65 

64.6 

6.8 

25 

124.3 

13.1 

85 

184.0 

19.3 

45 

243.7 

25.6 

6 

6.0 

0.6 

66 

65.6 

6.9 

26 

125.3 

13.2 

86 

185.0 

19.4 

46 

244.7 

25.7 

7 

7.0 

0.7 

67 

66.6 

7.0 

27 

126.3 

13.3 

87 

186.0 

19.6 

47 

245.6 

25.8 

8 

8.0 

0.8 

68 

67.6 

7.1 

28 

127.3 

13.4 

88 

187.0 

19.7 

48 

246.6 

25.9 

9 

9.0 

0.9 

69 

68.6 

7.2 

29 

128.3 

13.5 

89 

188.0 

19.8 

49 

247.6 

26.0 

10 

9.9 

1.0 

70 

69.6 

7.3 

30 

129.3 

13.6 

90 

189.0 

19.9 

50 

248.6 

26.1 

11 

10.9 

1.1 

71 

70.6 

7.4 

131 

130.3 

13.7 

191 

190.0 

20.0 

251 

249.6 

26.2 

12 

11.9 

1.3 

72 

71.6 

7.5 

32 

131.3 

13.8 

92 

190.9 

20.1 

52 

250.6 

26.3 

13 

12.9 

1.4 

73 

72.6 

7.6 

33 

132.3 

13.9 

93 

191.9 

20.2 

53 

251.6 

26.4 

14 

13.9 

1.5 

74 

73.6 

7.7 

34 

133.3 

14.0 

94 

192.9 

20.3 

54 

252.6 

26.6 

15 

14.9 

1.6 

75 

74.6 

7.8 

35 

134.3 

14.1 

95 

193.9 

20.4 

55 

253.6 

26.7 

16 

15.9 

1.7 

76 

75.6 

7.9 

36 

135.3 

14.2 

96 

194.9 

20.5 

56 

254.6 

26.8 

17 

16.9 

1.8 

77 

76.6 

8.0 

37 

136.2 

14.3 

97 

195.9 

20.6 

57 

255.6 

26.9 

18 

17.9 

1.9 

78 

77.6 

8.2 

38 

137.2 

14.4 

98 

196.9 

20.7 

58 

256.6 

27.0 

19 

18.9 

2.0 

79 

78.6 

8.3 

39 

138.2 

14.5 

99 

197.9 

20.8 

59 

257.6 

27.1 

20 

19.9 

2.1 

80 

79.6 

8.4 

40 

139.2 
140.2 

14.6 
14.7 

200 
201 

198.9 

20.9 

60 
261 

258.6 

27.2 

21 

20.9 

2.2 

81 

80.6 

8.5 

141 

199.9 

21.0 

259.6 

27.3 

22 

21.9 

2.3 

82 

81.6 

8.6 

42 

141.2 

14.8 

02 

200.9 

21.1 

62 

260.6 

27.4 

23 

22.9 

2.4 

83 

82.5 

8.7 

43 

142.2 

14.9 

03 

201.9 

21.2 

63 

261.6 

27.5 

24 

23.9 

2.5 

84 

83.5 

8.8 

44 

143.2 

15.1 

04 

202.9 

21.3 

64 

262.6 

27.6 

25 

24.9 

2.6 

85 

84.5 

8.9 

45 

144.2 

15.2 

05 

203.9 

21.4 

65 

263.5 

27.7 

26 

25.9 

2.7 

86 

85.5 

9.0 

46 

145.2 

15.3 

06 

204.9 

21.5 

66 

264.5 

27.8 

27 

26.9 

2.8 

87 

86.5 

9.1 

47 

146.2 

15.4 

07 

205.9 

21.6 

67 

265. 5 

27.9 

28 

27.8 

2.9 

88 

87.5 

9.2 

48 

147.2 

15.5 

08 

200.  9 

21.7 

68 

266.5 

28.0 

29 

28.8 

3.0 

89 

88.5 

9.3 

49 

148.2 

15.6 

09 

207.9 

21.8 

69 

267.5 

28.1 

30 

29.8 

3.1 

90 

89.5 

9.4 

50 

149.2 

15.7 

10 

208.8 

22.0 

70 

268.5 

28.2 

31 

30.8 

3.2 

91 

90.5 

9.5 

151 

150.  2 

15.8 

211 

209.8 

22.1 

271 

269. 5 

28.3 

32 

31.8 

3.3 

92 

91.5 

9.6 

52 

151.2 

15.9 

12 

210.8 

22.2 

72 

270. 5 

28.4 

33 

32.8 

3.4 

93 

92.5 

9.7 

53 

152.2 

16.0 

13 

211.8 

22.3 

73 

271.5 

28.6 

34 

33.8 

3.6 

94 

93.5 

9.8 

54 

153.2 

16.1 

14 

212.8 

22.4 

74 

272.5 

28.6 

35 

34.8 

3.7 

95 

94.5 

9.9 

55 

154.2 

16.2 

15 

213.8 

22.5 

75 

273.5 

28.7 

36 

35.8 

3.8 

96 

95.5 

10.0 

56 

155.1 

16.3 

16 

214.8 

22.6 

76 

274.5 

28.8 

37 

36.8 

3.9 

97 

96.5 

10.1 

57 

156.1 

16.4 

17 

215.  8 

22.7 

77 

275.5 

29.0 

38 

37.8 

4.0 

98 

97.5 

10.2 

58 

157.1 

16.5 

18 

216.8 

22.8 

78 

276.5 

29.1 

39 

38.8 

4.1 

99 

98.5 

10.3 

59 

158.1 

16.6 

19 

217.8 

22.9 

79 

277.5 

29.2 

40 

39.8 

4.2 

100 

99.5 

10.5 

60 

159.1 
160.1 

16.7 

20 

218.8 

23.0 
23.1 

80 

278.6 

29.3 
29.4 

41 

40.8 

4.3 

101 

100.4 

10.6 

161 

16.8 

221 

219.8 

281 

279.5 

42 

41.8 

4.4 

02 

101.4 

10.7 

62 

161.1 

16.9 

22 

220.8 

23.2 

82 

280.5 

29.5 

43 

42.8 

4.5 

03 

102.4 

10.8 

63 

162.1 

17.0 

23 

221.8 

23.3 

83 

281.4 

29.6 

44 

43.8 

4.6 

04 

103.4 

10.9 

64 

163.1 

17.1 

24 

222.8 

23.4 

84 

282.4 

29.7 

45 

44.8 

4.7 

05 

104.4 

11.0 

65 

164.1 

17.2 

25 

223.8 

23.5 

85 

283.4 

29.8 

46 

45.7 

4.8 

06 

105.4 

11.1 

66 

165.1 

17.4 

26 

224.8 

23.6 

86 

284.4 

29.9 

47 

46.7 

4.9 

07 

106.4 

11.2 

67 

166.1 

17.5 

27 

225.8 

23.7 

87 

285.4 

30.0 

48 

47.7 

5.0 

08 

107.4 

11.3 

68 

167.1 

17.6 

28 

226.8 

23.8 

88 

286.4 

30.1 

49 

48.7 

5.1 

09 

108.4 

11.4 

69 

168.1 

17.7 

29 

227.7 

23.9 

89 

287.4 

30.2 

50 

49.7 

5.2 

10 

109.4 

11.5 

70 

169.1 

17.8 

30 

228.7 
229.7 

24.0 

90 

288.4 

30.3 

51 

50.7 

5.3 

111 

110.4 

11.6 

171 

170.1 

17.9 

231 

24.1 

291 

289.4 

30.4 

52 

51.7 

5.4 

12 

111.4 

11.7 

72 

171.1 

18.0 

32 

230.7 

24.3 

92 

290.4 

30.5 

53 

52.7 

5.5 

13 

112.4 

11.8 

73 

172.1 

18.1 

33 

231.  7 

24.4 

93 

291.4 

30.6 

54 

53.7 

5.6 

14 

113.4 

11.9 

74 

173.0 

18.2 

34 

232.7 

24.5 

94 

292.4 

30.7 

55 

54.7 

5.7 

15 

114.4 

12.0 

75 

174.0 

18.3 

35 

233.7 

24.6 

95 

293.4 

30.8 

56 

55.7 

5.9 

16 

115.4 

12.1 

76 

175.0 

18.4 

36 

234.7 

24.7 

96 

294.4 

30.9 

57 

56.7 

6.0 

17 

116.4 

12.2 

77 

176.0 

18.5 

37 

235.7 

24.8 

97 

295.4 

31.0 

58 

57.7 

6.1 

18 

117.4 

12.3 

78 

177.0 

18.6 

38 

236.7 

24.9 

98 

296.4 

31.1 

59 

58.7 

6.2 

19 

118.3 

12.4 

79 

178.0 

18.7 

39 

237.7 

25.0 

99 

297.4 

31.3 

60 

59.7 

6.3 

20 

119.3 

12.5 

80 

179.0 

18.8 

40 

238.7 

25.1 

300 

298.4 

31.4 

Diet. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

84°  (« 

>6°,  264^ 

,  276°) 

TABLE  2. 

[Page  543 

Difference  of  Latitude  and  Departure  for  6°  (174°,  186°,  354°) 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

299.3 

31.5 

361 

369.0 

37.7 

421 

418.7 

44.0 

481 

478.4 

50.3 

541 

538.0 

56.5 

02 

300.3 

31.6 

62 

360.0 

37.8 

22 

419.7 

44.1 

82 

479.4 

50.4 

42 

539.0 

56.6 

03 

301.3 

31.7 

63 

361.0 

37.9 

23 

420.7 

44.2 

83 

480.4 

50.5 

43 

540.0 

56.7 

04 

302.3 

31.8 

64 

362.0 

38.0 

24 

421.7 

44.3 

84 

481.3 

50.6 

44 

541.0 

56.8 

05 

303.3 

31.9 

65 

363.0 

38.1 

25 

422.7 

44.4 

85 

482.3 

50.7 

45 

542.0 

56.9 

06 

304.3 

32.0 

66 

364.0 

38.3 

26 

423.7 

44.5 

86 

483.3 

50.8 

46 

543.0 

57.0 

07 

305.3 

32.1 

67 

365.0 

38.4 

27 

424.7 

44.6 

87 

484.3 

50.9 

47 

544.0 

57.1 

08 

306.3 

32.2 

68 

366.0 

38.5 

28 

425.7 

44.7 

88 

485.3 

51.0 

48 

545.0 

57.2 

09 

307.3 

32.3 

69 

367.0 

38.6 

29 

426.6 

44.8 

89 

486.3 

51.1 

49 

546.0 

57.3 

10 

308.3 

32.4 

70 

368.0 

38.7 

30 

427.6 

44.9 

90 

487.3 

51.2 

50 

547.0 

57.4 

311 

309.3 

32.5 

371 

369.0 

38.8 

431 

428.6 

45.0 

491 

488.3 

51.3 

551 

548.0 

57.5 

12 

310.3 

32.6 

72 

370.0 

38.9 

32 

429.6 

45.2 

92 

489.3 

51.4 

52 

549.0 

57.6 

13 

311.3 

32.7 

73 

371.0 

39.0 

33 

430.6 

45.3 

93 

490.3 

51.5 

53 

550.0 

57.7 

14 

312.3 

32.8 

74 

371.9 

39.1 

34 

431.6 

45.4 

94 

491.3 

51.6 

54 

551.0 

57.9 

15 

313.3 

32.9 

75 

372.9 

39.2 

35 

432.6 

45.5 

95 

492.3 

51.7 

55 

552.0 

58.0 

16 

314.3 

33.0 

76 

373.9 

39.3 

36 

433.6 

45.6 

96 

493.3 

51.8 

56 

553.0 

58.1 

17 

315.3 

33.1 

77 

374.9 

39.4 

37 

434.6 

45.7 

97 

494.3 

51.9 

57 

554.0 

58.2 

18 

316.3 

33.2 

78 

375.9 

39.5 

38 

435.6 

45.8 

98 

495.3 

52.0 

58 

555.0 

58.3 

19 

317.3 

33.3 

79 

376.9 

39.6 

39 

436.6 

45.9 

99 

496.3 

52.1 

59 

556.0 

58.4 

20 

318.2 

33.4 

80 

377.9 

39.7 

40 

437. 6 

46.0 

500 

497.3 

52.3 

60 

556.9 

58.5 

321 

319.2 

33.6 

381 

378.9 

39.8 

441 

438.6 

46.1 

501 

498.3 

52.4 

561 

557.9 

58.6 

22 

320.2 

33.7 

82 

379.9 

39.9 

42 

439.6 

46.2 

02 

499.3 

52.5 

62 

558.9 

58.7 

23 

321.2 

33.8 

83 

380.9 

40.0 

43 

440.6 

46.3 

03 

500.2 

52.6 

63 

559. 9 

58.8 

24 

322.2 

33.9 

84 

381.9 

40.1 

44 

441.6 

46.4 

04 

501.2 

52.7 

64 

560.9 

59.0 

25 

323.2 

34.0 

85 

382.9 

40.2 

45 

442.6 

46.5 

05 

502.2 

52.8 

65 

561.9 

59.1 

26 

324.2 

34.1 

86 

383.9 

40.3 

46 

443.6 

46.6 

06 

503.2 

52.9 

6& 

562.9 

59.2 

27 

325.2 

34.2 

87 

384.9 

40.5 

47 

444.5 

46.7 

07 

504.2 

53.0 

67 

563.9 

59.3 

28 

326.2 

34.3 

88 

385.9 

40.6 

48 

445.5 

46.8 

08 

505. 2 

53.1 

68 

564.9 

59.4 

29 

327.2 

34.4 

89 

386.9 

40.7 

49 

446.5 

46.9 

09 

506.2 

53.2 

69 

565.9 

59.5 

30 

328.2 

34.5 

90 

387.9 

40.8 

50 

447.5 

47.0 

10 

507.2 

53.3 

70 

566.9 

59.6 

331 

329.2 

34.6 

391 

388.9 

40.9 

451 

448.5 

47.1 

511 

508.2 

53.4 

571 

567.9 

59.7 

32 

330.2 

34.7 

92 

389.9 

41.0 

52 

449.5 

47.2 

12 

509.2 

53.5 

72 

568.9 

59.8 

33 

331.2 

34.8 

93 

390.8 

41.1 

53 

450.5 

47.3 

13 

510.2 

53.6 

73 

569.9 

59.9 

34 

332.2 

34.9 

94 

391.8 

41.2 

54 

451.5 

47.5 

14 

511.2 

53.7 

74 

570.9 

60.0 

35 

333.2 

35.0 

95 

392.8 

41.3 

55 

452.5 

47.6 

15 

512. 2 

53.8 

75 

571.9 

60.1 

36 

334.2 

35.1 

96 

393.8 

41.4 

56 

453.5 

47.7 

16 

513.2 

53.9 

76 

572.9 

60.2 

37 

335.2 

35.2 

97 

394.8 

41.5 

57 

454.5 

47.8 

17 

514.2 

54.0 

77 

573.9 

60.3 

38 

336.1 

35.3 

98 

395.8 

41.6 

58 

455.5 

47.9 

18 

515.2 

54.1 

78 

574.9 

60.4 

39 

337.1 

35.4 

99 

396.8 

41.7 

59 

456.5 

48.0 

19 

516.2 

54.2 

79 

575.8 

60.5 

40 

338.1 

35.5 

400 

397.8 

41.8 

60 

457.5 

48.1 

20 

517.2 

54.3 

80 

576.8 

60.6 

341 

339.1 

35.6 

401 

398.8 

41.9 

461 

458.5 

48.2 

521 

518.1 

54.5 

581 

577.8 

60.7 

42 

340.1 

35.7 

02 

399.8 

42.0 

62 

459.5 

48.3 

22 

519.1 

54.6 

82 

578.8 

60.8 

43 

341.1 

35.8 

03 

400.8 

42.1 

63 

460.5 

48.4 

23 

520.1 

54.7 

83 

579.8 

60.9 

44 

342.1 

36.0 

04 

401.8 

42.2 

64 

461.5 

48.5 

24 

521.1 

54.8 

84 

580.8 

61.1 

45 

343.1 

36.1 

05 

402.8 

42.3 

65 

462.5 

48.6 

25 

522.1 

54.9 

85 

581.8 

61.2 

46 

344.1 

36.2 

06 

403.8 

42.4 

66 

463.4 

48.7 

26 

523.1 

55.0 

86 

582.8 

61.3 

47 

345.1 

36.3 

07 

404.8 

42.5 

67 

464.4 

48.8 

27 

524.1 

55.1 

87 

583.8 

61.4 

48 

346.1 

36.4 

08 

405.8 

42.6 

68 

465.4 

48.9 

28 

525.1 

55.2 

88 

584.8 

61.5 

49 

347.1 

36.5 

09 

406.8 

42.7 

69 

466.4 

49.0 

29 

526.1 

55.3 

89 

585.8 

61.6 

50 

348.1 
349.1 

36.6 
36.7 

10 

407.8 

42.9 
43.0 

70 

467.4 

49.1 

30 

527.1 

55.4 

90 

586.8 

61.7 

351 

411 

408.7 

471 

468.4 

49.2 

531 

528.1 

55.5 

591 

587.8 

61.8 

52 

350.1 

36.8 

12 

409.7 

43.1 

72 

469.4 

49.3 

32 

529.1 

55.6 

92 

588.8 

61.9 

53 

351.1 

36.9 

13 

410.7 

43.2 

73 

470.4 

49.4 

33 

530.1 

55.7 

93 

589.8 

62.0 

54 

352.1 

37.0 

14 

411.7 

43.3 

74 

471.4 

49.5 

34 

531.1 

55.8 

94 

590.8 

62.1 

55 

353.1 

37.1 

15 

412.7 

43.4 

75 

472.4 

49.6 

35 

532.1 

55.9 

95 

591.8 

62.2 

56 

354.0 

37.2 

16 

413.7 

43.5 

76 

473.4 

49.8 

36 

533.1 

56.0 

96 

592.8 

62.3 

57 

355.0 

37.3 

17 

414.7 

43.6 

77 

474.4 

49.9 

37 

534.1 

56.1 

97 

593.8 

62.4 

58 

356.0 

37.4 

18 

415.7 

43.7 

78 

475.4 

50.0 

38 

535.1 

56.2 

98 

594.7 

62.5 

59 

357.0 

37.5 

19 

416.7 

43.8 

79 

476.4 

50.1 

39 

536.1 

56.3 

99 

595.7 

62.6 

60 

358.0 

37.6 

20 

417.7 

43.9 

80 

477.4 

50.2 

40 

537.1 

56.4 

600 

596.7 

62.7 

DlBt. 

Dep.         Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

84°  (96°,  264°,  276° 

). 

1 

Page  644 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  7°  (173°,  187°,  353°) 

• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.5 

7.4 

121 

120.1 

14.7 

181 

179.7 

22.1 

241 

239.  2 

29.4 

2 

2.0 

0.2 

62 

61.5 

7.6 

22 

121.1 

14.9 

82 

180.6 

22.2 

42 

240.2 

29.5 

3 

3.0 

0.4 

63 

62.5 

7.7 

23 

122.1 

15.0 

83 

181.6 

22.3 

43 

241.2 

29.6 

4 

4.0 

0.5 

64 

63.5 

7.8 

24 

123.1 

15.1 

84 

182.6 

22.4 

44 

242.2 

29.7 

5 

6.0 

0.6 

65 

64.5 

7.9 

25 

124.1 

15.2 

85 

183.6 

22.5 

45 

243.2 

29.9 

6 

6.0 

0.7 

66 

65.5 

8.0 

26 

125.1 

15.4 

86 

184.6 

22.7 

46 

244.2 

30.0 

7 

6.9 

0.9 

67 

66.5 

8.2 

27 

126.1 

15.5 

87 

185.6 

22.8 

47 

245.2 

30.1 

8 

7.9 

1.0 

68 

67.5 

8.3 

28 

127.0 

15.6 

88 

186.6 

22.9 

48 

246.2 

30.2 

9 

8.9 

1.1 

69 

68.5 

8.4 

29 

128.0 

15.7 

89 

187.6 

23.0 

49 

247.1 

30.3 

10 

9.9 

1.2 

70 

69.5 

8.5 

30 

129.0 

15.8 

90 

188.6 

23.2 

50 

248.1 

30.5 

11 

10.9 

1.3 

71 

70.5 

8.7 

131 

130.0 

16.0 

191 

189.6 

23.3 

251 

249.1 

30.6 

12 

11.9 

1.5 

72 

71.5 

8.8 

32 

131.0 

16.1 

92 

190.6 

23.4 

52 

250.1 

30.7 

13 

12.9 

1.6 

73 

72.5 

8.9 

33 

132.0 

16.2 

93 

191.6 

23.5 

53 

251.1 

30.8 

14 

13.9 

1.7 

74 

73.4 

9.0 

34 

133.0 

16.3 

94 

192.6 

23.6 

54 

252.1 

31.0 

15 

14.9 

1.8 

75 

74.4 

9.1 

35 

134.0 

16.5 

95 

193.5 

23.8 

55 

253.1 

31.1 

16 

15.9 

1.9 

76 

75.4 

9.3 

36 

135.0 

16.6 

96 

194.5 

23.9 

56 

254.1 

31.2 

17 

16.9 

2.1 

77 

76.4 

9.4 

37 

136.0 

16.7 

97 

195.5 

24.0 

57 

255.1 

31.3 

18 

17.9 

2.2 

78 

77.4 

9.5 

38 

137.0 

16.8 

98 

196.5 

24.1 

58 

256.] 

31.4 

19 

18.9 

2.3 

79 

78.4 

9.6 

39 

138.0 

16.9 

99 

197.5 

24.3 

59 

257.1 

31:6 

20 

19.9 

2.4 
2.6 

80 

79.4 

9.7 

40 

139.0 

17.1 

200 

198.5 

24.4 

60 

258.1 
259.1 

31.7 

21 

20.8 

81 

80.4 

9.9 

141 

139.9 

17.2 

201 

199.5 

24.5 

261 

31.8 

22 

21.8 

2.7 

82 

81.4 

10.0 

42 

140.9 

17.3 

02 

200.5 

24.6 

62 

260.0 

31.9 

23 

22.8 

2.8 

83 

82.4 

10.1 

43 

141.9 

17.4 

03 

201.5 

24.7 

63 

261.0 

32.1 

24 

23.8 

2.9 

84 

83.4 

10.2 

44 

142.9 

17.5 

04 

202.5 

24.9 

64 

262.0 

32.2 

25 

24.8 

3.0 

85 

84.4 

10.4 

45 

143.9 

17.7 

05 

203.5 

25.0 

65 

263.0 

32.3 

26 

25.8 

3.2 

86 

85.4 

10.5 

46 

144.9 

17.8 

06 

204.5 

25.1 

66 

264.0 

32.4 

27 

26.8 

3.3 

87 

86.4 

10.6 

47 

145.9 

17.9 

07 

205.5 

25.2 

67 

265.0 

32.5 

28 

27.8 

3.4 

88 

87.3 

10.7 

48 

146.9 

18.0 

08 

206.4 

25.3 

68 

266.0 

32.7 

29 

28.8 

3.5 

89 

88.3 

10.8 

49 

147.9 

18.2 

09 

207.4 

25.5 

69 

267.0 

32.8 

30 

29.8 

3.7 

90 

89.3 

11.0 

50 

148.9 

18.3 

10 

208.4 

25.6 

70 

268.0 

32.9 

31 

30.8 

3.8 

91 

90.3 

11:1 

151 

149.  9 

18.4 

211 

209.4 

25.7 

271 

269.0 

33.0 

32 

31.8 

3.9 

92 

91.3 

11.2 

52 

150.9 

18.5 

12 

210.4 

25.8 

72 

270.0 

33.1 

33 

32.8 

4.0 

93 

92.3 

11.3 

53 

151.9 

18.6 

13 

211.4 

26.0 

73 

271.0 

33.3 

34 

33.7 

4.1 

94 

93.3 

11.5 

54 

152.9 

18.8 

14 

212.4 

26.1 

74 

272.0 

33.4 

35 

34.7 

4.3 

95 

94.3 

11.6 

55 

153.8 

18.9 

15 

213.4 

26.2 

75 

273.0 

33.5 

36 

35.7 

4.4 

96 

95.3 

11.7 

56 

154.8 

19.0 

16 

214.4 

26.3 

76 

273.9 

33.6 

37 

36.7 

4.5 

97 

96.3 

11.8 

57 

155. 8 

19.1 

17 

215.4 

26.4 

77 

274.9 

33.8 

38 

37.7 

4.6 

98 

97.3 

11.9 

58 

156.8 

19.3 

18 

216.4 

26.6 

78 

275.9 

33.9 

39 

38.7 

4.8 

99 

98.3 

12.1 

59 

157.  8 

19.4 

19 

217.4 

26.7 

79 

276.9 

34.0 

40 
41 

39.7 
40.7 

4.9 

100 
101 

99.3 

12.2 

60 

158.8 

19.5 

20 

218.4 

26.8 

80 

277.9 

34.1 

5.0 

100.2 

12.3 

161 

159.8 

19.6 

221 

219.4 

26.9 

281 

278.9 

34.2 

42 

41.7 

5.1 

02 

101.2 

12.4 

62 

160.8 

19.7 

22 

220.3 

27.1 

82 

279.9 

34.4 

43 

42.7 

5.2 

03 

102.2 

12.6 

63 

161.8 

19.9 

23 

221.3 

27.2 

83 

280.9 

34.5 

44 

43.7 

5.4 

04 

103.2 

12.7 

64 

162.8 

20.0 

24 

222.  3 

27.3 

84 

281.9 

34.6 

45 

44.7 

5.5 

05 

104.2 

12.8 

65 

163.8 

20.1 

25 

223.3 

27.4 

85 

282.9 

34.7 

46 

45.7 

5.6 

06 

105.2 

12.9 

66 

164.8 

20.2 

26 

224  3 

27.5 

86 

283.9 

34.9 

47 

46.6 

5.7 

07 

106.2 

13.0 

67 

165.  8 

20.4 

27 

225.3 

27.7 

87 

284.9 

35.0 

48 

47.6 

5.8 

08 

107.2 

13.2 

68 

166.7 

20.5 

28 

226.3 

27.8 

88 

285.9 

35.1 

49 

48.6 

6.0 

09 

108.2 

13.3 

69 

167.7 

20.6 

29 

227.3 

27.9 

89 

286.8 

35.2 

50 

49.6 

6.1 
6.2 

10 

109.2 

13.4 

70 

168.7 

20.7 

30 

228.3 

28.0 

90 

287.8 
288.8 

35.3 

51 

50.6 

111 

110.2 

13.5 

171 

169.7 

20.8 

231 

229.3 

28.2 

291 

35.5 

52 

51.6 

6.3 

12 

111.2 

13.6 

72 

170.7 

21.0 

32 

230.3 

28.3 

92 

289.8 

35.6 

53 

52.6 

6.5 

13 

112.2 

13.8 

73 

171.7 

21.1 

33 

231.3 

28.4 

93 

290.8 

35.7 

54 

53.6 

6.6 

14 

113.2 

13.9 

74 

172.7 

21.2 

34 

232.3 

28.5 

94 

291.8 

35.8 

55 

54.6 

6.7 

15 

114.1 

14.0 

75 

173.7 

21.3 

35 

233.2 

28.6 

95 

292.8 

36.0 

56 

55.6 

6.8 

16 

115.1 

14.1 

76 

174.7 

21.4 

36 

234.2 

28.8 

96 

293.8 

36.1 

57 

56.6 

6.9 

17 

116.1 

14.3 

77 

175.7 

21.6 

37 

235.2 

28.9 

97 

294.8 

36.2 

58 

57.6 

7.1 

18 

117.1 

14.4 

78 

176.7 

21.7 

38 

236.2 

29.0 

98 

295.8 

36.3 

59 

58.6 

7.2 

19 

118.1 

14.5 

79 

177.7 

21.8 

39 

237.2 

29.1 

99 

296.8 

36.4 

60 

59.6 

7.3 

20 

119.1 

14.6 

80 

178.7 

21.9 

40 

238.2 

29.2 

300 

297.8 

36.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

83°  (97°,  263°,  277°, 

. 

TABLE  2. 

[Page  546 

Difference  of  Latitude  and  Departure  for 

7°  (173°,  187°,  353°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

298.7 

36.7 

361 

358.3 

44.0 

421 

417.9 

51.3 

481 

477.4 

58.6 

541 

537.0 

65.9 

02 

299.7 

36.8 

62 

359.3 

44.1 

22 

418.8 

51.4 

82 

478.4 

58.7 

42 

537.9 

66.0 

03 

300.7 

36.9 

63 

360.3 

44.2 

23 

419.8 

51.5 

83 

479.4 

58.8 

43 

538.9 

66.2 

04 

301.7 

37.0 

64 

361.3 

44.4 

24 

420.8 

51.7 

84 

480.4 

59.0 

44 

539. 9 

66.3 

05 

302.  7 

37.2 

65 

362.3 

44.5 

25 

421.8 

51.8 

85 

481.4 

59.1 

45 

540.9 

66.4 

06 

303.7 

37.3 

66 

363.3 

44.6 

26 

422.8 

51.9 

86 

482.4 

59.2 

46 

541.9 

66.6 

07 

304.7 

37.4 

67 

364.3 

44.7 

27 

423.8 

52.0 

87 

483.4 

59.4 

47 

542.9 

66.7 

08 

305.7 

37.5 

68 

365.2 

44.8 

28 

424.8 

52.2 

88 

484.3 

59.5 

48 

543.9 

66.8 

09 

306.7 

37.7 

69 

366.2 

45.0 

29 

425.8 

52.3 

89 

485.3 

59.6 

49 

544.9 

66.9 

10 

307.7 

37.8 

70 

367.2 

45.1 

30 

426.8 

52.4 

90 

486.3 

59.7 

50 

545.9 

67.0 

311 

308.7 

37.9 

371 

368.2 

45.2 

431 

427.8 

52.5 

491 

487.3 

59.8 

551 

546.9 

67.1 

12 

309.7 

38.0 

72 

369.2 

45.3 

32 

428.8 

52.6 

92 

488.3 

59.9 

52 

547.9 

67.2 

13 

310.7 

38.1 

73 

370.2 

45.5 

33 

429.8 

52.8 

93 

489.3 

60.1 

53 

548.9 

67.4 

14 

311.7 

38.3 

74 

371.2 

45.6 

34 

430.8 

52.9 

94 

490.3 

60.2 

54 

549.9 

67.5 

15 

312.6 

38.4 

75 

372.2 

45.7 

35 

431.7 

53.0 

95 

491.3 

60.3 

55 

550.8 

67.6 

16 

313.6 

38.5 

76 

373.2 

45.8 

36 

432.7 

53.1 

96 

492.3 

60.5 

56 

551.8 

67.8 

17 

314.6 

38.6 

77 

374.2 

45.9 

37 

433.7 

53.3 

97 

493.3 

60.6 

57 

552.8 

67.9 

18 

315.6 

38.7 

78 

375.2 

46.1 

38 

434.7 

53.4 

98 

494.3 

60.7 

58 

553.8 

68.0 

19 

316.6 

38.9 

79 

376.2 

46.2 

39 

435.7 

53.5 

99 

495.3 

60.8 

59 

554.8 

68.1 

20 

317.6 

39.0 

80 

377.2 

46.3 

40 

436.7 

53.6 

500 

496.3 

61.0 

60 

555.8 

68.3 

321 

318.6 

39.1 

381 

378.1 

46.4 

441 

437.7 

53.7 

501 

497.2 

61.1 

561 

556.8 

68.4 

22 

319.6 

39.2 

82 

379.1 

46.5 

42 

438.7 

53.9 

02 

498.2 

61.2 

62 

557.8 

68.5 

23 

320.6 

39.4 

83 

380.1 

46.7 

43 

439.7 

54.0 

03 

499.2 

61.3 

63 

558.8 

68.6 

24 

321.6 

39.5 

84 

381.1 

46.8 

44 

440.7 

54.1 

04 

500.2 

61.4 

64 

559.8 

68.7 

25 

322.6 

39.6 

85 

382.1 

46.9 

45 

441.7 

54.2 

05 

501.2 

61.5 

65 

560.8 

68.9 

26 

323.6 

39.7 

86 

383.1 

47.0 

46 

442.7 

54.3 

06 

502.2 

61.6 

66 

561.8 

69.0 

27 

324.6 

39.8 

87 

384.1 

47.2 

47 

443.7 

54.5 

07 

503.2 

61.8 

67 

562.8 

69.1 

28 

325.5 

40.0 

88 

385.1 

47.3 

48 

444.7 

54.6 

08 

504.2 

61.!) 

68 

563.8 

69.2 

29 

326.5 

40.1 

89 

386.1 

47.4 

49 

445.6 

54.7 

09 

505.2 

62.0 

69 

564.8 

69.3 

30 

327.5 

40.2 

90 

387.1 

47.5 

50 

446.6 

54.8 

10 

506.2 

62.1 

70 

571 

565.8 

69.4 

331 

328.5 

40.3 

391 

388.1 

47.6 

451 

447.6 

55.0 

511 

507.2 

62.3 

566.7 

69.6 

32 

329.5 

40.5 

92 

389.1 

47.8 

52 

448.6 

55.1 

12 

508.2 

62.4 

72 

567.7 

69.7 

33 

330.5 

40.6 

93 

390.1 

47.9 

53 

449.6 

55.2 

13 

509.2 

62.5 

73 

568.7 

69.8 

34 

331.5 

40.7 

94 

391.1 

48.0 

54 

450.6 

55.3 

14 

510.2 

62.6 

74 

569.7 

69.9 

35 

332.5 

40.8 

95 

392.0 

48.1 

55 

451.6 

55.4 

15 

511.1 

62.7 

75 

570.7 

70.1 

36 

333.5 

40.9 

96 

393.0 

48.3 

56 

452.6 

55.6 

16 

512.1 

62.9 

76 

571.7 

70.2 

37 

334.5 

41.1 

97 

394.0 

48.4 

57 

453.6 

55.7 

17 

513.1 

63.0 

77 

572.7 

70.3 

38 

335.5 

41.2 

98 

395.0 

48.5 

58 

454.6 

55.8 

18 

514.1 

63.1 

78 

573.7 

70.4 

39 

336.5 

41.3 

99 

396.0 

48.6 

59 

455.6 

55.-9 

19 

515.1 

63.2 

79 

574.7 

70.5 

40 

337.5 

41.4 

400 

397.0 

48.7 

60 

456.6 

56.1 

20 

516.1 

63.4 

80 

575.7 

70.7 

341 

338.4 

41.6 

401 

398.0 

48.9 

461 

457.6 

56.2 

521 

517.1 

63.5 

581 

576.7 

70.8 

42 

339.4 

41.7 

02 

399.0 

49.0 

62 

458.5 

56.3 

22 

518.1 

63.6 

82 

577.6 

70.9 

43 

340.4 

41.8 

03 

400.0 

49.1 

63 

459.5 

56.4 

23 

519.1 

63.7 

83 

578.6 

71.0 

44 

341.4 

41.9 

04 

401.0 

49.2 

64 

460.5 

56.5 

24 

520.1 

63.8 

84 

579.6 

71.2 

45 

342.4 

42.0 

05 

402.0 

49.4 

65 

461.5 

56.7 

25 

521.1 

64.0 

85 

580.6 

71.3 

46 

343.4 

42.2 

06 

403.0 

49.5 

66 

462.5 

56.8 

26 

522.1 

64.1 

86 

581.6 

71.4 

47 

344.4 

42.3 

07 

404.0 

49.6 

67 

463.5 

56.9 

27 

523.1 

64.2 

87 

582.6 

71.5 

48 

345.4 

42.4 

08 

405.0 

49.7 

68 

464.5 

57.0 

28 

524.1 

64.3 

88 

583.6 

71.6 

49 

346.4 

42.5 

09 

405.9 

49.8 

69 

465.5 

57.2 

29 

525.0 

64.5 

89 

584.6 

71.8 

50 

347.4 

42.6 

10 

406.9 

50.0 

70 

466.5 

57.3 

30 

526.0 

64.6 

90 

585.6 

71.9 

351 

348.4 

42.8 

411 

407.9 

50.1 

471 

467.5 

57.4 

531 

527.0 

64.7 

591 

586.6 

72.0 

52 

349.4 

42.9 

12 

408.9 

50.2 

72 

468.5 

57.5 

32 

528.0 

64.8 

92 

587.6 

72.1 

53 

350.4 

43.0 

13 

409.9 

50.3 

73 

469.5 

57.6 

33 

529.0 

64.9 

93 

588.6 

72.2 

54 

351.4 

43.1 

14 

410.9 

50.4 

74 

470.5 

57.8 

34 

530.0 

65.1 

94 

589.6 

72.4 

55 

352.3 

43.3 

15 

411.9 

50.6 

75 

471.5 

57.9 

35 

531.0 

65.2 

95 

590.6 

72.5 

56 

353.3 

43.4 

16 

412.9 

50.7 

76 

472.4 

58.0 

36 

532.0 

65.3 

96 

591.5 

72.6 

57 

354.3 

43.5 

17 

413.9 

50.8 

77 

473.4 

58.1 

37 

533.0 

65.4 

97 

592.5 

72.7 

58 

355.3 

43.6 

18 

414.9 

50.9 

78 

474.4 

58.2 

38 

534.0 

65.6 

98 

593.5 

72.9 

59 

356.3 

43.7 

19 

415.9 

51.1 

79 

475.4 

58.4 

39 

535.0 

65.7 

99 

594.5 

73.0 

60 

357.3 

43.9 

20 

416.9 

51.2 

80 

476.4 

58.5 

40 

536.0 

65.8 

600 

595.5 

73.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

83°  (97°,  263°,  277° 

1 

21594°— 14- 


-28 


Page  646] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  8°  (172°,  188 

°,  352° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.4 

8.5 

121 

119.8 

16.8 

181 

179.2 

25.2 

241 

238.7 

33.5 

2 

2.0 

0.3 

62 

61.4 

8.6 

22 

120.8 

17.0 

82 

180.2 

25.3 

42 

239.6 

33.7 

3 

3.0 

0.4 

63 

62.4 

8.8 

23 

121.8 

17.1 

83 

181.2 

25.5 

43 

240.6 

33.8 

4 

4.0 

0.6 

64 

63.4 

8.9 

24 

122.8 

17.3 

84 

182.2 

25.6 

44 

241.6 

34.0 

5 

5.0 

0.7 

65 

64.4 

9.0 

25 

123.8 

17.4 

85 

183.2 

25.7 

45 

242.6 

34.1 

6 

5.9 

0.8 

66 

65.4 

9.2 

26 

124.8 

17.5 

86 

184.2 

25.9 

46 

243.6 

34.2 

7 

6.9 

1.0 

67 

66.3 

9.3 

27 

125.8 

17.7 

87 

185.2 

26.0 

47 

244.6 

34.4 

8 

7.9 

1.1 

68 

67.3 

9.5 

28 

126.8 

17.8 

88 

186.2 

26.2 

48 

245.6 

34.5 

9 

8.9 

1.3 

69 

68.3 

9.6 

29 

127.7 

18.0 

89 

187.2 

26.3 

49 

246.6 

34.7 

10 

9.9 

1.4 

70 

69.3 

9.7 
9.9 

30 

128.7 

18.1 

90 

188.2 

26.4 

50 

247.6 

34.8 

11 

10.9 

1.5 

71 

70.3 

131 

129.7 

18.2 

191 

189.1 

26.6 

251 

248.6 

34.9 

12 

11.9 

1.7 

72 

71.3 

10.0 

32 

130.7 

18.4 

92 

190.1 

26.7 

52 

249.5 

35.1 

13 

12.9 

1.8 

73 

72.3 

10.2 

33 

131.7 

18.5 

93 

191.1 

26.9 

53 

250.5 

35.2 

14 

13.9 

1.9 

74 

73.3 

10.3 

34 

132.7 

18.6 

94 

192.1 

27.0 

54 

251. 5 

35.3 

15 

14.9 

2.1 

75 

74.3 

10.4 

35 

133.7 

18.8 

95 

193.1 

27.1 

55 

252.5 

35.5 

16 

15.8 

2.2 

76 

75.3 

10.6 

36 

134.7 

18.9 

96 

194.1 

27.3 

56 

253.5 

35.6 

17 

16.8 

2.4 

77 

76.3 

10.7 

37 

135.7 

19.1 

97 

195.1 

27.4 

57 

254.5 

35.8 

18 

17.8 

2.5 

78 

77.2 

10.9 

38 

136.7 

19.2 

98 

196.1 

27.6 

58 

255.5 

35.9 

19 

18.8 

2.6 

79 

78.2 

11.0 

39 

137.7 

19.3 

99 

197.1 

27.7 

59 

256.5 

36.0 

20 

19.8 

2.8 

80 

79.2 

11.1 

40 

138.6 

19.5 

200 

198.1 

27.8 

60 

257.5 

36.2 

21 

20.8 

2.9 

81 

80.2 

11.3 

141 

139.6 

19.6 

201 

199.0 

28.0 

261 

258.5 

36.3 

22 

21.8 

3.1 

82 

81.2 

11.4 

42 

140.6 

19.8 

02 

200.0 

28.1 

62 

259.5 

36.5 

23 

22.8 

3.2 

83 

82.2 

11.6 

43 

141.6 

19.9 

03 

201.0 

28.3 

63 

260.4 

36.6 

24 

23.8 

3.3 

84 

83.2 

11.7 

44 

142.6 

20.0 

04 

202.0 

28.4 

64 

261.4 

36.7 

26 

24.8 

3.5 

85 

84.2 

11.8 

45 

143.6 

20.2 

05 

203.0 

28.5 

65 

262.4 

36.9 

26 

25.7 

3.6 

86 

85.2 

12.0 

46 

144.6 

20.3 

06 

204.0 

28.7 

66 

263.4 

37.0 

27 

26.7 

3.8 

87 

86.2 

12.1 

47 

145.6 

20.5 

07 

205.0 

28.8 

67 

264.4 

37.2 

28 

27.7 

3.9 

88 

87.1 

12.2 

48 

146.6 

20.6 

08 

206.0 

28.9 

68 

265.4 

37.3 

29 

28.7 

4.0 

89 

88.1 

12.4 

49 

147.5 

20.7 

09 

207.0 

29.1 

69 

266.4 

37.4 

30 

29.7 

4.2 

90 

89.1 

12.5 

50 

148.5 

20.9 

10 

208.0 

29.2 

70 

267.4 

37.6 

31 

30.7 

4.3 

91 

90.1 

12.7 

151 

149.5 

21.0 

211 

208.9 

29.4 

271 

268.4 

37.7 

32 

31.7 

4.5 

92 

91.1 

12.8 

52 

150.5 

21.2 

12 

209.9 

29.5 

72 

269.4 

37.9 

33 

32.7 

4.6 

93 

92.1 

12.9 

53 

151.5 

21.3 

13 

210.9 

29.6 

73 

270.3 

38.0 

34 

33.7 

4.7 

94 

93.1 

13.1 

54 

152.5 

21.4 

14 

211.9 

29.8 

74 

271.3 

38.1 

35 

34.7 

4.9 

95 

94.1 

13.2 

55 

153.5 

21.6 

15 

212.9 

29.9 

75 

272.3 

38.3 

36 

35.6 

5.0 

96 

95.1 

13.4 

56 

154.  5 

21.7 

16 

213.9 

30.1 

76 

273.3 

38.4 

37 

36.6 

5.1 

97 

96.1 

13.5 

57 

155.5 

21.9 

17 

214.9 

30.2 

77 

274.3 

38.6 

38 

37.6 

5.3 

98 

97.0 

13.6 

58 

156.5 

22.0 

18 

215.9 

30.3 

78 

275.3 

38.7 

39 

38.6 

5.4 

99 

98.0 

13.8 

59 

157.5 

22.1 

19 

216.9 

30.5 

79 

276.3 

38.8 

40 

39.6 

5.6 

100 

99.0 

13.9 

60 

158.4 

22.3 

20 

217.9 

30.6 

80 

277.3 

39.0 

41 

40.6 

5.7 

101 

100.0 

14.1 

161 

159.4 

22.4 

221 

218.8 

30.8 

281 

278.3 

39.1 

42 

41.6 

5.8 

02 

101.0 

14.2 

62 

160.4 

22.5 

22 

219.8 

30.9 

82 

279.3 

39.2 

43 

42.6 

6.0 

03 

102.0 

14.3 

63 

161.4 

22.7 

23 

220.8 

31.0 

83 

280.2 

39.4 

44 

43.6 

6.1 

04 

103.0 

14.5 

64 

162.4 

22.8 

24 

221.8 

31.2 

84 

281.2 

39.5 

45 

44.6 

6.3 

05 

104.0 

14.6 

65 

163.4 

23.0 

25 

222.8 

31.3 

85 

282.2 

39.7 

46 

45.6 

6.4 

06 

105.0 

14.8 

66 

164.4 

23.1 

26 

223.8 

31.5 

86 

283.2 

39.8 

47 

46.5 

6.5 

07 

106.0 

14.9 

67 

165.4 

23.2 

27 

224.8 

31.6 

87 

284.2 

39.9 

48 

47.5 

6.7 

08 

106.9 

15.0 

68 

166.4 

23.4 

28 

225.8 

31.7 

88 

285.2 

40.1 

49 

48.5 

6.8 

09 

107.9 

15.2 

69 

167.4 

23.5 

29 

226.8 

31.9 

89 

286.2 

40.2 

50 

49.5 

7.0 

10 

108.9 

15.3 

70 

168.3 

23.7 

30 

227.8 

32.0 

90 

287.2 

40.4 

51 

50.5 

7.1 

111 

109.9 

15.4 

171 

169.3 

23.8 

231 

228.8 

32.1 

291 

288.2 

40.5 

52 

51.5 

7.2 

12 

110.9 

15.6 

72 

170.3 

23.9 

32 

229.7 

32.3 

92 

289.2 

40.6 

53 

52.5 

7.4 

13 

111.9 

15.7 

73 

171.3 

24.1 

33 

230.7 

32.4 

93 

290.1 

40.8 

54 

53.5 

7.5 

14 

112.9 

15.9 

74 

172.3 

24.2 

34 

231.7 

32.6 

94 

291.1 

40.9 

55 

54.5 

7.7 

15 

113.9 

16.0 

75 

173.3 

24.4 

35 

232.7 

32.7 

95 

292.1 

41.1 

56 

55.5 

7.8 

16 

114.9 

16.1 

76 

174.3 

24.5 

36 

233.7 

32.8 

96 

293.1 

41.2 

57 

56.4 

7.9 

17 

115.9 

16.3 

77 

175.3 

24.6 

37 

234.7 

33.0 

97 

294.1 

41.3 

58 

57.4 

8.1 

18 

116.9 

16.4 

78 

176.3 

24.8 

38 

235.7 

33.1 

98 

295.1 

41.5 

59 

58.4 

8.2 

19 

117.8 

16.6 

79 

177.3 

24.9 

39 

236.7 

33.3 

99 

296.1 

41.6 

60 

59.4 

8.4 

20 

118.8 

16.7 

80 

178.2 

25.1 

40 

237.7 

33.4 

300 

297.1 

41.8 

Dist. 

Dep. 

Lat. 

Di8t. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

82°  (< 

)8°,  262°,  278° 

. 

TABLE  2. 

[Page 

647 

Difference  of  Latitude  and  Departure  for  8°  (172°,  188°,  352° 

). 

DiBt. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

298.0 

41.9 

361 

357.5 

50.2 

421 

416.9 

58.6 

481 

476.3 

66.9 

641 

535.7 

75.2 

U2 

299.0 

42.0 

62 

358.5 

50.4 

22 

417.9 

68.7 

82 

477.3 

67.1 

42 

536.7 

75.4 

03 

300.0 

42.2 

63 

■359.4 

50.5 

23 

418.9 

58.9 

83 

478.3 

67.2 

43 

537.7 

75.5 

04 

301.0 

42.3 

64 

360.4 

50.7 

24 

419.8 

59.0 

84 

479.3 

67.4 

44 

538.7 

75.7 

05 

302.0 

42.5 

65 

361.4 

50.8 

25 

420.8 

69.2 

85 

480.3 

67.5 

46 

539.7 

75.8 

06 

303.0 

42.6 

66 

362.4 

50.9 

26 

421.8 

59.3 

86 

481.2 

67.6 

46 

540.6 

76.9 

07 

304.0 

42.7 

67 

363.4 

51.1 

27 

422.8 

59.4 

87 

482.2 

67.8 

47 

541.6 

76.1 

08 

305.0 

42.9 

68 

364.4 

51.2 

28 

423.8 

59.6 

88 

483.2 

67.9 

48 

542.6 

76.2 

09 

306.0 

43.0 

69 

365.4 

51.4 

29 

424.8 

59.7 

89 

484.2 

68.1 

49 

543. 6 

76.4 

10 

307.0 

43.1 

70 

366.4 

51.5 

30 

425.8 

59.8 

90 

485.2 

68.2 
68.3 

50 
551 

544.6 
545.6 

76.6 
76.6 

311 

307.9 

43.3 

371 

367.4 

51.6 

431 

426.8 

60.0 

491 

486.2 

^?, 

308.9 

43.4 

72 

368.4 

51.8 

32 

427.8 

60.1 

92 

487.2 

68.5 

52 

546.6 

76.8 

13 

309.9 

43.6 

73 

369.3 

51.9 

33 

428.8 

60.3 

93 

488.2 

68.6 

53 

547.6 

76.9 

14 

310.9 

43.7 

74 

370.3 

52.1 

34 

429.8 

60.4 

94 

489.2 

68.8 

54 

548.6 

77.1 

15 

311.9 

43.8 

75 

371.3 

52.2 

35 

430.7 

60.6 

95 

490.2 

68.9 

56 

549.6 

77.2 

16 

312.9 

44.0 

76 

372.3 

52.3 

36 

431.7 

60.7 

96 

491.2 

69.0 

56 

560.6 

77.4 

17 

313.9 

44.1 

77 

373.3 

52.5 

37 

432.7 

60.8 

97 

492.1 

69.2 

67 

551.5 

77.6 

18 

314.9 

44.3 

78 

374. 3 

52.6 

38 

433.7 

61.0 

98 

493.1 

69.3 

58 

552.6 

77.6 

19 

315.9 

44.4 

79 

375.3 

52.7 

39 

434.7 

61.1 

99 

494.1 

69.6 

59 

553.5 

77.8 

20 
321 

316.9 

44.5 

80 

376.3 

52.9 

40 

436.7 

61.2 

500 
501 

495.1 

69.6 

60 

564.6 

77.9 

317.9 

44.7 

381 

377.3 

53.0 

441 

436.7 

61.4 

496.1 

69.7 

561 

665.5 

78.1 

22 

318.8 

44.8 

82 

378.3 

53.2 

42 

437.7 

61.5 

02 

497.1 

69.9 

62 

556.6 

78.2 

23 

319.8 

45.0 

83 

379.2 

53.3 

43 

438.7 

61.7 

03 

498.1 

70.0 

63 

557.5 

78.3 

24 

320.8 

45.1 

84 

380.2 

53.4 

44 

439.7 

61.8 

04 

499.1 

70.2 

64 

558.6 

78.5 

25 

321.8 

45.2 

85 

381.2 

53.6 

45 

440.6 

61.9 

06 

500.1 

70.3 

65 

659.6 

78.6 

26 

322.8 

45.4 

86 

382.2 

53.7 

46 

441.6 

62.1 

06 

501.0 

70.4 

66 

560.6 

78.8 

27 

323.8 

45.5 

87 

383.2 

53.9 

47 

442.6 

62.2 

07 

502.0 

70.6 

67 

561.5 

78.9 

28 

324.8 

45.7 

88 

384.2 

54.0 

48 

443.6 

62.4 

08 

503.0 

70.7 

68 

562.5 

79.0 

29 

325.8 

45.8 

89 

385.2 

54.1 

49 

444.6 

62.6 

09 

504.0 

70.8 

69 

563.6 

79.1 

30 

326.8 

45.9 

90 

386.2 

54.3 

50 

446.6 

62.6 

10 

505.0 

70.9 

70 

564.5 

79.3 

331 

327.8 

46.1 

391 

387.2 

54.4 

451 

446.6 

62.8 

511 

506.0 

71.1 

571 

565.4 

79.4 

32 

328.7 

46.2 

92 

388.2 

54.6 

52 

447.6 

62.9 

12 

507.0 

71.2 

72 

566.4 

79.6 

33 

329.7 

46.3 

93 

389.1 

54.7 

53 

448.6 

63.0 

13 

508.0 

71.4 

73 

667.4 

79.7 

34 

330.7 

46.5 

94 

390.1 

54.8 

54 

449.6 

63.2 

14 

609. 0 

71.5 

74 

568.4 

79.8 

35 

331.7 

46.6 

95 

391.1 

55.0 

55 

460.5 

63.3 

16 

610.0 

71.6 

75 

569.4 

80.0 

36 

332.7 

46.8 

96 

392.1 

55.1 

56 

451.6 

63.5 

16 

610.9 

71.8 

76 

670.4 

80.1 

37 

333.7 

46.9 

97 

393.1 

55.3 

57 

452.6 

63.6 

17 

611.9 

71.9 

77 

571.4 

80.2 

38 

334.7 

47.0 

98 

394.1 

55.4 

58 

463.6 

63.7 

18 

512.9 

72.0 

78 

572.4 

80.4 

39 

335.7 

47.2 

99 

395.1 

55.5 

59 

464.6 

63.9 

19 

513.9 

72.2 

79 

573.4 

80.5 

40 

336.7 

47.3 

400 

396.1 

55.7 

60 

456.6 

64.0 

20 

614.9 

72.3 

80 

574.4 

80.6 

341 

337.7 

47.5 

401 

397.1 

55.8 

461 

466.5 

64.2 

521 

515.9 

72.4 

581 

575.4 

80.8 

42 

338.6 

47.6 

02 

398.1 

56.0 

62 

467.6 

64.3 

22 

516.9 

72.6 

82 

676.4 

80.9 

43 

339.6 

47.7 

03 

399.1 

56.1 

63 

468.5 

64.4 

23 

517.9 

72.8 

83 

677.4 

81.1 

44 

340.6 

47.9 

04 

400.0 

56.2 

64 

469.6 

64.6 

24 

518.9 

73.0 

84 

678.4 

81.3 

45 

341.6 

48.0 

05 

401.0 

56.4 

65 

460.4 

64.7 

25 

519.9 

73.1 

86 

679.4 

81.4 

46 

342.6 

48.2 

06 

402.0 

56.5 

66 

461.4 

64.9 

26 

520.9 

73.2 

86 

580.3 

81.6 

47 

343.6 

48.3 

07 

403.0 

56.6 

67 

462.4 

65.0 

27 

521.8 

73.4 

87 

581.3 

81.7 

48 

344.6 

48.4 

08 

404.0 

56.8 

68 

463.4 

65.1 

28 

622.8 

73.5 

88 

682.3 

81.8 

49 

345.6 

48.6 

09 

405.0 

56.9 

69 

464.4 

66.3 

29 

523.8 

73.7 

89 

683.3 

82.0 

50 

346.6 

48.7 

10 

406.0 

57.1 

70 

466.4 

65.4 

30 

524.8 

73.8 

90 

584.3 

82.1 

351 

347.6 

48.9 

411 

407.0 

57.2 

471 

466.4 

66.6 

631 

626.8 

73.9 

591 

685.3 

82.2 

52 

348.5 

49.0 

12 

408.0 

57.3 

72 

467.4 

66.7 

32 

526.8 

74.1 

92 

686.3 

82.4 

53 

349.6 

49.1 

13 

409.0 

57.5 

73 

468.4 

65.8 

33 

527.8 

74.2 

93 

587.3 

82.5 

54 

350.5 

49.3 

14 

409.9 

57.6 

74 

469.4 

66.0 

34 

628.8 

74.3 

94 

588.3 

82.6 

55 

351.5 

49.4 

15 

410.9 

57.8 

75 

470.4 

66.1 

36 

629.8 

74.6 

95 

589.3 

82.8 

56 

352.5 

49.5 

16 

411.9 

57.9 

76 

471.3 

66.2 

36 

530.8 

74.6 

96 

690.3 

83.0 

57 

353.5 

49.7 

17 

412.9 

58.0 

77 

472.3 

66.4 

37 

531.7 

74.7 

97 

591.2 

83.1 

58 

354.5 

49.8 

18 

413.9 

58.2 

78 

473.3 

66.6 

38 

532.7 

74.9 

98 

592.2 

83.2 

59 

355.5 

50.0 

19 

414.9 

58.3 

79 

474.3 

66.7 

39 

533.7 

75.0 

99 

593.2 

83.3 

60 

356.5 

50.1 

20 

415.9 

58.5 

80 

475.3 

66.8 

40 

534.7 

76.1 

600 

594.2 

83.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

82°  (98°,  262°,  278° 

)• 

Page  648] 

TABLE  2. 

^ 

Difference  of  Latitude  and  Departure  for  9°  (171°,  189°,  351°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

60.2 

9.5 

121 

119.5 

18.9 

181 

178.8 

28.3 

241 

238.0 

37.7 

2 

2.0 

0.3 

62 

61.2 

9.7 

22 

120.5 

19.1 

82 

179.8 

28.5 

42 

239.0 

37.9 

3 

3.0 

0.5 

63 

62.2 

9.9 

23 

121.5 

19.2 

83 

180.7 

28.6 

43 

240.0 

38.0 

4 

4.0 

0.6 

64 

63.2 

10.0 

24 

122.5 

19.4 

84 

181.7 

28.8 

44 

241.0 

38.2 

5 

4.9 

0.8 

65 

64.2 

10.2 

25 

123.5 

19.6 

85 

182.7 

28.9 

45 

242.0 

38.3 

6 

5.9 

0.9 

66 

65.2 

10.3 

26 

124.4 

19.7 

86 

183.7 

29.1 

46 

243.0 

38.5 

7 

6.9 

1.1 

67 

66.2 

10.5 

27 

125.4 

19.9 

87 

184.7 

29.3 

47 

244.0 

38.6 

8 

7.9 

1.3 

68 

67.2 

10.6 

28 

126.4 

20.0 

88 

185.7 

29.4 

48 

244.9 

38.8 

9 

8.9 

1.4 

69 

68.2 

10.8 

29 

127.4 

20.2 

89 

186.7 

29.6 

49 

245.9 

39.0 

10 
11 

9.9 
10.9 

1.6 

70 
71 

69.1 

11.0 

30 

128.4 

20.3 

90 
191 

187.7 

29.7 

50 

246.9 
247.9 

39.1 

1.7 

70.1 

11.1 

131 

129.4 

20.5 

188.6 

29.9 

251 

39.3 

12 

11.9 

1.9 

72 

71.1 

11.3 

32 

130.4 

20.6 

92 

189.6 

30.0 

52 

248.9 

39.4 

13 

12.8 

2.0 

73 

72.1 

11.4 

33 

131.4 

20.8 

93 

190.6 

30.2 

53 

249.9 

39.6 

14 

13.8 

2.2 

74 

73.1 

11.6 

34 

132.  4 

21.0 

94 

191.6 

30.3 

54 

250.9 

39.7 

15 

14.8 

2.3 

75 

74.1 

11.7 

35 

133.3 

21.1 

95 

192.6 

30.5 

55 

251.9 

39.9 

16 

15.8 

2.5 

76 

75.1 

11.9 

36 

134.3 

21.3 

96 

193.6 

30.7 

56 

252.8 

40.0 

17 

16.8 

2.7 

77 

76.1 

12.0 

37 

135.3 

21.4 

97 

194.6 

30.8 

57 

253.8 

40.2 

18 

17.8 

2.8 

78 

77.0 

12.2 

38 

136.3 

21.6 

98 

195.6 

31.0 

58 

254.8 

40.4 

19 

18.8 

3.0 

79 

78.0 

12.4 

39 

137.3 

21.7 

99 

196.5 

31.1 

59 

255.8 

40.5 

20 

19.8 

3.1 

80 

79.0 

12.5 

40 

138.3 

21.9 

200 
201 

197.5 

31.3 

60 

256.8 

40.7 

21 

20.7 

3.3 

81 

80.0 

12.7 

141 

139.3 

22.1 

198.5 

31.4 

261 

257.8 

40.8 

22 

21.7 

3.4 

82 

81.0 

12.8 

42 

140.3 

22.2 

02 

199.5 

31.6 

62 

258.8 

41.0 

23 

22.7 

3.6 

83 

82.0 

13.0 

43 

141.2 

22.4' 

03 

200.5 

31.8 

63 

259.8 

41.1 

24 

23.7 

3.8 

84 

83.0 

13.1 

44 

142.2 

22.5 

04 

201.5 

31.9 

64 

260.7 

41.3 

25 

24.7 

3.9 

85 

84.0 

13.3 

45 

143.2 

22.7 

05 

202.5 

32.1 

65 

261.7 

41.5 

26 

25.7 

4.1 

86 

84.9 

13.5 

46 

144.2 

22.8 

06 

203.5 

32.2 

66 

262.7 

41.6 

27 

26.7 

4.2 

87 

85.9 

13.6 

47 

145.2 

23.0 

07 

204.5 

32.4 

67 

263.7 

41.8 

28 

27.7 

4.4 

88 

86.9 

13.8 

48 

146.2 

23.2 

08 

205.4 

32.5 

68 

264.7 

41.9 

29 

28.6 

4.5 

89 

87.9 

13.9 

49 

147.2 

23.3 

09 

206.4 

32.7 

69 

265.7 

42.1 

30 

29.6 

4.7 

90 

88.9 

14.1 

50 

148.  2 

23.5 

10 

207.4 

32.9 

70 

266.7 

42.2 

31 

30.6 

4.8 

91 

89.9 

14.2 

151 

149.1 

23.6 

211 

203.4 

33.0 

271 

267.7 

42.4 

32 

31.6 

5.0 

92 

90.9 

14.4 

52 

150.1 

23.8 

12 

209.4 

33.2 

72 

268.7 

42.6 

33 

32.6 

5.2 

93 

91.9 

14.5 

53 

151.1 

23.9 

13 

210.4 

33.3 

73 

269.6 

42.7 

34 

33.6 

5.3 

94 

92.8 

14.7 

54 

152.1 

24.1 

14 

211.4 

33.5 

74 

270.6 

42.9 

35 

34.6 

5.5 

95 

93.8 

14.9 

55 

153. 1 

24.2 

15 

212.4 

33.6 

75 

271.6 

43.0 

36 

35.6 

5.6 

96 

94.8 

15.0 

56 

151.1 

24.4 

16 

213.3 

33.8 

76 

272.6 

43.2 

37 

36.5 

5.8 

97 

95.8 

15.2 

57 

155.1 

24.6 

17 

214.3 

33.9 

77 

273.6 

43.3 

38 

37.5 

5.9 

98 

96.8 

15.3 

58 

156.1 

24.7 

18 

215.3 

34.1 

78 

274.6 

43.5 

39 

38.5 

6.1 

99 

97.8 

15.5 

59 

157.0 

24.9 

19 

216.3 

34.3 

79 

275.6 

43.6 

40 

39.5 

6.3 

100 

98.8 

15.6 
15.8 

60 

158.0 

25.0 

20 

217.3 

34.4 

80 
281 

276.6 

43.8 
44.0 

41 

40.5 

6.4 

101 

99.8 

161 

159.0 

25.2 

221 

218.3 

34.6 

277.5 

42 

41.5 

6.6 

02 

100.7 

16.0 

62 

160.0 

25.3 

22 

219.3 

34.7 

82 

278.5 

44.1 

43 

42.5 

6.7 

03 

101.7 

16.1 

63 

161. 0 

25.5 

23 

220.3 

34.9 

83 

279.5 

44.3 

44 

43.5 

6.9 

04 

102.7 

16.3 

64 

162.0 

25.7 

24 

221.2 

35.0 

84 

280.5 

44.4 

45 

44.4 

7.0 

05 

103.7 

16.4 

65 

163.0 

25.8 

25 

222.2 

35.2 

85 

281.5 

44.6 

46 

45.4 

7.2 

06 

104.7 

16.6 

66 

164.0 

26.0 

26 

223.2 

35.4 

86 

282.5 

44.7 

47 

46.4 

7.4 

07 

105.7 

16.7 

67 

164.9 

26.1 

27 

224.2 

35.5 

87 

283.5 

44.9 

48 

47.4 

7.5 

08 

106.7 

16.9 

68 

165.9 

26.3 

28 

225.2 

35.7 

88. 

284.5 

45.1 

49 

48.4 

7.7 

09 

107.7 

17.1 

69 

166.9 

26.4 

29 

226.2 

35.8 

89 

285.4 

45.2 

50 

49.4 
50.4 

7.8 

10 

108.6 

17.2 

70 

167.9 
168.9 

26.6 

30 
231 

227.2 

36.0 

90 

286.4 

45.4 

51 

8.0 

111 

109.6 

17.4 

171 

26.8 

228.2 

36.1 

291 

287.4 

45.5 

52 

51.4 

8.1 

12 

110.6 

17.5 

72 

169.9 

26.9 

32 

229.1 

36.3 

92 

288.4 

45.7 

53 

52.3 

8.3 

13 

111.6 

17.7 

73 

170.9 

27.1 

33 

230.1 

36.4 

93 

289.4 

45.8 

54 

53.3 

8.4 

14 

112.6 

17.8 

74 

171.9 

27.2 

34 

231.1 

36.6 

94 

290.4 

46.0 

55 

54.3 

8.6 

15 

113.6 

18.0 

75 

172.8 

27.4 

35 

232.1 

36.8 

95 

291.4 

46.1 

56 

55.3 

8.8 

16 

114.6 

18.1 

76 

173.8 

27.5 

36 

233.1 

36.9 

96 

292.4 

46.3 

57 

56.3 

8.9 

17 

115.6 

18.3 

77 

174.8 

27.7 

37 

234.1 

37.1 

97 

293.3 

46.5 

58 

57.3 

9.1 

18 

116.5 

18.5 

78 

175.8 

27.8 

38 

235.1 

37,2 

98 

294.3 

46.6 

59 

58.3 

9.2 

19 

117.5 

18.6 

79 

176.8 

28.0 

39 

236.1 

37.4 

99 

295.3 

46.8 

60 

59.3 

9.4 

20 

118.5 

18.8 

80 

177.8 

28.2 

40 

237.0 

37.5 

300 

296.3 

46.9 

DUt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

81°  (99°,  261°,  279°). 

TABLE  2 

[Page  549 

Difference  of  Latitude  and  Departure  for 

9°  (171°,  189°,  351°) 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

297.3 

47.1 

361 

356.6 

56.5 

421 

415.8 

65.9 

481 

475.1 

75.2 

541 

534.4 

84.6 

02 

298.3 

47.2 

62 

357.5 

56.7 

22 

416.8 

66.0 

82 

476.1 

75.3 

42 

535.4 

84.7 

03 

299.3 

47.4 

63 

358.5 

56.8 

23 

417.8 

66.2 

83 

477.1 

75.5 

43 

536.3 

84.9 

04 

300.3 

47.6 

64 

359.5 

56.9 

24 

418.8 

66.3 

84 

478.0 

75.6 

44 

537.3 

85.1 

05 

301.2 

47.7 

65 

360.5 

57.1 

25 

419.8 

66.5 

85 

479.0 

75.8 

45 

538.3 

85.3 

06 

302.2 

47.9 

66 

361.5 

57.3 

26 

420.8 

66.6 

86 

480.0 

75.9 

46 

539.3 

85.4 

07 

303.2 

48.0 

67 

362.5 

57.4 

27 

421.7 

66.8 

87 

481.0 

76.1 

47 

540.3 

85.6 

08 

304.2 

48.2 

68 

363.5 

57.6 

28 

422.7 

67.0 

88 

482.0 

76.2 

48 

541.3 

85.7 

09 

305.2 

48.3 

69 

364.5 

57.7 

29 

423.7 

67.1 

89 

483.0 

76.4 

49 

542.3 

85.9 

10 
311 

306.2 
307.2 

48.5 

70 

365.4 

57.9 

30 

424.7 

67.3 

90 

484.0 

76.5 

50 

543.3 

86.0 

48.7 

371 

366.4 

58.1 

431 

425.7 

67.4 

491 

485.0 

76.7 

551 

544.3 

86.2 

12 

308.2 

48.8 

72 

367.4 

58.2 

32 

426.7 

67.6 

92 

485.9 

76.8 

52 

545.2 

86.3 

13 

309.1 

49.0 

73 

368.4 

58.4 

33 

427.7 

67.7 

93 

486.9 

77.0 

53 

546.2 

86.5 

14 

310.1 

49.1 

74 

369.4 

58.5 

34 

428.7 

67.9 

94 

487.9 

77.1 

54 

547.2 

86.6 

15 

311.1 

49.3 

75 

370.4 

58.7 

35 

429.6 

68.1 

95 

488.9 

77.3 

55 

548.2 

86.8 

16 

312.1 

49.4 

76 

371.4 

58.8 

36 

430.6 

68.2 

96 

489.9 

77.5 

56 

549.2 

87.0 

17 

313.1 

49.6 

77 

372.4 

59.0 

37 

431.6 

68.4 

97 

490.9 

77.7 

57 

550.2 

87.1 

18 

314.1 

49.8 

78 

373.3 

59.1 

38 

432.6 

68.5 

98 

491.9 

77.9 

58 

551.2 

87.3 

19 

315.1 

49.9 

79 

374.3 

59.3 

39 

433.6 

68.7 

99 

492.9 

78.0 

59 

552.2 

87.4 

20 

316.1 

50.1 

80 

375.3 

59.5 

40 

434.6 

68.8 

500 

493.8 

78.2 

60 

553.1 

87.6 

321 

317.0 

50.2 

381 

376.  3 

59.6 

441 

435.6 

69.0 

501 

494.8 

78.4 

561 

554.1 

87.7 

22 

318.0 

50,4 

82 

377.3 

59.8 

42 

436.6 

69.1 

02 

495.8 

78.5 

62 

555.1 

87.9 

23 

319.0 

50.5 

83 

378.3 

59.9 

43 

437.5 

69.3 

03 

496.8 

78.7 

63 

556.1 

88.0 

24 

320.0 

50.7 

84 

379.3 

60.1 

44 

438.5 

69.5 

04 

497.8 

78.8 

64 

557.1 

88.2 

25 

321.0 

50.8 

85 

380.3 

60.2 

45 

439.5 

69.6 

05 

498.8 

79.0 

65 

558.1 

88.3 

26 

322.0 

51.0 

86 

381.2 

60.4 

46 

440. 5 

69.8 

06 

499.8 

79.1 

66 

559.1 

88.5 

27 

323.0 

51.2 

87 

382.2 

60.5 

47 

441.5 

69.9 

07 

500.8 

79.2 

67 

560.1 

88.6 

28 

324.0 

51.3 

88 

383.2 

60.7 

48 

442.5 

70.1 

08 

501.7 

79.4 

68 

561.0 

88.8 

29 

324.9 

51.5 

89 

384.2 

60.9 

49 

443.5 

70.2 

09 

502.7 

79.5 

69 

562.0 

88.9 

30 

325.9 

51.7 

90 

385.2 

61.0 

50 

444.5 

70.4 

10 

503.7 

79.7 

70 

563.0 

89.1 

331 

326.9 

51.8 

391 

386.2 

61.2 

451 

445.4 

70.6 

511 

504.7 

79.8 

571 

564.0 

89.2 

32 

327.9 

51.9 

92 

387.2 

61.3 

52 

446.4 

70.7 

12 

505.7 

80.1 

72 

565.0 

89.4 

33 

328.9 

52.1 

93 

388.2 

61.5 

53 

447.4 

70.9 

13 

506.7 

80.2 

73 

566.0 

89.5 

34 

329.9 

52.3 

94 

389.1 

61.6 

54 

448.4 

71.0 

14 

507.7 

80.3 

74 

567.0 

89.7 

35 

330. 9 

52.4 

95 

390.1 

61.8 

55 

449.4 

71.2 

15 

508.7 

80.5 

75 

568.0 

89.9 

36 

331.9 

52.6 

96 

391.1 

62.0 

56 

450.4 

71.3 

16 

509.6 

80.6 

76 

568.9 

90.1 

37 

332.8 

52.7 

97 

392.1 

62.1 

57 

451.4 

71.5 

17 

510.6 

80.8 

77 

569.9 

90.2 

38 

333.8 

52.9 

98 

393.1 

62.3 

58 

452.4 

71.7 

18 

511.6 

80.9 

78 

570.9 

90.3 

39 

334.8 

53.0 

99 

394.1 

62.4 

59 

453.3 

71.8 

19 

512.6 

81.1 

79 

571.9 

90.5 

40 

335.8 

53.2 

400 

395.1 

62.6 

60 

454.3 

72.0 

20 

513.6 

81.3 

80 

572.9 

90.7 

341 

336.8 

53.3 

401 

396.1 

62.7 

461 

455.3 

72.1 

521 

514.6 

81.4 

581 

573.9 

90.9 

42 

337.  8 

53.5 

02 

397.0 

62.9 

62 

456.3 

72.3 

22 

515.6 

81.6 

82 

574.9 

91.0 

43 

338.8 

53.7 

03 

398.0 

63.0 

63 

457.3 

72.4 

23 

516.6 

81.8 

83 

575.9 

91.2 

44 

339.8 

53.8 

04 

399.0 

63.2 

64 

458.3 

72.6 

24 

517.6 

81.9 

84 

576.9 

91.3 

45 

340.8 

54.0 

05 

400.0 

63.4 

65 

459.3 

72.7 

25 

518.6 

82.1 

85 

577.9 

91.5 

46 

341.7 

54.1 

06 

401.0 

63.5 

66 

460.3 

72.9 

26 

519.5 

82.3 

86 

578.8 

91.7 

47 

342.7 

54.3 

07 

402.0 

63.7 

67 

461.2 

73.1 

27 

520.5 

82.4 

87 

579.8 

91.8 

48 

343.  7 

54.4 

08 

403.0 

63.8 

68 

462.2 

73.2 

28 

521.5 

82.6 

88 

580.8 

92.0 

49 

344.7 

54.6 

09 

404.0 

64.0 

69 

463.2 

73.4 

29 

522.5 

82.7 

89 

581.8 

92.1 

50 

345.7 

54.8 

10 

405.0 

64.1 

70 

464.2 

73.5 

30 

523.5 

82.9 

90 

582.8 

92.2 

351 

346.7 

54.9 

411 

405.9 

64.3 

471 

465.2 

73.7 

531 

524.5 

83.1 

591 

583.8 

92.4 

52 

347.7 

55.1 

12 

406.9 

64.5 

72 

466.2 

73.8 

32 

525.5 

83.2 

92 

584.8 

92.5 

53 

348.7 

55.2 

13 

407.9 

64.6 

73 

467.2 

74.0 

33 

526.5 

83.4 

93 

585.7 

92.7 

54 

349.6 

55.4 

14 

408.9 

64.8 

74 

468.2 

74.2 

34 

527.5 

83.5 

94 

586.7 

92.9 

55 

350.6 

55.5 

15 

409.9 

64.9 

75 

469.2 

74.3 

35 

528.4 

83.7 

95 

587.7 

93.1 

56 

351.6 

55.7 

16 

410.9 

65.1 

76 

470.1 

74.5 

36 

529.4 

83.8 

96 

588.7 

93.2 

57 

352.6 

55.9 

17 

411.9 

65.2 

77 

471.1 

74.6 

37 

530.4 

84.0 

97 

589.7 

93.4 

58 

353.6 

56.0 

18 

412.9 

65.4 

78 

472.1 

74.8 

38 

531.4 

84.1 

98 

590.7 

93.5 

59 

354.6 

56.2 

19 

413.8 

65.6 

79 

473.1 

74.9 

39 

532.4 

84.3 

99 

591.7 

93.7 

60 

355.6 

56.3 

20 

414.8 

65.7 

80 

474.1 

75.0 

40 

533.4 

84.4 

600 

592.6 

93.8 

Dlst. 

Dep. 

Lat. 

Dist.      Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

81°  (99°,  261 

°,  279° 

)• 

Page  650] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  10°  (170°,  19C 

°,  350°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

60.1 

10.6 

121 

119.2 

21.0 

181 

178.3 

31.4 

241 

237.3 

41.8 

2 

2.0 

0.3 

62 

61.1 

10.8 

22 

120.1 

21.2 

82 

179.2 

31.6 

42 

2.38. 3 

42.0 

3 

3.0 

0.5 

63 

62.0 

10.9 

23 

121.1 

21.4 

83 

180.2 

31.8 

43 

239.3 

42.2 

4 

3.9 

0.7 

64 

63.0 

11.1 

24 

122.1 

21.5 

84 

181.2 

32.0 

44 

240.3 

42.4 

6 

4.9 

0.9 

65 

64.0 

11.3 

25 

123.1 

21.7 

85 

182.2 

32.1 

45 

241.3 

42.5 

6 

5.9 

1.0 

66 

65.0 

11.5 

26 

124.1 

21.9 

86 

183.2 

32.3 

46 

242.3 

42.7 

7 

6.9 

1.2 

67 

66.0 

11.6 

27 

125.1 

22.1 

87 

184.2 

32.5 

47 

243.2 

42.9 

8 

7.9 

1.4 

68 

67.0 

11.8 

28 

126.1 

22.2 

88 

185.1 

32.6 

48 

244.2 

43.1 

9 

8.9 

1.6 

69 

68.0 

12.0 

29 

127.0 

22.4 

89 

186.1 

32.8 

49 

245.2 

43.2 

10 

9.8 

1.7 

70 

68.9 

12.2 

30 

128.0 

22.6 

90 

187.1 

33.0 

50 

246.2 

43.4 

11 

10.8 

1.9 

71 

69.9 

12.3 

131 

129.0 

22.7 

191 

188.1 

33.2 

251 

247.2 

43.6 

12 

11  8 

2.1 

72 

70.9 

12.5 

32 

130.0 

22.9 

92 

189.1 

33.3 

52 

248.2 

43.8 

13 

12.8 

2.3 

73 

71.9 

12.7 

33 

131.0 

23.1 

93 

190.1 

33.5 

53 

249.2 

43.9 

14 

13.8 

2.4 

74 

72.9 

12.8 

34 

132.0 

23.3 

94 

191.1 

33.7 

54 

250.1 

44.1 

15 

14.8 

2.6 

75 

73.9 

13.0 

35 

132.9 

23.4 

95 

192.0 

33.9 

55 

251.1 

44.3 

16 

15.8 

2.8 

76 

74.8 

13.2 

36 

133.9 

23.6 

96 

193.0 

34.0 

56 

252.1 

44.5 

17 

16.7 

3.0 

77 

75.8 

13.4 

37 

134.9 

23.8 

97 

194.0 

34.2 

57 

253.1 

44.6 

18 

17.7 

3.1 

78 

76.8 

13.5 

38 

135.9 

24.0 

98 

195.0 

34.4 

58 

254.1 

44.8 

19 

18.7 

3.3 

79 

77.8 

13.7 

39 

136.9 

24.1 

99 

196.0 

34.6 

59 

255.1 

45.0 

20 

19.7 

3.5 

80 

78.8 

13.9 

40 

137.9 

24.3 

200 

197.0 

34.7 

60 

256.1 

45.1 

21 

20.7 

3.6 

81 

79.8 

14.1 

141 

138.9 

24.5 

201 

197.9 

34.9 

261 

257.0 

45.3 

22 

21.7 

3.8 

82 

80.8 

14.2 

42 

139.8 

24.7 

02 

198.9 

35.1 

62 

258.0 

45.5 

23 

22.7 

4.0 

83 

81.7 

14.4 

43 

140.8 

24.8 

03 

199.9 

35.3 

63 

259.0 

45.7 

24 

23.6 

4.2 

84 

82.7 

14.6 

44 

141.8 

25.0 

04 

200.9 

35.4 

64 

260.0 

45.8 

25 

24.6 

4.3 

85 

83.7 

14.8 

45 

142.8 

25.2 

05 

201.9 

35.6 

65 

261.0 

46.0 

26 

25.6 

4.5 

86 

84.7 

14.9 

46 

143.8 

25.4 

06 

202.9 

35.8 

66 

262.0 

46.2 

27 

26.6 

4.7 

87 

85.7 

15.1 

47 

144.8 

25.5 

07 

203.9 

35.9 

67 

262.9 

46.4 

28 

27.6 

4.9 

88 

86.7 

15.3 

48 

145.8 

25.7 

08 

204.8 

36.1 

68 

263.9 

46.5 

29 

28.6 

5.0 

89 

87.6 

15.5 

49 

146.7 

25.9 

09 

205.8 

36.3 

69 

264.9 

46.7 

30 

29.5 

5.2 

90 

88.6 

15.6 

50 

147.7 
148.7 

26.0 

10 

206.8 

36.5 

70 

265.9 

46.9 

31 

30.5 

5.4 

91 

89.6 

15.8 

151 

26.2 

211 

207.8 

36.6 

271 

266.9 

47.1 

32 

31.5 

5.6 

92 

90.6 

16.0 

52 

149.7 

26.4 

12 

208.8 

36.8 

72 

267.9 

47.2 

33 

32.5 

5.7 

93 

91.6 

16.1 

53 

150.7 

26.6 

13 

209.8 

37.0 

73 

268.9 

47.4 

34 

33.5 

5.9 

94 

92.6 

16.3 

54 

151.7 

26.7 

14 

210.7 

37.2 

74 

269.8 

47.6 

35 

34.5 

6.1 

95 

93.6 

16.5 

55 

152.6 

26.9 

15 

211.7 

37.3 

75 

270.8 

47.8 

36 

35.5 

6.3 

96 

94.5 

16.7 

56 

153.6 

27.1 

16 

212.7 

37.5 

76 

271.8 

47.9 

37 

36.4 

6.4 

97 

95.5 

16.8 

57 

154.6 

27.3 

17 

213.7 

37.7 

77 

272.8 

48.1 

38 

37.4 

6.6 

98 

96.5 

17.0 

58 

155.6 

27.4 

18 

214.7 

37.9 

78 

273.8 

48.3 

39 

38.4 

6.8 

99 

97.5 

17.2 

59 

156.6 

27.6 

19 

215.7 

38.0 

79 

274.8 

48.4 

40 

39.4 

6.9 
7.1 

100 

98.5 

17.4 

60 

157.6 

27.8 

20 

216.7 

38.2 

80 

275.7 

48.6 

41 

40.4 

101 

99.5 

17.5 

161 

158.6 

28.0 

221 

217.6 

38.4 

281 

276.7 

48.8 

42 

41.4 

7.3 

02 

100.5 

17.7 

62 

159.5 

28.1 

22 

218.6 

38.5 

82 

277.7 

49.0 

43 

42.3 

7.5 

03 

101.4 

17.9 

63 

160.5 

28.3 

23 

219.6 

38.7 

83 

278.7 

49.1 

44 

43.3 

7.6 

04 

102.4 

18.1 

64 

161.5 

28.5 

24 

220.6 

38.9 

84 

279.7 

49.3 

45 

44.3 

7.8 

05 

103.4 

18.2 

65 

162.5 

28.7 

25 

221.6 

39.1 

85 

280.7 

49.5 

46 

45.3 

8.0 

06 

104.4 

18.4 

66 

163.5 

28.8 

26 

222.6 

39.2 

86 

281.7 

49.7 

47 

46.3 

8.2 

07 

105.4 

18.6 

67 

164.5 

29.0 

27 

223.6 

39.4 

87 

282.6 

49.8 

48 

47.3 

8.3 

08 

106.4 

18.8 

68 

165.4 

29.2 

28 

224.5 

39.6 

88 

283.6 

50.0 

49 

48.3 

8.5 

09 

107.3 

18.9 

69 

166.4 

29.3 

29 

225.5 

39.8 

89 

284.6 

50.2 

50 

49.2 

8.7 

10 

108.3 

19.1 

70 

167.4 

29.5 

30 

226.5 

39.9 

90 

285.6 

50.4 

51 

50.2 

8.9 

111 

109.3 

19.3 

171 

168.4 

29.7 

231 

227.5 

40.1 

291 

286.6 

50.5 

52 

51.2 

9.0 

12 

110.3 

19.4 

72 

169.4 

29.9 

32 

228.5 

40.3 

92 

287.6 

50.7 

53 

52.2 

9.2 

13 

111.3 

19.6 

73 

170.4 

30.0 

33 

229.5 

40.5 

93 

288.5 

50.9 

54 

53.2 

9.4 

14 

112.3 

19.8 

74 

171.4 

30.2 

34 

230.4 

40.6 

94 

289.5 

51.1 

55 

54.2 

9.6 

15 

113.3 

20.0 

75 

172.3 

30.4 

35 

231.4 

40.8 

95 

290.5 

51.2 

66 

55.1 

9.7 

16 

114.2 

20.1 

76 

173.3 

30.6 

36 

232.4 

41.0 

96 

291.5 

51.4    ■ 

57 

56.1 

9.9 

17 

115.2 

20.3 

77 

174.  S 

30.7 

37 

233.4 

41.2 

97 

292.5 

51.6    I 

58 

57.1 

10.1 

18 

116.2 

20.5 

78 

175.3 

30.9 

38 

234.4 

41.3 

98 

293.5 

51.7    I 

59 

58.1 

10.2 

19 

117.2 

20.7 

79 

176.3 

31.1 

39 

235.4 

41.5 

99 

294.5 

51.9    ■ 

60 

59.1 

10.4 

20 

118.2 

20.8 

80 

177.3 

31.3 

40 

236.4 

41.7 

300 

295.4 

52.1      ■ 

Diat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.      , 

f 

iO"  (1( 

)0°,  260 

=,  280° 

)• 

, 

TABLE  27                                          [Page 

551 

Difference  of  Latitude  and  Departure  for  10°  (170°,  190°,  350°) 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     j    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

301 

296.4 

52.3 

361 

355.5 

62.7 

421 

414.6 

73.1 

481 

473.7 

83.5 

541 

532.8 

93.9 

02 

297.4 

52.5 

62 

356.5 

62.9 

22 

415.6 

73.3 

82 

474.7 

83.7 

42 

533.8 

94.1 

03 

298.4 

52.6 

63 

357.5 

63.0 

23 

416.6 

73.5 

83 

475.7 

83.9 

43 

534.8 

94.3 

04 

299.4 

52.8 

64 

358.5 

63.2 

24 

417.6 

73.6 

84 

476.6 

84.1 

44 

535.7 

94.5 

05 

300.4 

53.0 

65 

359. 5 

63.4 

25 

418.5 

73.8 

85 

477.6 

84.2 

45 

536.7 

94.6 

06 

301.4 

53.1 

66 

360. 4 

63.6 

26 

419.5 

74.0 

86 

478.6 

84.4 

46 

537.7 

94.8 

07 

302.3 

53.3 

67 

361.4 

63.7 

27 

420.5 

74.2 

87 

479.6 

84.6 

47 

538.7 

95.0 

08 

303.3 

53.5 

68 

362.4 

63.9 

28 

421.5 

74.3 

88 

480.6 

84.7 

48 

539.7 

95.1 

09 

304.3 

53.7 

69 

363.4 

64.1 

29 

422.5 

74.5 

89 

481.6 

84.9 

49 

540.7 

95.3 

10 

305.3 

53.8 

70 

364.4 

64.3 

30 

423.5 

74.7 

90 

482.6 

85.1 

50 

541.6 

95.5 

311 

306.3 

54.0 

371 

365.4 

64.4 

431 

424.5 

74.9 

491 

483.5 

85.2 

551 

542.6 

95.6 

12 

307.3 

54.2 

72 

366.4 

64.6 

32 

425.4 

75.0 

92 

484.5 

85.4 

52 

543.6 

95.8 

13 

308.2 

54.3 

73 

367. 3 

64.8 

33 

426.4 

75.2 

93 

485.5 

85.6 

53 

544.6 

96.0 

14 

309.2 

54.5 

74 

368. 3 

65.0 

34 

427.4 

75.4 

94 

486.5 

85.8 

54 

545.6 

96.2 

15 

310.2 

54.7 

75 

369.3 

65.1 

35 

428.4 

75.5 

95 

487.5 

85.9 

55 

546.6 

96.3 

16 

311.2 

54.9 

76 

370.3 

65.3 

36 

429.4 

75.7 

96 

488.5 

86.1 

56 

547.5 

96.5 

17 

312.2 

55.1 

77 

371.3 

65.5 

37 

430.4 

75.9 

97 

489.4 

86.3 

57 

548.5 

96.7 

18 

313.2 

55.2 

78 

372.3 

65.6 

38 

431.3 

76.1 

98 

490.4 

86.5 

58 

549.5 

96.9 

19 

314.2 

55.4 

79 

373.2 

65.8 

39 

432.3 

76.2 

99 

491.4 

86.6 

59 

550.5 

97.0 

20 
321 

315.1 

55.6 

80 

374.2 

66.0 

40 

433.3 

76.4 

500 

492.4 

86.8 

60 

551.5 

97.2 

316.1 

55.8 

381 

375.2 

66.2 

441 

434.3 

76.6 

501 

493.4 

87.0 

561 

552.5 

97.4 

22 

317.1 

55.9 

82 

376.2 

66.3 

42 

435.3 

76.8 

02 

494.4 

87.2 

62 

553.5 

97.6 

23 

318.1 

56.1 

83 

377.2 

66.5 

43 

436.3 

76.9 

03 

495.3 

87.3 

63 

554.4 

97.7 

24 

319.1 

56.3 

84 

378.2 

66.7 

44 

437.3 

77.1 

04 

496.3 

87.5 

64 

555.4 

97.9 

25 

320.1 

56.4 

85 

379.2 

66.9 

45 

438.2 

77.3 

05 

497.3 

87.7 

65 

556.4 

98.1 

26 

321.0 

56.6 

86 

380.1 

67.0 

46 

439.2 

77.5 

06 

498.3 

87.9 

66 

557.4 

98.3 

27 

322.0 

56.8 

87 

381.1 

67.2 

47 

440.2 

77.6 

07 

499.3 

88.0 

67 

558.  4 

98.4 

28 

323.0 

57.0 

88 

382. 1 

67.4 

48 

441.2 

77.8 

08 

500.3 

88.2 

68 

559.4 

98.6 

29 

324.0 

57.1 

89 

383.1 

67.6 

49 

442.2 

78.0 

09 

501.3 

88.4 

69 

560.3 

98.8 

30 
331 

325.0 

57.3 

90 

384. 1 

67.7 

50 

443.2 

78.2 

10 

502.2 

88.6 

70 

561.3 

99.0 

326.0 

57.5 

391 

385.1 

67.9 

451 

444.2 

78.3 

511 

503.2 

88.7 

571 

562.3 

99.1 

32 

327.0 

57.7 

92 

386.0 

68.1 

52 

445.1 

78.5 

12 

504.2 

88.9 

72 

563.3 

99.3 

33 

327.9 

57.8 

93 

387.0 

68.2 

53 

446.1 

78.7 

13 

505.2 

89.1 

73 

564.3 

99.5 

34 

328.9 

58.0 

94 

388.0 

68.4 

54 

447.1 

78.8 

14 

506.2 

89.2 

74 

565.3 

99,6 

35 

329.9 

58.2 

95 

.389. 0 

68.6 

55 

448.1 

79.0 

15 

507.2 

89.4 

75 

566.3 

99.8 

36 

330.9 

58.4 

96 

390.0 

68.8 

56 

449.1 

79.2 

16 

508.2 

89.6 

76 

567.2 

100.0 

37 

331.9 

58.5 

97 

391.0 

68.9 

57 

450.1 

79.4 

17 

509.1 

89.8 

77 

568.2 

100.2 

38 

332.9 

58.7 

98 

392.0 

69.1 

58 

451.0 

79.5 

18 

510.1 

89.9 

78 

569.2 

100.3 

39 

333.9 

58.9 

99 

392.9 

69.3 

59 

452.0 

79.7 

19 

511.1 

90.1 

79 

570.2 

100.5 

40 

334.8 

59.1 

400 

393.9 

69.5 

60 

453.0 

79.9 

20 

512.1 

90.3 
90.5 

80 

571.2 

100.7 

341 

335.8 

59.2 

401 

394.9 

69.6 

461 

454.0 

80.1 

521 

513.1 

581 

572.2 

100.9 

42 

336.8 

59.4 

02 

395.9 

69.^ 

62 

455. 0 

80.2 

22 

514.1 

90.6 

82 

573.2 

101.0 

43 

337.8 

59.6 

03 

396.9 

70.0 

63 

456.0 

80.4 

23 

515.1 

90.8 

83 

574.1 

101.2 

44 

338.8 

59.8 

04 

397.9 

70.2 

64 

457.0 

80.6 

24 

516.0 

91.0 

84 

575.1 

101.4 

45 

339.8 

59.9 

05 

398.9 

70.3 

65 

457.9 

80.8 

25 

517.0 

91.2 

85 

576.1 

101.6 

46 

340.7 

60.1 

06 

399.8 

70.5 

66 

458.9 

80.9 

26 

518.0 

91.3 

86 

577.1 

101.7 

47 

341.7 

60.3 

07 

400.8 

70.7 

67 

459.9 

81.1 

27 

519.0 

91.5 

87 

578.1 

101.9 

48 

342.7 

60.4 

08 

401.8 

70.9 

68 

460.9 

81.3 

28 

520.0 

91.7 

88 

579.1 

102.1 

49 

343.7 

60.6 

09 

402.8 

71.0 

69 

461.9 

81.5 

29 

521.0 

91.9 

89 

580.0 

102.3 

50 

344.7 

60.8 

10 

403.8 

71.2 

70 

462.9 

81.6 

30 

521.9 

92.0 

90 

581.0 

102.4 

351 

345.7 

61.0 

411 

404.8 

71.4 

471 

463.8 

81.8 

531 

522.9 

92.2 

591 

582.0 

102.6 

52 

346.7 

61.1 

12 

405.7 

71.6 

72 

464.8 

82.0 

32 

523.9 

92.4 

92 

583.0 

102.8 

53 

347.6 

61.3 

13 

406.7 

71.7 

73 

465.8 

82.1 

33 

524.9 

92,5 

93 

584.0 

102.9 

54 

348.6 

61.5 

14 

407.7 

71.9 

74 

466.8 

82.3 

34 

525.9 

92.7 

94 

585.0 

103.1 

55 

349.6 

61.7 

15 

408.7 

72.1 

75 

467.8 

82.5 

35 

526.9 

92.9 

95 

586.0 

103.3 

56 

350.6 

61.8 

16 

409.7 

72.2 

76 

468.8 

82.7 

36 

527.9 

93.1 

96 

586.9 

103.5 

57 

351.6 

62.0 

17 

410.7 

72.4 

77 

469.8 

82.8 

37 

528.8 

93.2 

97 

587.9 

103.6 

58 

352.6 

62.2 

18 

411.7 

72.6 

78 

470.7 

83.0 

38 

529.8 

93.4 

98 

588.9 

103.8 

59 

353.5 

62.4 

19 

412.6 

72.8 

79 

471.7 

83.2 

39 

530.8 

93.6 

99 

589.9 

104.0 

60 

354.5 

62.5 

20 

413.6 

72.9 

80 

472.7 

83.4 

40 

531.8 

93.8 

600 

590.9 

104.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat.      Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

i 

50°  (100°,  260°,  280°). 

Page  552] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  11°  (169°,  191°,  349" 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.9 

11.6 

121 

118.8 

23.1 

181 

177.7 

34.5 

241 

236.6 

46.0 

2 

2.0 

0.4 

62 

60.9 

11.8 

22 

119.8 

23.3 

82 

178.7 

34.7 

42 

237.6 

46.2 

3 

2  9 

0.6 

63 

61.8 

12.0 

23 

120.7 

23.5 

83 

179.6 

34.9 

43 

238.5 

46.4 

4 

3.9 

0.8 

64 

62.8 

12.2 

24 

121.7 

23.7 

84 

180.6 

35.1 

44 

239.5 

46.6 

5 

4.9 

1.0 

65 

63.8 

12.4 

25 

122.7 

23.9 

85 

181.6 

35.3 

45 

240.5 

46.7 

6 

5.9 

1.1 

66 

64.8 

12.6 

26 

123.7 

24.0 

86 

182.6 

35.5 

46 

241.5 

46.9 

7 

6.9 

1.3 

67 

65.8 

12.8 

27 

124.7 

24.2 

87 

183.6 

35.7 

47 

242.5 

47.1 

8 

7.9 

1.5 

68 

66.8 

13.0 

28 

125.6 

24.4 

88 

184.5 

35.9 

48 

243.4 

47.3 

9 

8.8 

1.7 

69 

67.7 

13.2 

29 

126.6 

24.6 

89 

185.5 

36.1 

49 

244.4 

47.5 

10 

9.8 

1.9 

70 

68.7 

13.4 

30 

127.6 

24.8 

90 

186.5 

36.3 

50 

245.4 

47.7 

11 

10.8 

2.1 

71 

69.7 

13.5 

131 

128.6 

25.0 

191 

187.5 

36.4 

251 

246.4 

47.9 

12 

11.8 

2.3 

72 

70.7 

13.7 

32 

129.6 

25.2 

92 

188.5 

36.6 

52 

247.4 

48.1 

13- 

12.8 

2.5 

73 

71.7 

13.9 

33 

130.6 

25.4 

93 

189.5 

36.8 

53 

248.4 

48.3 

14 

13.7 

2.7 

74 

72.6 

14.1 

34 

131.5 

25.6 

94 

190.4 

37.0 

54 

249.3 

48.5 

15 

14.7 

2.9 

75 

73.6 

14.3 

35 

132.5 

25.8 

95 

191.4 

37.2 

55 

250.3 

48.7 

16 

15.7 

3.1 

76 

74.6 

14.5 

36 

133.5 

26.0 

96 

192.4 

37.4 

56 

251.3 

48.8 

17 

16.7 

3.2 

77 

75.6 

14.7 

37 

134.5 

26.1 

97 

193.4 

37.6 

57 

252.3 

49.0 

18 

17.7 

3.4 

78 

76.6 

14.9 

38 

135.5 

26.3 

98 

194.4 

37.8 

58 

253.3 

49.2 

19 

18.7 

3.6 

79 

77.5 

15.1 

39 

136.4 

26.5 

99 

195.3 

38.0 

59 

254.2 

49.4 

20 

19.6 

3.8 

80 

78.5 

15.3 

40 

137.4 

26.7 

200 

196.3 

38.2 

60 

255.2 

49.6 

21 

20.6 

4.0 

81 

79.5 

15.5 

141 

138.4 

26.9 

201 

197.3 

38.4 

261 

256.2 

49.8 

22 

21.6 

4.2 

82 

80.5 

15.6 

42 

139.4 

27.1 

02 

198.3 

38.5 

62 

257.2 

50.0 

23 

22.6 

4.4 

83 

81.5 

15.8 

43 

140.4 

27.3 

03 

199.3 

38.7 

63 

258.2 

50.2 

24 

23.6 

4.6 

84 

82.5 

16.0 

44 

141  4 

27.5 

04 

200.3 

38.9 

64 

259.1 

50.4 

25 

24.5 

4.8 

85 

83.4 

16.2 

45 

142.3 

27.7 

05 

201.2 

39.1 

65 

260.1 

'  50.6 

26 

25.5 

5.0 

86 

84.4 

16.4 

46 

143.3 

27.9 

06 

202.2 

39.3 

66 

261.1 

50.8 

27 

26.5 

5.2 

87 

85.4 

16.6 

47 

144.3 

28.0 

07 

203.2 

39.5 

67 

262.1 

50.9 

28 

27.5 

5.3 

88 

86.4 

16.8 

48 

145.3 

28.2 

08 

204.2 

39.7 

68 

263.1 

51.1 

29 

28.5 

5.5 

89 

87.4 

17.0 

49 

146.3 

28.4 

09 

205.2 

39.9 

69 

264.1 

51.3 

30 

29.4 

5.7 

90 

88.3 

17.2 

50 

147.2 

28.6 

10 

206.1 

40.1 

70 

265.0 

51.5 

31 

30.4 

5.9 

91 

89.3 

17.4 

151 

148.2 

28.8 

211 

207.1 

40.3 

271 

266.0 

51.7 

32 

31.4 

6.1 

92 

90.3 

17.6 

52 

149.2 

29.0 

12 

208.1 

40.5 

72 

267.0 

51.9 

33 

32.4 

6.3 

93 

91.3 

17.7 

53 

150.2 

29.2 

13 

209.1 

40.6 

73 

268.0 

52.1 

34 

33.4 

6.5 

94 

92.3 

17.9 

54 

151.2 

29.4 

14 

210.1 

40.8 

74 

269.0 

52.3 

35 

34.4 

6.7 

95 

93.3 

18.1 

55 

152.2 

29.6 

15 

211.0 

41.0 

75 

269.9 

52.5 

36 

35.3 

6.9 

96 

94.2 

18.3 

56 

153.1 

29.8 

16 

212.0 

41.2 

76 

270.9 

52.7 

37 

36.3 

7.1 

97 

95.2 

18.5 

57 

154.1 

30.0 

17 

213.0 

41.4 

77 

271.9 

52.9 

38 

37.3 

7.3 

98 

96.2 

18.7 

58 

155.1 

30.1 

18 

214.0 

41.6 

78 

272.9 

53.0 

39 

38.3 

7.4 

99 

97.2 

18.9 

59 

156.1 

30.3 

19 

215.0 

41.8 

79 

273.9 

53.2 

40 

39.3 

7.6 

100 

98.2 

19.1 

60 

157.1 

30.5 

20 

216.0 

42.0 

80 

274.9 

53.4 

41 

40.2 

7.8 

101 

99.1 

19.3 

161 

158.0 

30.7 

221 

216.  9 

42.2 

281 

275.8 

53.6 

42 

41.2 

8.0 

02 

100.1 

19.5 

62 

159.0 

30.9 

^2 

217.9 

42.4 

82  t  276. 8 

53.8 

43 

42.2 

8.2 

03 

101.1 

19.7 

63 

160.0 

31.1 

23 

218.9 

42.6 

83     277. 8 

54.0 

44 

43.2 

8.4 

04 

102.1 

19.8 

64 

161.0 

31.3 

24 

219.9 

42.7 

84 

278. 8 

54.2 

45 

44.2 

8.6 

05 

103. 1 

20.0 

65 

162.0 

31.5 

25 

220.9 

42.9 

85 

279.8 

54.4 

46 

45.2 

8.8 

06 

104.1 

20.2 

66 

163.0 

31.7 

26 

221.8 

43.1 

86 

280.7 

54.6 

47 

46.1 

9.0 

07 

105.0 

20.4 

67 

163.9 

31.9 

27 

222.8 

43.3 

87 

281.7 

54.8 

48 

47.1 

9.2 

08 

106.0 

20.6 

68 

164.9 

32.1 

28 

223.8 

43.5 

88 

282.7 

55.0 

49 

48.1 

9.3 

09 

107.0 

20.8 

69 

165.9 

32.2 

29 

224.8 

43.7 

89 

283.7 

55.1 

50 

49.1 

9.5 

10 

108.0 

21.0 

70 

166.9 

32.4 

30 

225.8 

43.9 

90 

284.7 

55.3 

51 

50.1 

9.7 

111 

109.0 

21.2 

171 

167.9 

32.6 

231 

226.8 

44.1 

291 

285.7 

55.5 

52 

51.0 

9.9 

12 

109.9 

21.4 

72 

168.8 

32.8 

32 

227.7 

44.3 

92 

286  6 

55.7 

53 

52.0 

10.1 

13 

110.9 

21.6 

73 

169.8 

33.0 

33 

228.7 

44.5 

93 

287.6 

55.9 

54 

53.0 

10.3 

14 

111.9 

21.8 

74 

170.8 

33.2 

34 

229.7 

44.6 

94 

288.6 

56.1 

55 

54.0 

10.5 

15 

112.9 

21.9 

75 

171.8 

33.4 

35 

230.7 

44.8 

95 

289.6 

56.3 

56 

55.0 

10.7 

16 

113.9 

22.1 

76 

172.8 

33.6 

36 

231.7 

45.0 

96 

290.6 

56.5 

57 

56.0 

10.9 

17 

114.9 

22.3 

77 

173.7 

33.8 

37 

232.6 

45.2 

97 

291.5 

56.7 

58 

56.9 

11.1 

18 

115.8 

22.5 

78 

174.7 

34.0 

38 

233.6 

45.4 

98 

292.5 

56.9 

59 

57.9 

11.3 

19 

116.8 

22.7 

79 

175.7 

34.2 

39 

234.6 

45.6 

99 

293.5 

57.1 

60 

58.9 

11.4 

20 

117.8 

22.9 

80 

176.7 

34.3 

40 

235.6 

45.8 

300 

294.5 

57.2 

Diet. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

79°  (1 

01°,  259 

°,  281°). 

TABLE  2. 

[Page  653     | 

.  Difference  of  Latitude  and  Departure  for  11°  (169°,  191°,  349° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

295.4 

57.4 

361 

354.3 

68.9 

421 

413.2 

80.3 

481 

472.1 

91.8 

541 

531.0 

103.2 

02 

296.4 

57.6 

62 

355.3 

69.1 

22 

414.2 

80.5 

82 

473.1 

92.0 

42 

532.0 

103.4 

03 

297.4 

57.8 

63 

356.3 

69.3 

23 

415.2 

80.7 

83 

474.1 

92.2 

43 

533.0 

103.6 

04 

298.4 

58.0 

64 

357.3 

69.5 

24 

416.2 

80.9 

84 

475.1 

92.4 

44 

534.0 

103.8 

05 

299.4. 

58.2 

65 

358.3 

69.6 

25 

417.2 

81.1 

85 

476.1 

92.6 

45 

535.0 

104.0 

06 

300.3 

58.4 

66 

359.2 

69.8 

26 

418.1 

81.3 

86 

477.0 

92.8 

46 

535.9 

104.2 

07 

301.3 

58.6 

67 

360.2 

70.0 

27 

419.1 

81.5 

87 

478.0 

93.0 

47 

536. 9 

104.4 

08 

302.3 

58.8 

68 

361.2 

70.2 

28 

420.1 

81.7 

88 

479.0 

93.2 

48 

537.9 

104.6 

09 

303.3 

59.0 

69 

362.2 

70.4 

29 

421.1 

81.9 

89 

480.0 

93.3 

49 

538.9 

104.8 

10 

304.3 
305.3 

59.2 

70 

363.2 

70.6 

30 

422.1 

82.1 

90 

481.0 

93.5 

50 

539.9 

105.0 

311 

59.3 

371 

364.1 

70.8 

431 

423.  0     82.  2 

491 

481.9 

93.6 

551 

540.8 

105.1 

12 

306.2 

59.5 

72 

365.1 

71.0 

32 

424.0 

82.4 

92 

482.9 

93.8 

52 

541.8 

105.3 

13 

307.2 

59.7 

73 

366.1 

71.2 

33 

425.0 

82.6 

93 

483.9 

94.0 

53 

542.8 

105.5 

14 

308.2 

59.9 

74 

367.1 

71.4 

34 

426.0 

82.8 

94 

484.9 

94.2 

54 

543.8 

106.7 

15 

309.2 

60.1 

75 

368.1 

71.6 

35 

427.0 

83.0 

95 

485.9 

94.4 

55 

544.8 

106.9 

16 

310.2 

60.3 

76 

369.1 

71.7 

36 

428.0 

83.2 

96 

486.9 

94.6 

56 

545.8 

106.1 

17 

311.1 

60.5 

77 

370.0 

71.9 

37 

428.9 

83.4 

97 

487.8 

94.8 

57 

546.7 

106.3 

18 

312.1 

60.7 

78 

371.0 

72.1 

38 

429.9 

83.6 

98 

488.8 

95.0 

58 

547.7 

106.5 

19 

313.1 

60.9 

79 

372.0 

72.3 

39 

430.9 

83.8 

99 

489.8 

95.2 

59 

548.7 

106.7 

20 

314.1 

61.1 

80 

373.0 

72.5 

40 

431.9 
432.9 

84.0 

500 

490.8 

95.4 

60 

549.7 
550.7 

106.9 

321 

315.1 

61.3 

381 

374.0 

72.7 

441 

84.1 

501 

491.8 

95.6 

561 

107.1 

22 

316.1 

61.4 

82 

374.9 

72.9 

42 

433.8 

84.3 

02 

492.7 

95.8 

62 

551.6 

107.2 

23 

317.0 

61.6 

83 

375.9 

73.1 

43 

434.8 

84.5 

03 

493.7 

96.0 

63 

552.6 

107.4 

24 

318.0 

61.8 

84 

376.9 

73.3 

44 

435.8 

84.7 

04 

494.7 

96.2 

64 

553.6 

107.6 

25 

319.0 

62.0 

85 

377.9 

73.5 

45 

436.8 

84.9 

05 

495.7 

96.4 

65 

554.6 

107.8 

26 

320.0 

62.2 

86 

378.9 

7.3.7 

46 

437.8 

85.1 

06 

496.7 

96.6 

66 

555.6 

108.0 

27 

321.0 

62.4 

87 

379.9 

73.8 

47 

438. 8 

85.3 

07 

497.7 

96.8 

67 

556.6 

108.2 

28 

321.9 

62.6 

88 

380.8 

74.0 

48 

439.7 

85.5 

08 

498.6 

97.0 

68 

557.6 

108.4 

29 

322.9 

62.8 

89 

381.8 

74.2 

49 

440.7 

85.7 

09 

499.6 

97.2 

69 

558.6 

108.6 

30 

323.9 

63.0 

90 

382.8 

74.4 

50 

441.7 

86.9 

10 

500.6 

97.3 

70 
571 

559.5 

108.8 

331 

324.9 

63.2 

391 

383.8 

74.6 

451 

442.7 

86.1 

511 

501.6 

97.5 

560.5 

109.0 

32 

325.9 

63.4 

92 

384.8 

74.8 

52 

443.7 

86.2 

12 

502.6 

97.6 

72 

561.5 

109.1 

33 

326.8 

63.5 

93     385.7 

75.0 

53 

444.6 

86.4 

13 

503.5 

97.8 

73 

562.5 

109.3 

34 

327.  8 

63.7 

94 

386.7 

75.2 

54 

445.6 

86.6 

14 

504.5 

98.0 

74 

563.5 

109.5 

35 

328.8 

63.9 

95 

387.7 

75.4 

55 

446.6 

86.8 

15 

505.5 

98.2 

75 

564.5 

109.7 

36 

329.8 

64.1 

96 

388.7 

75.6 

56 

447.6 

87.0 

16 

506.5 

98.4 

76 

565.4 

109.9 

37 

330.8 

64.3 

97 

389.7 

75.8 

57 

448.6 

87.2 

17 

507.5 

98.6 

77 

666.4 

110.1 

38 

331.8 

64.5 

98 

390.7 

75.9 

58 

449.6 

87.4 

18 

508.5 

98.8 

78 

667.4 

110.3 

39 

332.7 

64.7 

99 

391.6 

76.1 

59 

450.5 

87.6 

19 

509.4 

99.0 

79 

568.3 

110.5 

40 

333.  7 

64.9 

400 
401 

392.6 

76.3 

76.5 

60 
461 

451.5 

87.8 

20 

510.4 

99.2 

80 

569.3 

110.7 

341 

334.7 

65.1 

393.6 

452.5 

88.0 

521 

511.4 

99.4 

581 

570.3 

110.9 

42 

335.7 

65.3 

02 

394.6 

76.7 

62 

453.  5 

88.2 

22 

512.4 

99.6 

82 

571.3 

111.1 

43 

336.7 

65.5 

03 

395.6 

76.9 

63 

454.5 

88.3 

23 

513.4 

99.8 

83 

572.3 

111.3 

44 

337.6 

65.6 

04 

396.  5 

77.1 

64 

455.4 

88.5 

24 

514.3 

100.0 

84 

573.2 

111.5 

45 

338.6 

65.8 

05 

397.5 

77.3 

65 

456.4 

88.7 

25 

515.3 

100.2 

85 

574.2 

111.7 

46 

339.6 

66.0 

06 

398.5 

77.5 

66 

457. 4 

88.9 

26 

516.3 

100.4 

86 

575.2 

111.8 

47 

340.6 

66.2 

07 

399.5 

77.7 

67 

458.4 

89.1 

27 

517.3 

100.6 

87 

576.2 

112.1 

48 

341.6 

66.4 

08 

400.5 

77.9 

68 

459.4 

89.3 

28 

518.3 

100.8 

88 

577.2 

112.3 

49 

342.6 

66.6 

09 

401.5 

78.1 

69 

460.4 

89.5 

29 

519.3 

101.0 

89 

578.2 

112.4 

50 

343.5 

66.8 
67.0 

10 
411 

402.4 
403.4 

78.2 

70 

461.  3 

89.7 

30 

520.2 
521.2 

101.2 

90 

579.1 
580.1 

112.6 

351 

344.5 

78.4 

471 

462.3 

89.9 

531 

101.4 

591 

112.8 

52 

345.5 

67.2 

12 

404.4 

78.6 

72 

463.3 

90.1 

32 

522.2 

101.6 

92 

581.1 

113.0 

53 

346.5 

67.4 

13 

405.4 

78.8 

73 

464.3 

90.3 

33 

523.2 

101.7 

93 

582.1 

113.2 

54 

347.5 

67.5 

14 

406.4 

79.0 

74 

465.3 

90.4 

34 

524.2 

101.8 

94 

583. 1 

113.3 

55 

348.4 

67.7 

15 

407.3 

79.2 

75 

466.2 

90.6 

35 

525.1 

102.0 

95 

584.0 

113.5 

56 

349.4 

67.9 

16 

408.3 

79.4 

76 

467.2 

90.8 

36 

526.1 

102.2 

96 

585. 0 

113.7 

57 

350.4 

68.1 

17 

409.3 

79.6 

77 

468.2 

91.0 

37 

527.1 

102.4 

97 

586.0 

113.9 

58 

351.4 

68.3 

18 

410.3 

79.8 

78 

469.2 

91.2 

38 

.528. 1 

102.6 

98 

587.0 

114.1 

59 

352.4 

68.5 

19 

411.3 

80.0 

79 

470.2 

91.4 

39 

529.1 

102.8 

99 

688.0 

114.3 

60 

353.4 

68.7 

20 

412.3 

80.1 

80 

471.1 

91.6 

40 

530.1 

103.0 

600 

589.0 

114.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

79°  (101°,  259°,  281° 

). 

Page  554] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  12° 

(168°,  192°,  348°). 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.7 

12.7 

121 

118.4 

25.2 

181 

177.0 

37.6 

241 

235.7 

50.1 

2 

2.0 

0.4 

62 

60.6 

12.9 

22 

119.3 

25.4 

82 

178.0 

37.8 

42 

236.7 

50.3 

3 

2.9 

0.6 

63 

61.6 

13.1 

23 

120.3 

25.6 

83 

179.0 

38.0 

43 

237.7 

50.5 

4 

3.9 

0.8 

64 

62.6 

13.3 

24 

121.3 

25.8 

84 

180.0 

38.3 

44 

238.7 

50.7 

5 

4.9 

1.0 

65 

63.6 

13.5 

25 

122.3 

26.0 

85 

181.0 

38.5 

45 

239.6 

50.9 

6 

6.9 

1.2 

66 

64.6 

13.7 

26 

123.2 

26.2 

86 

181.9 

38.7 

46 

240.6 

51.1 

7 

6.8 

1.5 

67 

65.5 

13.9 

27 

124.  2 

26.4 

87 

182.9 

38.9 

47 

241.6 

51.4 

8 

7.8 

1.7 

68 

66.5 

14.1 

28 

125.2 

26.6 

88 

183.9 

39.1 

48 

242.6 

51.6 

9 

8.8 

1.9 

69 

67.5 

14.3 

29 

126.2 

26.8 

89 

184.9 

39.3 

49 

243.6 

51.8 

10 

9.8 

2.1 

70 

68.5 

14.6 

30 

127.  2  j  27.  0 

90 

185.8 

39.5 

50 

244.5 

52.0 

11 

10.8 

2.3 

71 

69.4 

14.8 

131 

128.1 

27.2 

191 

186.8 

39.7 

251 

245.5 

52.2 

12 

11.7 

2.5 

72 

70.4 

15.0 

32 

129.1 

27.4 

92 

187.8 

39.9 

52 

246.5 

52.4 

13 

12.7 

2.7 

73 

71.4 

15.2 

33 

130.1 

27.7 

93 

188.8 

40.1 

53 

247.5 

52.6 

14 

13.7 

2.9 

74 

72.4 

15.4 

34 

131.1     27.9 

94 

189.8 

40.3 

54 

248.4 

52.8 

15 

14.7 

3.1 

75 

73.4 

15.6 

35 

132. 0     28. 1 

95 

190.7 

40.5 

55 

249.4 

53.0 

16 

15.7 

3.3 

76. 

74.3 

15.8 

36 

133.0  1  28.3 

96 

191.7 

40.8 

56 

250.4 

53.2 

17 

16.6 

3.5 

77 

75.3 

16.0 

37 

134.0 

28.5 

97 

192.7 

41.0 

57 

251.4 

53.4 

18 

17.6 

3.7 

78 

76.3 

16.2 

38 

135.0 

28.7 

98 

193.7 

41.2 

58 

252.4 

53.6 

19 

18.6 

4.0 

79 

77.3 

16.4 

39 

136.0 

28.9 

99 

194.7 

41.4 

59 

253.3 

53.8 

20 

19.6 

4.2 

80 

78.3 

16.6 

40 

136.9 

29.1 

200 

195.6 

41.6 

60 

254.3 

54.1 

21 

20.5 

4.4 

81 

79.2 

16.8 

141 

137.9 

29.3 

201 

196.6 

41.8 

261 

255.3 

54.3 

22 

21.5 

4.6 

82 

80.2 

17.0 

42 

138.9 

29.5 

02 

197.6 

42.0 

62 

256.3 

54.5 

23 

22.5 

4.8 

83 

81.2 

17.3 

43 

139.9 

29.7 

03 

198.6 

42.2 

63 

257.3 

54.7 

24 

23.5 

5.0 

84 

82.2 

17.5 

44 

140.9 

29.9 

04 

199.5 

42.4 

64 

258.2 

54.9 

25 

24.5 

5.2 

85 

83.1 

17.7 

45 

141.8 

30.1 

05 

200.5 

42.6 

65 

259.2 

55.1 

26 

25.4 

5.4 

86 

84.1 

17.9 

46 

142.8 

30.4 

06 

201.5 

42.8 

66 

260.2 

55.3 

27 

26.4 

5.6 

87 

85.1 

18.1 

47 

143.8 

30.6 

07 

202.5 

43.0 

67 

261.2 

55.5 

28 

27.4 

5.8 

88 

86.1 

18.3 

48 

144.8 

30.8 

08 

203.5 

43.2 

68 

262.1 

55.7 

29 

28.4 

6.0 

89 

87.1 

18.5 

49 

145.7 

31.0 

09 

204.4 

43.5 

69 

263.1 

55.9 

30 

29.3 

6.2 

90 

88.0 

18.7 

50 

146.7 

31.2 

10 

205.4 

43.7 

70 

264.1 

56.1 

31 

30.3 

6.4 

91 

89.0 

18.9 

151 

147.7 

31.4 

211 

206.4 

43.9 

271 

265.1 

56.3 

32 

31.3 

6.7 

92 

90.0 

19.1 

52 

148.7 

31.6 

12 

207.4 

44.1 

72 

266.1 

56.6 

33 

32.3 

6.9 

93 

91.0 

19.3 

53 

149.7 

31.8 

13 

208.3 

44.3 

73 

267.0 

56.8 

34 

33.3 

7.1 

94 

91.9 

19.5 

54 

150.6 

32.0 

14 

209.3 

44.5 

74 

268.0 

57.0 

35 

34.2 

7.3 

95 

92.9 

19.8 

55 

151.6 

32.2 

15 

210.3 

44.7 

75 

269.0 

57.2 

36 

35.2 

7.5 

96 

93.9 

20.0 

56 

152.6 

32.4 

16 

211.3 

44.9 

76 

270.0 

57.4 

37 

36.2 

7.7 

97 

94.9 

20.2 

57 

153.6 

32.6 

17 

212.3 

45.1 

77 

270.9 

57.6 

38 

37.2 

7.9 

98 

95.9 

20.4 

58 

154.5 

32.9 

18 

213.2 

45.3 

78 

271.9 

57.8 

39 

38.1 

8.1 

99 

96.8 

20.6 

59 

155.5 

33.1 

19 

214.2 

45.5 

79 

272.9 

58.0 

40 

39.1 

8.3 

100 

97.8 

20.8 

60 

156. 5 

33.3 

20 

215.2 

45.7 

80 

273.9 

58.2 

41 

40.1 

8.5 

101 

98.8 

21.0 

161 

157.5 

33.5 

221 

216.2 

45.9 

281 

274.9 

58.4 

42 

41.1 

8.7 

02 

99.8 

21.2 

62 

158.5 

33.7 

22 

217.1 

46.2 

82 

275.8 

58.6 

43 

42.1 

8.9 

03 

100.7 

21.4 

63 

159.4 

33.9 

23 

218.1 

46.4 

83 

276.8 

58.8 

44 

43.0 

9.1 

04 

101.7 

21.6 

64 

160.4 

34.1 

24 

219.1 

46.6 

84 

277.8 

59.0 

45 

44.0 

9.4 

05 

102.7 

21.8 

65 

161.4 

34.3 

25 

220.1 

46.8 

85 

278.8 

59.3 

46 

45.0 

9.6 

06 

103.7 

22.0 

66 

162.4 

34.5 

26 

221.1 

47.0 

86 

279.8 

59.5 

47 

46.0 

9.8 

07 

104.7 

22.2 

67 

163.4 

34.7 

27 

222.0 

47.2 

87 

280.7 

59.7 

48 

47.0 

10.0 

08 

105.7 

22.5 

68 

164.3 

34.9 

28 

223.0 

47.4 

88 

281.7 

59.9 

49 

47.9 

10.2 

09 

106.6 

22.7 

69 

165.3 

35.1 

29 

224.0 

47.6 

89 

282.7 

60.1 

50 

48.9 

10.4 

10 

107.6 

22.9 

70 

166.3 

35.3 

30 
231 

225.0 
226.0 

47.8 
48.0 

90 

283.7 

60.3 

51 

49.9 

10.6 

111 

108.6 

23.1 

171 

167.3 

35.6 

291 

284.6 

60.5 

52 

50.9 

10.8 

12 

109.6 

23.3 

72 

168.2 

35.8 

32 

226.9 

48.2 

92 

285.6 

60.7 

53 

51.8 

11.0 

13 

110.5 

23.5 

73 

169.2 

36.0 

33 

227.9 

48.4 

93 

286.6 

60.9 

54 

52.8 

11.2 

14 

111.5 

23.7 

74 

170.2 

36.2 

34 

228.9 

48.7 

94 

287.6 

61.1 

55 

53.8 

11.4 

15 

112.5 

23.9 

75 

171.2 

36.4 

35 

229.9 

48.9 

95 

288.6 

61.3 

56 

54.8 

11.6 

16 

113.5 

24.1 

76 

172. 2 

36.6 

36 

230.8 

49.1 

96 

289.5 

61.5 

57 

55.8 

11.9 

17 

114.4 

24.3 

77 

173.1 

36.8 

37 

231.8 

49.3 

97 

290.5 

61.7 

58 

56.7 

12.1 

18 

115.4 

24.5 

78 

174.1 

37.0 

38 

232.8 

49.5 

98 

291.5 

62.0 

59 

57.7 

12.3 

19 

116.4 

24.7 

79 

175.1 

37.2 

39 

233.8 

49.7 

99 

292.5 

62.2 

60 

58.7 

12.5 

20 

117.4 

24.9 

80 

176.1 

37.4 

40 

234.8 

49.9 

300 

293.4 

62.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

rs"  (1 

02°,  258°,  282° 

)• 

TABLE  2. 

[Page  655 

Difference  of  latitude  and  Departure  for  12°  (168°,  192°,  348 

°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

294.4 

62.6 

361 

353.1 

75.0 

421 

411.8 

87.5 

481 

470.5 

100.0 

541 

529.2 

112.5 

02 

295.4 

62.8 

62 

354. 1 

75.2 

22 

412.8 

87.7 

82 

471.5 

100.2 

42 

530.2 

112.7 

03 

296.4 

63.0 

63 

355.1 

75.4 

23 

413.8 

87.9 

83 

472.5 

100.4 

43 

531.1 

112.9 

04 

297.4 

63.2 

64 

356.0 

75.7 

24 

414.7 

88.1 

84 

473.4 

100.6 

44 

532. 1 

113.1 

05 

298.3 

63.4 

65 

357.0 

75.9 

25 

415.7 

88.3 

85 

474.4 

100.8 

45 

533.1 

113.3 

06 

299.3 

63.6 

66 

358.0 

76.1 

26 

416.7 

88.6 

86 

475.4 

101.0 

46 

534.1 

113.5 

07 

300.3 

63.8 

67 

359.0 

76.3 

27 

417.7 

88.8 

87 

476.4 

101.2 

47 

535.1 

113.7 

08 

301.3 

64.0 

68 

360.0 

76.5 

28 

418.6 

89.0 

88 

477.3 

101.4 

48 

536.0 

113.9 

09 

302.2 

64.2 

69 

360.9 

76.7 

29 

419.6 

89.2 

89 

478.3 

101.6 

49 

537.0 

114.1 

10 

303.2 

64.4 

70 

361.9 

76.9 

30 

420.6 

89.4 

90 

479.3 

101.9 

50 

538.0 

114.4 

311 

304. 2 

64.6 

371 

362.9 

77.1 

431 

421.6 

89.6 

491 

480.3 

102.1 

551 

538.9 

114.6 

12 

305.2 

64.8 

72 

363.9 

77.3 

32 

422.6 

89.8 

92 

481.2 

102.3 

52 

539.9 

114.3 

13 

306.2 

65.1 

73 

364.8 

77.5 

77.7 

33 

423.5 

90.0 

93 

482.2 

102.5 

53 

540.9 

115.0 

14 

307.1 

65.3 

74 

365.8 

34 

424.5 

90.2 

94 

483.2 

102.7 

54 

541.9 

115.2 

15 

308.1 

65.5 

75 

366.8 

77.9 

35 

425.5 

90.4 

95 

484.2 

102.9 

55 

542.9 

115.4 

16 

309.1 

65.7 

76 

367.8 

78.2 

36 

426.  5 

90.6 

96 

485.2 

103.1 

56 

543.8 

115.6 

17 

310.1 

65.9 

77 

368.8 

78.4 

37 

427.5 

90.8 

97 

486.1 

103.3 

57 

544.8 

115.8 

18 

311.1 

66.1 

78 

369.7 

78.6 

38 

428.4 

91.0 

98 

487.1 

103.5 

58 

545.8 

116.0 

19 

312.0 

66.3 

79 

370.7 

78.8 

39 

429.4 

91.3 

99 

488.1 

103.8 

59 

546.8 

116.2 

20 

313.0 

66.5 

80 

371.7 

79.0 

40 

430.4 

91.5 

500 

489.1 

104.0 

60 

547.8 

116.4 

321 

314.0 

66.7 

381 

372.7 

79.2 

441 

431.4 

91.7 

501 

490.0 

104.2 

561 

548.7 

116.6 

22 

315.0 

66.9 

82 

373.7 

79.4 

42 

432.3 

91.9 

02 

491.0 

104.4 

62 

549.7 

116.8 

23 

315.9 

67.1 

83 

374.6 

79.6 

43 

433.3 

92.1 

03 

492.0 

104.6 

63 

550.7 

117.0 

24 

316.9 

67.3 

84 

375.6 

79.8 

44 

434.3 

92.3 

04 

493.0 

104.8 

64 

551.7 

117.2 

25 

317.9 

67.6 

85 

376.6 

80.0 

45 

435.3 

92.5 

05 

494.0 

105.0 

65 

552.7 

117.4 

26 

318.9 

67.8 

86 

377.6 

80.2 

46 

436.3 

92.7 

06 

495.0 

105.2 

66 

553.7 

117.6 

27 

319.9 

68.0 

87 

378.5 

80.4 

47 

437.2 

92.9 

07 

495.9 

105.4 

67 

554.6 

117.8 

28 

320.8 

68.2 

88 

379.5 

80.7 

48 

438.2 

93.1 

08 

496.9 

105.6 

68 

555.6 

118.0 

29 

321.8 

68.4 

89 

380.5 

80.9 

49 

439.2 

93.3 

09 

497.9 

105.8 

69 

556.6 

118.2 

30 
331 

322.8 
323.8 

68.6 
68.8 

90 
391 

381.5 
382.5 

81.1 

50 

440.2 

93.5 

10 

498.9 

106.0 

70 

557.5 

118.5 

81.3 

451 

441.1 

93.7 

511 

499.8 

106.2 

571 

558.5 

118.7 

32 

324.7 

69.0 

92 

383.4 

81.5 

52 

442.1 

93.9 

12 

500.8 

106.4 

72 

559.5 

118.9 

33 

325.7 

69.2 

93 

384.4 

81.7 

53 

443.1 

94.1 

13 

501.8 

106.6 

73 

560.5 

119.1 

34 

326.7 

69.4 

94 

385.4 

81.9 

54 

444.1 

94.4 

14 

502.8 

106.8 

74 

561.5 

119.3 

35 

327.7 

69.6 

95 

386.4 

82.1 

55 

445.1 

94.6 

15 

503.7 

107.0 

75 

562.4 

119.5 

36 

328.7 

69.8 

96 

387. 3 

82.3 

56 

446.0 

94.8 

16 

504.7 

107.2 

76 

563.4 

119.7 

37 

329.6 

70.0 

97 

388.3 

82.5 

57 

447.0 

95.0 

17 

505.7 

107.4 

77 

564.4 

119.9 

38 

330.6 

70.3 

98 

389.3 

82.7 

58 

448.0 

95.2 

18 

506.7 

107.6 

78 

565.4 

120.1 

39 

331. 6 

70.5 

99 

390.3 

82.9 

59 

449.0 

95.4 

19 

507.7 

107.8 

79 

566.4 

120.3 

40 

332.6 

70.7 

400 

391.3 

83.1 

60 

450.0 

95.6 

20 

508.7 

108.1 

80 

567.4 

120.6 

341 

333.5 

70.9 

401 

392. 2 

83.4 

461 

450.9 

95.8 

521 

509.6 

108.3 

581 

568.3 

120.8 

42 

334.5 

71.1 

02 

393.2 

83.6 

62 

451.9 

96.0 

22 

510.6 

108.5 

82 

569.3 

121.0 

43 

335.5 

71.3 

03 

394.2 

83.8 

63 

452.9 

96.2 

23 

511.6 

108.7 

83 

570.3 

121.2 

44 

336.5 

71.5 

04 

395.2 

84.0 

64 

453.9 

96.5 

24 

512.5 

108.9 

84 

571.2 

121.4 

45 

337.5 

71.7 

05 

396.2 

84.2 

65 

454.8 

96.7 

25 

513.5 

109.2 

85 

572.2 

121.6 

46 

338.4 

71.9 

06 

397.1 

84.4 

66 

455.8 

96.9 

26 

514.5 

109.4 

86 

573.2 

121.8 

47 

339.4 

72.1 

07 

398.1 

84.6 

67 

456. 8 

97.1 

27 

515.5 

109.6 

87 

574.2 

122.0 

48 

340.4 

72.3 

08 

399.1 

84.8 

68 

457.8 

97.3 

28 

516.5 

109.8 

88 

575.2 

122.2 

49 

341.4 

72.5 

09 

400.1 

85.0 

69 

458.8 

97.5 

29 

517.5 

110.0 

89 

576.2 

122.4 

50 

342.4 

72.7 

10 

401.0 

85.2 

70 

459.7 

97.7 

30 

518.4 

110.2 

90 

577.1 

122.6 

351 

343.3 

73.0 

411 

402.0 

85.4 

471 

460.7 

97.9 

531 

519.4 

110.4 

591 

578.1 

122.8 

52 

344.3 

73.2 

12 

403.0 

85.6 

72 

461.7 

98.1 

32 

520.4 

110.6 

92 

579.1 

123.0 

53 

345.3 

73.4 

13 

404.0 

85.8 

73 

462.7 

98.3 

33 

521.3 

110.8 

93 

580.0 

123.2 

54 

346.3 

73.6 

14 

405. 0 

86.1 

74 

463.6 

98.5 

34 

522.3 

111.0 

94 

581.0 

123.4 

55 

347.2 

73.8 

15 

405.9 

86.3 

75 

464.6 

98.7 

35 

523.3 

111.2 

95 

582.0 

123.6 

56 

348.2 

74.0 

16 

406.9 

86.5 

76 

465.6 

98.9 

36 

524.3 

111.4 

96 

583.0 

123.9 

57 

349.2 

74.2 

17 

407.9 

86.7 

77 

466.6 

99.1 

37 

525.3 

111.6 

97 

584.0 

124.1 

58 

350.2 

74.4 

18 

408.9 

86.9 

78 

467.6 

99.4 

38 

526.2 

111.8 

98 

584.9 

124.3 

59 

351.2 

74.6 

19 

409.8 

87.1 

79 

468.5 

99.6 

39 

527.2 

112.0 

99 

585.9 

124.5 

60 

352.1 

74.8 

20 

410.8 

87.3 

80 

469.5 

99.8 

40 

528.2 

112. 3 

600 

586.9 

124.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat. 

Dist. 

Dep. 

Lat. 

78°   (1 

02°,  258 

°,  282° 

)■ 

Page  656] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  13°  (167°,  193°,  347° 

)• 

Dist. 

J^t. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.4 

13.7 

121 

117.9 

27.2 

181 

176.4 

40.7 

241 

234.8 

54.2 

2 

1.9 

0.4 

62 

60.4 

13.9 

22 

118.9 

27.4 

82 

177.3 

40.9 

42 

235.8 

54.4 

3 

2.9 

0.7 

63 

61.4 

14.2 

23 

119.8 

27.7 

83 

178.3 

41.2 

43 

236.8 

54.7 

4 

3.9 

0.9 

64 

62.4 

14.4 

24 

120.8 

27.9 

84 

179.3 

41.4 

44 

237.7 

54.9 

5 

4.9 

1.1 

65 

63.3 

14.6 

25 

121.8 

28.1 

85 

180.3 

41.6 

45 

238.7 

55.1 

6 

5.8 

1.3 

66 

64.3 

14.8 

26 

122.8 

28.3 

86 

181.2 

41.8 

46 

239.7 

55.3 

7 

6.8 

1.6 

67 

65.3 

15.1 

27 

123.7 

28.6 

87 

182.2 

42.1 

47 

240.7 

55.6 

8 

7.8 

1.8 

68 

66.3 

15.3 

28 

124.7 

28.8 

88 

183.2 

42.3 

48 

241.6 

55.8 

9 

8.8 

2.0 

69 

67.2 

15.5 

29 

125.7 

29.0 

89 

184.2 

42.5 

49 

242.6 

56.0 

10 

9.7 

2.2 

70 

68.2 

15.7 

30 

126.7 

29.2 
29.5 

90 

185.1 

42.7 

50 

243.  6 

56.2 

11 

10.7 

2.5 

71 

69.2 

16.0 

131 

127.6 

191 

186.1 

43.0 

251 

244.6 

56.5 

12 

11.7 

2.7 

72 

70.2 

16.2 

32 

128.6 

29.7 

92 

187.1 

43.2 

52 

245.5 

56.7 

13 

12.7 

2.9 

73 

71.1 

16.4 

33 

129.6 

29.9 

93 

188.1 

43.4 

53 

246.5 

56.9 

14 

13.6 

3.1 

74 

72.1 

16.6 

34 

130.6 

30.1 

^4 

189.0 

43.6 

54 

247.5 

57.1 

15 

14.6 

3.4 

75 

73.1 

16.9 

35 

131.5 

30.4 

95 

190.0 

43.9 

55 

248.5 

57.4 

16 

15.6 

3.6 

76 

74.1 

17.1 

36 

132.5 

30.6 

96 

191.0 

44.1 

56 

249.4 

57.6 

17 

16.6 

3.8 

77 

75.0 

17.3 

37 

133.5 

30.8 

97 

192.0 

44.3 

57 

250.  4 

57.8 

18 

17.5 

4.0 

78 

76.0 

17.5 

38 

134.5 

31.0 

98 

192.9 

44.5 

58 

251.4 

58.0 

19 

18.5 

4.3 

79 

77.0 

17.8 

39 

135.4 

31.3 

99 

193.9 

44.8 

59 

252.4 

58.3 

20 

19.5 

4.5 

80 

77.9 

18.0 

40 

136.4 

31.5 

200 

194.9 
195.8 

45.0 

60 

253.3 

58.5 

21 

20.5 

4.7 

81 

78.9 

18.2 

141 

137.4 

31.7 

201 

45.2 

261 

254.3 

58.7 

22 

21.4 

4.9 

82 

79.9 

18.4 

42 

138.4 

31.9 

02 

196.8 

45.4 

62 

255.3 

58.9 

23 

22.4 

5.2 

83 

80.9 

18.7 

43 

139.3 

32.2 

03 

197.8 

45.7 

63 

256.3 

59.2 

24 

23.4 

5.4 

84 

81.8 

18.9 

44 

140.3 

32.4 

04 

198.8 

45.9 

64 

257.2 

59.4 

25 

24.4 

5.6 

85 

82.8 

19.1 

45 

141.3 

32.6 

05 

199.7 

46.1 

65 

258.2 

59.6 

26 

25.3 

5.8 

86 

83.8 

19.3 

46 

142.3 

32.8 

06 

200.7 

46.3 

66 

259.2 

59.8 

27 

26.3 

6.1 

87 

84.8 

19.6 

47 

143.2 

33.1 

07 

201.7 

46.6 

67 

260.2 

60.1 

28 

27.3 

6.3 

88 

85.7 

19.8 

48 

144.2 

33.3 

08 

202.7 

46.8 

68 

261.1 

60.3 

29 

28.3 

6.5 

89 

86.7 

20.0 

49 

145.2 

33.5 

09 

203.  6 

47.0 

69 

262.1 

60.5 

30 

29.2 

6.7 

90 

87.7 

20.2 

50 

146.2 

33.7 

10 

204.6 

47.2 

70 

263.1 

60.7 

31 

30.2 

7.0 

91 

88.7 

20.5 

151 

147.1 

34.0 

211 

205.6 

47.5 

271 

264.1 

61.0 

32 

31.2 

7.2 

92 

89.6 

20.7 

62 

148.1 

34.2 

12 

206.6 

47.7 

72 

265.0 

61.2 

33 

32.2 

7.4 

93 

90.6 

20.9 

53 

149.1 

34.4 

13 

207.5 

47.9 

73 

266.  0 

61.4 

34 

33.1 

7.6 

94 

91.6 

21.1 

54 

150. 1 

34.6 

14 

208.5 

48.1 

74 

267.0 

61.6 

35 

34.1 

7.9 

95 

92.6 

21.4 

55 

151.0 

34.9 

15 

209.5 

48.4 

75 

268.0 

61.9 

36 

35.1 

8.1 

96 

93.5 

21.6 

56 

152.0 

35.1 

16 

210.5 

48.6 

76 

268.9 

62.1 

37 

36.1 

8.3 

97 

94.5 

21.8 

57 

153.0 

35.3 

17 

211.4 

48.8 

77 

269.9 

62.3 

38 

37.0 

8.5 

98 

95.5 

22.0 

58 

154.0 

35.5 

18 

212.4 

49.0 

78 

270.9 

62.5 

39 

38.0 

8.8 

99 

96.5 

22.3 

59 

154.9 

35.8 

19 

213.4 

49.3 

79 

271.8 

62.8 

40 

39.0 

9.0 

100 

97.4 

22.5 

60 

155.9 

36.0 

20 

214.4 

49.5 

80 

272.8 

63.0 

41 

39.9 

9.2 

101 

98.4 

22.7 

161 

156.9 

36.2 

221 

215.3 

49.7 

281 

273.8 

63.2 

42 

40.9 

9.4 

02 

99.4 

22.9 

62 

157.8 

36.4 

22 

216.3 

49.9 

82 

274.8 

63.4 

43 

41.9 

9.7 

03 

100.4 

23.2 

63 

158.8 

36.7 

23 

217.3 

50.2 

83 

275.7 

63.7 

44 

42.9 

9.9 

04 

101.3 

23.4 

64 

159.8 

36.9 

24 

218.3 

50.4 

84 

276.7 

63.9 

45 

43.8 

10.1 

05 

102.3 

23.6 

65 

160.8 

37.1 

25 

219.2 

50.6 

85 

277.7 

64.1 

46 

44.8 

10.3 

06 

103.3 

23.8 

66 

161.7 

37.3 

26 

220.2 

50.8 

86 

278.7 

64.3 

47 

45.8 

10.6 

07 

104.3 

24.1 

67 

162.7 

37.6 

27 

221.2 

51.1 

87 

279.6 

64.6 

48 

46.8 

10.8 

08 

105.2 

24.3 

68 

163.7 

37.8 

28 

222.2 

51.3 

88 

280.6 

64.8 

49 

47.7 

11.0 

09 

106.2 

24.5 

69 

164.7 

38.0 

29 

223.1 

51.5 

89 

281.6 

65.0 

50 

48.7 
49.7 

11.2 

10 

107.2 

24.7 

70 

165. 6 

38.2 

30 

224.1 

51.7 

90 

282.6 

65.2 

51 

11.5 

111 

108.2 

25.0 

171 

166.6 

38.5 

231 

225.1 

52.0 

291 

283.5 

65.5 

52 

50.7 

11.7 

12 

109.1 

25.2 

72 

167. 6 

38.7 

32 

226.1 

52.2 

92 

284.5 

65.7 

53 

51.6 

11.9 

13 

110.1 

25.4 

73 

168.6 

38.9 

33 

227.0 

52.4 

93 

285.5 

65.9 

54 

52.6 

12.1 

14 

111.1 

25.6 

74 

169.5 

39.1 

34 

228.0 

52.6 

94 

286.5 

66.1 

55 

53.6 

12.4 

15 

112.1 

25.9 

75 

170. 5 

39.4 

35 

229.0 

52.9 

95 

287.4 

66.4 

56 

54.6 

12.6 

16 

113.0 

26.1 

76 

171.5 

39.6 

36 

230.0 

53.1 

96 

288.4 

66.6 

57 

55.5 

12.8 

17 

114.0 

26.3 

77 

172.5 

39.8 

37 

230.9 

53.3 

97 

289.4 

66.8 

58 

56.5 

13.0 

18 

115.0 

26.5 

78 

173.4 

40.0 

38 

231.9 

53.5 

98 

290.4 

67.0 

59 

57.5 

13.3 

19 

116.0 

26.8 

79 

174.4 

40.3 

39 

232.9 

53.8 

99 

291.3 

67.3 

60 

58.5 

13.5 

20 

116.9 

27.0 

80 

175.4 

40.5 

40 

233.8 

54.0 

300 

292.3 

67.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

77°  (1 

03°,  257 

°,  283°). 

TABLE  2. 

[Page  657     | 

Difference  of  Latitude  and  Departure  for  13°  (167°,  193 

°,  347° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

293.  3 

67.7 

361 

351.8 

81.2 

421 

410.2 

94.7 

481 

468.7 

108.2 

541 

527.2 

121.7 

02 

294.3 

67.9 

62 

352.7 

81.4 

22 

411.2 

94.9 

82 

469.7 

108.4 

42 

528.1 

121.9 

03 

295.  2 

68.1 

63 

353.7 

81.6 

23 

412.2 

95.1 

83 

470.6 

108.6 

43 

529.1 

122.1 

04 

296.2 

68.4 

64 

354.7 

81.9 

24 

413.1 

95.3 

84 

471.6 

108.8 

44 

530.1 

122.3 

05 

297.2 

68.6 

65 

355.6 

82.1 

25 

414.1 

95.6 

85 

472.6 

109.0 

45 

531.1 

122.5 

06 

298.2 

68.8 

66 

356. 6 

82.3 

26 

415.1 

95.8 

86 

473.6 

109.3 

46 

532.0 

122.8 

07 

299.1 

69.0 

67 

357.6 

82.5 

27 

416.1 

96.0 

87 

474.5 

109.5 

47 

533.0 

123.0 

08 

300.1 

69.3 

68 

358.6 

82.8 

28 

417.0 

96.2 

88 

475.5 

109.7 

48 

534.0 

123.2 

09 

301.1 

69.5 

69 

359.5 

83.0 

29 

418.0 

96.5 

89 

476.5 

109.9 

49 

535.0 

123.4 

10 

302.1 

69.7 

70 

360.5 

83.2 

30 

419.0 

96.7 

90 

477.5 

110.1 

50 

535.9 

123.7 

311 

303.0 

69.9 

371 

361.5 

83.4 

431 

420.0 

96.9 

491 

478.4 

110.4 

551 

536. 9 

123.9 

12 

304.0 

70.2 

72 

362.5 

83.7 

32 

420.9 

97.1 

92 

479.4 

110.6 

52 

537.9 

124.1 

13 

305.0 

70.4 

73 

363.  4 

83.9 

33 

421.9 

97.4 

93 

480.4 

110.9 

53 

538.9 

124.4 

14 

306.0 

70.6 

74 

364.4 

84.1 

34 

422.9 

97.6 

94 

481.4 

111.1 

54 

539.8 

124.6 

15 

306.9 

70.8 

75 

365.4 

84.3 

35 

423.9 

97.8 

95 

482.3 

111.3 

55 

540.8 

124.9 

16 

307.9 

71.1 

76 

366.4 

84.6 

36 

424.8 

98.0 

96 

483.3 

111.5 

56 

541.8 

125. 1 

17 

308.9 

71.3 

77 

367.3 

84.8 

37 

425.8 

98.3 

97 

484.3 

111.8 

57 

542.8 

125.3 

18 

309.9 

71.5 

78 

368.3 

85.0 

38 

426.8 

98.5 

98 

485.3 

112.0 

58 

543.7 

125.5 

19 

310.8 

71.7 

79 

369.3 

85.2 

39 

427.8 

98.7 

99 

486.2 

112.2 

59 

544.7 

125.8 

20 

311.8 

72.0 

80 

370.3 

85.5 

40 

428.7 

98.9 

500 

487.2 

112.4 

60 

545.7 

126.0 

321 

312.8 

72.2 

381 

371.2 

85.7 

441 

429.7 

99.2 

501 

488.2 

112.6 

561 

546.7 

126.2 

22 

313.8 

72.4 

82 

372.2 

85.9 

42 

430.7 

99.4 

02 

489.2 

112.9 

62 

547.6 

126.4 

23 

314.7 

72.6 

83 

373.2 

86.1 

43 

431.6 

99.6 

03 

490.1 

113.1 

63 

548.6 

126.7 

24 

315.7 

72.9 

84 

374.2 

86.4 

44 

432.6 

99.8 

04 

491.1 

113.3 

64 

549.6 

126.9 

25 

316.7 

73.1 

85 

375.1 

86.6 

45 

433.6 

100.1 

05 

492.1 

113.5 

65 

550.6 

127.1 

26 

317.6 

73.3 

86 

376.1 

86.8 

46 

434.6 

100.3 

06 

493.1 

113.8 

66 

551.5 

127.3 

27 

318.6 

73.5 

87 

377.1 

87.0 

47 

435.5 

100.5 

07 

494.0 

114.0 

67 

552.5 

127.6 

28 

319.6 

73.8 

88 

378.1 

87.3 

48 

436.5 

100.7 

08 

495.0 

114.2 

68 

553.5 

127.8 

29 

320.6 

74.0 

89 

379.0 

87.5 

49 

437.5 

101.0 

09 

496.0 

114.5 

69 

554.5 

128.0 

30 

821.5 

74.2 

90 

380.0 

87.7 

50 

438.5 

101.2 

10 

496.9 

114.7 

70 

555.4 

128.3 

331 

322.5 

74.4 

391 

381.0 

87.9 

451 

439.4 

101.4 

511 

497.9 

114.9 

571 

556.4 

128.5 

32 

323.5 

74.7 

92 

382.0 

88.2 

52 

440.4 

101.6 

12 

498.9 

115.1 

72 

557.4 

128.7 

33 

324.5 

74.9 

93 

382.9 

88.4 

53 

441.4 

101.9 

13 

499.9 

115.4 

73 

558.4 

128.9 

34 

325.  4 

75.1 

94 

383.9 

88.6 

54 

442.4 

102.1 

14 

500.8 

115.6 

74 

559.3 

129.2 

35 

326,4 

75.3 

95 

384.9 

88.8 

55 

443.3 

102.3 

15 

501.8 

115.8 

75 

560.3 

129.4 

36 

327.4 

75.6 

96 

385.9 

89.1 

56 

444.3 

102.5 

16 

502.8 

116.0 

76 

561.3 

129.6 

37 

328.4 

75.8 

97 

386.8 

89.3 

57 

445.3 

102.8 

17 

503.8 

116.3 

77 

562.3 

129.8 

38 

329.3 

76.0 

98 

387.8 

89.5 

58 

446.3 

103.0 

18 

504.7 

116.5 

78 

563.2 

130.0 

39 

330.3 

76.2 

99 

388.8 

89.7 

59 

447.2 

103.2 

19 

505.7 

116.7 

79 

564.2 

130.2 

40 

331.3 

76.5 

400 

389.8 

90.0 

60 

448.2 

103.4 
103.7 

20 
521 

506.7 

116.9 

80 

565.2 
566.2 

130.4 

341 

332.3 

76.7 

401 

390.7 

90.2 

461 

449.2 

507.7 

117.2 

581 

130.7 

42 

333.2 

76.9 

02 

391.7 

90.4 

62 

450.2 

103. 9 

22 

508.6 

117.5 

82 

567.1 

131.0 

43 

334.2 

77.1 

03 

392.7 

90.6 

63 

451.1 

104.1 

23 

509.6 

117.7 

83 

568.1 

131.2 

44 

335.2 

77.4 

04 

393.6 

90.8 

64 

452.1 

104.3 

24 

510.6 

117.9 

84 

569.1 

131. 4 

45 

336.2 

77.6 

05 

394.6 

91.1 

65 

453.1 

104.6 

25 

511.6 

118.1 

85 

570.1 

131.6 

46 

337.1 

77.8 

06 

395.6 

91.3 

66 

454.1 

104.8 

26 

512.5 

118.3 

86 

571.0 

131.8 

47 

338.1 

78.0 

07 

396.6 

91.5 

67 

455.0 

105.0 

27 

513.5 

118.5 

87 

572.0 

132. 0 

48 

339.1 

78.3 

08 

397.5 

91.7 

68 

456.0 

105.2 

28 

514.5 

118.7 

88 

573.0 

132.3 

49 

340.1 

78.5 

09 

398.5 

92.0 

69 

457.0 

105.5 

29 

515.5 

119.0 

89 

573.9 

132.5 

50 

341.0 

78.7 

10 

399.5 

92.2 

70 

458.0 

105.7 

30 

516.4 

119.2 

90 

574.9 

132.8 

351 

342.0 

78.9 

411 

400.5 

92.4 

471 

458.9 

105.9 

531 

517.4 

119.4 

591 

575.9 

133.0 

52 

343.0 

79.2 

12 

401.4 

92.6 

72 

459.9 

106.1 

32 

518.4 

119.6 

92 

576.9 

133.2 

53 

344.0 

79.4 

13 

402.4 

92.9 

73 

460.9 

106.4 

33 

519.4 

119.9 

93 

577.8 

133.4 

54 

344.9 

79.6 

14 

403.4 

93.1 

74 

461.9 

106.6 

34 

520.3 

120.1 

94 

578.8 

133.6 

55 

345.9 

79.8 

15 

404.4 

93.3 

75 

462.8 

106.8 

35 

521.3 

120.3 

95 

579.8 

133.8 

56 

346.9 

80.1 

16 

405.3 

93.5 

76 

463.8 

107.0 

36 

522.3 

120.5 

96 

580.8 

134.0 

57 

347.9 

80.3 

17 

406.3 

93.8 

77 

464.8 

107.3 

37 

523.3 

120.8 

97 

581.7 

134.3 

58 

348.8 

80.5 

18 

407.3 

94.0 

78 

465.8 

107.5 

38 

524.2 

121.0 

98 

582.7 

134.5 

59 

349.8 

80.7 

19 

408.3 

94.2 

79 

466.7 

107.7 

39 

525.2 

121.2 

99 

583.7 

134.8 

60 

350.8 

81.0 

20 

409.2 

94.4 

80 

467.7 

107.9 

40 

526.2 

121.5 

600 

584.6 

135.0 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

77°  (103°,  257 

°,  283° 

)• 

1     Page  668] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  14°  (166°,  194°,  346° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     1   Dep. 

Dist. 

Lat. 

Dep. 

1 

10 

0.2 

61 

59.2 

14.8 

121 

117.4 

29.3 

181 

175.6 

43.8 

241 

233.8 

58.3 

2 

1.9 

0.5 

62 

60.2 

15.0 

22 

118.4 

29.5 

82 

176.6 

44.0 

42 

234.8 

58.5 

3 

2.9 

0.7 

63 

61.1 

15.2 

23 

119.3 

29.8 

83 

177.6 

44.3 

43 

235.8 

58.8 

4 

3.9 

1.0 

64 

62.1 

15.5 

24 

120.3 

30.0 

84 

178.5 

44.5 

44 

236.8 

59.0 

5 

4.9 

1.2 

65 

63.1 

15.7 

25 

121.3 

30.2 

85 

179.5 

44.8 

45 

237.7 

59.3 

6 

5.8 

1.5 

66 

64.0 

16.0 

26 

122.3 

30.5 

86 

180.5 

45.0 

46 

238.7 

59.5 

7 

6.8 

1.7 

67 

65.0 

16.2 

27 

123.2 

30.7 

87 

181.4 

45.2 

47 

239.7 

59.8 

8 

7.8 

1.9 

68 

66.0 

16.5 

28 

124.2 

31.0 

88 

182.4 

45.5 

48 

240.6 

60.0 

9 

8.7 

2.2 

69 

67.0 

16.7 

29 

125.2 

31.2 

89 

183.4 

45.7 

49 

241.6 

60.2 

10 

9.7 

2.4 

70 

67.9 

16.9 

30 

126.1 

31.4 

90 

184.4 

46.0 

50 

242.6 

60.5 

11 

10.7 

2.7 

71 

68.9 

17.2 

131 

127.1 

31.7 

191 

185.  3 

46.2 

251 

243.5 

60.7 

12 

11.6 

2.9 

72 

69.9 

17.4 

32 

128.1 

31.9 

92 

186.3 

46.4 

52 

244.5 

61.0 

13 

12.6 

3.1 

73 

70.8 

17.7 

33 

129.0 

32.2 

93 

187.3 

46.7 

53 

245.5 

61.2 

14 

13.6 

3.4 

74 

71.8 

17.9 

34 

130.0 

32.4 

94 

188.2 

46.9 

54 

246.5 

61.4 

15 

14.6 

3.6 

75 

72.8 

18.1 

35 

131.0 

32.7 

95 

189.2 

47.2 

55 

247.4 

61.7 

16 

15.5 

3.9 

76 

73.7 

18.4 

36 

132.0 

32.9 

96 

190.2 

47.4 

56 

248.4 

61.9 

17 

16.5 

4.1 

77 

74.7 

18.6 

37 

132.9 

33.1 

97 

191.1 

47.7 

57 

249.4 

62.2 

18 

17.5 

4.4 

78 

75.7 

18.9 

38 

133.9 

33.4 

98 

192..1 

47.9 

58 

250.3 

62.4 

19 

18.4 

4.6 

79 

76.7 

19.1 

39 

134.9 

33.6 

99 

193.1 

48.1 

59 

251.3 

62.7 

20 

19.4 

4.8 

80 

77.6 

19.4 

40 

135.8 

33.9 

200 

194.1 

48.4 

60 

252.3 

62.9 

21 

20.4 

5.1 

81 

78.6 

19.6 

141 

136.8 

34.1 

201 

195.0 

48.6 

261 

253.2 

63.1 

22 

21.3 

5.3 

82 

79.6 

19.8 

42 

137.8 

34.4 

02 

196.0 

48.9 

62 

254.2 

63.4 

23 

22.3 

5.6 

83 

80.5 

20.1 

43 

138.8 

34.6 

03 

197.0 

49.1 

63 

255.2 

63.6 

24 

23.3 

5.8 

84 

81.5 

20.3 

44 

139.7 

34.8 

04 

197.9 

49.4 

64 

256.2 

63.9 

25 

24.3 

6.0 

85 

82.5 

20.6 

45 

140.7 

35.1 

05 

198.9 

49.6 

65 

257.1 

64.1 

26 

25.2 

6.3 

86 

83.4 

20.8 

46 

141.7 

35.3 

06 

199.9 

49.8 

66 

258.1 

64.4 

27 

26.2 

6.5 

87 

84.4 

21.0 

47 

142.6 

35.6 

07 

200.9 

50.1 

67 

259.1 

64.6 

28 

27.2 

6.8 

88 

85.4 

21.3 

48 

143.6 

35.8 

08 

201.8 

50.3 

68 

260.0 

64.8 

29 

28.1 

7.0 

89 

86.4 

21.5 

49 

144.  6 

36.0 

09 

202.8 

50.6 

69 

261.0 

65.1 

30 

29.1 

7.3 

90 

87.3 

21.8 

50 

145.  5 

36.3 
36.5 

10 
211 

203.8 
204.7 

50.8 
51.0 

70 
271 

262.0 

65.3 

31 

30.1 

7.5 

91 

88.3 

22.0 

151 

146.5 

263.0 

65.6 

32 

31.0 

7.7 

92 

89.3 

22.3 

52 

147.5 

36.8 

12 

205.7 

51.3 

72 

263.9 

65.8 

33 

32.0 

8.0 

93 

90.2 

22.5 

53 

148.5 

37.0 

13 

206.7 

51.5 

73 

264.9 

66.0 

34 

33.0 

8.2 

94 

91.2 

22.7 

54 

149.4 

37.3 

14 

207.6 

51.8 

74 

265.9 

66.3 

35 

34.0 

8.5 

95 

92.2 

23.0 

55 

150.4 

37.5 

15 

208.6 

52.0 

75 

266.8 

66.5 

36 

34.9 

8.7 

96 

93.1 

23.2 

56 

151.4 

37.7 

16 

209.6 

52.3 

76 

267.8 

66.8 

37 

35.9 

9.0 

97 

94.1 

23.5 

57 

152.3 

38.0 

17 

210.6 

52.5 

77 

268.8 

67.0 

38 

36.9 

9.2 

98 

95.1 

23.7 

58 

153.3 

38.2 

18 

211.5 

52.7 

78 

269.7 

67.3 

39 

37.8 

9.4 

99 

96.1 

24.0 

59 

154.3 

38.5 

19 

212.5 

53.0 

79 

270.7 

67.5 

40 

38.8 

9.7 

100 

97.0 

24.2 

60 

155.2 

38.7 

20 

213.5 

53.2 

80 

271.7 

67.7 

41 

39.8 

9.9 

101 

98.0 

24.4 

161 

156.2 

38.9 

221 

214.4 

53.5 

281 

272.7 

68.0 

42 

40.8 

10.2 

02 

99.0 

24.7 

62 

157.2 

39.2 

22 

215.4 

53.7 

82 

273.6 

68.2 

43 

41.7 

10.4 

03 

99.9 

24.9 

63 

158.2 

39.4 

23 

216.4 

53.9 

83 

274.6 

68.5 

44 

42.7 

10.6 

04 

100.9 

25.2 

64 

159.1 

39.7 

24 

217.3 

54.2 

84 

275.6 

68.7 

45 

43.7 

10.9 

05 

101.9 

25.4 

65 

160.1 

39.9 

25 

218.3 

54.4 

85 

276.5 

68.9 

46 

44.6 

11.1 

06 

102.9 

25.6 

66 

161.1 

40.2 

26 

219.3 

54.7 

86 

277.5 

69.2 

47 

45.6 

11.4 

07 

103.8 

25.9 

67 

162.0 

40.4 

27 

220.3 

54.9 

87 

278.5 

69.4 

48 

46.6 

11.6 

08 

104.8 

26.1 

68 

163.0 

40.6 

28 

221.2 

55.2 

88 

279.4 

69.7 

49 

47.5 

11.9 

09 

105.8 

26.4 

69 

164.0 

40.9 

29 

222.2 

55.4 

89 

280.4 

69.9 

50 

48.5 

12.1 

10 

106.7 

26.6 

70 

165.0 

41.1 

30 

223.2 

55.6 

90 

281.4 
282.4 

70.2 

51 

49.5 

12.3 

111 

107.7 

26.9 

171 

165.9 

41.4 

231 

224.1 

65.9 

291 

70.4 

52 

50.5 

12.6 

12 

108.7 

27.1 

72 

166.9 

41.6 

32 

225.1 

56.1 

92 

283.3 

70.6 

53 

51.4 

12.8 

13 

109.6 

27.3 

73 

167.9 

41.9 

33 

226.1 

56.4 

93 

284.3 

70.9 

54 

52.4 

13.1 

14 

110.6 

27.6 

74 

168.8 

42.1 

34 

227.0 

56.6 

94 

285.3 

71.1 

55 

53.4 

13.3 

15 

111.6 

27.8 

75 

169.8 

42.3 

35 

228.0 

56.9 

95 

286.2 

71.4 

56 

54.3 

13.5 

16 

112.6 

28.1 

76 

170.8 

42.6 

36 

229.0 

57.1 

96 

287.2 

71.6 

57 

55.3 

13.8 

17 

113.5 

28.3 

77 

171.7 

42.8 

37 

230.0 

57.3 

97 

288.2 

71.9 

58 

56.3 

14.0 

18 

114.5 

28.5 

78 

172.7 

43.1 

38 

230.9 

57.6 

98 

289.1 

72.1 

59 

57.2 

14.3 

19 

115.5 

28.8 

79 

173.7 

43.3 

39 

231.9 

57.8 

99 

290.1 

72.3 

60 

58.2 

14.5 

20 

116.4 

29.0 

80 

174.7 

43.5 

40 

232.9 

58.1 

300 

291.1 

72.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

/ 

'6°  (1( 

)4°,  256 

\  284° 

. 

TABLE  2. 

[Page  669     | 

Difference  of  Latitude  and  Departure  for  14°  (166°,  194°,  346° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

292.0 

72.8 

361 

350.2 

87.3 

421 

408.5 

101.8 

481 

466.7 

116.3 

541 

525.0 

130.9 

02 

293.0 

73.0 

62 

351.2 

87.6 

22 

409.4 

102.1 

82 

467.7 

116.6 

42 

525.9 

131.2 

03 

294.0 

73.3 

63 

352.2 

87.8 

23 

410.4 

102.3 

83 

468.6 

116.8 

43 

526.9 

131.4 

04 

294.9 

73.5 

64 

■  353. 2 

88.0 

24 

411.4 

102.6 

84 

469.6 

117.1 

44 

527.9 

131.6 

05 

295.9 

73.8 

65 

354.1 

88.3 

25 

412.3 

102.8 

85 

470.6 

117.3 

45 

528.8 

131.9 

06 

296.9 

74.0 

66 

355.1 

88.5 

26 

413.3 

103.  0 

86 

471.5 

117.6 

46 

529.8 

132.1 

07 

297.8 

74.2 

67 

356.1 

88.8 

27 

414.3 

103.3 

87 

472.5 

117.8 

47 

530.8 

132.3 

08 

298.8 

74.5 

68 

357.0 

89.0 

28 

415.3 

103.5 

88 

473.5 

118.0 

48 

531.7 

132.6 

09 

299.8 

74.7 

69 

358.0 

89.2 

29 

416.2 

103.8 

89 

474.5 

118.3 

49 

532.7 

132.8 

10 

300.8 

75.0 

70 

359.0 

89.5 

30 

417.2 

104.0 

90 

475.4 

118.5 

50 

533.7 

133.0 

311 

301.7 

75.2 

371 

359.9 

89.7 

431 

418.2 

104.2 

491 

476.4 

118.8 

551 

534.6 

133.3 

12 

302.7 

75.5 

72 

360.9 

90.0 

32 

419.1 

104.5 

92 

477.4 

119.0 

52 

535.6 

133.6 

13 

303.7 

75.7 

73 

361.9 

90.2 

33 

420.1 

104.7 

93 

478.3 

119.2 

53 

536.6 

133.8 

14 

304.6 

75.9 

74 

362.9 

90.5 

34 

421.1 

105.0 

94 

479.3 

119.5 

54 

537.5 

134.0 

15 

305.6 

76.2 

75 

363.8 

90.7 

35 

422.0 

105.  2 

95 

480.3 

119.7 

55 

538.5 

134.3 

16 

306.6 

76.4 

76 

364.8 

90.9 

36 

423.0 

105.5 

96 

481.3 

120.0 

56 

539.5 

134.5 

17 

307.6 

76.7 

77 

365.8 

91.2 

37 

424.0 

105.7 

97 

482.2 

120.2 

57 

540.5 

134.8 

18 

308.5 

76.9 

78 

366.7 

91.4 

38 

425.0 

105.9 

98 

483.2 

120.4 

58 

541.4 

135.0 

19 

309.5 

77.2 

79 

367.7 

91.7 

39 

425.9 

106.2 

99 

484.2 

120.7 

59 

542.4 

135.2 

20 

310.5 

77.4 

80 

368.7 

91.9 

40 

426.9 

106.4 

500 

485.1 

121.0 

60 

543.4 

135.5 
135.7 

321 

311.4 

77.6 

381 

369.6 

92.2 

441 

427.9 

106.7 

501 

486.1 

121.2 

561 

544.3 

22 

312.4 

77.9 

82 

370.6 

92.4 

42 

428.8 

106.9 

02 

487.1 

121.4 

62 

545.3 

135.9 

23 

313.4 

78.1 

83 

371.6 

92.6 

43 

429.8 

107.1 

03 

488.0 

121.7 

63 

546.3 

136.2 

24 

314.3 

78.4 

84 

372.6 

92.9 

44 

430.8 

107.4 

04 

489.0 

122.0 

64 

547.2 

136.5 

25 

315.3 

78.6 

85 

373.5 

93.1 

45 

431.7 

107.6 

05 

490.0 

122.1 

65 

548.2 

136.6 

26 

316.3 

78.8 

86 

374.5 

93.4 

46 

432.7 

107.9 

06 

491.0 

122.4 

66 

549.2 

136.9 

27 

317.3 

79.1 

87 

375.5 

93.6 

47 

433.7 

108.1 

07 

491.9 

122.6 

67 

550.1 

137.1 

28 

318.2 

79.3 

88 

376.4 

93.8 

48 

434.7 

108.4 

08 

492.9 

122.9 

68 

551.1 

137.4 

29 

319.2 

79.6 

89 

377.4 

94.1 

49 

435.6 

108.6 

09 

493.9 

123.1 

69 

552.1 

137.6 

30 

320.2 

79.8 

90 

378.4 

94.3 

50 

436.6 

108.8 

10 

494.9 

123.4 

70 

553.1 

137.9 

331 

321.1 

80.1 

391 

379.4 

94.6 

451 

437.6 

109.1 

511 

495.8 

123.6 

571 

554.0 

138.1 

32 

322.1 

80.3 

92 

380.3 

94.8 

52 

438,5 

109.3 

12 

496.8 

123.8 

72 

555.0 

138.3 

33 

323.1 

80.5 

93 

381.3 

95.1 

53 

439.5 

109.6 

13 

497.8 

124.1 

73 

556.0 

138.6 

34 

324.0 

80.8 

94 

382.3 

95.3 

54 

440.5 

109.8 

14 

498.7 

124.3 

74 

557.0 

138.8 

35 

325.0 

81.0 

95 

383.2 

95.5 

55 

441.5 

110.1 

15 

499.7 

124.6 

75 

557.9 

139.1 

36 

326.0 

81.3 

96 

384.2 

95.8 

56 

442.4 

110.3 

16 

500.7 

124.8 

76 

558.9 

139.3 

37 

327.0 

81.5 

97 

385.2 

96.0 

57 

443.4 

110.5 

17 

501.7 

125.0 

77 

559.9 

139.5 

38 

327.9 

81.7 

98 

386.1 

96.3 

58 

444.4 

110.8 

18 

502.6 

125.3 

78 

560.9 

139.8 

39 

328.9 

82.0 

99 

387.1 

96.5 

59 

445.3 

111.0 

19 

503.6 

125.6 

79 

561.8 

140.0 

40 
341 

329.9 

82.2 

400 

388.1 

96.7 

60 

446.3 

111.3 

20 

504.6 

125.8 

80 

562.8 

140.3 

330.8 

82.5 

401 

389.1 

97.0 

461 

447.3 

111.5 

521 

505.5 

126.0 

581 

563.8 

140.5 

42 

331.8 

82.7 

02 

390.0 

97.2 

62 

448.2 

111.7 

22 

506.5 

126.2 

82 

564.7 

140.8 

43 

332.8 

83.0 

03 

391.0 

97.5 

63 

449.2 

112.0 

23 

507.5 

126.5 

83 

565.7 

141.0 

44 

333.7 

83.2 

04 

392.0 

97.7 

64 

450.2 

112.2 

24 

508.4 

126.8 

84 

566.7 

141.3 

45 

334.7 

83.4 

05 

392.9 

98.0 

65 

451.2 

112.5 

25 

509.4 

127.0 

85 

567.6 

141.5 

46 

335.7 

83.7 

06 

393. 9 

98.2 

66 

452.1 

112.7 

26 

510.4 

127.2 

86 

568.6 

141.8 

47 

336.7 

83.9 

07 

394.9 

98.4 

67 

453.1 

113.0 

27 

511.4 

127.5 

87 

569.6 

142.0 

48 

337.6 

84.2 

08 

395.8 

98.7 

68 

454.1 

113.2 

28 

512.3 

127.8 

88 

570.6 

142.3 

49 

338.6 

84.4 

09 

396.8 

98.9 

69 

455.0 

113.4 

29 

513.3 

128.0 

89 

571.5 

142.5 

50 

339.6 

84.7 

10 

397.8 

99.2 

70 

456.0 

113.7 

30 

514.3 

128.2 

90 

572.5 

142.8 

351 

340.5 

84.9 

411 

398.8 

99.4 

471 

457.0 

113.9 

531 

515.3 

128.5 

591 

573.5 

143.0 

52 

341.5 

85.1 

12 

399.7 

99.7 

72 

457.9 

114.2 

32 

516.2 

128.8 

92 

574.4 

143.3 

53 

342.5 

85.4 

13 

400.7 

99.9 

73 

458.9 

114.4 

33 

517.2 

129.0 

93 

575.4 

143.5 

54 

343.5 

85.6 

14 

401.7 

100.1 

74 

459.9 

114.6 

34 

518.2 

129.2 

94 

576.4 

143. 8 

55 

344.4 

85.9 

15 

402.6 

100.4 

75 

460.9 

114.9 

35 

519.1 

129.4 

95 

577.3 

144.0 

56 

345.4 

86.1 

16 

403.6 

100.6 

76 

461.8 

115.1 

36 

520.1 

129.7 

96 

578.3 

144.2 

57 

346.4 

86.3 

17 

404.6 

100.9 

77 

462.8 

115.4 

37 

521.1 

129.9 

97 

579.3 

144.5 

58 

347.3 

86.6 

18 

405.5 

101.1 

78 

463.8 

115.6 

38 

522.1 

130.2 

98 

580.3 

144.7 

59 

348.3 

86.8 

19 

406.5 

101.3 

79 

464.7 

115.9 

39 

523.0 

130.4 

99 

581.2 

144.9 

60 

349.3 

87.1 

20 

407.5 

101.6 

80 

465.7 

116.1 

40 

524.0 

130.6 

600 

582.2 

145.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

76°  (104°,  256°,  284°). 

Page  560] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  15°  (165°,  195°,  345°) 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.9 

15.8 

121 

116.9 

31.3 

181 

174.8 

46.8 

241 

232.8 

62.4 

2 

1.9 

0.5 

62 

59.9 

16.0 

22 

117.8 

31.6 

82 

175.8 

47.1 

42 

233.8 

62.6 

3 

2.9 

0.8 

63 

60.9 

16.3 

23 

118.8 

31.8 

83 

176.8 

47.4 

43 

234.7 

62.9 

4 

3.9 

1.0 

64 

61.8 

16,6 

24 

119.8 

32.1 

84 

177.7 

47.6 

.   44 

235.7 

63.2 

5 

4.8 

1.3 

65 

62.8 

16.8 

25 

120.7 

32.4 

85 

178.7 

47.9 

45 

236.7 

63.4 

6 

5.8 

1.6 

66 

63.8 

17.1 

26 

121.7 

32.6 

86 

179.7 

48.1 

46 

237.6 

63.7 

7 

6.8 

1.8 

67 

64.7 

17.3 

27 

122.7 

32.9 

87 

180.6 

48.4 

47 

238.6 

63.9 

8 

7.7 

2.1 

68 

65.7 

17.6 

28 

123.6 

33.1 

88 

181.6 

48.7 

48 

239.5 

64.2 

9 

8.7 

2.3 

69 

66.6 

17.9 

29 

124.6 

33.4 

89 

182.6 

48.9 

49 

240.5 

64.4 

10 

9.7 

2.6 

70 

67.6 

18.1 

30 

125.6 

33.6 

90 

183.5 
184.5 

49.2 

50 

241.5 

64.7 
65.0 

11 

10.6 

2.8 

71 

68.6 

18.4 

131 

126.5 

33.9 

191 

49.4 

251 

242.4 

12 

11.6 

3.1 

72 

69.5 

18.6 

32 

127.5 

34.2 

92 

185.5 

49.7 

52 

243.4 

65.2 

13 

12.6 

3.4 

73 

70.5 

18.9 

33 

128.5 

34.4 

93 

186.4 

50.0 

53 

244.4 

65.5 

14 

13.5 

3.6 

74 

71.5 

19.2 

34 

129.4 

34.7 

94 

187.4 

50.2 

54 

245.3 

65.7 

15 

14.5 

3.9 

75 

72.4 

19.4 

35 

130.4 

34.9 

95 

188.4 

50.5 

55 

246.3 

66.0 

16 

15.5 

4.1 

76 

73.4 

19.7 

36 

131.4 

35.2 

96 

189.3 

50.7 

56 

247.3 

66.3 

17 

16.4 

4.4 

77 

74.4 

19.9 

37 

132.3 

35.5 

97 

190.3 

51.0 

57 

248.2 

66.5 

18 

17.4 

4.7 

78 

75.3 

20.2 

38 

133.3 

35.7 

98 

191.3 

51.2 

58 

249.2 

66.8 

19 

18.4 

4.9 

79 

76.3 

20.4 

39 

134.3 

36.0 

99 

192.2 

51.5 

59 

250.2 

67.0 

20 

19.3 

5.2 

80 

77.3 

20.7 

40 

135.2 

36.2 

200 

193.2 

51.8 

60 

251.1 

67.3 
67.6 

21 

20.3 

5.4 

81 

78.2 

21.0 

141 

136.2 

36.5 

201 

194.  2 

52.0 

261 

252.1 

22 

21.3 

5.7 

82 

79.2 

21.2 

42 

137.2 

36.8 

02 

195.1 

52.3 

62 

253.1 

67.8 

23 

22.2 

6.0 

83 

80.2 

21.5 

43 

138. 1 

37.0 

03 

196.1 

52.5 

63 

254.0 

68.1 

24 

23.2 

6.2 

84 

81.1 

21.7 

44 

139.1 

37.3 

04 

197.0 

52.8 

64 

255.0 

68.3 

25 

24.1 

6.5 

85 

82.1 

22.0 

45 

140.1 

37.5 

05 

198.0 

53.1 

65 

256.0 

68.6 

26 

25.1 

6.7 

86 

83.1 

22.3 

46 

141.0 

37.8 

06 

199.0 

53.3 

66 

256.9 

68.8 

27 

26.1 

7.0 

87 

84.0 

22.5 

47 

142.0 

38.0 

07 

199.9 

53.6 

67 

257.9 

69.1 

28 

27.0 

7.2 

88 

85.0 

22.8 

48 

143.0 

38.3 

08 

200.9 

53.8 

68 

258.9 

69.4 

29 

28.0 

7.5 

89* 

86.0 

23.0 

49 

143.9 

38.6 

09 

201.9 

54.1 

69 

259.8 

69.6 

30 

29.0 

7.8 

90 

86.9 

23.3 

50 
151 

144.9 

38.8 

10 

202.8 

54.4 

70 

260.8 

69.9 

31 

29.9 

8.0 

91 

87.9 

23.6 

145.9 

39.1 

211 

203.8 

54.6 

271 

261.8 

70.1 

32 

30.9 

8.3 

92 

88.9 

23.8 

52 

146.8 

39.3 

12 

204.8 

54.9 

72 

262.7 

70,4 

33 

31.9 

8.5 

93 

89.8 

24.1 

53 

147.8 

39.6 

13 

205.  7 

55.1 

73 

263.7 

70.7 

34 

32.8 

8.8 

94 

90.8 

24.3 

54 

148.8 

39.9 

14 

206.7 

55.4 

74 

264.7 

70.9 

35 

33.8 

9.1 

95 

91.8 

24.6 

55 

149.7 

40.1 

15 

207.7 

55.6 

75 

265.6 

71.2 

36 

34.8 

9.3 

96 

92.7 

24.8 

56 

150.7 

40.4 

16 

208.6 

55.9 

76 

266.6 

71.4 

37 

35.7 

9.6 

97 

93.7 

25.1 

57 

151.7 

40.6 

17 

209.6 

56.2 

77 

267.6 

71.7 

38 

36.7 

9.8 

98 

94.7 

25.4 

58 

152.6 

40.9 

18 

210.6 

56.4 

78 

268.5 

72.0 

39 

37.7 

10.1 

99 

95.6 

25.6 

59 

153.6 

41.2 

19 

211.5 

56.7 

79 

269.5 

72,2 

40 

38.6 

10.4 

100 

96.6 

25.9 

60 

154.5 

41.4 

20 

212.5 

56.9 

80 

281 

270.5 

72.5 

41 

39.6 

10.6 

101 

97.6 

26.1 

161 

155.5 

41.7 

221 

213.5 

67.2 

271.4 

72.7 

42 

40.6 

10.9 

02 

98.5 

26.4 

62 

156.5 

41.9 

22 

214.4 

57.5 

82 

272.4 

73.0 

43 

41.5 

11.1 

03 

99.5 

26.7 

63 

157.4 

42.2 

23 

215.4 

57.7 

83 

273.4 

73.2 

44 

42.5 

11.4 

04 

100.5 

26.9 

64 

158.4 

42.4 

24 

216.4 

58.0 

84 

274.3 

73.5 

45 

43.5 

11.6 

05 

101.4 

27.2 

65 

159.4 

42.7 

25 

217.3 

58.2 

85 

275.3 

73.8 

46 

44.4 

11.9 

06 

102.4 

27.4 

66 

160.3 

43.0 

26 

218.3 

58.5 

86 

276.3 

74.0 

47 

45.4 

12.2 

07 

103.4 

27.7 

67 

161.3 

43.2 

27 

219.3 

58.8 

87 

277.2 

74.3 

48 

46.4 

12.4 

08 

104.3 

28.0 

68 

162.3 

43.5 

28 

220.2 

59.0 

88 

278.2 

74.5 

49 

47.3 

12.7 

09 

105.3 

28.2 

69 

163.2 

43.7 

29 

221.2 

59.3 

89 

279.2 

74.8 

50 

48,3 

12.9 

10 

106.3 
107.2 

28.5 

70 

164.2 

44.0 

30 

222.2 

59.5 

90 

280.1 

75.1 

51 

49.3 

13.2 

111 

28.7 

171 

165.2 

44.3 

231 

223.1 

59.8 

291 

281,1 

75.3 

52 

50.2 

13.5 

12 

108.2 

29,0 

72 

166.1 

44.5 

32 

224.1 

60.0 

92 

282.1 

75.6 

53 

51.2 

13.7 

13 

109.1 

29.2 

73 

167.1 

44.8 

33 

225.1 

60.3 

93 

283.0 

75.8 

54 

52.2 

14.0 

14 

110.1 

29.5 

74 

168.1 

45.0 

34 

226.0 

60.6 

94 

284.0 

76.1 

55 

53.1 

14.2 

15 

111.1 

29.8 

75 

169.0 

45.3 

35 

227.0 

60.8 

95 

284.9 

76.4 

56 

54.1 

14.5 

16 

112.0 

30.0 

76 

170.0 

45.6 

36 

228.0 

61.1 

96 

285.9 

76.6 

57 

55.1 

14.8 

17 

113.0 

30.3 

77 

171.0 

45.8 

37 

228.9 

61.3 

97 

286.9 

76.9 

58 

56.0 

15.0 

18 

114.0 

30.5 

78 

171.9 

46.1 

38 

229.9 

61.6 

98 

287.8 

77.1 

59 

57.0 

15.3 

19 

114.9 

30.8 

79 

172.9 

46.3 

39 

230.9 

61.9 

99 

288.8 

77.4 

60 

58.0 

15.5 

20 

115,9 

31.1 

80 

173.9 

46.6 

40 

231.8 

62.1 

300 

289.8 

77.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

75°  (105°,  25{ 

)°,  285' 

'). 

• 

.... 

- 

^ 

TABLE  2. 

[Page 

561 

Difference  of  Latitude  and  Departure  for 

15°  (165°,  195 

°,  345° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

290.7 

77.9 

361 

348.7 

93.4 

421 

406.6 

109.0 

481 

464.6 

124.5 

541 

522.6 

140.0 

02 

291.7 

78.2 

62 

349.6 

93.7 

22 

407.6 

109.2 

82 

465.6 

124.8 

42 

523.5 

140.3 

03 

292.7 

78.4 

63 

350.6 

94.0 

23 

408.6 

109.5 

83 

466.5 

125.0 

43 

524.5 

140.5 

04 

293.6 

78.7 

64 

351.6 

94.2 

24 

409.5 

109.7 

84 

467.5 

125.3 

44 

525.5 

140.8 

05 

294.6 

78.9 

65 

352.5 

94.5 

25 

410.5 

110.0 

85 

468.5 

125.6 

45 

526.4 

141.1 

06 

295.6 

79.2 

66 

353.5 

94.7 

26 

411.5 

110.3 

86 

469.4 

125.8 

46 

527.4 

141.4 

07 

296.5 

79.5 

67 

354.5 

95.0 

27 

412.4 

110.5 

87 

470.4 

126.1 

47 

528.4 

141.6 

08 

297.5 

79.7 

68 

355.4 

95.3 

28 

413.4 

110.8 

88 

471.4 

126.4 

48 

529.3 

141.9 

09 

298.4 

80.0 

69 

356.4 

95.5 

29 

414.4 

111.0 

89 

472.3 

126.6 

49 

530.3 

142.1 

10 

299.4 

80.2 

70 

357.4 

95.8 

30 

415.3 
416.3 

111.3 
111.6 

90 

473.3 

126.9 

50 

531.3 

142.4 

311 

300.4 

80.5 

371 

358.3 

96.0 

431 

491 

474.3 

127.1 

551 

532.2 

142.6 

12 

301.3 

80.8 

72 

359.3 

96.3 

32 

417.3 

111.8 

92 

475.2 

127.4 

52 

533.2 

142.9 

13 

302.3 

81.0 

73 

360.3 

96.5 

33 

418.2 

112.1 

93 

476.2 

127.6 

53 

534.2 

143.1 

14 

303.  3 

81.3 

74 

361.2 

96.8 

34 

419.2 

112.3 

94 

477.2 

127.9 

54 

535.1 

143.4 

15 

304.2 

81.5 

75 

362.2 

97.1 

35 

420.2 

112.6 

95 

478.1 

128.1 

55 

536.1 

143.7 

16 

305.2 

81.8 

76 

363.2 

97.3 

36 

421.1 

112.9 

96 

479.1 

128.4 

56 

537.1 

143.9 

17 

306.2 

82.1 

77 

364.1 

97.6 

37 

422.1 

113.1 

97 

480.1 

128.6 

57 

538.0 

144.2 

18 

307.1 

82.3 

78 

365.1 

97.8 

38 

423.1 

113.4 

98 

481.0 

128.9 

58 

539.0 

144.4 

19 

308.1 

82.6 

79 

366.1 

98.1 

39 

424.0 

113.6 

99 

482.0 

129.1 

59 

540.0 

144.7 

20 

309.1 

82.8 

80 

367.0 

98.4 

40 

425,0 

113.9 

500 

483.0 

129.4 

60 

540.9 

144.9 

321 

310.  0 

83.1 

381 

368.0 

98.6 

441 

426.0 

114.1 

501 

483.9 

129.  7 

561 

541.9 

145.2 

22 

311.0 

83.3 

82 

369.0 

98.9 

42 

426.9 

114.4 

02 

484.9 

129.9 

62 

542.9 

145.4 

23 

312.0 

83.6 

83 

369.9 

99.1 

43 

427.9 

114.7 

03 

485.9 

130.2 

63 

543.8 

145.7 

24 

312.9 

83.9 

84 

370.9 

99.4 

44 

428.8 

114.9 

04 

486.8 

130.4 

64 

544.8 

146.0 

25 

313.9 

84.1 

85 

371.9 

99.6 

45 

429.8 

115.2 

05 

487.8 

130.7 

65 

545.8 

146.2 

26 

314.9 

84.4 

86 

372.8 

99.9 

46 

430.8 

115.4 

06 

488.8 

131.0 

66 

546.7 

146.5 

27 

315.8 

84.6 

87 

373.8 

100.2 

47 

431.7 

115.7 

07 

489.7 

131.2 

67 

547.7 

146.7 

28 

316.8 

84.9 

88 

374.8 

100.4 

48 

432.7 

116.0 

08 

490.7 

131.5 

68 

548.7 

147.0 

29 

317.8 

85.1 

89 

375.7 

100.7 

49 

433.7 

116.2 

09 

491.7 

131.7 

69 

549.6 

147.2 

30 
331 

318.  7 

85.4 

90 

376.7 

100.9 

50 

434.6 

116.5 

10 

492.6 

132.0 

70 

550.6 

147.5 

319.7 

85.7 

391 

377.7 

101.2 

451 

435.6 

116.7 

511 

493.6 

132.3 

571 

551.6 

147.8 

32 

320.  7 

85.9 

92 

378.6 

101.5 

52 

436.6 

117.0 

12 

494.5 

132.5 

72 

552.5 

148.0 

33 

321.6 

86.2 

93 

379.6 

101.7 

53 

437.5 

117.3 

13 

495.5 

132.8 

73 

553.5 

148.3 

34 

322.  6 

86.5 

94 

380.6 

102.0 

54 

438.5 

117.5 

14 

496.5 

133.0 

74 

554.4 

148.5 

35 

323.6 

86.7 

95 

381.5 

102.2 

55 

439.5 

117.8 

15 

497.4 

133.3 

75 

555.4 

148.8 

36 

324.5 

87.0 

96 

382. 5 

102.5 

56 

440.4 

118.0 

16 

498.4 

133.5 

76 

556.4 

149.0 

37 

325.5 

87.2 

97 

383.4 

102.8 

57 

441.4 

118.3 

17 

499.4 

133.8 

77 

557.3 

149.3 

38 

326.5 

87.5 

98 

384.4 

103.0 

58 

442.4 

118.5 

18 

500.3 

134.0 

78 

558.3 

149.5 

39 

327. 4 

87.7 

99 

385.4 

103.3 

59 

443.3 

118.8 

19 

501.3 

134.3 

79 

559.3 

149.8 

40 

328.4 

88.0 

400 

386.3 

103.5 

60 

444.3 

119.1 

20 

502.3 

134.6 

80 

560.2 

150.1 
150. 3 

341 

329.4 

88.3 

401 

387.3 

103.8 

461 

445.3 

119.3 

521 

503.2 

134.8 

581 

561.2 

42 

330.3 

88.5 

02 

388.3 

104.1 

62 

446.2 

119.6 

22 

504.2 

135.1 

82 

562.2 

150.6 

43 

331.3 

88.8 

03 

389.2 

104.3 

63 

447.2 

119.8 

23 

505.2 

135.3 

83 

563.1 

150.8 

44 

332.3 

89.0 

04 

390.2 

104.6 

64 

448.2 

120.1 

24 

506.1 

135.6 

84 

564.1 

151.1 

45 

333.2 

89.3 

05 

391.2 

104.8 

65 

449.1 

120.4 

25 

507.1 

135.9 

85 

565.1 

151.4 

46 

334.2 

89.6 

06 

392.1 

105.1 

66 

450.1 

120.6 

26 

508.1 

136.1 

86 

566.0 

151.6 

47 

335.2 

89.8 

07 

393.1 

105.3 

67 

451.1 

120.9 

27 

509.0 

136.4 

87 

567.0 

151.9 

48 

336.1 

90.1 

08 

394.1 

105.6 

68 

452.0 

121.1 

28 

510.0 

136.6 

88 

568.0 

152.2 

49 

337.1 

90.3 

09 

395.0 

105.9 

69 

453.0 

121.4 

29 

511.0 

136.9 

89 

568.9 

152.4 

50 

338.1 
339. 0 

90.6 

10 

396.0 

106.1 

70 

454.0 

121.7 

30 

511.9 

137.2 

90 

569.9 

152.7 

351 

90.9 

411 

397.0 

106.4 

471 

454.9 

121.9 

531 

512.9 

137.4 

591 

570.9 

153.0 

52 

340.0 

91.1 

12 

397.9 

106.6 

72 

455.9 

122.2 

32 

513.9 

137.7 

92 

571.8 

153.2 

53 

340.9 

91.4 

13 

398.9 

106.9 

73 

456.9 

122.4 

33 

514.8 

137.9 

93 

572.8 

153.5 

54 

341.9 

91.6 

14 

399.9 

107.2 

74 

457.8 

122.7 

34 

515.8 

138.2 

94 

573.8 

153.7 

55 

342.9 

91.9 

15 

400.8 

107.4 

75 

458.8 

122.9 

35 

516.8 

188.4 

95 

574.7 

154.0 

56 

343.8 

92.1 

16 

401.8 

107.7 

76 

459.8 

123.2 

36 

517.7 

138.7 

96 

575.7 

154.2 

57 

344.8 

92.4 

17 

402.8 

107.9 

77 

460.7 

123.5 

37 

518.7 

139.0 

97 

576.7 

154.5 

58 

345.8 

92.7 

18 

403.7 

108.2 

78 

461.7 

123.7 

38 

519.7 

139.2 

98 

577.6 

154.8 

59 

346.7 

92.9 

19 

404.7 

108.5 

79 

462.7 

124.0 

39 

520.6 

139.5 

99 

578.6 

155.0 

60 

347.7 

93.2 

20 

405.7 

108.7 

80 

463.6 

124.2 

40 

521.6 

139.7 

600 

579.5 

155.3 

Dist. 

Dep. 

Lav. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

75°  (1 

05°,  255 

°,  285° 

). 

21594°— 14r- 


-29 


Page  662] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  16°  (] 

L64°,  196°,  344°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
66.4 

1 

1.0 

0.3 

61 

58.6 

16.8 

121 

116.3 

33.4 

181 

174.0 

49.9 

241 

231.7 

2 

1.9 

0.6 

62 

59.6 

17.1 

22 

117.3 

33.6 

82 

174.9 

50.2 

42 

232.6 

66.7 

3 

2.9 

0.8 

63 

60.6 

17.4 

23 

118.2 

33.9 

83 

175.9 

50.4 

43 

233.6 

67.0 

4 

3.8 

1.1 

64 

61.5 

17.6 

24 

119.2 

34.2 

84 

176.9 

50.7 

44 

234.5 

67.3 

5 

4.8 

1.4 

65 

62.5 

17.9 

25 

120.2 

34.5 

85 

177.8 

51.0 

45 

235.5 

67.5 

6 

5.8 

1.7 

66 

63.4 

18.2 

26 

121.1 

34.7 

86 

178.8 

51.3 

46 

236.5 

67.8 

7 

6.7 

1.9 

67 

64.4 

18.5 

27 

122.1 

35.0 

87 

179.8 

51.5 

47 

237.4 

68.1 

8 

7.7 

2.2 

68 

65.4 

18.7 

28 

123.0 

35.3 

88 

180.7 

51.8 

48 

238.4 

68.4 

9 

8.7 

2.5 

69 

66.3 

19.0 

29 

124.0 

35.6 

89 

181.7 

52.1 

49 

239.4 

68.6 

10 

9.6 

2.8 

70 

67.3 

19.3 

30 

125.0 

35.8 

90 

182.6 

52.4 

50 

240.3 

68.9 

11 

10.6 

3.0 

71 

68.2 

19.6 

131 

125.9 

36.1 

191 

183.6 

52.6 

251 

241.3 

69.2 

12 

11.5 

3.3 

72 

69.2 

19.8 

32 

126.9 

36.4 

92 

184.6 

52.9 

52 

242.2 

69.5 

13 

12.5 

3.6 

73 

70.2 

20.1 

33 

127.8 

36.7 

93 

185.5 

53.2 

53 

243.2 

69.7 

14 

13.5 

3.9 

74 

71.1 

20.4 

34 

128.8 

36.9 

94 

186.5 

53.5 

54 

244.2 

70.0 

15 

14.4 

4.1 

75 

72.1 

20.7 

35 

129.8 

37.2 

95 

187.4 

53.7 

55 

245.1 

70.3 

16 

15.4 

4.4 

76 

73.1 

20.9 

36 

130.7 

37.5 

96 

188.4 

54.0 

56 

246.1 

70.6 

17 

16.3 

4.7 

77 

74.0 

21.2 

37 

131.7 

37.8 

97 

189.4 

54.3 

57 

247.0 

70.8 

18 

17.3 

5.0 

78 

75.0 

21.5 

38 

132.7 

38.0 

98 

190.3 

54.6 

58 

248.0 

71.1 

19 

18.3 

5.2 

79 

75.9 

21.8 

39 

133.6 

38.3 

99 

191.3 

54.9 

59 

249.0 

71.4 

20 

19.2 

5.5 

80 

76.9 

22.1 

40 
141 

134.6 

38.6 
38.9 

200 
201 

192.3 

55.1 

60 

249.9 
250.9 

71.7 

21 

20.2 

5.8 

81 

77.9 

22.3 

135.5 

193.2 

55.4 

261 

71.9 

22 

21.1 

6.1 

82 

78.8 

22.6 

42 

136.5 

39.1 

02 

194.  2 

55.7 

62 

251.9 

72.2 

23 

22.1 

6.3 

83 

79.8 

22.9 

43 

137.5 

39.4 

03 

195.1 

56.0 

63 

252.8 

72.5 

24 

23.1 

6.6 

84 

80.7 

23.2 

44 

138.4 

39.7 

04 

196.1 

56.2 

64 

253.8 

72.8 

25 

24.0 

6.9 

85 

81.7 

23.4 

45 

139.4 

40.0 

05 

197.1 

56.5 

65 

254.7 

73.0 

26 

25.0 

7.2 

86 

82.7 

23.7 

46 

140.3 

40.2 

06 

198.0 

56.8 

66 

255.7 

73.3 

27 

26.0 

7.4 

87 

83.6 

24.0 

47 

141.3 

40.5 

07 

199.0 

57.1 

67 

256.7 

73.6 

28 

26.9 

7.7 

88 

84.6 

24.3 

48 

142.3 

40.8 

08 

199.9 

57.3 

68 

257.6 

73.9 

29 

27.9 

8.0 

89 

85.6 

24.5 

49 

143.2 

41.1 

09 

200.9 

57.6 

69 

258.6 

74.1 

30 

28.8 

8.3 

90 

86.5 

24.8 

50 

144.2 

41.3 

10 

201.9 

57.9 

70 
271 

259.5 
260.5 

74.4 
74.7 

31 

29.8 

8.5 

91 

87.5 

25.1 

151 

145.2 

41.6 

211 

202.8 

58.2 

32 

30.8 

8.8 

92 

88.4 

25.4 

52 

146.1 

41.9 

12 

203.8 

58.4 

72 

261.5 

75.0 

33 

31.7 

9.1 

93 

89.4 

25.6 

53 

147.1 

42.2 

13 

204.7 

58.7 

73 

262.4 

75.2 

34 

32.7 

9.4 

94 

90.4 

25.9 

54 

148.0 

42.4 

14 

205.7 

59.0 

74 

263.4 

75.5 

35 

33.6 

9.6 

95 

91.3 

26.2 

55 

149.0 

42.7 

15 

206.7 

59.3 

75 

264.3 

75.8 

36 

34.6 

9.9 

96 

92.3 

26.5 

56 

150.0 

43.0 

16 

207.6 

59.5 

76 

265.3 

76.1 

37 

35.6 

10.2 

97 

93.2 

26.7 

57 

150.9 

43.3 

17 

208.6 

59.8 

77 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.0 

58 

151.9 

43.6 

18 

209.6 

60.1 

78 

267.2 

76.6 

39 

37.5 

10.7 

99 

95.2 

27.3 

59 

152.8 

43.8 

19 

210. 5 

60.4 

79 

268.2 

76.9 

40 

38.5 

11.0 

100 

96.1 

27.6 

60 

153.8 

44.1 

20 

211.5 

60.6 

80 

269.2 

77.2 

41 

39.4 

11.3 

101 

97.1 

27.8 

161 

154.8 

44.4 

221 

212.4 

60.9 

281 

270.1 

77.5 

42 

40.4 

11.6 

02 

98.0 

28.1 

62 

155.7 

44.7 

22 

213.4 

61.2 

82 

271.1 

77.7 

43 

41.3 

11.9 

03 

99.0 

28.4 

63 

156.7 

44.9 

23 

214.4 

61.5 

83 

272.0 

78.0 

44 

42.3 

12.1 

04 

100.0 

28.7 

64 

157.6 

45.2 

24 

215.  3 

61.7 

84 

273.0 

78.3 

45 

43.3 

12.4 

05 

100.9 

28.9 

65 

158.6 

45.5 

25 

216.3 

62.0 

85 

274.0 

78.6 

46 

44.2 

12.7 

06 

101.9 

29.2 

66 

159.6 

45.8 

26 

217.2 

62.3 

86 

274.9 

78.8 

47 

45.2 

13.0 

07 

102.9 

29.5 

67 

160.5 

46.0 

27 

218.2 

62.6 

87 

275.9 

79.1 

48 

46.1 

13.2 

08 

103.8 

29.8 

68 

161.5 

46.3 

28 

219.2- 

62.8 

88 

276.8 

79.4 

49 

47.1 

13.5 

09 

104.8 

30.0 

69 

162.5 

46.6 

29 

220.1 

63.1 

89 

277.8 

79.7 

50 

48.1 

13.8 

10 

105.7 

30.3 

70 

163.4 

46.9 

30 

221.1 

63.4 

90 

278.8 

79.9 

51 

49.0 

14.1 

111 

106.7 

30.6 

171 

164.4 

47.1 

231 

222.1 

63.7 

291 

279.7 

80.2 

52 

50.0 

14.3 

12 

107.7 

30.9 

72 

165.3 

47.4 

32 

223.0 

63.9 

92 

280.7 

80.5 

53 

50.9 

14.6 

13 

108.6 

31.1 

73 

166.  3 

47.7 

33 

224.0 

64.2 

93 

281.6 

80.8 

54 

51.9 

14.9 

14 

109.6 

31.4 

74 

167.3 

48.0 

34 

224.9 

64.5 

94 

282.6 

81.0 

55 

52.9 

15.2 

15 

110.5 

31.7 

75 

168.2 

48.2 

35 

225.9 

64.8 

95 

283.6 

81.3 

56 

53.8 

15.4 

16 

111.5 

32.0 

76 

169.2 

48.5 

36 

226.9 

65.1 

96 

284.5 

81.6 

57 

54.8 

15.7 

17 

112.5 

32.2 

77 

170.1 

48.8 

37 

227.8 

65.3 

97 

285.5 

81.9 

58 

55.8 

16.0 

18 

113.4 

32.5 

78 

171.1 

49.1 

38 

228.8 

65.6 

98 

286.5 

82.1 

59 

56.7 

16.3 

19 

114.4 

32.8 

79 

172.1 

49.3 

39 

229.7 

65.9 

99 

287.4 

82.4 

60 

57.7 

16.5 

20 

115.4 

33.1 

80 

173.0 

49.6 

40 

230.7 

66.2 

300 

288.4 

82.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

74°  (1 

06°,  254°,  286°). 

TABLE  2. 

[Page  563 

Difference  of  Latitude  and  Departure  for  16°  (164°,  19€ 

°,  344* 

). 

DIst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat.     1    Dep. 

Dist.  1     Lat. 

Dep. 

Dist. 

Lat.     1     Dep.    1 

301 

289.3 

82.9 

361 

347.0 

99.5 

421 

404.7 

116.0 

481 

462.4 

132.6 

541 

520.1 

149.1 

02 

290.3 

83.2 

62 

348.0 

99.7 

22 

405.6 

116.3 

82 

463.3 

132.8 

42 

521.0 

149.4 

03 

291.2 

83.5 

63 

348.9 

100.0 

23 

406.6 

116.6 

83 

464.3 

133.1 

43 

522.0 

149.7 

04 

292.2 

83.8 

64 

349.9 

100.3 

24 

407.6 

116.8 

84 

465.2 

133.4 

44 

523.0 

150.0 

05 

293.2 

84.0 

65 

350.8 

100.6 

25 

408.5 

117.1 

85 

466.2 

133.6 

46 

523.9 

150.2 

06 

294.1 

84.3 

66 

351.8 

100.8 

26 

409.5 

117.4 

86 

467.2 

133.9 

46 

524.9 

150.4 

07 

295.1 

84.6 

67 

352.8 

101.1 

27 

410.4 

117.7 

87 

468.1 

134.2 

47 

526.9 

150.7 

08 

296.0 

84.9 

68 

353.7 

101.4 

28 

411.4 

117.9 

88 

469.1 

134.5 

48 

526.8 

151.0 

09 

297.0 

85.1 

69 

354.7 

101.7 

29 

412.4 

118.2 

89 

470.1 

134.8 

49 

527.8 

151.3 

10 

298.0 

85.4 

70 

355.  6 

101.9 

30 

413.3 

118.5 

90 

471.0 

135.0 

50 

628.7 

151.6 

311 

298.9 

85.7 

371 

356.6 

102.2 

431 

414.3 

118.8 

491 

472.0 

135.3 

561 

629.7 

151.9 

12 

299. 9 

86.0 

72 

357.6 

102.5 

32 

416.2 

119.0 

92 

472.9 

136. 6 

62 

630.6 

152.2 

13 

300.9 

86.2 

73 

358.5 

102.8 

33 

416.2 

119.3 

93 

473.9 

136.9 

53 

631.6 

152.6 

14 

301.8 

86.5 

74 

359.5 

103.1 

34 

417.2 

119.6 

94 

474.9 

136.2 

54 

532.6 

152.8 

15 

302.8 

86.8 

75 

360.4 

103.3 

35 

418.1 

119.9 

95 

475.8 

136.4 

55 

536.5 

153.0 

16 

303.7 

87.1 

76 

361.4 

103.6 

36 

419.1 

120.1 

96 

476.8 

136.7 

66 

534.5 

153.2 

17 

304.7 

87.3 

77 

362.4 

103.  9 

37 

420.0 

120.4 

97 

477.7 

137. 0 

57 

636.4 

153.6 

18 

305.7 

87.6 

78 

363.3 

104.2 

38 

421.0 

120.7 

98 

478.7 

137.3 

58 

536.4 

163.8 

19 

306.6 

87.9 

79 

364.3 

104.4 

39 

422.0 

121.0 

99 

479.7 

137.5 

59 

537.4 

154,1 

20 

307.6 

88.2 

80 

365.3 

104.7 

40 

422.9 

121.  2 

500 

480.6 

137.8 

60 

638.3 

154.4 

321 

308.5 

88.4 

381 

366.2 

105. 0 

441 

423.9 

121.6 

601 

481.6 

138.1 

561 

539.3 

154.7 

22 

309. 5 

88.7 

82 

367.2 

105.3 

42 

424.9 

121.8 

02 

482.6 

138.3 

62 

540.3 

154.9 

23 

310.5 

89.0 

83 

368.1 

105.5 

43 

425.8 

122.1 

03 

483.5 

138.6 

63 

541.2 

166.2 

24 

311.4 

89.3 

84 

369.1 

105.8 

44 

426.8 

122. 3 

04 

484.5 

138. 9 

64 

542.2 

155.4 

25 

312.4 

89.5 

85 

370.1 

106.1 

45 

427.7 

122.6 

06 

486.4 

139. 2 

65 

543.1 

155.7 

26 

313.3 

89.8 

86 

371.0 

106.4 

46 

428.7 

122.9 

06 

486.4 

139.4 

66 

644.1 

166.0 

27 

314.3 

90.1 

87 

372.0 

106.6 

47 

429.7 

123.2 

07 

487.3 

139'.  7 

67 

546.1 

166.  3 

28 

315.3 

90.4 

88 

372.9 

106.9 

48 

430.6 

123.4 

08 

488.3 

140.0 

68 

546.0 

166.6 

29 

316.2 

90.6 

89 

373.9 

107.2 

49 

431.6 

123.7 

09 

489.3 

140.3 

69 

547.0 

156.9 

30 

317.2 

90.9 

90 

374.9 

107.5 

50 

432.6 

124.0 

10 

490.2 

140.6 

70 

547.9 

157.1 

331 

318.2 

91.2 

391 

375.  8 

107.7 

451 

433.6 

124.3 

511 

491.2 

140.8 

571 

548.9 

157.3 

32 

319.1 

91.5 

92 

376.8 

108.0 

52 

434.5 

124.6 

12 

492.1 

141.1 

72 

549.8 

157.6 

33 

320.1 

91.8 

93 

377.8 

108.3 

63 

435. 4    124. 8 

13 

493.1 

141.4 

73 

660.8 

157.9 

34 

321.0 

92.0 

94 

378.7 

108.6 

54 

436.4 

125.1 

14 

494.1 

141.7 

74 

551.8 

168.2 

35 

322.  0 

92.3 

95 

379.7 

108.8 

55 

437.4 

125.4 

15 

495.0 

141.9 

75 

662.7 

168.4 

36 

323.0 

92.6 

96 

380.6 

109.1 

56 

438.3 

125.7 

16 

496.0 

142.2 

76 

653.7 

158.7 

37 

323.9 

92.9 

97 

381.6 

109.4 

57 

439.3 

125.9 

17 

496.9 

142.5 

77 

664.6 

159.0 

38 

324.9 

93.1 

98 

382.6 

109.7 

58 

440.2 

126.2 

18 

497.9 

142.8 

78 

666.6 

159.3 

39 

325.8 

93.4 

99 

383.5 

109.9 

69 

441.2 

126.6 

19 

498.9 

143.0 

79 

556.6 

159.5 

40 

326.8 

93.7 

400 

384.5 

110.2 

60 

442.2 

126.8 
127. 0 

20 
521 

499.8 

143.3 

80 

557.6 

159.8 

341 

327.8 

94.0 

401 

385.4 

110.5 

461 

443.1 

500.8 

143.6 

581 

658.4 

160.1 

42 

328.7 

94.2 

02 

386.4 

110.8 

62 

444.1 

127.3 

22 

601.7 

143.9 

82 

659.4 

160.4 

43 

329.7 

94.5 

03 

387.4 

111.0 

63 

445.0 

127.6 

23 

602.7 

144.1 

83 

560.4 

160.6 

44 

330.7 

94.8 

04 

388.3 

111.3 

64 

446.0 

127.9 

24 

603.7 

144.4 

84 

661.3 

161.0 

45 

331.6 

95.1 

05 

389.3 

111.6 

65 

447.0 

128.1 

25 

504.6 

144.7 

86 

662.3 

161.3 

46 

332. 6 

95.3 

06 

390.2 

111.9 

66 

447.9 

128.4 

26 

505.6 

145.0 

86 

5a3.2 

161.6 

47 

333.  5 

95.6 

07 

391.2 

112.1 

67 

448.9 

128.7 

27 

506.6 

145.3 

87 

564.2 

161.8 

48 

334. 5 

95.9 

08 

392.2 

112.4 

68 

449.8 

129.0 

28 

507.6 

145.6 

88 

666.2 

162.1 

49 

335.5 

96.2 

09 

393.1 

112.7 

69 

450.8 

129.2 

29 

508.5 

145.8 

89 

666.1 

162.4 

50 
351 

336.4 

96.4 

10 

394.1 

113.0 

70 

451.8 

129.5 

30 
531 

509.4 

146.1 

90 

567.1 

162.7 

337. 4 

96.7 

411 

395.1 

113.3 

471 

452.7 

129.8 

610.4 

146.4 

691 

568.1 

162.9 

52 

338.  3 

97.0 

12 

396.0 

113. 5 

72 

453.7 

130.1 

32 

611.4 

146.7 

92 

569.0 

163.2 

53 

339.3 

97.3 

13 

397.0 

113.8 

73 

454.7 

130.3 

33 

512.3 

146.9 

93 

670.0 

163.5 

54 

340.3 

97.5 

14 

397.9 

114.1 

74 

456.6 

130.6 

34 

613.3 

147.2 

94 

671.0 

163.8 

55 

341.2 

97.8 

15 

398.9 

114.4 

75 

466.6 

130.9 

35 

514.3 

147.5 

95 

671.9 

164.0 

56 

342.2 

98.1 

16 

399.9 

114.6 

76 

467.6 

131.2 

36 

516.2 

147.8 

96 

572.9 

164.3 

57 

343.1 

98.4 

17 

400.8 

114.9 

77 

458.5 

131.4 

37 

516.2 

148.0 

97 

573.9 

164.6 

58 

344.1 

98.6 

18 

401.8 

115.2 

78 

459.5 

131.7 

38 

517.2 

148.2 

98 

574.8 

164.9 

59 

345.1 

98.9 

19 

402.7 

115.5 

79 

460.4 

132.0 

39 

518.1 

148.5 

99 

575.8 

166.1 

60 

346.0 

99.2 

20 

403.7 

115.8 

80 

461.4 

132.3 

40 

519.1 

148.8 

600 

576.8 

165.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

H°  (106°,  254°,  286° 

)• 

1 

Page  664] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  17°  (163°,  197°,  343° 

). 

Dist. 

Lat. 
1.0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.3 

61 

58.3 

17.8 

121 

115.7 

35.4 

181 

173.1 

52.9 

241 

230.5 

70.5 

2 

1.9 

0.6 

62 

59.3 

18.1 

22 

116.7 

35.7 

82 

174.0 

53.2 

42 

231.4 

70.8 

3 

2.9 

0.9 

63 

60.2 

18.4 

23 

117.6 

36.0 

83 

175.0 

53.5 

43 

232.4 

71.0 

4 

3.8 

1.2 

64 

61.2 

18.7 

24 

118.6 

36.3 

84 

176.0 

53.8 

44 

233.3 

71.3 

5 

4.8 

1.5 

65 

62.2 

19.0 

25 

119.5 

36.5 

85 

176.9 

54.1 

45 

234.3 

71.6 

6 

5.7 

1.8 

66 

63.1 

19.3 

26 

120.5 

36.8 

86 

177.9 

54.4 

46 

235.3 

71.9 

7 

6.7 

2.0 

67 

64.1 

19.6 

27 

121.5 

37.1 

87 

178.8 

54.7 

47 

236.2 

72.2 

8 

7.7 

2.3 

68 

65.0 

19.9 

28 

122.4 

37.4 

88 

179.8 

55.0 

48 

237.2 

72.5 

9 

8.6 

2.6 

69 

66.0 

20.2 

29 

123.4 

37.7 

89 

180.7 

55.3 

49 

238.1 

72.8 

10 

9.6 

2.9 

70 

66.9 

20.5 

30 

124.  3 
125.3 

38.0 

90 

181.7 

55.6 
55.8 

50 
251 

239.1 
240.0 

73.1 

11 

10.5 

3.2 

71 

67.9 

20.8 

131 

38.3 

191 

182.7 

73.4 

12 

11.5 

3.5 

72 

68.9 

21.1 

32 

126.2 

38.6 

92 

183.6 

56.1 

52 

241.0 

73.7 

13 

12.4 

3.8 

73 

69.8 

21.3 

33 

127.2 

38.9 

93 

184.6 

56.4 

53 

241.9 

74.0 

14 

13.4 

4.1 

74 

70.8 

21.6 

34 

128.1 

39.2 

94 

185.5 

56.7 

54 

242.9 

74.3 

15 

14.3 

4.4 

75 

71.7 

21.9 

35 

129.1 

39.5 

95 

186.5 

57.0 

55 

243.9 

74.6 

16 

15.3 

4.7 

76 

72.7 

22.2 

36 

130. 1 

39.8 

96 

187.4 

57.3 

56 

244.8 

74.8 

17 

16.3 

5.0 

77 

73.6 

22.5 

37 

131.0 

40.1 

97 

188.4 

57.6 

57 

245.8 

75.1 

18 

17.2 

5.3 

78 

74.6 

22.8 

38 

132.0 

40.3 

98 

189.3 

57.9 

58 

246.7 

75.4 

19 

18.2 

5.6 

79 

75.5 

23.1 

39 

132.9 

40.6 

99 

190.3 

58.2 

59 

247.7 

75.7 

20 

19.1 

5.8 
6.1 

80 

76.5 

23.4 

40 

133.9 

40.9 

200 

191.3 

58.5 

60 

248.6 

76.0 

21 

20.1 

81 

77.5 

23.7 

141 

134.  8 

41.2 

201 

192.2 

58.8 

261 

249.6 

76.3 

22 

21.0 

6.4 

82 

78.4 

24.0 

42 

135.8 

41.5 

02 

193.2 

59.1 

62 

250.  6 

76.6 

23 

22.0 

6.7 

83 

79.4 

24.3 

43 

136.8 

41.8 

03 

194.1 

59.4 

63 

251.5 

76.9 

24 

23.0 

7.0 

84 

80.3 

24.6 

44 

137.7 

42.1 

04 

195.1 

59.6 

64 

252.5 

77.2 

25 

23.9 

7.3 

85 

81.3 

24.9 

45 

138.7 

42.4 

05 

196.0 

59.9 

65 

253.4 

77.5 

26 

24.9 

7.6 

86 

82.2 

25.1 

46 

139.6 

42.7 

06 

197.0 

60.2 

66 

254.4 

77.8 

27 

25.8 

7.9 

87 

83.2 

25.4 

47 

140.6 

43.0 

07 

198. 0 

60.5 

67 

255.3 

78.1 

28 

26.8 

8.2 

88 

84.2 

25.7 

48 

141.5 

43.3 

08 

198.9 

60.8 

68 

256.3 

78.4 

29 

27.7 

8.5 

89 

85.1 

26.0 

49 

142.5 

43.6 

09 

199.9 

61.1 

69 

257.2 

78.6 

30 

28.7 

8.8 

90 

86.1 

26.3 

50 

143. 4 

43.9 

10 
211 

200.8 

61.4 

70 

258.2 

78.9 

31 

29.6 

9.1 

91 

87.0 

26.6 

151 

144.  4 

44.1 

201.8 

61.7 

271 

259.2 

79.2 

32 

30.6 

9.4 

92 

88.0 

26.9 

52 

145.4 

44.4 

12 

202.7 

62.0 

72 

260.1 

79.5 

33 

31.6 

9.6 

93 

88.9 

27.2 

53 

146.3 

44.7 

13 

203.7 

62.3 

73 

261.1 

79.8 

34 

32.5 

9.9 

94 

89.9 

27.5 

54 

147.3 

45.0 

14 

204.6 

62.6 

74 

262.0 

80.1 

35 

33.5 

10.2 

95 

90.8 

27.8 

55 

148.2 

45.3 

15 

205.6 

62.9 

75 

263.0 

80.4 

36 

34.4 

10.5 

96 

91.8 

28.1 

56 

149.2 

45.6 

16 

206.6 

63.2 

76 

263.9 

80.7 

37 

35.4 

10.8 

97 

92.8 

28.4 

57 

150.1 

45.9 

17 

207.5 

63.4 

77 

264.9 

81.0 

38 

36.3 

11.1 

98 

93.7 

28.7 

58 

151.1 

46.2 

18 

208.5 

63.7 

78 

265.9 

81.3 

39 

37. 3 

11.4 

99 

94.7 

28.9 

59 

152.1 

46.5 

19 

209.4 

64.0 

79 

266.8 

81.6 

40 

38.3 

11.7 

100 
101 

95.6 

29.2 

60 

153.0 
154. 0 

46.8 

20 

210.4 

64.3 

80 

267.8 

81.9 

41 

39.2 

12.0 

96.6 

29.5 

161 

47.1 

221 

211.3 

64.6 

281 

268.7 

82.2 

42 

40.2 

12.3 

02 

97.5 

29.8 

62 

154.9 

47.4 

22 

212.3 

64.9 

82 

269.7 

82.4 

43 

41.1 

12.6 

03 

98.5 

30.1 

63 

155.9 

47.7 

23 

213.3 

65.2 

83 

270.6 

82.7 

44 

42.1 

12.9 

04 

99.5 

30.4 

64 

156.8 

47.9 

24 

214.2 

65.5 

84 

271.6 

83.0 

45 

43.0 

13.2 

05 

100.4 

30.7 

65 

157.8 

48.2 

25 

215.2 

65.8 

85 

272.5 

83.3 

46 

44.0 

13.4 

06 

101.4 

31.0 

66 

158.7 

48.5 

26 

216.1 

66.1 

86 

273.5 

83.6 

47 

44.9 

13.7 

07 

102.3 

31.3 

67 

159.7 

48.8 

27 

217.1 

66.4 

87 

274.5 

83.9 

48 

45.9 

14.0 

08 

103.3 

31.6 

68 

160.7 

49.1 

28 

218.0 

66.7 

88 

275.4 

84.2 

49 

46.9 

14.3 

09 

104.2 

31.9 

69 

161.6 

49.4 

29 

219.0 

67.0 

89 

276.4 

84.5 

50 

47.8 

14.6 

10 

105.2 

32.2 

70 

162.6 

49.7 

30 

220.0 

67.2 

90 

277.3 

84.8 

51 

48.8 

14.9 

111 

106.1 

32.5 

171 

163.5 

50.0 

231 

220.9 

67.5 

291 

278.3 

85.1 

52 

49.7 

15.2 

12 

107.1 

32.7 

72 

164.5 

50.3 

32 

221.9 

67.8 

92 

279.2 

85.4 

53 

50.7 

15.5 

13 

108.1 

33.0 

73 

165.4 

50.6 

33 

222.8 

68.1 

93 

280.2 

85.7 

54 

51.6 

15.8 

14 

109.0 

33.3 

74 

166.4 

50.9 

34 

223.8 

68.4 

94 

281.2 

86.0 

55 

52.6 

16.1 

15 

110.0 

33.6 

75 

167.4 

51.2 

35 

224.7 

68.7 

95 

282.1 

86.2 

56 

53.6 

16.4 

16 

110.9 

33.9 

76 

168.3 

51.5 

36 

225.7 

69.0 

96 

283.1 

86.5 

57 

54.5 

16.7 

17 

111.9 

34.2 

77 

169.3 

51.7 

37 

226.6 

69.3 

97 

284.0 

86.8 

58 

55.5 

17.0 

18 

112.8 

34.5 

78 

170.2 

52.0 

38 

227.6 

69.6 

98 

285.0 

87.1 

59 

56.4 

17.2 

19 

113.8 

34.8 

79 

171.2 

52.3 

39 

228.6 

69.9 

99 

285.9 

87.4 

60 

57.4 

17.5 

20 

114.8 

35.1 

80 

172.1 

52.6 

40 

229.5 

70.2 

300 

286.9 

87.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

73°  (1 

07°,  252 

°,  287° 

). 

i 

TABLE  2. 

[Page  565 

Difference  of  Latitude  and  Departure  for  17°  (163°,  197°,  343 

°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

287.8 

88.0 

361 

345.2 

105.5 

421 

402.6 

123.1 

481 

460.0 

140.6 

541 

517.3 

158.2 

02 

288.8 

88.3 

62 

346.1 

105.8 

22 

403.5 

123.4 

82 

460.9 

140.9 

42 

518.3 

158.5 

03 

289.7 

88.6 

63 

347.1 

106.1 

23 

404.5 

123.7 

83 

461.9 

141.2 

43 

519.2 

158.8 

04 

290.7 

88.9 

64 

348.1 

106.4 

24 

405.4 

124.0 

84 

462.8 

141.5 

44 

520.2 

159.1 

05 

291.6 

89.2 

65 

349.0 

106.7 

25 

406.4 

124.3 

85 

463.8 

141.8 

45 

521.2 

159.3 

06 

292.6 

89.5 

66 

350.0 

107.0 

26 

407.3 

124.6 

86 

464.7 

142.1 

46 

522.1 

159.6 

07 

293.5 

89.8 

67 

350.9 

107.3 

27 

408.3 

124.8 

87 

465.7 

142.3 

47 

523.1 

159.9 

08 

294.5 

90.1 

68 

351.9 

107.6 

28 

409.3 

125.1 

88 

466.7 

142.6 

48 

524.0 

160.2 

09 

295.  5 

90.3 

69 

352.  8 

107.9 

29 

410.2 

125.4 

89 

467.6 

142.9 

49 

525.0 

160.5 

10 

296.4 

90.6 

70 

353.8 

108.2 

30 

411.2 

125.7 

90 

468.6 

143.2 

50 

526.0 

160.8 

311 

297.4 

90.9 

371 

354.8 

108.5 

431 

412.1 

126.0 

491 

469.5 

143.5 

551 

526.9 

161.1 

12 

298.3 

91.2 

72 

355.  7 

108.8 

32 

413.1 

126.3 

92 

470.5 

143.8 

52 

527.9 

161.4 

13 

299.3 

91.5 

73 

356.7 

109.1 

33 

414.0 

126.6 

93 

471.4 

144.1 

53 

528.8 

161.7 

14 

300.2 

91.8 

74 

357.6 

109.4 

34 

415.0 

126.9 

94 

472.4 

144.4 

54 

529.8 

162.0 

15 

301.2 

92.1 

75 

358.6 

109.6 

35 

416.0 

127.2 

95 

473.4 

144.7 

55 

530.8 

162.3 

16 

302.2 

92.4 

76 

359.5 

109.9 

36 

416.9 

127.5 

96 

474.3 

145.0 

56 

531.7 

162.6 

17 

303.1 

92.7 

77 

360.5 

110.2 

37 

417.9 

127.8 

97 

475.3 

145.3 

57 

532.7 

162.9 

18 

304.1 

93.0 

78 

361.4 

no.  5 

38 

418.8 

128.1 

98 

476.2 

145.6 

58 

533.6 

163.2 

19 

305.0 

93.3 

79 

362.4 

110.8 

39 

419.8 

128.4 

99 

477.2 

145.9 

59 

534.6 

163.5 

20 

306,0 

93.6 

80 

363.4 

111.1 

40 

420.7 

128.6 

500 

478.1 

146.2 

60 

535.5 

163.8 

321 

306.9 

93.9 

381 

364.  3 

111.4 

441 

421.7 

128.9 

501 

479.1 

146.5 

561 

536.5 

164.1 

22 

307.9 

94.1 

82 

365.  3 

111.7 

42 

422.7 

129.2 

02 

480.1 

146.8 

62 

537.5 

164.4 

23 

308.8 

94.4 

83 

366.2 

112.0 

43 

423.6 

129.5 

03 

481.0 

147.1 

63 

538.4 

164.6 

24 

309.8 

94.7 

84 

367.2 

112.3 

44 

424.6 

129.8 

04 

482.0 

147.4 

64 

539.4 

164.8 

25 

310.8 

95.0 

85 

368.1 

112.6 

45 

425. 5 

130.1 

05 

482.9 

147.7 

65 

540.3 

165.1 

26 

311.7 

95.3 

86 

369.1 

112.9 

46 

426.5 

130.4 

06 

483.9 

148.0 

66 

541.3 

165.4 

27 

312.7 

95.6 

87 

370.1 

113.2 

47 

427.4 

130.7 

07 

484.8 

148.3 

67 

542.2 

165.7 

28 

313.6 

95.9 

88 

371.0 

113.4 

48 

428.4 

131.0 

08 

485.8 

148.6 

68 

543.2 

166.0 

29 

314.6 

96.2 

89 

372.0 

113.7 

49 

429.3 

131.3 

09 

486.7 

148.9 

69 

544.1 

166.4 

30 

315.5 

96.5 

90 

372.9 
373.9 

114.0 

50 

430.3 

131.6 

10 

487.7 

149. 1 

70 

545.1 

166.7 

331 

316.5 

96.8 

391 

114.3 

451 

431.3 

131.9 

511 

488.7 

149.4 

571 

546.1 

167.0 

32 

317.5 

97.1 

92 

374.8 

114.6 

52 

432.2 

132.2 

12 

489.6 

149.7 

72 

547.0 

167.2 

33 

318.4 

97.4 

93 

375.8 

114.9 

53 

433.2 

132.4 

13 

490.6 

150.0 

73 

548.0 

167.5 

34 

319.4 

97.7 

94 

376.7 

115.2 

54 

434.1 

132.7 

14 

491.5 

150.2 

74 

548.9 

167.8 

35 

320.3 

97.9 

95 

377.7 

115. 5 

5.5 

435.1 

133.0 

15 

492.5 

150.5 

75 

549.9 

168.1 

36 

321.3 

98.2 

96 

378.7 

115.8 

56 

436.0 

133.3 

16 

493.4 

150.8 

76 

550.8 

168.4 

37 

322.2 

98.5 

97 

379.6 

116.1 

57 

437.0 

133.6 

17 

494.4 

151.1 

77 

551.8 

168.7 

38 

323.2 

98.8 

98 

380.6 

116.4 

58 

438.0 

133.9 

18 

495. 3 

151.4 

78 

552.7 

169.0 

39 

324.2 

99.1 

99 

381.5 

116.7 

59 

438.9 

134.2 

19 

496.3 

151.  7 

79 

553.7 

169.3 

40 

325.1 

99.4 

400 

382.  5 

117.0 

60 

439.9 

134.5 

20 

497.2 

152.  0 

80 

554.6 

169.6 

341 

326.1 

99.  7 

401 

383.4 

117.2 

461 

440.8 

1.34.  8 

521 

498.2 

152.3 

581 

555.  6 

169.9 

42 

327.0 

100.0 

02 

384.4 

117.5 

62 

441.8 

135.1 

22 

499.2 

152.6 

82 

556. 5 

170.2 

43 

328.0 

100.3 

03 

385.4 

117.8 

63 

442.7 

135. 4 

23 

500.1 

152.9 

83 

557.5 

170.5 

44 

328.9 

100.6 

04 

386.3 

118.1 

64 

443.7 

135.7 

24 

501.1 

153.2 

84 

558.4 

170.8 

45 

329.9 

100.9 

05 

387.3 

118.4 

65 

444.6 

136.0 

25 

502.0 

153. 5 

85 

559.4 

171.1 

46 

330.  8 

101.2 

06 

388.2 

118.7 

66 

445.6 

136.2 

26 

503.0 

153.8 

86 

560.4 

171.3 

47 

331.8 

101.5 

07 

389.2 

119.0 

67 

446.6 

136.5 

27 

503. 9 

154.1 

87 

561.3 

171.6 

48 

332.8 

101.8 

08 

390.1 

119.3 

68 

447.5 

136.8 

28 

504.9 

154.4 

88 

562.3 

171.9 

49 

333.7 

102.0 

09 

391.1 

119.6 

69 

448.5 

137.1 

.29 

505. 9 

154.7 

89 

563.2 

172.2 

50 

334.  7 

102.3 

10 

392.0 

119.9 

70 

449.4 

137.4 

30 

506.8 

155.0 

90 

564.2 

172.5 

351 

335.6 

102.6 

411 

393.0 

120.2 

471 

450.4 

137.7 

531 

507.8 

155. 3 

591 

565. 1 

172.8 

52 

336.6 

102.9 

12 

394.0 

120.5 

72 

451.3 

138.0 

32 

508.7 

155.6 

92 

566.1 

173.1 

53 

337.5 

103.2 

13 

394.9 

120.8 

73 

452.3 

138.3 

33 

509.7 

155,9 

93 

567.1 

173.4 

54 

338.5 

103.5 

14 

395.9 

121.0 

74 

453.3 

138.6 

34 

510.6 

156.2 

94 

568.0 

173.7 

55 

339.5 

103.8 

15 

396.8 

121.3 

75 

454.2 

138.9 

35 

511.6 

156.5 

95 

569.0 

174.0 

56 

340.4 

104.1 

16 

397.8 

121.6 

76 

455.2 

139.2 

36 

512.6 

156.8 

96 

569.9 

174.3 

57 

341.4 

104.4 

17 

398.7 

121.9 

77 

456.1 

139.5 

37 

513.5 

157.1 

97 

570.9 

174.6 

58 

342.3 

104.7 

18 

399.7 

122.2 

78 

457.1 

139.8 

38 

514.5 

157.3 

98 

571.8 

174.9 

59 

343.3 

105.0 

19 

400.7 

122.5 

79 

458.0 

140.0 

39 

515.4 

157.6 

99 

572.8 

175.2 

60 

344.2 

105.3 

20 

401.6 

122.8 

80 

459.0 

140.3 

40 

516.4 

157.9 

600 

573.8 

175.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

73°  (107°,  253°,  287° 

)• 

1 

Page  566] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  18°  (162°,  198 

°,  342° 

). 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.0 

18.9 

121 

115.1 

37.4 

181 

172.1 

55.9 

241 

229.2 

74.5 

.2 

1.9 

0.6 

62 

59.0 

19.2 

22 

116.0 

37.7 

82 

173.1 

56.2 

42 

230.2 

74.8 

3 

2.9 

0.9 

63 

59'.  9 

19.5 

23 

117.0 

38.0 

83 

174.0 

56.6 

43 

231.1 

75.1 

4 

3.8 

1.2 

64 

60.9 

19.8 

24 

117.9 

38.3 

84 

175.0 

56.9 

44 

232.1 

75.4 

5 

4.8 

1.5 

65 

61.8 

20.1 

25 

118.9 

38.6 

85 

175.9 

57.2 

45 

233.0 

75.7 

6 

5.7 

1.9 

66 

62.8 

20.4 

26 

119.8 

38.9 

86 

176.9 

57.5 

46 

234.0 

76.0 

7 

6.7 

2.2 

67 

63.7 

20.7 

27 

120.  8 

39.2 

87 

177.8 

57.8 

47 

234.9 

76.3 

8 

7.6 

2.5 

68 

64.7 

21.0 

28 

121.7 

39.6 

88 

178.8 

58.1 

48 

235.9 

76.6 

9 

8.6 

2.8 

69 

65.6 

21.3 

29 

122.7 

39.9 

89 

179.7 

58.4 

49 

236.8 

76.9 

10 

9.5 

3.1 

70 

66.6 

21.6 

30 

123.6 

40.2 

90 

180.7 
181.7 

58.7 

50 

237.8 

77.3 

11 

10.5 

3.4 

71 

67.5 

21.9 

131 

124.6 

40.5 

191 

59.0 

251 

238.7 

77.6 

12 

11.4 

3.7 

■   72 

68.5 

22.2 

32 

125. 5 

40.8 

92 

182. 6 

59.3 

52 

239.7 

77.9 

13 

12.4 

4.0 

73 

69.4 

22.6 

33 

126.5 

41.1 

93 

183.6 

59.6 

53 

240.6 

78.2 

14 

13.3 

4.3 

74 

70.4 

22.9 

34 

127.4 

41.4 

94 

184.5 

59.9 

54 

241.6 

78.5 

15 

14.3 

4.6 

75 

71.3 

23.2 

35 

128.4 

41.7 

95 

185.5 

60.3 

55 

242.5 

78.8 

16 

15.2 

4.9 

76 

72.3 

23.5 

36 

129.3 

42.0 

96 

186.4 

60.6 

56 

243.  5 

79.1 

17 

16.2 

5.3 

77 

73.2 

23.8 

37 

130.3 

42.3 

97 

187.4 

60.9 

57 

244.4 

79.4 

18 

17.1 

5.6 

78 

74.2 

24.1 

38 

131.2 

42.6 

98 

188.  3 

61.2 

58 

245.4 

79.7 

19 

18.1 

5.9 

79 

75.1 

24.4 

39 

132.2 

43.0 

99 

189.3 

61.5 

59 

246.3 

80.0 

20 

19.0 

6.2 

80 
81 

76.1 

24.7 

40 

133. 1 

43.3 

200 

190.2 

61.8 

60 

247.3 

80.3 

21 

20.0 

6.6 

77.0 

25.0 

141 

134.1 

43.6 

201 

191.2 

62.1 

261 

248.2 

80.7 

22 

20.9 

6.8 

82 

78.0 

25.3 

42 

135.1 

43.9 

02 

192.1 

62.4 

62 

249.2 

81.0 

23 

21.9 

7.1 

83 

78.9 

25.6 

43 

136.0 

44.2 

03 

193.1 

62.7 

63 

250.1 

81.3 

24 

22.8 

7.4 

84 

79.9 

26.0 

44 

137.0 

44.5 

04 

194.0 

63.0 

64 

251.1 

81.6 

25 

23.8 

7.7 

85 

80.8 

26.3 

45 

137.9 

44.8 

05 

195.0 

63.3 

65 

252.0 

81.9 

26 

24.7 

8.0 

86 

81.8 

26.6 

46 

138.9 

45.1 

06 

195.9 

63.7 

66 

253.0 

82.2 

27 

25.7 

8.3 

87 

82.7 

26.9 

47 

139.8 

45.4 

07 

196.9 

64.0 

67 

253.9 

82.5 

28 

26.6 

8.7 

88 

83.7 

27.2 

48 

140.8 

45.7 

08 

197.8 

64.3 

68 

254.9 

82.8 

29 

27.6 

9.0 

89 

84.6 

27.5 

49 

141.7 

46.0 

09 

198.8 

64.6 

69 

255.8 

83:1 

30 

28.5 

9.3 

90 

85.6 

27.8 

50 

142.7 

46.4 

10 

199.7 

64.9 

70 

256.8 

257.7 

83.4 
83.7 

31 

29.5 

9.6 

91 

86.5 

28.1 

151 

143.6 

46.7 

211 

200.7 

65.2 

271 

32 

30.4 

9.9 

92 

87.5 

28.4 

52 

144.6 

47.0 

12 

201.6 

65.5 

72 

258.7 

84.1 

33 

31.4 

10.2 

93 

88.4 

28.7 

53 

145.5 

47.3 

13 

202.6 

65.8 

73 

259.6 

84.4 

34 

32.3 

10.5 

94 

89.4 

29.0 

54 

146.5 

47.6 

14 

203.5 

66.1 

74 

260.6 

84.7 

35 

33.3 

10.8 

95 

90.4 

29.4 

55 

147.4 

47.9 

15 

204.5 

66.4 

75 

261.5 

85.0 

36 

34.2 

11.1 

96 

91.3 

29.7 

56 

148.4 

48.2 

16 

205.4 

66.7 

76 

262.5 

85.3 

37 

35.2 

11.4 

97 

92.3 

30.0 

57 

149.3 

48.5 

17 

206.4 

67.1 

77 

263.4 

85.6 

38 

36.1 

11.7 

98 

93.2 

30.3 

58 

150.3 

48.8 

18 

207.3 

67.4 

78 

264.4 

85.9 

39 

37.1 

12.1 

99 

94.2 

30.6 

59 

151.2 

49.1 

19 

208.3 

67.7 

79 

265.3 

86.2 

40 

38.0 

12.4 

100 

95.1 

30.9 

60 

152.2 

49.4 

20 

209.2 
210.2 

68.0 

80 

266.3 

86.5 

41 

39.0 

12.7 

101 

96.1 

31.2 

161 

153.1 

49.8 

221 

68.3 

281 

267.2 

86.8 

42 

39.9 

13.0 

02 

97.0 

31.5 

62 

154.1 

50.1 

22 

211.1 

68.6 

82 

268.2 

87.1 

43 

40.9 

13.3 

03 

98.0 

31.8 

63 

155.0 

50.4 

23 

212.1 

68.9 

83 

269.1 

87.5 

44 

41.8 

13.6 

04 

98.9 

32.1 

64 

156.0 

50.7 

24 

213.0 

69.2 

84 

270.1 

87.8 

45 

42.8 

13.9 

05 

99.9 

32.4 

65 

156.9 

51.0 

25 

214.0 

69.5 

85 

271.1 

88.1 

46 

43.7 

14.2 

06 

100.8 

32.8 

66 

157.9 

51.3 

26 

214.9 

69.8 

86 

272.0 

88.4 

47 

44.7 

14.5 

07 

101.8 

33.1 

67 

158.8 

51.6 

27 

215.9 

70.1 

87 

273.0 

88.7 

48 

45.7 

14.8 

08 

102.7 

33.4 

68 

159.8 

51.9 

28 

216.8 

70.5 

88 

273.9 

89.0 

49 

46.6 

15.1 

09 

103.7 

33.7. 

69 

160.7 

52.2 

29 

217.8 

70.8 

89 

274.9 

89.3 

50 

47.6 

15.5 

10 

104.6 

34.0 

70 

161.7 

52.5 

52.8 

30 

218.7 

71.1 

90 

275.8 

89.6 

51 

48.5 

15.8 

111 

105.6 

34.3 

171 

162.6 

231 

219.7 

71.4 

291 

276.8 

89.9 

52 

49.5 

16.1 

12 

106.5 

34.6 

72 

163.6 

53.2 

32 

220.6 

71.7 

92 

277.7 

90.2 

53 

50.4 

16.4 

13 

107.5 

34.9 

73 

164.5 

53.5 

33 

221.6 

72.0 

93 

278.7 

90.5 

54 

51.4 

16.7 

14 

108. 4 

35.2 

74 

165.5 

53.8 

34 

222.5 

72.3 

94 

279.6 

90.9 

55 

52.3 

17.0 

15 

109.4 

35.5 

75 

166.4 

54.1 

35 

223.5 

72.6 

95 

280.6 

91.2 

56 

53.3 

17.3 

16 

110.3 

35.8 

76 

167.4 

54.4 

36 

224.4 

72.9 

96 

281.5 

91.5     . 

57 

54.2 

17.6 

17 

111.3 

36.2 

77 

168.3 

54.7 

37 

225.4 

73.2 

97 

282.5 

91.8    ■ 

58 

55.2 

17.9 

18 

112.2 

36.5 

78 

169.  3 

55.0 

38 

226.4 

73. 5 

98 

283.4 

92.1    ■ 

59 

56.1 

18.2 

19 

113.  2 

36.8 

79 

170.2 

55.3 

39 

227.3 

73.9 

99 

284.4 

92.4    ■ 

60 

57.1 

18.5 

20 

114.1 

37.1 

80 

171.2 

55.6 

40 

228.3 

74.2 

300 

285.3 

92.7    ■ 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.     I 

i 

'2°  (108°,  252 

°,  288° 

)• 

1 

1 

TABLE  2. 

[Page  567 

Difference  of  Latitude  and  Departure  for 

18°  (162°,  198°,  342° 

)• 

DIst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

l.at. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

286.3 

93.0 

361 

343.3 

111.6 

421 

400.4 

130.1 

481 

457.5 

148.6 

541 

514.5 

.167.  2 

02 

287.2 

93.3 

62 

344.3 

111.9 

22 

401.4 

130.4 

82 

458.5 

148.9 

42 

515.5 

167.5 

03 

288.2 

93.7 

63 

345.2 

112.2 

23 

402.3 

130.7 

83 

459.4 

149.3 

43 

516.4 

167.9 

04 

289.1 

94.0 

64 

346.2 

112.5 

24 

403.3 

131.0 

84 

460.4 

149.6 

44 

517.4 

168.2 

05 

290.1 

94.3 

65 

347.1 

112.8 

25 

404.2 

131.3 

85 

461.3 

149.9 

45 

518.3 

168.5 

06 

291.0 

94.6 

66 

348.1 

113.1 

26 

405.2 

131.7 

86 

462.3 

150.2 

46 

519.3 

168.8 

07 

292.0 

94.9 

67 

349.0 

113.4 

27 

406.1 

132.0 

87 

463.2 

150.5 

47 

520.2 

169.1 

08 

292.9 

95.2 

68 

350.0 

113.7 

28 

407.1 

132.3 

88 

464.2 

150.8 

48 

521.2 

169.4 

09 

293.9 

95.5 

69 

350.9 

114.0 

29 

408.0 

132.6 

89 

465.1 

151.1 

49 

522.1 

169.7 

10 
311 

294.8 
295.8 

95.8 

70 

351.9 

114.3 

30 

409.0 
409.9 

132.9 

90 

466.1 

151.4 

50 
551 

523.1 
524. 0 

170.0 

96.1 

371 

352.9 

114.7 

431 

133.2 

491 

467.0 

151.7 

170.3 

12 

296.7 

96.4 

72 

353.8 

115.0 

32 

410.9 

133.5 

92 

468.0 

152.0 

52 

525.0 

170.6 

13 

297.7 

96.7 

73 

354.8 

115.3 

33 

411.8 

133.8 

93 

468.9 

152.3 

53 

525.9 

170.9 

14 

298.6 

97.0 

74 

355.7 

115.6 

34 

412.8 

134.1 

94 

469.8 

152.6 

54 

526.9 

171.2 

15 

299.6 

97.4 

75 

356.7 

115.9 

35 

413.7 

134.4 

95 

470.8 

153.0 

55 

527.8 

171.5 

16 

300.5 

97.7 

76 

357.6 

116.2 

36 

414.7 

134.7 

96 

471.7 

153.3 

56 

528.8 

171.8 

17 

301. 5 

98.0 

77 

358.6 

116.5 

37 

415.6 

135.1 

97 

472.7 

153.6 

57 

529.7 

172.1 

18 

302.4 

98.3 

78 

359.5 

116.8 

38 

416.6 

135.4 

98 

473.6 

153.9 

58 

530.7 

172.4 

19 

303.4 

98.6 

79 

360.5 

117.1 

39 

417.5 

135.7 

99 

474.6 

154.2 

59 

531.6 

172.7 

20 

304.3 

98.9 

80 

361.4 

117.4 

40 

418.5 

136.0 

500 

475.5 

154.5 

60 

532.6 

173.0 

321 

305.3 

99.2 

381 

362.4 

117.7 

441 

419.4 

136.3 

501 

476.5 

154.8 

561 

533. 5 

173.3 

22 

306.2 

99.5 

82 

363.3 

118.1 

42 

420.4 

136.6 

02 

477.4 

155.1 

62 

534.5 

173.6 

23 

307.2 

99.8 

83 

364.3 

118.4 

43 

421.3 

136.9 

03 

478.4 

155.4 

63 

535. 4 

173.9 

24 

308.2 

100.1 

84 

365.2 

118.7 

44 

422.3 

137.2 

04 

479.3 

155.7 

64 

536.4 

174.2 

25 

309.1 

100.4 

85 

366.2 

119.0 

45 

423.2 

137.5 

05 

480.3 

156.1 

65 

537.3 

174.6 

26 

310.1 

100.7 

86 

367.1 

119.3 

46 

424.2 

137.8 

06 

481.2 

156.4 

66 

538.3 

174.9 

27 

311.0 

101.1 

87 

368.1 

119.6 

47 

425.1 

138.1 

07 

482.2 

156.7 

67 

539.2 

175.2 

28 

312.0 

101.4 

88 

369.0 

119.9 

48 

426.1 

138.4 

08 

483.2 

157. 0 

68 

540.2 

175.5 

29 

312.9 

101.7 

89 

370.0 

120.2 

49 

427.0 

138.8 

09 

484.1 

157.3 

69 

541.1 

175.8 

30 

313.9 

102.0 
102.  3 

90 
391 

370.9 

120.5 

50 

428.0 

139.1 

10 

485.1 

157.6 

70 

542.1 

176.1 

331 

314.8 

371.9 

120.8 

451 

428.9 

139.4 

511 

486.0 

157.9 

571 

543.0 

176.4 

32 

315.8 

102.6 

92 

372.8 

121.1 

52 

429.9 

139.7 

12 

487.0 

158.2 

72 

544.0 

176.7 

33 

316.7 

102.9 

93 

373.8 

121.5 

53 

430.8 

140.0 

13 

487.9 

158.5 

73 

544.9 

177.0 

34 

317.7 

103.2 

94 

374.7 

121.8 

54 

431.8 

140.3 

14 

488.9 

158. 8 

74 

545.9 

177.3 

35 

318.6 

103.5 

95 

375.7 

122.1 

55 

432.7 

140.6 

15 

489.8 

159.1 

75 

546.8 

177.6 

36 

319.6 

103.8 

96 

376.6 

122.4 

56 

433.7 

140.9 

16 

490.8 

159.4 

76 

547.8 

178.0 

37 

320.5 

104.1 

97 

377.6 

122.  7 

57 

434. 6 

141.2 

17 

491.7 

159.7 

77 

548.7 

178.3 

38 

321.5 

104.5 

98 

378.5    123.0 

58 

435.6 

141.5 

18 

492.7 

160.0 

78 

549.7 

178.6 

39 

322.4 

104.8 

99 

379.  5 

123.3 

59 

436.5 

141.8 

19 

493.6 

160.3 

79 

550.6 

178.9 

40 

323. 4 

105.1 

400 

380.4 

123.6 

60 

437.5 

142.2 

20 

494.6 

160.7 

80 

551.6 

179.2 

341 

324.3 

105.4 

401 

381.4 

123.9 

461 

438.4 

142.5 

521 

495.5 

161.0 

581 

552.5 

179.5 

42 

325.3 

105.7 

02 

382.3 

124.2 

62 

439.4 

142.8 

22 

496.5 

161.3 

82 

553.5 

179.8 

43 

326.2 

106.0 

03 

383.3 

124.5 

63 

440.3 

143.1 

23 

497.4 

161.6 

83 

554.4 

180.1 

44 

327.2 

106.3 

04 

384.2 

124.9 

64 

441.3 

143.4 

24 

498.4 

161.9 

84 

555.4 

180.4 

45 

328.1 

106.6 

05 

385.2 

125.2 

65 

442.2 

143.7 

25 

499.3 

162.2 

85 

556.3 

180.7 

46 

329.1 

106.9 

06 

386.1 

125.5 

66 

443.2 

144.0 

26 

500.3 

162.5 

86 

557.  3 

181.1 

47 

330.0 

107.2 

07 

387.1 

125.8 

67 

444.2 

144.3 

27 

501.2 

162.9 

87 

558.2 

181.4 

48 

331.0 

107.5 

08 

388.0 

126.1 

68 

445.1 

144.6 

28 

502.2 

163.2 

88 

559.2 

181.7 

49 

331.9 

107.9 

09 

389.0 

126.4 

69 

446.1 

144.9 

29     503.1  1 

163.5 

89 

560.1 

182.0 

50 
351 

332.9 

108.2 

10 

389.9 
390.9 

126.7 

70 

447.0 

145.2 

30 

504.1 

163.  8 

90 

561.1 

182.3 

333.8 

108.5 

411 

127.0 

471 

448.0 

145.6 

531 

505. 0 

164.1 

591 

562.0 

182.7 

52 

334.8 

108.8 

12 

391.8 

127.3 

72 

448.9 

145.9 

32 

506.0 

164.4 

92 

563.0 

J  83.0 

53 

335.7 

109.1 

13 

392.8 

127.6 

73 

449.9 

146.2 

33 

506.9 

164.7 

93 

563.9 

183.3 

54 

336.7 

109.4 

14 

393.7 

127.9 

74 

450.8 

146.5 

34 

507.9 

165.0 

94 

564.9 

183.6 

55 

337.6 

109.7 

15 

394.7 

128.3 

75 

451.  8 

146.8 

35 

508.8 

165.3 

95 

565.8 

183.9 

56 

338.6 

110.0 

16 

395.6 

128.6 

76 

452.7 

147.1 

36 

509.8 

165.6 

96 

566.8 

184.2 

57 

339.5 

110.3 

17 

396.6 

128.9 

77 

453.7 

147.4 

37 

510.7 

165.9 

97 

567.7 

184.5 

58 

340.5 

110.6 

18 

397.5 

129.2 

78 

454.6 

147.7 

38 

511.7 

166.2 

98 

568.7 

184.8 

59 

341.4 

110.9 

19 

398.5 

129.5 

79 

455.6 

148.0 

39 

512.6 

166.  5 

99 

569.6 

185.1 

60 

342.4 

111.3 

20 

399.5 

129.8 

80 

456.5 

148.3 

40 

513.6 

166.9 

600 

570.6 

185.4 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

72°  (108,  252°,  288° 

. 

Page  668] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for 

19°  (161°,  199 

°,  341° 

)• 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.3 

61 

57.7 

19.9 

121 

114.4 

39.4 

181 

171.1 

58.9 

241 

227.9 

78.5 

2 

1.9 

0.7 

62 

58.6 

20.2 

22 

115.4 

39.7 

82 

172.1 

59.3 

42 

228.8 

78.8 

3 

2.8 

1.0 

63 

59.6 

20.5 

23 

116.3 

40.0 

83 

173.0 

59.6 

43 

229.8 

79.1 

4 

3.8 

1.3 

64 

60.5 

20.8 

24 

117.2 

40.4 

84 

174.0 

59.9 

44 

230.  7 

79.4 

5 

4.7 

1.6 

66 

61.5 

21.2 

25 

118.2 

40.7 

85 

174.9 

60.2 

45 

231.7 

79.8 

6 

5.7 

2.0 

66 

62.4 

21.5 

26 

119.1 

41.0 

86 

175.9 

60.6 

46 

232.6 

80.1 

7 

6.6 

2.3 

67 

63.3 

21.8 

27 

120.1 

41.3 

87 

176.8 

60.9 

47 

233.5 

80.4 

8 

7.6 

2.6 

68 

64.3 

22.1 

28 

121.0 

41.7 

88 

177.8 

61.2 

48 

234.5 

80.7 

9 

8.5 

2.9 

69 

65.2 

22.5 

29 

122.0 

42.0 

89 

178.7 

61.5 

49 

235.4 

81.1 

10 

9.5 

3.3 

70 

66.2 

22.8 

30 

122.9 

42.3 

90 

179.6 

61.9 

50 

236.4 

81.4 

11 

10.4 

3.6 

71 

67.1 

23.1 

131 

123.9 

42.6 

191 

180.6 

62.2 

251 

237.3 

81.7 

12 

11.3 

3.9 

72 

68.1 

23.4 

32 

124.8 

43.0 

92 

181.5 

62.5 

52 

238.3 

82.0 

13 

12.3 

4.2 

73 

69.0 

23.8 

33 

125.8 

43.3 

93 

182.5 

62.8 

53 

239.2 

82.4 

14 

13.2 

4.6 

74 

70.0 

24.1 

34 

126.7 

43.6 

94 

183.4 

63.2 

54 

240.2 

82.7 

15 

14.2 

4.9 

75 

70.9 

24.4 

35 

127.6 

44.0 

95 

184.4 

63.5 

55 

241.1 

83.0 

16 

15.1 

5.2 

76 

71.9 

24.7 

36 

128.6 

44.3 

96 

185.3 

63.8 

56 

242.1 

83.3 

17 

16.1 

5.5 

77 

72.8 

25.1 

37 

129.5 

44.6 

97 

186.3 

64.1 

57 

243.0 

83.7 

18 

17.0 

5.9 

78 

73.8 

25.4 

38 

130.5 

44.9 

98 

187.2 

64.5 

58 

243.9 

84.0 

19 

18.0 

6.2 

79 

74.7 

25.7 

39 

131.4 

45.3 

99 

188.2 

64.8 

59 

244.9 

84.3 

20 

18.9 

6.5 

80 

75.6 

26.0 

40 

132.4 

45.6 

200 

189.1 

65.1 

60 

245.8 

84.6 

21 

19.9 

6.8 

81 

76.6 

26.4 

141 

133.3 

45.9 

201 

190.0 

65.4 

261 

246.8 

85.0 

22 

20.8 

7.2 

82 

77.5 

26.7 

42 

134.3 

46.2 

02 

191.0 

65.8 

62 

247.7 

85.3 

23 

21.7 

7.5 

83 

78.5 

27.0 

43 

135.2 

46.6 

03 

191.9 

66.1 

63 

248.7 

85.6 

24 

22.7 

7.8 

84 

79.4 

27.3 

44 

136.2 

46.9 

04 

192.9 

66.4 

64 

249.6 

86.0 

25 

23.6 

8.1 

85 

80.4 

27.7 

45 

137.1 

47.2 

05 

193.8 

66.7 

65 

250.6 

86.3 

26 

24.6 

8.5 

86 

81.3 

28.0 

46 

138.0 

47.5 

06 

194.8 

67.1 

66 

251.5 

86.6 

27 

25.5 

8.8 

87 

82.3 

28.3 

47 

139.0 

47.9 

07 

195.7 

67.4 

67 

252.5 

86.9 

28 

26.5 

9.1 

88 

83.2 

28.7 

48 

139.9 

48.2 

08 

196.7 

67.7 

68 

253.4 

87.3 

29 

27.4 

9.4 

89 

84.2 

29.0 

49 

140.9 

48.5 

09 

197.6 

68.0 

69 

254.3 

87.6 

30 

28.4 

9.8 

90 

85.1 

29.3 

50 

141.8 

48.8 

10 

198.6 

68.4 

70 

255.3 

87.9 

31 

29.3 

10.1 

91 

86.0 

29.6 

151 

142.8 

49.2 

211 

199.5 

68.7 

271 

256.2 

88.2 

32 

30.3 

10.4 

92 

87.0 

30.0 

52 

143.7 

49.5 

12 

200.4 

69.0 

72 

257.2 

88.6 

33 

31.2 

10.7 

93 

87.9 

30.3 

53 

144.7 

49.8 

13 

201.4 

69.3 

73 

258.1 

88.9 

34 

32.1 

11.1 

94 

88.9 

30.6 

54 

145.6 

50.1 

14 

202.3 

69.7 

74 

259.1 

89.2 

35 

33.1 

11.4 

95 

89.8 

30.9 

55 

146.6 

50.5 

15 

203.3 

70.0 

75 

260.0 

89.5 

36 

34.0 

11.7 

96 

90.8 

31.3 

56 

147.5 

50.8 

16 

204.2 

70.3 

76 

261.0 

89.9 

37 

35.0 

12.0 

97 

91.7 

31.6 

57 

148.4 

51.1 

17 

205.2 

70.6 

77 

261.9 

90.2 

38 

35.9 

12.4 

98 

92.7 

31.9 

58 

149.4 

51.4 

18 

206.1 

71.0 

78 

262.9 

90.5 

39 

36.9 

12.7 

99 

93.6 

.32.2 

59 

150.3 

51.8 

19 

207.1 

71.3 

79 

263.8 

90.8 

40 

37.8 

13.0 

100 

94.6 

32.6 

60 

151.3 

52.1 

20 

208.0 
209.0 

71.6 

80 

264.7 

91.2 

41 

38.8 

13.3 

101 

95.5 

32.9 

161 

152.2 

52.4 

221 

72.0 

281 

265.7 

91.5 

42 

39.7 

13.7 

02 

96.4 

33.2 

62 

153.2 

52.7 

22 

209.9 

72.3 

82 

266.6 

91.8 

43 

40.7 

14.0 

03 

97.4 

33.5 

63 

154.1 

53.1 

23 

210.9 

72.6 

83 

267.6 

92.1 

44 

41.6 

14.3 

04 

98.3 

33.9 

64 

155.1 

53.4 

24 

211.8 

72.9 

84 

268.5 

92.5 

45 

42.5 

14.7 

05 

99.3 

34.2 

65 

156.0 

53.7 

25 

212.7 

73.3 

85 

269.5 

92.8 

46 

43.5 

15.0 

06 

100.2 

34.5 

66 

157.0 

54.0 

26 

213.7 

73.6 

86 

270.4 

93.1 

47 

44.4 

15.3 

07 

101.2 

34.8 

67 

157.9 

54.4 

27 

214.6 

73.9 

87 

271.4 

93.4 

48 

45.4 

15.6 

08 

102.1 

35.2 

68 

158.8 

54.7 

28 

215.6 

74.2 

88 

272.3 

93.8 

49 

46.3 

16.0 

09 

103.1 

35.5 

69 

159.8 

55.0 

29 

216.  5 

74.6 

89 

273.3 

94.1 

50 

47.3 

16.3 

10 

104.0 

35.8 

70 

160.7 

55.3 

30 

217.5 

74.9 

90 

274.2 

94.4 

51 

48.2 

16.6 

111 

105.0 

36.1 

171 

161.7 

55.7 

231 

218.4 

75.2 

291 

275.1 

94.7 

52 

49.2 

16.9 

12 

105.9 

36.5 

72 

162.6 

56.0 

32 

219.4 

75.5 

92 

276.1 

95.1 

53 

50.1 

17.3 

13 

106.8 

36.8 

73 

163.6 

56.3 

33 

220.3 

75.9 

93 

277.0 

95.4 

54 

51.1 

17.6 

14 

107.8 

37.1 

74 

164.5 

56.6 

34 

221.3 

76.2 

94 

278.0 

95.7 

55 

52.0 

17.9 

15 

108.7 

37.4 

75 

165.5 

57.0 

35 

222.2 

76.5 

95 

278.9 

96.0 

56 

52.9 

18.2 

16 

109.7 

37.8 

76 

166.4 

57.3 

36 

223.1 

76.8 

96 

279.9 

96.4 

57 

53.9 

18.6 

17 

110.6 

38.1 

77 

167.4 

57.6 

37 

224.1 

77.2 

97 

280.8 

96.7 

58 

54.8 

18.9 

18 

111.6 

38.4 

78 

168.3 

58.0 

38 

225.0 

77.5 

98 

281.8 

97.0 

59 

55.8 

19.2 

19 

112.5 

38.7 

79 

169.2 

58.3 

39 

226.0 

77.8 

99 

282.7 

97.3 

60 

56.7 

19.5 

20 

113.5 

39.1 

80 

170.2 

58.6 

40 

226.9 

78.1 

300 

283.7 

97.7 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Diet. 

Dep. 

Lat. 

ri°  (1 

09°,  251 

°,  289° 

). 

TABLE  2. 

[Page  569 

Difference  of  Latitude  and  Departure  for  19°  (161°,  199°,  341° 

)• 

Dist.     ; 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep.  1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.          Dep. 

301 

284.6 

98.0 

361 

341.3 

117.5 

421 

398.1 

137.0 

481 

454.8 

156.6 

541 

511.5 

176.1 

02     285.5  1 

98.3 

62 

342.3 

117.8 

22 

399.0 

137.4 

82 

455.7 

156.9 

42 

512.4 

176.4 

03 

286.5 

98.6 

63 

343.2 

118.2 

23 

400.0 

137.  7 

83 

456.7 

157.2 

43 

513.4 

176.8 

04 

287.4 

99.0 

64 

344.2 

118.5 

24 

400.9 

138.0 

84 

457.6 

157.6 

44 

514.3 

177.1 

05 

288.4 

99.3 

65 

345.1 

118.8 

25 

401.8 

138.4 

85 

458.6 

157.9 

45 

515.3 

177.4 

06 

289.3 

99.6 

66 

346.1 

119.1 

26 

402.8 

138.7 

86 

459.5 

158.2 

46 

516.2 

177.7 

07 

290.3 

99.9 

67 

347.0 

119.5 

27 

403.7 

139.0 

87 

460.5 

158.5 

47 

517.2 

178.1 

08 

291.2 

100.3 

68 

348.0 

119.8 

28 

404.7 

139.3 

88 

461.4 

158.9 

48 

518.1 

178.4 

09 

292.2 

100.6 

69 

348.9 

120.1 

29 

405.6 

139.7 

89 

462.4 

159.2 

49 

519.1 

178.7 

10 

293.1 

100.9 

70 

349.8 

120.4 

30 

406.6 

140.0 

90 

463.3 

159.5 

50 

520.0 

179.0 

311 

294.1 

101.2 

371 

350.8 

120.8 

431 

407.5 

140.3 

491 

464.3 

159.8 

551 

521.0 

179.4 

12 

295.0 

101.6 

72 

351.7 

121.1 

32 

408.5 

140.6 

92 

465.2 

160.2 

52 

521.9 

179.7 

13 

295.9 

101.9 

73 

352.7 

121.4 

33 

409.4 

141.0 

93 

466.1 

160.5 

53 

522.8 

180.0 

14 

296.9 

102.2 

74 

353.6 

121.7 

34 

410.4 

141.3 

94 

467.1 

160.8 

54 

523.8 

180.3 

15 

297.8 

102.5 

75 

354.6 

122.1 

35 

411.3 

141.6 

95 

468.0 

161.1 

55 

524.7 

180.7 

16 

298.8 

102.9 

76 

355.5 

122.4 

36 

412.2 

141.9 

96 

469.0 

161.5 

56 

525.7 

181.0 

17 

299.7 

103.2 

77 

356.5 

122.7 

37 

413.2 

142.3 

97 

469.9 

161.8 

57 

526.6 

181.3 

18 

300.7 

103.5 

78 

357.4 

123.0 

38 

414.1 

142.6 

98 

470.9 

162.1 

58 

527.6 

181.6 

19 

301.6 

103.8 

79 

358.4 

123.4 

39 

415.1 

142.9 

99 

471.8 

162.4 

59 

528.5 

182.0 

20 
321 

302.6 

104.2 

80 

359.3 

123.7 
124. 0 

40 
441 

416.0 

143.2 

500 

472.8 

162.8 

60 

529.5 

182.3 

182.6 

303.5 

104.5 

381 

360.2 

417.0 

143.6 

501 

473.7 

163.1 

561 

530.4 

22 

304.5 

104.8 

82 

361.2 

124.4 

42 

417.9 

143.9 

02 

474.7 

163.4 

62 

531.4 

182.9 

23 

305.4 

105. 1 

83 

362.1 

124.7 

43 

418.9 

144.2 

03 

475.6 

163.7 

63 

532.3 

183.3 

24 

306.3 

105.  5 

84 

363.1 

125.0 

44 

419.8 

144.5 

04 

476.5 

164.1 

64 

533.2 

183.6 

25 

307.3 

105.8 

85 

364.0 

125.3 

45 

420.8 

144.9 

05 

477.5 

164.4 

65 

534.2 

183.9 

26 

308.2 

106.1 

86 

365.0 

125.7 

46 

421.7 

145.2 

06 

478.4 

164.7 

66 

535.1 

184.2 

27 

309.2 

106.4 

87 

365. 9 

126.0 

47 

422.6 

145.5 

07 

479.4 

165.0 

67 

536.1 

184.6 

28 

310.1 

106.8 

88 

366.9 

126.3 

48 

423.6 

145.8 

08 

480.3 

165.4 

68 

537.0 

184.9 

29 

311.1 

107.1 

89 

367.8 

126.6 

49 

424.5 

146.2 

09 

481.2 

165.7 

69 

538.0 

185.2 

30 

312.0 

107.4 

90 

368.8 

127.0 

50 

425.5 

146.5 

10 

482.2 

166.1 

70 

538.9 

185.6 

331 

313.0 

107.7 

391 

369.7 

127.3 

451 

426.4 

146.8 

611 

483.1 

166.4 

571 

539.9 

185.9 

32 

313.9 

108.1 

92 

370.6 

127.6 

52 

427.4 

147.1 

12 

484.1 

166.7 

72 

540.8 

186.2 

33 

314.9 

108.4 

93 

371.6 

127.9 

53 

428.3 

147.5 

13 

485.0 

167.0 

73 

541.7 

186.5 

34 

315.8 

108.7 

94 

372.5 

128.3 

54 

429.3 

147.8 

14 

486.0 

167.4 

74 

542.7 

186.9 

35 

316.7 

109.1 

95 

373.5 

128.6 

55 

430.2 

148.1 

15 

486.9 

167.7 

75 

543.6 

187.2 

36 

317.7 

109.4 

96 

374.4 

128.9 

56 

431.2 

148.4 

16 

487.9 

168.0 

76 

544.6 

187.5 

37 

318.6 

109.7 

97 

375.4 

129.2 

57 

432.1 

148.8 

17 

488.8 

168.3 

77 

545.5 

187.8 

38 

319.6 

110.0 

98 

376.3 

129.6 

58 

433.0 

149.1 

18 

489.7 

168.7 

78 

546.5 

188.2 

39 

320.5 

110.4 

99 

377.3 

129.9 

59 

434.0 

149.4 

19 

490.7 

169.0 

79 

547.4 

188.5 

40 

321.5 

110.7 

400 

378.2 

130.2 

60 

434.9 

149.7 

20 

491.6 

169.3 

80 

548.4 

188.8 

341 

322.4 

111.0 

401 

379.2 

130.5 

461 

435.9 

150.1 

521 

492.6 

169.6 

581 

549.3 

189.1 

42 

323. 4 

111.3 

02 

380.1 

130.9 

62 

436.8 

150.4 

22 

493.5 

170.0 

82 

550.3 

189.5 

43 

324.3 

111.7 

03 

381.0 

131.  2 

63 

437.8 

150.7 

23 

494.5 

170.3 

^3 

551.2 

189.8 

44 

825.3 

112.0 

04 

382.0 

131.5 

64 

438.7 

151.0 

24 

495.4 

170.6 

84 

552.2 

190.1 

45 

326.2 

112.3 

05 

382.9 

131.8 

65 

439.7 

151.4 

25 

496.4 

170.9 

85 

553. 1 

190.4 

46 

327.1 

112.6 

06 

383.9 

132.2 

66 

440.6 

151.7 

2a 

497.3 

171.2 

86 

554. 1 

190.8 

47 

328.1 

113.0 

07 

384.8 

132.5 

67 

441.6 

152.0 

27 

498.3 

171.6 

87 

555.0 

191.1 

48 

329.0 

113.3 

08 

385.8 

132.8 

68 

442.5 

152.4 

28 

499.2 

171.9 

88 

555. 9 

191.4 

49 

330. 0 

113.6 

09 

386.7 

133.1 

69 

443.4 

152.7 

29 

500.1  :172.2 

89 

556.9 

191.7 

50 

330.9 

113.9 

10 

387.7 

133.5 

70 

444.4 

153.0 

30 

501.1 
502.0 

172.5 

90 

557.8 

192.1 

351 

331.9 

114.3 

411 

388.6 

133.8 

471 

445.3 

153.3 

531 

172.9 

591 

558.8 

192.4 

52 

332.8 

114.6 

12 

389.6 

134.1 

72 

446.3 

153.7 

32 

503.0 

173.2 

92 

559.7 

192.7 

53 

333.8 

114.9 

13 

390.5 

134.4 

73 

447.2 

154.0 

33 

503.9 

173.5 

93 

560.7 

193.0 

54 

334.7 

115.2 

14 

391.4 

134.8 

74 

448.2 

154.3 

34 

504.9 

173.8 

94 

561.6 

193.4 

55 

335.  7 

115.6 

15 

392.4 

135.1 

75 

449.1 

154.6 

35 

505.8 

174.2 

95 

562.6 

193.7 

56 

336.6 

115.9 

16 

393.3 

135.4 

76 

450.1 

155. 0 

36 

506.8 

174.5 

96 

563.5 

194.0 

57 

337.5 

116.2 

17 

394.  3 

135.7 

77 

451.0 

155.3 

37 

507.7 

174.8 

97 

564.5 

194.3 

58 

338.  5 

116.5 

18 

395.2 

136.1 

78 

452.0 

155.6 

38 

508.7 

175.1 

98 

565.4 

194.7 

59 

339.4 

116.9 

19 

396.2 

136.4 

79 

452.9 

155.9 

39 

509.6 

175.  5 

99 

566.4 

195.0 

60 

340.4 

117.2 

20 

397.1 

136.7 

80 

453.8 

156.3 

40 

510.6 

175.8 

600 

567.3 

195.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

71°  (109°,  251°,  289° 

)• 

Page  670] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  20°  (160°,  200 

°,  340° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.3 

61 

57.3 

20.9 

121 

113.7 

41.4 

181 

170.1 

61.9 

241 

226.5 

82.4 

2 

1.9 

0.7 

62 

58.3 

21.2 

22 

114.6 

41.7 

82 

171.0 

62.2 

42 

227.4 

82.8 

3 

2.8 

1.0 

63 

59.2 

21.5 

23 

115.6 

42.1 

83 

172.0 

62.6 

43 

228.3 

83.1 

4 

3.8 

1.4 

64 

60.1 

21.9 

24 

116.5 

42.4 

84 

172.9 

62.9 

44 

229.3 

83.5 

5 

4.7 

1.7 

65 

61.1 

22.2 

25 

117.5 

42.8 

85 

173.8 

63.3 

45 

230.2 

83.8 

6 

5.6 

2.1 

66 

62.0 

22.6 

26 

118.4 

43.1 

86 

174.8 

63.6 

46 

231.2 

84.1 

7 

6.6 

2.4 

67 

63.0 

22.9 

27 

119.3 

43.4 

87 

175.7 

64.0 

47 

232.1 

84.5 

8 

7.5 

2.7 

68 

63.9 

23.3 

28 

120.3 

43.8 

88 

176.7 

64.3 

48 

233.0 

84.8 

9 

8.5 

3.1 

69 

64.8 

23.6 

29 

,  121.2 

44.1 

89 

177.6 

64.6 

49 

234.0 

85.2 

10 

9.4 

3.4 

70 

65.8 

23.9 

30 

122.2 

44.5 

90 

178.5 

65.0 

50 

234.9 
235.  9 

85.5 

11 

10.3 

3.8 

71 

66.7 

24.3 

131 

123.1 

44.8 

191 

179.5 

65.3 

251 

85.8 

12 

11.3 

4.1 

72 

67.7 

24.6 

32 

124.0 

45.1 

92 

180.4 

65.7 

52 

236.8 

86.2 

13 

12.2 

4.4 

73 

68.6 

25.0 

33 

125.0 

45.5 

93 

181.4 

66.0 

53 

237.7 

86.5 

14 

13.2 

4.8 

74 

69.5 

25.3 

34 

125.9 

45.8 

94 

182.3 

66.4 

54 

238.7 

86.9 

15 

14.1 

5.1 

75 

70.5 

25.7 

35 

126.9 

46.2 

95 

183.2 

66.7 

55 

239.6 

87.2 

16 

15.0 

5.5 

76 

71.4 

26.0 

36 

127.8 

46.5 

96 

184.2 

67.0 

56 

240.6 

87.6 

17 

16.0 

5.8 

77 

72.4 

26.3 

37 

128.7 

46.9 

97 

185.1 

67.4 

57 

241.5 

87.9 

18 

16.9 

6.2 

78 

73.3 

26.7 

38 

129.7 

47.2 

98 

186.1 

67.7 

58 

242.4 

88.2 

19 

17.9 

6.5 

79 

74.2 

27.0 

39 

130.6 

47.5 

99 

187.0 

68.1 

59 

243.4 

88.6 

20 

18.8 

6.8 

80 
81 

75.2 

27.4 

40 

131.6 

47.9 

200 

187.9 

68.4 

60 

244.3 

88.9 

21 

19.7 

7.2 

76.1 

27.7 

141 

132.5 

48.2 

201 

188.9 

68.7 

261 

245.3 

89.3 

22 

20.7 

7.5 

82 

77.1 

28.0 

42 

133.4 

48.6 

02 

189.8 

69.1 

62 

246.2 

89.6 

23 

21.6 

7.9 

83 

78.0 

28.4 

43 

134.4 

48.9 

03 

190.8 

69.4 

63 

247.1 

90.0 

24 

22.6 

8.2 

84 

78.9 

28.7 

44 

135.3 

49.3 

04 

191.7 

69.8 

64 

248.1 

90.3 

25 

23.5 

8.6 

85 

79.9 

29.1 

45 

136.3 

49.6 

05 

192.6 

70.1 

65 

249.0 

90.6 

26 

24.4 

8.9 

86 

80.8 

29.4 

46 

137. 2 

49.9 

06 

193.6 

70.5 

66 

250.0 

91.0 

27 

25.4 

9.2 

87 

81.8 

29.8 

47 

138.1 

50.3 

07 

194.5 

70.8 

67 

250.9 

91.3 

28 

26.3 

9.6 

88 

82.7 

30.1 

48 

139.1 

50.6 

08 

195.5 

71.1 

68 

251.8 

91.7 

29 

27.3 

9.9 

89 

83.6 

30.4 

49 

140.0 

51.0 

09 

196.4 

71.5 

69 

252.8 

92.0 

30 

28.2 

10.3 

90 

84.6 

30.8 

50 

140.9 

51.3 

10 

197.3 

71.8 

70 

253.  7 
254.7 

92.3 

31 

29.1 

10.6 

91 

85.5 

31.1 

151 

141.9 

51.6 

211 

198.3 

72.2 

271 

92.7 

32 

30.1 

10.9 

92 

86.5 

31.5 

52 

142.8 

52.0 

12 

199.2 

72.5 

72 

255.6 

93.0 

33 

31.0 

11.3 

93 

87.4 

31.8 

53 

143.8 

52.3 

13 

200.2 

72.9 

73 

256.5 

93.4 

34 

31.9 

11.6 

94 

88.3 

32.1 

54 

144.7 

52.7 

14 

201.1 

73.2 

74 

257.5 

93.7 

35 

32.9 

12.0 

95 

89.3 

32.5 

55 

145.7 

53.0 

15 

202.0 

73.5 

75 

258.4 

94.1 

36 

33.8 

12.3 

96 

90.2 

32.8 

56 

146.6 

53.4 

16 

203.0 

73.9 

76 

259.4 

94.4 

37 

34.8 

12.7 

97 

91.2 

33.2 

57 

147.5 

53.7 

17 

203.9 

74.2 

77 

260.3 

94.7 

38 

35.7 

13.0 

98 

92.1 

33.5 

58 

148.5 

54.0 

18 

204.9 

74.6 

78 

261.2 

95.1 

39 

36.6 

13.3 

99 

93.0 

33.9 

59 

149.4 

54.4 

19 

205.  8 

74.9 

79 

262.2 

95.4 

40 

37.6 

13.7 

100 

94.0 

34.2 

60 

150.4 
151.3 

54.7 

20 

206.7 

75.2 

80 
281 

263.1 

95.8 

41 

38.5 

14.0 

101 

94.9 

34.5 

161 

55.1 

221 

207.7 

75.6 

264.1 

96.1 

42 

39.5 

14.4 

02 

95.8 

34.9 

62 

152.2 

55.4 

22 

208.6 

75.9 

82 

265.0 

96.4 

43 

40.4 

14.7 

03 

96.8 

35.2 

63 

153.2 

55.7 

23 

209.6 

76.3 

83 

265.9 

96.8 

44 

41.3 

15.0 

04 

97.7 

35.6 

64 

154.1 

56.1 

24 

210.5 

76.6 

84 

266.9 

97.1 

45 

42.3 

15.4 

05 

98.7 

35.9 

65 

155.0 

56.4 

25 

211.4 

77.0 

85 

267.8 

97.5 

46 

43.2 

15.7 

06 

99.6 

36.3 

66 

156.0 

56.8 

26 

212.4 

77.3 

86 

268.8 

97.8 

47 

44.2 

16.1 

07 

100.5 

36.6 

67 

156.9 

57.1 

27 

213.3 

77.6 

87 

269.7 

98.2 

48 

45.1 

16.4 

08 

101.5 

36.9 

68 

157.9 

57.5 

28 

214.2 

78.0 

88 

270.6 

98.5 

49 

46.0 

16.8 

09 

102.4 

37.3 

69 

158.8 

57.8 

29 

215.2 

78.3 

89 

271.6 

98.8 

50 

47.0 

17.1 

10 

103.4 

37.6 

70 

159.7 

58.1 

30 

216.1 

78.7 

90 

272.5 

99.2 
99.5 

51 

47.9 

17.4 

111 

104.3 

38.0 

171 

160.7 

58.5 

231 

217.1 

79.0 

291 

273.5 

52 

48.9 

17.8 

12 

105.2 

38.3 

72 

161.6 

58.8 

32 

218.0 

79.3 

92 

274.4 

99.9 

53 

49.8 

18.1 

13 

106.2 

38.6 

73 

162.6 

59.2 

33 

218.9 

79.7 

93 

275.3 

100.2 

54 

50.7 

18.5 

14 

107.1 

39.0 

74 

163.5 

59.5 

34 

219.9 

80.0 

94 

276.3 

100.6 

55 

51.7 

18.8 

15 

108.1 

39.3 

75 

164.4 

59.9 

35 

220.8 

80.4 

95 

277.2 

100.9 

56 

52.6 

19.2 

16 

109.0 

39.7 

76 

165.4 

60.2 

36 

221.8 

80.7 

96 

278.1 

101.2 

57 

53.6 

19.5 

17 

109.9 

40.0 

77 

166.3 

60.5 

37 

222.7 

81.1 

97 

279.1 

101.6 

58 

54.5 

19.8 

18 

110.9 

40.4 

78 

167.3 

60.9 

38 

223.6 

81.4 

98 

280.0 

101.9 

59 

55.4 

20.2 

19 

111.8 

40.7 

79 

168.2 

61.2 

39 

224.6 

81.7 

99 

281.0 

102.3 

60 

56.4 

20.5 

20 

112.8 

41.0 

80 

169.1 

61.6 

40 

225.5 

82.1 

300 

281.9 

102.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

'0°  (110°,  250 

°,  290° 

). 

TABLE  2. 

[Page  571 

Difference  of  Latitude  and  Depart 

are  for  20°  (160°,  200°,  340 

')• 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

282.9 

103.0 

361 

339.2 

123.5 

421 

395.6 

144.0 

481 

452.0 

164.5 

541 

508.4 

185.0 

02 

283.8 

103.  3 

62 

340.  2 

123.8 

22 

396.6 

144.3 

82 

453.0 

164.8 

42 

509.3 

185.4 

03 

284.7 

103. 6 

63 

341.1 

124.2 

23 

397.5 

144.7 

83 

453.9 

165.2 

43 

510.3 

185.7 

04 

285.  7 

104.0 

64 

342.1 

124.5 

24 

398.4 

145.0 

84 

454.8 

165.5 

44 

511.2 

186.0 

05 

286.6 

104.3 

65 

343.0 

124.8 

25 

399.4 

145.4 

85 

455.8 

165.9 

45 

512.1 

186.4 

06 

287.6 

104.7 

66 

343.9 

125.2 

26 

400.3 

145.7 

86 

456.7 

166.3 

46 

513.1 

186.8 

07 

288.5 

105.0 

67 

344.9 

125.5 

27 

401.3 

146.1 

87 

457.7 

166.6 

47 

514.0 

187.1 

08 

289.4 

105.4 

68 

345.8 

125.9 

28 

402.2 

146.4 

88 

458.6 

166.9 

48 

515.0 

187.4 

09 

290.4 

105.7 

69 

346.8 

126.2 

29 

403.1 

146.7 

89 

459.5 

167.  3 

49 

515.9 

187.8 

10 

291.3 

106.0 

70 

347.7 

126.6 

30 

404.1 

147.1 

90 

460.5 

167.7 

50 

516.8 

188.2 

311 

292.3 

106.4 

371 

348.6 

126.9 

431 

405.0 

147.4 

491 

461.4 

168.0 

551 

517.8 

188.5 

12 

293.2 

106.7 

72 

349.6 

127.  2. 

32 

406.0 

147.8 

92 

462.4 

168.3 

52 

518.7 

188.8 

13 

294.1 

107.1 

73 

350.5 

127.6 

33 

406.9 

148.1 

93 

463.3 

168.6 

53 

519.7 

189.1 

14 

295.1 

107.4 

74 

351.5 

127.9 

34 

407.8 

148.4 

94 

464.2 

168.9 

54 

520.6 

189.4 

15 

296.0 

107.7 

75 

352.4 

128.3 

35 

408.8 

148.8 

95 

465.2 

169.3 

55 

521.5 

189.8 

16 

297.0 

108.1 

76 

353.  3 

128.6 

36 

409.7 

149.1 

96 

466.1 

169.6 

56 

522.5 

190.2 

17 

297.9 

108.4 

77 

354.  3 

129.0 

37 

410.7 

149.5 

97 

467.0 

170.0 

57 

523.4 

190.5 

18 

298.8 

108.8 

7^ 

355.2 

129.3 

38 

411.6 

149.8 

98 

468.0 

170.3 

58 

524.4 

190.8 

19 

299.8 

109.1 

79 

356.  2 

129.6 

39 

412.5 

150.2 

99 

468.9 

170.7 

59 

525.3 

191.2 

20 
321 

300.7 

109.5 

80 

357.1 

130.0 

40 

413.5 

150.5 

500 

469.9 

171.0 
171.3 

60 
.561 

526.2 

191.6 

301.6 

109.8 

381 

358.0 

130.3 

441 

414.4 

150.8 

501 

470.8 

527.2 

191.9 

22 

302.6 

110.1 

82 

359. 0 

130.7 

42 

415.4 

151.2 

02 

471.7 

171.7 

62 

528.1 

192.2 

23 

303.5 

110.5 

83 

359.9 

131.0 

43 

416.3 

151.5 

03 

472.7 

172.0 

63 

529.0 

192.0 

24 

304.5 

110.8 

84 

360.8 

131.3 

44 

417.2 

151.9 

04 

473.6 

172.4 

64 

530.0 

192.9 

25 

305.4 

111.2 

85 

361.8 

131.7 

45 

418.2 

152.2 

05 

474.5 

172.7 

65 

530.9 

193.2 

26 

306.3 

111.5 

86 

362.7 

132.0 

46 

419.1 

152.5 

06 

475.4 

173.0 

66 

531.8 

193.6 

27 

307.3 

111.8 

87 

363.7 

132.4 

47 

420.0 

152.9 

07 

476.4 

173.4 

67 

532.8 

193.9 

28 

308.2 

112.2 

88 

364.6 

132.7 

48 

421.0 

153.2 

08 

477.3 

173.7 

68 

533.7 

194.2 

29 

309.2 

112.5 

89 

365.5 

133.1 

49 

421.9 

153.6 

09 

478.3 

174.1 

69 

534.7 

194.6 

30 

310.1 

112.9 

90 

366.5 

133.4 

50 

422.9 

153.9 

10 

479.2 

174.4 

70 

535.6 

195.0 

331 

311.0 

113.2 

391 

367.4 

133.7 

451 

423.8 

154.3 

511 

480.2 

174.8 

571     536. 6 

195.3 

32 

312.0 

113.6 

92 

368.4 

134.1 

52 

424.7 

154.6 

12 

481.1 

175.1 

72 

537.5 

195,6 

33 

312.9 

113.9 

93 

369.  3 

134.4 

53 

425.7 

154.9 

13 

482.1 

175.4 

73 

538.5 

195.9 

34 

313.9 

114.2 

94 

370.2 

134.8 

54 

426.6 

155.3 

14 

483.0 

175.8 

74 

539.4 

196.3 

35 

314.8 

114.6 

95 

371.2 

135.1 

55 

427.6 

155.6 

15 

484.0 

176.1 

75 

540.  3 

196.6 

36 

315.7 

114.9 

96 

372.1 

135.4 

56 

428.5 

156.0 

16 

484.9 

176.5 

76 

541.3 

197.0 

37 

316.7 

115.3 

97 

373.1 

135.8 

57 

429.4 

156.3 

17 

485. 8 

176.8 

77 

542.2 

197.3 

38 

317.6 

115.6 

98 

374.0 

136.1 

58 

430.4 

156.7 

18 

486.8 

177.2 

78 

543.2 

197.7 

39 

318.6 

116.0 

99 

374.9 

136.5 

59 

431.3 

157.0 

19 

487.7 

177.5 

79 

544.1 

198.0 

40 
341 

319.5 

116.3 

400 

375.9 

136.8 

60 

432.  3 

157.4 

20 

488.7 

177.9 

80 

545.0 

198.4 

320.4 

116.6 

401 

376.8 

137.2 

461 

433.2 

157.7 

521 

489.6 

178.2 

581 

546.0 

198.7 

42 

321.4 

117.0 

02 

377.8 

137.5 

62 

434.1 

158.0 

22 

490.5 

178.5 

82 

546.9 

199.0 

43 

322.  3 

117.3 

03 

378.7 

137.8 

63 

435.1 

158.4 

23 

491.5 

178.9 

83 

547.9 

199.4 

44 

323.3 

117.7 

04 

379.6 

138.2 

64 

436.0 

158.7 

24 

492.4 

179.2 

84 

548.8 

199.8 

45 

324.2 

118.0 

05 

380.6 

138.5 

65 

437.0 

159.0 

25 

493.4 

179.6 

85 

549.8 

200.1 

46 

325.1 

118.4 

06 

381.5 

138.9 

66 

437.9 

159.4 

26 

494.3 

179.9 

86 

550.7 

200.4 

47 

326. 1 

118.7 

07 

382.5 

139.2 

67 

438.  8 

159.7 

27 

495.3 

180.2 

87 

551.7 

200.8 

48 

327.0 

119.0 

08 

383.4 

139.6 

68 

439.8 

160.1 

28 

496.2 

180.6 

88 

552. 6 

201.2 

49     328. 0 

119.4 

09 

384.  3 

139.9 

69 

440.7 

160.4 

29 

497.1 

181.0 

89 

553.5 

201.5 

50     328. 9 

119.7 

10 

385.3 

140.2 

70 

441.7 

160.8 

30 

498.1 

181.3 

90 

554.4 

201.8 

351     329. 8 

120.1 

411 

386.2 

140.6 

471 

442.6 

161.1 

531 

499.0 

181.6 

591 

555. 4 

202.1 

52  1  330.8 

120.4 

12 

387.2 

140. 9 

72 

443.5 

161.4 

32 

499.9 

181.9 

92 

556.3 

202.4 

53  1  331.7 

120.7 

13 

388.1 

141.3 

73 

444.5 

161.8 

33 

500.9 

182.3 

93 

557.3 

202.8 

54  j  332. 7 

121.1 

14 

389.0 

141.6 

74 

445.4 

162.1 

34 

501.8 

182.6 

94 

558.2 

203.2 

55 

333.6 

121.4 

15 

390.0 

141.9 

75 

446.4 

162.5 

35 

502.7 

183.0 

95 

559. 1 

203.5 

56 

334.5 

121.8 

16 

390.9 

142.3 

76 

447.3 

162.8 

36 

503.7 

183.3 

96 

560.0 

203.8 

57 

335.5 

122.1 

17 

391.9 

142.6 

77 

448.2 

163.2 

37 

504.6 

183.7 

97 

561.0 

204.2 

58 

336. 4 

122.5 

18 

392.8 

143.0 

78 

449.2 

163.5 

38 

505.5 

184.0 

98 

561.9 

204.6 

59 

337.4 

122.8 

19 

393.7 

143.3 

79 

450.1 

163.8 

39 

506.5 

184.3 

99 

562.9 

204.9 

60 

338.3 

123.1 

20 

394.7 

143.7 

80 

451.1 

164.2 

40 

507.4 

184.7 

600 

563.8 

205.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

70°  (1 

10°,  25C 

»°,  290' 

). 

Page  572] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for 

21°  (159°,  201 

°,  339°). 

Diet 

1 

Lat. 

Dep. 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

0.9 

0.4 

61 

56.9 

21.9 

121 

113.0 

43.4 

181 

169.0 

64.9 

241 

225.0 

86.4 

2 

1.9 

0.7 

62 

57.9 

22.2 

22 

113.9 

43.7 

82 

169.9 

65.2 

42 

225.9 

86.7 

3 

2.8 

1.1 

63 

58.8 

22.6 

23 

114.8 

44.1 

83 

170.8 

65.6 

43 

226.9 

87.1 

4 

3.7 

1.4 

64 

59.7 

22.9 

24 

115.8 

44.4 

84 

171.8 

65.9 

44 

227.8 

87.4 

5 

4.7 

1.8 

65 

60.7 

23.3 

25 

116.7 

44.8 

85 

172.7 

66.3 

45 

228.7 

87.8 

6 

5.6 

2.2 

66 

61.6 

23.7 

26 

117.6 

45.2 

86 

173.6 

66.7 

46 

229.7 

88.2 

7 

6.5 

2.5 

67 

62.5 

24.0 

27 

118.6 

45.5 

87 

174.6 

67.0 

47 

230.6 

88.5 

8 

7.5 

2.9 

68 

63.5 

24.4 

28 

119.5 

45.9 

88 

175.5 

67.4 

48 

231.5 

88.9 

9 

8.4 

3.2 

69 

64.4 

24.7 

29 

120.4 

46.2 

89 

176.4 

67.7 

49 

232.5 

89.2 

10 

9.3 

3.6 

70 

65.4 

25.1 

30 

121.4 

46.6 

90 

177.4 

68.1 

50 

233.4 

89.6 

11 

10.3 

3.9 

71 

66.3 

25.4 

131 

122.3 

46.9 

191 

178.3 

68.4 

251 

234.3 

90.0 

12 

11.2 

4.3 

72 

67.2 

25.8 

32 

123.2 

47.3 

92 

179.2 

68.8 

52 

235.3 

90.3 

13 

12.1 

4.7 

73 

68.2 

26.2 

33 

124.2 

47.7 

93 

180.2 

69.2 

53 

236.2 

90.7 

14 

13.1 

5.0 

74 

69.1 

26.5 

34 

125.1 

48.0 

94 

181.1 

69.5 

54 

237.1 

91.0 

15 

14.0 

5.4 

75 

70.0 

26.9 

35 

126.0 

48.4 

95 

182.0 

69.9 

55 

238.1 

91.4 

16 

14.9 

5.7 

76 

71.0 

27.2 

36 

127.0 

48.7 

96 

183.0 

70.2 

56 

239.0 

91.7 

17 

15.9 

6.1 

77 

71.9 

27.6 

37 

127.9 

49.1 

97 

183.9 

70.6 

57 

239.9 

92.1 

18 

16.8 

6.5 

78 

72.8 

28.0 

38 

128.8 

49.5 

98 

184.8 

71^0 

58 

240.9 

92.5 

19 

17.7 

6.8 

79 

73.8 

28.3 

39 

129.8 

49.8 

99 

185.8 

71.3 

59 

241.8 

92.8 

20 

18.7 

7.2 

80 

74.7 

28.7 

40 

130.7 

50.2 

200 

186.7 

71.7 

60 

242.7 

93.2 

21 

19.6 

7.5 

81 

75.6 

29.0 

141 

131.6 

50.5 

201 

187.6 

72.0 

261 

243.7 

93.5 

22 

20.5 

7.9 

82 

76.6 

29.4 

42 

132.6 

50.9 

02 

188.6 

72.4 

62 

244.6 

93.9 

23 

21.5 

8.2 

83 

77.5 

29.7 

43 

133.5 

51.2 

03 

189.5 

72.7 

63 

245.5 

94.3 

24 

22.4 

8.6 

84 

78.4 

30.1 

44 

134.4 

51.6 

04 

190.5 

73.1 

64 

246.5 

94.6 

25 

23.3 

9.0 

85 

79.4 

30.5 

45 

135.4 

52.0 

05 

191.4 

73.6 

65 

247.4 

95.0 

26 

24.3 

9.3 

86 

80.3 

30.8 

46 

136.3 

52.3 

06 

192.3 

73.8 

66 

248.3 

95.3 

27 

25.2 

9.7 

87 

81.2 

31.2 

47 

137.2 

52.7 

07 

193.3 

74.2 

67 

249.3 

95.7 

28 

26.1 

10.0 

88 

82.2 

31.5 

48 

138.2 

53.0 

08 

194.2 

74.5 

68 

250.2 

96.0 

29 

27.1 

10.4 

89 

83.1 

31.9 

49 

139.1 

53.4 

09 

195.1 

74.9 

69 

251.1 

96.4 

30 

28.0 

10.8 
11.1 

90 

84.0 

32.3 

50 

140.0 

53.8 

10 

196.1 

75.3 
75.6 

70 

252.1 
258.0 

96.8 

31 

28.9 

91 

85.0 

32.6 

151 

141.0 

54.1 

211 

197.0 

271 

97.1 

32 

29.9 

11.5 

92 

85.9 

33.0 

52 

141.9 

54.5 

12 

197.9 

76.0 

72 

253.9 

97.5 

33 

30.8 

11.8 

93 

86.8 

33.3 

53 

142.8 

54.8 

13 

198.9 

76.3 

73 

254.9 

97.8 

34 

31.7 

12.2 

94 

87.8 

33.7 

54 

143.8 

55.2 

14 

199.8 

76.7 

74 

255.8 

98.2 

35 

32.7 

12.5 

95 

88.7 

34.0 

55 

144.7 

55.5 

15 

200.7 

77.0 

75 

256.7 

98.6 

36 

33.6 

12.9 

96 

89.6 

34.4 

56 

145.6 

55.9 

16 

201.7 

77.4 

76 

257.7 

98.9 

37 

34.5 

13.3 

97 

90.6 

34.8 

57 

146.6 

56.3 

17 

202.6 

77.8 

77 

258.6 

99.3 

38 

35.5 

13.6 

98 

91.5 

35.1 

58 

147.5 

56.6 

18 

203.5 

78.1 

78 

259.  5 

99.6 

39 

36.4 

14.0 

99 

92.4 

35.5 

59 

148.4 

57.0 

19 

204.5 

78.5 

79 

260.5 

100.0 

40 

37.3 

14.3 

100 

93.4 

35.8 

60 

149.4 

57.3 

20 

205.4 

78.8 

80 

261.4 

100.3 

41 

38.3 

14.7 

101 

94.3 

36.2 

161 

150.3 

57.7 

221 

206.3 

79.2 

281 

262.3 

100.7 

42 

39.2 

15.1 

02 

95.2 

36.6 

62 

151.2 

58.1 

22 

207.3 

79.6 

82 

263.3 

101.1 

43 

40.1 

15.4 

03 

96.2 

36.9 

63 

152.2 

58.4 

23 

208.2 

79.9 

83 

264.2 

101.4 

44 

41.1 

15.8 

04 

97.1 

37.3 

64 

153.1 

58.8 

24 

209.1 

80.3 

84 

265.1 

101.8 

45 

42.0 

16.1 

05 

98.0 

37.6 

65 

154.0 

59.1 

25 

210.1 

80.6 

85 

266.1 

102.1 

46 

42.9 

16.5 

06 

99.0 

38.0 

66 

155.0 

59.5 

26 

211.0 

81.0 

86 

267.0 

102.5 

47 

43.9 

16.8 

07 

99.9 

38.3 

67 

155.9 

59.8 

27 

211.9 

81.3 

87 

267.9 

102.9 

48 

44.8 

17.2 

08 

100.8 

38.7 

68 

156.8 

60.2 

28 

212.9 

81.7 

88 

268.9 

103.2 

49 

45.7 

17.6 

09 

101.8 

39.1 

69 

157.8 

60.6 

29 

213.8 

82.1 

89 

269.8 

103.6 

50 

46.7 

17.9 

10 

102.7 

39.4 

70 

158.7 

60.9 

30 

214.7 

82.4 

90 

270.7 

103.9 

51 

47.6 

18.3 

111 

103.6 

39.8 

171 

159.6 

61.3 

231 

215.7 

82.8 

291 

271.7 

104.3 

52 

48.5 

18.6 

12 

104.6 

40.1 

72 

160.6 

61.6 

32 

216.6 

83.1 

92 

272.6 

104.6 

53 

49.5 

19.0 

13 

105.5 

40.5 

73 

161.5 

62.0 

33 

217.5 

83.5 

93 

273.5 

105.0 

54 

50.4 

19.4 

14 

106.4 

40.9 

74 

162.4 

62.4 

34 

218.5 

83.9 

94 

274.5 

105.4 

55 

51.3 

19.7 

15 

107.4 

41.2 

75 

163.4 

62.7 

35 

219.4 

84.2 

95 

275.4 

105.7 

56 

52.3 

20.1 

16 

108.3 

41.6 

76 

164.3 

63.1 

36 

220.3 

84.6 

96 

276.3 

106.1 

57 

53.2 

20.4 

17 

109.2 

41.9 

77 

165.2 

63.4 

37 

221.3 

84.9 

97 

277.  3 

106.4 

58 

54.1 

20.8 

18 

110.2 

42.3 

78 

166.2 

63.8 

38 

222.2 

85.3 

98 

278.2 

106.8 

59 

55.1 

21.1 

19 

111.1 

42.6 

79 

167.1 

64.1 

39 

233.1 

85.6 

99 

279.1 

107.2 

60 

56.0 

21.5 

20 

112.0 

43.0 

80 

168.0 

64.5 

40 

224.1 

86.0 

300 

280.1 

107.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

69°  ( 

111°,  249°,  291 

°)- 

TABLE  2. 

[Page  673 

Difference  of  Latitude  and  Departure  for  21°  (159°,  201°,  339 

'). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

281.0 

107.9 

361 

337.0 

129.4 

421 

393.0 

150.9 

481 

449.0 

172.4 

541 

505.1 

193.9 

02 

281.9 

108.2 

62 

337.9 

129.7 

22 

394.0 

151.2 

82 

450.0 

172.7 

42 

506.0 

194.2 

03 

282.9 

108.6 

63 

338.9 

130.1 

23 

394.9 

151.6 

83 

450.9 

173.1 

43 

507.0 

194.6 

04 

283.8 

108.9 

64 

339.8 

130.4 

24 

395.8 

152.0 

84 

451.8 

173.5 

44 

507.9 

195.0 

05 

284.7 

109.3 

65 

340.7 

130.8 

25 

396.8 

152.3 

85 

452.8 

173.8 

45 

508.8 

195.3 

06 

285.7 

109.7 

66 

341.7 

131.2 

26 

397.7 

152.7 

86 

453.7 

174.2 

46 

509.8 

195.7 

07 

286.6 

110.0 

67 

342.6 

131.5 

27 

398.6 

153.0 

87 

454.6 

174.5 

47 

510.7 

196.0 

08 

287.5 

110.4 

68 

343.  5 

131.9 

28 

399.6 

153.4 

88 

455.6 

174.9 

48 

511.6 

196.4 

09 

288.5 

110.7 

79 

344.5 

132.2 

29 

400.5 

153.7 

89 

456.5 

175.2 

49 

512.6 

196.8 

10 

289.4 
290.3 

111.1 
111.5 

70 

345.4 

132.6 

30 

401.4 

154.1 

90 

457.4 

175.6 

50 
551 

513.5 
514.4 

197.1 

311 

371 

346.3 

133. 0 

431 

402.4 

154.5 

491 

458.4 

176.0 

197.5 

12 

291.3 

111.8 

72 

347.3 

133.3 

32 

403.3 

154.8 

92 

459.3 

176.3 

52 

515.4 

197.8 

13 

292.2 

112.2 

73 

348.2 

133.7 

33 

404.2 

155.2 

93 

460.2 

176.7 

53 

516.3 

198.2 

14 

293.1 

112.5 

74 

349.1 

134.0 

34 

405.2 

155. 5 

94 

461.2 

177.0 

54 

517.2 

198.6 

15 

294.1 

112.9 

75 

350.1 

134.4 

35 

406.1 

155.9 

95 

462.1 

177.4 

55 

518.2 

198.9 

16 

295.0 

113.2 

76 

351.0 

134.7 

36 

407.0 

156.3 

96 

463.0 

177.8 

56 

519.1 

199.3 

17 

295.9 

113.6 

77 

351.9 

135.1 

37 

408.0 

156.6 

97 

464.0 

178.1 

57 

520.0 

199.6 

18 

296.9 

114.0 

78 

352.9 

135.5 

38 

408.9 

157.0 

98 

464.9 

178.5 

58 

521.0 

200.0 

19 

297.8 

114.3 

79 

353.8 

135.8 

39 

409.8 

157.3 

99 

465.8 

178.8 

59 

521.9 

200.3 

20 

298.7 
299.7 

114.7 

80 

354.7 

136.2 

40 

410.8 

157.7 

500 

466.8 

179.2 

60 

522.8 

200.7 

321 

115.0 

381 

355.7 

136.  5 

441 

411.7 

158.0 

501 

467.7 

179.5 

561 

523.8 

201.0 

22 

300.6 

115.4 

82 

356.6 

136.9 

42 

412.6 

158.4 

02 

468.6 

179.9 

62 

524.7 

201.4 

23 

301.5 

115.8 

83 

357. 5 

137.3 

43 

413.6 

158.8 

03 

469.6 

180.3 

63 

525.6 

201.8 

24 

302.5 

116.1 

84 

358.5 

137.6 

44 

414.5 

159.1 

04 

470.5 

180.6 

64 

526.6 

202.1 

25 

303.4 

116.5 

85 

359.4 

138.0 

45 

415.4 

159.5 

05 

471.5 

181.0 

65 

527.5 

202.5 

26 

304.3 

116.8 

86 

360.3 

138.3 

46 

416.4 

159.8 

06 

472.4 

181.3 

66 

528.4 

202.8 

27 

305.3 

117.2 

87 

361.3 

138.7 

47 

417.3 

160.2 

07 

473.3 

181.7 

67 

529.4 

203.2 

28 

306.2 

117.5 

88 

362.2 

139. 1 

48 

418.2 

160.5 

08 

474.3 

182.0 

68 

530.3 

203.5 

29 

307.1 

117.9 

89 

363.1 

139.4 

49 

419.2 

16*0. 9 

09 

475.2 

182.4 

69 

531.2 

203.9 

30 
331 

308.1 

118.3 

90 

364.1 

139. 8 

50 

420.1 

161.3 

10 

476.1 

182.8 

70 

532.2 

204.3 

309.0 

118.6 

391 

365.0 

"140. 1 

451 

421.0 

161.6 

511 

477.1 

183.1 

571 

533.1 

204.6 

32 

309.9 

119.0 

92 

365.9 

140.5 

52 

422.0 

162.0 

12 

478.0 

183.5 

72 

534.0 

205.0 

33 

310.9 

119.3 

93 

366.9 

140.8 

53 

422.9 

162.3 

13 

478.9 

183.8 

73 

535.0 

205. 4 

34 

311.8 

119.7 

94 

367.8 

141.2 

54 

423.8 

162.7 

14 

479.9 

184.2 

74 

535.9 

205.7 

35 

312.7 

120.1 

95 

368.7 

141.6 

55 

424.8 

163.1 

15 

480.8 

184.6 

75 

536.8 

206.1 

36 

313.7 

120.4 

96 

369.7 

141.9 

56 

425.7 

163.4 

16 

481.7 

184.9 

76 

537.8 

206.4 

37 

314.6 

120.8 

97 

370.6 

142.3 

57 

426.6 

163.8 

17 

482.7 

185.3 

77 

538.7 

206.8 

38 

315.5 

121.1 

98 

371.5 

142.6 

58 

427.6 

164.1 

18 

483.6 

185.6 

78 

539.6 

207.1 

39 

316.5 

121.5 

99 

372.5 

143.0 

59 

428.5 

164.5 

19 

484.5 

186.0 

79 

540.6 

207.5 

40 

317.4 

121.8 

400 

373.4 

143.4 

60 

429.4 

164.9 

20 

485.5 

186.4 

80 

541.5 

207.9 

341 

318.3 

122.2 

401 

374.3 

143.7 

461 

430.4 

165.2 

521 

486.4 

186.7 

581 

542.4 

208.2 

42 

319.3 

122.6 

02 

375.3 

144.1 

62 

431.3 

165.6 

22 

487.3 

187.1 

82 

543.4 

208.6 

43 

320.2 

122.9 

03 

376.2 

144.4 

63 

432.2 

165.9 

23 

488.3 

187.4 

83 

544.3 

208.9 

44 

321.1 

123.2 

04 

377.1 

144.8 

64 

433.2 

166.3 

24 

489.2 

187.8 

84 

545.2 

209.3 

45 

322.1 

123.6 

05 

378.1 

145.1 

65 

434.1 

166.6 

25 

490.1 

188.1 

85 

546.2 

209.6 

46 

323.0 

124.0 

06 

379.0 

145.5 

66 

435.0 

167.0 

26 

491.1 

188.5 

86 

547.1 

210.0 

47 

323.9 

124.4 

07 

379.9 

145.9 

67 

436.0 

167.4 

27 

492.0 

188.9 

87 

548.0 

210.4 

48 

324.9 

124.7 

08 

380.9 

146.2 

68 

436.9 

167.7 

28 

492.9 

189.2 

88 

549.0 

210.7 

49 

325.8 

125.1 

09 

381.8 

146.6 

69 

437.8 

168.1 

29 

493.9 

189.6 

89 

549.9 

211.1 

50 

326.7 

125.4 

10 

382.7 

146.9 

70 

438.8 

168.4 

30 

494.8 

189.9 

90 

550.8 

211.4 

351 

327.7 

125.8 

411 

383.7 

147.3 

471 

439.7 

168.8 

531 

495.7 

190.3 

591 

551.8 

211.8 

52 

328.6 

126.1 

12 

384.6 

147.7 

72 

440.6 

169.2 

32 

496.7 

190.7 

92 

552.  7 

212.2 

53 

329.5 

126.5 

13 

385.5 

148.0 

73 

441.6 

169.5 

33 

497.6 

191.0 

93 

553.6 

212.5 

54 

330.5 

126.9 

14 

386.5 

148.4 

74 

442.5 

169.9 

34 

498.5 

191.4 

94 

554.6 

212.9 

55 

331.4 

127.2 

15 

387.4 

148.7 

75 

443.4 

170.2 

35 

499.5 

191.7 

95 

555.5 

213.2 

56 

332.3 

127.6 

16 

388.4 

149.1 

76 

444.4 

170.6 

36 

500.4 

192.1 

96 

556.4 

213.6 

57 

333.3 

127.9 

17 

389.3 

149.4 

77 

445.3 

170.9 

37 

501.3 

192.4 

97 

557.4 

213.9 

58 

334.2 

128.3 

18 

390.2 

149.8 

78 

446.2 

171.3 

38 

502.3 

192.8 

98 

558.2 

214.3 

59 

335.1 

128.7 

19 

391.2 

150.2 

79 

447.2 

171.7 

39 

503.2 

193.2 

99 

559.2 

214.7 

60 

336.1 

129.0 

20 

392.1 

150.5 

80 

448.1 

172.0 

40 

504.1 

193.5 

600 

560.1 

215.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

t 

59°  (1 

11°,  249°,  291° 

)• 

1    Page  674] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  22°  (158°,  202,  338°; 

. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.6 

22.9 

121 

112.2 

45.3 

181 

167.8 

67.8 

241 

223.5 

90.3 

2 

1.9 

0.7 

62 

57.5 

23.2 

22 

113.1 

45.7 

82 

168.  7 

68.2 

42 

224.4 

90.7 

3 

2.8 

1.1 

63 

58.4 

23.6 

23 

114.0 

46.1 

83 

169.7 

68.6 

43 

225.3 

91.0 

4 

3.7 

1.5 

64 

59.3 

24.0 

24 

115.0 

46.5 

84 

170.6 

68.9 

44 

226.2 

91.4 

5 

4.6 

1.9 

65 

60.3 

24.3 

25 

115.9 

46.- 8 

85 

171.5 

69.3 

45 

227.2 

91.8 

6 

5.6 

2.2 

66 

61.2 

24.7 

26 

116.8 

47.2 

86 

172.5 

69.7 

46 

228.1 

92.2 

7 

6.5 

2.6 

67 

62.1 

25.1 

27 

117.8 

47.6 

87 

173.4 

70.1 

47 

229.0 

92.5 

8 

7.4 

3.0 

68 

63.0 

25.5 

28 

118.7 

47.9 

88 

174.3 

70.4 

48 

229.9 

92.9 

9 

8.3 

3.4 

69 

64.0 

25.8 

29 

119.6 

48.3 

89 

175.2 

70.8 

49 

230.9 

93.3 

10 

9.3 

3.7 

70 

64.9 

26.2 

30 

120.5 

48.7 

90 

176.2 

71.2 

50 

231.8 

93.7 

11 

10.2 

4.1 

71 

65.8 

26.6 

131 

121.5 

49.1 

191 

177.1 

71.5 

251 

232.7 

94.0 

12 

11.1 

4.5 

72 

66.8 

27.0 

32 

122.4 

49.4 

92 

178.0 

71.9 

52 

233.7 

94.4 

13 

12.1 

4.9 

73 

67.7 

27.3 

33 

123.3 

49.8 

93 

178.9 

72.3 

53 

234.6 

94.8 

14 

13.0 

5.2 

74 

68.6 

27.7 

34 

124.2 

50.2 

94 

179.9 

72.7 

54 

2.35. 5 

95.2 

15 

13.9 

5.6 

75 

69.5 

28.1 

35 

125.2 

50.6 

95 

180.8 

73.0 

55 

236.4 

95.5 

16 

14.8 

6.0 

76 

70.5 

28.5 

36 

126.1 

50.9 

96 

181.7 

73.4 

56 

237.4 

95.9 

17 

15.8 

6.4 

77 

71.4 

28.8 

37 

127.0 

51.3 

97 

182.7 

73.8 

57 

238.3 

96.3 

18 

16.7 

6.7 

78 

72.3 

29.2 

38 

128.0 

51.7 

98 

183.6 

74.2 

58 

239.2 

96.6 

19 

17.6 

7.1 

79 

73.2 

29.6 

39 

128.9 

52.1 

99 

184.5 

74.5 

59 

240.1 

97.0 

20 

18.5 

7.5 

80 

74.2 

30.0 

40 

129.8 
130.7 

52.4 

200 

185.4 

74.9 

60 

241.1 

97.4 

21 

19.5 

7.9 

81 

75.1 

30.3 

141 

52.8 

201 

186.4 

75.3 

261 

242.0 

97.8 

22 

20.4 

8.2 

82 

76.0 

30.7 

42 

131.7 

53.2 

02 

187.3 

75.7 

62 

242.9 

98.1 

23 

21.3 

8.6 

83 

77.0 

31.1 

43 

132.6 

53.6 

03 

188.2 

76.0 

63 

243.8 

98.5 

24 

22.3 

9.0 

84 

77.9 

31.5 

44 

133.5 

53.9 

04 

189.1 

76.4 

64 

244.8 

98.9 

25 

23.2 

9.4 

85 

78.8 

31.8 

45 

134.4 

54.3 

05 

190.1 

76.8 

65 

245.7 

99.3 

26 

24.1 

9.7 

86 

79.7 

32.2 

46 

135.4 

54.7 

06 

191.0 

77.2 

66 

246.6 

99.6 

27 

25.0 

10.1 

87 

80.7 

32.6 

47 

136.3 

55.1 

07 

191.9 

77.5 

67 

247.6 

100.0 

28 

26.0 

10.5 

88 

81.6 

33.0 

48 

137.2 

55.4 

08 

192.9 

77.9 

68 

248.5 

100.4 

29 

26.9 

10.9 

89 

82.5 

33.3 

49 

138.2 

55.8 

09 

193.8 

78.3 

69 

249.4 

100.8 

30 

27.8 

11.2 

90 

83.4 

33.7 

50 

139.1 

56.2 

10 

194.7 

78.7 

70 

250.3 
251.3 

101.1 

31 

28.7 

11.6 

91 

84.4 

34.1 

151 

140.0 

56.6 

211 

195.6 

79.0 

271 

101.5 

32 

29.7 

12.0 

92 

85.3 

34.5 

52 

140.9 

56.9 

12 

196.6 

79.4 

72 

252.2 

101.9 

33 

30.6 

12.4 

93 

86.2 

34.8 

53 

141.9 

57.3 

13 

197.5 

79.8 

73 

253.1 

102.3 

34 

31.5 

12.7 

94 

87.2 

35.2 

54 

142.8 

57.7 

14 

198.4 

80.2 

74 

254.0 

102.6 

35 

32.5 

13.1 

95 

88.1 

35.6 

55 

143.7 

58.1 

15 

199.3 

80.5 

75 

255.0 

103.0 

36 

33.4 

13.5 

96 

89.0 

36.0 

56 

144.6 

58.4 

16 

200.3 

80.9 

76 

255.9 

103.4 

37 

34.3 

13.9 

97 

89.9 

36.3 

57 

145.6 

58.8 

17 

201.2 

81.3 

77 

256.8 

103.8 

38 

35.2 

14.2 

98 

90.9 

36.7 

58 

146.5 

59.2 

18 

202.1 

81.7 

78 

257.8 

104.1 

39 

36.2 

14.6 

99 

91.8 

37.1 

59 

147.4 

59.6 

19 

203.1 

82.0 

79 

258.7 

104.5 

40 

41 

37.1 

15.0 

100 

92.7 

37.5 

60 

148.3 

59.9 
60.3 

20 

204.0 

82.4 

80 

259.6 
260.5 

104.9 

38.0 

15.4 

101 

93.6 

37.8 

161 

149.3 

221 

204.9 

82.8 

281 

105.3 

42 

38.9 

15.7 

02 

94.6 

38.2 

62 

150.2 

60.7 

22 

205.8 

83.2 

82 

261.5 

105.6 

43 

39.9 

16.1 

03 

95.5 

38.6 

63 

151.1 

61.1 

23 

206.8 

83.5 

83 

262.4 

106.0 

44 

40.8 

16.5 

04 

96.4 

39.0 

64 

152. 1 

61.4 

24 

207.7 

83.9 

84 

263.3 

106.4 

45 

41.7 

16.9 

05 

97.4 

39.3 

65 

153.0 

61.8 

25 

208.6 

84.3 

85 

264.2 

106.8 

46 

42.7 

17.2 

06 

98.3 

39.7 

66 

153.9 

62.2 

26 

209.5 

84.7 

86 

265.2 

107.1 

47 

43.6 

17.6 

07 

99.2 

40.1 

67 

154.8 

62.6 

27 

210.5 

85.0 

87 

266.1 

107.5 

48 

44.5 

18.0 

08 

100.1 

40.5 

68 

155.8 

62.9 

28 

211.4 

85.4 

88 

267.0 

107.9 

49 

45.4 

18.4 

09 

101.1 

40.8 

69 

156.7 

63.3 

29 

212.3 

85.8 

89 

268.0 

108.3 

50 
51 

46.4 
47.3 

18.7 

10 

102.0 
102.9 

41.2 

70 

157.6 

63.7 

30 

213.3 
214.2 

86.2 

90 

268.9 
269.8 

108.6 

19.1 

111 

41.6 

171 

158.5 

64.1 

231 

86.5 

291 

109.0 

52 

48.2 

19.5 

12 

103.8 

42.0 

72 

159.5 

64.4 

32 

215.1 

86.9 

92 

270.7 

109.4 

53 

49.1 

19.9 

13 

104.8 

42.3 

73 

160.4 

64.8 

33 

216.0 

87.3 

93 

271.7 

109.8 

54 

50.1 

20.2 

14 

105.7 

42.7 

74 

161.8 

65.2 

34 

217.0 

87.7 

94 

272.6 

110.1 

55 

51.0 

20.6 

15 

106.6 

43.1 

75 

162.3 

65.6 

35 

217.9 

88.0 

95 

273.5 

110.5 

56 

51.9 

21.0 

16 

107.6 

43.5 

76 

163.2 

65.9 

36 

218.8 

88.4 

96 

274.4 

110.9 

57 

52.8 

21.4 

17 

108.5 

43.8 

77 

164.1 

66.3 

37 

219.7 

88.8 

97 

275.4 

111.3 

58 

53.8 

21.7 

18 

109.4 

44.2 

78 

165.0 

66.7 

38 

220.7 

89.2 

98 

276.3 

111.6 

59 

54.7 

22.1 

19 

110.3 

44.6 

79 

166.0 

67.1 

39 

221.6 

89.5 

99 

277.2 

112.0 

60 

55.6 

22.5 

20 

111.3 

45.0 

80 

166.9 

67.4 

40 

222.5 

89.9 

300 

278.2 

112.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

68°  (] 

L12°,  24{ 

i°,  292°). 

TABLE  2. 

[Page 

676 

Difference  of  l^atitude  and  Departure  for 

22°  (158°,  202°,  338' 

'). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

279.1 

112.7 

361 

334.7 

135.2 

421 

390.3 

157.7 

481 

446.0 

180.2 

641 

601.6 

202.7 

02 

280.0 

113.1 

62 

335.6 

135.6 

22 

391.3 

158.1 

82 

446.9 

180.6 

42 

602.6 

203.1 

03 

280.9 

113.5 

63 

336.6 

136.0 

23 

392.  2 

158.4 

83 

447.8 

180.9 

43 

503.4 

203.5 

04 

281.9 

113.9 

64 

337.5 

136.3 

24 

393.1 

158.8 

84 

448.8 

181.3 

44 

604.4 

203.8 

05 

282.8 

114.2 

65 

338.4 

136.7 

25 

394.1 

159.2 

85 

449.7 

181.7 

45 

605.3 

204.2 

06 

283.7 

114.6 

66 

339.3 

137.1 

26 

395.0 

159.6 

86 

450.6 

182.1 

46 

506.2 

204.6 

07 

284.6 

115.0 

67 

340.3 

137.5 

27 

395.9 

159.9 

87 

451.6 

182.4 

47 

507.2 

205.0 

08 

285.6 

115.4 

68 

341.2 

137.8 

28 

396.8 

160.3 

88 

452.5 

182.8 

48 

508.1 

205.3 

09 

286.5 

115.7 

69 

342.1 

138.2 

29 

397.8 

160.7 

89 

453.4 

183.2 

49 

509.0 

205.7 

10 

287.4 

116.1 

70 

343.1 

138.6 

30 

398.7 

161.1 

90 

464.3 

183.6 

50 

510.0 

206.1 

311 

288.4 

116.5 

371 

344.0 

139.0 

431 

399.6 

161.4 

491 

465.3 

184.0 

551 

610.9 

206.5 

12 

289.3 

116.8 

72 

344.9 

139.3 

32 

400.5 

161.8 

92 

456.2 

184.3 

52 

511.8 

206.8 

13 

290.2 

117.2 

73 

345.  8 

139.7 

33 

401.5 

162.2 

93 

457.1 

184.7 

53 

512.7 

207.2 

14 

291.1 

117.6 

74 

346.8 

140.1 

34 

402.4 

162.6 

94 

458.0 

185.1 

54 

613.6 

207.6 

15 

292.1 

118.0 

75 

347.7 

140.5 

35 

403.3 

162.9 

95 

459.0 

185.4 

56 

514.6 

208.0 

16 

293.0 

118.3 

76 

348.6 

140.8 

36 

404.3 

163.3 

96 

459.9 

185.8 

66 

516.5 

208.  3 

17 

293.9 

118.7 

77 

349.5 

141.2 

37 

405.2 

163.7 

97 

460.8 

186.2 

57 

616.4 

208.7 

18 

294.8 

119.1 

78 

350.5 

141.6 

38 

406.1 

164.1 

98 

461.8 

186.6 

68 

517.4 

209.1 

19 

295.8 

119.5 

79 

351.4 

141.9 

39 

407.0 

164.4 

99 

462.7 

186.9 

69 

518.3 

209.4 

20 
321 

296.7 
297.6 

119.8 

80 

352.3 

142.3 

40 

408.0 

164.8 

500 

463.6 

187.3 

60 

519.2 

209.8 

120.2 

381 

353.3 

142.7 

441 

408.9 

165.2 

501 

464.6 

187.7 

661 

620.1 

210.2 

22 

298.6 

120.6 

82 

354.2 

143.1 

42 

409.8 

166.5 

02 

466.4 

188.0 

62 

621.0 

210.5 

23 

299.5 

121.0 

83 

355.1 

143.4 

43 

410.7 

165.9 

03 

466.4 

188.4 

63 

522.0 

210.9 

24 

300.4 

121.3 

84 

356.0 

143.8 

44 

411.7 

166.3 

04 

467.3 

188.8 

64 

622.9 

211.3 

25 

301.3 

121.7 

85 

357.0 

144.2 

45 

412.6 

166.7 

05 

468.2 

189.2 

66 

523.8 

211.7 

26 

302.3 

122.1 

86 

357.9 

144.6 

46 

413.5 

167.0 

06 

469.2 

189.6 

66 

524.8 

212.0 

27 

303. 2 

122.5 

87 

358.8 

144.9 

47 

414.5 

167.4 

07 

470.1 

189.9 

67 

526.7 

212.4 

28 

304.1 

122.8 

88 

359.7 

145.3 

48 

415.4 

167.8 

08 

471.0 

190.3 

68 

626.6 

212.8 

29 

305.0 

123.2 

89 

360.7 

145.7 

49 

416.3 

168.2 

09 

471.9 

190.7 

69 

627.5 

213.2 

30 

306.0 

123.6 

90 

361.6 

146.1 

50 

417.2 

168.5 

10 

472.9 

191.1 

70 

628.6 

213.5 

331 

306.9 

124.0 

391 

362.5 

146.4 

451 

418.2 

168.9 

511 

473.8 

191.4 

671 

629.4 

213.9 

32 

307.8 

124.3 

92 

363.5 

146.8 

52 

419.1 

169.3 

12 

474.  7 

191.8 

72 

530.3 

214.3 

33 

308.8 

124.7 

93 

364.4 

147.2 

53 

420.0 

169.7 

13 

475.6 

192.2 

73 

631.2 

214.7 

34 

309.7 

125. 1 

94 

365.3 

147.6 

54 

420.9 

170.0 

14 

476.6 

192.6 

74 

532.2 

215.0 

35 

310.6 

125.5 

95 

366.2 

147.9 

55 

421.9 

170.4 

15 

477.5 

192.9 

76 

633.1 

215.4 

36 

311.5 

125.  8 

96 

367.2 

148.3 

56 

422.8 

170.8 

16 

478.4 

193.3 

76 

534.0 

215.8 

37 

312.5 

126.2 

97 

368.1 

148.7 

57 

423.7 

171.2 

17 

479.3 

193.7 

77 

534.9 

216.2 

38 

313.4 

126.6 

98 

369.0 

149.1 

58 

424.6 

171.5 

18 

480.3 

194.0 

78 

536.9 

216.6 

39 

314.3 

127.0 

99 

369.9 

149.4 

59 

425.6 

171.9 

19 

481.2 

194.4 

79 

636.8 

216.9 

40 
341 

315.2 
316.2 

127.3 

400 

370.9 

149.8 

60 

426.5 

172.3 

20 

482.1 

194.8 
195.2 

80 

537.7 

217.3 

127.7 

401 

371.8 

150.2 

461 

427.4 

172.7 

521 

483.0 

681 

538.6 

217.7 

42 

317.1 

128.1 

02 

372.7 

150.6 

62 

428.4 

173.0 

22 

484.0 

195.5 

82 

539.6 

218.0 

43 

318.0 

128.5 

03 

373.7 

150.9 

63 

429.3 

173.4 

23 

484.9 

195.9 

83 

640.6 

218.4 

44 

319.0 

128.8 

04 

374.6 

151.3 

64 

430.2 

173.8 

24 

485.8 

196.3 

84 

641.4 

218.8 

45 

319.9 

129.2 

05 

375.5 

151.7 

65 

431.1 

174.2 

25 

486.7 

196.7 

86 

642.4 

219.2 

46 

320.8 

129.6 

06 

376.4 

152.1 

66 

432.1 

174.5 

26 

487.7 

197.0 

86 

543.3 

219.6 

47 

321.7 

130.0 

07 

377.4 

152.4 

67 

433.0 

174.9 

27 

488.6 

197.4 

87 

544.2 

219.9 

48 

322.7 

130.3 

08 

378.3 

152.8 

68 

433.9 

175.3 

28 

489.5 

197.8 

88 

646.1 

220.3 

49 

323. 6 

130.7 

09 

379.2 

153.2 

69 

434.8 

175.7 

29 

490.4 

198.2 

89 

546.1 

220.7 

50 

324.5 

131.1 

10 

380.1 

153.6 

70 

435.8 

176.0 

30 

491.4 

198.5 

90 

547.0 

221.0 

351 

325.4 

131.5 

411 

381.1 

153.9 

471 

436.7 

176.4 

631 

492.3 

198.9 

591 

547.9 

221.4 

52 

326.4 

131.8 

12 

382.0 

154.3 

72 

437.6 

176.8 

32 

493.2 

199.3 

92 

548.9 

221.8 

53 

327.  3 

132.2 

13 

382.9 

154.7 

73 

438.6 

177.2 

33 

494.2 

199.7 

93 

549.8 

222.2 

54 

328.2 

132.6 

14 

383.9 

155.1 

74 

439.5 

177.5 

34 

495.1 

200.0 

94 

650.7 

222.5 

55 

329.2 

133.0 

15 

384.8 

155.4 

75 

440.4 

177.9 

35 

496.0 

200.4 

95 

651.7 

222.9 

56 

330.1 

133.3 

16 

385.7 

155.8 

76 

441.3 

178.3 

36 

496.9 

200.8 

96 

552.6 

223.3 

57 

331.0 

133.7 

17 

386.6 

156.2 

77 

442.3 

178.7 

37 

497.9 

201.2 

97 

553.5 

223.7 

58 

332.0 

134.1 

18 

387.6 

156.6 

78 

443.2 

179.0 

38 

498.8 

201.6 

98 

554.4 

224.0 

59 

332.9 

134.5 

19 

388.5 

156.9 

79 

444.1 

179.4 

39 

499.7 

201.9 

99 

655.4 

224.4 

60 

333.8 

134.8 

20 

389.4 

157.3 

80 

445.0 

179.8 

40 

500.7 

202.3 

600 

556.3 

224.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.      Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

.  Lat. 

68°  (112°,  248°,  292° 

. 

Page  676] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

23°  (157°,  203°,  337 

°)- 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.2 

23.8 

121 

111.4 

47.3 

181 

166.6 

70.7 

241 

221.8 

94.2 

2 

1.8 

0.8 

62 

57.1 

24.2 

22 

112.3 

47.7 

82 

167.5 

71.1 

42 

222.8 

94.6 

3 

2.8 

1.2 

63 

58.0 

24.6 

23 

113.2 

48.1 

83 

168.5 

71.5 

43 

223.7 

94.9 

4 

3.7 

1.6 

64 

58.9 

25.0 

24 

114.1 

48.5 

84 

169.4 

71.9 

44 

224.6 

95.3 

0 

4.6 

2.0 

65 

59.8 

25.4 

25 

115.1 

48.8 

85 

170.3 

72.3 

45 

225.5 

95.7 

6 

5.5 

2.3 

66 

60.8 

25.8 

26 

116.0 

49.2 

86 

171.2 

72.7 

46 

226.4 

96.1 

7 

6.4 

2.7 

67 

61.7 

26.2 

27  1  116.9 

49.6 

87 

172.1 

73.1 

47 

227.4 

96.5 

8 

7.4 

3.1 

68 

62.6 

26.6 

28 

117.8 

50.0 

88 

173.1 

73.5 

48 

228.3 

96.9 

9 

8.3 

3.5 

69 

63.5 

27.0 

29 

118.7 

50.4 

89 

174.0 

73.8 

49 

229,2 

97.3 

10 
11 

9.2 

3.9 

70 

64.4 

27.4 

30 

119.7 

50.8 

90 

174.9 

74.2 

50 

230.1 

97.7 

10.1 

4.3 

71 

65.4 

27.7 

131 

120.6 

51.2 

191 

175.8 

74.6 

251 

231.0 

98.1 

12 

11.0 

4.7 

72 

66.3 

28.1 

32 

121.5 

51.6 

92 

176.7 

75.0 

52 

232.0 

98.5 

13 

12.0 

5.1 

73 

67.2 

28.5 

33 

122.4 

52.0 

93 

177.7 

75.4 

53 

232.9 

98.9 

14 

12.9 

5.5 

74 

68.1 

28.9 

34 

123.3 

52.4 

94 

178.6 

75.8 

54 

233.8 

99.2 

15 

13.8 

5.9 

75 

69.0 

29.3 

35 

124.3 

52.7 

95 

179.5 

76.2 

55 

234.7 

99.6 

16 

14.7 

6.3 

76 

70.0 

29.7 

36 

125.2 

53.1 

96 

180.4 

76.6 

56 

235.6 

100.0 

17 

15.6 

6.6 

77 

70.9 

30.1 

37 

126.1 

53.5 

97 

181.3 

77.0 

57 

236.6 

100.4 

18 

16.6 

7.0 

78 

71.8 

30.5 

38 

127.0 

53.9 

98 

182.3 

77.4 

58 

237.5 

100.8 

19 

17.5 

7.4 

79 

72.7 

30.9 

39 

128.0 

54.3 

99 

183.2 

77.8 

59 

238.4 

101.2 

20 

18.4 

7.8 

80 

73.6 

31.3 

40 

128.9 

54.7 

200 

184.1 

78.1 

60 

239.3 

101.6 

21 

19.3 

8.2 

81 

74.6 

31.6 

141 

129.8 

55.1 

201 

185.0 

78.5 

261 

240.3 

102.0 

22 

20.3 

8.6 

82 

75.5 

32.0 

42 

130.7 

55.5 

02 

185.9 

78.9 

62 

241.2 

102.4 

23 

21.2 

9.0 

83 

76.4 

32.4 

43 

131.6 

55.9 

03 

186.9 

79.3 

63 

242.1 

102.8 

24 

22.1 

9.4 

84 

77.3 

32.8 

44 

132.6 

56.3 

04 

187.8 

79.7 

64 

243.0 

103.2 

25 

23.0 

9.8 

85 

78.2 

33.2 

45 

133.5 

56.7 

05 

188.7 

80.1 

65 

243.9 

103.5 

26 

23.9 

10.2 

86 

79.2 

33.6 

46 

134.4 

57.0 

06 

189.6 

80.5 

66 

244.9 

103.9 

•  27 

24.9 

10.5 

87 

80.1 

34.0 

47 

135.3 

57.4 

07 

190.5 

80.9 

67 

245.8 

104.3 

28 

25.8 

10.9 

88 

81.0 

34.4 

48 

136.2 

57.8 

08 

191.5 

81.3 

68 

246.7 

104.7 

29 

26.7 

11.3 

89 

81.9 

34.8 

49 

137.2 

58.2 

09 

192.4 

81.7 

69 

247.6 

105.1 

30 

27.6 

11.7 

90 

82.8 

35.2 

50 

138.1 

58.6 

10 

193.3 

82.1 

70 

248.5 

105.5 
105.9 

31 

28.5 

12.1 

91 

83.8 

35.6 

151 

139.0 

59.0 

211 

194.2 

82.4 

271 

249.5 

32 

29.5 

12.5 

92 

84.7 

35.9 

52 

139.9 

59.4 

12 

195.1 

82.8 

72 

250.4 

106.3 

33 

30.4 

12.9 

93 

85.6 

36.3 

53 

140.8 

59.8 

13 

196.1 

83.2 

73 

251.3 

106.7 

34 

31.3 

13.3 

94 

86.5 

36.7 

54 

141.8 

60.2 

14 

197.0 

83.6 

74 

252.2 

107.1 

35 

32.2 

13.7 

95 

87.4 

37.1 

55 

142.7 

60.6 

15 

197.9 

84.0 

75 

253.1 

107.5 

36 

33.1 

14.1 

96 

88.4 

37.5 

56 

143.6 

61.0 

16 

198.8 

84.4 

76 

254.1 

107.8 

37 

34.1 

14.5 

97 

89.3 

37.9 

57 

144.5 

61.3 

17 

199.7 

84.8 

77 

255.0 

108.2 

38 

35.0 

14.8 

98 

90.2 

38.3 

58 

145.4 

61.7 

18 

200.7 

85.2 

78 

255.9 

108.6 

39 

35.9 

15.2 

99 

91.1 

38.7 

59 

146.4 

62.1 

19 

201.6 

85.6 

79 

256.8 

109.0 

40 

36.8 

15.6 

100 

92.1 

39.1 

60 

147.3 

62.5 

20 

202.5 

86.0 

80 

257.7 

109.4 

41 

37.7 

16.0 

101 

93.0 

39.5 

161 

148.2 

62.9 

221 

203.4 

86.4 

281 

258.7 

109.8 

42 

38.7 

16.4 

02 

93.9 

39.9 

62 

149.1 

63.3 

22 

204.4 

86.7 

82 

259.6 

110.2 

43 

39.6 

16.8 

03 

94.8 

40.2 

63 

150.0 

63.7 

23 

205.3 

87.1 

83 

260.5 

110.6 

44 

40.5 

17.2 

04 

95.7 

40.6 

64 

151.0 

64.1 

24 

206.2 

87.5 

84 

261.4 

111.0 

45 

41.4 

17.6 

05 

96.7 

41.0 

65 

151.9 

64.5 

25 

207.1 

87.9 

85 

262.3 

111.4 

46 

42.3 

18.0 

06 

97.6 

41.4 

66 

152.8 

64.9 

26 

208.0 

88.3 

86 

263.3 

111.7 

47 

43.3 

18.4 

07 

98.5 

41.8 

67 

153.7 

65.3 

27 

209.0 

88.7 

87 

264.2 

112.1 

48 

44.2 

18.8 

08 

99.4 

42.2 

68 

154.6 

65.6 

28 

209.9 

89.1 

88 

265.1 

112.5 

49 

45.1 

19.1 

09 

100.3 

42.6 

69 

155.6 

66.0 

29 

210.8 

89.5 

89 

266.0 

112.9 

50 

46.0 

19.5 

10 

101.3 

43.0 

70 

156.5 

66.4 

30 

211.7 

89.9 

90 

266.9 

113.3 

51 

46.9 

19.9 

111 

102.2 

43.4 

171 

157.4 

66.8 

231 

212.6 

90.3 

291 

267.9 

113.7 

52 

47.9 

20.3 

12 

103.1 

43.8 

72 

158.3 

67.2 

32 

213.6 

90.6 

92 

268.8 

114.1 

53 

48.8 

20.7 

13 

104.0 

44.2 

73 

159.2 

67.6 

33 

214.5 

91.0 

93 

269.7 

114.5 

54 

49.7 

21.1 

14 

104.9 

44.5 

74 

160.2 

68.0 

34 

215.4 

91.4 

94 

270.6 

114.9 

55 

50.6 

21.5 

15 

105.9 

44.9 

75 

161.1 

68.4 

35 

216.3 

91.8 

95 

271.5 

115.3 

56 

51.5 

21.9 

16 

106.8 

45.3 

76 

162.0 

68.8 

36 

217. 2 

92.2 

96 

272.5 

115.7 

57 

52.5 

22.3 

17 

107.7 

45.7 

77 

162.9 

69.2 

37 

218.2 

92.6 

97 

273.4 

116.0 

58 

53.4 

22.7 

18 

108.6 

46.1 

78 

163.8 

69.6 

38 

219.1 

93.0 

98 

274.3 

116.4 

59 

54.3 

23.1 

19 

109.5 

46.5 

79 

164.8 

69.9 

39 

220.0 

93.4 

99 

275.2 

116.8 

60 

55.2 

23.4 

20 

110.5 

46.9 

80 

165.7 

70.3 

40 

220.9 

93.8 

300 

276.2 

117.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

67°  (113°,  24* 

^°,  293' 

')• 

TABLE  2. 

[Page 

677 

Difference  of  Latitude  and  Departure  for  23°  (157°,  203 

.°,  337" 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

277.1 

117.6 

361 

332.3 

141.1 

421 

387.5 

164.5 

481 

442.7 

188.0 

541 

498.0 

211.4 

02 

278.0 

118.0 

62 

333.2 

141.5 

22 

388. 5 

164.9 

82 

443.7 

188.4 

42 

498.9 

211.8 

03 

278.9 

118.4 

63 

334.1 

141.8 

23 

389.4 

165.3 

83 

444.6 

188.8 

43 

499.8 

212.2 

04 

279.8 

118.8 

64 

335. 1 

142.2 

24 

390.3 

165.7 

84 

445.5 

189.2 

44 

500.7 

212.6 

05 

280.8 

119.2 

65 

336. 0 

142.6 

25 

391.2 

166.1 

85 

446.4 

189.5 

45 

501.7 

213.0 

06 

281.7 

119.6 

66 

336.9 

143.0 

26 

392.1 

166.5 

86 

447.3 

189.9 

46 

502.6 

213.4 

07 

282.6 

120.0 

67 

337.8 

143.4 

27 

393.1 

166.8 

87 

448.3 

190.2 

47 

503.5 

213.8 

08 

283.5 

120.4 

68 

338.  7 

143.8 

28 

394.0 

167.2 

88 

449.2 

190.6 

48 

504.4 

214.2 

09 

284.4 

120.8 

69 

339.7 

144.2 

29 

394.9 

167.6 

89 

450.1 

191.0 

49 

505.3 

214.6 

10 

285.  4 

121.2 

70 

340.6 

144.6 

30 

395.8 

168.0 

90 

451.0 

191.4 

50 

506.3 
507.2 

215.0 
215.3 

311 

286.3 

121.6 

371 

341.5 

145.0 

431 

396.7 

168.4 

491 

451.9 

191.8 

551" 

12 

287.2 

121.9 

72 

342.4 

145.4 

32 

397.7 

168.8 

92 

452.9 

192.2 

52 

508.1 

215.6 

13 

288. 1 

122.3 

73 

343.4 

145.7 

33 

398.6 

169.2 

93 

453.8 

192.6 

53 

509.0 

216.0 

14 

289.0 

122.7 

74 

344.  3 

146.1 

34 

399.5 

169.6 

94 

454.7 

193.0 

54 

509.9 

216.4 

15 

290.  0 

123.1 

75 

345.2 

146.5 

35 

400.4 

170.0 

95 

455.6 

193.4 

55 

510.9 

216.8 

16 

290.9 

123.5 

76 

346.1 

146.9 

36 

401.3 

170.4 

96 

456.6 

193.8 

56 

511.8 

217.2 

17 

291.  8 

123.9 

77 

347.0 

147.3 

37 

402.3 

170.8 

97 

457.5 

194.2 

57 

512.7 

217.6 

18 

292.7 

124.3 

78 

348.  0 

147.7 

38 

403.2 

171.1 

98 

458.4 

194.6 

58 

513.6 

218.0 

19 

293.6 

124.6 

79 

348.9 

148.1 

39 

404.1 

171.  5 

99 

459. 3 

195. 0 

59 

514.5 

218.4 

20 

294.6 

125.0 

80 

349.8 

148.5 

40 

405.0 

171.9 

500 

460.2 

195.4 

60 

515.5 

218.8 

321 

295.5 

125.4 

381 

350.7 

148.9 

441 

405.9 

172.3 

501 

461.2 

195.  8 

561 

516.4 

219.2 

22 

296.4 

125.8 

82 

351.6 

149.3 

42 

406.9 

172.7 

02 

462.1 

196.2 

62 

517.3 

219.6 

23 

297.3 

126.2 

83 

352.6 

149.7 

43 

407.8 

173.1 

03 

463.0 

196.6 

63 

518.2 

220.0 

24 

298.2 

126.6 

84 

353.5 

150.0 

44 

408.7 

173.5 

04 

463.9 

197.0 

64 

519.2 

220.4 

25 

299.2 

127.0 

85 

354.4 

150.4 

45 

409.6 

173.9 

05 

464.9 

197.4 

65 

520.1 

220.8 

26 

300.1 

127.4 

86 

355.3 

150.8 

46 

410.5 

174.3 

06 

465.8 

197.8 

66 

521.0 

221.2 

27 

301.0 

127.8 

87 

356.2 

151.2 

47 

411.5 

174.7 

07 

466.7 

198.1 

67 

521.9 

221.6 

28 

301.9 

128.2 

88 

357.2 

151.6 

48 

412.4 

175.1 

08 

467.6 

198.5 

68 

522.8 

222.0 

29 

302.8 

128.6 

89 

358.1 

152.0 

49 

413.3 

175. 4 

09 

468.5 

198.8 

69 

523.8 

222.3 

30 

303.8 

128.9 

90 

359.0 

152.4 

50 

414.2 

175.8 

10 

469.5 

199.3 

70 

524.7 

222.7 

331 

304.7 

129.3 

391 

359.9 

152.8 

451 

415.2 

176.2 

611 

470.4 

199.7 

571 

525.6 

223.1 

32 

305.6 

129.  7 

92 

360.8 

153.2 

52 

416.1 

176.6 

12 

471.3 

200.0 

72 

526.5 

223.4 

33 

306.5 

130.1 

93 

361.8 

153.6 

53 

417.0 

177.0 

13 

472.2 

200.4 

73 

527.4 

223.8 

34 

307.5 

130.5 

94 

362.7 

154.0 

54 

417.9 

177.4 

14 

473.1 

200.8 

74 

528.4 

224.2 

35 

308.4 

130.9 

95 

363.6 

154.3 

55 

418.8 

177.8 

15 

474.0 

201.2 

75 

529.3 

224.6 

36 

309.3 

131.3 

96 

364.5 

154.7 

56 

419.8 

178.2 

16 

475.0 

201.6 

76 

530.2 

225.0 

37 

310.2 

131.7 

97 

365.4 

155.1 

57 

420.7 

178.6 

17 

475.9 

202.0 

77 

531.1 

225.4 

38 

311.1 

132.1 

98 

366.4 

155.5 

58 

421.6 

179.0 

18 

476.8 

202.4 

78 

532.0 

225.8 

39 

312.1 

132.5 

99 

367.3 

155.9 

59 

422.5 

179.4 

19 

477.7 

202.8 

79 

533.0 

226.2 

40 

313.0 

132.9 

400 

368.2 

156.3 

60 

423.4 

179.7 

20 

478.6 

203.2 

80 

533.9 

226.6 

341 

313.9 

133.2 

401 

369.1 

156.7 

461 

424.4 

180.1 

521 

479.6 

203.6 

581 

534.8 

227.0 

42 

314.  8 

133.6 

02 

370.0 

157.1 

62 

425.3 

180.5 

22 

480.5 

204.0 

82 

535.7 

227.4 

43 

315.7 

134.0 

03 

371.0 

157.5 

63 

426.2 

180.9 

23 

481.4 

204.4 

83 

536.6 

227.8 

44 

316.7 

134.4 

04 

371.9 

157.9 

64 

427.1 

181.3 

24 

482.3 

204.8 

84 

537.6 

228.2 

45 

317.6 

134.8 

05 

372.8 

158.3 

65 

428.0 

181.7 

25 

483.2 

205.2 

85 

538.5 

228.6 

46 

318.5 

135.2 

06 

373.7 

158.6 

66 

429.0 

182.1 

26 

484.2 

205.5 

86 

539.4 

229.0 

47 

319.4 

135.6 

07 

374.6 

159.0 

67 

429.9 

182.5 

27 

485. 1 

205. 9 

87 

540.3 

229.4 

48 

320.3 

136.0 

08 

375.6 

159.4 

68 

430.8 

182.9 

28 

486.0 

206.3 

88 

541.2 

229.8 

49 

321.3 

136.4 

09 

376.5 

159.8 

69 

431.7 

183.3 

29 

486.9 

206.7 

89 

542.2 

230.2 

50 

322.2 

136.8 

10 

377.4 

160.2 

70 

432.6 

183.7 

30 

487.8 

207.1 

90 

543.1 

230.6 

351 

323.1 

137.2 

411 

378.3 

160.6 

471 

433.6 

184.0 

531 

488.8 

207.4 

591 

544.0 

231.0 

52 

324.0 

137.5 

12 

379.3 

161.0 

72 

434.5 

184.4 

32 

489.7 

207.8 

92 

544.9 

231.3 

53 

324.9 

137.9 

13 

380.2 

161.4 

73 

435.4 

184.8 

33 

490.6 

208.2 

93 

545.8 

231.7 

54 

325.9 

138.3 

14 

381.1 

161.8 

74 

436.3 

185.2 

34 

491.5 

208.6 

94 

546.8 

232.0 

55 

326.8 

138.7 

15 

382.0 

162.2 

75 

437.2 

185.  6 

35 

492.5 

209.0 

95 

547.7 

232.4 

56 

327.7 

139.1 

16 

382.9 

162.5 

76 

438.2 

186.0 

36 

493.4 

209.4 

96 

548.6 

232.8 

57 

328.6 

139.5 

17 

383.9 

162.9 

77 

439.1 

186.4 

37 

494.3 

209.8 

97 

549.5 

233.2 

58 

329.5 

139.9 

18 

384.8 

163.3 

78 

440.0 

186.8 

38 

495.2 

210.2 

98 

550.4 

233.6 

59 

330.5 

140.3 

19 

385.7 

163.7 

79 

440.9 

187.2 

39 

496.1 

210.6 

99 

551.3 

234.0 

60 

331.4 

140.7 

20 

386.6 

164.1 

80 

441.8 

187.6 

40 

497.1 

211.0 

600 

552.3 

234.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

S7°(l] 

3°,  247°,  293°] 

. 

21594°— 14- 


-30 


Page  678] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  24°  ( 156 

°, 204°, 336°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

55.7 

24.8 

121 

110.5 

49.2 

181 

165.4 

73.6 

241 

220.2 

98.0 

2 

1.8 

0.8 

62 

56.6 

25.2 

22 

111.5 

49.6 

82 

166.3 

74.0 

42 

221.1 

98.4 

3 

2.7 

1.2 

63 

57.6 

25.6 

23 

112.4 

50.0 

83 

167.2 

74.4 

43 

222.0 

98.8 

4 

3.7 

1.6 

64 

58.5 

26.0 

24 

113.3 

60.4 

84 

168.1 

74.8 

44 

222.9 

99.2 

5 

4.6 

2.0 

65 

59.4 

26.4 

25 

114.2 

50.8 

85 

169.0 

75.2 

45 

223.8 

99.7 

6 

5.5 

2.4 

66 

60.3 

26.8 

26 

115.1 

51.2 

86 

169.9 

75.7 

46 

224.7 

100.1 

7 

6.4 

2.8 

67 

61.2 

27.3 

27 

116.0 

51.7 

87 

170.8 

76.1 

47 

225.6 

100.5 

8 

7.3 

3.3 

68 

62.1 

27.7 

28 

116.9 

52.1 

88 

171.7 

76.5 

48 

226.6 

100.9 

9 

8.2 

3.7 

69 

63.0 

28.1 

29 

117.8 

52.5 

89 

172.7 

76.9 

49 

227.5 

101.3 

10 

9.1 

4.1 

70 

63.9 

28.5 

30 

118.8 

52.9 

90 

173.6 

77.3 

50 

228.4 

101.7 

11 

10.0 

4.5 

71 

64.9 

28.9 

131 

119.7 

53.3 

191 

174.5 

77.7 

251 

229.3 

102.1 

12 

11.0 

4.9 

72 

65.8 

29.3 

32 

120.6 

53.7 

92 

175.4 

78.1 

52 

230.2 

102.5 

13 

11.9 

5.3 

73 

66.7 

29.7 

33 

121.5 

54.1 

93 

176.3 

78.5 

53 

231.1 

102.9 

14 

12.8 

5.7 

74 

67.6 

30.1 

34 

122.4 

54.5 

94 

177.2 

78.9 

54 

232.0 

103.3 

15 

13.7 

6.1 

75 

68.5 

30.5 

35 

123.3 

54.9 

95 

178.1 

79.3 

55 

233.0 

103.7 

16 

14.6 

6.5 

76 

69.4 

30.9 

36 

124.2 

55.3 

96 

179. 1 

79.7 

56 

233.9 

104.1 

17 

15.5 

6.9 

77 

70.3 

31.3 

37 

125.2 

55.7 

97 

180.0 

80.1 

57 

234.8 

104.5 

18 

16.4 

7.3 

78 

71.3 

31.7 

38 

126.1 

56.1 

98 

180.9 

80.5 

58 

235.7 

104.9 

19 

17.4 

7.7 

79 

72.2 

32.1 

39 

127.0 

56.5 

99 

181.8 

80.9 

59 

236.6 

105.3 

20 

18.3 

8.1 

80 

73.1 

32.5 

40 

127.9 

56.9 

200 

182.7 

81.  3 

60 
261" 

237.5 

105.8 

21 

19.2 

8.5 

81 

74.0 

32.9 

141 

128.8 

57.3 

201 

183.6 

81.8 

238.4 

106.2 

22 

20.1 

8.9 

82 

74.9 

33.4 

42 

129.7 

57.8 

02 

184.5 

82.2 

62 

239.3 

106.6 

23 

21.0 

9.4 

83 

75.8 

33.8 

43 

130.6 

58.2 

03 

185.4 

82.6 

63 

240.3 

107.0 

24 

21.9 

9.8 

84 

76.7 

34.2 

44 

131.6 

58.6 

04 

186.4 

83.0 

64 

241.2 

107.4 

25 

22.8 

10.2 

85 

77.7 

34.6 

45 

132.5 

59.0 

05 

187.3 

83.4 

65 

242.1 

107.8 

26 

23.8 

10.6 

86 

78.6 

35.0 

46 

133.4 

59.4 

06 

188.2 

83.8 

66 

243.0 

108.2 

27 

24.7 

11.0 

87 

79.5 

35.4 

47 

134.3 

59.8 

07 

189.1 

84.2 

67 

243.9 

108.6 

28 

25.6 

11.4 

88 

80.4 

35.8 

48 

135.2 

60.2 

08 

190.0 

84.6 

68 

244.8 

109.0 

29 

26.5 

11.8 

89 

81.3 

36.2 

49 

136.1 

60.6 

09 

190.9 

85.0 

69 

245.7 

109.4 

30 

27.4 

12.2 

90 

82.2 

36.6 

50 

137.0 

61.0 

10 

191.8 

85.4 

70 

246.7 

109.8 

31 

28.3 

12.6 

91 

83.1 

37.0 

151 

137.9 

61.4 

211 

192.8 

85.8 

271 

247.6 

110.2 

32 

29.2 

13.0 

92 

84.0 

37.4 

52 

138.9 

61.8 

12 

193.7 

86.2 

72 

248.5 

110.6 

33 

30.1 

13.4 

93 

85.0 

37.8 

53 

139.8 

62.2 

13 

194.6 

86.6 

73 

249.4 

111.0 

34 

31.1 

13.8 

94 

85.9 

38.2 

54 

140.7 

62.6 

14 

195.5 

87.0 

74 

250.3 

111.4 

35 

32.0 

14.2 

95 

86.8 

38.6 

55 

141.6 

63.0 

15 

196.4 

87.4 

75 

251.2 

111.9 

36 

32.9 

14.6 

96 

87.7 

39.0 

56 

142.5 

63.5 

16 

197.3 

87.9 

76 

252.1 

112.3 

37 

33.8 

15.0 

97 

88.6 

39.5 

57 

143.4 

63.9 

17 

198.2 

88.3 

77 

253.1 

112.7 

38 

34.7 

15.5 

98 

89.5 

39.9 

58 

144.3 

64.3 

18 

199.2 

88.7 

78 

254.0 

113.1 

39 

35.6 

15.9 

99 

90.4 

40.3 

59 

145.3 

64.7 

19 

200.1 

89.1 

79 

254.9 

113.5 

40 

36.5 

16.3 

100 

91.4 

40.7 

60 

146.2 

65.1 

20 

201.0 

89.5 

80 

255.8 

113.9 
114.3 

41 

37.5 

16.7 

101 

92.3 

41.1 

161 

147.1 

65.5 

221 

201.9 

89.9 

281 

256.7 

42 

38.4 

17.1 

02 

93.2 

41.5 

62 

148.0 

65.9 

22 

202.8 

90.3 

82 

257.6 

114.7 

43 

39.3 

17.5 

03 

94.1 

41.9 

63 

148.9 

66.3 

23 

203.7 

90.7 

83 

258.5 

115.1 

44 

40.2 

17.9 

04 

95.0 

42.3 

64 

149.8 

66.7 

24 

204.6 

91.1 

84 

259.4 

115.5 

45 

41.1 

18.3 

05 

95.9 

42.7 

65 

150.7 

67.1 

25 

205.5 

91.5 

85 

260.4 

115.9 

46 

42.0 

18.7 

06 

96.8 

43.1 

66 

151.6 

67.5 

26 

206.5 

91.9 

86 

261.3 

116.3 

47 

42.9 

19.1 

07 

97.7 

43.5 

67 

152.6 

67.9 

27 

207.4 

92.3 

87 

262.2 

116.7 

48 

43.9 

19.5 

08 

98.7 

43.9 

68 

153. 5 

68.3 

28 

208.3 

92.7 

88 

263.1 

117.1 

49 

44.8 

19.9 

09 

99.6 

44.3 

69 

154.4 

68.7 

29 

209.2 

93.1 

89 

264.0 

117.5 

50 

45.7 

20.3 

10 

100. 5 

44.7 

70 

155.3 

69.1 

30 

210.1 

93.5 

90 

264.9 

118.0 

51 

46.6 

20.7 

111 

101.4 

45.1 

171 

156.2 

69.  6 

231 

211.0 

94.0 

291 

265.8 

118.4 

52 

47.5 

21.2 

12 

102.3 

45.6 

72 

157.1 

70.0 

32 

211.9 

94.4 

92 

266.8 

118.8 

53 

48.4 

21.6 

13 

103.2 

46.0 

73 

158.0 

70.4 

33 

212.9 

94.8 

93 

267.7 

119. 2  1 

54 

49.3 

22.0 

14 

104.1 

46.4 

74 

159.0 

70.8 

34 

213.8 

95.2 

94 

268.6 

119.6 

55 

50.2 

22.4 

15 

105.1 

46.8 

75 

159.9 

71.2 

35 

214.7 

95.6 

95 

269.5 

120.0 

56 

51.2 

22.8 

16 

106.0 

47.2 

76 

160.8 

71.6 

36 

215.6 

96.0 

96 

270.4 

120.4 

57 

52.1 

23.2 

17 

106.9 

47.6 

77 

161.7 

72.0 

37 

216.5 

96.4 

97 

271.3 

120.8 

58 

53.0 

23.6 

18 

107.8 

48.0 

78 

162.6 

72.4 

38 

217.4 

96.8 

98 

272.2 

121.2 

59 

53.9 

24.0 

19 

108.7 

48.4 

79 

163.5 

72.8 

38 

218.3 

97.2 

99 

273.2 

121.6 

60 

54.8 

24.4 

20 

109.6 

48.8 

80 

164.4 

73.2 

40 

219.3 

97.6 

300 

274.1 

122.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

)6°  (1 

14°,  246 

°,  294° 

). 

TABLE  2. 

[Page  579 

Difference  of  Latitude  and  Departure  for  24°  (156°,  204 

°,  336°). 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

301 

275.0 

122.4 

361 

329.8 

146.8 

421 

384.6 

171.2 

481 

439.4 

195.6 

541 

494.2 

220.  0 

02 

275.9 

122.8 

62 

330.7 

147.2 

22 

385.  5 

171.6 

82 

440.3 

196.0 

42 

495.1 

220.4 

03 

276.8 

123.2 

63 

331.6 

147.6 

23 

386.4 

172.1 

83 

441.2 

196.5 

43 

496.0 

220.9 

04 

277.7 

123.7 

64 

332.5 

148.1 

24 

387.3 

172.5 

84 

442.1 

196.9 

44 

496.9 

221.3 

05 

278.6 

124.1 

65 

33l4 

148.5 

25 

388.2 

172.9 

85 

443.0 

197.3 

45 

497.8 

221.7 

06 

279.5 

124.5 

66 

334.3 

148.9 

26 

389.2 

173.3 

86 

444.0 

197.7 

46 

498.8 

222.1 

07 

280.4 

124.9 

67 

335.3 

149.3 

27 

390.1 

173.7 

87 

444.9 

198.1 

47 

499.7 

222.5 

08 

281.4 

125.3 

68 

336.2 

149.7 

28 

391.0 

174.1 

88 

445.8 

198.5 

48 

500.6 

222.9 

09 

282.3 

125.7 

69 

337.1 

150.1 

29 

391.9 

174.5 

89 

446.7 

198.9 

49 

501.5 

223.3 

10 

283.2 

126.1 

70 

338.0 

150.5 

30 

392.8 

174.9 

90 

447.6 

199.3 

50 

502. 4 

223.7 
224.1 

311 

284.1 

126.5 

371 

338.9 

150.9 

431 

393.7 

175.3 

491 

448.6 

199.7 

551 

503.4 

12 

285.0 

126.9 

72 

339.8 

151.3 

32 

.394.  6 

175.7 

92 

449.5 

200.1 

52 

504.3 

224.5 

13 

285.9 

127.3 

73 

340.7 

151.7 

33 

395.6 

176.1 

93 

450.4 

200.5 

53 

505.  2 

224.9 

14 

286.8 

127.7 

74 

341.7 

152.1 

34 

396.5 

176.5 

94 

451.3 

200.9 

54 

506.1 

225.3 

15 

287.8 

128.1 

75 

342.6 

152.5 

35 

397.4 

176.9 

95 

452.2 

201.3 

55 

507.0 

225.7 

16 

288.7 

128.5 

76 

343. 5 

152.9 

36 

398.3 

177.3 

96 

453.1 

201.7 

56 

507.9 

226.1 

17 

289.6 

128.9 

77 

344.4 

153. 3 

37 

399.2 

177.7 

97 

454.0 

202.2 

57 

508.8 

226.6 

18 

290.5 

129.3 

78 

345.3 

153.7 

38 

400.1 

178.2 

98 

454.9 

202.6 

58 

509.7 

227.0 

19 

291.4 

129.8 

79 

346.2 

154.2 

39 

401.0 

178.6 

99 

455.8 

203.0 

59 

510.6 

227.4 

20 

292.3 

130.2 
130.6 

80 
381 

347.1 
348.1 

154.6 

40 

402.0 

179.0 

500 

456.8 

203.4 

60 

511.6 
512.5 

227.8 

321 

293.2 

155. 0 

441 

402.9 

179.4 

501 

457.7 

203.8 

561 

228.2 

22 

294.2 

131.0 

82 

349.0 

155.4 

42 

403.8 

179.8 

02 

458.6 

204.2 

62 

513.4 

228.6 

23 

295.1 

131.4 

83 

348.9 

156.8 

43 

404.7 

180.2 

03 

459.5 

204.6 

63 

514.3 

229.0 

24 

296.0 

131.8 

84 

350.8 

156.2 

44 

405.6 

180.6 

04 

460.4 

205. 0 

64 

515.2 

229.4 

25 

296.9 

132.2 

85 

351.7 

156.6 

45 

406.5 

181.0 

05 

461.3 

205.4 

65 

516.1 

229.8 

26 

297.8 

132.6 

86 

352.6 

157.0 

46 

407.4 

181.4 

06 

462.2 

205.  8 

66 

517.0 

230.2 

27 

298.7 

133.0 

87 

353.5 

157.4 

47 

408.3 

181.8 

07 

463.2 

206.2 

67 

518.0 

230. 6 

28 

299.6 

133.4 

88 

354.4 

157.8 

48 

409.3 

182.2 

08 

464.1 

206.6 

68 

518.9 

231.0 

29 

300.5 

133.8 

89 

355.4 

158.2 

49 

410.2 

182.6 

09 

465.0 

207.0 

69 

519.8 

231.4 

30 

301.5 

134.  2 

90 

356.3 

158.6 

50 

411.1 

183.0 
183.4 

10 
511 

465.9 

207.4 

70 

520.7 

231.8 
232. 2 

331 

302.4 

134.6 

391 

357.2 

159.0 

451 

412.0 

466.8 

207.8 

571 

521.6 

32 

303.3 

135.0 

92 

358.1 

159.4 

52 

412.9 

183.8 

12 

467.7 

208.2 

72 

522.5 

232.7 

33 

304.2 

135,4 

93 

359.0 

159.8 

53 

413.8 

184.3 

13 

468.6 

208.7 

73 

523.4 

233.1 

34 

305. 1 

135.9 

94 

359.9 

160.3 

54 

414.7 

184.7 

14 

469.5 

209.1 

74 

524.3 

233.5 

35 

306.0 

136.3 

95 

360.8 

160.7 

55 

415.7 

185.1 

15 

470.5 

209.5 

75 

525.3 

233.9 

36 

306.9 

136.7 

96 

361.8 

161.1 

56 

416.6 

185.5 

16 

471.4 

209.9 

76 

526.2 

234.3 

37 

307.9 

137.1 

97 

362.7 

161.5 

57 

417.5 

185.9 

17 

472.3 

210.3 

77 

527.1 

234.7 

38 

308.8 

137.5 

98 

363.6 

161.9 

58 

418.4 

186.3 

18 

473.2 

210.7 

78 

528.0 

235.1 

39 

309.7 

137.9 

99 

364.5 

162.3 

59 

419.3 

186.7 

19 

474.1 

211.1 

79 

528. 9 

235.5 

40 

310.6 

138.3 

400 

365.4 
366.3" 

162.7 

60 

420.2 

187.1 

20 

475. 0 

211.5 
211.9 

80 
581 

529.8 

235.9 
236. 3 

341 

311.5 

138.7 

401 

163.1 

461 

421.1 

187.5 

521 

475.9 

530.8 

42 

312.4 

139.1 

02 

367.2 

163.5 

62 

422.0 

187.9 

22 

476.8 

212.3 

82 

531.7 

236.7 

43 

313.3 

139.5 

03 

368.2 

163.9 

63 

423.0 

188.3 

23 

477.8 

212.7 

83 

532.  6 

237.1 

44 

314.  3 

139.9 

04 

369.1 

164.3 

64 

423.9 

188.7 

24 

478.7 

213.1 

84 

533.5 

237.5 

45 

315.2 

140.3 

05 

370.0 

164.7 

65 

424.8 

189.1 

25 

479.6 

213.5 

85 

534. 4 

237. 9 

46 

316.1 

140.7 

06 

370.9 

165.1 

66 

425.7 

189.5 

26 

480.5 

213.9 

86 

535.3 

238.3 

47 

317.0 

141.1 

07 

371.8 

165. 5 

67 

426.6 

189.9 

27 

481.4 

214.4 

87 

536.2 

238.8 

48 

317.9 

141.5 

08 

372.7 

165.9 

68 

427.5 

190.4 

28 

482.3 

214.8 

88 

537. 1 

239.2 

49 

318.8 

142.0 

09 

373.6 

166.4 

69 

428.4 

190.8 

29 

483.2 

215.2 

89 

538.0 

239.6 

50 

319.  7 
320.6 

142.4 

10 

374.5 

166.8 

70 

429.4 

191.2 

30 

484.2 

215.6 

90 

539.0 
539.9 

240.0 

351 

142.8 

411 

375.5 

167.2 

471 

430.3 

191.6 

531 

485.1 

216.0 

591 

240.4 

52 

321.6 

143.2 

12 

376.4 

167.6 

72 

431.2 

192.0 

32 

486.0 

216.4 

92 

540.8 

240.8 

53 

322.5 

143.6 

13 

377.3 

168.0 

73 

432.1 

192.4 

33 

486.9 

216.8 

93 

541.7 

241.2 

54 

323.4 

144.0 

14 

378.2 

168.4 

74 

433.0 

192.8 

34 

487.8 

217.2 

94 

542.6 

241.6 

55 

324.3 

144.4 

15 

379.1 

168.8 

75 

433.9 

193.2 

35 

488.7 

217.6 

95 

543.5 

242.0 

56 

325.2 

144.8 

16 

380.0 

169.2 

76 

434.8 

193.6 

36 

489.6 

218.0 

96 

544.4 

242.4 

57 

326.1 

145.2 

17 

380.9 

169.6 

77 

435.8 

194.0 

37 

490.6 

218.4 

97 

545.4 

242.8 

58 

327.0 

145.6 

18 

381.9 

170.0 

78 

436.7 

194.4 

38 

491.5 

218.8 

98 

546.3 

243.2 

59 

328.0 

146.0 

19 

382.8 

170.4 

79 

437.6 

194.8 

39 

492.4 

219.2 

99 

547.2 

243.6 

60 

328.9 

146.4 

20 

383.7 

170.8 

80 

438.5 

195.2 

40 

493.3 

219.6 

600 

548.1 

244.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     1     Lat. 

( 

J6°  (1 

14°,  246 

=,294° 

). 

Page  680] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  25°  (155°,  205°,  335° 

)• 

Bist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

55.3 

25.8 

121 

109.7 

51.1 

181 

164.0 

76.5 

241 

218.4 

101.9 

2 

1.8 

0.8 

62 

56.2 

26.2 

22 

110.6 

51.6 

82 

164.9 

76.9 

42 

219.3 

102.3 

3 

2.7 

1.3 

63 

57.1 

26.6 

23 

111.5 

52.0 

83 

165.9 

77.3 

43 

220.2 

102.7 

4 

3.6 

1.7 

64 

58.0 

27.0 

24 

112.4 

52.4 

84 

166.8 

77.8 

44 

221.1 

103.1 

5 

4.5 

2.1 

65 

58.9 

27.5 

25 

113.3 

52.8 

85 

167.7 

78.2 

45 

222.0 

103.5 

6 

5.4 

2.5 

66 

59.8 

27.9 

26 

114.2 

53.2 

86 

168.6 

78.6 

46 

223.0 

104.0 

7 

6.3 

3.0 

67 

60.7 

28.3 

27 

115.1 

53.7 

87 

169.5 

79.0 

47 

223.9 

104.4 

8 

7.3 

3.4 

68 

61.6 

28.7 

28 

116.0 

54.1 

88 

170.4 

79.5 

48 

224.8 

104.8 

9 

8.2 

3.8 

69 

62.5 

29.2 

29 

116.9 

54.5 

89 

171.3 

79.9 

49 

225.7 

105.2 

10 

9.1 

4.2 

70 

63.4 

29.6 

30 

117.8 

54.9 

90 

172.2 

80.3 

50 

226.6 

105.7 

11 

10.0 

4.6 

71 

64.3 

30.0 

131 

118.7 

55.4 

191 

173.1 

80.7 

251 

227.5 

106.1 

12 

10.9 

5.1 

72 

65.3 

30.4 

32 

119.6 

55.8 

92 

174.0 

81.1 

52 

228.4 

106.5 

13 

11.8 

5.5 

73 

66.2 

30.9 

33 

120.5 

56.2 

93 

174.9 

81.6 

53 

229.3 

106.9 

14 

12.7 

5.9 

74 

67.1 

31.3 

34 

121.4 

56.6 

94 

175.8 

82.0 

54 

230.2 

107.3 

15 

13.6 

6.3 

75 

68.0 

31.7 

35 

122.4 

57.1 

95 

176.7 

82.4 

55 

231.1 

107.8 

16 

14.5 

6.8 

76 

68.9 

32.1 

36 

123.3 

57.5 

96 

177.6 

82.8 

56 

232.0 

108.2 

17 

15.4 

7.2 

77 

69.8 

32.5 

37 

124.2 

57.9 

97 

178.5 

83.3 

57 

232.9 

108.6 

18 

16.3 

7.6 

78 

70.7 

33.0 

38 

125.1 

58.3 

98 

179.4 

83.7 

58 

233.8 

109.0 

19 

17.2 

8.0 

79 

71.6 

33.4 

39 

126.0 

58.7 

99 

180.4 

84.1 

59 

234.7 

109.5 

20 

18.1 

8.5 

80 

72.5 
73.4 

33.8 
34.2 

40 
141 

126.9 

59.2 

200 
201 

181.3 
182.2 

84.5 

60 

235.6 
236.5 

109.9 
110.3 

21 

19.0 

8.9 

81 

127.8 

59.6 

84.9 

261 

22 

19.9 

9.3 

82 

74.3 

34.7 

42 

128.7 

60.0 

02 

183.1 

85.4 

62 

237.5 

110.7 

23 

20.8 

9.7 

83 

75.2 

3.5.1 

43 

129.6 

60.4 

03 

184.0 

85.8 

63 

238.4 

111.1 

24 

21.8 

10.1 

84 

76.1 

35.5 

44 

130.5 

60.9 

04 

184.9 

86.2 

64 

239.3 

111.6 

25 

22.7 

10.6 

85 

77.0 

35.9 

45 

131.4 

61.3 

05 

185.8 

86.6 

65 

240.2 

112.0 

26 

23.6 

11.0 

86 

77.9 

36.3 

46 

132.3 

61.7 

06 

186.7 

87.1 

66 

241.1 

112.4 

27 

24.5 

11.4 

87 

78.8 

36.8 

47 

133.2 

62.1 

07 

187.6 

87.5 

67 

242.0 

112.8 

28 

25.4 

11.8 

88 

79.8 

37.2 

48 

134.1 

62.5 

08 

188.5 

87.9 

68 

242.9 

113.3 

29 

26.3 

12.3 

89 

80.7 

37.6 

49 

135.0 

63.0 

09 

189.4 

88.3 

69 

243.8 

113.7 

30 

27.2 

12.7 

90 

81.6 

38.0 

50 

135.9 

63.4 

10 

190.3 

88.7 

70 

244.7 

114.1 

31 

28.1 

13.1 

91 

82.5 

38.5 

151 

136.9 

63.8 

211 

191.2 

89.2 

271 

245.6 

114.5 

32 

29.0 

13.5 

92 

83.4 

38.9 

52 

137.8 

64.2 

12 

192.1 

89.6 

72 

246.5 

115.0 

33 

29.9 

13.9 

93 

84.3 

39.3 

53 

138.7 

64.7 

13 

193.0 

90.0 

73 

247.4 

115.4 

34 

30.8 

14.4 

94 

85.2 

39.7 

54 

139.6 

65.1 

14 

193.9 

90.4 

74 

248.3 

115.8 

36 

31.7 

14.8 

95 

86.1 

40.1 

55 

140.5 

65.5 

15 

194.9 

90.9 

75 

249.2 

116.2 

36 

32.6 

15.2 

96 

87.0 

40.6 

56 

141.4 

6.5.9 

16 

195.8 

91.3 

76 

250.1 

116.6 

37 

33.5 

15.6 

97 

87.9 

41.0 

57 

142. 3 

66.4 

17 

196.7 

91.7 

77 

251.0 

117.1 

38 

34.4 

16.1 

98 

88.8 

41.4 

58 

143.2 

66.8 

18 

197.6 

92.1 

78 

252.0 

117.5 

39 

35.3 

16.5 

99 

89.7 

41.8 

59 

144.1 

67.2 

19 

198.5 

92.6 

79 

252.9 

117.9 

40 

36.3 

16.9 

100 

90.6 

42.3 

60 

145.0 

67.6 

20 

199.4 

93.0 

80 

253.8 

118.3 

41 

37.2 

17.3 

101 

91.5 

42.7 

161 

145.9 

68.0 

221 

200.3 

93.4 

281 

254.7 

118.8 

42 

38.1 

17.7 

02 

92.4 

43.1 

62 

146.8 

68.5 

22 

201.2 

93.8 

82 

255.6 

119.2 

43 

39.0 

18.2 

03 

93.3 

43.5 

63 

147.7 

68.9 

23 

202.1 

94.2 

83 

256. 5 

119.6 

44 

39.9 

18.6 

04 

94.3 

44.0 

64 

148.6 

69.3 

24 

203.0 

94.7 

84 

257.4 

120.0 

45 

40.8 

19.0 

05 

95.2 

44.4 

65 

149.5 

69.7 

25 

203.9 

95.1 

85 

258.3 

120.4 

46 

41.7 

19.4 

06 

96.1 

44.8 

66 

150.4 

70.2 

26 

204.8 

95.5 

86 

259.2 

120.9 

47 

42.6 

19.9 

07 

97.0 

45.2 

67 

151.4 

70.6 

27 

205.7 

95.9 

87 

260.1 

121.3 

48 

43.5 

20.3 

08 

97.9 

45.6 

68 

152.3 

71.0 

28 

206.6 

96.4 

88 

261.0 

121.7 

49 

44.4 

20.7 

09 

98.8 

46.1 

69 

153.2 

71.4 

29 

207.5 

96.8 

89 

261.9 

122.1 

50 

45.3 

21.1 

10 

99.7 

46.5 

70 

154.1 
155.0 

71.8 

30 

208.5 

97.2 

90 

262.8 

122.6 

51 

46.2 

21.6 

111 

100.6 

46.9 

171 

72.3 

231 

209.4 

97.6 

291 

263.7 

123.0 

52 

47.1 

22.0 

12 

101.5 

47.3 

72 

155.9 

72.7 

32 

210.3 

98.0 

92 

264.6 

123.4 

53 

48.0 

22.4 

13 

102.4 

47.8 

73 

156.8 

73.1 

33 

211.2 

98.5 

93 

265.5 

123.8 

54 

48.9 

22.8 

14 

103.3 

48.2 

74 

157.7 

73.5 

34 

212.1 

98.9 

94 

266.5 

124.2 

55 

49.8 

23.2 

15 

104.2 

48.6 

75 

158.6 

74.0 

35 

213.0 

99.3 

95 

267.4 

124.7 

56 

50.8 

2.3.7 

16 

105.1 

49.0 

76 

159.5 

74.4 

36 

213.9 

99.7 

96 

268.3 

125.1 

57 

51.7 

24.1 

17 

106.0 

49.4 

77 

160.4 

74.8 

37 

214.8 

100.2 

97 

269.2 

125.5 

58 

52.6 

24.5 

18 

106.9 

49.9 

78 

161.3 

75.2 

38 

215.7 

100.6 

98 

270.1 

125.9 

59 

53.5 

24.9 

19 

107.9 

50.3 

79 

162.2 

75.6 

39 

216.6 

101.0 

99 

271.0 

126.4 

60 

54.4 

25.4 

20 

108.8 

50.7 

80 

163.1 

76.1 

40 

217.5 

101.4 

300 

271.9 

126.8 

DiBt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

D«p. 

Lat. 

Dist. 

Dep. 

Lat. 

35°  (1 

15°,  245°,  295° 

)• 

TABLE  2. 

[Page 

681 

Difference  of  Latitude  and  Departure  for  25°  (155°,  205°,  335° 

)• 

Dist. 

Lat.     1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

272.8 

127.2 

361 

327.1 

152.5 

421 

381.5 

177.9 

481 

435.9 

203.3 

541 

490.3 

228.6 

02 

273.7 

127.6 

62 

328.0 

153.0 

22 

382.4 

178.3 

82 

436.8 

203.7 

42 

491.2 

229.0 

03 

274.6 

128.0 

63 

329.0 

153.4 

23 

383.3 

178.7 

83 

437.7 

204.1 

43 

492.1 

229.4 

04 

275.5 

128.4 

64 

329.9 

153.8 

24 

384.2 

179.2 

84 

438.6 

204.6 

44 

493.0 

229.9 

05 

276.4 

128.9 

65 

330.8 

154.2 

25 

385.1 

179.6 

86 

439.6 

204.9 

45 

493.9 

230.3 

06 

277.3 

129.3 

66 

331.7 

154.6 

26 

386.0 

180.0 

86 

440.4 

206.4 

46 

494.8 

•230.7 

07 

278.2 

129.7 

67 

332.6 

155. 1 

27 

387.0 

180.4 

87 

441.3 

205.8 

47 

495.7 

231.1 

08 

279.1 

130.1 

68 

333.5 

155.5 

28 

387.9 

180.9 

88 

442.2 

206.2 

48 

496.6 

231.6 

09 

280.0 

130.6 

69 

334.4 

155.9 

29 

388.8 

181.3 

89 

443.1 

206.6 

49 

497. 5 

232.0 

10 

280.9 

131.0 

70 

335.3 

156.3 

30 

389.7 

181.7 

90 

444.0 

207.1 

60 

498.4 

232.4 

311 

281.8 

131.4 

371 

336.2 

156.8 

431 

390.6 

182.1 

491 

444.9 

207.6 

651 

499.  3 

232.8 

12 

282.7 

131.8 

72 

337. 1 

157.2 

32 

391.5 

182.5 

92 

445.9 

207.9 

62 

500.2 

2.33. 2 

13 

283.6 

132.2 

73 

338.0 

157.6 

33 

392.4 

183.0 

93 

446.8 

208. 3 

53 

501.1 

233.7 

14 

284.5 

132.7 

74 

338.9 

158.0 

34 

393.3 

183.4 

94 

447.7 

208.7 

54 

502.0 

234.1 

15 

285.4 

133.1 

75 

339.8 

158.5 

35 

394.2 

183.8 

95 

448.6 

209.1 

66 

503.0 

234.5 

16 

286.4 

133.5 

76 

340.7 

158.9 

36 

395.1 

184.2 

96 

449.6 

209.6 

66 

503.9 

235.0 

17 

287.3 

133.9 

77 

341.6 

159.3 

37 

396.0 

184.7 

97 

450.4 

210.0 

57 

604.8 

236.4 

18 

288.2 

134.4 

78 

342.5 

159.7 

38 

396.9 

185.1 

98 

451.3 

210.4 

58 

505.7 

236.8 

19 

289.1 

134.8 

79 

343.5 

160.1 

39 

397.8 

185.5 

99 

462.2 

210.9 

59 

506.6 

236.2 

20 

290.0 

135.2 

80 

344.4 

160.6 

40 

398.7 

185.9 

500 

453.1 

211.3 

60 

607.5 

236.6 

321 

290.9 

135.6 

381 

345.3 

161.0 

441 

399.6 

186.3 

501 

454.0 

211.7 

561 

508.4 

237.1 

22 

291.8 

136.1 

82 

346.2 

161.4 

42 

400.6 

186.8 

02 

464.9 

212.1 

62 

609.3 

237. 6 

23 

292.7 

136.5 

83 

347.1 

161.8 

43 

401.5 

187.2 

03 

456.8 

212.5 

63 

510.2 

237.9 

24 

293.6 

136.9 

84 

348.0 

162.3 

44 

402.4 

187.6 

04 

456.7 

213.0 

64 

511.1 

238.3 

25 

294.5 

137.3 

85 

348.9 

162.7 

45 

403.3 

188.0 

05 

467.7 

213.4 

66 

512.0 

238.7 

26 

295.4 

137.7 

86 

349.8 

163.1 

46 

404.2 

188.5 

06 

468.6 

213.8 

66 

512.9 

239.2 

27 

296.3 

138.2 

87 

350.7 

163.5 

47 

405.1 

188.9 

07 

459.5 

214.2 

67 

613.8 

239.6 

28 

297.2 

138.6 

88 

351.6 

163.9 

48 

406.0 

189.3 

08 

460.4 

214.7 

68 

514.8 

240.1 

29 

298.1 

139.0 

89 

352.5 

164.4 

49 

406.9 

189.7 

09 

461.3 

215.1 

69 

515.7 

240.6 

30 
331 

299.0 

139.4 

90 

363.4 

164.8 

50 

407.8 

190.1 

10 

462.2 

215.5 

70 

616.6 

240.9 

300.0 

139.9 

391 

354.3 

165.2 

451 

408.7 

190.6 

511 

463.1 

215.9 

571 

517.5 

241.  J 

32 

300.9 

140.3 

92 

355.2 

165.6 

52 

409.6 

191.0 

12 

464.0 

216.4 

72 

518.4 

241.7 

33 

301.8 

140.7 

93 

356.1 

166.1 

53 

410.5 

191.4 

13 

464.9 

216.8 

73 

519.3 

242.1 

34 

302.7 

141.1 

94 

357.0 

166.5 

54 

411.4 

191.8 

14 

466.8 

217.2 

74 

520.2 

242.6 

35 

303.6 

141.5 

95 

358.0 

166.9 

55 

412.3 

192.3 

15 

466.7 

217.7 

75 

521.1 

243.0 

36 

304.5 

142.0 

96 

358.9 

167.3 

56 

413.  2 

192.7 

16 

467.6 

218. 1 

76 

522.0 

243.4 

37 

305.4 

142.4 

97 

359.8 

167.7 

57 

414.1 

193.1 

17 

468.5 

218.5 

77 

622.9 

243.8 

38 

306.3 

142.8 

98 

360.7 

168.2 

58 

415.1 

193.5 

18 

469.4 

218.9 

78 

523.8 

244.3 

39 

307.2 

143.2 

99 

361.6 

168.6 

59 

416.0 

194.0 

19 

470.3 

219.3 

79 

524.7 

244.7 

40 

308.1 

143.7 

400 

362.5 

169.0 

60 

416.9 

194.4 

20 

471.2 

219.8 

80 

525.6 

245.1 

341 

309.0 

144.1 

401 

363.4 

169.4 

461 

417.8 

194.8 

521 

472.2 

220.2 

581 

526.5 

245.5 

42 

309.9 

144.5 

02 

364.3 

169.9 

62 

418.7 

195.2 

22 

473.1 

220.6 

82 

527. 4 

246.0 

43 

310.8 

144.9 

03 

365.2 

170.3 

63 

419.6 

195.6 

23 

474.0 

221.0 

83 

528.  3 

246.4 

44 

311.7 

145.4 

04 

366.1 

170.7 

64 

420.5 

196.1 

24 

474.9 

221.4 

84 

529.3 

246.8 

45 

312.6 

145.8 

05 

367.0 

171.1 

66 

421.4 

196.5 

26 

475.8 

221.9 

85 

530.2 

247.2 

46 

313.5 

146.2 

06 

367.9 

171.6 

66 

422.3 

196.9 

26 

476.7 

222.3 

86 

531.1 

247.7 

47 

314.5 

146.6 

07 

368.8 

172.0 

67 

423.2 

197.3 

27 

477.6 

222.7 

87 

532.0 

248.1 

48 

315.4 

147.0 

08 

369.7 

172.4 

68 

424.1 

197.8 

28 

478.5 

223.2 

88 

532.9 

248.5 

49 

316.3 

147.5 

09 

370.6 

172.8 

69 

425.0 

198.2 

29 

479.4 

223.6 

89 

533.  8 

248.9 

50 

317.2 

147.9 

10 

371.5 

173.2 

70 

425.9 
426.8 

198.6 

30 

480.3 
481.2 

224.0 
224.  4 

90 
591 

534.7 
635.6 

249.4 
249.8 

351 

318.1 

148.3 

411 

372.5 

173.7 

471 

199.0 

631 

52 

319.0 

148.7 

12 

373.4 

174.1 

72 

427.7 

199.4 

32 

482.1 

224.8 

92 

636.5 

250.2 

53 

319.9 

149.2 

13 

374.3 

174.5 

73 

428.6 

199.9 

33 

483.0 

225.3 

93 

537.4 

260.6 

54 

320.8 

149.6 

14 

375.2 

174.9 

74 

429.6 

200.3 

34 

483.9 

226.7 

94 

538.3 

261.1 

55 

321.7 

150.0 

15 

376.1 

175.4 

75 

430.5 

200.7 

36 

484.8 

226.1 

96 

539.2 

251.5 

56 

322.6 

150.4 

16 

377.0 

175.8 

76 

431.4 

201.1 

36 

485.7 

226.5 

96 

540.1 

251.9 

57 

323.5 

150.8 

17 

377.9 

176.2 

77 

432.3 

201.6 

37 

486.7 

226.9 

97 

541.0 

262.3 

58 

324.4 

151.3 

18 

378.8 

176.6 

78 

433.2 

202.0 

38 

487.6 

227.4 

98 

541.9 

262.7 

59 

325.3 

151.7 

19 

379.7 

177.0 

79 

434.1 

202.4 

39 

488.6 

227.8 

99 

542.8 

263.1 

60 

326.2 

152.1 

20 

380.6 

177.5 

80 

435.0 

202.8 

40 

489.4 

228.2 

600 

543.8 

253.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

.. 

( 

55°  (1 

16°,  245 

°,  295° 

)• 

Page  682] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for 

26°  (154°,  206°,  334= 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Disl. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

54.8 

26.7 

121 

108.8 

53.0 

181 

162.7 

79.3 

241 

216.6 

105.6 

2 

1.8 

0.9 

62 

55.7 

27.2 

22 

109.7 

53.5 

82 

163.6 

79.8 

42 

217.5 

106.1 

3 

2.7 

1.3 

63 

56.6 

27.6 

23 

110.6 

53.9 

83 

164.5 

80.2 

43 

218.4 

106.5 

4 

3.6 

1.8 

64 

57.5 

28.1 

24 

111.5 

54.4 

84 

165.4 

80.7 

44 

219.3 

107.0 

5 

4.5 

2.2 

65 

58.4 

28.5 

25 

112.3 

54.8 

85 

166.3 

81.1 

45 

220.2 

107.4 

6 

f    5.4 

2.6 

66 

59.3 

28.9 

26 

113.2 

55.2 

86 

167.2 

81.5 

46 

221.1 

107.8 

7 

6.3 

3.1 

67 

60.2 

29.4 

27 

114.1 

55.7 

87 

168.1 

82.0 

47 

222.0 

108.  3 

8 

7.2 

3.5 

68 

61.1 

29.8 

28 

115.0 

56.1 

88 

169.0 

82.4 

48 

222.9 

108.7 

9 

8.1 

3.9 

69 

62.0 

30.2 

29 

115.9 

56.5 

89 

169.9 

82.9 

49 

223.8 

109.2 

10 
11 

9.0 
9.9 

4.4 

70 

62.9 

30.7 

30 

116.8 

57.0 

90 
191 

170.8 

83.3 

50 

224.7 

109.6 

4.8 

71 

63.8 

31.1 

131 

117.7 

57.4 

171.7 

83.7 

251 

225.6 

110.0 

12 

10.8 

5.3 

72 

64.7 

31.6 

32 

118.6 

57.9 

92 

172.6 

84.2 

52 

226.5 

110.5 

13 

11.7 

5.7 

73 

65.6 

32.0 

33 

119.5 

58.3 

93 

173.5 

84.6 

53 

227.4 

110.9 

14 

12.6 

6.1 

74 

66.5 

32.4 

34 

120.4 

58.7 

94 

174.4 

85.0 

54 

228.3 

111.3 

15 

13.5 

6.6 

75 

67.4 

32.9 

35 

121.3 

59.2 

95 

175.3 

85.5 

55 

229.2 

111.8 

16 

14.4 

7.0 

76 

68.3 

33.3 

36 

122.2 

59.6 

96 

176.2 

85.9 

56 

230.1 

112.2 

17 

15.3 

7.5 

77 

69.2 

33.8 

37 

123.1 

60.1 

97 

177.1 

86.4 

57 

231.  0 

112.7 

18 

16.2 

7.9 

78 

70.1 

34.2 

38 

124.0 

60.5 

98 

178.0 

86.8 

58 

231.9 

113.1 

19 

17.1 

8.3 

79 

71.0 

34.6 

39 

124.9 

60.9 

99 

178.9 

87.2 

59 

232.8 

113.5 

20 

18.0 

8.8 

80 

71.9 

35.1 

40 

125.8 

61.4 

200 

179.8 

87.7 

60 

233.7 

114.0 

21 

18.9 

9.2 

81 

72.8 

35.5 

141 

126.7 

61.8 

201 

180.7 

88.1 

261 

234.6 

114.4 

22 

19.8 

9.6 

82 

73.7 

35.9 

42 

127.6 

62.2 

02 

181.6 

88.6 

62 

235.5 

114.9 

23 

20.7 

10.1 

83 

74.6 

36.4 

43 

128.5 

62.7 

03 

182.5 

89.0 

63 

236.4 

115.3 

24 

21.6 

10.5 

84 

75.5 

36.8 

44 

129.4 

63.1 

04 

183.4 

89.4 

64 

237.3 

115.7 

25 

22.5 

11.0 

85 

76.4 

37.3 

45 

130.3 

63.6 

05 

184.3 

89.9 

65 

238.2 

116.2 

26 

23.4 

11.4 

86 

77.3 

37.7 

46 

131.2 

64.0 

06 

185.2 

90.3 

66 

239.1 

116.6 

27 

24.3 

11.8 

87 

78.2 

38.1 

47 

132.1 

64.4 

07 

186.1 

90.7 

67 

240.0 

117.0 

28 

25.2 

12.3 

88 

79.1 

38.6 

48 

133.0 

64.9 

08 

186.9 

91.2 

68 

240.9 

117.5 

29 

26.1 

12.7 

89 

80.0 

39.0 

49 

133.9 

65.3 

09 

187.  8 

91.6 

69 

241.8 

117.9 

30 

27.0 

13.2 

90 

80.9 

39.5 

50 

134.8 

65.8 

10 

188.7 

92.1 
92.5 

70 
271 

242.7 

118.4 

31 

27.9 

13.6 

91 

81.8 

39.9 

151 

135.7 

66.2 

211 

189.6 

243.6 

118.8 

32 

28.8 

14.0 

92 

82.7 

40.3 

52 

136.6 

66.6 

12 

190.5 

92.9 

72 

244.5 

119.2 

33 

29.7 

14.5 

93 

83.6 

40.8 

53 

137.5 

67.1 

13 

191.4 

93.4 

73 

245.4 

119.7 

34 

30.6 

14.9 

94 

84.5 

41.2 

54 

138.4 

67.5 

14 

192.3 

93.8 

74 

246.3 

120.1 

35 

31.5 

15.3 

95 

85.4 

41.6 

55 

139.3 

67.9 

15 

193.2 

94.2 

75 

247.2 

120.6 

36 

32.4 

15.8 

96 

86.3 

42.1 

56 

140.2 

68.4 

16 

194. 1. 

94.7 

76 

248.1 

121.0 

37 

33.3 

16.2 

97 

87.2 

42.5 

57 

141.1 

68.8 

17 

195.0 

95.1 

77 

249.0 

121.4 

38 

34.2 

16.7 

98 

88.1 

43.0 

58 

142.0 

69.3 

18 

195.9 

95.6 

78 

249.9 

121.9 

39 

35.1 

17.1 

99 

89.0 

43.4 

59 

142.9 

69.7 

19 

196.8 

96.0 

79 

250.8 

122.3 

40 

36.0 
36.9 

17.5 

100 

89.9 

43.8 
44.3 

60 
161 

143.8 

70.1 

20 

197.7 

96.4 

80 

251.7 

122.7 

41 

18.0 

101 

90.8 

144.7 

70.6 

221 

198.6 

96.9 

281 

252.6 

123.2 

42 

37.7 

18.4 

02 

91.7 

44.7 

62 

145.6 

71.0 

22 

199.5 

97.3 

82 

253.5 

123.6 

43 

38.6 

18.8 

03 

92.6 

45.2 

63 

146.5 

71.5 

23 

200.4 

97.8 

83 

254.4 

124.1 

44 

39.5 

19.3 

04 

93.5 

45.6 

64 

147.4 

71.9 

24 

201.3 

98.2 

84 

255.3 

124.5 

45 

40.4 

19.7 

05 

94.4 

46.0 

65 

148.3 

72.3 

25 

202.2 

98.6 

85 

256.2 

124.9 

46 

41.3 

20.2 

06 

95.3 

46.5 

66 

149.2 

72.8 

26 

203.1 

99.1 

86 

257.1 

125.4 

47 

42.2 

20.6 

07 

96.2 

46.9 

67 

150.1 

73.2 

27 

204.0 

99.5 

87 

258.0 

125.8 

48 

43.1 

21.0 

08 

97.1 

47.3 

68 

151.0 

73.6 

28 

204.9 

99.9 

88 

258.9 

126.3 

49 

44.0 

21.5 

09 

98.0 

47.8 

69 

151.9 

74.1 

29 

205.8 

100.4 

89 

259.8 

126.7 

50 
51 

44.9 

21.9 
22.4 

10 

98.9 

48.2 

70 

152.8 

74.5 

30 

206.7 

100.8 

90 

260.7 

127.1 

45.8 

111 

99.8 

48.7 

171 

153.7 

75.0 

231 

207.6 

101.3 

291 

261.5 

127.6 

52 

46.7 

22.8 

12 

100.7 

49.1 

72 

154.6 

75.4 

32 

208.5 

101.7 

92 

262.4 

128.0 

53 

47.6 

23.2 

13 

101.6 

49.5 

73 

155.5 

75.8 

33 

209.4 

102.1 

93 

263.3 

128.4 

54 

48.5 

23.7 

14 

102.5 

50.0 

74 

156.4 

76.3 

34 

210.3 

102.6 

94 

264.2 

128.9 

55 

49.4 

24.1 

15 

103.4 

50.4 

75 

157.3 

76.7 

35 

211.2 

103.0 

95 

265.1 

129.3 

56 

50.3 

24.5 

16 

104.3 

50.9 

76 

158.2 

77.2 

36 

212.1 

103.5 

96 

266.0 

129.8 

57 

51.2 

25.0 

17 

105.2 

51.3 

77 

159.1 

77.6 

37 

213.0 

103.9 

97 

266.9 

130.2 

58 

52.1 

25.4 

18 

106.1 

51.7 

78 

160.0 

78.0 

38 

213.9 

104.3 

98 

267.8 

130.6 

59 

53.0 

25.9 

19 

107.0 

52.2 

79 

160.9 

78.5 

39 

214.8 

104.8 

99 

268.7 

131.1 

60 

53.9 

26.3 

20 

107.9 

52.6 

80 

161.8 

78.9 

40 

215.7 

105.2 

300 

269.6 

131.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

34°  (1 

16°,  244 

°,  296° 

). 



TABLE  2. 

[Page  683 

Difference  of  Latitude  and  Departure  for  26°  (154°,  206°,  334).                                   1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

270.5 

132.0 

361 

324.  5 

158.  3 

421 

378.4 

184.6 

481 

432.3 

210.9 

541 

486.2 

237.2 

02 

271.4 

132.4 

62 

325.4 

158.7 

22 

379.3 

185.0 

82 

433.2 

211.3 

42 

487.1 

237.6 

03 

272.3 

132.8 

63 

326.3 

159.1 

23 

380.2 

185.4 

83 

434.1 

211.7 

43 

488.0 

238.0 

04 

273.2 

133.3 

64 

327.2 

159.6 

24 

381.1 

185.9 

84 

435.0 

212.2 

44 

488.9 

238.5 

05 

274.1 

133.7 

65 

328.1 

160.0 

25 

382.0 

186.3 

85 

435.9 

212.6 

45 

489.8 

238.9 

06 

275.0 

134.1 

66 

329.0 

160.4 

26 

382.9 

186.7 

86 

436.8 

213.0 

46 

490.7 

239.3 

07 

275.9 

134.6 

67 

329.9 

160.9 

27 

383.8 

187.2 

87 

437.7 

213.5 

47 

491.6 

239.8 

08 

276.8 

135.  0 

68 

330.8 

161.3 

28 

384.7 

187.6 

88 

438.6    213.9 

48 

492.5 

240.2 

09 

277.7 

135. 5 

69 

331.7 

161.8 

29 

385.6 

188.1 

89 

439.5    214.4 

49 

493.4 

240.7 

10 

278.6 

135. 9 
136.3 

70 

332.6 

162.  2 

30 
431 

386.5 
387.4 

188.5 

90 
491 

440. 4    214.  8 

50 

494.3 

241.1 
241.5 

311 

279.5 

371 

333.  5 

162.6 

188.9 

441.3 

215.2 

551 

495.2 

12 

280.4 

136.8 

72 

334.4 

163.1 

32 

388.3 

189.4 

92 

442.2 

215.7 

52 

496.1 

242.0 

13 

281.  3 

137.2 

73 

335.3 

163.5 

33 

389.2 

189.8 

93 

443.1 

216.1 

53 

497.0 

242.4 

14 

282.2 

137.7 

74 

336.2 

164.0 

34 

390.1 

190.3 

94 

444.0 

216.6 

54 

497.9 

242.9 

15 

283.1 

138.1 

75 

337.1 

164.4 

35 

391.0 

190.7 

95 

444.9 

217.0 

55 

498.8 

243.3 

16 

284.0 

138.5 

76 

338.0 

164.8 

36 

391.9 

191.1 

96 

445.8 

217.4 

56 

499.7 

243.7 

17 

284.9 

139.0 

77 

338.9 

165.3 

37 

392.8 

191.6 

97 

446.7 

217.9 

57 

500.6 

244.2 

18 

285.8 

139.4 

78 

339.8 

165.7 

38 

393.7 

192.0 

98 

447.6 

218.3 

58 

501.5 

244.6 

19 

286.7 

139.8 

79 

340.7 

166.2 

39 

394.6 

192.4 

99 

448.5 

218.7 

59 

502.4 

245.0 

20 

287.6 

288.5 

140.3 

80 
381 

341.5 
342.4 

166.6 
167.0 

40 

395.5 

192.9 

500 

449.4 

219.2 

60 
561 

503.3 
504.2 

245.5 

321 

140.7 

441 

396.4 

193.3 

501 

450.3 

219.6 

245.9 

22 

289.4 

141.2 

82 

343.3 

167.5 

42 

397.3 

193.8 

02 

451.2 

220.1 

62 

505.1 

246.4 

23 

290.3 

141.6 

83 

344.2 

167.9 

43 

398.2 

194.2 

03 

452.1 

220.5 

63 

506.0 

246.8 

24 

291.2 

142.0 

84 

345. 1 

168.3 

44 

399.1 

194.7 

04 

453.0 

221.0 

64 

506.9 

247.3 

25 

292.1 

142.5 

85 

346.0 

168.8 

45 

400.0 

195.1 

05 

453.9 

221.4 

66 

507.8 

247.7 

26 

293.0 

142.9 

86 

346.9 

169.2 

46 

400.9 

195.5 

06 

454.8 

221.8 

66 

508.7 

248.1 

27 

293.9 

143.4 

87 

347.8 

169.7 

47 

401.8 

196.0 

07 

455.7 

222.3 

67 

509.6 

248.6 

28 

294.8 

143.8 

88 

348.7 

170.1 

48 

402.7 

196.4 

08 

456.6 

222.7 

68 

510.5 

249.0 

29 

295.7 

144.2 

89 

349.6 

170.5 

49 

403.6 

196.8 

09 

457.5 

223.1 

69 

511.4 

249.4 

30 

296.6 

144.7 
145.1 

90 
391 

350.5 
351.4 

171.0 

50 

404.5 

197.3 
197. 7 

10 

458.4 

223.6 

70 

512.3 
513.2 

249.9 

331 

297.5 

171.4 

451 

405.4 

511 

459.3 

224.0 

571 

250.3 

32 

298.4 

145.6 

92 

352.3 

171.8 

52 

406.3 

198.1 

12 

460.2 

224.4 

72 

514.1 

250.8 

33 

299.3 

146.0 

93 

353.2 

172.3 

53 

407.2 

198.6 

13 

461.1 

224.9 

73 

515.0 

251.2 

34 

300.2 

146.4 

94 

354.1 

172.7 

54 

408.1 

199.0 

14 

462.0 

225.3 

74 

515.9 

251.6 

35 

301.1 

146.9 

95 

355.0 

173.2 

55 

409.0 

199.5 

15 

462.9 

225.8 

75 

516.8 

252.1 

36 

302.0 

147.3 

96 

355.9 

173.6 

56 

409.9 

199.9 

16 

463.8 

226.2 

76 

517.7 

252.5 

37 

302.9 

147.7 

97 

356.8 

174.0 

57 

410.8 

200.3 

17 

464.7 

226.6 

77 

518.6 

252.9 

38 

303.8 

148.2 

98 

357.7 

174.5 

58 

411.7 

200.8 

18 

465.6 

227.1 

78 

519.5 

253.4 

39 

304.7 

148.6 

99 

358.6 

174.9 

59 

412.6 

201.2 

19 

466.5 

227.5 

79 

520.4 

253.8 

4Q 

305.6 

149.0 

400 

359.5 

175.4 

60 

413.5 

201.7 

20 
521 

467.4 

228.0 

80 

521.3 

254.3 

341 

306.5 

149.5 

401 

360.4 

175.8 

461 

414.4 

202.1 

468.3 

228.4 

581 

522.2 

254.7 

42 

307.4 

149.9 

02 

361.3 

176.2 

62 

415.2 

202.5 

22 

469.2 

228.8 

82 

523.1 

255.1 

43 

308.3 

150.4 

03 

362.2 

176.7 

63 

416.1 

203.0 

23 

470.1 

229.3 

83 

524.0 

255.6 

44 

309.2 

150.8 

04 

363.1 

177.1 

64 

417.0 

203.4 

24 

471.0 

229.7 

84 

524.9 

256.0 

45 

310.1 

151.2 

05 

364.0 

177.5 

65 

417.9 

203.8 

25 

471.9 

230.1 

85 

525.8 

256.4 

46 

311.0 

151.7 

06 

364.9 

178.0 

66 

418.8 

204.3 

26 

472.8 

230.6 

86 

526.7 

256.9 

47 

311.9 

152.1 

07 

365.8 

178.4 

67 

419.7 

204.7 

27 

473.7 

231.0 

87 

527.6 

257.3 

48 

312.8 

152.6 

08 

366.7 

178.9 

68 

420.6 

205.2 

28 

474.6 

231.5 

88 

528.5 

257.8 

49 

313.7 

153.0 

09 

367.6 

179.3 

69 

421.5 

205.6 

29 

475.5 

231.9 

89 

529.4 

258.2 

50 

314.6 
315. 5 

153.4 

10 

368.5 

179.7 

70 
471 

422.4 

206.0 

30 

476.4 

232.3 

90 

530.3 

258.6 
259.1 

351 

153.9 

411 

369.4 

180.2 

423.3 

206.5 

531 

477.3 

232.8 

591 

531.2 

52 

316.4 

154.3 

12 

370.3 

180.6 

72 

424.2 

206.9 

32 

478.2 

233.2 

92 

532.1 

259.5 

53 

317.3 

154.7 

13 

371.2 

181.1 

73 

425.1 

207.3 

33 

479.1 

233.6 

93 

533.0 

259.9 

54 

318.2 

155.2 

14 

372.1 

181.5 

74 

426.0 

207.8 

34 

480.0 

234.1 

94 

533.9 

260.4 

55 

319.1 

155.6 

15 

373.0 

181.9 

75 

426.9 

208.2 

35 

480.9 

234.5 

95 

534.8 

260.8 

56 

320.0 

156.1 

16 

373.9 

182.4 

76 

427.8 

208.7 

36 

481.8 

235.0 

96 

535.7 

261.3 

57 

320.9 

156.5 

17 

374.8 

182.8 

77 

428.7 

209.1 

37 

482.7 

235.4 

97 

536.6 

261.7 

58 

321.8 

156.9 

18 

375.7 

183.2 

78 

429.6 

209.5 

38 

483.6 

235.8 

98 

537.5 

262.1 

59 

322.7 

157.4 

19 

376.6 

183.7 

79 

430.5 

210.0 

39 

484.5 

236.3 

90 

538.4 

262.6 

60 

323.6 

157.8 

20 

377.5 

184.1 

80 

431.4 

210.4 

40 

485.3 

236.7 

600 

539.3 

263.0 

DiBt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

64° 

(116°,  244°,  296°). 

Page  684] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  27°  (153°,  207 

°,  333° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

54.4 

27.7 

121 

107.8 

54.9 

181 

161.3 

82.2 

241 

214.7 

109.4 

2 

1.8 

0.9 

62 

55.2 

28.1 

22 

108.7 

55.4 

82 

162.2 

82.6 

42 

215.6 

109.9 

3 

2.7 

1.4 

63 

56.1 

28.6 

23 

109.6 

55.8 

83 

163.1 

83.1 

43 

216.5 

110.3 

4 

3.6 

1.8 

64 

57.0 

29.1 

24 

110.5 

56.3 

84 

163.9 

83.5 

44 

217.4 

110.8 

5 

4.5 

2.3 

65 

57.9 

29.5 

25 

111.4 

56.7 

85 

164.8 

84.0 

45 

218.3 

111.2 

6 

5.3 

2.7 

66 

58.8 

30.0 

26 

112.3 

57.2 

86 

165.7 

84.4 

46 

219.2 

111.7 

7 

6.2 

3.2 

67 

59.7 

30.4 

27 

113.2 

57.7 

87 

166.6 

84.9 

47 

220.1 

112.1 

8 

7.1 

3.6 

68 

60.6 

30.9 

28 

114.0 

58.1 

88 

167.5 

85.4 

48 

221.0 

112.6 

9 

8.0 

4.1 

69 

61.5 

31.3 

29 

114.9 

58.6 

89 

168.4 

85.8 

49 

221.9 

113.0 

10 

8.9 

4.5 

70 

62.4 

31.8 

30 

115.8 
116.7 

59.0 

90 

169.3 

86.3 

50 

222.8 

113.5 

11 

9.8 

5.0 

71 

63.3 

32.2 

131 

59.5 

191 

170.2 

86.7 

251 

223.6 

114.0 

12 

10.7 

5.4 

72 

64.2 

32.7 

32 

117.6 

59.9 

92 

171.1 

87.2 

52 

224.5 

114.4 

13 

11.6 

5.9 

73 

65.0 

33.1 

33 

118.5 

60.4 

93 

172.0 

87.6 

53 

225.4 

114.9 

14 

12.5 

6.4 

74 

65.9 

33.6 

34 

119.4 

60.8 

94 

172.9 

88.1 

54 

226.3 

115.3 

15 

13.4 

6.8 

75 

66.8 

34.0 

35 

120.3 

61.3 

95 

173.7 

88.5 

55 

227.2 

115.8 

16 

14.3 

7.3 

76 

67.7 

34.5 

36 

121.2 

61.7 

96 

174.6 

89.0 

56 

228.1 

116.2 

17 

15.1 

7.7 

77 

68.6 

35.0 

37 

122.1 

62.2 

97 

175.5 

89.4 

57 

229.0 

116.7 

18 

16.0 

8.2 

78 

69.5 

35.4 

38 

123.0 

62.7 

98 

176.4 

89.9 

58 

229.9 

117.1 

19 

16.9 

8.6 

79 

70.4 

35.9 

39 

123.8 

63.1 

99 

177.3 

90.3 

59 

230.8 

117.6 

20 

17.8 

9.1 

80 

71.3 

36.3 

40 

124.7 

63.6 

200 

178.2 

90.8 

60 

231.7 

118.0 

21 

18.7 

9.5 

81 

72.2 

36.8 

141 

125.6 

64.0 

201 

179.1 

91.3 

261 

232.6 

118.5 

22 

19.6 

10.0 

82 

73.1 

37.2 

42 

126.5 

64.5 

02 

180.0 

91.7 

62 

233.4 

118.9 

23 

20.5 

10.4 

83 

74.0 

37.7 

43 

127.4 

64.9 

03 

180.9 

92.2 

63 

234.3 

119.4 

24 

21.4 

10.9 

84 

74.8 

38.1 

44 

128.3 

65.4 

04 

181.8 

92.6 

64 

235.2 

119.9 

25 

22.3 

11.3 

85 

75.7 

38.6 

45 

129.2 

65.8 

05 

182.7 

93.1 

65 

236.1 

120.3 

26 

23.2 

11.8 

86 

76.6 

39.0 

46 

130.1 

66.3 

06 

183.5 

93.5 

66 

237.0 

120.8 

27 

24.1 

12.3 

87 

77.5 

39.5 

47 

131.0 

66.7 

07 

184.4 

94.0 

67 

237.9 

121.2 

28 

24.9 

12.7 

88 

78.4 

40.0 

48 

131.9 

67.2 

08 

185.3 

94.4 

68 

238.8 

121.7 

29 

25.8 

13.2 

89 

79.3 

40.4 

49 

132.8 

67.6 

09 

186.2 

94.9 

69 

239.7 

122.1 

30 

26.7 

13.6 

90 

80.2 

40.9 

50 

133.7 

68.1 

10 

187.1 

95.3 

70 

240.6 

122. 6 

31 

27.6 

14.1 

91 

81.1 

41.3 

151 

134.5 

68.6 

211 

188.0 

95.8 

271 

241.5 

123.0 

32 

28.5 

14.5 

92 

82.0 

41.8 

52 

135.4 

69.0 

12 

188.9 

96.2 

72 

242.4 

123.5 

33 

29.4 

15.0 

93 

82.9 

42.2 

53 

136.3 

69.5 

13 

189.8 

96.7 

73 

243.2 

123.9 

34 

30.3 

15.4 

94 

83.8 

42.7 

54 

137.2 

69.9 

14 

190.7 

97.2 

74 

244.1 

124.4 

35 

31.2 

15.9 

95 

84.6 

43.1 

55 

138.1 

70.4 

15 

191.6 

97.6 

75 

245.0 

124.8 

36 

32.1 

1G.3 

96 

85.5 

43.6 

56 

139.0 

70.8 

16 

192.5 

98.1 

76 

245.9 

125.3 

37 

33.0 

16.8 

97 

86.4 

44.0 

57 

139.9 

71.3 

17 

193.3 

98.5 

77 

246.8 

125.8 

38 

33.9 

17.3 

98 

87.3 

44.5 

58 

140.8 

71.7 

18 

194.2 

99.0 

78 

247.7 

126.2 

39 

34.7 

17.7 

99 

88.2 

44.9 

59 

141.7 

72.2 

19 

195.1 

99.4 

79 

248.6 

126.7 

40 

35.6 

18.2 

100 

89.1 

45.4 

60 

142.6 

72.6 

20 

196.0 

99.9 

80 

249.5 

127.1 

41 

36.5 

18.6 

101 

90.0 

45.9 

161 

143.5 

73.1 

221 

196.9 

100.3 

281 

250.4 

127.6 

42 

37.4 

19.1 

02 

90.9 

46.3 

62 

144.3 

73.5 

22 

197.8 

100.8 

82 

251.3 

128.0 

43 

38.3 

19.5 

03 

91.8 

46.8 

63 

145.2 

74.0 

23 

198.7 

101.2 

83 

252.2 

128.5 

44 

39.2 

20.0 

04 

92.7 

47.2 

64 

146.1 

74.5 

24 

199.6 

101.7 

84 

253.0 

128.9 

45 

40.1 

20.4 

05 

93.6 

47.7 

65 

147.0 

74.9 

25 

200.5 

102.1 

85 

253.9 

129.4 

46 

41.0 

20.9 

06 

94.4 

48.1 

66 

147.9 

75.4 

26 

201.4 

102.6 

86 

254.  8 

129.8 

47 

41.9 

21.3 

07 

95.3 

48.6 

67 

148.8 

75.8 

27 

202.3 

103.1 

87 

255.7 

130.3 

48 

42.8 

21.8 

08 

96.2 

49.0 

68 

149.7 

76.3 

28 

203.1 

103.5 

88 

256.6 

130.7 

49 

43.7 

22.2 

09 

97.1 

49.5 

69 

150.6 

76.7 

29 

204.0 

104.0 

89 

257.5 

131.2 

50 

44.6 

22.7 

10 

98.0 

49.9 

70 

151.5 

77.2 

30 

204.9 

104.4 

90 

258.4 

131.7 

51 

45.4 

23.2 

111 

98.9 

50.4 

171 

152.4 

77.6 

231 

205.8 

104.9 

291 

259.3 

132.1 

52 

46.3 

23.6 

12 

99.8 

50.8 

72 

153.3 

78.1 

32 

206.7 

105.3 

92 

260.2 

132.6 

53 

47.2 

24.1 

13 

100.7 

51.3 

73 

154.1 

78.5 

33 

207.6 

105.8 

93 

261. 1 

133.0 

54 

48.1 

24.5 

14 

101.6 

51.8 

74 

155.0 

79.0 

34 

208.5 

106.2 

94 

262.0 

133.5 

55 

49.0 

25.0 

15 

102.5 

52.2 

75 

155.9 

79.4 

35 

209.4 

106.7 

95 

262.8 

133.9 

56 

49.9 

25.4 

16 

103.4 

52.7 

76 

156.8 

79.9 

36 

210.3 

107.1 

96 

263.7 

134.4 

57 

50.8 

25.9 

17 

104.2 

53.1 

77 

157.7 

80.4 

37 

211.2 

107.6 

97 

264.6 

134.8 

58 

51.7 

26.3 

18 

105.1 

53.6 

78 

158.6 

80.8 

38 

212.1 

108.0 

98 

265.5 

135.3 

59 

52.6 

26.8 

19 

106.0 

54.0 

79 

159.5 

81.3 

39 

213.0 

108.5 

99 

266.4 

135.  7 

60 

53.5 

27.2 

20 

106.9 

54.5 

80 

160.4 

81.7 

40 

213.8 

109.0 

300 

267.  3 

136.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

63°  (117°,  243°,  297° 

). 

TABLE  2. 

[Page  585 

Difference  of  Latitude  and  Departure  for  27°  (153°,  207°,  333° 

). 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

268.2 

136.7 

361 

321.7 

163.9 

421 

375.1 

191.1 

481 

428.6 

218.3 

541 

482.0 

245.6 

02 

269.1 

137.1 

62 

322.5 

164.4 

22 

376.0 

191.6 

82 

429.4 

218.8 

42 

482.9 

246.1 

03 

270.0 

137.6 

63 

323.4 

164.8 

23 

376.9 

192.0 

83 

430.3 

219.2 

43 

483.8 

246.5 

04 

270.9 

138.0 

64 

324.3 

165.3 

24 

377.8 

192.5 

84 

431.2 

219.7 

44 

484.7 

247.0 

05 

271.8 

138.  5 

65 

325.2 

165.7 

25 

378.7 

193.0 

85 

432.1 

220.1 

45 

485.6 

247.4 

06 

272.7 

138.9 

66 

326.1 

166.2 

26 

379.6 

193.4 

86 

433.0 

220.6 

46 

486.4 

247.9 

07 

273.5 

139.4 

67 

327.0 

166.6 

27 

380.5 

193.9 

87 

433.9 

221.1 

47 

487.3 

248.4 

08 

274.4 

139.8 

68 

327.9 

167.1 

28 

381.4 

194.3 

88 

434.8 

221.5 

48 

488.2 

248.8 

09 

275.3 

140.3 

69 

328.8 

167.5 

29 

382.2 

194.8 

89 

435.7 

222.0 

49 

489.1 

249.2 

10 

276.2 

140.7 

70 

329.7 

168.0 

30 

383.1 

195.2 

90 

436.6 

222.4 

50 

490.0 

249.7 

311 

277.1 

141.2 

371 

330.6 

168.4 

431 

384.0 

195.7 

491 

437.5 

222.  9 

551 

490.9 

250.1 

12 

278.0 

141.7 

72 

331.5 

168.9 

32 

384.9 

196.1 

92 

438.3 

223.3 

52 

491.8 

250.6 

13 

278.9 

142.1 

73 

332.3 

169.3 

33 

385.8 

196.6 

93 

439.2 

223.8 

53 

492.7 

251.0 

14 

279.8 

142.6 

74 

333.  2 

169.8 

34 

386.7 

197.0 

94 

440.1 

224.2 

54 

493.6 

251.5 

15 

280.7 

143.0 

75 

334.1 

170.3 

35 

387.6 

197.5 

95 

441.0 

224.7 

55 

494.5 

252.0 

16 

281.6 

143.  5 

76 

335.0 

170.7 

36 

388.5 

197.9 

96 

441.9 

225.2 

56 

495.4 

252.4 

17 

282.5 

143.9 

77 

335.9 

171.2 

37 

389.4 

198.4 

97 

442.8 

225.6 

57 

496.3 

252.9 

18 

283.  3 

144.4 

78 

336.8 

171.6 

38 

390.3 

198.9 

98 

443.7 

226.1 

58 

497.2 

253.  3 

19 

284.2 

144.8 

79 

337.7 

172.1 

39 

391.2 

199.3 

99 

444.6 

226.5 

59 

498.1 

253.8 

20 

285.1 

145.3 

80 

338.6 

172.5 

40 

392.0 

199.8 

500 

445.5 

227.0 

60 

499.0 

254.2 

321 

286.0 

145.7 

381 

339.5 

173.0 

441 

392.9 

200.2 

501 

446.4 

227.5 

561 

499.8 

254.7 

22 

286.9 

146.2 

82 

340.4 

173.4 

42 

393.8 

200.7 

02 

447.3 

227.9 

62 

500.7 

255.1 

23 

287.8 

146.6 

83 

341.3 

173.9 

43 

394.7 

201.1 

03 

448.2 

228.4 

63 

501.6 

255.6 

24 

288.7 

147.1 

84 

342.1 

174.3 

44 

395.6 

201.6 

04 

449.0 

228.8 

64 

502.5 

256.0 

25 

289.6 

147.6 

85 

343.0 

174.8 

45 

396.5 

202.0 

05 

449.9 

229.3 

65 

503.4 

256.5 

26 

290.5 

148.0 

86 

343.9 

175.2 

46 

397.4 

202.5 

06 

450.8 

229.8 

66 

504.3 

257.0 

27 

291.4 

148.5 

87 

344.8 

175.7 

47 

398.3 

202.9 

07 

451.7 

230.2 

67 

505.2 

257.4 

28 

292.3 

148.9 

88 

345.7 

176.2 

48 

399.2 

203.4 

08 

452.6 

230.6 

68 

506.1 

257.9 

29 

293.2 

149.4 

89 

346.6 

176.6 

49 

400.1 

203.8 

09 

453.5 

231.0 

69 

507.0 

258. 3 

30 

294.0 
294.9 

149.8 

90 

347. 5 

177.1 
177. 5 

50 

401.0 

204.3 

10 

454.4 

231.5 

70 
571 

507.9 
508.7 

258.  8 

259.  2 

331 

150. 3 

391 

348.4 

451 

401.8 

204.7 

511 

455.3 

231.9 

32 

295.8 

150.7 

92 

349.3 

178.0 

52 

402.7 

205.2 

12 

456.2 

232.4 

72 

509.6 

259.  7 

33 

296.7 

151.2 

93 

350.2 

178.4 

53 

403.6 

205.7 

13 

457.1 

232.9 

73 

510.5 

260.1 

34 

297.6 

151.6 

94 

351.1 

178.9 

54 

404.5 

206.1 

14 

458.0 

233.3 

74 

511.4 

260.6 

35 

298.5 

152.1 

95 

352.0 

179.3 

55 

405.4 

206.6 

15 

458.  8 

233.8 

75 

512.3 

261.1 

36 

299.4 

152. 5 

96 

352.8 

179.8 

56 

406.3 

207.0 

16 

459.7 

234.2 

76 

513.2 

261.5 

37 

300.3 

153.0 

97 

353.7 

180.2 

57 

407.2 

207.5 

17 

460.6 

234.7 

77 

514.1 

262.0 

38 

301.2 

153.5 

98 

354.6 

180.7 

58 

408.1 

207.9 

18 

461.5 

235.2 

78 

515.0 

262.4 

39 

302.1 

153.9 

99 

355.5 

181.2 

59 

409.0 

208.4 

19 

462.4 

235.7 

79 

515.9 

262.9 

40 

302.9 

154.4 

400 
401 

356.4 
357.3 

181.6 

60 

409.9 

208.8 
209. 3~ 

20 
521 

463.3 
464.  2 

236.1 

80 

516.8 

263.4 

341 

303.8 

154.8 

182.1 

461 

410.8 

236.6 

581 

517.7 

263.8 

42 

304.7 

155.3 

02 

358.2 

182.5 

62 

411.6 

209.8 

22 

465.1 

237.0 

82 

518.5 

264.3 

43 

305.6 

155.7 

03 

359.1 

183.0 

63 

412.5 

210.2 

23 

466.0 

237.5 

83 

519.4 

264.7 

44 

306.5 

156.2 

04 

360.0 

183.4 

64 

413.4 

210.7 

24 

466.9 

237.9 

84 

520.3 

265.2 

45 

307.4 

156.6 

05 

360.9 

183.9 

65 

414.3 

211.1 

25 

467.8 

238.4 

85 

521.2 

265.6 

46 

308.3 

157.1 

06 

361.8 

184.3 

66 

415.2 

211.6 

26 

468.7 

238.8 

86 

522. 1  1  266. 0  1 

47 

309.2 

157.5 

07 

362.6 

184.8 

67 

416.1 

212.0 

27 

469.5 

239.3 

87 

523.0 

266.5 

48 

310.1 

158.0 

08 

363.5 

185.2 

68 

417.0 

212.5 

28 

470.4 

239.7 

88 

523.9 

267.0 

49 

311.0 

158.5 

09 

364.4 

185.  7 

69 

417.9 

212.9 

29 

471.3 

240.2 

89 

524.8 

267.4 

50 

311.9 

158.9 

10 

365. 3 

186.1 

70 

418.8 

213.4 

30 

472.2 

240.6 

90 

525.  7 

267.9 

351 

312.7 

159.4 

411 

366.2 

186.6 

471 

419.7 

213.8 

531 

473.1 

241.1 

591 

526.6 

268.3 

52 

313.6 

159.8 

12 

367.1 

187.1 

72 

420.6 

214.3 

32 

474.0 

241.5 

92 

527.5 

268.8 

53 

314.5 

160.3 

13 

368.0 

187.5 

73 

421.4 

214.7 

33 

474.9 

242.0 

93 

528.4 

269.2 

54 

315.4 

160.7 

14 

368.9 

188.0 

74 

422.3 

215.2 

34 

475.8 

242.4 

94 

529.3 

269.7 

55 

316.3 

161.2 

15 

369.8 

188.4 

75 

423.2 

215.7 

35 

476.7 

242.9 

95 

530.1 

270.1 

56 

317.2 

161.6 

16 

370.7 

188.9 

76 

424.1 

216.1 

36 

477.6 

243.4 

96 

531.0 

270.6 

57 

318.1 

162. '1 

17 

371.6 

189.3 

77 

425.0 

216.6 

37 

478.4 

243.8 

97 

531.9 

271.1 

58 

319.0 

162.5 

18 

372.4 

189.8 

78 

425.9 

217.0 

38 

479.3 

244.3 

98 

532.8 

271.5 

59 

319.9 

163.0 

19 

373.3 

190.2 

79 

426.8 

217.5 

39 

480.2 

244.7 

99 

533.7 

272.0 

60 

320.8 

163.4 

20 

374.2 

190.7 

80 

427.7 

217.9 

40 

481.1 

245,2 

600 

534.6 

272.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

63°  (1 

17°,  243°,  297° 

). 

1 

Page  586] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  28°  (152°,  208 

°,  332° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

53.9 

28.6 

121 

106.8 

56.8 

181 

159.8 

85.0 

241 

212.8 

113.1 

2 

1.8 

0.9 

62 

54.7 

29.1 

22 

107.7 

57.3 

82 

160.7 

85.4 

42 

213.7 

113.6 

3 

2.6 

1.4 

63 

55.6 

29.6 

23 

108.6 

57.7 

83 

161.6 

85.9 

43 

214.6 

114.1 

.    4 

3.5 

1.9 

64 

56.5 

30.0 

24 

109.5 

58.2 

84 

162.5 

86.4 

44 

215.4 

114.6 

5 

4.4 

2.3 

65 

67.4 

30.5 

25 

110.4 

58.7 

85 

163.3 

86.9 

45 

216.3 

115.0 

6 

5.3 

2.8 

66 

58.3 

31.0 

26 

111.3 

59.2 

86 

164.2 

87.3 

46 

217.2 

115.5 

7 

6.2 

3.3 

67 

59.2 

31.5 

27 

112.1 

59.6 

87 

165.1 

87.8 

47 

218.1 

116.0 

8 

7.1 

3.8 

68 

60.0 

31.9 

28 

113.0 

60.1 

88 

166.0 

88.3 

48 

219.0 

116.4 

9 

7.9 

4.2 

69 

60.9 

32.4 

29 

113.9 

60.6 

89 

166.9 

88.7 

49 

219.9 

116.9 

10 

8.8 

4.7 

70 

61.8 

32.9 

30 

114.8 

61.0 

90 

167.8 

89.2 

50 

220.7 

117.4 

11 

9.7 

5.2 

71 

62.7 

33.3 

131 

115.7 

61.5 

191 

168.6 

89.7 

251 

221.  6 

117.8 

12 

10.6 

5.6 

72 

63.6 

33.8 

32 

116.5 

62.0 

92 

169.5 

90.1 

52 

222.5 

118.3 

13 

11.5 

6.1 

73 

64.5 

34.3 

33 

117.4 

62.4 

93 

170.4 

90.6 

53 

223.4 

118.8 

14 

12.4 

6.6 

74 

65.3 

34.7 

34 

118.3 

62.9 

94 

171.3 

91.1 

54 

224.3 

119.2 

15 

13.2 

7.0 

75 

66.2 

35.2 

35 

119.2 

63.4 

95 

172.2 

91.5 

55 

225.2 

119.7 

16 

14.1 

7.5 

76 

67.1 

35.7 

36 

120.1 

63.8 

96 

173.1 

92.0 

56 

226.0 

120.2 

17 

15.0 

8.0 

77 

68.0 

36.1 

37 

121.0 

64.3 

97 

173.9 

92.5 

57 

226.9 

120.7 

18 

15.9 

8.5 

78 

68.9 

36.6 

38 

121.8 

64.8 

98 

174.8 

93.0 

58 

227.8 

121.1 

19 

16.8 

8.9 

79 

69.8 

37.1 

39 

122.7 

65.3 

99 

175.7 

93.4 

59 

228.7 

121.6 

20 

17.7 

9.4 

80 

70.6 

37.6 

40 

123.6 

65.7 

200 

176.6 

93.9 

60 

229.6 

122.1 
122.5 

21 

18.5 

9.9 

81 

71.5 

38.0 

141 

124.5 

66.2 

201 

177.5 

94.4 

261 

230.4 

22 

19.4 

10.3 

82 

72.4 

38.5 

42 

125.4 

66.7 

02 

178.4 

94.8 

62 

231.3 

123.0 

23 

20.3 

10.8 

83 

73.3 

39.0 

43 

126.3 

67.1 

03 

179.2 

95.3 

63 

232.2 

123.5 

24 

21.2 

11.3 

84 

74.2 

39.4 

44 

127.1 

67.6 

04 

180.1 

95.8 

64 

233.1 

123.9 

25 

22.1 

11.7 

85 

75.1 

39.9 

45 

128.0 

68.1 

05 

181.0 

96.2 

65 

234. 0 

124.4 

26 

23.0 

12.2 

86 

75.9 

40.4 

46 

128.9 

68.5 

06 

181.9 

96.7 

66 

234.9 

124.9 

27 

23.8 

12.7 

87 

76.8 

40.8 

47 

129.8 

69.0 

07 

182.8 

97.2 

67 

235.7 

125.3 

28 

24.7 

13.1 

88 

77.7 

41.3 

48 

130.7 

69.5 

08 

183.7 

97.7 

68 

236.6 

125.8 

29 

25.6 

13.6 

89 

78.6 

41.8 

49 

131.6 

70.0 

09 

184.5 

98.1 

69 

237.5 

126.3 

30 

26.5 

14.1 

90 

79.5 

42.3 

'42.7 

50 

132.4 

70.4 

10 

185.4 

98.6 

70 

238.4 
239.3 

126.8 

31 

27.4 

14.6 

91 

80.3 

151 

133.3 

70.9 

211 

186.3 

99.1 

271 

127.2 

32 

28.3 

15.0 

92 

81.2 

43.2 

52 

134.2 

71.4 

12 

187.2 

99.5 

72 

240.2 

127.7 

33 

29.1 

15.5 

93 

82.1 

43.7 

53 

135.1 

71.8 

13 

188.1 

100.0 

73 

241.0 

128.2 

34 

30.0 

16.0 

94 

83.0 

44.1 

54 

136.0 

72.3 

14 

189.0 

100.5 

74 

241.9 

128.6 

35 

30.9 

16.4 

95 

83.9 

44.6 

55 

136.9 

72.8 

15 

189.8 

100.9 

75 

242.8 

129.1 

36 

31.8 

16.9 

96 

84.8 

45.1 

56 

137.7 

73.2 

16 

190.7 

101.4 

76 

243.7 

129.6 

37 

32.7 

17.4 

97 

85.6 

45.5 

57 

138.6 

73.7 

17 

191.6 

101.9 

77 

244.6 

130.0 

38 

33.6 

17.8 

98 

86.5 

46.0 

58 

139.5 

74.2 

18 

192.5 

102.3 

78 

245.5 

130.5 

39 

34.4 

18.3 

99 

87.4 

46.5 

59 

140.4 

74.6 

19 

193.*  4 

102.8 

79 

246.3 

131.0 

40 

35.3 

18.8 

100 

88.3 

46.9 

60 

141.3 

75.1 

20 

194.2 

103.3 
"103. 8 

80 

247.2 
248. 1 

131.5 

41 

36.2 

19.2 

101 

89.2 

47.4 

161 

142.2 

75.6 

221 

195.1 

281 

131.9 

42 

37.1 

19.7 

02 

90.1 

47.9 

62 

143.0 

76.1 

22 

196.0 

104.2 

82 

249.0 

132.4 

43 

38.0 

20.2 

03 

90.9 

48.4 

63 

143.9 

76.5 

23 

196.9 

104.7 

83 

249.9 

132.9 

44 

38.8 

20.7 

04 

91.8 

48.8 

64 

144.8 

77.0 

24 

197.8 

105.2 

84 

250.8 

133.3 

45 

39.7 

21.1 

05 

92.7 

49.3 

65 

145,  7 

77.5 

25 

198.7 

105.6 

85 

251.6 

133.8 

46 

40.6 

21.6 

06 

93.6 

49.8 

66 

146.6 

77.9 

26 

199.5 

106.1 

86 

252.5 

134.3 

47 

41.5 

22.1 

07 

94.5 

50.2 

67 

147.5 

78.4 

27 

200.4 

106.6 

87 

253.4 

134.7 

48 

42.4 

22.5 

08 

95.4 

50.7 

68 

148.3 

78.9 

28 

201.3 

107.0 

88 

254.3 

135.2 

49 

43.3 

23.0 

09 

96.2 

51.2 

69 

149.2 

79.3 

29 

202.2 

107.5 

89 

255.2 

135.7 

50 

44.1 

23.5 

10 

97.1 

51.6 

70 

150.1 

79.8 

30 

203.1 
204.0 

108.0 
108.4 

90 

256.1 

136.1 

51 

45.0 

23.9 

111 

98.0 

52.1 

171 

151.0 

80.3 

231 

291 

256.9 

136.6 

52 

45.9 

24.4 

12 

98.9 

52.6 

72 

151.9 

80.7 

32 

204.8 

108.9 

92 

257.8 

137.1 

53 

46.8 

24.9 

13 

99.8 

53.1 

73 

152.7 

81.2 

33 

205.7 

109.4 

93 

258.7 

137.6 

54 

47.7 

25.4 

14 

100.7 

53.5 

74 

153.6 

81.7 

34 

206.6 

109.9 

94 

259.6 

138.0 

55 

48.6 

25.8 

15 

101.5 

54.0 

75 

154.5 

82.2 

35 

207.5 

110.3 

95 

260.5 

138.5 

56 

49.4 

26.3 

16 

102.4 

54.5 

76 

155.4 

82.6 

36 

208.4 

110.8 

96 

261.4 

139.0 

57 

50.3 

26.8 

17 

103.3 

54.9 

77 

156.3 

83.1 

37 

209.3 

111.3 

97 

262.2 

139.4 

58 

51.2 

27.2 

18 

104.2 

55.4 

78 

157.2 

83.6 

38 

210.1 

111.7 

98 

263.1 

139.9 

59 

52.1 

27.7 

19 

105.1 

55.9 

79 

158.0 

84.0 

39 

211.0 

112.2 

99 

264.0 

140.4 

60 

53.0 

28.2 

20 

106.0 

56.3 

80 

158.9 

84.5 

40 

211.9 

112.7 

300 

264.9 

140.8 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

62°  (1 

18°,  242 

°,  298°). 

, 

TABLE  2. 

[Page  687 

Dist. 

Difference  of  Latitude  and  Departure  for  28°  (152°,  208°,  332' 

). 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

265.7 

141.3 

361 

318.7 

169.5 

421 

371.7 

197.7 

481 

424.7 

225.8 

541 

477,7 

254.0 

02 

266.6 

141.8 

62 

319.6 

170.0 

22 

372.6 

198.1 

82 

425.6 

226.  3 

42 

478.6 

254.5 

03 

267.5 

142.3 

63 

320.5 

170.4 

23 

373.5 

198.6 

83 

426.5 

226,8 

43 

479.4 

255.0 

04 

268.4 

142.7 

64 

321.4 

170.9 

24 

374.3 

199.1 

84 

427.4 

227.3 

44 

480.3 

255.5 

05 

269.3 

143.2 

65 

322.2 

171.4 

25 

375.2 

199.5 

85 

428.3 

227.7 

45 

481.1 

255.9 

06 

270.2 

143.7 

66 

323.1 

171.8 

26 

376.1 

200.0 

86 

429.2 

228.2 

46 

482.0 

256.4 

07 

271.0 

144.1 

67 

324.0 

172.3 

27 

377.0 

200.5 

87 

430.1 

228,6 

47 

482.9 

256.9 

08 

271.9 

144.6 

68 

324.9 

172.8 

28 

377.9 

200.9 

88 

430.9 

229.1 

48 

483.8 

257.  3 

09 

272.8 

145.1 

69 

325.8 

173.2 

29 

378.8 

201.4 

89 

431.8 

229.6 

49 

484.7 

257.8 

10 

273.7 
274.6 

145.5 

70 
371 

326.7 

173.7 

30 

379.6 

201.9 

90 

432.6 

230.0 

50 

485.6 

258.2 

311 

146.0 

327.5 

174.2 

431 

380.5 

202.3 

491 

433.5 

230.5 

551 

486.5 

258.7 

12 

275.5 

146.5 

72 

328.4 

174.6 

32 

381.4 

202.8 

92 

434.4 

231.0 

52 

487.4 

259.1 

13 

276.3 

146.9 

73 

329.3 

175.1 

33 

382.3 

203.3 

93 

435.3 

231.4 

53 

488.3 

259.6 

14 

277.2 

147.4 

74 

330.2 

175.6 

34 

383.2 

203.8 

94 

436.2 

231.9 

54 

489.2 

260.1 

15 

278.1 

147.9 

75 

331.1 

176.1 

35 

384.1 

204.2 

95 

437.1 

232.4 

55 

490.1 

260.6 

16, 

279.0 

148.4 

76 

332.0 

176.5 

36 

384.9 

204.7 

96 

437.9 

232.9 

56 

490.9 

261.0 

17 

279.9 

148.8 

77 

332.8 

177.0 

37 

385.8 

205.2 

97 

438.8 

233.4 

57 

491.8 

261.5 

18 

280.7 

149.3 

78 

333.7 

177.5 

38 

386.7 

205.6 

98 

439.7 

233.8 

58 

492.7 

262.0 

19 

281.6 

149.  8 

79 

334.6 

177.9 

39 

387.6 

206.1 

99 

440.6 

234.3 

59 

493.5 

262.6 

20 

282.5 

150.2 

80 

335.5 

178.4 

40 

388.5 

206.6 

500 

441.5 

234.  7 
235. 2 

60 

494,4 

262.9 

321 

283.4 

150.7 

381 

336.4 

178.9 

441 

389.4 

207.0 

501 

442.3 

561 

495,3 

263.4 

22 

284.3 

151.2 

82 

337.3 

179.3 

42 

390.2 

207.5 

02 

443.2 

235.6 

62 

496.  2  !  263.  8  1 

23 

285.2 

151.6 

83 

338.1 

179.8 

43 

391.1 

208.0 

03 

444.1 

236.1 

63 

497. 1  !  264.  3  1 

24 

286.0 

152.1 

84 

339. 0 

180.3 

44 

392.0 

208.4 

04 

445.0 

236.6 

64 

498.0 

264.7 

25 

286.9 

152.6 

85 

339.9 

180.8 

45 

392.9 

208.9 

05 

445.9 

237.1 

65 

498.9 

265,2 

26 

287.8 

153.1 

86 

340.8 

181.2 

46 

393.8 

209.4 

06 

446.8 

237. 5 

66 

499.8 

265,7 

27 

288.7 

153.5 

87 

341.7 

181.7 

47 

394.6 

209.9 

07 

447.6 

238.0 

67 

500.7 

266.2 

28 

289.6 

154.0 

88 

342.6 

182.2 

48 

395.5 

210.3 

08 

448.5 

238.5 

68 

501.6 

266.6 

29 

290.5 

154. 5 

89 

343.4 

182.6 

49 

396.4 

210.8 

09 

449.4 

239.0 

69 

502.4 

267. 1 

30 

291.3 
292.2 

154.9 
155.4 

90 
391 

344.3 
345.2 

183.1 

50 

397.3 

211.3 

10 

450.3 

239.4 

70 

503.3 
504.2 

267.6 
268.0 

331 

183.6 

451 

398.2 

211.7 

511 

451.2 

239.9 

571 

32 

293.1 

155.9 

92 

346.1 

184.0 

52 

399.1 

212,2 

12 

452.1 

240.4 

72 

505.1 

268.5 

33 

294.0 

156.3 

93 

347.0 

184.5 

53 

399.9 

212.7 

13 

452.9 

240.8 

73 

505.9 

269.0 

34 

294.9 

156.8 

94 

347.9 

185.0 

54 

400.8 

213.1 

14 

453.8 

241,3 

74 

506.8 

269.4 

35 

295.8 

157.3 

95 

348.7 

185.4 

55 

401.7 

213.6 

15 

454.7 

241.8 

75 

507.7 

269.9 

36 

296.6 

157.7 

96 

349.6 

185.9 

56 

402.6 

214.1 

16 

455.6 

242.2 

76 

508.6 

270. 4 

37 

297.5 

158.2 

97 

350.5 

186.4 

57 

403.5 

214.6 

17 

456.4 

242.7 

77 

509.4 

270.9 

38 

298.4 

158.7 

98 

351.4 

186.9 

58 

404.4 

215.0 

18 

457.3 

243.2 

78 

510.3 

271.3 

39 

299.3 

159.2 

99 

352.3 

187.3 

59 

405.2 

215.5 

19 

458.2 

243.7 

79 

511.2 

271.8 

40 

300.2 

159.6 

400 

353.1 

187.8 

60 

406.1 

216.0 

20 

459.1 

244.1 

80 

512.1 
513.0 

272.3 

341 

301.0 

160.1 

401 

354.0 

188.3 

461 

407.0 

216.4 

521 

460.0 

244.6 

581 

272,7 

42 

301.9 

160.6 

02 

354.9 

188.7 

62 

407.9 

216.9 

22 

460.9 

245. 0 

82 

513.9 

273,2 

43 

302.8 

161.0 

03 

355.8 

189.2 

63 

408.8 

217.4 

23 

461.8 

245.5 

83 

514.8 

273.7 

44 

303.7 

161.5 

04 

356.7 

189.7 

64 

409.7 

217.8 

24 

462.7 

246.0 

84 

515.7 

274.2 

45 

304.6 

162.0 

05 

357.6 

190.1 

65 

410.5 

218.3 

25 

463.5 

246.5 

85 

516,5 

274.7 

46 

305.5 

162.4 

06 

358.4 

190.6 

66 

411.4 

218.8 

26 

464.4 

246.9 

86 

517.4 

275.1 

47 

306.4 

162.9 

07 

359.3 

191.1 

67 

412.3 

219.2 

27 

465.3 

247,4 

87 

518.3 

276.5 

48 

307.2 

163.4 

08 

360.2 

191.5 

68 

413.2 

219.7 

28 

466.2 

247.9 

88 

519,2 

276.0 

49 

308.1 

163.8 

09 

361.1 

192.0 

69 

414.1 

220.2 

29 

467.1 

248.3 

89 

520.1 

276.5 

50 

309.0 

164.3 

10 

362.0 

192.5 

70 

415.0 

220.7 

30 

468.0 

248.8 

90 

521.0 

277.0 

361 

309.9 

164.8 

411 

362.9 

193.0 

471 

415.8 

221.1 

531 

468.9 

249.3 

591 

521.8 

277.4 

52 

310.8 

165.3 

12 

363.7 

193.4 

72 

416.7 

221.6 

32 

469.8 

249.8 

92 

522.6 

277.9 

58 

311.7 

165.7 

13 

364.6 

193.9 

73 

417.6 

222.1 

33 

470.7 

250.2 

93 

523.6 

278.4 

54 

312.5 

166.2 

14 

365.5 

194.4 

74 

418.5 

222.5 

34 

471.5 

250.7 

94 

524,4 

278.8 

55 

313.4 

166.7 

15 

366.4 

194.8 

75 

419.4 

223.0 

35 

472.4 

251.1 

95 

625.3 

279.3 

56 

314.3 

167.1 

16 

367.3 

195.3 

76 

420.3 

223.5 

36 

473.3 

251.6 

96 

626.2 

279.8 

57 

315.2 

167.6 

17 

368.2 

195.8 

77 

421.1 

223,9 

37 

474.2 

252.1 

97 

527.1 

280.3 

58 

316.1 

168.1 

18 

369.0 

196.2 

78 

422.0 

224,4 

38 

475.1 

252.6 

98 

528.0 

280.8 

59 

316.9 

168.5 

19 

369.9 

196.7 

79 

422.9 

224.9 

39 

476.0 

253.1 

99 

528.9 

281.3 

60 

317.8 

169.0 

20 

370.8 

197.2 

80 

423.8 

225,3 

40 

476.8 

253.6 

600 

529.8 

281.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

Dist, 

Dep. 

Lat. 

Dist. 

Dep, 

Lat. 

( 

32°  (1 

18°,  242°,  298° 

). 

Page  588] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  29°  ( 

151°,  209°,  331 

n- 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

53.4 

29.6 

121 

105.8 

58.7 

181 

158.3 

87.8 

241 

210.8 

116.8 

2 

1.7 

1.0 

62 

54.2 

30.1 

22 

106.7 

59.1 

82 

159.2 

88.2 

42 

211.7 

117.3 

3 

2.6 

1.5 

63 

55.1 

30.5 

23 

107.6 

59.6 

83 

160.1 

88.7 

43 

212.5 

117.8 

4 

3.5 

1.9 

64 

56.0 

31.0 

24 

108.5 

60.1 

84 

160.9 

89.2 

44 

213.4 

118.3 

5 

4.4 

2.4 

65 

56.9 

31.5 

25 

109.3 

60.6 

85 

161.8 

89.7 

45 

214.3 

118.8 

6 

5.2 

2.9 

66 

57.7 

32.0 

26 

110.2 

61.1 

86 

162.7 

90.2 

46 

215.2 

119.3 

7 

6.1 

3.4 

67 

58.6 

32.5 

27 

111.1 

61.6 

87 

163.6 

90.7 

47 

216.0 

119.7 

8 

7.0 

3.9 

68 

59.5 

33.0 

28 

112.0 

62.1 

88 

164.4 

91.1 

48 

216.9 

120.2 

9 

7.9 

4.4 

69 

60.3 

33.5 

29 

112.8 

62.5 

89 

165.3 

91.6 

49 

217.8 

120.7 

10 

8.7 

4.8 

70 

61.2 

33.9 

30 

113.7 

63.0 

90 

166.2 

92.1 

50 

218.7 
219.5 

121.2 

11 

9.6 

5.3 

71 

62.1 

34.4 

131 

114.6 

63.5 

191 

167.1 

92.6 

251 

121.7 

12 

10.5 

5.8 

72 

63.0 

34.9 

32 

115.4 

64.0 

92 

167.9 

93.1 

52 

220.4 

122.2 

13 

11.4 

6.3 

73 

63.8 

35.4 

33 

116.3 

64.5 

93 

168.8 

93.6 

53 

221.3 

122.7 

14 

12.2 

6.8 

74 

64.7 

35.9 

34 

117.2 

65.0 

94 

169.7 

94.1 

54 

222.2 

123.1 

15 

13.1 

7.3 

75 

65.6 

36.4 

35 

118.1 

65.4 

95 

170.6 

94.5 

55 

223.0 

123.6 

16 

14.0 

7.8 

76 

66.5 

36.8 

36 

118.9 

65.9 

96 

171.4 

95.0 

56 

223.9 

124.1 

17 

14.9 

8.2 

77 

67.3 

37.3 

37 

119.8 

66.4 

97 

172.3 

95.5 

67 

224.8 

124.6 

18 

15.7 

8.7 

78 

68.2 

37.8 

38 

120.7 

66.9 

98 

173.2 

96.0 

58 

225.7 

125.1 

19 

16.6 

9.2 

79 

69.1 

38.3 

39 

121.6 

67.4 

99 

174.0 

96.5 

59 

226.5 

125.6 

20 

17.5 

9.7 

80 

70.0 

38.8 

40 

122.4 

67.9 

200 

174.9 

97.0 

60 

227.4 

126.1 

21 

18.4 

10.2 

81 

70.8 

39.3 

141 

123.3 

68.4 

201 

175.8 

97.4 

261 

228.3 

126.5 

22 

19.2 

10.7 

82 

71.7 

39.8 

42 

124.2 

68.8 

02 

176.7 

97.9 

62 

229.2 

127.0 

23 

20.1 

11.2 

83 

72.6 

40.2 

43 

125.1 

69.3 

03 

177.5 

98.4 

63 

230.0 

127.5 

24 

21.0 

11.6 

84 

73.5 

40.7 

44 

125.9 

69.8 

04 

178.4 

98.9 

64 

230.9 

128.0 

25 

21.9 

12.1 

85 

74.3 

41.2 

45 

126.8 

70.3 

05 

179.3 

99.4 

65 

231.8 

128.5 

26 

22.7 

12.6 

86 

75.2 

41.7 

46 

127.7 

70.8 

06 

180.2 

99.9 

66 

232.6 

129.0 

27 

23.6 

13.1 

87 

76.1 

42.2 

47 

128.6 

71.3 

07 

181.0 

100.4 

67 

233.5 

129.4 

28 

24.5 

13.6 

88 

77.0 

42.7 

48 

129.4 

71.8 

08 

181.9 

100.8 

68 

234.4 

129.9 

29 

25.4 

14.1 

89 

77.8 

43.1 

49 

130.3 

72.2 

09 

182.8 

101.3 

69 

235.3 

130.4 

30 

26.2 

14.5 

90 

78.7 

43.6 

50 

131.2 

72.7 

10 

183.7 

101.8 

70 

236.1 

130.9 

31 

27.1 

15.0 

91 

79.6 

44.1 

151 

132.1 

73.2 

211 

184.5 

102.3 

271 

237.0 

131.4 

32 

28.0 

15.5 

92 

80.5 

44.6 

52 

132.9 

73.7 

12 

185.4 

102.8 

72 

237.9 

131.9 

33 

28.9 

16.0 

93 

81.3 

45.1 

53 

133. 8 

74.2 

13 

186.3 

103.3 

73 

238.8 

132.4 

34 

29.7 

16.5 

94 

82.2 

45.6 

54 

134.7 

74.7 

14 

187.2 

103.7 

74 

239.6 

132.8 

35 

30.6 

17.0 

95 

83.1 

46.1 

55 

135.6 

75.1 

15 

188.0 

104.2 

75 

240.5 

133.3 

36 

31.5 

17.5 

96 

84.0 

46.5 

56 

136.4 

75.6 

16 

188.9 

104.7 

76 

241.4 

133.8 

37 

32.4 

17.9 

97 

84.8 

47.0 

57 

137.3 

76.1 

17 

189.8 

105.2 

77 

242.3 

134.3 

38 

33.2 

18.4 

98 

85.7 

47.5 

58 

138.2 

76.6 

18 

190.7 

105.7 

78 

243.1 

134.8 

39 

34.1 

18.9 

99 

86.6 

48.0 

59 

139.1 

77.1 

19 

191.5 

106.2 

79 

244.0 

135.3 

40 

35.0 
35.9 

19.4 

100 

87. 5 

48.5 

60 

139.9 

77.6 

20 

192.4 

106.7 

80 

244.9 

135.7 

41 

19.9 

101 

88.3 

49.0 

161 

140.8 

78.1 

221 

193.3 

107.1 

281 

245.8 

136.2 

42 

36.7 

20.4 

02 

89.2 

49.5 

62 

141.7 

78.5 

22 

194.2 

107.6 

82 

246.6 

136.7 

43 

37.6 

20.8 

03 

90.1 

49.9 

63 

142.6 

79.0 

23 

195.0 

108.1 

83 

247.5 

137.2 

44 

38.5 

21.3 

04 

91.0 

50.4 

64 

143.4 

79.5 

24 

195.9 

108.6 

84 

248.4 

137.7 

45 

39.4 

21.8 

05 

91.8 

50.9 

65 

144.3 

80.0 

25 

196.8 

109.1 

85 

249.3 

138.2 

46 

40.2 

22.3 

06 

92.7 

51.4 

66 

145.2 

80.5 

26 

197.7 

109.  6 

86 

250.1 

138.7 

47 

41.1 

22.8 

07 

93.6 

51.9 

67 

146.1 

81.0 

27 

198.5 

110. 1 

87 

251.0 

139.1 

48 

42.0 

23.3 

08 

94.5 

52.4 

68 

146.9 

81.4 

28 

199.  4 

110.5 

88 

251.9 

139.6 

49 

42.9 

23.8 

09 

95.3 

52.8 

69 

147.8 

81.9 

29 

200.3 

111.0 

89 

252.8 

140.1 

50 

43.7 

24.2 

10 

96.2 

53.3 

70 

148.7 

82.4 

30 

201.2 

111.5 

90 

253.6 

140.6 

51 

44.6 

24.7 

111 

97.1 

53.8 

171 

149.6 

82.9 

231 

202.0 

112.0 

291 

254.  5 

141.1 

52 

45.5 

25.2 

12 

98.0 

54.3 

72 

150.4 

83.4 

32 

202.9 

112.5 

92 

255.4 

141.6 

53 

46.4 

25.7 

13 

98.8 

54.8 

73 

151.3 

83.9 

33 

203.8 

113.0 

93 

256.3 

142.0 

54 

47.2 

26.2 

14 

99.7 

55.3 

74 

152.2 

84.4 

34 

204.7 

113.4 

94 

257.1 

142.5 

55 

48.1 

26.7 

15 

100.6 

55.8 

75 

153. 1 

84.8 

35 

205.5 

113.9 

95 

258.0 

143.0 

56 

49.0 

27.1 

16 

101.5 

56.2 

76 

153.9 

85.3 

36 

206.4 

114.4 

96 

258.9 

143.5 

57 

49.9 

27.6 

17 

102.3 

56.7 

77 

154.8 

85.8 

37 

207.3 

114.9 

97 

259.8 

144.0 

58 

50.7 

28.1 

18 

103.2 

57.2 

78 

155.7 

86.3 

38 

208.2 

115.4 

98 

260.6 

144.5 

59 

51.6 

28.6 

19 

104.1 

57.7 

79 

156.6 

86.8 

39 

209.0 

115.9 

99 

261.5 

145.0 

60 

52.5 

29.1 

20 

105.0 

58.2 

80 

157.4 

87.3 

40 

209.9 

116.4 

300 

262.4 

145.4 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

61°  (1 

19°,  241°,  299° 

)• 

TABLE  2. 

[Page  589 

Difference  of  Latitude  and  Departure  for 

29°  (151°,  209°,  331° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

263.2 

145.9 

361 

315.7 

175.0 

421 

368.2 

204.1 

481 

420.7 

233.2 

541 

473.2 

262.3 

02 

264.1 

146.4 

62 

316.6 

175.5 

22 

369.1 

204.6 

82 

421.5 

233.7 

42 

474.0 

262.8 

03 

265.0 

146.9 

63 

317.5 

176.0 

23 

369.9 

205.1 

83 

422.4 

234.2 

43 

474.9 

263.2 

04 

265.9 

147.4 

64 

318.  3 

176.5 

24 

370.8 

205.6 

84 

423.3 

234.6 

44 

475.8 

263.7 

05 

266.7 

147.9 

65 

319.2 

177.0 

25 

371.7 

206.0 

85 

424.2 

235.1 

45 

476.6 

264.2 

06 

267.6 

148.4 

66 

320.1 

177.4 

26 

372.6 

206.5 

86 

425.0 

235.6 

46 

477.5 

264.7 

07 

268.5 

148.  8 

67 

321.0 

177.9 

27 

373.4 

207.0 

87 

425.9 

236.1 

47 

478.4 

265.  2 

08 

269.4 

149.3 

68 

321.8 

178.4 

28 

374.3 

207.5 

88 

426.8 

236.6 

48 

479.3 

265.7 

09 

270.2 

149.8 

69 

322.7 

178.9 

29 

375.2 

208.0 

89 

427.7 

237.1 

49 

480.1 

266.2 

10 
311 

271.1 

150.3 

70 

323.6 

179.4 

30 

376.1 

208.5 

90 
491 

428.5 

237.6 

50 

481.0 

266.6 

272.0 

150.8 

371 

324.5 

179.9 

431 

376.9 

209.0 

429.4 

238.0 

551 

481.9 

267.1 

12 

272.9 

151.3 

72 

325.3 

180.4 

32 

377.8 

209.4 

92 

430.3 

238.5 

52 

482.8 

267.6 

13 

273.7 

151.7 

73 

326.2 

180.8 

33 

378.7 

209.9 

93 

431.2 

239.0 

53 

483.6 

268.1 

14 

274.6 

152.2 

74 

327.1 

181.3 

34 

379.6 

210.4 

94 

432.0 

239.5 

54 

484.5 

268.6 

15 

275.5 

152.7 

75 

328.0 

181.8 

35 

380.4 

210.9 

95 

432.9 

240.0 

55 

485.4 

269.1 

16 

276.3 

153.2 

76 

328.8 

182.3 

36 

381.3 

211.4 

96 

433. 8 

240.5 

56 

486.3 

269.5 

17 

277.2 

153.7 

77 

329.7 

182.8 

37 

382.2 

211.9 

97 

434.7 

240.9 

57 

487.1 

270.0 

18 

278.1 

154.2 

78 

330.6 

183.3 

38 

383.1 

212.3 

98 

435.5 

241.4 

58 

488.0 

270.5 

19 

279.0 

154.7 

79 

331.4 

183.7 

39 

383.9 

212.8 

99 

436.4 

241.9 

59 

488.9 

271.0 

20 

279.8 

155.1 

80 

332.3 

184.2 
184.7 

40 

384.8 

213.3 

500 

437.3 

242.4 

60 

489.8 

271.5 

321 

280.7 

155.  6 

381 

333.2 

441 

385.7 

213.8 

501 

438.2 

242.9 

561 

490.6 

272.0 

22 

281.6 

156.1 

82 

334.1 

185.2 

42 

386.6 

214.3 

02 

439.0 

243.  4 

62 

491.5 

272.5 

23 

282.5 

156.6 

83 

334.  9 

185.7 

43 

387.4 

214.8 

03 

439.9 

243.9 

63 

492.4 

272.9 

24 

283.3 

157.1 

84 

335.8 

186.2 

44 

388.3 

215.3 

04 

440.8 

244.3 

64 

493.2 

273.4 

25 

284.2 

157.6 

85 

336.7 

186.7 

45 

389.2 

215.  7 

05 

441.6 

244.8 

65 

494.1 

273.9 

26     285. 1 

158.1 

86 

337.6 

187.1 

46 

390.0 

216.2 

06 

442.5 

245.3 

66 

495.0 

274.4 

27  i  286.0 

158.5 

87 

338.4 

187.6 

47 

390.9 

216.7 

07 

443.4 

245.8 

67 

495.9 

274.9 

28     286. 8 

159.0 

88 

339.3 

188.1 

48 

391.8 

217.2 

08 

444.3 

246.3 

68 

496.8 

275.4 

29 

287.7 

159.5 

89 

340.2 

188.6 

49 

392.7 

217.7 

09 

445.2 

246.8 

69 

497.7 

275.9 

30 

288.6 
289.5 

160.0 

90 

341.1 

189.1 

50 

393.5 

218.2 
218.7 

10 
511 

446.1 

247.3 

70 

498.5 

276.3 
276.8 

331 

160.5 

391 

341.9 

189.6 

451 

394.4 

447.0 

247.8 

571 

499.4 

32 

290.3 

161.0 

92 

342.8 

190.0 

52 

395.3 

219.1 

12 

447.8 

248.2 

72 

500.3 

277.3 

33 

291.2 

161.4 

93 

343.7 

190.5 

53 

396.2 

219.6 

13 

448.6 

248.7 

73 

501.1 

277.8 

34 

292.1 

161.9 

94 

344.6 

191.0 

54 

397.0 

220.1 

14 

449.5 

249.2 

74 

502.0 

278.3 

35 

293.0 

162.4 

95 

345.4 

191.5 

55 

397.9 

220.6 

15 

450.4 

249.7 

75 

502.9 

278.8 

36 

293.8 

162.9 

96 

346.3 

192.0 

56 

398.8 

221.1 

16 

451.3 

250.2 

76 

503.7 

279.2 

37 

294.7 

163.4 

97 

347.2 

192.5 

57 

399.7 

221.6 

17 

452.2 

250.6 

77 

504.6 

279.7 

38 

295.6 

163.9 

98 

348.1 

193.0 

58 

400.5 

222.0 

18 

453.1 

251.1 

78 

505.5 

280.2 

39 

296.5 

164.4 

99 

348.9 

193.4 

59 

401.4 

222.5 

19 

463.9 

251.6 

79 

506.4 

280.7 

40 

297.3 
298.2 

164.8 

400 

349.8 

193.9 

60 

402.3 

223.0 

20 

454.8 

252. 1 

80 

507.2 

281.2 

341 

165.3 

401 

350.7 

194.4 

461 

403.2 

223.5 

521 

455.6 

252.6 

581 

508.1 

281.7 

42 

299.1 

165.8 

02 

351.6 

194.9 

62 

404.0 

224.0 

22 

456.5 

253.1 

82 

509.0 

282.2 

43 

300.0 

166.3 

03 

352.4 

195.4 

63 

404.9 

224.5 

23 

457.4 

253.6 

83 

509.9 

282.7 

44 

300.8 

166.8 

04 

353.3 

195.9 

64 

405.8 

225.0 

24 

458.3 

254.0 

84 

510.7 

283.2 

45 

301.7 

167.3 

05 

354.2 

196.3 

65 

406.7 

225.4 

25 

459.1 

254.5 

85 

511.6 

283.6 

46 

302.6 

167.7 

06 

355.1 

196.8 

66 

407.5 

225.9 

26 

460.0 

255.0 

86 

512.5 

284.1 

47 

303.5 

168.2 

07 

355.9 

197.3 

67 

408.4 

226.4 

27 

460.9 

255.5 

87 

513.4 

284.6 

48 

304.3 

168.7 

08 

356.8 

197.8 

68 

409.3 

226.9 

28 

461.8 

256.0 

88 

514. 3 

285.0 

49 

305.2 

169.2 

09 

357.7 

198.3 

69 

410.2 

227.4 

29 

462.6 

256.5 

89 

515.1 

285.5 

50 

306.1 

169.7 

10 

358.6 

198.8 

70 

411.0 

227.9 
228.3 

30 
531 

463.5 

256.9 

90 

516.0 

286.0 

351 

307.0 

170.2 

411 

359.4 

199.3 

471 

411.9 

464.4 

257.4 

591 

516.9 

286.5 

52 

307.8 

170.7 

12 

360.3 

199.7 

72 

412.8 

228.8 

32 

465.3 

257.9 

92 

517.7 

287.0 

53 

308.7 

171.1 

13 

361.2 

200.2 

73 

413.7 

229.3 

33 

466.1 

258.4 

93 

518.6 

287.5 

54 

309.6 

171.6 

14 

362.1 

200.7 

74 

414.5 

229.8 

34 

467.0 

258.9 

94 

519. 5 

288.0 

55 

310.5 

172.1 

15 

362.9 

201.2 

75 

415.4 

230.  3 

35 

467.9 

259.4 

95 

520.4 

288.5 

56 

311.3 

172.6 

16 

363.8 

201.7 

76 

416.3 

230.8 

36 

468.8 

259.9 

96 

521.2 

288.9 

57 

312.2 

173.1 

17 

364.7 

202.2 

77 

417.2 

231.3 

37 

469.6 

260.3 

97 

522.1 

289.4 

58 

313.1 

173.6 

18 

365.6 

202.7 

78 

418.0 

231.7 

38 

470.5 

260.8 

98 

523.0 

289.9 

59 

314.0 

174.0 

19 

366.4 

203.1 

79 

418.9 

232.2 

39 

471.4 

261.3 

99 

523.9 

290.4 

60 

314.8 

174.5 

20 

367.3 

203.6 

80 

419.8 

232.7 

40 

472.3 

261.8 

600 

524.  8 

290.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat.     1 

6 

1°   (119°,  241°,  299°] 

. 

Page  690] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for . 

30°  (150°,  210 

°,  330° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.8 

30.5 

121 

104.8 

60.5 

181 

156.8 

90.5 

241 

208.7 

120.6 

2 

1.7 

1.0 

62 

53.7 

31.0 

22 

105.7 

61.0 

82 

157.6 

91.0 

42 

209.6 

121.0 

3 

2.6 

1.5 

63 

54.6 

31.5 

23 

106.5 

61.5 

83 

158.5 

91.5 

43 

210.4 

121.5 

4 

3.5 

2.0 

64 

55.4 

32.0 

24 

107.4 

62.0 

84 

159.3 

92.0 

44 

211.3 

122.0 

5 

4.3 

2.5 

65 

56.3 

32.5 

25 

108.3 

62.5 

85 

160.2 

92.5 

45 

212.2 

122.5 

6 

5.2 

3.0 

66 

57.2 

33.0 

26 

109.1 

63.0 

86 

161.1 

93.0 

46 

213.0 

123.0 

7 

6.1 

3.5 

67 

58.0 

33.5 

27 

110.0 

63.5 

87 

161.9 

93.5 

47 

213.9 

123.5 

8 

6.9 

4.0 

68 

58.9 

34.0 

28 

110.9 

64.0 

88 

162.8 

94.0 

48 

214.8 

124.0 

9 

7.8 

4.5 

69 

59.8 

34.5 

29 

111.7 

64.5 

89 

163.7 

94.5 

49 

215.6 

124.5 

10 
11 

8.7 

5.0 

70 

60.6 

35.0 

30 

112.6 

65.0 

90 

164. 5 

95.0 

50 

216.5 

125.0 

9.5 

5.5 

71 

61.5 

35.5 

131 

113.4 

65.5 

191 

165.4 

95.5 

251 

217.4 

125.5 

12 

10.4 

6.0 

72 

62.4 

36.0 

32 

114.3 

66.0 

92 

166.3 

96.0 

52 

218.2 

126.0 

13 

11.3 

6.5 

73 

63.2 

36.5 

33 

115.2 

66.5 

93 

167.1 

96.5 

53 

219.1 

126.5 

14 

12.1 

7.0 

74 

64.1 

37.0 

34 

116.0 

67.0 

94 

168.0 

97.0 

54 

220.0 

127.0 

15 

13.0 

7.5 

75 

65.0 

37.5 

35 

116.9 

67.5 

95 

168.9 

97.5 

55 

220.8 

127.5 

16 

13.9 

8.0 

76 

65.8 

38.0 

36 

117.8 

68.0 

96 

169.7 

98.0 

56 

221.7 

128.0 

17 

14.7 

8.5 

77 

66.7 

38.5 

37 

118.6 

68.5 

97 

170.6 

98.5 

57 

222.6 

128.5 

18 

15.6 

9.0 

78 

67.5 

39.0 

38 

119.5 

69.0 

98 

171.5 

99.0 

58 

223.  4 

129.0 

19 

16.5 

9.5 

79 

68.4 

39.5 

39 

120.4 

69.5 

99 

172.3 

99.5 

59 

224.3 

129.5 

20 

17.3 

10.0 

80 

69.3 

40.0 
40.5 

40 
141 

121.2 

70.0 

200 

173.2 

100.0 

60 

225.2 

1.30.  0 

21 

18.2 

10.5 

81 

70.1 

122.1 

70.5 

201 

174.1 

100.5 

261 

226.0 

130.5 

22 

19.1 

11.0 

82 

71.0 

41.0 

42 

123.0 

71.0 

02 

174.9 

101.0 

62 

226.9 

131.0 

23 

19.9 

11.5 

83 

71.9 

41.5 

43 

123.8 

71.5 

03 

175.8 

101.5 

63 

227.8 

131.5 

24 

20.8 

12.0 

84 

72.7 

42.0 

44 

124.7 

72.0 

04 

176.7 

102.0 

64 

228.6 

132.0 

25 

21.7 

12.5 

85 

73.6 

42.5 

45 

125.6 

72.5 

05 

177.5 

102.5 

65 

229.5 

132.5 

26 

22.5 

13.0 

86 

74.5 

43.0 

46 

126.4 

73.0 

06 

178.4 

103.0 

66 

230. 4 

133.0 

27 

23.4 

13.5 

•   87 

75.3 

43.5 

47 

127.3 

73.5 

07 

179.3 

103.5 

67 

231.2 

133.5 

28 

24.2 

14.0 

88 

76.2 

44.0 

48 

128.2 

74.0 

08 

180.1 

104.0 

68 

232.1 

134.0 

29 

25.1 

14.5 

89 

77.1 

44.5 

49 

129.0 

74.5 

09 

181.0 

104.5 

69 

233.0 

134.5 

30 

26.0 

15.0 

90 

77.9 
78.8 

45.0 
45.5 

50 
151 

129.9 

75.0 

10 

181.9 

105.  0 

70 

233.  8 

135.0 
135.5 

31 

26.8 

15.5 

91 

130.8 

75.5 

211 

182.7 

105.5 

271 

234.7 

32 

27.7 

16.0 

92 

79.7 

46.0 

52 

131.6 

76.0 

12 

183.  6 

106.0 

72 

23-3.  6 

136.0 

33 

28.6 

16.5 

93 

80.5 

46.5 

53 

132.5 

76.5 

13 

184.5 

106.5 

73 

236.4 

136.5 

34 

29.4 

17.0 

94 

81.4 

47.0 

54 

133.4 

77.0 

14 

185.3 

107.0 

74 

237.3 

137.0 

35 

30.3 

17.5 

95 

82.3 

47.5 

55 

134.2 

77.5 

15 

186.2 

107.5 

75 

238.2 

137.5 

36 

31.2 

18.0 

96 

83.1 

48.0 

56 

135.1 

78.0 

16 

187.1 

108.0 

76 

239.0 

138. 0 

37 

32.0 

18.5 

97 

84.0 

48.5 

57 

136.0 

78.5 

17 

187.9 

108.5 

77 

239. 9 

138.5 

38 

32.9 

19.0 

98 

84.9 

49.0 

58 

136.8 

79.0 

18 

188.8 

109.0 

78 

240.8 

139.0 

39 

33.8 

19.5 

99 

85.7 

49.5 

59 

137.7 

79.5 

19 

189.7 

109.5 

79 

241.6 

139.5 

40 

34.6 

20.0 

100 

86.6 

50.0 

60 

138.6 

80.0 

20 

190.5 

110.0 

80 

242.5 
243.4 

140.0 
140.5 

41 

35.5 

20.5 

101 

87.5 

50.5 

161 

139.4 

80.5 

221 

191.4 

110.5 

281 

42 

36.4 

21.0 

02 

88.3 

51.0 

62 

140.3 

81.0 

22 

192.3 

111.0 

82 

244.2 

141.0 

43 

37.2 

21.5 

03 

89.2 

51.5 

63 

141.2 

81.5 

23 

193.1 

111.5 

83 

245. 1 

141.5 

44 

38.1 

22.0 

04 

90.1 

52.0 

64 

142.0 

82.0 

24 

194.0 

112.0 

84 

246.0 

142.0 

45 

39.0 

22.5 

05 

90.9 

52.5 

65 

142.9 

82.5 

25 

194.9 

112.5 

85 

246.8 

142.5 

46 

39.8 

23.0 

06 

91.8 

^3.0 

66 

143.8 

83.0 

26 

195.7 

113.0 

86 

247.7 

143.0 

47 

40.7 

23.5 

07 

92.7 

53.5 

67 

144.6 

83.5 

27 

196.6 

113.5 

87 

248.5 

143.5 

48 

41.6 

24.0 

08 

93.5 

54.0 

68 

145.5 

84.0 

28 

197.5 

114.0 

88 

249.4 

144.0 

49 

42.4 

24.5 

09 

94.4 

54.5 

69 

146.4 

84.5 

29 

198.3 

114.5 

89 

250.3 

144.5 

50 

43.3 

25.0 

10 

95.3 

55.0 
55.5 

70 
171 

147.2 
148.1 

85.0 

30 

199.2 

115.0 

90 

251.1 

145.0 

51 

44.2 

25.5 

111 

96.1 

85.5 

231 

200.1 

115.5 

291 

252.  0 

145.5 

52 

45.0 

26.0 

12 

97.0 

56.0 

72 

149.0 

86.0 

32 

200.9 

116.0 

92 

252.9 

146.0 

53 

45.9 

26.5 

13 

97.9 

56.5 

73 

149.8 

86.5 

33 

201.8 

116.5 

93 

253.7 

146.5 

54 

46.8 

27.0 

14 

98.7 

57.0 

74 

150.7 

87.0 

34 

202.6 

117.0 

94 

254.  6 

147.0 

55 

47.6 

27.5 

15 

99.6 

57.5 

75 

151.6 

87.5 

35 

203.5 

117.5 

95 

255.5 

147.5 

56 

48.5 

28.0 

16 

100.5 

58.0 

76 

152.4 

88.0 

36 

204.4 

118.0 

96 

256.3 

148.0 

57 

49.4 

28.5 

17 

101.3 

58.5 

77 

153.3 

88.5 

37 

205.2 

118.5 

97 

257.2 

148.5 

58 

50.2 

29,0 

18 

102.2 

59.0 

78 

154.2 

89.0 

38 

206.1 

119.0 

98 

258.1 

149.0 

59 

51.1 

29.5 

19 

103.1 

59.5 

79 

155. 0 

89.5 

39 

207.0 

119.5 

99 

258.9 

149.5 

60 

52.0 

30.0 

20 

103.9 

60.0 

80 

155.9 

90.0 

40 

207.8 

120.0 

300 

259.8 

150.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

60°  (1 

20°,  240°,  300° 

). 

TABLE  2. 

[Page  691 

Difference  of  Latitude  and  Departure  for  30 

°  (150°,  210°,  330°). 

Dist.  [     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

260.7 

150.5 

361 

312.6 

180.5 

421 

364.6 

210.5 

481 

416.6 

240.5 

541 

468.5 

270.5 

02 

261.5 

151.0 

62 

313.5 

181.0 

22 

365.5 

211.0 

82 

417.4 

241.0 

42 

469.4 

271.0 

03 

262.4 

151.5 

63 

314.4 

181.5 

23 

366. 3 

211.5 

83 

418.3 

241.5 

43 

470.3 

271.5 

04 

263.3 

152.0 

64 

315.2 

182.0 

24 

367.2 

212.0 

84 

419.2 

242.0 

44 

471.1 

272.0 

05 

264.1 

152.5 

65 

316.1 

182.5 

25 

368.1 

212.5 

85 

420.0 

242.5 

45 

472.0 

272.5 

06 

265.0 

153.0 

66 

317.0 

183.0 

26 

368.9 

213.0 

86 

420.9 

243.0 

46 

472.9 

273.0 

07 

265.9 

153.5 

67 

317.8 

183.5 

27 

369. 8 

213.5 

87 

421.8 

243.5 

47 

473.7 

273.5 

08 

266.7 

154.0 

68 

318.7 

184.0 

28 

370.7 

214.0 

88 

422.6 

244.0 

48 

474.6 

274.0 

09 

267.6 

154.5 

69 

319.6 

184.5 

29 

371.5 

214.5 

89 

423.5 

244.5 

49 

475.5 

274.5 

10 

268.5 

155.0 

70 

320.4 

185.0 

30 

372.4 

215.0 

90 

424.4 

245.0 

50 

476.3 

275.0 

311 

269.3 

155.5 

371 

321.3 

185.5 

431 

373.3 

215.5 

491 

425.2 

245.5 

551 

477.2 

275.5 

12 

270.2 

156.0 

72 

322.2 

186.0 

32 

374.1 

216.0 

92 

426.1 

246.0 

52 

478.1 

276.0 

13 

271.1 

156.5 

73 

323.0 

186.5 

33 

375.0 

216.5 

93 

426.9 

246.5 

53 

478.9 

276.5 

14 

271.9 

157.0 

74 

323.9 

187.0 

34 

375.9 

217.0 

94 

427.8 

247.0 

54 

479.8 

277.0 

15 

272.8 

157.5 

75 

324.8 

187.5 

35 

376.7 

217.5 

95 

428.7 

247.5 

55 

480.7 

277.5 

16 

273.7 

158.0 

76 

325.6 

188.0 

36 

377.6 

218.0 

96 

429.6 

248.0 

56 

481.5 

278.0 

17 

274.5 

158.5 

77 

326.5 

188.5 

37 

378.5 

218.5 

97 

430.4 

248.5 

57 

482.4 

278.5 

18 

275.4 

159.0 

78 

327.4 

189.0 

38 

379. 3 

219.0 

98 

431.3 

249.0 

58 

483.3 

279.0 

19 

276.3 

159.5 

79 

328.2 

189.5 

39 

380.2 

219.5 

99 

432.2 

249.5 

59 

484.1 

279.5 

20 

277.1 

160.0 

80 

329. 1 

190.0 

40 

381.1 

220.0 

500 

433. 0 

250.0 

60 

485.0 

280.0 

321 

278.0 

160.5 

381 

330.0 

190.5 

441 

381.9 

220.  5 

501 

433.9 

250. 5 

561 

485.9 

280.5 

22 

278.9 

161.0 

82 

330.8 

191.0 

42 

382.8 

221.0 

02 

434.8 

251.0 

62 

486.7 

281.0 

23 

279.7 

161.5 

83 

331.7 

191.5 

43 

383.7 

221.5 

03 

435.6 

251.5 

63 

487.6 

281.5 

24 

280.6 

162.0 

84 

332.6 

192. 0 

44 

384.5 

222.0 

04 

436.5 

252.0 

64 

488.5 

282.0 

25 

281.5 

162.5 

85 

333. 4 

192.5 

45 

385.4 

222.5 

05 

437.4 

252.5 

65 

489.3 

282.5 

26 

282.3 

163. 0 

86 

334.3 

193.0 

46 

386. 3 

223.0 

06 

438.2 

253.0 

66 

490.2 

283.0 

27 

283.2 

163. 5 

87 

335.2 

193.5 

47 

387.1 

223.5 

07 

439.1 

253.5 

67 

491.1 

283.5 

28 

284.1 

164.0 

88 

336.0 

194.0 

48 

388.0 

224.0 

08 

440.0 

254.0 

68 

491.9 

284.0 

29 

284.9 

164.5 

89 

336.9 

194.5 

49 

388.9 

224.5 

09 

440.8 

254.5 

69 

492.8 

284.5 

30 
331 

285.8 

165.0 

90 

337.8 

195.0 

50 

389.7 
390.6 

225.0 

10 

441.7 

255.0 

70 

493.6 

285. 0 

286.7 

165.5 

391 

338.6 

195.5 

451 

225.5 

511 

442.6 

255.5 

571 

494.5 

285. 5 

32 

287.5 

166.0 

92 

339.  5 

196.0 

52 

391.5 

226.0 

12 

443.4 

256.0 

72 

495.4 

286.0 

33 

288.4 

166.5 

93 

340.4 

196.5 

53 

392.3 

226.5 

13 

444.3 

256.5 

73 

496.3 

286.5 

34 

289.3 

167.0 

94 

341.2 

197.0 

54 

393.2 

227.0 

14 

445.2 

257.0 

74 

497.1 

287.0 

35 

290.1 

167.5 

95 

342.1 

197.5 

55 

394.0 

227.5 

15 

446.0 

257.5 

75 

497.9 

287.5 

36 

291.0 

168.0 

96 

343.0 

198.0 

56 

394.9 

228.0 

16 

446.9 

258.0 

76 

498.8 

288.0 

37 

291.9 

168.5 

97 

343.8 

198.  5 

57 

395.8 

228.5 

17 

447.8 

258.5 

77 

499.7 

288.  5 

38 

292.7 

169.0 

98 

344.7 

199.0 

58 

396.6 

229.0 

18 

448.6 

259. 0 

78 

500.5 

289.0 

39 

293.6 

169.5 

99 

345.6 

199.5 

59 

397.5 

229.5 

19 

449.4 

259.5 

79 

501.3 

289.5 

40 
341 

294.5 

170.0 

400 

346.4 

200.0 

60 

398.4 

230.0 

20 

450.3 

260.0 

80 

502.2 
503.1 

290.0 
290.5 

295.3 

170.5 

401 

347.3 

200.5 

461 

399.2 

230.5 

521 

451.2 

260.5 

581 

42 

296.2 

171.0 

02 

348.1 

201.0 

62 

400.1 

231.0 

22 

452.1 

261.0 

82 

504.0 

291.0 

43 

297.1 

171.5 

03 

349.0 

201.5 

63 

401.0 

231.5 

23 

452.9  '261.5 

83 

504.9 

291.5 

44 

297.9 

172.0 

04 

349.9 

202.0 

64 

401.8 

232.0 

24 

453.8 

262.0 

84 

505.8 

292.0 

45 

298.8 

172.5 

05 

350.7 

202.5 

65 

402.7 

232.5 

25 

454.7 

262.5 

85 

506.6 

292.5 

46 

299.7 

173.0 

06 

351.6 

203.0 

66 

403.6 

233.0 

26 

455.5 

263.0 

86 

507.5 

293.0 

47 

300.5 

173.5 

07 

352. 5 

203.5 

67 

404.4 

233.5 

27 

456.4 

263.5 

87 

508.4 

293.5 

48 

301.4 

174.0 

08 

353.3 

204.0 

68 

405.3 

234.0 

28 

457.3 

264.0 

88 

509.2 

294.0 

49 

302.3 

174.5 

09 

354.2 

204.5 

69 

406.2 

234.5 

29 

458.1 

264.5 

89 

510.1 

294.5 

50 
351 

303.1 

175.0 

10 

355.1 
355.9 

205.0 

70 

407.0 

235.0 

30 

459.0 

265.0 

90 

511.0 

295.0 

304.0 

175.5 

411 

205.5 

471 

407.9 

235.5 

531 

459.9 

265.5 

591 

511.8 

295.5 

52 

304.8 

176.0 

12 

356.  8 

206.0 

72 

408.8 

236.0 

32 

460.7 

266.0 

92 

512.7 

296.0 

53 

305.7 

176.5 

13 

357.7 

206.5 

73 

409.6 

236.5 

33 

461.6 

266.5 

93 

513.6 

296.5 

54 

306.6 

177.0 

14 

358.5 

207.0 

74 

410.5 

237.0 

34 

462.5 

267.0 

94 

514.4 

297.0 

55 

307.4 

177.5 

15 

359.4 

207.5 

75 

411.4 

237.5 

35 

463.3 

267.5 

95 

515.3 

297.5 

56 

308.3 

178.0 

16 

360.3 

208.0 

76 

412.2 

238.0 

36 

464.2 

268.0 

96 

516.2 

298.0 

57 

309.2 

178. 5 

17 

361.1 

208.5 

77 

413.1 

238.5 

37 

465.1 

268.5 

97 

517.0 

298.5 

58 

310.0 

179.0 

18 

362.  0 

209.0 

78 

414.0 

239.  0 

38 

465.9 

269.0 

98 

517.9 

299.0 

59 

310.9 

179.5 

19 

362.9 

209.5 

79 

414.8 

2.39.  5 

39 

466.8 

269.5 

99 

518.8 

299.5 

60 

311.8 

180.0 

20 

363.7 

210.0 

80 

415.7 

240.0 

40 

467.7 

270.0 

600 

519.6 

300.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

60°  (120°,  240°,  300° 

). 

1 

Page  592] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  31°  (149°,  211 

°,  329° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.3 

31.4 

121 

103.7 

62.3 

181 

155.1 

93.2 

241 

206.6 

124.1 

2 

1.7 

1.0 

62 

53.1 

31.9 

22 

104.6 

62.8 

82 

156.0 

93.7 

42 

207.4 

124.6 

3 

2.6 

1.5 

63 

54  0 

32.4 

23 

105.4 

63.3 

83 

156.9 

94.3 

43 

208.3 

125.2 

4 

3.4 

2.1 

64 

54.9 

33.0 

24 

106.3 

63.9 

84 

157.7 

94.8 

44 

209.1 

125.7 

5 

4.8 

2.6 

65 

55.7 

33.5 

25 

107.1 

64.4 

85 

158.6 

95.3 

45 

210.0 

126.2 

6 

5.1 

3.1 

66 

56.6 

34.0 

26 

108.0 

64.9 

86 

159.4 

95.8 

46 

210.9 

126.7 

7 

6.0 

3.6 

67 

57.4 

34.5 

27 

108.9 

65.4 

87 

160.3 

96.3 

47 

211.7 

127.2 

8 

6.9 

4.1 

68 

58.3 

35.0 

28 

109.7 

65.9 

88 

161.1 

96.8 

48 

212.6 

127.7 

9 

7.7 

4.6 

69 

59.1 

35.5 

29 

110.6 

66.4 

89 

162.0 

97.3 

49 

213.4 

128.2 

10 

8.6 

5.2 

70 

60.0 

36.1 

30 

111.4 

67,0 

90 

162.9 

97.9 

50 

214.3 

128.8 

11 

9.4 

5.7 

71 

60.9 

36.6 

131 

112.3 

67.5 

191 

163.7 

98.4 

251 

215.1 

129.3 

12 

10.3 

6.2 

72 

61.7 

37.1 

32 

113.1 

68.0 

92 

164.6 

98.9 

52 

216.0 

129.8 

13 

11.1 

6.7 

73 

62.6 

37.6 

33 

114.0 

68.5 

93 

165.4 

99.4 

53 

216.9 

130.3 

14 

12.0 

7.2 

74 

63.4 

38.1 

34 

114.9 

69.0 

94 

166.3 

99.9 

54 

217.7 

130.8 

15 

12.9 

7.7 

75 

64.3 

38.6 

35 

115.7 

69.5 

95 

167.1 

100.4 

55 

218.6 

131.3 

16 

13.7 

8.2 

76 

65.1 

39.1 

36 

116.6 

70.0 

96 

168.0 

100.9 

56 

219.4 

131.8 

17 

14.6 

8.8 

77 

66,0 

39.7 

37 

117.4 

70.6 

97 

168.9 

101.5 

57 

220.3 

132.4 

18 

15.4 

9.3 

78 

66.9 

40.2 

38 

118.3 

71.1 

98 

169.7 

102.0 

58 

221.1 

132.9 

19 

16.3 

9.8 

79 

67.7 

40.7 

39 

119.1 

71.6 

99 

170.6 

102.5 

59 

222.0 

133.4 

20 

17.1 

10.3 

80 

68.6 

41.2 

40 

120.0 

72.1 

200 

171.4 

103.0 

60 

222.9 

133.9 

21 

18.0 

10.8 

81 

69.4 

41.7 

141 

120.9 

72.6 

201 

172.3 

103.5 

261 

223.7 

134.4 

22 

18.9 

11.3 

82 

70.3 

42.2 

42 

121.7 

73.1 

02 

173.1 

104.0 

62 

224.6 

134.9 

23 

19.7 

11.8 

83 

71.1 

42.7 

43 

122.6 

73,7 

03 

174.0 

104.6 

63 

225.4 

135.5 

24 

20.6 

12.4 

84 

72.0 

43.3 

44 

123.4 

74.2 

04 

174.9 

105.1 

64 

22(5.3 

136.0 

25 

21.4 

12.9 

85 

72.9 

43.8 

45 

124.3 

74.7 

05 

175.7 

105.6 

65 

227.1 

136.5 

26 

22.3 

13.4 

86 

73.7 

44.3 

46 

125.1 

75.2 

06 

176.6 

106.1 

66 

228.0 

137.0 

27 

23.1 

13.9 

87 

74.6 

44.8 

47 

126.0 

75.7 

07 

177.4 

106.6 

67 

228.9 

137.5 

28 

24.0 

14.4 

88 

75.4 

45.3 

48 

126.9 

76.2 

08 

178.3 

107.1 

68 

229.7 

138.0 

29 

24.9 

14.9 

89 

76.3 

45.8 

49 

127.7 

76.7 

09 

179.1 

107.6 

69 

230.6 

138.5 

30 

25.7 

15.5 

90 

77.1 

46.4 

50 

128.6 

77.3 

10 

180.0 
180.9 

108.2 

70 

231.4 

139.1 

31 

26.6 

16.0 

91 

78.0 

46.9 

151 

129.4 

77.8 

211 

108.7 

271 

232.3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47.4 

52 

130.3 

78.3 

12 

181.7 

109.2 

72 

233.1 

140.1 

33 

28.3 

17.0 

93 

79.7 

47.9 

53 

131.1 

78.8 

13 

182.6 

109.7 

73 

234.0 

140.6 

34 

29.1 

17.5 

94 

80.6 

48.4 

54 

132.0 

79.3 

14 

183.4 

110.2 

74 

234.9 

141.1 

35 

30.0 

18.0 

95 

81.4 

48.9 

55 

132.9 

79.8 

15 

184.3 

110.7 

75 

235.7 

141.6 

36 

30.9 

18.5 

96 

82.3 

49.4 

56 

133.7 

80.3 

16 

185.1 

111.2 

76 

236.6 

142.2 

37 

31.7 

19.1 

97 

83.1 

50.0 

57 

134.6 

80.9 

17 

186.0 

111.8 

77 

237.4 

142.7 

38 

32.6 

19.6 

98 

84.0 

50.5 

58 

135.4 

81.4 

18 

186.9 

112.3 

78 

238.3 

143.2 

39 

33.4 

20.1 

99 

84.9 

51.0 

59 

136.3 

81.9 

19 

187.7 

112.8 

79 

239.1 

143.  7 

40 

34.3 

20.6 

100 

85.7 

51.5 

60 

137.1 

82.4 

20 

188.6 
189.4 

113.3 

80 

240.0 

144.2 

41 

35.1 

21.1 

101 

86.6 

52.0 

161 

138.0 

82.9 

221 

113.8 

281 

240.9 

144.7 

42 

36.0 

21.6 

02 

87.4 

52.5 

62 

138.9 

83.4 

22 

190.3 

114.3 

82 

241.7 

145.2 

43 

36.9 

22.1 

03 

88.3 

53.0 

63 

139.7 

84.0 

23 

191.1 

114.9 

83 

242.6 

145.8 

44 

37.7 

22.7 

04 

89.1 

53.6 

64 

140.6 

84.5 

24 

192.0 

115.4 

84 

243.4 

146.3 

45 

38.6 

23.2 

05 

90.0 

54.1 

65 

141.4 

85.0 

25 

192.9 

115.9 

85 

244.3 

146.8 

46 

39.4 

23.7 

06 

90.9 

54.6 

66 

142.3 

85.5 

26 

193.7 

116.4 

86 

245.1 

147.3 

47 

40.3 

24.2 

07 

91.7 

55.1 

67 

143.1 

86.0 

27 

194.6 

116.9 

87 

246.0 

147.8 

48 

41.1 

24.7 

08 

92.6 

55.6 

68 

144.0 

86.5 

28 

195.4 

117.4 

88 

246.9 

148.3 

49 

42.0 

25.2 

09 

93.4 

56.1 

69 

144.9 

87.0 

29 

196.3 

117.9 

89 

247.7 

148.8 

50 

42.9 

25.8 

10 

94.3 

56.7 

70 

145.7 

87.6 

30 

197.1 

118.5 

90 
291 

248.6 

149.4 

51 

43.7 

26.3 

111 

95.1 

57.2 

171 

146.6 

88.1 

231 

198.0 

119.0 

249.4 

149.9 

52 

44.6 

26.8 

12 

96.0 

57.7 

72 

147.4 

88.6 

32 

198.9 

119.5 

92 

250.3 

150.4 

1 

53 

45.4 

27.3 

13 

96.9 

58.2 

73 

148.3 

89.1 

33 

199.7 

120.0 

93 

251.2 

150.9 

1 

54 

46.3 

27.8 

14 

97.7 

58.7 

74 

149.1 

89.6 

34 

200.6 

120.5 

94 

252.0 

151.4 

1 

56 

47.1 

28.3 

15 

98.6 

59.2 

75 

150.0 

90.1 

35 

201.4 

121.0 

95 

252.9 

151.9 

1 

56 

48.0 

28.8 

16 

99.4 

59.7 

76 

150.9 

90.6 

36 

202.3 

121.5 

96 

253.7 

152.5 

1 

57 

48.9 

29.4 

17 

100.3 

60.3 

77 

151.7 

91.2 

37 

203.1 

122.1 

97 

254.6 

153.0 

58 

49.7 

29.9 

18 

101.1 

60.8 

78 

152.6 

91.7 

38 

204.0 

122.6 

98 

255.4 

153.5 

59 

50.6 

30.4 

19 

102.0 

61.3 

79 

153.4 

92.2 

39 

204.9 

123.1 

99 

256.3 

154.0 

1 

60 

51.4 

30.9 

20 

102.9 

61.8 

80 

154.3 

92.7 

40 

205.7 

123.6 

300 

257.1 

154.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

59°  (1 

21°,  239 

°,  301° 

)• 

1 

TABLE  2. 

[Page  693 

Difference  of  Latitude  and  Departure  for  31°  (149",  211°,  329° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

258.0 

155.0 

361 

309.4 

185.9 

421 

360.9 

216.8 

481 

412.3 

247.7 

541 

463.7 

278.6 

02 

258.9 

155.5 

62 

310.3 

186.4 

22 

361.7 

217.3 

82 

413.2 

248.2 

42 

464.6 

279.1 

03 

259.7 

156.1 

63 

311.2 

187.0 

23 

362.6 

217.9 

83 

414.0 

248.8 

43 

465.4 

279.7 

04 

260.6 

156.6 

64 

312.0 

187.5 

24 

363.4 

218.4 

84 

414.9 

249.3 

44 

466.3 

280.2 

05 

261.4 

157.1 

65 

312.9 

188.0 

25 

364.3 

218.9 

85 

415.7 

249.8 

45 

467.2 

280.7 

06 

262.3 

157.6 

66 

313.7 

188.5 

26 

365.2 

219.4 

86 

416.6 

250.3 

46 

468.0 

281.2 

07 

263.2 

158.1 

67 

314.6 

189.0 

27 

366.0 

219.9 

87 

417.4 

250.8 

47 

468.9 

281.7 

08 

264.0 

158.6 

68 

315.4 

189.5 

28 

366.9 

220.4 

88 

418.3 

251.3 

48 

469.7 

282.3 

09 

264.9 

159.2 

69 

316.3 

190.1 

29 

367.7 

221.0 

89 

419.2 

251.9 

49 

470.6 

282.8 

10 

265.7 

159.7 

70 

317.2 

190.6 

30 
431 

368.6 

221.5 

90 

420.0 

252.4 

50 
551 

471.4 
472.3 

283.3 

311 

266.6 

160.2 

371 

318.0 

191.1 

369.4 

222.0 

491 

420.9 

'252. 9 

283.8 

12 

267.4 

160.7 

72 

318.9 

191.6 

32 

370.3 

222.5 

92 

421.7 

253.4 

52 

473.2 

284.3 

13 

268.3 

161.2 

73 

319.7 

192.1 

33 

371.2 

223.0 

93 

422.6 

253.9 

53 

474.0 

284.8 

14 

269.2 

161.7 

74 

320.6 

192.6 

34 

372.0 

223.5 

94 

423.4 

254.4 

54 

474.9 

285.3 

15 

270.0 

162.2 

75 

321.4 

193.1 

35 

372.9 

224.0 

95 

424.3 

254.9 

55 

475.7 

285.8 

16 

270.9 

162.8 

76 

322.3 

193.7 

36 

373.7 

224.6 

96 

425.2 

255.5 

56 

476.6 

286.4 

17 

271.  7 

163.3 

77 

323.2 

194.2 

37 

374.6 

225.1 

97 

426.0 

256.0 

57 

477.4 

286.9 

18 

272.6 

163.8 

78 

324.0 

194.7 

38 

375.4 

225.6 

98 

426.9 

256.5 

58 

478.3 

287.4 

19 

273.4 

164.3 

79 

324.9 

195.2 

39 

376.3 

226.1 

99 

427.7 

257.0 

59 

479.2 

287.9 

20 
321 

274.3 

164.8 

80 

325.7 

195.7 

40 

377.2 

226.6 

500 

428.6 

257.5 

60 

480.0 

288.4 

275.2 

165.3 

381 

326.6 

196.2 

441 

378.0 

227.1 

501 

429.4 

258.0 

561 

480.9 

288.9 

22 

276.0 

165.8 

82 

327.4 

196.7 

42 

378.9 

227.7 

02 

430.3 

258.6 

62 

481.7 

289.5 

23 

276.9 

166.4 

83 

328.3 

197.3 

43 

379.7 

228.2 

03 

431.2 

259.1 

63 

482.6 

290.0 

24 

277.7 

166.9 

84 

329.2 

197.8 

44 

380.6 

228.7 

04 

432.0 

259.6 

64 

483.4 

290.5 

25 

278.6 

167.4 

85 

330.0 

198.3 

45 

381.4 

229.2 

05 

432.9 

260.1 

65 

484.3 

291.0 

26 

279.4 

167.9 

86 

330.9 

198.8 

46 

382.3 

229.7 

06 

433.7 

260.6 

66 

485.2 

291.5 

27 

280.3 

168.4 

87 

331.7 

199.3 

47 

383.2 

230.2 

07 

434.6 

261.1 

67 

486.0 

292.0 

28 

281.2 

168.9 

88 

332.6 

199.8 

48 

384.0 

230.7 

08 

435.4 

261.6 

68 

486.9 

292.5 

29 

282.0 

169.5 

89 

333.4 

200.4 

49 

384.9 

231.3 

09 

436.3 

262.2 

69 

487.7 

293.1 

30 

282  9 

170.0 

90 

334.3 

200.9 

50 

385.7 

231.8 

10 

437.2 

262.7 

70 

488.6 

293.6 

331 

283.7 

170.5 

391 

335.2 

201.4 

451 

386.6 

232.3 

511 

438.0 

263.2 

571 

489.4 

294.1 

32 

284.6 

171.0 

92 

336.0 

201.9 

52 

387.4 

232.8 

12 

438.9 

263.7 

72 

490.3 

294.6 

33 

285.4 

171.5 

93 

336.9 

202.4 

53 

388.3 

233.3 

13 

439.7 

264.2 

73 

491.2 

295.1 

34 

286.3 

172.0 

94 

337.7 

202.9 

54 

389.2 

233.8 

14 

440.6 

264.7 

74 

492.0 

295.6 

35 

287.2 

172.5 

95 

338.6 

203.4 

55 

390.0 

234.3 

15 

441.4 

265.2 

75 

492.9 

296.1 

36 

288.0 

173.1 

96 

339.4 

204.0 

56 

390.9 

234.9 

16 

442.3 

265.8 

76 

493.7 

296.7 

37 

288.9 

173.6 

97 

340.3 

204.5 

57 

391.7 

235.4 

17 

443.2 

266.3 

77 

494.6 

297.2 

38 

289.7 

174.1 

98 

341.2 

205.0 

58 

392.6 

235.9 

18 

444.0 

266.8 

78 

495.4 

297.7 

39 

290.6 

174.6 

99 

342.0 

205.5 

59 

393.4 

236.4 

19 

444.9 

267.3 

79 

496.3 

298.2 

40 

291.4 

175.1 

400 

342.9 

206.0 

60 

394.3 

236.9 

20 

445.7 

267.8 

80 

497.2 

298.7 

341 

292.3 

175.6 

401 

343.7 

206.5 

461 

395.2 

237.4 

521 

446.6 

268.3 

581 

498.0 

299.2 

42 

293.2 

176.1 

02 

344.6 

207.0 

62 

396.0 

238.0 

22 

447.4 

268.9 

82 

498.9 

299.8 

43 

294.0 

176.7 

03 

345.4 

207.6 

63 

396.9 

238.5 

23 

448.3 

269.4 

83 

499.7 

300.3 

44 

294.9 

177.2 

04 

346.3 

208.1 

64 

397.7 

239.0 

24 

449.2 

269.9 

84 

500.6 

300.8 

45 

295.7 

177.7 

05 

347.2 

208.6 

65 

398.6 

239.5 

25 

450.0 

270.4 

85 

501.4 

301.3 

46 

296.6 

178.2 

06 

348.0 

209.1 

66 

399.4 

240.0 

26 

450.9 

270.9 

86 

502.3 

301.8 

47 

297.4 

178.7 

07 

348.9 

209.6 

67 

400.3 

240.5 

27 

451.7 

271.4 

87 

503.2 

302.3 

48 

298.3 

179.2 

08 

349.7 

210.1 

68 

401.2 

241.0 

28 

452.6 

271.9 

88 

504.0 

302.8 

49 

299.2 

179.8 

09 

350.6 

210.7 

69 

402.0 

241.5 

29 

453.4 

272.4 

89 

504.9 

303.3 

50 

300.0 

180.3 

10 

351.4 

211.2 

70 

402.9 

242.1 

30 

454.3 

273.0 

90 

505.7 

303.9 

351 

300.9 

180.8 

411 

352.3 

211.7 

471 

403.7 

242.6 

531 

455.2 

273.5 

591 

506.6 

304.4 

52 

301.7 

181.3 

12 

353.2 

212.2 

72 

404.6 

243.1 

32 

456.0 

274.0 

92 

507.4 

304.9 

53 

302.6 

181.8 

13 

354.0 

212.7 

73 

405.4 

243.6 

33 

456.9 

274.5 

93 

508.3 

305.4 

54 

303.4 

182.3 

14 

354.9 

213.2 

74 

406.3 

244.1 

34 

457.7 

275.0 

94 

509.2 

305.9 

55 

304.3 

182.8 

15 

355.7 

213.7 

75 

407.2 

244.6 

35 

458.6 

275.5 

95 

510.0 

306.4 

56 

305.2 

183.4 

16 

356.6 

214.3 

76 

408.0 

245.2 

36 

459.4 

276.1 

96 

510.9 

307.0 

57 

306.0 

183.9 

17 

357.4 

214.8 

77 

408.9 

245.7 

37 

460.3 

276.6 

97 

511.7 

307.5 

58 

306.9 

184.4 

18 

358.3 

215.3 

78 

409.7 

246.2 

38 

461.2 

277.1 

98 

512.6 

308.0 

59 

307.7 

184.9 

19 

359.2 

215.8 

79 

410.6 

246.7 

39 

462.0 

277.6 

99 

513.4 

308.5 

60 

308.6 

186.4 

20 

360.0 

216.3 

80 

411.4 

247.2 

40 

462.9 

278.1 

600 

514.3 

309.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

59°  (1 

21°,  239°,  301° 

). 

1 

21594°— 14- 


-31 


Page  694] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  32°  (148°,  212°,  328° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

1 

0.8 

0.5 

61 

51.7 

32.3 

121 

102.6 

64.1 

181 

153.5 

95.9 

241 

204.4 

127.7 

2 

1.7 

1.1 

62 

52.6 

32.9 

22 

103.5 

64.7 

82 

154.3 

96.4 

42 

205.2 

128.2 

3 

2.5 

1.6 

63 

53.4 

33.4 

23 

104.3 

65.2 

83 

155.2 

97.0 

43 

206.1 

128.8 

4 

3.4 

2.1 

64 

54.3 

33.9 

24 

105.2 

65.7 

84 

156.0 

97.5 

44 

206.9 

129.3 

5 

4.2 

2.6 

65 

55.1 

34.4 

25 

106.0 

66.2 

85 

156.9 

98.0 

45 

207.8 

129.8 

6 

5.1 

3.2 

66 

56.0 

35.0 

26 

106.9 

66.8 

86 

157.7 

98.6 

46 

208.6 

130.4 

7 

5.9 

3.7 

67 

56.8 

35.5 

27 

107.7 

67.3 

87 

158.6 

99.1 

47 

209.5 

130.9 

8 

6.8 

4.2 

68 

57.7 

36.0 

28 

108.6 

67.8 

88 

159.4 

99.6 

48 

210.3 

131.4 

9 

7.6 

4.8 

69 

58.5 

36.6 

29 

109.4 

68.4 

89 

160.3 

100.2 

49 

211.2 

131.9 

10 

8.5 

5.3 

70 

59.4 

37.1 

30 

110.2 

68.9 

90 

161.1 

100.7 

50 

212.0 

132.5 

11 

9.3 

5.8 

71 

60.2 

37.6 

131 

111.1 

69.4 

191 

162.0 

101.2 

251 

212.9 

133.0 

12 

10.2 

6.4 

72 

61.1 

38.2 

32 

111.9 

69.9 

92 

162.8 

101.7 

52 

213.7 

133.5 

13 

11.0 

6.9 

73 

61.9 

38.7 

33 

112.8 

70.5 

93 

163.7 

102.3 

53 

214.6 

134.1 

14 

11.9 

7.4 

74 

62.8 

39.2 

34 

113.6 

71.0 

94 

164.5 

102.8 

54 

215.4 

134.6 

15 

12.7 

7.9 

75 

63.6 

39.7 

35 

114.5 

71.5 

95 

165.4 

103.3 

55 

216.3 

135.1 

16 

13.6 

8.5 

76 

64.5 

40.3 

36 

115.3 

72.1 

96 

166.2 

103.9 

56 

217.1 

135.7 

17 

14.4 

9.0 

77 

65.3 

40.8 

37 

116.2 

72.6 

97 

167.1 

104.4 

57 

217.9 

136.2 

18 

15.3 

9.5 

78 

66.1 

41.3 

38 

117.0 

73.1 

98 

167.9 

104.9 

58 

218.8 

136.7 

19 

16.1 

10.1 

79 

67.0 

41.9 

39 

117.9 

73.7 

99 

168.8 

105.5 

59 

219.6 

137.2 

20 

17.0 

10.6 

80 

67.8 

42.4 

40 

118.7 

74.2 

200 

169.6 
170.5 

106.0 
106.5 

60 
261 

220.5 
221.3 

137.8 

21 

17.8 

11.1 

81 

68.7 

42.9 

141 

119.6 

74.7 

201 

138.3 

22 

18.7 

11.7 

82 

69.5 

43.5 

42 

120.4 

75.2 

02 

171.  3 

107.0 

62 

222.2 

138.8 

23 

19.5 

12.2 

83 

70.4 

44.0 

43 

121.3 

75.8 

03 

172.2 

107.6 

63 

223.0 

139.4 

24 

20.4 

12.7 

84 

71.2 

44.5 

44 

122.1 

76.3 

04 

173.0 

108.1 

64 

223.9 

139.9 

25 

21.2 

13.2 

85 

72.1 

45.0 

45 

123.0 

76.8 

05 

173.8 

108.6 

65 

224.7 

140.4 

26 

22.0 

13.8 

86 

72.9 

45.6 

46 

123.8 

77.4 

06 

174.7 

109.2 

66 

225.6 

141. 0 

27 

22.9 

14.3 

87 

73.8 

46.1 

47 

124.7 

77.9 

07 

175.5 

109.7 

67 

226.4 

141.5 

28 

23.7 

14.8 

88 

74.6 

46.6 

48 

125.5 

78.4 

08 

176.4 

110.2 

68 

227.3 

142.0 

29 

24.6 

15.4 

89 

75.5 

47.2 

49 

126.4 

79.0 

09 

177.2 

110.8 

69 

228.1 

142.  5 

30 

25.4 

15.9 

90 

76.3 

47.7 

50 

127.2 

79.5 

10 

178.1 

111.3 

70 

229.0 

143.1 

31 

26.3 

16.4 

91 

77.2 

48.2 

151 

128.1 

80.0 

211 

178.9 

111.8 

271 

229.8 

143.6 

32 

27.1 

17.0 

92 

78.0 

48.8 

52 

128.9 

80.5 

12 

179.8 

112.3 

72 

230.7 

144.1 

33 

28.0 

17.5 

93 

78.9 

49.3 

53 

129.8 

81.1 

13 

180.6 

112.9 

73 

231.5 

144.7 

34 

28.8 

18.0 

94 

79.7 

49.8 

54 

130.6 

81.6 

14 

181.5 

113.4 

74 

232.4 

145.2 

35 

29.7 

18.5 

95 

80.6 

50.3 

55 

131.4 

82.1 

15 

182.  3 

113.9 

75 

233.2 

145.7 

36 

30.5 

19.1 

96 

81.4 

50.9 

56 

132.3 

82.7 

16 

183.2 

114.5 

76 

234.1 

146.3 

37 

31.4 

19.6 

97 

82.3 

51.4 

57 

133.1 

83.2 

17 

184.0 

115.0 

77 

234.9 

146.8 

38 

32.2 

20.1 

98 

83.1 

51.9 

58 

134.0 

83.7 

18 

184.9 

115.5 

78 

235.8 

147.3 

39 

33.1 

20.7 

99 

84.0 

52.5 

59 

134.8 

84.3 

19 

185.7 

116.1 

79 

236.6 

147.8 

40 

33.9 

21.2 

100 

84.8 

53.0 

60 

135.7 

84.8 

20 

186.6 

116.6 

80 

237.5 
238.3 

148.4 

41 

34.8 

21.7 

101 

85.7 

53.5 

161 

136.5 

85.3 

221 

187.4 

117.1 

281 

148.9 

42 

35.6 

22.3 

02 

86.5 

54.1 

62 

137.4 

85.8 

22 

188.3 

117.6 

82 

239.1 

149.4 

43 

36.5 

22.8 

03 

87.3 

54.6 

63 

138.2 

86.4 

23 

189.1 

118.2 

83 

240.0 

150.0 

44 

37.3 

23.3 

04 

88.2 

55.1 

64 

139.1 

86.9 

24 

190.0 

118.7 

84 

240.8 

150.5 

45 

38.2 

23.8 

05 

89.0 

55.6 

65 

139.9 

87.4 

25 

190.8 

119.2 

85 

241.7 

151.0 

46 

39.0 

24.4 

06 

89.9 

56.2 

66 

140.8 

88.0 

26 

191.7 

119.8 

86 

242.5 

151.6 

47 

39.9 

24.9 

07 

90.7 

56.7 

67 

141.6 

88.5 

27 

192.5 

120.3 

87 

243.4 

152.1 

48 

40.7 

25.4 

08 

91.6 

57.2 

68 

142.5 

89.0 

28 

193.4 

120.8 

88 

244.2 

152. 6 

49 

41.6 

26.0 

09 

92.4 

57.8 

69 

143.3 

89.6 

29 

194.2 

121.4 

89 

245.1 

153.1 

50 

42.4 

26.5 

10 

93.3 

58.3 

70 

144.2 

90.1 

30 

195.1 

121.9 

90 

245.9 

153.7 

51 

43.3 

27.0 

111 

94.1 

58.8 

171 

145.0 

90.6 

231 

195.9 

122.4 

291 

246.8 

154.2 

52 

44.1 

27.6 

12 

95.0 

59.4 

72 

145.9 

91.1 

32 

196.7 

122.9 

92 

247.6 

154.7 

53 

44.9 

28.1 

13 

95.8 

59.9 

73 

146.7 

91.7 

33 

197.6 

123.5 

93 

248.5 

155.3 

54 

45.8 

28.6 

14 

96.7 

60.4 

74 

147.6 

92.2 

34 

198.4 

124.0 

94 

249.3 

155.8 

55 

46.6 

29.1 

15 

97.5 

60.9 

75 

148.4 

92.7 

35 

199.  3 

124.5 

95 

250.2 

156.3 

56 

47.5 

29.7 

16 

98.4 

61.5 

76 

149.3 

93.3 

36 

200.1 

125.1 

96 

251.0 

156.9 

57 

48.3 

30.2 

17 

99.2 

62.0 

77 

150.1 

93.8 

37 

201.0 

125.6 

97 

251.9 

157,4 

58 

49.2 

30.7 

18 

100.1 

62.5 

78 

151.0 

94.3 

38 

201.8 

126.1 

98 

252.7 

157.9 

59 

50.0 

31.3 

19 

100.9 

63.1 

79 

151.8 

94.9 

39 

202.7 

126.7 

99 

253.6 

158.4 

60 

50.9 

31.8 

20 

101.8 

63.6 

80 

152.6 

95.4 

40 

203.5 

127.2 

300 

254.4 

159.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

{ 

58°   (122°,  238°,  302' 

). 

: 

TABLE  2. 

[Page  595 

Difference  of  Latitude  and  Departure  for  32°  (148°,  212°,  328* 

). 

[DIst. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

255.3 

159.5 

361 

306.2 

191.3 

421 

357.0 

223.1 

481 

407.9 

254.9 

541 

458.8 

286.7 

0*2 

256.1 

160.0 

62 

307.0 

191.8 

22 

367.9 

223.6 

82 

408.8 

266.4 

42 

459.6 

287.2 

03 

257.0 

160.5 

63 

307.9 

192.3 

23 

368.7 

224.1 

83 

409.6 

255.9 

43 

460.6 

287.7 

04 

257.8 

161.1 

64 

308.7 

192.9 

24 

359. 6 

224.7 

84 

410.6 

256.5 

44 

461.3 

288.3 

05 

258.7 

161.6 

65 

309.5 

193.4 

25 

360.4 

225.2 

85 

411.3 

267.0 

45 

462.2 

288.8 

06 

259.5 

162.1 

66 

310. 4 

193.9 

26 

361.3 

225.7 

86 

412.2 

257.5 

46 

463.0 

289.3 

07 

260.4 

162.7 

67 

311.2 

194.5 

27 

362.1 

226.3 

87 

413.0 

258.1 

47 

463.9 

289.9 

08 

261.2 

163.2 

68 

312.1 

195.0 

28 

363.0 

226.8 

88 

413.9 

258.6 

48 

464.7 

290.4 

09 

262.1 

163.7 

69 

312.9 

195.5 

29 

363. 8 

227.3 

89 

414.7 

259.1 

49 

466.6 

290.9 

10 

262.9 

164.3 
164.8 

70 
371 

313.8 

196.0 

30 

364.7 

227.8 

90 

416.6 

259.6 

50 

466.4 

291.5 

311 

263.8 

314.6 

196.6 

431 

365.6 

228.4 

491 

416.4 

260.2 

551 

467.3 

292.0 

12 

264.6 

165.3 

72 

315.5 

197.1 

32 

366.4 

228.9 

92 

417.3 

260.7 

52 

468.1 

292.5 

13 

265.4 

165.8 

73 

316.3 

197.6 

33 

367.2 

229.4 

93 

418.1 

261.2 

53 

469.0 

293.0 

14 

266.3 

166.4 

74 

317.2 

198.2 

34 

368. 1 

230.0 

94 

419.0 

261.8 

54 

469.8 

293.6 

15 

267.1 

166.9 

75 

318.0 

198.7 

35 

368.9 

230.5 

95 

419,8 

262.3 

65 

470.7 

294.1 

16 

268.0 

167.4 

76 

318.9 

199.2 

36 

369.8 

231.0 

96 

420.6 

262.8 

56 

471.6 

294.6 

17 

268.8 

168.0 

77 

319.7 

199.8 

37 

370.6 

231.6 

97 

421.5 

263.4 

57 

472.4 

295.2 

18 

269.7 

168.5 

78 

320.6 

200.3 

38 

371.5 

232.1 

98 

422. 3 

263,9 

58 

473.2 

295.7 

19 

270.5 

169.0 

79 

321.4 

200,8 

39 

372.3 

232.6 

99 

423.2 

264.4 

69 

474.1 

296.2 

20 

271.4 

169.6 

80 

322.3 

201.3 

40 

373.2 

233.1 

500 

424.0 

265.0 

60 

474.9 

296.7 

321 

272.2 

170.1 

381 

323.1 

201.9 

441 

374.0 

233.7 

601 

424.9 

26.5.  5 

561 

475.8 

297.3 

22 

273.1 

170.6 

82 

324.0 

202.4 

42 

374.8 

234.2 

02 

425.7 

266.0 

62 

476.6 

297.8 

23 

273.9 

171.1 

83 

324.8 

202.9 

43 

375.7 

234.7 

03 

426.6 

266.5 

63 

477.5 

298.3 

24 

274.8 

171.7 

84 

325.7 

203.5 

44 

376.5 

235.3 

04 

427.4 

267.1 

64 

478.3 

298.9 

25 

275.6 

172.2 

85 

326.5 

204.0 

45 

377.4 

235.8 

05 

428.3 

267.6 

65 

479.2 

299.4 

26 

276.5 

172.7 

86 

327.4 

204.5 

46 

378.2 

236.3 

06 

429.1 

268.1 

66 

480.0 

299.9 

27 

277.3 

173.3 

87 

328.2 

205.1 

47 

379.1 

236.9 

07 

430.0 

268.7 

67 

480.9 

300.5 

28 

278.2 

173.8 

88 

329.1 

205.6 

48 

379.9 

237.4 

08 

430.8 

269.2 

68 

481.7 

301.0 

29 

279.0 

174.3 

89 

329.9 

206.1 

49 

380.8 

237.9 

09 

431.7 

269.7 

69 

482.6 

301.5 

30 

279.9 

174.9 

90 

330.8 

206.6 

50 

381.6 

238.  4 

10 

432.5 

270.3 

70 

483.4 

302.1 

331 

280.7 

175.4 

391 

331.  6 

207.2 

451 

382.5 

239.0 

511 

433.4 

270.8 

571 

484.3 

302.6 

32 

281.6 

176.9 

92 

332.5 

207.7 

52 

383.3 

239.  5 

12 

434.2 

271.4 

72 

486.1 

303.2 

33 

282.4 

176.4 

93 

333.3 

208.2 

53 

384.2 

240.0 

13 

435.1 

271.9 

73 

486.0 

303.  7 

34 

283.3 

177.0 

94 

334.2 

208.8 

54 

385.0 

240.6 

14 

436.9 

272.4 

74 

486.8 

304.2 

35 

284.1 

177.5 

95 

335.0 

209.3 

55 

385.9 

241.1 

16 

436.8 

272.9 

75 

487.7 

304.7 

36 

285.0 

178.0 

96 

335.8 

209.8 

56 

386.7 

241.6 

16 

437.6 

273.5 

76 

488.6 

305.3 

37 

285.8 

178.6 

97 

336.7 

210.4 

57 

387.6 

242.2 

17 

438.5 

274.0 

77 

489.4 

305.8 

38 

286.7 

179.1 

98 

337.5 

210.9 

58 

388.4 

242.7 

18 

439.3 

274.5 

78 

490.2 

306.3 

39 

287.5 

179.6 

99 

338.4 

211.4 

59 

389.3 

243.2 

19 

440.2 

275.0 

79 

491.1 

306.8 

40 

288.3 

180.2 

400 

339.2 

211.9 

60 

390.1 

243.8 

20 

441.0 

276.6 

80 

491.9 

307.4 

341 

289.2 

180.7 

401 

340.1 

212.5 

461 

391.0 

244.3 

521 

441.9 

276.1 

581 

492.8 

307.9 

42 

290.0 

181.2 

02 

340.9 

213.0 

62 

391.8 

244.8 

22 

442.7 

276.6 

82 

493,6 

308.4 

43 

290.9 

181.7 

03 

341.8 

213.5 

63 

392.7 

245.4 

23 

443.6 

277.2 

83 

494.5 

309.0 

44 

291.7 

182.3 

04 

342.6 

214.1 

64 

393.5 

246.9 

24 

444.4 

277.7 

84 

495.  3 

309.5 

45 

292.6 

182.8 

05 

343.5 

214.6 

66 

394.4 

246.4 

25 

445.3 

278.2 

85 

496.2 

310.0 

46 

293.4 

183.3 

06 

344.3 

215.1 

66 

395.2 

246.9 

26 

446.1 

278.7 

86 

497.0 

310.6 

47 

294.3 

183.9 

07 

345.2 

215.7 

67 

396.0 

247.5 

27 

446.9 

279.3 

87 

497.8 

311.1 

48 

295.1 

184.4 

08 

346.0 

216.2 

68 

396.9 

248.0 

28 

447.8 

279.8 

88 

498.7 

311.6 

49 

296.0 

184.9 

09 

346.9 

216.7 

69 

397.7 

248.5 

29 

448.6 

280.3 

89 

499.5 

312.1 

50 

296.8 

185.4 

10 

347.7 

217.2 

70 

398.6 

249.0 

30 

449.5 

280,9 

90 

500.3 

312.6 

351 

297.7 

186.0 

411 

348.6 

217.8 

471 

399.4 

249.6 

531 

450.3 

281,4 

591 

601.2 

313.2 

52 

298.5 

186.5 

12 

349.4 

218.3 

72 

400.3 

250.1 

32 

461.1 

281,9 

92 

502.0 

313.7 

53 

299.4 

187.0 

13 

350.3 

218.8 

73 

401.1 

250.6 

33 

462.0 

282.4 

93 

502.9 

314.2 

54 

300.2 

187.6 

14 

351.1 

219.4 

74 

402.0 

251.2 

34 

452.8 

283.0 

94 

503.7 

314.8 

55 

301.1 

188.1 

15 

352.0 

219.9 

75 

402.8 

261.7 

35 

453.7 

283.5 

95 

504.6 

315.3 

56 

301.9 

188.6 

16 

352.8 

220.4 

76 

403.7 

262.2 

36 

464.6 

284.0 

96 

605.4 

315.8 

57 

302.8 

189.2 

17 

353.6 

221.0 

77 

404.5 

252.8 

37 

465.4 

284.6 

97 

606.2 

316.4 

58 

303.6 

189.7 

18 

354.5 

221.5 

78 

405.4 

253.3 

38 

456.2 

285.1 

98 

607.1 

316.9 

59 

304.5 

190.2 

19 

355.3 

222.0 

79 

406.2 

253.8 

39 

457.1 

286.6 

•99 

508.0 

317.4 

60 

305.  3 

190.8 

20 

356.2 

222.5 

80 

407.1 

254.3 

40 

457.9 

286.2 

600 

508. 8     318. 0  1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.    1 

5 

8°  (122°,  238°,  302° 

)• 

1 

Page  596] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  33°  (147°,  213",  327= 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

as 

0.5 

61 

51.2 

33.2 

121 

101.5 

65.9 

181 

151.8 

98.6 

241 

202.1 

131.3 

2 

L7 

1.1 

62 

52.0 

33.8 

22 

102.3 

66.4 

82 

152.6 

99.1 

42 

203.0 

131.8 

3 

2.5 

1.6 

63 

52.8 

34.3 

23 

103.2 

67.0 

83 

153.5 

99.7 

43 

203.8 

132.3 

4 

8.4 

2.2 

64 

53.7 

34.9 

24 

104.0 

67.5 

84 

154.3 

100.2 

44 

204.6 

132.9 

5 

4.2 

2.7 

65 

54.5 

35.4 

25 

104.8 

68.1 

85 

155.2 

100.8 

45 

205.5 

133.4 

6 

5.0 

8.3 

66 

55.4 

35.9 

26 

105.  7  i  68. 6 

86 

156.0 

101.3 

46 

206.3 

134.0 

7 

5.9 

3.8 

67 

56.2 

36.5 

27 

106.5 

69.2 

87 

156.8 

101.8 

47 

207.2 

134.5 

8 

6.7 

4.4 

68 

57.0 

37.0 

28 

107.3 

69.7 

88 

157.7 

102.4 

48 

208.0 

135.1 

9 

7.5 

4.9 

69 

57.9 

37.6 

29 

108.2 

70.3 

89 

158.5 

102.9 

49 

208.8 

135.6 

10 

8.4 

5.4 

70 

58.7 

38.1 

30 

109.0 

70.8 

90 

159.3 

103.5 

50 

209.7 
210.5' 

136.2 

11 

9.2 

6.0 

71 

59.5 

38.7 

131 

109.9 

71.3 

191 

160.2 

104.0 

251 

136.7 

12 

10.1 

6,5 

72 

60.4 

39.2 

32 

110.7 

71.9 

92 

161.0 

104.6 

52 

211.3 

137.2 

13 

10.9 

7.1 

73 

61.2 

39.8 

33 

111.5 

72.4 

93 

161.9 

105.1 

53 

212.2 

137.8 

14 

11.7 

7.6 

74 

62.1 

40.3 

34 

112.4 

73.0 

94 

162.7 

105.7 

54 

213.0 

138.3 

15 

12.6 

8.2 

75 

62.9 

40.8 

35 

113.2 

73.5 

95 

163.5 

106.2 

55 

213.9 

138.9 

16 

13.4 

8.7 

76 

63.7 

41.4 

36 

114.1 

74.1 

96 

164.4 

106.7 

56 

214.7 

139.4 

17 

14.3 

9.3 

77 

64.6 

41.9 

37 

114.9 

74.6 

97 

165.2 

107.3 

57 

215.5 

140.0 

18 

15.1 

9.8 

78 

65.4 

42.5 

38 

115.7 

75.2 

98 

166.1 

107.8 

58 

216.4 

140.5 

19 

15.9 

10.3 

79 

66.3 

43.0 

39 

116.6 

75.7 

99 

166.9 

108.4 

59 

217.2 

141.1 

20 

16.8 

10.9 

80 

67.1 

43.6 

40 

117.4 

76.2 

200 

167.7 

108.9 

60 

218.1 
218.9 

141.6 

21 

17.6 

11.4 

81 

67.9 

44.1 

141 

118.3 

76.8 

201 

168.6 

109.5 

261 

142.2 

22 

18.5 

12.0 

82 

68.8 

44.7 

42 

119.1 

77.3 

02 

169.4 

110.0 

62 

219.7 

142.7 

23 

19.3 

12.5 

83 

69.6 

45.2 

43 

119.9 

77.9 

03 

170.3 

110.6 

63 

220.6 

143.2 

24 

20.1 

13.1 

84 

70.4 

45.7 

44 

120.8 

78.4 

04 

171.1 

111.1 

64 

221.4 

143.8 

25 

21.0 

13.6 

85 

71.3 

46.3 

45 

121.6 

79.0 

05 

171.9 

111.7 

65 

222.2 

144.3 

26 

21.8 

14.2 

86 

72.1 

46.8 

46 

122.4 

79.5 

06 

172.8 

112.2 

66 

223.1 

144.9 

27 

22.6 

14.7 

87 

73.0 

47.4 

47 

123.3 

80.1 

07 

173.6 

112.7 

67 

223.9 

145.4 

28 

23.5 

15.2 

88 

73.8 

47.9 

48 

124.1 

80.6 

08 

174.4 

113.3 

68 

224.8 

146.0 

29 

,   24.3 

15.8 

89 

74.6 

48.5 

49 

125.0 

81.2 

09 

175.3 

113.8 

69 

225.6 

146.5 

30 
31 

25.2 
26.0 

16.3 

90 

75.5 

49.0 

50 

125.8 

81.7 

10 

176.1 

114.4 

70 

226.4 

147.1 

16.9 

9il 

76.3 

49.6 

151 

126.6 

82.2 

211 

177.0 

114.9 

271 

227.3 

147.6 

32 

26.8 

17.4 

92 

77.2 

50.1 

52 

127.5 

82.8 

12 

177.8 

115.5 

72 

228.1 

148.1 

33 

27.7 

18.0 

93 

78.0 

50.7 

53 

128.3 

83.3 

13 

178.6 

116.0 

73 

229.0 

148.7 

34 

28.5 

18.5 

94 

78.8 

51.2 

54 

129.2 

83.9 

14 

179.5 

116.6 

74 

229.8 

149.2 

35 

29.4 

19.1 

95 

79.7 

51.7 

55 

130.0 

84.4 

15 

180.3 

117.1 

75 

230.6 

149.8 

36 

30.2 

19.6 

96 

80.5 

52.3 

56 

130.8 

85.0 

16 

181.2 

117.6 

76 

231.5 

150.3 

37 

31.0 

20.2 

97 

81.4 

52.8 

57 

131.7 

85.5 

17 

182.0 

118.2 

77 

232.3 

150.9 

38 

31.9 

20.7 

98 

82.2 

53.4 

58 

132.5 

86.1 

18 

182.8 

118.7 

78 

233.2 

151.4 

39 

32.7 

21.2 

99 

83.0 

53.9 

59 

133.3 

86.6 

19 

183.7 

119.3 

79 

234.0 

152.0 

40 

33.5 

21.8 

100 

83.9 

54.5 

60 

134.2 

87.1 

20 

184.5 

119.8 

80 

234.8 

152.5 

41 

34.4 

22.3 

101 

84.7 

55.0 

161 

135.0 

87.7 

221 

185.3 

120.4 

281 

235.7 

153.0 

42 

35.2 

22.9 

02 

85.5 

55.6 

62 

135.9 

88.2 

22 

186.2. 

120.9 

82 

236.5 

153.6 

43 

36.1 

23.4 

03 

86.4 

56.1 

63 

136.7 

88.8 

23 

187.0 

121.5 

83 

237.3 

154.1 

44 

36.9 

24.0 

04 

87.2 

56.6 

64 

137.5 

89.3 

24 

187.9 

122.0 

84 

238.2 

154.7 

45 

37.7 

24.5 

05 

88.1 

57.2 

65 

138.4 

89.9 

25 

188.7 

122.5 

85 

239.0 

155.2 

46 

38.6 

25.1 

06 

88.9 

57.7 

66 

139.2 

90.4 

26 

189.5 

123.1 

86 

239.9 

155.8 

47 

39.4 

25.6 

07 

89.7 

58.3 

67 

140.1 

91.0 

27 

190.4 

123.6 

87 

240.7 

156.3 

48 

40.3 

26.1 

08 

90.6 

58.8 

68 

140.9 

91.5 

28 

191.2 

124.2 

88 

241.5 

156.9 

49 

41.1 

26.7 

09 

91.4 

59.4 

69 

141.7 

92.0 

29 

192.1 

124.7 

89 

242.4 

157.4 

50 
51 

41.9 

27.2 

10 

92.3 

59.9 

70 

142.6 

92.6 

30 

192.9 

125.3 

90 

243.2 

157.9 

42.8 

27.8 

111 

93.1 

60.5 

171 

143.4 

93.1 

231 

193.7 

125.8 

291 

244.1 

158.5 

52 

43.6 

28.3 

12 

93.9 

61.0 

72 

144.3 

93.7 

32 

194.6 

126.4 

92 

244.9 

159.0 

53 

44.4 

28.9 

13 

94.8 

61.5 

73 

145.1 

94.2 

33 

195.4 

126.9 

93 

245.7 

159.6 

54 

45.3 

29.4 

14 

95.6 

62.1 

74 

145.9 

94.8 

34 

196.2 

127.4 

94 

246.6 

160.1 

55 

46.1 

30.0 

15 

96.4 

62.6 

75 

146.8 

95.3 

35 

197.1 

128.0 

95 

247.4 

160.7 

56 

47.0 

30.5 

16 

97.3 

63.2 

76 

147.6 

95.9 

36 

197.9 

128.5 

96 

248.2 

161.2 

57 

47.8 

31.0 

17 

98.1 

63.7 

77 

148.4 

96.4 

37 

198.8 

129.1 

97 

249.1 

161.8 

58 

48.6 

31.6 

18 

99.0 

64.3 

78 

149.3 

96.9 

38 

199.6 

129.6 

98 

249.9 

162.3 

59 

49.5 

32.1 

19 

99.8 

64.8 

79 

150.1 

97.5 

39 

200.4 

130.2 

99 

250.8 

162.8 

60 

50.3 

32.7 

20 

100.6 

65.4 

80 

151.0 

98.0 

40 

201.3 

130.7 

300 

251.6 

163.4 

Dlst. 

Dep. 

Lat. 

Diat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

5 

7°  (15 

J3°,  237°,  303°) 

. 

TABLE  2. 

[Page  597 

Difference  of  Latitude  and  Departure  for  33°  (147°,  213°,  327' 

)• 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

:Dist. 

Lat. 

Dep. 

301 

252.4 

163.9 

361 

302.8 

196.6 

421 

353.1 

229.3 

481 

403.4 

262.0 

541 

453.7 

294.6 

02 

253.3 

164.4 

62 

303.6 

197.1 

22 

363.9 

229.8 

82 

404.2 

262.5 

42 

464.6 

296.2 

03 

254.1 

165.0 

63 

304.4 

197.7 

23 

364.7 

230.4 

83 

405.1 

263.1 

43 

455.4 

296.7 

04 

255.0 

165.5 

64 

305.3 

198.2 

24 

356.6 

230.9 

84 

405.9 

263.6 

44 

456.2 

296.2 

05 

255.8 

166.1 

65 

306.1 

198.8 

26 

356.4 

231.4 

86 

406.7 

264.1 

45 

467.1 

296.8 

06 

256.6 

166.6 

66 

307.0 

199.3 

26 

357.3 

232.0 

86 

407.6 

264.7 

46 

467.9 

297.3 

07 

257.5 

167.2 

67 

307.8 

199.8 

27 

358.1 

232.5 

87 

408.4 

265.2 

47 

458.8 

297.9 

08 

258.3 

167.7 

68 

308.6 

200.4 

28 

359.0 

233.1 

88 

409.3 

266.8 

48 

459.6 

298.4 

09 

259.2 

168.3 

69 

309.5 

200.9 

29 

359.8 

233.6 

89 

410.1 

266.3 

49 

460.4 

299.0 

10 

260.0 

168.8 

70 

310.3 

201.6 

30 

360.6 

234.2 

90 

411.0 

266.8 

60 

461.3 

299.5 

311 

260.8 

169.3 

371 

311.2 

202.0 

431 

361.6 

234.7 

491 

411.8 

267.4 

651 

462.1 

300.1 

12 

261.7 

169.9 

72 

312.0 

202.6 

32 

362.3 

235.2 

92 

412.6 

267.9 

52 

463.0 

300.6 

13 

262.5 

170.4 

73 

312.8 

203.1 

33 

363.1 

235.8 

93 

413.6 

268.6 

63 

463.8 

301.2 

14 

263.3 

171.0 

74 

313.7 

203.7 

34 

364.0 

236.3 

94 

414.3 

269.0 

64 

464.6 

301.7 

15 

264.2 

171.5 

75 

314.5 

204.2 

36 

364.8 

236.9 

95 

416.1 

269.6 

55 

465.5 

302.3 

16 

265.0 

172.1 

76 

315.3 

204.7 

36 

366.7 

237.4 

96 

416.0 

270.1 

56 

466.3 

302.9 

17 

265.9 

172.6 

77 

316.2 

205.3 

37 

366.5 

238.0 

97 

416.8 

270.7 

57 

467.2 

303.4 

18 

266.7 

173.2 

78 

317.0 

205.8 

38 

367.3 

238.5 

98 

417.6 

271.2 

58 

468.0 

303.9 

19 

267.5 

173.7 

79 

317.9 

206.4 

39 

368.2 

239.1 

99 

418.5 

271.8 

69 

468.8 

304.5 

20 

268.4 

174.2 

80 

318.7 

206.9 

40 

369.0 

239.6 

500 

419.3 

272.3 

60 

469.7 

305.0 

321 

269.2 

174.8 

381 

319.6 

207.6 

441 

369.9 

240.1 

601 

420.2 

272.8 

661 

470.5 

305.5 

22 

270.1 

175.3 

82 

320.4 

208.0 

42 

370.7 

240.7 

02 

421.0 

273.4 

62 

471.3 

306.1 

23 

270.9 

176.9 

83 

321.2 

208.6 

43 

371.6 

241.2 

03 

421.9 

273.9 

63 

472.2 

306.6 

24 

271.7 

176.4 

84 

322.1 

209.1 

44 

372.4 

241.8 

04 

422.7 

274.5 

64 

473.0 

307.2 

25 

272.6 

177.0 

85 

322.9 

209.6 

46 

373.2 

242.3 

06 

423.5 

275.0 

65 

473.8 

307.7 

26 

273.4 

177.5 

86 

323.7 

210.2 

46 

374.1 

242.9 

06 

424.4 

276.6 

66 

474.7 

308.3 

27 

274.2 

178.1 

87 

324.6 

210.7 

47 

374.9 

243.4 

07 

425.2 

276.1 

67 

475.5 

308.8 

28 

275.1 

178.6 

88 

325.4 

211.3 

48 

375.7 

244.0 

08 

426.0 

276.7 

68 

476.4 

309.4 

29 

275.9 

179.1 

89 

326.2 

211.8 

49 

376.6 

244.5 

09 

426.9 

277.2 

69 

477.2 

309.9 

30 

276.8 

179.7 

90 

327.1 

212.4 
212. 9 

50 

377.4 

245.1 

10 

427.7 

277.8 

70 

478.0 

310.4 

331 

277.6 

180.2 

391 

327.9 

451 

378.2 

245.6 

511 

428.5 

278.3 

571 

478.9 

311.0 

32 

278.4 

180.8 

92 

328.8 

213.6 

52 

379.1 

246.1 

12 

429.4 

278.8 

72 

479.7 

311.6 

33 

279.3 

181.3 

93 

329.6 

214.0 

53 

379.9 

246.7 

13 

430.2 

279.4 

73 

480.6 

312.0 

34 

280.1 

181.9 

94 

330.4 

214.6 

54 

380.8 

247.2 

14 

431.1 

279.9 

74 

481.4 

312.6 

35 

281.0 

182.4 

95 

331.3 

215.1 

56 

381.6 

247.8 

16 

431.9 

280.4 

75 

482.2 

313.1 

36 

281.8 

183.0 

96 

332.1 

215.6 

56 

382.4 

248.3 

16 

432.7 

281.0 

76 

483.1 

313.7 

37 

282.6 

183.5 

97 

333.0 

216.2 

57 

383.3 

248.9 

17 

433.6 

281.5 

77 

483.9 

314.2 

38 

283.5 

184.1 

98 

333.8 

216.7 

58 

384.1 

249.4 

18 

434.4 

282.1 

78 

484.7 

314.8 

39 

284.3 

184.6 

99 

334.6 

217.3 

69 

385.0 

260.0 

19 

436.3 

282.6 

79 

485.6 

315.3 

40 

285.2 

185.1 

400 

335.5 

217.8 

60 

386.8 

250.5 

20 

436.1 

283.2 

80 

486.4 

315.9 

341 

286.0 

185.7 

401 

336.3 

218.4 

461 

386.6 

261.0 

521 

436.9 

283.7 

581 

487.2 

316.4 

42 

286.8 

186.2 

02 

337.1 

218.9 

62 

387.  6 

251.6 

22 

437.8 

284.3 

82 

488.1 

317.0 

43 

287.7 

186.8 

03 

338.0 

219.6 

63 

388.3 

252.1 

23 

438.6 

284.8 

83 

488.9 

317.5 

44 

288.5 

187.3 

04 

338.8 

220.0 

64 

389.1 

252.7 

24 

439.4 

286.4 

84 

489.8 

318.1 

45 

289.3 

187.9 

05 

339.7 

220.5 

65 

390.0 

263.2 

26 

440.3 

285.9 

86 

490.6 

318.6 

46 

290.2 

188.4 

06 

340.5 

221.1 

66 

390.8 

263.8 

26 

441.1 

286.5 

86 

491.5 

319.2 

47 

291.0 

189.0 

07 

341.3 

221.6 

67 

391.7 

254.3 

27 

442.0 

287.0 

87 

492.3 

319.7 

48 

291.9 

189.5 

08 

342.2 

222.2 

68 

392.5 

264.9 

28 

442.8 

287.5 

88 

493.1 

320.2 

49 

292.7 

190.0 

09 

343.0 

222.7 

69 

393.3 

265.4 

29 

443.6 

288.1 

89 

494.0 

320.8 

50 

293.5 

190.6 

10 

343.9 

223.3 

70 

394.2 

255.9 

30 

444.6 

288.6 

90 

494.8 

321.3 

351 

294.4 

191.1 

411 

344.7 

223.8 

471 

395.0 

256.6 

531 

445.3 

289.2 

591 

496.7 

321.9 

52 

295.2 

191.7 

12 

345.5 

224.4 

72 

395.8 

267.0 

32 

446.1 

289.7 

92 

496.6 

322.4 

53 

296.1 

192.2 

13 

346.4 

224.9 

73 

396.7 

267.6 

33 

447.0 

290.3 

93 

497.3 

322.9 

54 

296.9 

192.8 

14 

347.2 

225.4 

74 

397.5 

258.1 

34 

447.8 

290.8 

94 

498.1 

323.6 

55 

297.7 

193.3 

15 

348.1 

226.0 

75 

398.3 

258.7 

35 

448.7 

291.4 

95 

499.0 

324.1 

56 

298.6 

193.9 

16 

348.9 

226.5 

76 

399.2 

269.2 

36 

449.6 

291.9 

96 

499.8 

324.6 

57 

299.4 

194.4 

17 

349.7 

227.1 

77 

400.0 

259.8 

37 

460.3 

292.6 

97 

600.6 

325.1 

58 

300.2 

194.9 

18 

350.6 

227.6 

78 

400.9 

260.3 

38 

451.2 

293.0 

98 

501.5 

326.7 

59 

301.1 

195.5 

19 

361.4 

228.2 

79 

401.7 

260.9 

39 

452.0 

293.6 

99 

502.3 

326.2 

60 

301.9 

196.0 

20 

362.2 

228.7 

80 
Dist. 

402.6 

261.4 

40 

452.9 

294.1 

600 

503.2 

326.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

57°  (1 

23°,  237°,  303°] 

. 

Page  598] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  34°  (146°,  214 

°,  326° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.6 

34.1 

121 

100.3 

67.7 

181 

150.1 

101.2 

241 

199.8 

134.8 

2 

1.7 

1.1 

62 

51.4 

34.7 

22 

101.1 

68.2 

82 

150.9 

101.8 

42 

200.6 

135.3 

3 

2.5 

1.7 

63 

52.2 

35.2 

23 

102.0 

68.8 

83 

151.7 

102.3 

43 

201.5 

135.9 

4 

3.3 

2.2 

64 

53.1 

35.8 

24 

102.8 

69.3 

84 

152.  5 

102.9 

44 

202.3 

136.4 

6 

4.1 

2.8 

65 

53.9 

36.3 

25 

103.6 

69.9 

85 

153.4 

103.5 

45 

203.1 

137.0 

6 

5.0 

3.4 

66 

54.7 

36.9 

26 

104.5 

70.5 

86 

154.2 

104.0 

46 

203.9 

137.6 

7 

5.8 

3.9 

67 

55.5 

37.5 

27 

105.3 

71.0 

87 

155.0 

104.6 

47 

204.8 

138.1 

8 

6.6 

4.5 

68 

56.4 

38.0 

28 

106.1 

71.6 

88 

155.9 

105.1 

48 

205.6 

138.7 

9 

7.5 

5.0 

69 

57.2 

38.6 

29 

106.9 

72.1 

89 

156.7 

105.7 

49 

206.4 

139.2 

10 

8.3 

5.6 

70 

58.0 
58.9 

39.1 

30 

107.8 

72.7 

90 

157.5 

106.2 

50 

207.3 
208.1 

139.8 

11 

9.1 

6.2 

71 

39.7 

131 

108. 6 

73.3 

191 

158.3 

106.8 

251 

140.4 

12 

9.9 

6.7 

72 

59.7 

40.3 

32 

109.4 

73.8 

92 

159.2 

107.4 

52 

208.9 

140.9 

13 

10.8 

7.3 

73 

60.5 

40.8 

33 

110.3 

74.4 

93 

160.0 

107.9 

53 

209.7 

141.5 

14 

11.6 

7.8 

74 

61.3 

41.4 

34 

111.1 

74.9 

94 

160.8 

108.5 

54 

210.6 

142.0 

15 

12.4 

8.4 

75 

62.2 

41.9 

35 

111.9 

75.5 

95 

161.7 

109.0 

55 

211.4 

142.6 

16 

13.3 

8.9 

76 

63.0 

42.5 

36 

112.7 

76.1 

96 

162.5 

109.6 

56 

212.2 

143.2 

17 

14.1 

9.5 

77 

63.8 

43.1 

37 

113.6 

76.6 

97 

163.3 

110.2 

57 

213.1 

143.7 

18 

14.9 

10.1 

78 

64.7 

43.6 

38 

114.4 

77.2 

98 

164.1 

110.7 

58 

213.9 

144.3 

19 

15.8 

10.6 

79 

65.5 

44.2 

39 

115.2 

77.7 

99 

165.0 

111.3 

59 

214.7 

144.8 

20 

16.6 

11.2 

80 

66.3 

44.7 

40 

116.1 

78.3 

200 

165.8 

111.8 

60 
261 

215.5 
216.4 

145.4 

21 

17.4 

11.7 

81 

67.2 

45.3 

141 

116.9 

78.8 

201 

166.6 

112.4 

145.9 

22 

18.2 

12.3 

82 

68.0 

45.9 

42 

117.7 

79.4 

02 

167.5 

113.0 

62 

217.2 

146.5 

23 

19.1 

12.9 

83 

68.8 

46.4 

43 

118.6 

80.0 

03 

168.3 

113.5 

63 

218.0 

147.1 

24 

19.9 

13.4 

84 

69.6 

47.0 

44 

119.4 

80.5 

04 

169.1 

114.1 

64 

218.9 

147.6 

25 

20.7 

14.0 

85 

70.5 

47.5 

45 

120.2 

81.1 

05 

170.0 

114.6 

65 

219.7 

148.2 

26 

21.6 

14.5 

86 

71.3 

48.1 

46 

121.0 

81.6 

06 

170.8 

115.2 

66 

220.5 

148.7 

27 

22.4 

15.1 

87 

72.1 

48.6 

47 

121.9 

82.2 

07 

171.6 

115.8 

67 

221.4 

149.3 

28 

23.2 

15.7 

88 

7.3.0 

49.2 

48 

122.7 

82.8 

08 

172.4 

116.3 

68 

222.2 

149.9 

29 

24.0 

16.2 

89 

73.8 

49.8 

49 

123.5 

83.3 

09 

173.3 

116.9 

69 

223.0 

150.4 

30 

24.9 

16.8 

90 

74.6 

50.3 

50 

124.4 

83.9 

10 

174.1 

117.4 

70 

223.8 

151.0 

31 

25.7 

17.3 

91 

75.4 

50.9 

1.51 

125.2 

84.4 

211 

174.9 

118.0 

271 

224.7 

151.5 

32 

26.5 

17.9 

92 

76.3 

51.4 

52 

126.0 

85.0 

12 

175.8 

118.5 

72 

225. 5 

152.1 

33 

27.4 

18.5 

93 

77.1 

52.0 

53 

126.8 

85.6 

13 

176.6 

119.1 

73 

226.3 

152.7 

34 

28.2 

19.0 

94 

77.9 

52.6 

54 

127.7 

86.1 

14 

177.4 

119.7 

74 

227.2 

153.2 

35 

29.0 

19.6 

95 

78.8 

53.1 

55 

128.5 

86.7 

15 

178.2 

120.2 

75 

228.0 

153.8 

36 

29.8 

20.1 

96 

79.6 

53.7 

56 

129.3 

87.2 

16 

179.1 

120.8 

76 

228.8 

154.3 

37 

30.7 

20.7 

97 

80.4 

54.2 

57 

130.2 

87.8 

17 

179.9 

121.3 

77 

229.6 

154.9 

38 

31.5 

21.2 

98 

81.2 

54.8 

58 

131.0 

88.4 

18 

180.7 

121.9 

78 

230.5 

155.5 

39 

32.3 

21.8 

99 

82.1 

55.4 

59 

131.8 

88.9 

19 

181.6 

122.5 

79 

231.3 

156. 0 

40 

33.2 

22.4 

100 

82.9 

55.9 

60 

132.6 

89.5 

20 

182.4 

123.0 

80 

232.1 

156.6 

41 

34.0 

22.9 

101 

83.7 

56.5 

161 

133.5 

90.0 

221 

183.2 

123.6 

281 

233.0 

157. 1 

42 

34.8 

23.5 

02 

84.6 

57.0 

62 

134.3 

90.6 

22 

184.0 

124.1 

82 

233.8 

157.7 

43 

35.6 

24.0 

03 

85.4 

57.6 

63 

135.1 

91.1 

23 

184.9 

124.7 

83 

234. 6 

158.3 

44 

36.5 

24.6 

04 

86.2 

58.2 

64 

136.0 

91.7 

24 

185.7 

125.3 

84 

235.4 

158.8 

45 

37.3 

25.2 

05 

87.0 

58.7 

65 

136.8 

92.3 

25 

186.5 

125.8 

85 

236.3 

159.4 

46 

38.1 

25.7 

06 

87.9 

59.3 

66 

137.6 

92.8 

26 

187.4 

126.4 

86 

237.1 

159.9 

47 

39.0 

26.3 

07 

88.7 

59.8 

67 

138.4 

93.4 

27 

188.2 

126.9 

87 

237.9 

160.5 

48 

39.8 

26.8 

08 

89.5 

60.4 

68 

139.3 

93.9 

28 

189.0 

127.5 

88 

238.8 

161.0 

49 

40.6 

27.4 

09 

90.4 

61.0 

69 

140.1 

94.5 

29 

189.8 

128.1 

89 

239.6 

161.6 

50 

41.5 

28.0 

10 

91.2 

61.5 

70 

140.9 

95.1 

30 

190.7 

128.6 

90 

240.4 
241.2 

162.2 
162.7 

51 

42.3 

28.5 

111 

92.0 

62.1 

171 

141.8 

95.6 

231 

191.5 

129.2 

291 

52 

43.1 

29.1 

12 

92.9 

62.6 

72 

142.6 

96.2 

32 

192.3 

129.7 

92 

242.1 

163.3 

53 

43.9 

29.6 

13 

93.7 

63.2 

73 

143.4 

96.7 

33 

193.2 

130.3 

93 

242.9 

163.8 

54 

44.8 

30.2 

14 

94.5 

63.7 

74 

144.3 

97.3 

34 

194.0 

130.9 

94 

243.7 

164.4 

55 

45.6 

30.8 

15 

95.3 

64.3 

75 

145.1 

97.9 

35 

194.8 

131.4 

95 

244.6 

165.0 

56 

46.4 

31.3 

16 

96.2 

64.9 

76 

145.9 

98.4 

36 

195.  7 

132.0 

96 

245.4 

165. 5 

57 

47.3 

31.9 

17 

97.0 

65.4 

77 

146.7 

99.0 

37 

196.5 

132.5 

97 

246.2 

166.1 

58 

48.1 

32.4 

18 

97.8 

66.0 

78 

147.6 

99.5 

38 

197.3 

133.1 

98 

247.1 

166.6 

59 

48.9 

33.0 

19 

98.7 

66.5 

79 

148.4 

100.1 

39 

198.1 

133.6 

99 

247.9 

167.2 

60 

49.7 

33.6 

20 

99.5 

67.1 

80 

149.2 

100.7 

40 

199.0 

134.2 

300 

248.7 

167.8 

Diet. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

1 

)6°  (1 

24°,  236 

°,  304° 

). 

TABLE  2. 

[Page  599     | 

Difference  of  Latitude  and  Departure  for  34°  (146°,  214 

»,  326° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

249.5 

168.3 

361 

299.3 

201.9 

421 

349.0 

235.4 

481 

398.8 

269.0 

541 

448.5 

302.5 

02 

250.4 

168.9 

62 

300.1 

202.4 

22 

349.9 

236.0 

82 

399.6 

269.5 

42 

449.4 

303.1 

03 

251.2 

169.4 

63 

300.9 

203.0 

23 

350.7 

236. 5 

83 

400.4 

270.1 

43 

450.2 

303.6 

04 

252.  0 

170.0 

64 

301.8 

203.5 

24 

351.5 

237.1 

84 

401.3 

270.6 

44 

451.0 

304.2 

05 

252.  9 

170.6 

65 

302.6 

204.1 

25 

352.3 

237.7 

85 

402.1 

271.2 

45 

451.8 

304.8 

06 

253.7 

171.1 

66 

303.4 

204.7 

26 

353.2 

238.2 

86 

402.9 

271.8 

46 

452.6 

305.3 

07 

254.5 

171.7 

67 

304.3 

205.2 

27 

354.0 

238.8 

87 

403.8 

272.3 

47 

453.5 

305.9 

08 

255.  3 

172.2 

68 

305.1 

205.8 

28 

354.8 

239.3 

88 

404.6 

272.8 

48 

454.3 

306.4 

09 

256.2 

172.8 

69 

305. 9 

206.3 

29 

355.7 

239.  9 

89 

405.4 

273.4 

49 

455.2 

307.0 

10 

257.0 

173.3 

70 

306.7 

206.9 

30 

356.5 
357.3 

240.4 

90 

406.2 

274.0 

50 

456.0 

307.5 

311 

257.8    173.9 

371 

307.6 

207.5 

431 

241.0 

491 

407.1 

274.6 

551 

456.8 

308.1 

12 

258.7  !l74.5 

72 

308.4 

208.0 

32 

358.1 

241.6 

92 

407.9 

275.1 

52 

457.6 

308.7 

13 

259.5    175.0 

73 

309.2 

208.6 

33 

359.0 

242.1 

93 

408.7 

275.7 

53 

458.4 

309.2 

14 

260.3 

175.6 

74 

310.1 

209.1 

34 

359.8 

242.7 

94 

409.5 

276.2 

54 

459.3 

309.8 

15 

261.2 

176.1 

75 

310.9 

209.7 

35 

360.6 

243.2 

95 

410.4 

276.8 

55 

460.1 

310.3 

16 

262.0 

176.7 

76 

311.7 

210.3 

36 

361.5 

243.8 

96 

411.2 

277.4 

56 

460.9 

310.9 

17 

262.8 

177.3 

77 

312.6 

210.8 

37 

362.3 

244.4 

97 

412.0 

277.9 

57 

461.7 

311.5 

18 

263.7 

177.8 

78 

313.4 

211.4 

38 

363.1 

244.9 

98 

412.8 

278.4 

58 

462.6 

312.0 

19 

264.5 

178.4 

79 

314.2 

211.9 

39 

364.0 

245.5 

99 

413.7 

279.0 

59 

463.4 

312.6 

20 

265.3 

178.9 

80 

315.0 

212.5 

40 

364.8 

246.0 

500 

414.5 

279.6 

60 

464.2 

313.1 

321 

266.1 

179.5 

381 

315.9 

213.0 

441 

365.6 

246.6 

501 

415.3 

280.1 

561 

465.1 

313.7 

22 

267.0 

180.1 

82 

316.7 

213.6 

42 

366.4 

247.2 

02 

416.2 

280.7 

62 

465.9 

314.3 

23 

267.8 

180.6 

83 

317.5 

214.2 

43 

367.3 

247.7 

03 

417.0 

281.3 

63 

466.8 

314.8 

24 

268.6 

181.2 

84 

318.4 

214.7 

44 

368.1 

248.3 

04 

417.8 

281.8 

64 

467.6 

315.4 

25 

269.5 

181.7 

85 

319.2 

215.3 

45 

368.9 

248.8 

05 

418.6 

282.4 

65 

468.4 

315.9 

26 

270.3 

182.3 

86 

320.0 

215.8 

46 

369.8 

249.4 

06 

419.4 

282.9 

66 

469.2 

316.5 

27 

271.1 

182.9 

87 

320.8 

216.4 

47 

370.6 

250.0 

07 

420.3 

283.5 

67 

470.1 

317.1 

28 

271.9 

183.4 

88 

321.7 

217.0 

48 

371.4 

250.5 

08 

421.1 

284.1 

68 

470.9 

317.6 

29 

272.8 

184.0 

89 

322.5 

217.5 

49 

372.2 

251.1 

09 

421.9 

284.6 

69 

471.7 

318.2 

30 

273.6 
274.4 

184.5 

90 

323.3 

218.1 

50 

373.1 

251.6 

10 

422.8 

285.2 

70 

472.6 

318.7 
319.3 

331 

185.1 

391 

324.2 

218.6 

451 

373.9 

252.2 

511 

423.6 

285.8 

571 

473.4 

32 

275.2 

185.6 

92 

325.0 

219.2 

52 

374.7 

252.8 

12 

424.4 

286.3 

72 

474.2 

319.9 

33 

276.1 

186.2 

93 

325.8 

219.8 

53 

375.6 

253.3 

13 

425.3 

286.9 

73 

475.0 

320.4 

34 

276.9 

186.8 

94 

326.6 

220.3 

54 

376.4 

253.9 

14 

426.1 

287.4 

74 

475.9 

321.0 

35 

277.7 

187.3 

95 

327.5 

220.9 

55 

377.2 

254.4 

15 

426.9 

288.0 

75 

476.7 

321.5 

36 

278.6 

187.9 

96 

328.3 

221.4 

56 

378.0 

255.0 

16 

427.8 

288.5 

76 

477.5 

322.1 

37 

279.4 

188.4 

97 

329.1 

222.0 

57 

378.9 

255.5 

17 

428.6 

289.1 

77 

478.3 

322.7 

38 

280.2 

189.0 

98 

330.0 

222.6 

58 

379.7 

256.1 

18 

429.4 

289.6 

78 

479.2 

323.2 

39 

281.0 

189.6 

99 

330.8 

223.1 

59 

380.5 

256.7 

19 

430.3 

290.2 

79 

480.0 

323.8 

40 

281.9 

190.1 

400 

331.6 

223.7 

60 

381.3 

257.2 

20 

431.1 

290.8 

80 

480.8 

324.3 

341 

282.  7 

190.7 

401 

332.4 

224. 2 

461 

382.2 

257.8 

521 

431.9 

291.3 

581 

481.6 

324.9 

42 

283.5 

191.2 

02 

333.3 

224.8 

62 

383.0 

258.3 

22 

432.8 

291.9 

82 

482.5 

325.4 

43 

284.4 

191.8 

03 

334.1 

225.4 

63 

383.8 

258.9 

23 

433.6 

292.5 

83 

483.3 

326.0 

44 

285.2 

192.4 

04 

334.9 

225.9 

64 

384.7 

259.5 

24 

434.4 

293.0 

84 

484.1 

326.6 

45 

286.0 

192.9 

05 

335.8 

226.5 

65 

385.5 

260.0 

25 

435.3 

293.6 

85 

485.0 

327.2 

46 

286.9 

193.5 

06 

336.6 

227.0 

66 

386.3 

260.6 

26 

436.1 

294.1 

86 

485.8 

327.7 

47 

287.7 

194.0 

07 

337.4 

227.6 

67 

387.2 

261.1 

27 

436.9 

294.7 

87 

486.6 

328.2 

48 

288.5 

194.6 

08 

338.3 

228.1 

68 

388.0 

261.7 

28 

437.8 

295.3 

88 

487.5 

328.8 

49 

289.3 

195.2 

09 

339.1 

228.7 

69 

388.8 

262.3 

29 

438.6 

295.8 

89 

488.3 

329.4 

50 

290.2 

195.7 

10 

339.9 

229.3 

70 

389.7 

262.8 

30 

439.4 

296.4 

90 

489.2 

329.9 

351 

291.0 

196.3 

411 

340.7 

229.8 

471 

390.5 

263.4 

531 

440.3 

296.9 

591 

490.0 

330.5 

52 

291.8 

196.8 

12 

341.6 

230.4 

72 

391.3 

263.9 

32 

441.1 

297.4 

92 

490.8 

331.0 

53 

292.7 

197.4 

13 

342.4 

230.9 

73 

392.1 

264.5 

33 

441.9 

298.0 

93 

491.6 

331.6 

54 

293.5 

198.0 

14 

343.2 

231.5 

74 

393.0 

265.0 

34 

442.7 

298.6 

94 

492.5 

332.2 

55 

294.3 

198.5 

15 

344.1 

232.1 

75 

393.8 

265.6 

35 

443.6 

299.1 

95 

493.3 

332.7 

56 

295.1 

199.1 

16 

344.9 

232.6 

76 

394.6 

266.2 

36 

444.4 

299.7 

96 

494.1 

333.3 

57 

296.0 

199.6 

17 

345.7 

233.2 

77 

395.5 

266.7 

37 

445.3 

300.2 

97 

494.9 

333.8 

58 

296.8 

200.2 

18 

346.5 

233.7 

78 

396.3 

267.3 

38 

446.1 

300.8 

98 

495.8 

334.4 

59 

297.6 

200.7 

19 

347.4 

234.3 

79 

397.1 

267.9 

39 

446.9 

301.4 

99 

496.6 

334.9 

60 

298.5 

201.3 

20 

348.2 

234.9 

80 

397.9 

268.4 

40 

447.7 

302.0 

600 

497.4 

335.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

DUt. 

Dep. 

Lat. 

56°  (124°,  236°,  304°).                                                                      1 

Page  600] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  35°  (145°,  215°,  325° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.0 

35.0 

121 

99.1 

69.4 

181 

148.3 

103.8 

241 

197.4 

138.2 

2 

1.6 

1.1 

62 

50.8 

35.6 

22 

99.9 

70.0 

82 

149.1 

104.4 

42 

198.2 

138.8 

3 

2.5 

1.7 

63 

51.6 

36.1 

23 

100.8 

70.5 

83 

149.9 

105.0 

43 

199.1 

139.4 

4 

3.3 

2.3 

64 

52.4 

36.7 

24 

101.6 

71.1 

84 

150.7 

105.5 

44 

199.9 

140.0 

5 

4.1 

2.9 

65 

53.2 

37.3 

25 

102.4 

71.7 

85 

151.5 

106.1 

45 

200.7 

140.5 

6 

4.9 

3.4 

66 

54.1 

37.9 

26 

103.2 

72.3 

86 

153.4 

106.7 

46 

201.5 

141.1 

7 

5.7 

4.0 

67 

54.9 

38.4 

27 

104.0 

72.8 

87 

153.2 

107.3 

47 

202.3 

141.7 

8 

6.6 

4.6 

68 

55.7 

39.0 

28 

104.9 

73.4 

88 

154.0 

107.8 

48 

203.1 

142.2 

9 

7.4 

5.2 

69 

56.5 

39.6 

29 

105.7 

74.0 

89 

154.8 

108.4 

49 

204.0 

142.8 

10 

8.2 

5.7 

70 

57.3 

40.2 

30 

106.5 
107.3 

74.6 

90 

155.6 

109.0 

50 

204.8 

143.4 

11 

9.0 

6.3 

71 

58.2 

40.7 

131 

75.1 

191 

156.5 

109.6 

251 

205.6 

144.0 

12 

9.8 

6.9 

72 

59.0 

41.3 

32 

108.1 

75.7 

92 

157.3 

110.1 

52 

206.4 

144.5 

13 

10.6 

7.5 

73 

59.8 

41.9 

33 

108.9 

76.3 

93 

158.1 

110.7 

53 

207.2 

145.1 

14 

11.5 

8.0 

74 

60.6 

42.4 

34 

109.8 

76.9 

94 

158.9 

111.3 

54 

208.1 

145.7 

15 

12.3 

8.6 

75 

61.4 

43.0 

35 

110.6 

77.4 

95 

159.7 

111.8 

55 

208.9 

146.3 

16 

13.1 

9.2 

76 

62.3 

43.6 

36 

111.4 

78.0 

96 

160.6 

112.4 

56 

209.7 

146.8 

17 

13.9 

9.8 

77 

63.1 

44.2 

37 

112.2 

78.6 

97 

161.4 

113.0 

57 

210.5 

147.4 

18 

14.7 

10.3 

78 

63.9 

44.7 

38 

113.0 

79.2 

98 

162.2 

113.6 

58 

211.3 

148.0 

19 

15.6 

10.9 

79 

64.7 

45.3 

39 

113.9 

79.7 

99 

163.0 

114.1 

59 

212.2 

148.6 

20 

16.4 

11.5 

80 

65.5 

45.9 

40 

114.7 

80.3 

200 

163.8 

114.7 

60 

213.0 
213.8 

149.1 

21 

17.2 

12.0 

81 

66.4 

46.5 

141 

115.5 

80.9 

201 

164.6 

115.3 

261 

149.7 

22 

18.0 

12.6 

82 

67.2 

47.0 

42 

116.3 

81.4 

02 

165.5 

115.9 

62 

214.6 

150.3 

23 

18.8 

13.2 

83 

68.0 

47.6 

43 

117.1 

82.0 

03 

166.3 

116.4 

63 

215.4 

150.9 

24 

19.7 

13.8 

84 

68.8 

48.2 

44 

118.0 

82.6 

04 

leiV.i 

117.0 

64 

216.3 

151.4, 

25 

20.5 

14.3 

85 

69.6 

48.8 

45 

118.8 

83.2 

05 

167.9 

117.6 

65 

217.1 

152.0 

26 

21.3 

14.9 

86 

70.4 

49.3 

46 

119.6 

83.7 

06 

168.7 

118.2 

66 

217.9 

152.6 

27 

22.1 

15.5 

87 

71.3 

49.9 

47 

120.4 

84.3 

07 

169.6 

118.7 

67 

218.7 

153.1 

28 

22.9 

16.1 

88 

72.1 

50.5 

48 

121.2 

84.9 

08 

170.4 

119.3 

68 

219.5 

153.7 

29 

23.8 

16.6 

89 

72.9 

51.0 

49 

122.1 

85.5 

09 

171.2 

119.9 

69 

220.4 

154.3 

30 

24.6 

17.2 

90 

73.7 

51.6 

50 

122.9 

86.0 

10 

172.0 

120.5 

70 

221.2 

154.9 

31 

26.4 

17.8 

91 

74.5 

52.2 

151 

123.7 

86.6 

211 

172.8 

121.0 

271 

222.0 

155.4 

32 

26.2 

18.4 

92 

75.4 

52.8 

52 

124.5 

87.2 

12 

173.7 

121.6 

72 

222.8 

156.0 

33 

27.0 

18.9 

93 

76.2 

53.3 

53 

125.3 

87.8 

13 

174.5 

122.2 

73 

223.6 

156.6 

34 

27.9 

19.5 

94 

77.0 

53.9 

54 

126.1 

88.3 

14 

175.3 

122.7 

74 

224.4 

157.2 

35 

28.7 

20.1 

95 

77.8 

54.5 

55 

127.0 

88.9 

15 

176.1 

123.3 

75 

225.3 

157.7 

36 

29.5 

20.6 

96 

78.6 

55.1 

56 

127.8 

89.5 

16 

176.9 

123.9 

76 

226.1 

158.3 

37 

30.3 

21.2 

97 

79.5 

55.6 

57 

128.6 

90.1 

17 

177.8 

124.5 

77 

226.9 

158.9 

38 

31.1 

21.8 

98 

80.3 

56.2 

58 

129.4 

90.6 

18 

178.6 

125.0 

78 

227.7 

159.5 

39 

31.9 

22.4 

99 

81.1 

56.8 

59 

130.2 

91.2 

19 

179.4 

125.6 

79 

228.5 

160.0 

40 

32.8 

22.9 

100 

81.9 

57.4 

60 

131.1 

91.8 

20 

180.2 
181.0 

126.2 

80 

229.4 

160.6 

41 

33.6 

23.5 

101 

82.7 

57.9 

161 

131.9 

92.3 

221 

126.8 

281 

230.2 

161.2 

42 

34.4 

24.1 

02 

83.6 

58.5 

62 

132.7 

92.9 

22 

181.9 

127.3 

82 

231.0 

161.7 

43 

35.2 

24.7 

03 

84.4 

59.1 

63 

133.5 

93.5 

23 

182.7 

127.9 

83 

231.8 

162.3 

44 

36.0 

25.2 

04 

85.2 

59.7 

64 

134.3 

94.1 

24 

183.5 

128.5 

84 

232.6 

162.9 

45 

36.9 

25.8 

05 

86.0 

60.2 

65 

135.2 

94.6 

25 

184.3 

129.1 

85 

233.5 

163.5 

46 

37.7 

26.4 

06 

86.8 

60.8 

66 

136.0 

95.2 

26 

185.1 

129.6 

86 

234.3 

164.0 

47 

38.5 

27.0 

07 

87.6 

61.4 

67 

136.8 

95.8 

27 

185.9 

130.2 

87 

235.1 

164.6 

48 

39.3 

27.5 

08 

88.5 

61.9 

68 

137.6 

96.4 

28 

186.8 

130.8 

88 

235.9 

165.2 

49 

40.1 

28.1 

09 

89.3 

62.5 

69 

138.4 

96.9 

29 

187.6 

131.3 

89 

236.  7 

165.8 

50 

41.0 

28.7 

10 

90.1 

63.1 

70 

139.3 

97.5 

30 

188.4 

131.9 

90 

237.6 

166.3 

51 

41.8 

29.3 

111 

90.9 

63.7 

171 

140.1 

98.1 

231 

189.2 

132.5 

291 

238.4 

166.9 

52 

42.6 

29.8 

12 

91.7 

64.2 

72 

140.9 

98.7 

32 

190.0 

133.1 

92 

239.2 

167.5 

53 

43.4 

30.4 

13 

92.6 

64.8 

73 

141.7 

99.2 

33 

190.9 

133.6 

93 

240.0 

168.1 

54 

44.2 

31.0 

14 

93.4 

65.4 

74 

142.5 

99.8 

34 

191.7 

134.2 

94 

.  240.  8 

168.6 

55 

45.1 

31.5 

15 

94.2 

66.0 

75 

143.4 

100.4 

35 

192.5 

134.8 

95 

241.6 

169.2 

56 

45.9 

32.1 

16 

95.0 

66.5 

76 

144.2 

100.9 

36 

193.3 

135.4 

96 

242.5 

169.8 

57 

46.7 

32.7 

17 

95.8 

67.1 

77 

145.0 

101.5 

37 

194.1 

135.9 

97 

243.3 

170.4 

58 

47.5 

33.3 

18 

96.7 

67.7 

78 

145.8 

102.1 

38 

195.0 

136.5 

98 

244.1 

170.9 

59 

48.3 

33.8 

19 

97.5 

68.3 

79 

146.6 

102.7 

39 

195.8 

137.1 

99 

244.9 

171.5 

60 

49.1 

34.4 

20 

98.3 

68.8 

80 

147.4 

103.2 

40 

196.6 

137.7 

300 

245.7 

172.1 

Diet. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

55°  (1 

25°,  235 

°,  305° 

). 

TABLE  2. 

[Page  601 

Difference  of  Latitude  and  Departure  for 

35°  (145°,  215°,  325° 

)• 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

246.6 

172.6 

361 

295.7 

207.0 

421 

344.9 

241.5 

481 

394.0 

275.9 

541 

443.2 

310.3 

02 

247.4 

173. 2 

62 

296.5 

207.6 

22 

345.7 

242.0 

82 

394.8 

276.4 

42 

444.0 

310.9 

03 

248.2 

173.8 

63 

297.4 

208.2 

23 

346.5 

242.6 

83 

395.7 

277.0 

43 

444.8 

311.4 

04 

249.0 

174.3 

64 

298.2 

208.8 

24 

347.3 

243.2 

84 

396.5 

277.6 

44 

445.6 

312.0 

05 

249.9 

174.9 

65 

299.0 

209.3 

25 

348.1 

243.8 

85 

397.3 

278.2 

45 

446.4 

312.6 

06 

250.7 

175.5 

66 

299.8 

209.9 

26 

349.0 

244.3 

86 

398.1 

278.7 

46 

447.3 

313.2 

07 

251.5 

176.1 

67 

300.6 

210.5 

27 

349.8 

244.9 

87 

398.9 

279.3 

47 

448.1 

313.7 

08 

232.3 

176.6 

68 

301.5 

211.1 

28 

350.6 

245.5 

88 

399.8 

279.9 

48 

448.9 

314.3 

09 

253.1 

177.2 

69 

302.3 

211.6 

29 

351.4 

246.0 

89 

400.6 

280.5 

49 

449.7 

314.9 

10 

253.9 

177.8 

70 

303.1 

212.2 

30 

352.2 
353.1 

246.6 

90 

401.4 

281.0 

50 

450.5 

315.4 

311 

254.8 

178.4 

371 

303.9 

212.8 

431 

247.2 

491 

402.2 

281.6 

551 

451.4 

316.0 

12 

255.6 

178.9 

72 

304.7 

213.4 

32 

353.9 

247.8 

92 

403.0 

282.2 

52 

452.2 

316.6 

13 

256.4 

179.5 

73 

305.6 

213.9 

33 

354.7 

248.3 

93 

403.9 

282.8 

53 

453.0 

317.2 

14 

257.2 

180.1 

74 

306.4 

214.5 

34 

355.5 

248.9 

94 

404.7 

283.3 

54 

453.8 

317.7 

15 

258.0 

180.7 

75 

307.2 

215.1 

35 

356.3 

249.5 

95 

405.5 

283.9 

55 

454.6 

318.3 

16 

258.9 

181.2 

76 

308.0 

215.6 

36 

357.2 

250.1 

96 

406.3 

284.5 

56 

455.5 

318.9 

17 

259.7 

181.8 

77 

308.8 

216.2 

37 

358.0 

250.6 

97 

407.1 

285.1 

57 

456.3 

319.5 

18 

260.5 

182.4 

78 

309.6 

216.8 

38 

358.8 

251.2 

98 

408.0 

285.6 

58 

457.1 

320.0 

19 

261.3 

183.0 

79 

310.5 

217.4 

39 

359.6 

251.8 

99 

408.8 

286.2 

59 

457.9 

320.6 

20 
321 

262.1 

183.5 

80 

311.3 

217.9 

40 

360.4 

252.4 

500 

409.6 

286.8 

60 

458.7 

321.2 

263.0 

184.1 

381 

312.1 

218.5 

441 

361.3 

252.9 

501 

410.4 

287.4 

561 

459.6 

321.8 

22 

263.8 

184.7 

82 

312.9 

219.1 

42 

362.1 

253.5 

02 

411.2 

287.9 

62 

460.4 

322.3 

23 

264.6 

185.2 

83 

313.7 

219.7 

43 

362.9 

254.1 

03 

412.1 

288.5 

63 

461.2 

322.9 

24 

265.4 

185.8 

84 

314.  ff 

220.2 

44 

363.7 

254.7 

04 

412.9 

289.1 

64 

462.0 

323.5 

25 

266.2 

186.4 

85 

315.4 

220.8 

45 

364. 5 

255.2 

05 

413.7 

289.7 

65 

462.8 

324.1 

26 

267.1 

187.0 

86 

316.2 

221.4 

46 

365.4 

255.8 

06 

414.5 

290.2 

66 

463.7 

324.6 

27 

267.9 

187.5 

87 

317.0 

222.0 

47 

366.2 

256.4 

07 

415.3 

290.8 

67 

464.5 

325.2 

28 

268.7 

188.1 

88 

317.8 

222.5 

48 

367.0 

256.9 

08 

416.1 

291.4 

68 

465.3 

325.8 

29 

269.5 

188.7 

89 

318.7 

223.1 

49 

367.8 

257.5 

09 

417.0 

291.9 

69 

466.1 

326.4 

30 
331 

270.3 

189.3 

90 

319.5 

223.7 

50 

368.6 

258.1 

10 

417.8 

292.5 

70 

466.9 

326.9 
327.5 

271.1 

189.8 

391 

320.3 

224.3 

451 

369.4 

258.7 

511 

418.6 

293.1 

571 

467.8 

32 

272.0 

190.4 

92 

321.1 

224.8 

52 

370.3 

259.2 

12 

419.4 

293.7 

72 

468.6 

328.1 

33 

272.8 

191.0 

93 

321.9 

225.4 

53 

371.1 

259.8 

13 

420.2 

294.2 

73 

469.4 

328.7 

34 

273.6 

191.6 

94 

322.8 

226.0 

54 

371.9 

260.4 

14 

421.1 

294.8 

74 

470.2 

329.2 

35 

274.4 

192.1 

95 

323.6 

226.5 

55 

372.7 

261.0 

15 

421.9 

295.4 

75 

471.0 

329.8 

36 

275.2 

192.7 

96 

324.4 

227.1 

56 

373.5 

261.5 

16 

422.7 

296.0 

76 

471.9 

330.4 

37 

276.1 

193.3 

97 

325.2 

227.7 

57 

374.4 

262.1 

17 

423.5 

296.5 

77 

472.7 

331.0 

38 

276.9 

193.9 

98 

326.0 

228.3 

58 

375.2 

262.7 

18 

424.3 

297.1 

78 

473.5 

331.5 

39 

277.7 

194.4 

99 

326.9 

228.8 

59 

376.0 

263.3 

19 

425.2 

297.7 

79 

474.3 

332.1 

40 

278.5 

195.0 

400 

327.7 

229.4 

60 

376.8 

263.8 

20 

426.0 

298.3 

80 

475.1 

332.7 
333.3 

341 

279.3 

195.6 

401 

328.5 

230.0 

461 

377.6 

264.4 

521 

426.8 

298.8 

581 

476.0 

42 

280.2 

196.1 

02 

329.3 

230.6 

62 

378.5 

265.0 

22 

427.6 

299.4 

82 

476.8 

333.8 

43 

281.0 

196.7 

03 

330.1 

231. 1 

63 

379.3 

265.5 

23 

428.4 

300.0 

83 

477.6 

334.4 

44 

281.8 

197.3 

04 

330.9 

231.7 

64 

380.1 

266.1 

24 

429.3 

300.5 

84 

478.4 

335.0 

45 

282.6 

197.9 

05 

331.8 

232.3 

65 

380.9 

266.7 

25 

430.1 

301.1 

85 

479.2 

335.6 

46 

283.4 

198.4 

06 

332.6 

232.9 

66 

381.7 

267.3 

26 

430.9 

301.7 

86 

480.1 

336.1 

47 

284.3 

199.0 

07 

333.4 

233.4 

67 

382.6 

267.8 

27 

431.7 

302.3 

87 

480.9 

336.7 

48 

285.1 

199.6 

08 

334.2 

234.0 

68 

383.4 

268.4 

28 

432.5 

302.8 

88 

481.7 

337.3 

49 

285.9 

200.2 

09 

335.0 

234.6 

69 

384.2 

269.0 

29 

433.4 

303.4 

89 

482.5 

337.9 

50 

286.7 

200.7 

10 

335.9 

235.1 

70 

385.0 

269.6 

30 

434.2 

304.0 

90 

483.3 

338.4 

351 

287.5 

201.3 

411 

336.7 

235.7 

471 

385.8 

270.1 

531 

435.0 

304.5 

591 

484.2 

339.0 

52 

288.3 

201.9 

12 

337.5 

236.3 

72 

386.6 

270.7 

32 

435.8 

305.1 

92 

485.0 

339.6 

53 

289.2 

202.5 

13 

338.3 

236.9 

73 

387.5 

271.3 

33 

436.6 

305.7 

93 

485.8 

340.2 

54 

290.0 

203.0 

14 

339.1 

237.4 

74 

388.3 

271.9 

34 

437.5 

306.3 

94 

486.6 

340.7 

55 

290.8 

203.6 

15 

340.0 

238.0 

75 

389.1 

272.4 

35 

438.3 

306.8 

95 

487.4 

341.3 

56 

291.6 

204.2 

16 

340.8 

238.6 

76 

389.9 

273.0 

36 

439,1 

307.4 

96 

488.3 

341.9 

57 

292.4 

204.7 

17 

341.6 

239.2 

77 

390.7 

273.6 

37 

439.9 

308.0 

97 

489.1 

342.5 

58 

293.3 

205.3 

18 

342.4 

239.7 

78 

391.6 

274.2 

38 

440.7 

308.6 

98 

489.9 

343.0 

59 

294.1 

205.9 

19 

343.2 

240.3 

79 

392.4 

274.7 

39 

441.5 

309.1 

99 

490.7 

343.6 

60 

294.9 

206.5 

20 

344.1 

240.9 

80 

393.2 

275.3 

40 

442.3 

309.7 

600 

491.5 

344.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

55°  (1 

25°,  235°,  305° 

)• 

Page  602] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  36°  (144°,  216°,  324° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

49.4 

35.9 

121 

97.9 

71.1 

181 

146.4 

106.4 

241 

195.0 

141.7 

2 

1.6 

1.2 

62 

50.2 

36.4 

22 

98.7 

71.7 

82 

147.2 

107.0 

42 

195.8 

142.2 

3 

2.4 

1.8 

63 

51.0 

37.0 

23 

99.5 

72.3 

83 

148.1 

107.6 

43 

196.6 

142.8 

4 

3.2 

2.4 

64 

51.8 

37.6 

24 

100.3 

72.9 

84 

148.9 

108.2 

44 

197.4 

143.4 

5 

4.0 

2.9 

65 

52.6 

38.2 

25 

101.1 

73.5 

85 

149.7 

108.7 

45 

198.2 

144.0 

6 

4.9 

3.5 

66 

53.4 

38.8 

26 

101.9 

74.1 

86 

150.5 

109.3 

46 

199.0 

144.6 

7 

5.7 

4.1 

67 

54.2 

39.4 

27 

102.7 

74.6 

87 

151.3 

109.9 

47 

199.8 

145.2 

8 

6.5 

4.7 

68 

55.0 

40.0 

28 

103.6 

75.2 

88 

152.1 

110.5 

48 

200.  6. 

145.8 

9 

7.3 

5.3 

69 

55.8 

40.6 

29 

104.4 

75.8 

89 

152.9 

111.1 

49 

201.4 

146.4 

10 

8.1 

5.9 

70 

56.6 

41.1 

30 

105.2 
106.0 

76.4 

90 

153.7 

111.7 

50 

202.3 

146.9 

11 

8.9 

6.5 

71 

57.4 

41.7 

131 

77.0 

191 

154.5 

112.3 

251 

203.1 

147.5 

12 

9.7 

7.1 

72 

58.2 

42.3 

32 

106.8 

77.6 

92 

155.3 

112.9 

52 

203.9 

148.1 

13 

10.5 

7.6 

73 

59.1 

42.9 

33 

107.6 

78.2 

93 

156.1 

113.4 

53 

204.7 

148.7 

14 

11.3 

8.2 

74 

59.9 

43.5 

34 

108.4 

78.8 

94 

156.9 

114.0 

54 

205.5 

149.3 

15 

12.1 

8.8 

75 

60.7 

44.1 

35 

109.2 

79.4 

95 

157.8 

114.6 

55 

206.3 

149.9 

16 

12.9 

9.4 

76 

61.5 

44.7 

36 

110.0 

79.9 

96 

158.6 

115.2 

56 

207.1 

150.5 

17 

13.8 

10.0 

77 

62.3 

45.3 

37 

110.8 

80.5 

97 

159.4 

115.8 

57 

207.9 

151.1 

18 

14.6 

10.6 

78 

63.1 

45.8 

38 

111.6 

81.1 

98 

160.2 

116.4 

58 

208.7 

151.6 

19 

15.4 

11.2 

79 

63.9 

46.4 

39 

112.5 

81.7 

99 

161.0 

117.0 

59 

209.5 

152.2 

20 
21 

16.2 
17.0 

11.8 
12.3 

80 
81 

64.7 

47.0 

40 

113.3 

82.3 

200 

161.8 
162.6 

117.6 

60 

210.3 

152.8 

65.5 

47.6 

141 

114.1 

82.9 

201 

118.1 

261 

211.2 

153.4 

22 

17.8 

12.9 

82 

66.3 

48.2 

42 

114.9 

83.5 

02 

163.4 

118.7 

62 

212.0 

154.0 

23 

18.6 

13.5 

83 

67.1 

48.8 

43 

115.7 

84.1 

03 

164.2 

119.3 

63 

212.8 

154.6 

24 

19.4 

14.1 

84 

68.0 

49.4 

44 

116.5 

84.6 

04 

165.0 

119.9 

64 

213.6 

155.2 

25 

20.2 

14.7 

85 

68.8 

50.0 

45 

117.3 

85.2 

05 

165.8 

120.5 

65 

214.4 

155.8 

26 

21.0 

15.3 

86 

69.6 

50.5 

46 

118.1 

85.8 

06 

166.7 

121.1 

66 

215.2 

156.4 

27 

21.8 

15.9 

87 

70.4 

51.1 

47 

118.9 

86.4 

07 

167.5 

121.7 

67 

216.0 

156.9 

28 

22.7 

16.5 

88 

71.2 

51.7 

48 

119.7 

87.0 

08 

168.3 

122.3 

68 

216.8 

157.5 

29 

23.5 

17.0 

89 

72.0 

52.3 

49 

120.5 

87.6 

09 

169.1 

122.8 

69 

217.6 

158.1 

30 

24.3 
25.1 

17.6 

90 

72.8 

52.9 

50 

121.4 

88.2 

10 

169.9 

123.4 

70 

218.4 

158.7 

31 

18.2 

91 

73.6 

53.^ 

151 

122.2 

88.8 

211 

170.7 

124.0 

271 

219.2 

159.3 

32 

25.9 

18.8 

92 

74.4 

54.1 

52 

123.0 

89.3 

12 

171.5 

124.6 

72 

220.1 

159.9 

33 

26.7 

19.4 

93 

75.2 

54.7 

53 

123.8 

89.9 

13 

172.3 

125.2 

73 

220.9 

160.5 

34 

27.5 

20.0 

94 

76.0 

55.3 

54 

124.6 

90.5 

14 

173. 1 

125.8 

74 

221.7 

161.1 

35 

28.3 

20.6 

95 

76.9 

55.8 

55 

125.4 

91.1 

15 

173.9 

126.4 

75 

222.5 

161.6 

36 

29.1 

21.2 

96 

77.7 

56.4 

56 

126.2 

91.7 

16 

174.7 

127.0 

76 

223.3 

162.2 

37 

29.9 

21.7 

97 

78.5 

57.0 

57 

127.0 

92.3 

17 

175.6 

127.5 

77 

224.1 

162.8 

38 

30.7 

22.3 

98 

79.3 

57.6 

58 

127.8 

92.9 

18 

176.4 

128.1 

78 

224.9 

163. 4 

39 

31.6 

22.9 

99 

80.1 

58.2 

59 

128.6 

93.5 

19 

177.2 

128.7 

79 

225.7 

164.0 

40 

32.4 

23.5 

100 

80.9 

58.8 

60 

129.4 

94.0 

20 

178.0 

129.3 

80 

226.5 

164.6 

41 

33.2 

24.1 

101 

81.7 

59.4 

161 

130.3 

94.6 

221 

178.8 

129.9 

281 

227.3 

165.  2 

42 

34.0 

24.7 

02 

82.5 

60.0 

62 

131.1 

95.2 

22 

179.6 

130.5 

82 

228.1 

165.8 

43 

34.8 

25.3 

03 

83.3 

60.5 

63 

131.9 

95.8 

23 

180.4 

131.1 

83 

229.0 

166.3 

44 

35.6 

25.9 

04 

84.1 

61.1 

64 

132.7 

96.4 

24 

181  2 

131.7 

84 

229.8 

166.9 

45 

36.4 

26.5 

05 

84.9 

61.7 

65 

133.5 

97.0 

25 

182.0 

132.3 

85 

230.6 

167.5 

46 

37.2 

27.0 

06 

85.8 

62.3 

66 

134.3 

97.6 

26 

182.8 

132.8 

86 

231.4 

168.1 

47 

38.0 

27.6 

07 

86.6 

62.9 

67 

135.1 

98.2 

27 

183.6 

133.4 

87 

232.2 

168.7 

48 

38.8 

28.2 

08 

87.4 

63.5 

68 

135.9 

98.7 

28 

184.5 

134.0 

88 

233.0 

169.3 

49 

39.6 

28.8 

09 

88.2 

64.1 

69 

136.7 

99.3 

29 

185.3 

134.6 

89 

233.  8 

169.9 

50 

40.5 

29.4 

10 

89.0 

64.7 

70 

137.5 
138.3 

99.9 

30 

186.1 

135.2 

90 

234.6 
235.4 

170.5 

51 

41.3 

30.0 

111 

89.8 

65.2 

171 

100.5 

231 

186.9 

135.8 

291 

171.0 

52 

42.1 

30.6 

12 

90.6 

65.8 

72 

139.2 

101.1 

32 

187.7 

136.4 

92 

236.2 

171.6 

53 

42.9 

31.2 

13 

91.4 

66.4 

73 

140.0 

101.7 

33 

188.5 

137.0 

93 

237.0 

172.2 

54 

43.7 

31.7 

14 

92.2 

67.0 

74 

140.8 

102.3 

34 

189.3 

137.5 

94 

237.9 

172.8 

55 

44.5 

32.3 

15 

93.0 

67.6 

75 

141.6 

102.9 

35 

190.1 

138.1 

95 

238.7 

173.4 

56 

45.3 

32.9 

16 

93.8 

68.2 

76 

142.4 

103.5 

36 

190.9 

138.7 

96 

239.5 

174.0 

57 

46.1 

33.5 

17 

94.7 

68.8 

77 

143.2 

104.0 

37 

191.7 

139.3 

97 

240.3 

174.6 

58 

46.9 

34.1 

18 

95.5 

69.4 

78 

144.0 

104.6 

38 

192.5 

139.9 

98 

241.1 

175.2 

59 

47.7 

34.7 

19 

96.3 

69.9 

79 

144.8 

105.2 

39 

193.4 

140.5 

99 

241.9 

175.7 

60 

48.6 

35.3 

20 

97.1 

70.5 

80 

145.6 

105.8 

40 

194.2 

141.1 

300 

242.7 

176.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

54°  (1 

26°,  234 

°,  306° 

)• 

TABLE  2. 

[Page  603 

Difference  of  Latitude  and  Departure  for  36°  (144°,  216°,  324° 

). 

Dist.       Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

301 

243.5 

176.9 

361 

292.1 

212.2 

421 

340.6 

247.5 

481 

389.1 

282.7 

541 

437.7 

318.0 

02 

244.3 

177.5 

62 

292.9 

212.8 

22 

341.4 

248.1 

82 

390.0 

283.3 

42 

438.5 

318.6 

03 

245.1 

178.1 

63 

293.7 

213.4 

23 

342.2 

248.6 

83 

390.8 

283.9 

43 

439.3 

319.1 

04 

246.0 

178.7 

64 

294.5 

214.0 

24 

343.0 

249.2 

84 

391.6 

284.5 

44 

440.2 

319.7 

05 

246.8 

179.3 

65 

295.3 

214.6 

25 

343.8 

249.8 

85 

392.4 

285.1 

45 

441.0 

320.3 

06 

247.6 

179.9 

66 

296.1 

215.1 

26 

344.7 

250.4 

86 

393.2 

285.6 

46 

441.8 

320.9 

07 

248.4 

180.5 

67 

296.9 

215.7 

27 

345.5 

251.0 

87 

394.0 

286.2 

47 

442.6 

321.5 

08 

249.2 

181.1 

68 

297.7 

216.3 

28 

346.3 

251.6 

88 

394.8 

286.8 

48 

443.4 

322.1 

09     250. 0  1 

181.6 

69 

298.5 

216.9 

29 

347.1 

252.2 

89 

395.6 

287.4 

49 

444.2 

322.7 

10 

250.8 

182.2 

70 

299.3 

217.5 

30 

347.9 

252.8 

90 

396.4 

288.0 

50 

445.0 

323.3 

311 

251.6 

182.8 

371 

300.2 

218.1 

431 

348.7 

253.3 

491 

397.3 

288.6 

551 

445.8 

323.8 

12 

252.4 

183.4 

72 

301.0 

218.7 

32 

349.5 

253.9 

92 

398.1 

289.2 

52 

446.6 

324.4 

13 

253.2 

184.0 

73 

301.8 

219.3 

33 

350.3 

254.5 

93 

398.9 

289.8 

53 

447.4 

325.0 

14 

254.0 

184.6 

74 

302.6 

219.8 

34 

351.1 

255.1 

94 

399.7 

290.3 

54 

448.2 

325.6 

15 

254.9 

185.2 

75 

303.4 

220.4 

35 

351.9 

255.7 

95 

400.5 

290.9 

55 

449.0 

326.2 

16 

255.7 

185.8 

76 

304.2 

221.0 

36 

352.7 

256.3 

96 

401.3 

291.5 

56 

449.8 

326.8 

17 

256.5 

186.4 

77 

305.0 

221.6 

37 

353.6 

256.9 

97 

402.1 

292.1 

57 

450.7 

327.4 

18 

257.3 

186.9 

78 

305.8 

222.2 

38 

354.4 

257.5 

98 

402.9 

292.7 

58 

451.5 

328.0 

19 

258.1 

187.5 

79 

306.6 

222.8 

39 

355.2 

258.0 

99 

403.7 

293.3 

59 

452.3 

328.5 

20 

258.9 

188.1 

80 

307.4 

223.4 

40 

356.0 

258.6 

500 

404.5 

293. 9 

60 

453.1 

329.1 

321 

259.7 

188.7 

381 

308.2 

224.0 

441 

356.8 

259.2 

501 

405.3 

294.5 

561 

453.9 

329.7 

22 

260.5 

189.3 

82 

309.1 

224.5 

42 

357.6 

259.8 

02 

406.1 

295.0 

62 

454.7 

330.3 

23 

261.3 

189.9 

83 

309.9 

225.1 

43 

358.4 

260.4 

03 

407.0 

295.6 

63 

455.5 

330.9 

24 

262.1 

190.5 

84 

310.7 

225.7 

44 

359.2 

261.0 

04 

407.8 

296.2 

64 

456.3 

331.5 

25 

262.9 

191.0 

85 

311.5 

226.3 

45 

360.0 

261.6 

05 

408.6 

296.8 

65 

457.1 

332.1 

26 

263.7 

191.6 

86 

312.3 

226.9 

46 

360.8 

262.2 

06 

409.4 

297.4 

66 

457.9 

332.7 

27 

264.6 

192.2 

87 

313.1 

227.5 

47 

361.6 

262.8 

07 

410.2 

298.0 

67 

458.7 

333.3 

28 

265.4 

192.8 

88 

313.9 

228.1 

48 

362.4 

263.3 

08 

411.0 

298.6 

68 

459.5 

333.8 

29 

266.2 

193.4 

89 

314.7 

228.7 

49 

363.3 

263.9 

09 

411.8 

299.2 

69 

460.3 

334.4 

30 

267.0 

194.0 

90 

315.5 

229.2 

50 

364.1 

264.5 

10 

412.6 

299.8 

70 

461.1 

335.0 

331 

267.8 

194.6 

391 

316.3 

229.8 

451 

364.9 

265.1 

511 

413.4 

300.3 

571 

462.0 

335.6 

32 

268.6 

195.2 

92 

317.1 

230.4 

52 

365.7 

265.7 

12 

414.2 

300.9 

72 

462.8 

336.2 

33 

269.4 

195.7 

93 

318.0 

231.0 

53 

366.5 

266.3 

13 

415.1 

301.5 

73 

463.6 

336.8 

34 

270:2 

196.3 

94 

318.8 

231.6 

54 

367.3 

266.9 

14 

415.9 

302.1 

74 

464.4 

337.4 

36 

271.0 

196.9 

95 

319.6 

232.2 

55 

368.1 

267.5 

15 

416.7 

302.7 

75 

465.2 

338.0 

36 

271.8 

197.5 

96 

320.4 

232.8 

56 

368.9 

268.0 

16 

417.5 

303.3 

76 

466.0 

338.5 

37 

272.6 

198.1 

97 

321.2 

233.4 

57 

369.7 

268.6 

17 

418.3 

303.9 

77 

466.8 

339.1 

38 

273.5 

198.7 

98 

322.0 

233.9 

58 

370. 5 

269.2 

18 

419.1 

304.4 

78 

467.6 

339.7 

39 

274.3 

199.3 

99 

322.8 

234.5 

59 

371.3 

269.8 

19 

419.9 

305.0 

79 

468.4 

340.3 

40 

275.1 

199.9 

400 

323.6 

235.1 

60 

372.2 

270.4 

20 

420.7 

305.6 

80 

469.3 

340.9 

341 

275.9 

200.4 

401 

324.4 

235.7 

461 

373.0 

271.0 

521 

421.5 

306.2 

581 

470.1 

341.5 

42 

276.7 

201.0 

02 

325.2 

236.3 

62 

373.8 

271.6 

22 

422.3 

306.8 

82 

470.9 

342.1 

43 

277.5 

201.6 

03 

326.0 

236.9 

63 

374.6 

272.2 

23 

423.1 

307.4 

83 

471.7 

342.7 

44 

278.3 

202.2 

04 

326.9 

237.5 

64 

375.4 

272.7 

24 

423.9 

308.0 

84 

472.5 

343.2 

45 

279.1 

202.8 

05 

327.7 

238.1 

65 

376.2 

273.3 

25 

424.7 

308.6 

85 

473.3 

343.8 

46 

279.9 

203.4 

06 

328.5 

238.7 

66 

377.0 

273.9 

26 

425.5 

309.2 

86 

474.1 

344.4 

47 

280.7 

204.0 

07 

329.3 

239.2 

67 

377.8 

274.5 

27 

426.4 

309.7 

87 

474.9 

345.0 

48 

281.5 

204.6 

08 

330.1 

239.8 

68 

378.6 

275.1 

28 

427.2 

310.3 

88 

475.7 

345.6 

49 

282.4 

205.1 

09 

330.9 

240.4 

69 

379.4 

275.7 

J9 

428.0 

310.9 

89 

476.5 

346.2 

50 

283.2 

205.7 

10 

331.7 

241.0 

70 

380.2 

276.3 

30 

428.8 

311.5 

90 

477.3 

346.8 

351 

284.0 

206.3 

411 

332.5 

241.6 

471 

381.1 

276.9 

531 

429.6 

312.1 

591 

478.2 

347.4 

52 

284.8 

206.9 

12 

333.3 

242.2 

72 

381.9 

277.4 

32 

430.4 

312.7 

92 

479.0 

347.9 

53 

285.6 

207.5 

13 

334.1 

242.8 

73 

382.7 

278.0 

33 

431.2 

313.3 

93 

479.8 

348.5 

54 

286.4 

208.1 

14 

334.9 

243.4 

74 

383.5 

278.6 

34 

432.0 

313.9 

94 

480.6 

349.1 

55 

287.2 

208.7 

15 

335.8 

243.9 

75 

384.3 

279.2 

35 

432.9 

314.4 

95 

481.4 

349.7 

56 

288.0 

209.3 

16 

336.6 

244.5 

76 

385.1 

279.8 

36 

433.7 

315.0 

96 

482.2 

350.3 

57 

288.8 

209.8 

17 

337. 4 

245.1 

77 

385.9 

280.4 

37 

434.5 

315.6 

97 

483.0 

350.9 

58 

289.6 

210.4 

18 

338.2 

245.7 

78 

386.7 

281.0 

38 

435.3 

316.2 

98 

483.8 

351.5 

59 

290.4 

211.0 

19 

339.0 

246.3 

79 

387.5 

281.6 

39 

436.1 

316.8 

99 

484.6 

352.1 

60 

291.3 

211.6 

20 

339.8 

246.9 

80 

388.3 

282.1 

40 

436.9 

317.4 

600 

485.4 

352.7 

Diat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Diat. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

54°  (] 

26°,  23^ 

1°,  306'= 

). 

Page  604] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  37*  (143°,  217",  823* 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

48.7 

36.7 

121 

96.6 

72.8 

181 

144.6 

108.9 

241 

192.5 

145.0 

2 

1.6 

1.2 

62 

49.5 

37.3 

22 

97.4 

73.4 

82 

145.4 

109.5 

42 

193.3 

145.6 

3 

2.4 

1.8 

63 

50.3 

37.9 

23 

98.2 

74.0 

83 

146.2 

110.1 

43 

194.1 

146.2 

4 

3.2 

2.4 

64 

51.1 

38.5 

24 

99.0 

74.6 

84 

146.9 

110.7 

44 

194.9 

146.8 

5 

4.0 

3.0 

65 

51.9 

39.1 

25 

99.8 

75.2 

85 

147.7 

111.3 

45 

195.7 

147.4 

6 

4.8 

3.6 

66 

52.7 

39.7 

26 

100.6 

75.8 

86 

148.5 

111.9 

46 

196.5 

148.0 

7 

5.6 

4.2 

67 

53.5 

40.3 

27 

101.4 

76.4 

87 

149.3 

112.5 

47 

197.3 

148.6 

8 

6.4 

4.8 

68 

54.3 

40.9 

28 

102.2 

77.0 

88 

150.1 

113.1 

48 

198.1 

149.3 

9 

7.2 

5.4 

69 

55.1 

41.5 

29 

103.0 

77.6 

89 

150.9 

113.7 

49 

198.9 

149.9 

10 

8.0 

6.0 

70 

55.9 

42.1 

30 

103.8 

78.2 

90 

151.7 

114.3 

50 

199.7 

150.5 

11 

8.8 

6.6 

71 

56.7 

42.7 

131 

104.6 

78.8 

191 

152.5 

114.9 

251 

200.5 

151.1 

12 

9.6 

7.2 

72 

57.5 

43.3 

32 

105.-4 

79.4 

92 

153.3 

115.5 

52 

201.3 

151.7 

13 

10.4 

7.8 

73 

58.3 

43.9 

33 

106.2 

80.0 

93 

154.1 

116.2 

53 

202.1 

152.3 

14 

11.2 

8.4 

74 

59.1 

44.5 

34 

107.0 

80.6 

94 

154.9 

116.8 

54 

202.9 

152.9 

15 

12.0 

9.0 

75 

59.9 

45.1 

35 

107.8 

81.2 

95 

155.7 

117.4 

55 

203.7 

153.5 

16 

12.8 

9.6 

76 

60.7 

45.7 

36 

108.6 

81.8 

96 

156.5 

118.0 

56 

204.5 

154.1 

17 

13.6 

10.2 

77 

61.5 

46.3 

37 

109.4 

82.4 

97 

157.3 

118.6 

57 

205.2 

154.7 

18 

14.4 

10.8 

78 

62.3 

46.9 

38 

110.2 

83.1 

98 

158.1 

119.2 

58 

206.0 

155.3 

19 

16.2 

11.4 

79 

63.1 

47.5 

39 

111.0 

83.7 

99 

158.9 

119.8 

59 

206.8 

155.9 

20 

16.0 

12.0 

80 

63.9 

48.1 

40 

111.8 
112.6 

84.3 

200 

159.7 

120.4 

60 

207.6 
208.4 

156.5 

21 

16.8 

12.6 

81 

64.7 

48.7 

141 

84.9 

201 

160.5 

121.0 

261 

157.1 

22 

17.6 

13.2 

82 

65.5 

49.3 

42 

113.4 

85.5 

02 

161.3 

121.6 

62 

209.2 

157.7 

23 

18.4 

13.8 

83 

66.3 

50.0 

43 

114.2 

86.1 

03 

162.1 

122.2 

63 

210.0 

158.3 

24 

19.2 

14.4 

84 

67.1 

50.6 

44 

115.0 

86.7 

04 

162.9 

122.8 

64 

210.8 

158.9 

25 

20.0 

15.0 

85 

67.9 

51.2 

45 

115.8 

87.3 

05 

163.7 

123.4 

65 

211.6 

159.5 

26 

20.8 

15.6 

86 

68.7 

51.8 

46 

116.6 

87.9 

06 

164.5 

124.0 

66 

212.4 

160.1 

27 

21.6 

16.2 

87 

69.5 

52.4 

47 

117.4 

88.5 

07 

165.3 

124.6 

67 

213.2 

160.7 

28 

22.4 

16.9 

88 

70.3 

53.0 

48 

118.2 

89.1 

08 

166.1 

125.2 

68 

214.0 

161.3 

29 

23.2 

17.5 

89 

71.1 

53.6 

49 

119.0 

89.7 

09 

166.9 

125.8 

69 

214.8 

161.9 

30 

24.0 

18.1 

90 

71.9 

54.2 

50 

119.8 

90.3 

10 

167.7 

126.4 

70 

215.6 

162.5 

31 

24.8 

18.7 

91 

72.7 

54.8 

151 

120.6 

90.9 

211 

168.5 

127.0 

271 

216.4 

163.1 

32 

25.6 

19.3 

92 

73.5 

55.4 

52 

121.4 

91.5 

12 

169.3 

127.6 

72 

217.2 

163.7 

33 

26.4 

19.9 

93 

74.3 

56.0 

53 

122.2 

92.1 

13 

170.1 

128.2 

73 

218.0 

164.3 

34 

27.2 

20.5 

94 

75.1 

56.6 

54 

123.0 

92.7 

14 

170.9 

128.8 

74 

218.8 

164.9 

35 

28.0 

21.1 

95 

75.9 

57.2 

55 

123.8 

93.3 

15 

171.7 

129.4 

75 

219.6 

165.5 

36 

28.8 

21.7 

96 

76.7 

57.8 

56 

124.6 

93.9 

16 

172.5 

130.0 

76 

220.4 

166.1 

37 

29.5 

22.3 

97 

77.5 

58.4 

57 

125.4 

94.5 

17 

173.3 

130.6 

77 

221.2 

166.7 

38 

30.3 

22.9 

98 

78.3 

59.0 

58 

126.2 

95.1 

18 

174.1 

131.2 

78 

222.0 

167.3 

39 

31.1 

23.5 

99 

79.1 

59.6 

59 

127.0 

95.7 

19 

174.9 

131.8 

79 

222.8 

167.9 

40 

31.9 

24.1 

100 

79.9 

60.2 

60 

127.8 

96.3 

20 

175.7 

132.4 

80 

223.6 

168.5 

41 

32.7 

24.7 

101 

80.7 

60.8 

161 

128.6 

96.9 

221 

176.5 

133.0 

281 

224.4 

169.1 

42 

33.5 

25.3 

02 

81.5 

61.4 

62 

129.4 

97.5 

22 

177.3 

133.6 

82 

225.2 

169.7 

43 

34.3 

25.9 

03 

82.3 

62.0 

63 

130.2 

98.1 

23 

178.1 

134.2 

83 

226.0 

170.3 

44 

35.1 

26.5 

04 

83.1 

62.6 

64 

131.0 

98.7 

24 

178.9 

134.8 

84 

226.8 

170.9 

45 

35.9 

27.1 

05 

83.9 

63.2 

65 

131.8 

99.3 

25 

179.7 

135.4 

85 

227.6 

171.5 

46 

36.7 

27.7 

06 

84.7 

63.8 

66 

132.6 

99.9 

26 

180.5 

136.0 

86 

228.4 

172.1 

47 

37.5 

28.3 

07 

85.5 

64.4 

67 

133.4 

100.5 

27 

181.3 

136.6 

87 

229.2 

172.7 

48 

38.3 

28.9 

08 

86.3 

65.0 

68 

134.2 

101.1 

28 

182.1 

137.2 

88 

230.0 

173.3 

49 

39.1 

29.5 

09 

87.1 

65.6 

69 

135.0 

101.7 

29 

182.9 

137.8 

89 

230.8 

173.9 

50 

39.9 

30.1 

10 

87.8 

66.2 

70 

135.8 

102.3 

30 

183.7 

138.4 

90 

231.6 

174.5 

51 

40.7 

30.7 

111 

88.6 

66.8 

171 

136.6 

102.9 

231 

184.5 

139.0 

291 

232.4 

175.1 

52 

41.5 

31.3 

12 

89.4 

67.4 

72 

137.4 

103.5 

32 

185.3 

139.6 

92 

233.2 

175.7 

53 

42.3 

31.9 

13 

90.2 

68.0 

73 

138.2 

104.1 

33 

186.1 

140.2 

93 

234.0 

176.3 

54 

43.1 

32.5 

14 

91.0 

68.6 

74 

139.0 

104.7 

34 

186.9 

140.8 

94 

234.8 

176.9 

55 

43.9 

33.1 

15 

91.8 

69.2 

75 

139.8 

105.3 

35 

187.7 

141.4 

95 

235.6 

177.5 

56 

44.7 

33.7 

16 

92.6 

69.8 

76 

140.6 

105.9 

36 

188.5 

142.0 

96 

236.4 

178.1 

57 

45.5 

34.3 

17 

93.4 

70.4 

77 

141.4 

106.5 

37 

189.3 

142.6 

97 

237.2 

178.7 

58 

46.3 

34.9 

18 

94.2 

71.0 

78 

142.2 

107.1 

38 

190.1 

143.2 

98 

238.0 

179.3 

59 

47.1 

35.5 

19 

95.0 

71.6 

79 

143.0 

107.7 

39 

190.9 

143.8 

99 

238.8 

179.9 

60 
Dist. 

47.9 

36.1 

20 

95.8 

72.2 

80 

143.8 

108.3 

40 

191.7 

144.4 

300 

239.6 

180.5 

Dep. 

Lat. 

DiBt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

53°  (127°,  233 

°,  307° 

)• 

TABLE  2. 

[Page  605     I 

Difference  of  Latitude  and  Departure  for  37°  (143°,  217°,  323°).                                 1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

240.4 

181.1 

361 

288.3 

217.3 

421 

336.2 

253.4 

481 

384.1 

289.5 

541 

432.0 

325.6 

02 

241.2 

181.7 

62 

289.1 

217.9 

22 

337.0 

254.0 

82 

384.9 

290.0 

42 

432.8 

326.2 

03 

242.0 

182.4 

63 

289.9 

218.5 

23 

337.8 

254.6 

83 

385.7 

290.6 

43 

433.6 

326.8 

04 

242.7 

183.0 

64 

290.7 

219.1 

24 

338.6 

255.2 

84 

386.5 

291.2 

44 

434.4 

327.3 

05 

243.5 

183.6 

65 

291.5 

219.7 

25 

339.4 

255.8 

85 

387.3 

291.8 

45 

435.2 

327.9 

06 

244.3 

184.2 

66 

292.3 

220.3 

26 

340.2 

256.4 

86 

388.1 

292.4 

46 

436.0 

328.5 

07 

245.1 

184.8 

67 

293.1 

220.9 

27 

341.0 

257.0 

87 

388.9 

293.0 

47 

436.8 

329.1 

08 

245.9 

185.4 

68 

293.9 

221.5 

28 

341.8 

257.6 

88 

389.7 

293.6 

48 

437.6 

329.7 

09 

246.7 

186.0 

69 

294.7 

222.1 

29 

342.6 

258.2 

89 

390.5 

294.2 

49 

438.4 

330.3 

10 

247.5 

186.6 

70 

295.5 

222.7 

30 

343.4 

258.8 

90 

391.3 

294.8 

50 

439.2 

330.9 

311 

248.3 

187.2 

371 

296.3 

223.3 

431 

344.2 

259.4 

491 

392.1 

295.4 

551 

440.0 

331.5 

12 

249.1 

187.8 

72 

297.1 

223.9 

32 

345.0 

260.0 

92 

392.9 

296.0 

52 

440.8 

332.1 

13 

249.9 

188.4 

73 

297.9 

224.5 

33 

345.8 

260.6 

93 

393.7 

296.6 

53 

441.6 

332.7 

14 

250.7 

189.0 

74 

298.7 

225.1 

34 

346.6 

261.2 

94 

394.5 

297.2 

54 

442.4 

333. 3 

15 

251.5 

189.6 

75 

299.5 

225.  7 

35 

347.4 

261.8 

95 

395.3 

297.8 

55 

443.2 

333.9 

16 

252.3 

190.2 

76 

300.3 

226.3 

36 

348.2 

262.4 

96 

396.1 

298.5 

56 

444.0 

334.6 

17 

253.1 

190.8 

77 

301.1 

226.9 

37 

349.0 

263.0 

97 

396.9 

299.1 

57 

444.8 

235.2 

18 

253.9 

191.4 

78 

301.8 

227.5 

38 

349.8 

263.6 

98 

397.7 

399.7 

58 

445.6 

335.8 

19 

254.7 

192.0 

79 

302.6 

228.1 

39 

350.  6 

264.2 

99 

398.5 

300.3 

59 

446.4 

336.4 

20 

255.5 
256.3 

192.6 

80 

303.4 

228.7 

40 

351.4 

264.8 

500 

399.3 

300.9 

60 

447.2 

337.0 

321 

193.2 

381 

304.2 

229.3 

441 

352.2 

265.4 

501 

400.1 

301.5 

561 

448.0 

337.6 

22 

257.1 

193.8 

82 

305.0 

229.9 

42 

353.0 

266.0 

02 

400.9 

302.1 

62 

448.8 

338.2 

23 

257.9 

194.4 

83 

305.8 

230.5 

43 

353.8 

266.6 

03 

401.7 

302.7 

63 

449.6 

338.8 

24 

258.7 

195.0 

84 

306.6 

231.1 

44 

354.6 

267.2 

04 

402.5 

303.3 

64 

450.4 

339.4 

25 

259.5 

195. 6 

85 

307.4 

231.7 

45 

355.4 

267.8 

05 

403.3 

303.9 

65 

451.2 

340.0 

26 

260.3 

196.2 

86 

308.2 

232.3 

46 

356.2 

268.4 

06 

404.1 

304.5 

66 

452.0 

340.6 

27 

261.1 

196.8 

87 

309.0 

232.9 

47 

357.0 

269.0 

07 

404.9 

305.1 

67 

452.8 

341.2 

28 

261.9 

197.4 

88 

309.8 

233.5 

48 

357.8 

269.6 

08 

405.7 

305.7 

68 

453.6 

341.8 

29 

262.7 

198.0 

89 

310.6 

234.1 

49 

358.6 

270.2 

09 

406.5 

306.3 

69 

454.4 

342.4 

30 

263.5 
264.3 

198.6 

90 

311.4 

234.7 

50 

359.4 

270.8 

10 

407.3 

306.9 

70 

455.2 

343.0 

331 

199.2 

391 

312.2 

235.3 

451 

360.1 

271.4 

511 

408.1 

307.5 

571 

456.0 

343.6 

32 

265.1 

199.8 

92 

313.0 

235.9 

52 

360.9 

272.0 

12 

408.9 

308.2 

72 

456.8 

344.3 

33 

265.9 

200.4 

93 

313.8 

236. 5 

53 

361.7 

272.6 

13 

409.7 

308.8 

73 

457.6 

344.9 

34 

266.7 

201.0 

94 

314.6 

237.1 

54 

362.5 

273.2 

14 

410.5 

309.4 

74 

458.4 

345.5 

35 

267.5 

201.6 

95 

315.4 

237.7 

55 

363.3 

273.8 

15 

411.3 

310.0 

75 

459.2 

346.1 

36 

268.3 

202.2 

96 

316.2 

238.3 

56 

364.1 

274.4 

16 

412.1 

310.6 

76 

460.0 

346.7 

37 

269.1 

202.8 

97 

317.0 

238.9 

57 

364.9 

275.0 

17 

412.9 

311.2 

77 

460.8 

347.3 

38 

269.9 

203.4 

98 

317.8 

239. 5 

58 

365.7 

275.6 

18 

413.7 

311.8 

78 

461.6 

347.9 

39 

270.7 

204.0 

99 

318.6 

240.1 

59 

366.5 

276.2 

19 

414.5 

312.4 

79 

462.4 

348.5 

40 

271.5 

204.6 

400 

319.4 

240.7 

60 

367.3 

276.8 

20 

415.3 

313.0 

80 

463.2 

349.1 

341 

272.3 

205.2 

401 

320.2 

241.3 

461 

368.1 

277.4 

521 

416.1 

313.6 

581 

464.0 

349.7 

42 

273.1 

205.8 

02 

321.0 

241.9 

62 

368.9 

278.0 

22 

416.9 

314.2 

82 

464.8 

350.3 

43 

273.9 

206.4 

03 

321.8 

242.5 

63 

369.7 

278.6 

23 

417.7 

314.8 

83 

465.6 

350.9 

44 

274.7 

207.0 

(^4 

322.6 

243.1 

64 

370.5 

279.2 

24 

418.5 

315.4 

84 

466.4 

351.5 

45 

275.5 

207.6 

05 

323.4 

243.7 

65 

371.3 

279.8 

25 

419.3 

316.0 

85 

467.2 

352.1 

46 

276.3 

208.2 

06 

324.2 

244.3 

66 

372.1 

280.4 

26 

420.1 

316.6 

86 

468.0 

352.7 

47 

277.1 

208.8 

07 

325.0 

244.9 

67 

372.9 

281.0 

27 

420.9 

317.2 

87 

468.8 

353.3 

48 

277.9 

209.4 

08 

325.8 

245.5 

68 

373.7 

281.6 

28 

421.7 

317.8 

88 

469.6 

353.9 

49 

278.7 

210.0 

09 

326.6 

246.1 

69 

374.5 

282.3 

29 

422.5 

318.4 

89 

470.4 

354.5 

50 

279.5 

210.6 

10 

327.4 

246.7 

70 

375.3 

282.9 

30 

423.3 

319.0 

90 

471.2 

355.1 

351 

280.3 

211.2 

411 

328.2 

247.3 

471 

376.1 

283.5 

531 

424.1 

319.6 

591 

472.0 

355.7 

52 

281.1 

211.8 

12 

329.0 

247.9 

72 

376.9 

284.1 

32 

424.9 

320.2 

92 

472.8 

356.3 

53 

281.9 

212.4 

13 

329.8 

248.5 

73 

377.7 

284.7 

33 

425.7 

320.8 

93 

473.6 

356.9 

54 

282.7 

213.0 

14 

330.6 

249.2 

74 

378.5 

285.3 

34 

426.5 

321.4 

94 

474.4 

357.5 

55 

283.5 

213.6 

15 

331.4 

249.8 

75 

379.3 

285.9 

35 

427.3 

322.0 

95 

475.2 

358.1 

56 

284.3 

214.2 

16 

332.2 

250.4 

76 

380.1 

286.5 

36 

428.1 

322.6 

96 

476.0 

358.7 

57 

285.1 

214.8 

17 

333.0 

251.0 

77 

380.9 

287.1 

37 

428.9 

323.2 

97 

476.8 

359.3 

58 

285.9 

215.4 

18 

333.8 

251.6 

78 

381.7 

287.7 

38 

429.7 

323.8 

98 

477.6 

359.9 

59 

286.7 

216.1 

19 

334.6 

252.2 

79 

382.5 

288.3 

39 

430.5 

324.4 

99 

478.4 

360.5 

60 

287.5 

216.7 

20 

335.4 

252.8 

80 

383.3 

288.9 

40 

431.3 

325.0 

600 

479.2 

361.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep.         Lat.     1 

e 

)3°  (127°,  233°,  307° 

). 

1 

Page  606] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  38°  (142°,  218°,  322' 

')• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

1 

0.8 

0.6 

61 

48.1 

37.6 

121 

95.3 

74.5 

181 

142.6 

111.4 

241 

189.9 

148.4 

2 

1.6 

1.2 

62 

48.9 

38.2 

22 

96.1 

75.1 

82 

143.4 

112.1 

42. 

190.7 

149.0 

3 

2.4 

1.8 

63 

49.6 

38.8 

23 

96.9 

75.7 

83 

144.2 

112.7 

43 

191.5 

149.6 

4 

3.2 

2.5 

64 

50.4 

39.4 

24 

97.7 

76.3 

84 

145.0 

113.3 

44 

192.3 

150.2 

5 

3.9 

3.1 

65 

51.2 

40.0 

25 

98.5 

77.0 

85 

145.8 

113.9 

45 

193.1 

150.8 

6 

4.7 

3.7 

66 

52.0 

40.6 

26 

99.3 

77.6 

86 

146.6 

114.5 

46 

193.9 

151.5 

7 

5.5 

4.3 

67 

52.8 

41.2 

27 

100.1 

78.2 

87 

147.4 

115.1 

47 

194.6 

152.1 

8 

6.3 

4.9 

68 

53.6 

41.9 

28 

100.9 

78.8 

88 

148.1 

115.7 

48 

195.4 

152.7 

9 

7.1 

5.5 

69 

54.4 

42.5 

29 

101.7 

79.4 

89 

148.9 

116.4 

49 

196.2 

153.3 

10 

7.9 

6.2 

70 

55.2 

43.1 

30 

102.4 

80.0 

90 

149.7 

117.0 

50 

197.0 

153.9 

11 

8.7 

6,8 

71 

55.9 

43.7 

131 

103.2 

80.7 

191 

150.5 

117.6 

251 

197.8 

154.5 

12 

9.5 

7.4 

72 

56.7 

44.3 

32 

104.0 

81.3 

92 

151.3 

118.2 

52 

198.6 

155.1 

13 

10.2 

8.0 

73 

57.5 

44.9 

33 

104.8 

81.9 

93 

152.1 

118.8 

53 

199.4 

155.8 

14 

11.0 

8.6 

74 

58.3 

45.6 

34 

105.6 

82.5 

94 

152.9 

119.4 

54 

200.2 

156.4 

15 

11.8 

9.2 

75 

59.1 

46.2 

35 

106.4 

83.1 

95 

153.7 

120.1 

55 

200.9 

157.0 

16 

12.6 

9.9 

76 

59.9 

46.8 

36 

107.2 

83.7 

96 

154.5 

120.7 

56 

201.7 

157.6 

17 

13.4 

10.5 

77 

60.7 

47.4 

37 

108.0 

84.3 

97 

155.2 

121.3 

57 

202.5 

158.2 

18 

14.2 

11.1 

78 

61.5 

48.0 

38 

108.7 

85.0 

98 

156.0 

121.9 

58 

203.3 

158.8 

19 

15.0 

11.7 

79 

62.3 

48.6 

39 

109.5 

85.6 

99 

156.8 

122.5 

59 

204.1 

159.6 

20 

15.8 

12.3 
12. 9 

80 

63.0 

49.3 

40 

110.3 

86.2 

200 

157.6 

123.1 

60 

204.9 

160.1 

21 

16.5 

81 

63.8 

49.9 

141 

111.1 

86.8 

201 

158.4 

123.7 

261 

205.  7 

160.7 

22 

17.3 

13.5 

82 

64.6 

50.5 

42 

111.9 

87.4 

02 

159.2 

124.4 

62 

206.5 

161.3 

23 

18.1 

14.2 

83 

65.4 

51.1 

43 

112.7 

•88.0 

03 

160.0 

125.0 

63 

207.2 

161.9 

24 

18.9 

14.8 

84 

66.2 

51.7 

44 

113.5 

88.7 

04 

160.8 

125.6 

64 

208.0 

162.6 

25 

19.7 

15.4 

85 

67.0 

52.3 

45 

114.3 

89.3 

05 

161.5 

126.2 

65 

208.8 

163. 2 

26 

20.5 

16.0 

86 

67.8 

52.9 

46 

115.0 

89.9 

06 

162.3 

126.8 

66 

209.6 

163.8 

27 

21.3 

16.6 

87 

68.6 

53.6 

47 

115.8 

90.5 

07 

163.1 

127.4 

67 

210.4 

164.4 

28 

22.1 

17.2 

88 

69.3 

54.2 

48 

116.6 

91.1 

08 

163.9 

128.1 

68 

211.2 

165.0 

29 

22.9 

17.9 

89 

70.1 

54.8 

49 

117.4 

91.7 

09 

164.7 

128.7 

69 

212.0 

165.6 

30 

23.6 

18.5 
19.1 

90 

70.9 

55.4 

50 

118.2 
119.0 

92.3 

10 

165.5 

129.3 

70 

212.8 

166.2 

31 

24.4 

91 

71.7 

56.0 

151 

93.0 

211 

166.3 

129.9 

271 

213.6 

166.8 

32 

25.2 

19.7 

92 

72.5 

56.6 

52 

119.8 

93.6 

12 

167.1 

130.5 

72 

214.3 

167.5 

33 

26.0 

20.3 

93 

73.3 

57.3 

53 

120.6 

94.2 

13 

167.8 

131.1 

73 

215. 1 

168.1 

34 

26.8 

20.9 

94 

74.1 

57.9 

54 

121.4 

94.8 

14 

168.6 

131.8 

74 

215.9 

168.7 

35 

27.6 

21.5 

95 

74.9 

58.5 

55 

122.1 

95.4 

15 

169.4 

132.4 

75 

216.7 

169.3 

36 

28.4 

22.2 

96 

75.6 

59.1 

56 

122.9 

96.0 

16 

170.2 

133.0 

76 

217.5 

169.9 

37 

29.2 

22.8 

97 

76.4 

59.7 

57 

123.7 

96.7 

17 

171.0 

133.6 

77 

218.3 

170.5 

38 

29.9 

23.4 

98 

77.2 

60.3 

58 

124.5 

97.3 

18 

171.8 

134.2 

78 

219.1 

171.2 

39 

30.7 

24.0 

99 

78.0 

61.0 

59 

125.3 

97.9 

19 

172.6 

134.8 

79 

219.9 

171.8 

40 

31.5 

24.6 

100 

78.8 

61.6 

60 

126.1 

98.5 

20 

173.4 

135.4 

80 

220.6 

172.4 

41 

32.3 

25.2 

101 

79.6 

62.2 

161 

126.9 

99.1 

221 

174.2 

136.1 

281 

221.4 

173.0 

42 

33.1 

25.9 

02 

80.4 

62.8 

62 

127.7 

99.7 

22 

174.9 

136.7 

82 

222.2 

173.6 

43 

33.9 

26.5 

03 

81.2 

63.4 

63 

128.4 

100.4 

23 

175.7 

137.3 

83 

223.0 

174.2 

44 

34.7 

27.1 

04 

82.0 

64.0 

64 

129.2 

101.0 

24 

176. 5 

137.9 

84 

223.8 

174.8 

45 

35.5 

27.7 

05 

82.7 

64.6 

65 

130.0 

101.6 

25 

177.3 

138.5 

85 

224.6 

175.5 

46 

36.2 

28.3 

06 

83.5 

65.3 

66 

130.8 

102.2 

26 

178.1 

139.1 

86 

225.4 

176.1 

47 

37.0 

28.9 

07 

84.3 

65.9 

67 

131.6 

102.8 

27 

178.9 

139.8 

87 

226.2 

176.7 

48 

37.8 

29.6 

08 

85.1 

66.5 

68 

132.4 

103.4 

28 

179.7 

140.4 

88 

226.9 

177.3 

49 

38.6 

30.2 

09 

85.9 

67.1 

69 

133.2 

104.0 

29 

180.  5 

141.0 

89 

227.7 

177.9 

50 

39.4 

30.8 

10 

86.7 

67.7 

70 

134.0 

104.7 

30 

181.2 
182.0 

141.6 
142.2 

90 

228.5 

178.5 

51 

40.2 

31.4 

111 

87.5 

68.3 

171 

134.7 

105.3 

231 

291 

229.3 

179.2 

52 

41.0 

32.0 

12 

88.3 

69.0 

72 

135.5 

105.9 

32 

182.8 

142.8 

92 

230.1 

179.8 

53 

41.8 

32.6 

13 

89.0 

69.6 

73 

136.  3 

106.5 

33 

183.6 

143.4 

93 

230.9 

180.4 

54 

42.6 

33.2 

14 

89.8 

70.2 

74 

137.1 

107.1 

34 

184.4 

144.1 

94 

231.7 

181.0 

55 

43.3 

33.9 

15 

90.6 

70.8 

75 

137.9 

107.7 

35 

185.2 

144,7 

95 

232.5 

181.6 

56 

44.1 

34.5 

16 

91.4 

71.4 

76 

138.7 

108.4 

36 

186.0 

145.3 

96 

233.3 

182.2 

57 

44.9 

35.1 

17 

92.2 

72.0 

77 

139.5 

109.0 

37 

186.8 

145.9 

97 

234.0 

182.9 

58 

45.7 

35.7 

18 

93.0 

72.6 

78 

140.3 

109.6 

38 

187.5 

146.5 

98 

234.8 

183.6 

59 

46.5 

36.3 

19 

93.8 

73.3 

79 

141.1 

110.2 

39 

188.3 

147.1 

99 

235.6 

184.1 

60 

47.3 

36.9 

20 

94.6 

73.9 

80 

141.8 

110.8 

40 

189.1 

147.8 

300 

236.4 

184.7 

Dist. 

Dep. 

Lat. 

Dl8t. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

52' 

'  (128°,  232°, 

308°). 

. 

TABLE  2. 

[Page  607 

Difference  of  Latitude  and  Departure  for  38°  (142°,  218°,  322° 

)• 

Dist. 

Lat.        Dep.   1 

DlBt. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     j    Dep. 

301 

237.2 

186.3 

361 

284.5 

222.3 

421 

331.8 

259.2 

481 

379.0 

296.2 

541 

i 
426.  3     333. 1 

02 

238.0 

185.9 

62 

285.3 

222.9 

22 

332.5 

259.8 

82 

379.8 

296.8 

42 

427.1  '  333.7 

03 

238.8 

186.6 

63 

286.0 

223.5 

23 

333.3 

260.4 

83 

380.6 

297.4 

43 

427.  9  1  334. 3 

04 

239.6 

187.2 

64 

286.8 

224.1 

24 

334.1 

261.0 

84 

381.4 

298.0 

44 

428.7  1  335.0 

05 

240.3 

187.8 

65 

287.6 

224.7 

25 

334.9 

261.7 

85 

382.2 

298.6 

45 

429.  5     335. 6 

06 

241.1 

188.4 

66 

288.4 

225.3 

26 

335.7 

262.3 

86 

383.0 

299.2 

46 

430.3 

336.2 

07 

241.9 

189.0 

67 

289.2 

226.0 

27 

336.5 

262.9 

87 

383.8 

299.8 

47 

431.0 

336.8 

08 

242.7 

189.6 

68 

290.0 

226.6 

28 

337.3 

263.5 

88 

384.5 

300.4 

48 

431.8 

337.4 

09 

243.5 

190.2 

69 

290.8 

227.2 

29 

338.1 

264.1 

89 

385.3 

301.1 

49 

432.6 

338.0 

10 

244.3 

190.9 

70 

291.6 

227.8 

30 

338.8 

264.7 

90 

386.1 

301.7 

50 

433.4 

338.6 

311 

245.1 

191.5 

371 

292.4 

228.4 

431 

339.6 

265.4 

491 

386.9 

302.3 

551 

434.2 

339.3 

12 

245.9 

192.1 

72 

293.1 

229.0 

32 

340.4 

266.0 

92 

387.7 

302.9 

52 

435.0 

339.9 

13 

246.6 

192.7 

73 

293.9 

229.6 

33 

341.2 

266.6 

93 

388.5 

303.5 

53 

435.8 

340.6 

14 

247.4 

193.3 

74 

294.7 

230.3 

34 

342.0 

267.2 

94 

389.3 

304.2 

54 

436.6 

341. 1 

15 

248.2 

193.9 

75 

295.5 

230.9 

35 

342.8 

267.8 

95 

390.1 

304.8 

55 

437.4 

341.7 

16 

249.0 

194.6 

76 

296.3 

231.5 

36 

343.6 

268.4 

96 

390.9 

305.4 

56 

438.1 

342.3 

17 

249.8 

195.2 

77 

297.1 

232.1 

37 

344.4 

269.1 

97 

391.6 

306.0 

57 

438.9 

348.0 

18 

250.6 

195.8 

78 

297.9 

232.7 

38 

345.2 

269.7 

98 

392.4 

306.6 

58 

439.7 

343.6 

19 

251.4 

196.4 

79 

298.7 

233.3 

39 

345.9 

270.3 

99 

393.2 

307.2 

69 

440.5 

344.2 

20 
321 

252.2 

197.0 

80 

299.4 

234.0 

40 

346.7 

270.9 

500 

394.0 

307.8 

60 

441.3 

344.8 

253.0 

197.6 

381 

300.2 

234.6 

441 

347.5 

271.5 

501 

394.8 

308.4 

561 

442.1 

345.4 

22 

253.7 

198.2 

82 

301.0 

235.2 

42 

348.3 

272.1 

02 

395.6 

309.1 

62 

442.9 

346.0 

23 

254.6 

198.9 

83 

301.8 

235.8 

43 

349.1 

272.7 

03 

396.4 

309.7 

63 

443.  7     346. 6  1 

24 

255.3 

199.5 

84 

302.6 

236.4 

44 

349.9 

273.4 

04 

397.2 

310.3 

64 

444.4 

347.2 

25 

256.1 

200.1 

85 

303.4 

237.0 

45 

350.7 

274.0 

05 

397.9 

310.9 

65 

445.2 

347. 8 

26 

256.9 

200.7 

86 

304.2 

237.7 

46 

351.5 

274.6 

06 

398.7 

311.6 

66 

446.0 

348.6 

27 

257.7 

201.3 

87 

305.0 

238.3 

47 

352.2 

275.2 

07 

399.5 

312.2 

67 

446.8 

349.1 

28 

258.5 

201.9 

88 

305.7 

238.9 

48 

353.0 

275.8 

08 

400.3 

312.8 

68 

447.6 

349.7 

29 

259.3 

202.6 

89 

306.5 

239.5 

49 

353.8 

276.4 

09 

401.1 

313.4 

69 

448. 4     350. 3 

30 

260.0 

203.2 

90 

307.3 

240.1 

50 

354.6 

277.1 

10 

401.9 

314.0 

70 

449.2     350.9 

331 

260.8 

203.8 

391 

308.1 

240.7 

451 

355.4 

277.7 

511 

402.7 

314.6 

671 

460. 0     361. 6 

32 

261.6 

204.4 

92 

308.9 

241.3 

52 

356.2 

278.3 

12 

403.6 

316.2 

72 

460.  7     352. 2 

33 

262.4 

205.0 

93 

309.7 

242.0 

53 

357.0 

278.9 

13 

404.2 

316.8 

73 

461.5  !  352.8 

34 

263.2 

205.6 

94 

310.5 

242.6 

54 

357.8 

279.5 

14 

405.0 

316.4 

74 

452.3  ;  353.4 

35 

264.0 

206.3 

95 

311.3 

243.2 

55 

358.5 

280.1 

15 

405.8 

317.1 

76 

463.1  1  354.0 

36 

264.8 

206.9 

96 

312.1 

243.8 

56 

359.3 

280.7 

16 

406.6 

317.7 

76 

453.9  !  :i54.6 

37 

265.6 

207.5 

97 

312.8 

244.4 

57 

360.1 

281.4 

17 

407. 4 

318.3 

77 

464.  7  '  365.  2 

38 

266.3 

208.1 

98 

313.6 

245.0 

58 

360.9 

282.0 

18 

408.2 

318.9 

78 

455. 5     :355. 8 

39 

267.1 

208.7 

99 

314.4 

245.7 

59 

361.7 

282.6 

19 

409.0 

319.5 

79 

456. 3     356. 4 

40 

267.9 

209.3 

400 

315.2 

246.3 

60 

362.5 

283.2 

20 

409.8 

320.2 

80 

467. 1     357. 1 

341 

268.7 

209.9 

401 

316.0 

246.9 

461 

363.3 

283.8 

521 

410.6 

320.8 

581 

457. 8     357.  7 

42 

269.5 

210.6 

02 

316.8 

247.5 

62 

364.1 

284.4 

22 

411.3 

321.4 

82 

458. 6     358. 3 

43 

270.3 

211.2 

03 

317.6 

248.1 

63 

364.9 

285.1 

23 

412.1 

322.0 

83 

459. 4     358. 9 

44 

271.1 

211.8 

04 

318.4 

248.7 

64 

365.6 

285.7 

24 

412.9 

322.6 

84 

460.  2     359. 6 

45 

271.9 

212.4 

05 

319.1 

249.3 

65 

366.4 

286.3 

25 

413.7 

323.2 

85 

461. 0     360. 2 

46 

272.7 

213.0 

06 

319.9 

250.0 

66 

367.2 

286.9 

26 

414.5 

323.8 

86 

461. 8     360. 8 

47 

273.4 

213.6 

07 

320.7 

250.6 

67 

368.0 

287.5 

27 

415.3 

324.5 

87 

462. 6     361. 4 

48 

274.2 

214.3 

08 

321.5 

251.2 

68 

368.8 

288.1 

28 

416.1 

325.1 

88 

463.3 

362.0 

49 

275.0 

214.9 

09 

322.3 

251.8 

69 

369.6 

288.7 

29 

416.9 

325.7 

89 

464.1 

362. 6 

50 

275.8 

215.5 

10 

323.1 

252.4 

70 

370.4 

289.3 

30 

417.6 

326.3 

90 

464.9 

363.2 

351 

276.6 

216.1 

411 

323.9 

253.0 

471 

371.2 

290.0 

531 

418.4 

326.9 

591 

466.7 

363.8 

52 

277.4 

216.7 

12 

324.7 

253.7 

72 

371.9 

290.6 

32 

419.2 

327.5 

92 

466.6 

364.4 

53 

278.2 

217.3 

13 

325.5 

254.3 

73 

372.7 

291.2 

33 

420.0 

328.2 

93 

467.3 

365.1 

M 

279.0 

218.0 

14 

326.2 

254.9 

74 

373.5 

291.8 

34 

420.8 

328.8 

94 

468.1 

365.7 

55 

279.7 

218.6 

15 

327.0 

255.5 

75 

374.3 

292.4 

35 

421.6 

329.4 

95 

468.9 

366.3 

56 

280.5 

219.2 

16 

327.8 

256.1 

76 

375.1 

293.1 

36 

422.4 

330.0 

96 

469.7 

366.9 

57 

281.3 

219.8 

17 

328.6 

256.7 

77 

375.9 

293.7 

37 

423.2 

330.6 

97 

470.6 

367.5 

58 

282.1 

220.4 

18 

329.4 

257.4 

78 

376.7 

294.3 

38 

424.0 

331.2 

98 

471.2 

368.1 

59 

282.9 

221.0 

19 

330.2 

258.0 

79 

377. 5 

294.9 

39 

424.7 

331.8 

99 

472.0 

368.7 

60 

283.7 

221.6 

20 

331.0 

258.6 

80 

378.2 

295.5 

40 

425.5 

332.5 

600 

472.8 

369.4 

Dist. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

52°  (128°,  235 

2°,  308°). 

1 

Page  608] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  39°  (141°,  219°,  321° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0,8 

0.6 

61 

47.4 

38.4 

121 

94.0 

76.1 

181 

140.7 

113.9 

241 

187.3 

151.7 

2 

1.6 

1.3 

62 

48.2 

39.0 

22 

94.8 

76.8 

82 

141.4 

114.5 

42 

188.1 

152.3 

3 

2.3 

1.9 

63 

49.0 

39.6 

23 

95.6 

77.4 

83 

142.2 

115.  2 

43 

188.8 

152.9 

4 

3.1 

2.5 

64 

49.7 

40.3 

24 

96.4 

78.0 

84 

143.0 

115.8 

44 

189.6 

153.6 

5 

3.9 

3.1 

65 

50.5 

40.9 

25 

97.1 

78.7 

85 

143.8 

116.4 

45 

190.4 

154.2 

6 

4.7 

3.8 

66 

51.3 

41.5 

26 

97.9 

79.3 

86 

144.5 

117.1 

46 

191.2 

154.8 

7 

5.4 

4.4 

67 

52.1 

42.2 

27 

98.7 

79.9 

87 

145.3 

117.7 

47 

192.0 

155.4 

8 

6.2 

5.0 

68 

52.8 

42.8 

28 

99.5 

80.6 

88 

146.1 

118.3 

48 

192.7 

156.1 

9 

7.0 

5.7 

69 

53.6 

43.4 

29 

100.3 

81.2 

89 

146.9 

118.9 

49 

193.5 

156.7 

10 

7.8 

6.3 

70 

54.4 

44.1 

80 

101.0 

81.8 

90 

147.7 

119.6 

50 

194.3 

157.3 

11 

8.5 

6.9 

71 

55.2 

44.7 

131 

101.8 

82.4 

191 

148.4 

120.2 

251 

195.1 

158.0 

12 

9.3 

7.6 

72 

56.0 

45.3 

32 

102.6 

83.1 

92 

149.2 

120.8 

52 

195.8 

158.6 

13 

10.1 

8.2 

73 

56.7 

45.9 

33 

103.4 

83.7 

93 

150.0 

121.5 

53 

196.6 

159.2 

14 

10.9 

8.8 

74 

57.5 

46.6 

34 

104.1 

84.3 

94 

150.8 

122.1 

54 

197.4 

159.8 

15 

11.7 

9.4 

75 

58.3 

47.2 

35 

104.9 

85.0 

95 

151.5 

122.7 

55 

198.2 

160.5 

16 

12.4 

10.1 

76 

59.1 

47.8 

36 

105.7 

85.6 

96 

152.3 

123.3 

56 

198.9 

161.1 

17 

13.2 

10.7 

77 

59.8 

48.5 

37 

106.5 

86.2 

97 

153.1 

124.0 

57 

199.7 

161.7 

18 

14.0 

11.3 

78 

60.6 

49.1 

38 

107.2 

86.8 

98 

153.9 

124.6 

58 

200.5 

162.4 

19 

14.8 

12.0 

79 

61.4 

49.7 

39 

108.0 

87.5 

99 

154.7 

125.2 

59 

201.3 

163.0 

20 

15.5 

12.6 

80 

62.2 

50.3 

40 

108.8 

88.1 

200 

155.4 

125.9 

60 

202.1 

163.6 

21 

16.3 

13.2 

81 

62.9 

51.0 

141 

109.6 

88.7 

201 

156.2 

126.5 

261 

202.8 

164.3 

22 

17.1 

13.8 

82 

63.7 

51.6 

42 

110.4 

89.4 

02 

157.0 

127.1 

62 

203.6 

164.9 

23 

17.9 

14.5 

83 

64.5 

52.2 

43 

111.1 

90.0 

03 

157.8 

127.8 

63 

204.4 

165.5 

24 

18.7 

15.1 

84 

65.3 

52.9 

44 

111.9 

90.6 

04 

158.5 

128.4 

64 

205.2 

166.1 

25 

19.4 

15.7 

85 

66.1 

53.5 

45 

112.7 

91.3 

05 

159.3 

129.0 

65 

205.9 

166.8 

26 

20.2 

16.4 

86 

66.8 

54.1 

46 

113.5 

91.9 

06 

160.1 

129.6 

66 

206.7 

167.4 

27 

21.0 

17.0 

87 

67.6 

54.8 

47 

114.2 

92.5 

07 

160.9 

130.3 

67 

207.5 

168.0 

28 

21.8 

17.6 

88 

68.4 

55.4 

48 

115.0 

93.1 

08 

161.6 

130.9 

68 

208.3 

168.7 

29 

22.5 

18.3 

89 

69.2 

56.0 

49 

115.8 

93.8 

09 

162.4 

131.5 

69 

209.1 

169.3 

30 

23.3 

18.9 

90 

69.9 

56.6 

50 

116.6 

94.4 

10 

163.2 

132.2 

70 

209.8 

169.9 

31 

24.1 

19.5 

91 

70.7 

57.3 

151 

117.3 

95.0 

211 

164.0 

132.8 

271 

210.6 

170.5 

32 

24.9 

20.1 

92 

71.5 

57.9 

52 

118.1 

95.7 

12 

164.8 

133.4 

72 

211.4 

171.2 

33 

25.6 

20.8 

93 

72.3 

58.5 

53 

118.9 

96.3 

13 

165.5 

134.0 

73 

212.2 

171.8 

34 

26.4 

21.4 

94 

73.1 

59.2 

54 

119.7 

96.9 

14 

166.3 

134.7 

74 

212.9 

172.4 

35 

27.2 

22.0 

95 

73.8 

59.8 

55 

120.5 

97.5 

15 

167.1 

135.3 

75 

213.7 

173.1 

36 

28.0 

22.7 

96 

74.6 

60.4 

56 

121.2 

98.2 

16 

167.9 

135.9 

76 

214.5 

173.7 

37 

28.8 

23.3 

97 

75.4 

61.0 

57 

122.0 

98.8 

17 

168.6 

136.6 

77 

215.3 

174.3 

38 

29.5 

23.9 

98 

76.2 

61.7 

58 

122.8 

99.4 

18 

169.4 

137.2 

78 

216.0 

175.0 

39 

30.3 

24.5 

99 

76.9 

62.3 

59 

123.6 

100.1 

19 

170.2 

137.8 

79 

216.8 

175.6 

40 

31.1 

25.2 

100 

77.7 

62.9 

60 

124.3 

100.7 

20 

171.0 

138.5 

80 

217.6 
218.4 

176.2 

41 

31.9 

25.8 

101 

78.5 

63.6 

161 

125.1 

101.3 

221 

171.7 

139.1 

281 

176.8 

42 

32.6 

26.4 

02 

79.3 

64.2 

62 

125.9 

101.9 

22 

172.5 

139.7 

82 

219.2 

177.5 

43 

33.4 

27.1 

03 

80.0 

64.8 

63 

126.7 

102.6 

23 

173.3 

140.3 

83 

219.9 

178.1 

44 

34.2 

27.7 

04 

80.8 

65.4 

64 

127.5 

103.2 

24 

174.1 

141.0 

84 

220.7 

178.7 

45 

35.0 

28.3 

05 

81.6 

66.1 

65 

128.2 

103.8 

25 

174.9 

141.6 

85 

221.5 

179.4 

46 

35.7 

28.9 

06 

82.4 

66.7 

66 

129.0 

104.5 

26 

175.6 

142.2 

86 

222.3 

180.0 

47 

36.5 

29.6 

07 

83.2 

67.3 

67 

129.8 

105.1 

27 

176.4 

142.9 

87 

223.0 

180.6 

48 

37.3 

30.2 

,08 

83.9 

68.0 

68 

130.6 

105.7 

28 

177.2 

143.5 

88 

223.8 

181.2 

49 

38.1 

30.8 

09 

84.7 

68.6 

69 

131.3 

106.4 

29 

178.0 

144.1 

89 

224.6 

181.9 

50 

38.9 

31.5 

10 

85.5 

69.2 

70 

132.1 

107.0 

30 

178.7 

144.7 

90 

225.4 

182.5 

51 

39.6 

32.1 

111 

86.3 

69.9 

171 

132.9 

107.6 

231 

179.5 

145.4 

291 

226.1 

183.1 

52 

40.4 

32.7 

12 

87.0 

70.5 

72 

133.7 

108.2 

32 

180.3 

146.0 

92 

226.9 

183.8 

53 

41.2 

33.4 

13 

87.8 

71.1 

73 

134.4 

108.9 

33 

181.1 

146.6 

93 

227.7 

184.4 

54 

42.0 

34.0 

14 

88.6 

71.7 

74 

135.2 

109.5 

34 

181.9 

147.3 

94 

228.5 

185.0 

55 

42.7 

34.6 

15 

89.4 

72.4 

75 

136.0 

110.1 

35 

182.6 

147.9 

95 

229.3 

185.6 

56 

43.5 

35.2 

16 

90.1 

73.0 

76 

136.8 

110.8 

36 

183.4 

148.5 

96 

230.0 

186.3 

57 

44.3 

35.9 

17 

90.9 

73.6 

77 

137.6 

111.4 

37 

184.2 

149.1 

97 

230.8 

186.9 

58 

45.1 

36.5 

18 

91.7 

74.3 

78 

138.3 

112.0 

38 

185.0 

149.8 

98 

231.6 

187.5 

59 

45.9 

37.1 

19 

92.5 

74.9 

79 

139.1 

112.6 

39 

185.7 

150.4 

99 

232.4 

188.2 

60 

46.6 

37.8 

20 

93.3 

75.5 

80 

139.9 

113.3 

40 

186.5 

151.0 

300 

233.1 

188.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

51°  (129°,  231°,  309°). 

TABLE  2. 

[Page  609 

Difference  of  Latitude  and  Departure  for  39°  (141",  219°,  321° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

233.9 

189.4 

361 

280.6 

227.1 

421 

327.2 

264.9 

481 

373.8 

302.6 

541 

420.4 

340.4 

02 

234.7 

190.0 

62 

281.3 

227.8 

22 

328.0 

265.5 

82 

374.6 

303.3 

42 

421.2 

341.0 

03 

235.5 

190.6 

63 

282.1 

228.4 

23 

328.7 

266.2 

83 

375.4 

303.9 

43 

422.0 

341.7 

04 

236.3 

191.3 

64 

282.9 

229.0 

24 

329.5 

266.8 

84 

376.1 

304.5 

44 

422.7 

342.3 

05 

237.0  1191.9 

65 

283.7 

229.7 

25 

330.3 

267.4 

85 

376.9 

305.2 

45 

423.5 

342.9 

06 

237.8 

192.5 

66 

284.4 

230.3 

26 

331.1 

268.0 

86 

377.7 

305.8 

46 

424.3 

343.6 

07 

238.6 

193.2 

67 

285.2 

230.9 

27 

331.9 

268.7 

87 

378.5 

306.4 

47 

425.1 

344.2 

08 

239.4 

193.8 

68 

286.0 

231.5 

28 

332.6 

269.3 

88 

379.3 

307.1 

48 

425.9 

344.8 

09 

240.1 

194.4 

69 

286.8 

232.2 

29 

333.4 

269.9 

89 

380.0 

307.7 

49 

426.6 

345.5 

10 
311 

240.9 

195.0 

70 

287.6 

232.8 

30 

334.2 

270.6 
'271.'2 

90 

380.8 

308.3 
308.9 

50 

427.4 

346.1 

241.7 

195.7 

371 

288.3 

233.4 

431 

335.0 

491 

381.6 

551 

428.2 

346.7 

12 

242.5 

196.3 

72 

289.1 

234.1 

32 

335.7 

271.8 

92 

382.4 

309.6 

52 

429.0 

347.4 

13 

243.3 

196.9 

73 

289.9 

234.7 

33 

336.5 

272.5 

93 

383.1 

310.2 

53 

429.7 

348.0 

14 

244.0 

197.6 

74 

290.7 

235.3 

34 

337.3 

273.1 

94 

383.9 

310.8 

54 

430.5 

348.6 

15 

244.8 

198.2 

75 

291.4 

236.0 

35 

338.1 

273.7 

95 

384.7 

311.5 

55 

431.3 

349.2 

16 

245.6 

198.8 

76 

292.2 

236.6 

36 

338.8 

274.3 

96 

386.5 

312.1 

56 

432.1 

349.9 

17 

246.4 

199.5 

77 

293.0 

237.2 

37 

339.6 

275.0 

97 

386.2 

312.7 

57 

432.8 

350.6 

18 

247.1 

200.1 

78 

293.8 

237.8 

38 

340.4 

275.6 

98 

387.0 

313.3 

58 

433.6 

361.1 

19 

247.9 

200.7 

79 

294.5 

238.5 

39 

341.2 

276.2 

99 

387.8 

314.0 

59 

434.4 

351.7 

20 

248.7 

201.3 

80 

295.3 

239.1 

40 

342.0 

276.9 

500 

388.6 

314.7 

60 

436.2 

352,4 

321 

249.5 

202.0 

381 

296.1 

239.7 

441 

342.7 

277.5 

501 

389.4 

315.3 

561 

436.9 

353.0 

22 

250.3 

202.6 

82 

296.9 

240.4 

42 

343.5 

278.1 

02 

390.1 

315.9 

62 

436.7 

363.6 

23 

251.0 

203.2 

83 

297.7 

241.0 

43 

344.3 

278.7 

03 

390.9 

316.5 

63 

437.5 

364.3 

24 

251.8 

203.9 

84 

298.4 

241.6 

44 

345.1 

279.4 

04 

391.7 

317.1 

64 

438.3 

364.9 

25 

252.6 

204.5 

85 

299.2 

242.2 

45 

345.8 

280.0 

05 

392.5 

317.8 

65 

439.1 

355.5 

26 

253.4 

205.1 

86 

300.0 

242.9 

46 

346.6 

280.6 

06 

393.2 

318.4 

66 

439.8 

366.2 

27 

254.1 

205.7 

87 

300.8 

243.5 

47 

347.4 

281.3 

07 

394.0 

319.0 

67 

440.6 

366.8 

28 

254.9 

206.4 

88 

301.5 

244.1 

48 

348.2 

281.9 

08 

394.8 

319.6 

68 

441.4 

357.4 

29 

255.7 

207.0 

89 

302.3 

244.8 

49 

349.0 

282.5 

09 

395.6 

320.3 

69 

442.2 

358.1 

30 

256.5 

207.6 

90 

303.1 

245.4 

50 

349.7 

283.2 

10 

396.3 

320.9 

70 

443.0 
443.7 

358.7 

331 

257.2 

208.3 

391 

303.9 

246.0 

451 

350.5 

283.8 

511 

397.1 

321.6 

571 

369.3 

32 

258.0 

208.9 

92 

304.7 

246.7 

52 

351.3 

284.4 

12 

397.9 

322.2 

72 

444.5 

359.9 

33 

258.8 

209.5 

93 

305.4 

247.3 

53 

352.1 

285.0 

13 

398.7 

322.8 

73 

445.3 

360.6 

34 

259.6 

210.2 

94 

306.2 

247.9 

54 

352.8 

285.7 

14 

399.4 

323.4 

74 

446.1 

361.2 

35 

260.4 

210.8 

95 

307.0 

248.5 

55 

353.6 

286.3 

15 

400.2 

324.1 

76 

446.9 

361.8 

36 

261.1 

211.4 

96 

307.8 

249.2 

56 

354.4 

286.9 

16 

401.0 

324.7 

76 

447.6 

362.4 

37 

261.9 

212.0 

97 

308.5 

249.8 

57 

355.2 

287.6 

17 

401.8 

325.3 

77 

448.4 

363.1 

38 

262.7 

212.7 

98 

309.3 

250.4 

58 

355.9 

288.2 

18 

402.5 

325.9 

78 

449.2 

363.7 

39 

263.5 

213.3 

99 

310.1 

251.1 

59 

356.7 

288.8 

19 

403.3 

326.6 

79 

450.0 

364.3 

40 

264.2 

213.9 

400 

310.9 

251.7 

60 

357.5 

289.4 

20 

404.1 

327.2 

80 

450.7 

365.0 

341 

265.0 

214.6 

401 

311.6 

252.3 

461 

358.3 

290.1 

521 

404.9 

327.8 

581 

451.5 

366.6 

42 

265.8 

215.2 

02 

312.4 

252.9 

62 

359.1 

290.7 

22 

405.7 

328.5 

82 

452.3 

366.2 

43 

266.6 

215.8 

03 

313.2 

253.6 

63 

359.8 

291.3 

23 

406.4 

329.1 

83 

453.1 

366.9 

44 

267.3 

216.4 

04 

314.0 

254.2 

64 

360.6 

292.0 

24 

407.2 

329.7 

84 

453.9 

367.6 

45 

268.1 

217.1 

05 

314.8 

254.8 

65 

361.4 

292.6 

25 

408.0 

330.4 

85 

464.6 

368.1 

46 

268.9 

217.7 

06 

315.5 

255.5 

66 

362.2 

293.2 

26 

408.8 

331.0 

86 

455.4 

368.8 

47 

269.7 

218.3 

07 

316.3 

256.1 

67 

362.9 

293.8 

27 

409.5 

331.6 

87 

456.2 

369.4 

48 

270.5 

219.0 

08 

317.1 

256.7 

68 

363.7 

294.5 

28 

410.3 

332.3 

88 

467.0 

370.0 

49 

271.2 

219.6 

09 

317.9 

257.3 

69 

364.5 

295.1 

29 

411.1 

332.9 

89 

457.8 

370.6 

50 

272.0 

220.2 

10 
411 

318.6 

258.0 

70 

365.3 

295.7 

30 

411.9 

333.5 

90 

458.5 

371.3 

351 

272.8 

220.8 

319.4 

258.6 

471 

366.0 

296.4 

531 

412.6 

334.1 

591 

459.3 

371.9 

52 

273.6 

221.5 

12 

320.2 

259.2 

72 

366.8 

297.0 

32 

413.4 

334.8 

92 

460.1 

372.6 

53 

274.3 

222.1 

13 

321.0 

259.9 

73 

367.6 

297.6 

33 

414.2 

335.4 

93 

460.9 

373.2 

54 

275.1 

222.7 

14 

321.8 

260.5 

74 

368.4 

298.3 

34 

415.0 

336.1 

94 

461.6 

373.8 

55 

275.9 

223.4 

15 

322.5 

261.1 

75 

369.2 

298.9 

35 

415.8 

336.7 

96 

462.4 

374.4 

56 

276.7 

224.0 

16 

323.3 

261.8 

76 

369.9 

299. 5 

36 

416.5 

337.3 

96 

463.2 

375.1 

57 

277.5 

224.6 

17 

324.1 

262.4 

77 

370.7 

300.1 

37 

417.3 

337.9 

97 

464.0 

375.7 

58 

278.2 

225.3 

18 

324.9 

263.0 

78 

371.5 

300.8 

38 

418.1 

338.5 

98 

464.8 

376.3 

59 

279.0 

225.9 

19 

325.6 

263.6 

79 

372.3 

301.4 

39 

418.9 

339.1 

99 

465.6 

376.9 

60 

279.8 

226.5 

20 

326.4 

264.3 

80 

373.0 

302.0 

40 

419.6 

339.8 

600 

466.3 

377.6 

Diflt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat.   | 

Dist      Dep. 

Lat. 

1 

)1°  (1 

29°,  231°,  309° 

). 

1 

21594°— 14- 


-32 


Page  610] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  40°  (140°,  220°,  320° 

)• 

Di8t. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

46.7 

39.2 

121 

92.7 

77.8 

181 

138.7 

116.3 

241 

184.6 

164.9 

2 

1.5 

1.3 

62 

47.5 

39.9 

22 

93.5 

78.4 

82 

139.4 

117.0 

42 

185.4 

155.6 

3 

2.3 

1.9 

63 

48.3 

40.5 

23 

94.2 

79.1 

83 

140.2 

117.6 

43 

186.1 

156.2 

4 

3.1 

2.6 

64 

49.0 

41.1 

24 

95.0 

79.7 

84 

141.0 

118.3 

44 

186.9 

166.8 

5 

3.8 

3.2 

65 

49.8 

41.8 

25 

95.8 

80.3 

85 

141.7 

118.9 

45 

187.7 

167.5 

6 

4.6 

3.9 

66 

50.6 

42.4 

26 

96.5 

81.0 

86 

142.5 

119.6 

46 

188.4 

158.1 

7 

5.4 

4.5 

67 

51.3 

43.1 

27 

97.3 

81.6 

87 

143.3 

120.2 

47 

189.2 

158.8 
159.4 

8 

6.1 

5.1 

68 

52.1 

43.7 

28 

98.1 

82.3 

88 

144.0 

120.8 

48 

190.0 

9 

6.9 

5.8 

69 

52.9 

44.4 

29 

98.8 

82.9 

89 

144.8 

121.5 

49 

190.7 

160.1 

10 

7.7 

6.4 

70 

53.6 

45.0 

30 

99.6 

83.6 

90 

145.5 

122.1 

60 

191.5 

160.7 

11 

8.4 

7.1 

71 

54.4 

45.6 

131 

100.4 

84.2 

191 

146.3 

122.8 

251 

192.3 

161.3 

12 

9.2 

7.7 

72 

55.2 

46.3 

32 

101.1 

84.8 

92 

147.1 

123.4 

52 

193.0 

162.0 

13 

10.0 

8.4 

73 

55.9 

46.9 

33 

101.9 

85.5 

93 

147.8 

124.1 

53 

193.8 

162.6 

14 

10.7 

9.0 

74 

56.7 

47.6 

34 

102.6 

86.1 

94 

148.6 

124.7 

64 

194.6 

163.3 

15 

11.5 

9.6 

75 

57.5 

48.2 

35 

103.4 

86.8 

95 

149.4 

125.3 

55 

195.3 

163.9 

16 

12,3 

10.3 

76 

58.2 

48.9 

36 

104.2 

87.4 

96 

150.1 

126.0 

56 

196.1 

164.6 

17 

13.0 

10.9 

77 

59.0 

49.5 

37 

104.9 

88.1 

97 

150.9 

126.6 

57 

196.9 

165.2 

18 

13.8 

11.6 

78 

59.8 

50.1 

38 

105.7 

88.7 

98 

151.7 

127.3 

58 

197.6 

165,8 

19 

14.6 

12.2 

79 

60.5 

50.8 

39 

106.5 

89.3 

99 

152.4 

127.9 

59 

198.4 

166.5 

20 

15.3 

12.9 

80 

61.3 

51.4 

40 

107.2 

90.0 
90.6 

200 

153.2 

128.6 

60 

199.2 

167.1 

21 

16.1 

13.5 

81 

62.0 

52.1 

141 

108.0 

201 

154.0 

129.2 

261 

199.9 

167.8 

22 

16.9 

14.1 

82 

62.8 

52.7 

42 

108.8 

91,3 

02 

154.7 

129.8 

62 

200.7 

168.4 

23 

17.6 

14.8 

83 

63.6 

53.4 

43 

109.5 

91.9 

03 

155.5 

130.5 

63 

201.5 

169.1 

24 

18.4 

15.4 

84 

64.3 

54.0 

44 

110.3 

92.6 

04 

156.3 

131.1 

64 

202.2 

169.7 

25 

19.2 

16.1 

85 

65.1 

54.6 

45 

111.1 

93.2 

05 

157.0 

131.8 

65 

203,0 

170.3 

26 

19.9 

16.7 

86 

65.9 

55.3 

46 

111.8 

93.8 

06 

157.8 

132.4 

66 

203.8 

171.0 

27 

20.7 

17.4 

87 

66.6 

55.9 

47 

112.6 

94.5 

07 

158.6 

133,1 

67 

204.5 

171.6 

28 

21.4 

18.0 

88 

67.4 

56.6 

48 

113.4 

95.1 

08 

159.3 

133.7 

68 

205,3 

172.3 

29 

22.2 

18.6 

89 

68.2 

57.2 

49 

114.1 

95.8 

09 

160.1 

134,3 

69 

206,1 

172.9 

30 

23.0 

19.3 

90 

68.9 

57.9 

50 

114.9 

96.4 

10 

160.9 

135.0 

70 

206,8 

173.6 

31 

23.7 

19.9 

91 

69.7 

58.5 

151 

115.7 

97.1 

211 

161.6 

135.6 

271 

207.6 

174.2 

32 

24.5 

20.6 

92 

70.5 

59.1 

52 

116.4 

97.7 

12 

162.4 

136.3 

72 

208.4 

174.8 

33 

25.3 

21.2 

93 

71.2 

59.8 

53 

117.2 

98.3 

13 

163.2 

136.9 

73 

209.1 

175.5 

34 

26.0 

21.9 

94 

72.0 

60.4 

54 

118.0 

99.0 

14 

163.9 

137,6 

74 

209.9 

176.1 

35 

26.8 

22.5 

95 

72.8 

61.1 

55 

118.7 

99.6 

15 

164.7 

138,2 

75 

210,7 

176.8 

36 

27.6 

23.1 

96 

73.5 

61.7 

56 

119.5 

100.3 

16 

165.5 

138.8 

76 

211,4 

177,4 

37 

28.3 

23.8 

97 

74.3 

62.4 

57 

120.3 

100.9 

17 

166.2 

139.5 

77 

212,2 

178,1 

38 

29.1 

24.4 

98 

75.1 

63.0 

58 

121.0 

101.6 

18 

167.0 

140.1 

78 

213.0 

178.7 

39 

29.9 

25.1 

99 

75.8 

63.6 

59 

121.8 

102.2 

19 

167.8 

140.8 

79 

213.7 

179.3 

40 

30.6 

25.7 

100 

76.6 

64.3 

60 

122.6 

102.8 

20 

168.5 

141.4 

80 

214,5 

180,0 

41 

31.4 

26.4 

101 

77.4 

64.9 

161 

123.3 

103.5 

221 

169.3 

142.1 

281 

215,3 

180,6 

42 

32.2 

27.0 

02 

78.1 

65.6 

62 

124.1 

104.1 

22 

170.1 

142.7 

82 

216.0 

181,3 

43 

32.9 

27.6 

03 

78.9 

66.2 

63 

124.9 

104,8 

23 

170,8 

143,3 

83 

216.8 

181.9 

44 

33.7 

28.3 

04 

79.7 

66.8 

64 

125.6 

105.4 

24 

171.6 

144.0 

84 

217.6 

182.6 

46 

34.5 

28.9 

05 

80.4 

67.5 

65 

126.4 

106.1 

25 

172.4 

144.6 

85 

218,3 

183.2 

46 

35.2 

29.6 

06 

81.2 

68.1 

66 

127.2 

106.7 

26 

173.1 

145.3 

86 

219.1 

183.8 

47 

36,0 

30.2 

07 

82.0 

68.8 

67 

127.9 

107.3 

27 

173.9 

145.9 

87 

219.9 

184.5 

48 

36.8 

30.9 

08 

82.7 

69.4 

68 

128.7 

108.0 

28 

174.7 

146.6 

88 

220.6 

186.1 

49 

37.5 

31.5 

09 

83.5 

70.1 

69 

129.5 

108.6 

29 

175.4 

147.2 

89 

221.4 

186.8 

50 

38.3 

32.1 

10 

84.3 

70.7 

70 

130.2 

109.3 

30 

176.2 

147.8 

90 

222.2 

186.4 

51 

39.1 

32.8 

111 

85.0 

71.3 

171 

131.0 

109.9 

231 

177.0 

148.5 

291 

222.9 

187.1 

52 

39.8 

33.4 

12 

85.8 

72.0 

72 

131.8 

110.6 

32 

177,7 

149.1 

92 

223.7 

187.7 

53 

40.6 

34.1 

13 

86.6 

72.6 

73 

132.5 

111.2 

33 

178.5 

149.8 

93 

224.5 

188.3 

54 

41.4 

34.7 

14 

87.3 

73,3 

74 

133.3 

111.8 

34 

179.3 

150.4 

94 

225.2 

189.0 

55 

42.1 

35.4 

15 

88.1 

73.9 

75 

134.1 

112.5 

35 

180.0 

151.1 

95 

226.0 

189.6 

56 

42.9 

36.0 

16 

88.9 

74.6 

76 

134.8 

113.1 

36 

180.8 

151.7 

96 

226.7 

190.3 

57 

43.7 

36.6 

17 

89.6 

75.2 

77 

135.6 

113.8 

37 

181.6 

152.3 

97 

227.5 

190.9 

58 

44.4 

37.3 

18 

90.4 

75.8 

78 

136.4 

114,4 

38 

182.3 

153.0 

98 

228.3 

191.6 

59 

45.2 

37.9 

19 

91.2 

76.5 

79 

137.1 

115.1 

39 

183.1 

153.6 

99 

229.0 

192,2 

60 

46.0 

38.6 

20 

91.9 

77.1 

80 

137.9 

115.7 

40 

183.9 

154,3 

300 

229.8 

192.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.      Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

50°  (130°,  230°,  310°). 

TABLE  2. 

[Page  611     1 

DifiEerence  of  Latitude  and  Departure  for 

40°  (140°,  220°,  320° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep.  1 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

230.6 

193.5 

361 

276,5 

232.1 

421 

322.5 

270.6 

481 

368.5 

309.2 

541 

414.4 

347.7 

02 

231.3 

194.1 

62 

277.3 

232.7 

22 

323.3 

271.3 

82 

369.2 

309.8 

42 

415.2 

348.4 

03 

232.1 

194.8 

63 

278.1 

233.3 

23 

324.0 

271.9 

83 

370.0 

310.5 

43 

416.0 

349.0 

04 

232.9 

195.4 

64 

278.8 

234.0 

24 

324.8 

272.6 

84 

370.8 

311.1 

44 

416.7 

349.7 

05 

233.6 

196.1 

65 

279.6 

234.6 

25 

325.6 

273.2 

85 

371.5 

311.7 

45 

417.5 

350.3 

06 

234.4 

196.7 

66 

280.4 

235.3 

26 

326.3 

273.8 

86 

372.3 

312.4 

46 

418.3 

361.0 

07 

235.2 

197.3 

67 

281.1 

235.9 

27 

327.1 

274.5 

87 

373.1 

313.0 

47 

419.0 

351.6 

08 

235.9 

198.0 

68 

281.9 

236.6 

28 

327.9 

275.1 

88 

373.8 

313.6 

48 

419.8 

352.2 

09 

236.7 

198.6 

69 

282.7 

237.  2 

29 

328.6 

275.8 

89 

374,6 

314.3 

49 

420.6 

352.9 

10 

237.5 

199.3 

70 

283.4 

237.8 

30 

329.4 

276.4 

90 

375,4 

314.9 

50 
551 

421.3 

363.5 

311 

238.2 

199.9 

371 

284.2 

238.5 

431 

330.2 

277.1 

491 

376,1 

315.6 

422.1 

354.2 

12 

239.0 

200.6 

72 

285.0 

239.1 

32 

330.9 

277.7 

92 

376.9 

316.2 

52 

422.9 

354.8 

13 

239.8 

201.2 

73 

285.7 

239.7 

33 

331.7 

278.3 

93 

377.7 

316.9 

53 

423.6 

355.5 

14 

240.5 

201.8 

74 

286.5 

240.4 

34 

332.5 

279.0 

94 

378.4 

317.5 

54 

424.4 

356.1 

15 

241.3 

202.5 

75 

287.3 

241.0 

35 

333.2 

279.6 

95 

379.2 

318.2 

55 

425.2 

356.8 

16 

242.1 

203.1 

76 

288.0 

241,7 

36 

334.0 

280.3 

96 

380.0 

318.8 

56 

425.9 

357.4 

17 

242.8 

203.8 

77 

288.8 

242.3 

37 

334.8 

280.9 

97 

380.7 

319.5 

57 

426.7 

358.0 

18 

243.6 

204.4 

78 

289.6 

243.0 

38 

335.5 

281.6 

98 

381.5 

320.1 

58 

427.5 

358.7 

19 

244.4 

205.1 

79 

290.3 

243.6 

39 

336.3 

282.2 

99 

382.3 

320.8 

59 

428.2 

359.3 

20 

245.1 

205.7 

80 

291.1 

244.3 

40 

337.1 

282.8 

500 

383.0 

321.4 

60 

429.0 

360.0 

321 

245.9 

206.3 

381 

291.9 

244.9 

441 

337.8 

283.5 

501 

383.8 

322.0 

561 

429.8 

360.6 

22 

246.7 

207.0 

82 

292.6 

245.6 

42 

338.6 

284.1 

02 

384.6 

322.7 

62 

430.5 

361.2 

23 

247.4 

207.6 

83 

293.4 

246.2 

43 

339.4 

284.8 

03 

385.3 

323.3 

63 

431.3 

361.9 

24 

248.2 

208.3 

84 

294.2 

246.8 

44 

340.1 

285.4 

04 

386.1 

324.0 

64 

432.1 

362.5 

25 

249.0 

208.9 

85 

294.9 

247.5 

45 

340.9 

286.0 

05 

386.8 

324.6 

65 

432.8 

363.2 

26 

249.7 

209.6 

86 

295.7 

248.1 

46 

341.7 

286.7 

06 

387,6 

325.2 

66 

433.6 

363.8 

27 

250.5 

210.2 

87 

296.5 

248.8 

47 

342.4 

287.3 

07 

388,4 

325.9 

67 

434.3 

364.5 

28 

251.3 

210.8 

88 

297.2 

249.4 

48 

343.2 

288.0 

08 

389.2 

326,5 

68 

435.1 

366.1 

29 

252.0 

211.5 

89 

298.0 

250.1 

49 

344.0 

288.6 

09 

389.9 

327.1 

69 

435.9 

366,8 

30 

252.8 

212.1 

90 

298.8 

250.7 

50 

344.7 

289.3 

10 

390.7 

327.8 

70 

436.6 

366,4 

331 

253.6 

212.8 

391 

299.5 

251.3 

451 

345.5 

289,9 

511 

391.5 

328.4 

571 

437.4 

367,0 

32 

254.3 

213.4 

92 

300.3 

252.0 

52 

346.3 

290,5 

12 

392.2 

329.1 

72 

438.2 

367.7 

33 

255.1 

214.1 

93 

301.1 

252.6 

53 

347.0 

291.2 

13 

393.0 

329.7 

73 

438.9 

368.3 

34 

255.9 

214.7 

94 

301.8 

253.3 

54 

347.8 

291.8 

14 

393.8 

330.4 

74 

439.7 

369.0 

35 

256.6 

215.3 

95 

302.6 

253.9 

55 

348.6 

292.5 

15 

394.5 

331.0 

75 

440.5 

369.6 

36 

257.4 

216.0 

96 

303.4 

254.6 

56 

349.3 

293.1 

16 

395.3 

331.6 

76 

441.2 

370.2 

37 

258.2 

216.6 

97 

304.1 

255.2 

57 

350.1 

293.8 

17 

396.1 

332.3 

77 

442.0 

370.9 

38 

258.9 

217.3 

98 

304.9 

255.8 

58 

350.8 

294.4 

18 

396.8 

332.9 

78 

442.8 

371.6 

39 

259.7 

217.9 

99 

305.7 

256.5 

59 

351.6 

295.0 

19 

397.6 

333.6 

79 

443.5 

372.2 

40 

260.5 

218.6 

400 

306.4 

257.1 

60 

352.4 

295.7 

20 

398.3 

334.2 

80 

444.3 

372.8 

341 

261.2 

219.2 

401 

307.2 

257.8 

461 

353.1 

296.3 

521 

399.1 

334.9 

581 

445.1 

373.6 

42 

262.0 

219.8 

02 

308.0 

258.4 

62 

353.9 

297.0 

22 

399.9 

335.5 

82 

445,8 

374.1 

43 

262.8 

220.5 

03 

308.7 

259.1 

63 

354.7 

297,6 

23 

400,6 

336.1 

83 

446.6 

374.8 

44 

263.5 

221.1 

04 

309.5 

259.7 

64 

355.4 

298.3 

24 

401.4 

336.8 

84 

447.4 

375.4 

45 

264.3 

221.8 

05 

310.2 

260.3 

65 

356.2 

298.9 

25 

402.2 

337.4 

85 

448.1 

376,0 

46 

265.1 

222.4 

06 

311.0 

261.0 

66 

357.0 

299.5 

26 

402.9 

338.1 

86 

448.9 

376.7 

47 

265.8 

223.1 

07 

311.8 

261.6 

67 

367.7 

300.2 

27 

403.7 

338.7 

87 

449.7 

377.3 

48 

266.6 

223.7 

08 

312.5 

262.3 

68 

358.5 

300.8 

28 

404.5 

339.4 

88 

450.4 

378.0 

49 

267.4 

224.3 

09 

313.3 

262.9 

69 

359.3 

301.5 

29 

405.2 

340.0 

89 

451.2 

378.6 

50 

268.1 

225.0 

10 

314.1 

263.6 

70 

360.0 

302.1 

30 

406.0 

340.6 
341.3 

90 

452.0 

379.2 

351 

268.9 

225.6 

411 

314.8 

264.2 

471 

360.8 

302.8 

531 

406. 8 

591 

452.7 

379.9 

52 

269.6 

226.3 

12 

315.6 

264.8 

72 

361.6 

303.4 

32 

407.5 

341.9 

92 

453.5 

380.5 

53 

270.4 

226.9 

13 

316.4 

265.5 

73 

362.3 

304.0 

33 

408.3 

342.6 

93 

454.3 

381.2 

54 

271.2 

227.6 

14 

317.1 

266.1 

74 

363.1 

304.7 

34 

409.1 

343.2 

94 

455.0 

381.8 

55 

271.9 

228.2 

15 

317.9 

266.8 

75 

363.9 

305.3 

35 

409.8 

343.9 

95 

455.8 

382.4 

56 

272.7 

228.8 

16 

318.7 

267.4 

76 

364.6 

306.0 

36 

410.6 

344.5 

96 

456.6 

383.1 

57 

273.5 

229.5 

17 

319.4 

268.1 

77 

365.4 

306.6 

37 

411.4 

345.2 

97 

457.3 

383.7 

58 

274.2 

230.1 

18 

320.2 

268.7 

78 

366.2 

307.3 

38 

412.1 

345.8 

98 

458.1 

384.4 

59 

275.0 

230.8 

19 

321.0 

269.3 

79 

366.9 

307.9 

39 

412,9 

346.4 

99 

458.9 

386.0 

60 

275.8 

231.4 

20 

321.7 

270.0 

80 

367,7 

308.5 

40 

413,7 

347.1 

600 

459.6 

385,7 

Dist. 

Dep.        Lat. 

Dist.       Dep. 

Lat. 

Diflt.       Dep. 

Lat. 

Dist. 

Dep.         Lat. 

Dist. 

Dep. 

Lat, 

50°  (130°,  230°,  310° 

)• 

Page  612] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  41°  (139°,  221°,  319° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.7 

61 

46.0 

40.0 

121 

91.3 

79.4 

181 

136.6 

118.7 

241 

181.9 

158.1 

2 

1.5 

1.3 

62 

46.8 

40.7 

22 

92.1 

80.0 

82 

137.4 

119.4 

42 

182.6 

158.8 

3 

2.3 

2.0 

63 

47.5 

41.3 

23 

92.8 

80.7 

83 

138.1 

120.1 

43 

183.4 

159.4 

4 

3.0 

2.6 

64 

48.3 

42.0 

24 

93.6 

81.4 

84 

138.9 

120.7 

44 

184.1 

160.1 

5 

3.8 

3.3 

65 

49.1 

42.6 

25 

94.3 

82.0 

85 

139.6 

121.4 

45 

184.9 

160.7 

6 

4.6 

3.9 

66 

49.8 

43.3 

26 

95.1 

82.7 

86 

140.4 

122.0 

46 

185.7 

161.4 

7 

5.3 

4.6 

67 

50.6 

44.0 

27 

95.8 

83.3 

87 

141.1 

122.7 

47 

186.4 

162.0 

8 

6.0 

5.2 

68 

51.3 

44.6 

28 

96.6 

84.0 

88 

141.9 

123.3 

48 

187.2 

162.7 

9 

6.8 

5.9 

69 

52.1 

45.3 

29 

97.4 

84.6 

89 

142.6 

124.0 

49 

187.9 

163.4 

10 

7.5 

6.6 

70 

52.8 

45.9 

30 

98.1 

85.3 

90 

143.4 

124.7 

50 

188.7 

164.0 

11 

8.3 

7.2 

71 

53.6 

46.6 

131 

98.9 

85.9 

191 

144.1 

125.3 

251 

189.4 

164.7 

12 

9.1 

7.9 

72 

54.3 

47.2 

32 

99.6 

86.6 

92 

144.9 

126.0 

52 

190.2 

165.3 

13 

9.8 

8.5 

73 

55.1 

47.9 

33 

100.4 

87.3 

93 

145.7 

126.6 

53 

190.9 

166.0 

14 

10.6 

9.2 

74 

55.8 

48.5 

34 

101.1 

87.9 

94 

146.4 

127.3 

54 

191.7 

166.6 

15 

11.3 

9.8 

75 

56.6 

49.2 

35 

101.9 

88.6 

95 

147.2 

127.9 

55 

192.5 

167.3 

16 

12.1 

10.5 

76 

57.4 

49.9 

36 

102.6 

89.2 

96 

147.9 

128.6 

56 

193.2 

168.0 

17 

12.8 

11.2 

77 

58.1 

50.5 

37 

103.4 

89.9 

97 

148.7 

129.2 

57 

194.0 

168.6 

18 

13.6 

11.8 

78 

58.9 

51.2 

38 

104.1 

90.5 

98 

149.4 

129.9 

58 

194.7 

169.3 

19 

14.3 

12.5 

79 

59.6 

51.8 

39 

104.9 

91.2 

99 

150.2 

130.6 

59 

195.5 

169.9 

20 

15.1 

13.1 

80 

60.4 

52.5 

40 

105.7 

91.8 

200 

150.9 

131.2 

60 

196.2 

170.6 

21 

15.8 

13.8 

81 

61.1 

53.1 

141 

106.4 

92.5 

201 

151.7 

131.9 

261 

197.0 

171.2 

22 

16.6 

14.4 

82 

61.9 

53.8 

42 

107.2 

93.2 

02 

152.5 

132.5 

62 

197.7 

171.9 

23 

17.4 

15.1 

83 

62.6 

54.5 

43 

107.9 

93.8 

03 

153.2 

133.2 

63 

198.5 

172.5 

24 

18.1 

15.7 

84 

63.4 

55.1 

44 

108.7 

94.5 

04 

154.0 

133.8 

64 

199.2 

173.2 

25 

18.9 

16.4 

85 

64.2 

55.8 

45 

109.4 

95.1 

05 

154.7 

134.5 

65 

200.0 

173.9 

26 

19.6 

17.1 

86 

64.9 

56.4 

46 

110.2 

95.8 

06 

155.5 

135.1 

66 

200.8 

174.5 

27 

20.4 

17.7 

87 

65.7 

57.1 

47 

110.9 

96.4 

07 

156.2 

135.8 

67 

201.5 

175.2 

28 

21.1 

18.4 

88 

66.4 

57.7 

48 

111.7 

97.1 

08 

157.0 

136.5 

68 

202.3 

175.8 

29 

21.9 

19.0 

89 

67.2 

58.4 

49 

112.5 

97.8 

09 

157.7 

137.1 

69 

203.0 

176.5 

30 

22.6 

19.7 

90 

67.9 

59.0 

50 

113.2 

98.4 

10 

158.5 

137.8 

70 

203.8 

177.1 
177.8 

31 

23.4 

20.3 

91 

68.7 

59.7 

151 

114.0 

99.1 

211 

159.2 

138.4 

271 

204.5 

32 

24.2 

21.0 

92 

69.4 

60.4 

52 

114.7 

99.7 

12 

160.0 

139.1 

72 

205.3 

178.4 

33 

24.9 

21.6 

93 

70.2 

61.0 

53 

115.5 

100.4 

13 

160.8 

139.7 

73 

206.0 

179.1 

34 

25.7 

22.3 

94 

70.9 

61.7 

54 

116.2 

101.0 

14 

161.5 

140.4 

74 

206.8 

179.8 

35 

26.4 

23.0 

95 

71.7 

62.3 

55 

117.0 

101.7 

15 

162.3 

141.1 

75 

207.5 

180.4 

36 

27.2 

23.6 

96 

72.5 

63.0 

56 

117.7 

102.3 

16 

163.0 

141.7 

76 

208.3 

181.1 

37 

27.9 

24.3 

97 

73.2 

63.6 

57 

118.5 

103.0 

17 

163.8 

142.4 

77 

209.1 

181.7 

38 

28.7 

24.9 

98 

74.0 

64.3 

58 

119.2 

103.7 

18 

164.5 

143.0 

78 

209.8 

182.4 

39 

29.4 

25.6 

99 

74.7 

64.9 

59 

120.0 

104.3 

19 

165.3 

143.7 

79 

210.6 

183.0 

40 

30.2 

26.2 

100 

75.5 

65.6 

60 

120.8 

105.0 

20 

166.0 

144.3 

80 

211.3 

183.7 

41 

30.9 

26.9 

101 

76.2 

66.3 

161 

121.5 

105.6 

221 

166.8 

145.0 

281 

212.1 

184.4 

42 

31.7 

27.6 

02 

77.0 

66.9 

62 

122.3 

106.3 

22 

167.5 

145.6 

82 

212.8 

185.0 

43 

32.5 

28.2 

03 

77.7 

67.6 

63 

123.0 

106.9 

23 

168.3 

146.3 

83 

213.6 

185.7 

44 

33.2 

28.9 

04 

78.5 

68.2 

64 

123.8 

107.6 

24 

169.1 

147.0 

84 

214.3 

186.3 

45 

34.0 

29.5 

05 

79.2 

68.9 

65 

124.5 

108.2 

25 

169.8 

147.6 

85 

215.1 

187.0 

46 

34.7 

30.2 

06 

80.0 

69.5 

66 

125.3 

108.9 

26 

170.6 

148.3 

86 

215.8 

187.6 

47 

35.5 

30.8 

07 

80.8 

70.2 

67 

126.0 

109.6 

27 

171.3 

148.9 

87 

216.6 

188.3 

48 

36.2 

31.5 

08 

81.5 

70.9 

68 

126.8 

110.2 

28 

172.1 

149.6 

88 

217.4 

188.9 

49 

37.0 

32.1 

09 

82.3 

71.5 

69 

127.5 

110.9 

29 

172.8 

150.2 

89 

218.1 

189.6 

50 

37.7 

32.8 

10 

83.0 

72.2 

70 

128.3 

111.5 

30 

173.6 

150.9 

90 

218.9 

190.3 

51 

38.5 

33.5 

111 

83.8 

72.8 

171 

129.1 

112.2 

231 

174.3 

151.5 

291 

219.6 

190.9 

52 

39.2 

34.1 

12 

84.5 

73.5 

72 

129.8 

112.8 

32 

175.1 

152.2 

92 

220.4 

191.6 

53 

40.0 

34.8 

13 

85.3 

74.1 

73 

130.6 

113.5 

33 

175.8 

152.9 

93 

221.1 

192.2 

54 

40.8 

35.4 

14 

86.0 

74.8 

74 

131.3 

114.2 

34 

176.6 

153.5 

94 

221.9 

192.9 

55 

41.5 

36.1 

15 

86.8 

75.4 

75 

132.1 

114.8 

35 

177.4 

154.2 

95 

222.6 

193.5 

56 

42.3 

36.7 

16 

87.5 

76.1 

76 

132.8 

115.5 

36 

178.1 

154.8 

96 

223.4 

194.2 

57 

43.0 

37.4 

17 

88.3 

76.8 

77 

133.6 

116.1 

37 

178.9 

155.5 

97 

224.1 

194.8 

58 

43.8 

38.1 

18 

89.1 

77.4 

78 

134.3 

116.8 

38 

179.6 

156.1 

98 

224.9 

195.5 

59 

44.5 

38.7 

19 

89.8 

78.1 

79 

135.1 

117.4 

39 

180.4 

156.8 

99 

225.7 

196.2 

60 

45.3 

39.4 

20 

90.6 

78.7 

80 

135.8 

118.1 

40 

181.1 

157.5 

300 

226.4 

196.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Diat. 

Dep. 

Lat. 

49°  (131°,  229°,  311° 

). 

1 

TABLE  2. 

[Page  613 

Difference  of  Latitude  and  Departure  for  41°  (139°,  221°,  319° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

227.2 

197.5 

361 

272.5 

236.9 

421 

317.7 

276.2 

481 

363.0 

315.6 

641 

408.3 

354.9 

02 

227.9 

198.1 

62 

273.2 

237.5 

22 

318.5 

276.9 

82 

363.8 

316.2 

42 

409.0 

355.6 

03 

228.7 

198.8 

63 

274.0 

238.2 

23 

319.2 

277.5 

83 

364.5 

316.9 

43 

409.8 

356.2 

04 

229.4 

199.4 

64 

274.7 

238.8 

24 

320.0 

278.2 

84 

365.3 

317.5 

44 

410.6 

356.9 

05 

230.2 

200.1 

65 

275.5 

239.5 

25 

320.8 

278.8 

85 

366.0 

318.2 

46 

411.3 

367.5 

06 

230.9 

200.8 

66 

276.2 

240.1 

26 

321.5 

279.5 

86 

366.8 

318.8 

46 

412.1 

358.2 

07 

231.7 

201.4 

67 

277.0 

240.8 

27 

322.3 

280.1 

87 

367.5 

319.5 

47 

412.8 

358.8 

08 

232.5 

202.1 

68 

277.7 

241.4 

28 

323.0 

280.8 

88 

368.3 

320.1 

48 

413.6 

359.5 

09 

233.2 

202.7 

69 

278.5 

242.1 

29 

323.8 

281.5 

89 

369.0 

320.8 

49 

414.3 

360.2 

10 

234.0 

203.4 

70 

279.2 

242.7 

30 

324.5 

282.1 

90 

369.8 

321.5 

50 

415.1 

360.8 

311 

234.7 

204.0 

371 

280.0 

243.4 

431 

325.3 

282.8 

491 

370.6 

322.1 

551 

415.8 

361.5 

12 

235.5 

204.7 

72 

280.8 

244.1 

32 

326.0 

283.4 

92 

371.3 

322.8 

52 

416.6 

362.1 

13 

236.2 

205.4 

73 

281.5 

244.7 

33 

326.8 

284.1 

93 

372.1 

323.4 

63 

417.3 

362.8 

14 

237.0 

206.0 

74 

282.3 

245.4 

34 

327.5 

284.7 

94 

372.8 

324.1 

54 

418.1 

363.4 

15 

237.7 

206.7 

75 

283.0 

246.0 

36 

328.3 

285.4 

95 

373.6 

324.7 

55 

418.9 

364.1 

16 

238.5 

207.3 

76 

283.8 

246.7 

36 

329.1 

286.0 

96 

374.3 

325.4 

56 

419.6 

364.8 

17 

239.2 

208.0 

77 

284.5 

247.3 

37 

329.8 

286.7 

97 

375.1 

326.0 

57 

420.4 

365.4 

18 

240.0 

208.6 

78 

285.3 

248.0 

38 

330.6 

287.4 

98 

375.8 

326.7 

58 

421.1 

366.1 

19 

240.8 

209.3 

79 

286.0 

248.7 

39 

331.3 

288.0 

99 

376.6 

327.4 

59 

421.9 

366.7 

20 

241.5 

209.9 

80 

286.8 

249.3 

40 

332.1 

288.7 

500 

377.3 

328.0 

60 

422.6 

367.4 

321 

242.3 

210.6 

381 

287.5 

250.0 

441 

332.8 

289.3 

501 

378.1 

328.7 

661 

423.4 

368.0 

22 

243.0 

211.3 

82 

288.3 

250.6 

42 

333.6 

290.0 

02 

378.9 

329.3 

62 

424.1 

368.7 

23 

243.8 

211.9 

83 

289.1 

251.3 

43 

334.3 

290.6 

03 

379.6 

330.0 

63 

424.9 

369.4 

24 

244.5 

212.6 

84 

289.8 

251.9 

44 

335.1 

291.3 

04 

380.4 

330.6 

64 

425.7 

370.0 

25 

245.3 

213.2 

85 

290.6 

252.6 

45 

335.8 

292.0 

05 

381.1 

331.3 

66 

426.4 

370.7 

26 

246.0 

213.9 

86 

291.3 

253.2 

46 

336.6 

292.6 

06 

381.9 

332.0 

66 

427.2 

371.3 

27 

246.8 

214.5 

87 

292.1 

253.9 

47 

337.4 

293.3 

07 

382.6 

332.6 

67 

427.9 

372.0 

28 

247.5 

215.2 

88 

292.8 

254.6 

48 

338.1 

293.9 

08 

383.4 

333.3 

68 

428.7 

372.6 

29 

248.3 

215.9 

89 

293.6 

255.2 

49 

338.9 

294.6 

09 

384.1 

333.9 

69 

429.4 

373.3 

30 

249.1 

216.5 

90 

294.3 

255.9 

50 

339.6 

295.2 

10 

384.9 

334.6 

70 

430.2 

374.0 

331 

249.8 

217.2 

391 

295.1 

256.5 

451 

340.4 

295.9 

511 

385.7 

335.2 

571 

430.9 

374.6 

32 

250.6 

217.8 

92 

295.8 

257.2 

52 

341.1 

296.5 

12 

386.4 

335.9 

72 

431.7 

375.3 

33 

251.3 

218.5 

93 

296.6 

257.8 

53 

341.9 

297.2 

13 

387.2 

336.5 

73 

432.4 

375.9 

34 

252.1 

219.1 

94 

297.4 

258.5 

54 

342.6 

297.9 

14 

387.9 

337.2 

74 

433.2 

376.6 

35 

252.8 

219.8 

95 

298.1 

259.2 

55 

343.4 

298.5 

15 

388.7 

337.9 

75 

434.0 

377.2 

36 

253.6 

220.4 

96 

298.9 

259.8 

56 

344.1 

299.2 

16 

389.4 

338.5 

76 

434.7 

377.9 

37 

254.3 

221.1 

97 

299.6 

260.5 

57 

344.9 

299.8 

17 

390.2 

339.2 

77 

435.6 

378.5 

38 

255.1 

221.8 

98 

300.4 

261.1 

58 

345.7 

300.5 

18 

390.9 

339.8 

78 

436.2 

379.2 

39 

255.8 

222.4 

99 

301.1 

261.8 

59 

346.4 

301.1 

19 

391.7 

340.5 

79 

437.0 

379.8 

40 

256.6 

223.1 

400 

301.9 

262.4 

60 

347.2 

301.8 

20 

392.4 

341.1 

80 

437.7 

380.5 

341 

257.4 

223.7 

401 

302.6 

263.1 

461 

347.9 

302.6 

521 

393.2 

341.8 

581 

438.5 

381.2 

42 

258.1 

224.4 

02 

303.4 

263.7 

62 

348.7 

303.1 

22 

394.0 

342.6 

82 

439.2 

381.8 

43 

258.9 

225.0 

03 

304.2 

264.4 

63 

349.4 

303.8 

23 

394.7 

343.1 

83 

440.0 

382.6 

44 

259.6 

225.7 

04 

304.9 

265.1 

64 

350.2 

304.4 

24 

395.5 

343.8 

84 

440.7 

383.2 

45 

260.4 

226.3 

05 

305.7 

265.7 

65 

350.9 

305.1 

25 

396.2 

344.4 

85 

441.5 

383.8 

46 

261.1 

227.0 

06 

306.4 

266.4 

66 

351.7 

305.7 

26 

397.0 

346.1 

86 

442.3 

384.5 

47 

261.9 

227.7 

07 

307.  2 

267.0 

67 

352.5 

306.4 

27 

397.7 

346.7 

87 

443.0 

385.1 

48 

262.6 

228.3 

08 

307.9 

267.7 

68 

353.  2 

307.0 

28 

398.5 

346.4 

88 

443.8 

386.8 

49 

263.4 

229.0 

09 

308.7 

268.3 

69 

354.0 

307.7 

29 

399.2 

347.0 

89 

444.6 

386.4 

50 
851 

264.2 

229.6 

10 

309.4 

269.0 

70 

354.7 

308.4 

30 

400.0 

347.7 

90 

445.3 

387.1 

264.9 

230.3 

411 

310.2 

269.6 

471 

355.5 

309.0 

531 

400.7 

348.4 

591 

446.0 

387.7 

52 

265.7 

230.9 

12 

310. 9 

270.3 

72 

356.2 

309.7 

32 

401.6 

349.0 

92 

446.8 

388.4 

53 

266.4 

231.6 

13 

311.7 

271.0 

73 

357.0 

310.3 

33 

402.2 

349.7 

93 

447.5 

389.1 

54 

267.2 

232.3 

14 

312.5 

271.6 

74 

357.7 

311.0 

34 

403.0 

360.3 

94 

448.3 

389.7 

55 

267.9 

232.9 

15 

313.2 

272.3 

75 

358.5 

311.6 

36 

403.8 

351.0 

96 

449.1 

390.4 

56 

268.7 

233.6 

16 

314.0 

272.9 

76 

359.2 

312.3 

36 

404.5 

351.6 

96 

449.8 

391.0 

57 

269.4 

234.2 

17 

314.7 

273.6 

77 

360.0 

312.9 

37 

406.3 

352.3 

97 

450.6 

391.7 

58 

270.2 

234.9 

18 

315.5 

274.2 

78 

360.8 

313.6 

38 

406.0 

362.9 

98 

451.3 

392.3 

59 

270.9 

235.5 

19 

316.2 

274.9 

79 

361.5 

314.3 

39 

406.8 

353.6 

99 

452.1 

393.0 

60 

271.7 

236.2 

20 

317.0 

275.6 

80 

362.3 

314.9 

40 

407.5 

364.3 

600 

452.8 

393.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

i9°  (1 

31°,  229°,  311° 

)• 

Page  614] 

TABLE 

2. 

Difference  of  Latitude  and  Departure  for  42°  (138°,  222°,  318° 

). 

Dlst. 

Lai. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

45.3 

40.8 

121 

89.9 

81.0 

181 

134.5 

121.1 

241 

179.1 

161.3 

2 

1.5 

1.3 

62 

46.1 

41.5 

22 

90.7 

81.6 

82 

135.3 

121.8 

42 

179.8 

161.9 

3 

2.2 

2.0 

63 

46.8 

42.2 

23 

91.4 

82.3 

83 

136.0 

122.5 

43 

180.6 

162.6 

4 

3.0 

2.7 

64 

47.6 

42.8 

24 

92.1 

83.0 

84 

136.7 

123.1 

44 

181.3 

163.3 

5 

3.7 

3.3 

65 

48.3 

43.5 

25 

92.9 

83.6 

85 

137.5 

123.8 

45 

182.1 

163.9 

6 

4.5 

4.0 

66 

49.0 

44.2 

26 

93.6 

84.3 

86 

138.2 

124.5 

46 

182.8 

164.6 

7 

5.2 

4.7 

67 

49.8 

44.8 

27 

94.4 

85.0 

87 

139.0 

125.1 

47 

183.  6 

165.3 

8 

5.9 

5.4 

68 

50.5 

45.5 

28 

95.1 

85.6 

88 

139.7 

125.8 

48 

184.3 

165.9 

9 

6.7 

6.0 

69 

51.3 

46.2 

29 

95.9 

86.3 

89 

140.5 

126.5 

49 

185.0 

166.6 

10 

7.4 

6.7 

70 

52.0 

46.8 

30 

96.6 

87.0 

90 

141.2 

127.1 

50 

185.8 

167.3 

11 

8.2 

7.4 

71 

52.8 

47.5 

131 

97.4 

87.7 

191 

141.9 

127.8 

251 

186.5 

168.0 

12 

8.9 

8.0 

72 

53.5 

48.2 

32 

98.1 

88.3 

92 

142.7 

128.5 

52 

187.3 

168.6 

13 

9.7 

8.7 

73 

54.2 

48.8 

33 

98.8 

89.0 

93 

143.4 

129.1 

53 

188.0 

169.3 

14 

10.4 

9.4 

74 

55.0 

49.5 

34 

99.6 

89.7 

94 

144.2 

129.8 

54 

188.8 

170.0 

15 

11.1 

10.0 

75 

55.7 

50.2 

35 

100.3 

90.3 

95 

144.9 

130.5 

55 

189.5 

170.6 

16 

11.9 

10.7 

76 

56.5 

50.9 

36 

101.1 

91.0 

96 

145.7 

131.1 

56 

190.2 

171.3 

17 

12.6 

11.4 

77 

57.2 

51.5 

37 

101.8 

91.7 

97 

146.4 

131.8 

57 

191.0 

172.0 

18 

13.4 

12.0 

78 

58.0 

52.2 

38 

102.6 

92.3 

98 

147.1 

132.5 

58 

191.7 

172.6 

19 

14.1 

12.7 

79 

58.7 

52.9 

39 

103.3 

93.0 

99 

147.9 

133.2 

59 

192.5 

173.3 

20 

14.9 

13.4 

80 

59.5 

53.5 

40 

104.0 

93.7 

200 

148.6 

133.8 

60 

193.2 

174.0 

21 

15.6 

14.1 

81 

60.2 

54.2 

141 

104.8 

94.3 

201 

149.4 

134.5 

261 

194.0 

174.6 

22 

16.3 

14.7 

82 

60.9 

54.9 

42 

105.5 

95.0 

02 

150.1 

135.2 

62 

194.7 

175. 3 

23 

17.1 

15.4 

83 

61.7 

55.5 

43 

106.3 

95.7 

03 

150.9 

135.8 

63 

195.4 

176.0 

24 

17.8 

16.1 

84 

62.4 

56.2 

44 

107.0 

96.4 

04 

151.6 

136.5 

64 

196.2 

17(5.  7 

25 

18.6 

16.7 

85 

63.2 

56.9 

45 

107.8 

97.0 

05 

152.3 

137.2 

65 

196.9 

177.3 

26 

19.3 

17.4 

86 

63.9 

57.5 

46 

108.5 

97.7 

06 

153.1 

137.8 

66 

197.7 

178.0 

27 

20.1 

18.1 

87 

64.7 

58.2 

47 

109.2 

98.4 

07 

153.8 

138.5 

67 

198.4 

178.7 

28 

20.8 

18.7 

88 

65.4 

58.9 

48 

110.0 

99.0 

08 

154.6 

139.2 

68 

199.2 

179.3 

29 

21.6 

19.4 

89 

66.1 

59.6 

49 

110.7 

99.7 

09 

155.3 

139.8 

69 

199.9 

180.0 

30 

22.3 

20.1 

90 

66.9 

60.2 

50 

111.5 

100.4 

10 

156.1 

140.5 

70 

200.6 

180.7 

31 

23.0 

20.7 

91 

67.6 

60.9 

151 

112.2 

101.0 

211 

156.8 

141.2 

271 

201.4 

181.3 

32 

23.8 

21.4 

92 

68.4 

61.6 

52 

113.0 

101.7 

12 

157.5 

141.9 

72 

202.1 

182.0 

33 

24.5 

22.1 

93 

69.1 

62.2 

53 

113.7 

102.4 

13 

158.3 

142.5 

73 

202.9 

182.7 

34 

25.3 

22.8 

94 

69.9 

62.9 

54 

114.4 

103.0 

14 

159.0 

143.2 

74 

203.6 

183.3 

35 

26.0 

23.4 

95 

70.6 

63.6 

55 

115.2 

103.7 

15 

159.8 

143.9 

75 

204.4 

184.0 

36 

26.8 

24.1 

96 

71.3 

64.2 

56 

115.9 

104.4 

16 

160.5 

144.  5 

76 

205. 1 

184.7 

37 

27.5 

24.8 

97 

72.1 

64.9 

57 

116.7 

105.1 

17 

161.3 

145.2 

77 

205.9 

185.3 

38 

28.2 

25.4 

98 

72.8 

65.6 

58 

117.4 

105.7 

18 

162.0 

145.9 

78 

206.6 

186.0 

39 

29.0 

26.1 

99 

73.6 

66.2 

59 

118.2 

106.4 

19 

162.7 

146.5 

79 

207.3 

186.7 

40 

29.7 

26.8 

100 
101 

74.3 
75.1 

66.9 

60 

118.9 

107.1 

20 

163.5 

147.2 

80 

208.1 
208.8 

187.4 
188.0 

41 

30.5 

27.4 

67.6 

161 

119.6 

107.7 

221 

164.2 

147.9 

281 

42 

31.2 

28.1 

02 

75.8 

68.3 

62 

120.4 

108.4 

22 

165.0 

148.5 

82 

209.6 

188.7 

43 

32.0 

28.8 

03 

76.5 

68.9 

63 

121.1 

109.1 

23 

165.7 

149.2 

83 

210.3 

189.4 

44 

32.7 

29.4 

04 

77.3 

69.6 

64 

121.9 

109.7 

24 

166.5 

149.9 

84 

211.1 

190.0 

45 

33.4 

30.1 

05 

78.0 

70.3 

65 

122.6 

110.4 

25 

167.2 

150.6 

85 

211.8 

190.7 

46 

34.2 

30.8 

06 

78.8 

70.9 

66 

123.4 

111.1 

26 

168.0 

151.2 

86 

212. 5 

191.4 

47 

34.9 

31.4 

07 

79.5 

71.6 

67 

124.1 

111.7 

27 

168.7 

151.9 

87 

213.3 

192.0 

48 

35.7 

32.1 

08 

80.3 

72.3 

68 

124.8 

112.4 

28 

169.4 

152.6 

88 

214.  0 

192.7 

49 

36.4 

32.8 

09 

81.0 

72.9 

69 

125.6 

113.1 

29 

170.2 

153.2 

89 

214.8 

193.4 

50 

37.2 

33.5 

10 

81.7 

73.6 

70 

126.3 

113.8 

30 

170.9 

153.9 

90 

215.5 

194.0 

51 

37.9 

34.1 

111 

82.5 

74.3 

171 

127.1 

114.4 

231 

171.7 

154.6 

291 

216.3 

194.7 

52 

38.6 

34.8 

12 

83.2 

74.9 

72 

127.8 

115.1 

32 

172.4 

155.2 

92 

217.0 

195.  4 

53 

39.4 

35.5 

13 

84.0 

75.6 

73 

128.6 

115.8 

33 

173.2 

155.9 

93 

217.7 

196.1 

54 

40.1 

36.1 

14 

84.7 

76.3 

74 

129.3 

116.4 

34 

173.9 

156.6 

94 

218.5 

196.7 

55 

40.9 

36.8 

15 

85.5 

77.0 

75 

130.1 

117.1 

35 

174.6 

157.2 

95 

219.2 

197.4 

56 

41.6 

37.5 

16 

86.2 

77.6 

76 

130.8 

117.8 

36 

175.4 

157.9 

96 

220.0 

198. 1 

57 

42.4 

38.1 

17 

86.9 

78.3 

77 

131.5 

118.4 

37 

176.1 

158.6 

97 

220.7 

198.7 

58 

43.1 

38.8 

18 

87.7 

79.0 

78 

132.3 

119.1 

38 

176.9 

159.3 

98 

221.5 

199.4 

59 

43.8 

39.5 

19 

88.4 

79.6 

79 

133.0 

119.8 

39 

177.6 

159.9 

99 

222.2 

200.1 

60 

44.6 

40.1 

20 

89.2 

80.3 

80 

133.8 

120.4 

40 

178.4 

160.6 

300 

222.9 

200.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

4 

18°  (i: 

J2°,  228° 

,312). 

TABLE  2. 

[Page  615 

Difference  of  latitude  and  Departure  for  42°  (138°,  222°,  318° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     1     Dep. 

301 

223.7 

201.4 

361 

268.3 

241.6 

421 

312.9 

281.7 

481 

357.5 

321.9 

541 

402.1 

362.0 

02 

224.4 

202.1 

62 

269.0 

242.2 

22 

313.6 

282.4 

82 

358.2 

322.5 

42 

402.8 

362.7 

03 

225.2 

202.8 

63 

269.8 

242.9 

23 

314.4 

283.0 

83 

358.9 

323.2 

43 

403.5 

363.3 

04 

225.9 

203.4 

64 

270.5 

243.6 

24 

315.1 

283.7 

84 

359.7 

323.9 

44 

404.3 

364.0 

05 

226.6 

204.1 

65 

271.2 

244.2 

25 

315.8 

284.4 

85 

360.4 

324.6 

45 

405.0 

364.7 

06 

227.4 

204.8 

66 

272.0 

244.9 

26 

316.6 

285.1 

86 

361.2 

325.2 

46 

405.8 

365.4 

07 

228.1 

205.4 

67 

272.7 

245.6 

27 

317.3 

285.7 

87 

361.9 

325.9 

47 

406.5 

366.0 

08 

228.9 

206.1 

68 

273.5 

246.2 

28 

318.1 

286.4 

88 

362.7 

326.6 

48 

407.2 

366.7 

09 

229.6 

206.8 

69 

274.2 

246.9 

29 

318.8 

287.1 

89 

363.4 

327.2 

49 

408.0 

367.4 

10 
311 

230.4 
231.1 

207.4 

70 

275.0 

247.6 

30 

319.6 

287.7 

90 

364. 1 

327.9 

50 

408.7 

368.0 

208.1 

371 

275.7 

248.3 

431 

320.3 

288.4 

491 

364.9 

328.6 

551 

409.5 

368.7 

12 

231.9 

208.8 

72 

276.5 

248.9 

32 

321.0 

289.1 

92 

365.6 

329.2 

52 

410.2 

369.4 

13 

232.6 

209.4 

73 

277.2 

249.6 

33 

321.8 

289.7 

93 

366. 4 

329.9 

53 

411.0 

370.0 

14 

233.3 

210.1 

74 

277.9 

250.3 

34 

322.5 

290.4 

94 

367.1 

330,6 

54 

411.7 

370.7 

15 

234.1 

210.8 

75 

278.7 

250.9 

35 

323.3 

291.1 

95 

367.9 

331.3 

55 

412.4 

371.4 

16 

234.8 

211.5 

76 

279.4 

251.6 

36 

324.0 

291.7 

96 

368.6 

331.9 

56 

413.2 

372.0 

17 

235.6 

212.1 

77 

280.2 

252.3 

37 

324.8 

292.4 

97 

369.3 

332.6 

57 

413.9 

372.7 

18 

236.3 

212.8 

78 

280.9 

252.9 

38 

325.5 

293. 1 

98 

370.1 

333. 3 

58 

414.7 

373.4 

19 

237.1 

213.5 

79 

281.7 

253.  6 

39 

326.2 

293.8 

99 

370.8 

333.9 

59 

415.4 

374.1 

20 

237.8 

214.1 

80 

282.4 

254.3 

40 

327.0 

294.4 

500 

371.6 

334.6 

60 

416.2 

374.7 

321 

238.6 

214.8 

381 

283.1 

254.9 

441 

327.  7 

295.1 

501 

372.3 

335.3 

561 

416.9 

375.4 

22 

239.3 

215.5 

82 

283.9 

255.6 

42 

328.  5 

295.8 

02 

373.1 

335.9 

62 

417.6 

376.1 

23 

240.0 

216.1 

83 

284.6 

256.3 

43 

329.2 

296.4 

03 

373.8 

336.6 

63 

418.4 

376.7 

24 

240.8 

216.8 

84 

285.4 

257.0 

44 

330.0 

297.1 

04 

374.5 

337.2 

64 

419.1 

377.4 

25 

241.5 

217.5 

85 

286.1 

257.6 

45 

330.7 

297.8 

05 

375.3 

337.9 

65 

419.9 

378.1 

26 

242.3 

218.1 

86 

286.9 

258.3 

46 

331.4 

298.4 

06 

376.0 

338.6 

66 

420.6 

378.7 

27 

243.0 

218.8 

87 

287.6 

259.0 

47 

332.2 

299.1 

07 

376.8 

339.3 

67 

421,4 

379.4 

28 

243.8 

219.5 

88 

288.3 

259.6 

48 

332.9 

299.8 

08 

377.5 

339.9 

68 

422.1 

380.1 

29 

244.5 

220.1 

89 

289.1 

260.3 

49 

333.  7 

300.4 

09 

378.3 

340.6 

69 

422.8 

380.7 

30 

245.2 

220.8 

90 

289.8 

261.0 

50 

334.4 
335.2 

301.1 

10 

379.0 

341.3 

70 

423.6 

381.4 

331 

246.0 

221.5 

391 

290.6 

261.6 

451 

301.8 

511 

379.7 

341.9 

571 

424.3 

382.1 

32 

246.7 

222.2 

92 

291.3 

262.3 

52 

335.9 

302.5 

12 

380.5 

342.6 

72 

425.1 

382.8 

33 

247.5 

222.8 

93 

292.1 

263.0 

53 

336.6 

303.1 

13 

381.2 

343.3 

73 

425.8 

383.4 

34 

248.2 

223.5 

94 

292.8 

263.6 

54 

337.4 

303.8 

14 

382.0 

343.9 

74 

426.6 

384.1 

35 

249.0 

224.2 

95 

293.5 

264.3 

55 

338.1 

304.5 

15 

382.7 

344.6 

75 

427.3 

384.8 

36 

249.7 

224.8 

96 

294.3 

265.0 

56 

338.9 

305.1 

16 

383.5 

345.3 

76 

428.0 

385.4 

37 

250.4 

225.5 

97 

295.0 

265.7 

57 

339.6 

305.8 

17 

384.2 

346.0 

77 

428.8 

386.1 

38 

251.2 

226.2 

98 

295.8 

266.3 

58 

340.4 

306.5 

18 

384.9 

346.6 

78 

429.5 

386.8 

39 

251.9 

226.8 

99 

296.5 

267.0 

59 

341.1 

307.1 

19 

385.7 

347.3 

79 

430.3 

387.4 

40 

252.7 

227.5 

400 

297.3 

267.7 

60 

341.8 

307.8 

20 

386.4 

348.0 

80 

431.0 

388.1 

341 

253.4 

228.2 

401 

298.0 

268.3 

461 

342.6 

308.5 

521 

387.2 

348.6 

581 

431.8 

388.8 

42 

254.2 

228.8 

02 

298.7 

269.0 

62 

343.3 

309.1 

22 

387.9 

349.3 

82 

432.5 

389.4 

43 

254.9 

229.5 

03 

299.5 

269.7 

63 

344.1 

309.8 

23 

388.7 

350.0 

83 

433.2 

390.1 

44 

255.6 

230.2 

04 

300.2 

270.3 

64 

344.8 

310.5 

24 

389.4 

350.6 

84 

434.0 

390.8 

45 

256.4 

230.9 

05 

301.0 

271.0 

65 

345.6 

311.2 

25 

390.1 

351.3 

85 

434.7 

391.4 

46 

257.1 

231.5 

06 

301.7 

271.7 

66 

346.3 

311.8 

26 

390.9 

352.0 

86 

435.5 

392.1 

47 

257.9 

232.2 

07 

302.5 

272.3 

67 

347.0 

312.5 

27 

391.6 

352.6 

87 

436.2 

392.8 

48 

258.6 

232.9 

08 

303.2 

273.0 

68 

347.8 

313.2 

28 

392.4 

353.3 

88 

437.0 

393.4 

49 

259.4 

233.5 

09 

303.9 

273.7 

69 

348.5 

313.8 

29 

393.1 

354.0 

89 

437.7 

394.1 

50 

260.1 

234.2 

10 

304.7 

274.3 

70 

349.3 
350.0 

314.5 

30 

393.9 

354.6 

90 

438.4 

394.8 

351 

260.8 

234.9 

411 

305.4 

275.0 

471 

315.2 

531 

394.6 

355.3 

591 

439.2 

395.4 

52 

261.6 

235.5 

12 

306.2 

275.7 

72 

350.8 

315.8 

32 

395.3 

356.0 

92 

440.0 

396.1 

53 

262.3 

236.2 

13 

306.9 

276.4 

73 

351.5 

316.5 

33 

396.1 

356.6 

93 

440.7 

396.8 

54 

263.1 

236.9 

14 

307.7 

277.0 

74 

352.3 

317.2 

34 

396.8 

357.3 

94 

441.4 

397.5 

55 

263.8 

237.5 

15 

308.4 

277.7 

75 

353.0 

317.8 

35 

397.6 

358.0 

95 

442.2 

398.1 

56 

264.6 

238.2 

16 

309.1 

278.4 

76 

353.7 

318.5 

36 

398.3 

358.6 

96 

442.9 

398.8 

67 

265.3 

238.9 

17 

309.9 

279.0 

77 

354.5 

319.2 

37 

399.1 

359.3 

97 

443.7 

399.5 

58 

266.0 

239.6 

18 

310.6 

279.7 

78 

355.2 

319.9 

38 

399.8 

360.0 

98 

444.4 

400.1 

59 

266.8 

240.2 

19 

311.4 

280.4 

79 

356.0 

320.5 

39 

400.6 

360.6 

99 

445.2 

400.8 

60 

267.5 

240.9 

20 

312.1 

281.0 

80 

356.7 

321.2 

40 

401.3 

361.3 

600 

445.9 

401.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

DiBt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

48°  (132°,  228°,  312°). 

Page  616] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  43°  (137°,  22S 

°,  317° 

)• 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0,7 

0.7 

61 

44.6 

41.6 

121 

88.5 

82.5 

181 

132.4 

123.4 

241 

176.3 

164.4 

2 

1.5 

1.4 

62 

45.3 

42.3 

22 

89.2 

83.2 

82 

133.1 

124.1 

42 

177.0 

165.0 

3 

2.2 

2.0 

63 

46.1 

43.0 

23 

90.0 

83.9 

83 

133.8 

124.8 

43 

177.7 

165.7 

4 

2.9 

2.7 

64 

46.8 

43.6 

24 

90.7 

84.6 

84 

134.6 

125.5 

44 

178.6 

166.4 

5 

3.7 

3.4 

65 

47.5 

44.3 

25 

91.4 

85.2 

85 

135.3 

126.2 

46 

179.2 

167.1 

6 

4.4 

4.1 

66 

48.3 

45.0 

26 

92.2 

85.9 

86 

136.0 

126.9 

46 

179.9 

167.8 

7 

5.1 

4.8 

67 

49.0 

45.7 

27 

92.9 

86.6 

87 

136.8 

127.6 

47 

180.6 

168.5 

8 

5.9 

5.6 

68 

49.7 

46.4 

28 

93.6 

87.3 

88 

137.5 

128.2 

48 

181.4 

169.1 

9 

6.6 

6.1 

69 

50.5 

47.1 

29 

94.3 

88.0 

89 

138.2 

128.9 

49 

182.1 

169.8 

10 

7.3 

6.8 

70 

51.2 

47.7 

30 

96.1 

88.7 

90 

139.0 

129.6 

60 

182.8 

170.5 

11 

8.0 

7.5 

71 

51.9 

48.4 

131 

95.8 

89.3 

191 

139.7 

130.3 

251 

183.6 

171.2 

12 

8.8 

8.2 

72 

52.7 

49.1 

32 

96.5 

90.0 

92 

140.4 

130.9 

52 

184.3 

171.9 

13 

9.5 

8.9 

73 

53.4 

49.8 

33 

97.3 

90.7 

93 

141.2 

131.6 

53 

185.0 

172.5 

14 

10.2 

9.5 

74 

54.1 

50.5 

34 

98.0 

91.4 

94 

141.9 

132.3 

54 

185.8 

173.2 

15 

11.0 

10.2 

75 

54.9 

61.1 

35 

98.7 

92.1 

96 

142.6 

133.0 

55 

186.5 

173.9 

16 

11.7 

10.9 

76 

55.6 

51.8 

36 

99.6 

92.8 

96 

143.3 

133.7 

56 

187.2 

174.6 

17 

12.4 

11.6 

77 

56.3 

52.5 

37 

100.2 

93.4 

97 

144.1 

134.4 

57 

188.0 

175.3 

18 

13.2 

12.3 

78 

57.0 

53.2 

38 

100.9 

94.1 

98 

144.8 

136.0 

58 

188.7 

176.0 

19 

13.9 

13.0 

79 

57.8 

53.9 

39 

101.7 

94.8 

99 

145.6 

136.7 

59 

189.4 

176.6 

20 

14.6 

13.6 

80 

58.5 

54.6 

40 

102.4 
103.1 

95.6 

200 

146.3 

136.4 

60 

190.2 

177.3 

21 

15.4 

14.3 

81 

59.2 

55.2 

141 

96.2 

201 

147.0 

137.1 

261 

190.9 

178.0 

22 

16.1 

15.0 

82 

60.0 

55.9 

42 

103.9 

96.8 

02 

147.7 

137.8 

62 

191.6 

178.7 

23 

16.8 

15.7 

83 

60.7 

56.6 

43 

104.6 

97.6 

03 

148.5 

138.4 

63 

192.3 

179.4 

24 

17.6 

16.4 

84 

61.4 

57.3 

44 

105.3 

98.2 

04 

149.2 

139.1 

64 

193.1 

180.0 

25 

18.3 

17.0 

85 

62.2 

58.0 

46 

106.0 

98.9 

06 

149.9 

139.8 

65 

193.8 

180.7 

26 

19.0 

17.7 

86 

62.9 

58.7 

46 

106.8 

99.6 

06 

150.7 

140.6 

66 

194.5 

181.4 

27 

19.7 

18.4 

87 

63.6 

59.3 

47 

107.6 

100.  3. 

07 

151.4 

141.2 

67 

195.3 

182.1 

28 

20.5 

19.1 

88 

64.4 

60.0 

48 

108.2 

100.9 

08 

152.1 

141.9 

68 

196.0 

182.8 

29 

21.2 

19.8 

89 

65.1 

60.7 

49 

109.0 

101.6 

09 

162.9 

142.6 

69 

196.7 

183.5 

30 

21.9 

20.5 

90 

65.8 

61.4 

50 

109.7 

102.3 

10 

163.6 

143.2 

70 

197.6 

184.1 

31 

22.7 

21.1 

91 

66.6 

62.1 

151 

110.4 

103.  0 

211 

164.3 

143.9 

271 

198.2 

184.8 

32 

23.4 

21.8 

92 

67.3 

62.7 

52 

111.2 

103.7 

12 

156.0 

144.6 

72 

198.9 

185.6 

33 

24.1 

22.5 

93 

68.0 

63.4 

53 

111.9 

104.3 

13 

155.8 

146.3 

73 

199.7 

186.2 

34 

24.9 

23.2 

94 

68.7 

64.1 

54 

112.6 

106.0 

14 

156.6 

145.9 

74 

200.4 

186.9 

35 

25.6 

23.9 

95 

69.5 

64.8 

55 

113.4 

106.7 

16 

157.2 

146.6 

76 

201.1 

187.5 

36 

26.3 

24.6 

96 

70.2 

65.5 

66 

114.1 

106.4 

16 

168.0 

147.3 

76 

201.9 

188.2 

37 

27.1 

25.2 

97 

70.9 

66.2 

67 

114.8 

107.1 

17 

168.7 

148.0 

77 

202.6 

188.9 

38 

27.8 

25.9 

98 

71.7 

66.8 

68 

115.6 

107.8 

18 

159.4 

148.7 

78 

203.3 

189.6 

39 

28.5 

26.6 

99 

72.4 

67.5 

69 

116.3 

108.4 

19 

160.2 

149.4 

79 

204.0 

190.3 

40 

29.3 

27.3 

100 

73.1 

68.2 

60 

117.0 

109.1 

20 

160.9 

160.0 

80 
281 

204.8 
205.5" 

191.0 

41 

30.0 

28.0 

101 

73.9 

68.9 

161 

117.7 

109.8 

221 

161.6 

150.7 

191.6 

42 

30.7 

28.6 

02 

74.6 

69.6 

62 

118.5 

110.6 

22 

162.4 

151.4 

82 

206.2 

192.3 

43 

31.4 

29.3 

03 

75.3 

70.2 

63 

119.2 

111.2 

23 

163.1 

162.1 

83 

207.0 

193.0 

44 

32.2 

30.0 

04 

76.1 

70.9 

64 

119.9 

111.8 

24 

163.8 

152.8 

84 

207.7 

193.7 

45 

32.9 

30.7 

05 

76.8 

71.6 

65 

120.7 

112.6 

26 

164.6 

163.4 

85 

208.4 

194.4 

46 

33.6 

31.4 

06 

77.5 

72.3 

66 

121.4 

113.2 

26 

165.3 

164.1 

86 

209.2 

195.1 

47 

34.4 

32.1 

07 

78.3 

73.0 

67 

122.1 

113.9 

27 

166.0 

154.8 

87 

209.9 

195.7 

48 

35.1 

32.7 

08 

79.0 

73.7 

68 

122.9 

114.6 

28 

166.7 

155.5 

88 

210.6 

196.4 

49 

35.8 

33.4 

09 

79.7 

74.3 

69 

123.6 

115.3 

29 

167.5 

156.2 

89 

211.4 

197.1 

50 

36.6 

34.1 

10 

80.4 

75.0 
75.7 

70 

124.3 

116.9 

30 

168.2 

156.9 
157.5 

90 

212.1 

197.8 

51 

37.3 

34.8 

111 

81.2 

171 

125.1 

116.6 

231 

168.9 

291 

212.8 

198.5 

52 

38.0 

35.5 

12 

81.9 

76.4 

72 

126.8 

117.3 

32 

169.7 

158.2 

92 

213.6 

199.1 

53 

38.8 

36.1 

13 

82.6 

77.1 

73 

126.6 

118.0 

33 

170.4 

158.9 

93 

214.3 

199.8 

54 

39.5 

36.8 

14 

83.4 

77.7 

74 

127.3 

118.7 

34 

171.1 

169.6 

94 

215.0 

200.6 

55 

40.2 

37.5 

15 

84.1 

78.4 

75 

128.0 

119.3 

35 

171.9 

160.3 

96 

215.7 

201.2 

56 

41.0 

38.2 

16 

84.8 

79.1 

76 

128.7 

120.0 

36 

172.6 

161.0 

96 

216.5 

201.9 

57 

41.7 

38.9 

17 

85.6 

79.8 

77 

129.4 

120.7 

37 

173.3 

161.6 

97 

217.2 

202.6 

58 

42.4 

39.6 

18 

86.3 

80.5 

78 

130.2 

121.4 

38 

174.1 

162.3 

98 

217.9 

203.2 

59 

43.1 

40.2 

19 

87.0 

81.2 

79 

130.9 

122.1 

39 

174.8 

163.0 

99 

218.7 

203.9 

60 

43.9 

40.9 

20 

87.8 

81.8 

80 

131.6 

122.8 

40 

175.5 

163.7 

300 

219.4 

204.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

17°  (1 

33°,  227°,  313° 

)• 

TABLE  2. 

[Page  617 

Difference  of  Latitude  and  Departure  for  43"  (137°,  223°,  317° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

220.1 

205.3 

361 

264.0 

246.2 

421 

307.9 

287.1 

481 

351.8 

328.1 

541 

396.7 

369.0 

02 

220.9 

206.0 

62 

264.8 

246.9 

22 

308.6 

287.8 

82 

352.5 

328.7 

42 

396.4 

369.7 

03 

221.6 

206.7 

63 

265.5 

247.6 

23 

309.4 

288.5 

83 

353.2 

329.4 

43 

397.1 

370.3 

04 

222.3 

207.3 

64 

266.2 

248.3 

24 

310.1 

289.2 

84 

354.0 

330.1 

44 

397.9 

371.0 

05 

223.1 

208.0 

65 

267.0 

248.9 

25 

310.8 

289.9 

85 

354.7 

330.8 

45 

398.6 

371.7 

06 

223.8 

208.7 

66 

267.7 

249.6 

26 

311.6 

290.5 

86 

355.4 

331.4 

46 

399.3 

372.4 

07 

224.5 

209.4 

67 

268.4 

250.3 

27 

312.3 

291.2 

87 

356.2 

332.1 

47 

400.1 

373.1 

08 

225.3 

210.1 

68 

269.1 

251.0 

28 

313.0 

291.9 

88 

356.9 

332.8 

48 

400.8 

373.7 

09 

226.0 

210.7 

69 

269.9 

251.7 

29 

313.8 

292.6 

89 

357.7 

333.5 

49 

401.5 

374.4 

10 

226.7 

211.4 

70 

270.6 

252.  3 

30 

314.5 

293.3 

90 

358.4 

334.2 

50 

402.2 
403.0 

375.1 

311 

227.5 

212.1 

371 

271.3 

253.0 

431 

315.2 

293.9 

491 

359.1 

334.9 

561 

375.8 

12 

228.2 

212.8 

72 

272.1 

253.7 

32 

316.0 

294.6 

92 

359.8 

335.5 

52 

403.7 

376.5 

13 

228.9 

213.5 

73 

272.8 

254.4 

33 

316.7 

295.3 

93 

360.6 

336.2 

53 

404.4 

377.1 

14 

229.7 

214.2 

74 

273.5 

255.1 

34 

317.4 

296.0 

94 

361.3 

336.9 

54 

405.2 

377.8 

15 

230.4 

214.8 

75 

274.3 

255.8 

35 

318.1 

296.7 

95 

362.0 

337.6 

•55 

405.9 

378.5 

16 

231.1 

215.5 

76 

275.0 

256.4 

36 

318.9 

297.4 

96 

362.8 

338.3 

56 

406.6 

379.2 

17 

231.8 

216.2 

77 

275.7 

257.1 

37 

319.6 

298.0 

97 

363.5 

338.9 

67 

407.4 

379.9 

18 

232.6 

216.9 

78 

276.5 

257.8 

38 

320.3 

298.7 

98 

364.2 

339.6 

58 

408.1 

380.6 

19 

233.3 

217.6 

79 

277.2 

258.5 

39 

321.1 

299.4 

99 

364.9 

340.3 

59 

408.8 

381.2 

20 
321 

234.0 

218.2 

80 

277.9 

259.2 

40 

321.8 

300.1 

500 

365.7 
366.4 

341.0 

60 

409.6 

381.9 

234.8 

218.9 

381 

278.7 

259.8 

441 

322.5 

300.8 

501 

341.7 

561 

410.3 

382.6 

22 

235.5 

219.6 

82 

279.4 

260.5 

42 

323.3 

301.4 

02 

367.1 

342.4 

62 

411.0 

383.3 

23 

236.2 

220.3 

83 

280.1 

261.2 

43 

324.0 

302.1 

03 

367.8 

343.0 

63 

411.8 

384.0 

24 

237.0 

221.0 

84 

280.8 

261.9 

44 

324.7 

302.8 

04 

368.6 

343.7 

64 

412.5 

384.6 

25 

237.7 

221.7 

85 

281.6 

262.6 

45 

325.5 

303.5 

05 

369.3 

344.4 

65 

413.2 

385.3 

26 

238.4 

222.3 

86 

282.3 

263.3 

46 

326.2 

304.2 

06 

370.0 

345.1 

66 

414.0 

386.0 

27 

239.2 

223.0 

87 

283.0 

263.9 

47 

326.9 

304.9 

07 

370.8 

345.8 

67 

414.7 

386.7 

28 

239.9 

223.7 

88 

283.7 

264.6 

48 

327.7 

305.5 

08 

371.5 

346.5 

68 

415.4 

387.4 

29 

240.6 

224.4 

89 

284.5 

265.3 

49 

328.4 

306.2 

09 

372.3 

347,1 

69 

416.2 

388.1 

30 

241.4 

225.1 

90 

285.2 

266.0 

50 

329.1 

306.9 

10 

373.0 

347.8 

70 

416.9 

388.  7 
389.4 

331 

242.1 

225.7 

391 

286.0 

266.7 

451 

329.9 

307.6 

511 

373.8 

348.5 

571 

417.6 

32 

242.8 

226.4 

92 

286.7 

267.3 

52 

330.6 

308.3 

12 

374.5 

349.2 

72 

418.3 

390.1 

33 

243.5 

227.1 

93 

287.4 

268.0 

53 

331.3 

309.0 

13 

375.2 

349.9 

73 

419.1 

390.8 

34 

244.3 

227.8 

94 

288.2 

268.7 

54 

332.1 

309.6 

14 

376.0 

350.5 

74 

419.8 

391.5 

35 

245.0 

228.5 

95 

288.9 

269.4 

55 

332.8 

310.3 

15 

376.6 

351.2 

75 

420.5 

392.2 

36 

245.7 

229.2 

96 

289.6 

270.1 

56 

333.5 

311.0 

16 

377.4 

361.9 

76 

421.3 

392.8 

37 

246.5 

229.8 

97 

290.4 

270.8 

57 

334.3 

311.7 

17 

378.2 

362.6 

77 

422.0 

393.5 

38 

247.2 

230. 5 

98 

291.1 

271.4 

58 

335.0 

312.4 

18 

378.9 

353.3 

78 

422.7 

394.2 

39 

247.9 

231.2 

99 

291.8 

272.1 

59 

335.7 

313.0 

19 

379.6 

354.0 

79 

423. 5 

394.9 

40 

248.7 

231.9 

400 

292.6 

272.8 

60 

336.5 

313.7 

20 

380.3 

354.6 

80 

424.2 

395.6 

341 

249.4 

232.6 

401 

293.3 

273.5 

461 

337.2 

314.4 

521 

381.1 

365.  3 

681 

424.9 

396.2 

42 

250.1 

233.2 

02 

294.0 

274.2 

62 

337.9 

315.1 

22 

381.8 

356.0 

82 

426.7 

396.9 

43 

250.9 

233.9 

03 

294.7 

274.9 

63 

338.7 

315.8 

23 

382.6 

366.7 

83 

426.4 

397.6 

44 

251.6 

234.6 

04 

295.5 

275.5 

64 

339.4 

316.5 

24 

383.3 

357.4 

84 

427.1 

398.3 

45 

252.3 

235.3 

05 

296.2 

276.2 

65 

340.1 

317.1 

25 

384.0 

358.1 

85 

427.9 

399.0 

46 

253.1 

236.0 

06 

296.9 

276.9 

66 

340.8 

317.8 

26 

384.7 

368.7 

86 

428.6 

399.6 

47 

253.8 

236.7 

07 

297.7 

277.6 

67 

341.6 

318.5 

27 

385.5 

359.4 

87 

429.3 

400.3 

48 

254.5 

237.3 

08 

298.4 

278.3 

68 

342.3 

319.2 

28 

386.2 

360.1 

88 

430.1 

401.0 

49 

255.3 

238.0 

09 

299.1 

278.9 

69 

343.0 

319.9 

29 

386.9 

360.8 

89 

430.8 

401.7 

50 

256.0 

238.7 

10 

299.9 

279.6 

70 

343.7 
344.5 

320.5 
321.2 

30 

387.6 
388.4 

361.5 

90 

431.5 

402.4 

351 

256.7 

239.4 

411 

300.6 

280.3 

471 

531 

362.1 

591 

432.3 

403.1 

52 

257.4 

240.1 

12 

301.3 

281.0 

72 

345.2 

321.9 

32 

389.1 

362.8 

92 

433.0 

403.7 

53 

258.2 

240.8 

13 

302.1 

281.7 

73 

345.9 

322.6 

33 

389.9 

363.5 

93 

433.7 

404.4 

54 

258.9 

241.4 

14 

302.8 

282.4 

74 

346.7 

323.3 

34 

390.6 

364.2 

94 

434.5 

405.1 

55 

259.6 

242.1 

15 

303.5 

283.0 

75 

347.4 

324.0 

35 

391.3 

364.9 

95 

436.2 

405.8 

56 

260.4 

242.8 

16 

304.3 

283.7 

76 

348.1 

324.6 

36 

392.0 

366.5 

96 

436.9 

406.5 

57 

261.1 

243.5 

17 

305.0 

284.4 

77 

348.9 

325.3 

37 

392.8 

366.2 

97 

436.7 

407.2 

58 

261.8 

244.2 

18 

305.7 

286.1 

78 

349.6 

326.0 

38 

393.5 

366.9 

98 

437.4 

407.8 

59 

262.6 

244.8 

19 

306.4 

285.8 

79 

350.3 

326.7 

39 

394.2 

367.6 

99 

438.1 

408.6 

60 

263.3 

245.5 

20 

307.2 

286.4 

80 

351.1 

327.4 

40 

394.9 

368.3 

600 

438.8 

409.2 

Dist. 

I)ep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

4 

17°  (1 

33°,  227 

°,  313° 

)• 

Page  618] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  44°  (136°,  224°,  316« 

'). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.9 

42.4 

121 

87.0 

84.1 

181 

130.2 

125.7 

241 

173.4 

167.4 

2 

1.4 

1.4 

62 

44.6 

43.1 

22 

87.8 

84.7 

82 

130.9 

126.4 

42 

174.1 

168.1 

3 

2.2 

2.1 

63 

45.3 

43.8 

23 

88.5 

85.4 

83 

131.6 

127.1 

43 

174.8 

168.8 

4 

2.9 

2.8 

64 

46.0 

44.5 

24 

89.2 

86.1 

84 

132.4 

127.8 

44 

175.5 

169.5 

5 

3.6 

3.5 

65 

46.8 

45.2 

25 

89.9 

86.8 

85 

133.1 

128.5 

45 

176.2 

170.2 

6 

4.3 

4.2 

66 

47.5 

45.8 

26 

90.6 

87.5 

86 

133.8 

129.2 

46 

177.0 

170.9 

7 

5.0 

4.9 

67 

48.2 

46.5 

27 

91.4 

88.2 

87 

134.5 

129.9 

47 

177.7 

171.6 

8 

5.8 

5.6 

68 

48.9 

47.2 

28 

92.1 

88.9 

88 

135.2 

130.6 

48 

178.4 

172.3 

9 

6.5 

6.3 

69 

49.6 

47.9 

29 

92.8 

89.6 

89 

136.0 

131.3 

49 

179.1 

173.0 

10 

7.2 

6.9 

70 

50.4 

48.6 

30 

93.5 

90.3 

90 

136.7 

132.0 

50 

179.8 

173.7 

11 

7.9 

7.6 

71 

51.1 

49.3 

131 

94.2 

.  91.0 

191 

137.4 

132.7 

251 

180.6 

174.4 

12 

8.6 

8.3 

72 

51.8 

50.0 

32 

95.0 

91.7 

92 

138.1 

133.4 

52 

181.3 

175.1 

13 

9.4 

9.0 

73 

52.5 

50.7 

33 

95.7 

92.4 

93 

138.8 

134.1 

53 

182.0 

175.7 

14 

10.1 

9.7 

74 

53.2 

51.4 

34 

96.4 

93.1 

94 

139.6 

134.8 

54 

182.7 

176.4 

15 

10.8 

10.4 

75 

54.0 

52.1 

35 

97.1 

93.8 

96 

140.3 

135.5 

55 

183.4 

177.1 

16 

11.5 

11.1 

76 

54.7 

52.8 

36 

97.8 

94.5 

96 

141.0 

136.2 

56 

184.2 

177.8 

17 

12.2 

11.8 

77 

55.4 

53.5 

37 

98.5 

95.2 

97 

141.7 

136.8 

57 

184.9 

178.5 

18 

12.9 

12.5 

78 

56.1 

54.2 

38 

99.3 

95.9 

98 

142.4 

137.5 

58 

185.6 

179.2 

19 

13.7 

13.2 

79 

56.8 

54.9 

39 

100.0 

96.6 

99 

143.1 

138.2 

59 

186.3 

179.9 

20 

14.4 

13.9 

80 
81 

57.5 

55.6 

40 

100.7 

97.3 

200 

143.9 

138.9 

60 

187.0 

180.6 

21 

15.1 

14.6 

58.3 

56.3 

141 

101.4 

97.9 

201 

144.6 

139.6 

261 

187.7 

181.3 

22 

15.8 

15.3 

82 

59.0 

57.0 

42 

102.1 

98.6 

02 

145.3 

140.3 

62 

188.5 

182.0 

23 

16.5 

16.0 

83 

59.7 

57.7 

43 

102.9 

99.3 

03 

146.0 

141.0 

63 

189.2 

182.7 

24 

17.3 

16.7 

84 

60.4 

58.4 

44 

103.6 

100.0 

04 

146.7 

141.7 

64 

189.9 

183.  4 

25 

18.0 

17.4 

85 

61.1 

59.0 

45 

104.3 

100.7 

05 

147.5 

142.4 

65 

190.6 

184.1 

26 

18.7 

18.1 

86 

61.9 

59.7 

46 

105.0 

101.4 

06 

148.2 

143.1 

66 

191.3 

184.8 

27 

19.4 

18.8 

87 

62.6 

60.4 

47 

105.7 

102.1 

07 

148.9 

143.8 

67 

192.1 

185.5 

28 

20.1 

19.5 

88 

63.3 

61.1 

48 

106.5 

102.8 

08 

149.6 

144.5 

68 

192.8 

186.2 

29 

20.9 

20.1 

89 

64.0 

61.8 

49 

107.2 

103.5 

09 

150.3 

145.2 

69 

193.5 

186.9 

30 
31 

21.6 

20.8 

90 

64.7 

62.5 

50 

107.9 

104.2 

10 

151.1 

145.  9 

70 

194.2 

187.6 

22.3 

21.5 

91 

65.5 

63.2 

151 

108.6 

104.9 

211 

151.8 

146.6 

271 

194.9 

188.3 

32 

23.0 

22.2 

92 

66.2 

63.9 

52 

109.3 

105.6 

12 

152.5 

147.3 

72 

195.7 

188.9 

33 

23.7 

22.9 

93 

66.9 

64.6 

53 

110.1 

106.3 

13 

153.2 

148.0 

73 

196.4 

189.6 

34 

24.5 

23.6 

94 

67.6 

65.3 

54 

110.8 

107.0 

14 

153.9 

148.7 

74 

197.1 

190.3 

35 

25.2 

24.3 

95 

68.3 

66.0 

55 

111.5 

107.7 

15 

154.7 

149.4 

75 

197.8 

191.0 

36 

25.9 

25.0 

96 

69.1 

66.7 

56 

112.2 

108.4 

16 

155.4 

150.0 

76 

198.5 

191.7 

37 

26.6 

25.7 

97 

69.8 

67.4 

57 

112.9 

109.1 

17 

156.1  il50.7 

77 

199.  3 

192.4 

38 

27.3 

26.4 

98 

70.5 

68.1 

58 

113.7 

109.8 

18 

156.8    151.4 

78 

200.0 

193.1 

39 

28.1 

27.1 

99 

71.2 

68.8 

59 

114.4 

110.5 

19 

157. 5  i  152. 1 

79 

200.7 

193.8 

40 

28.8 

27.8 

100 

71.9 

69.5 

60 

115.1 

111.1 

20 

158.3 

152.8 

80 

201.4 

194.5 

41 

29.5 

28.5 

101 

72.7 

70.2 

161 

115.8 

111.8 

221 

159.0 

153.5 

281 

202. 1 

195.2 

42 

30.2 

29.2 

02 

73.4 

70.9 

62 

116.5 

112.5 

22 

159.7 

154.2 

82 

202.9 

195.9 

43 

30.9 

29.9 

03 

74.1 

71.5 

63 

117.3 

113.2 

23 

160.4 

154.9 

83 

203.6 

196.6 

44 

31.7 

30.6 

04 

74.8 

72.2 

64 

118.0 

113.9 

24 

161.1 

155.6 

84 

204.3 

197.3 

45 

32.4 

31.3 

05 

75.5 

72.9 

65 

118.7 

114.6 

25 

161.9 

156.3 

85 

205.0 

198.0 

46 

33.1 

32.0 

06 

76.3 

73.6 

66 

119.4 

115.3 

26 

162.6 

157.0 

86 

205.7 

198.7 

47 

33.8 

32.6 

07 

77.0 

74.3 

67 

120.1 

116.0 

27 

163.3 

157.7 

87 

206.5 

199.4 

48 

34.5 

33.3 

08 

77.7 

75.0 

68 

120.8 

116.7 

28 

164.0 

158.4 

88 

207.2 

200.1 

49 

35.2 

34.0 

09 

78.4 

75.7 

69 

121.6 

117.4 

29 

164.7 

159.1 

89 

207.9 

200.8 

50 

36.0 

34.7 

10 

79.1 

76.4 

70 

122.3 

118.1 

30 

165.4 
166.2 

159.8 

90 

208.6 

201.5 

51 

36.7 

35.4 

111 

79.8 

77.1 

171 

123.0 

118.8 

231 

160.5 

291 

209.3 

202.1 

52 

37.4 

36.1 

12 

80.6 

77.8 

72 

123.7 

119.5 

32 

166.9 

161.2 

92 

210.0 

202.8 

53 

38.1 

36.8 

13 

81.3 

78.5 

73 

124.4 

120.2 

33 

167.6 

161.9 

93 

210.8 

203.5 

54 

38.8 

37.5 

14 

82.0 

79.2 

74 

125.2 

120.9 

34 

168.3 

162.6 

94 

211.5 

204.2 

55 

39.6 

38.2 

15 

82.7 

79.9 

75 

125.9 

121.6 

35 

169.0 

163.2 

95 

212.2 

204.9 

56 

40.3 

38.9 

16 

83.4 

80.6 

76 

126.6 

122.3 

36 

169.8 

163.9 

96 

212.9 

205.6 

57 

41.0 

39.6 

17 

84.2 

81.3 

77 

127.3 

123.0 

37 

170.5 

164.6 

97 

213.6 

206.3 

58 

41.7 

40.3 

18 

84.9 

82.0 

78 

128.0 

123.6 

38 

171.2 

165.3 

98 

214.4 

207.0 

59 

42.4 

41.0 

19 

85.6 

82.7 

79 

128.8 

124.3 

39 

171.9 

166.0 

99 

215.1 

207.7 

60 

43.2 

41.7 

20 

86.3 

83.4 

80 

129.5 

125.0 

40 

172.6 

166.7 

300 

215.8 

208.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

i 

16°  (1 

J4°,  226°,  314° 

). 

TABLE  2. 

[Page  619 

] 

Mfference  of  Latitude  and  Depart 

are  for  44°  (136°,  224°,  316 

'). 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

216.5 

209.1 

361 

259.7 

250.8 

421 

302.8 

292.5 

481 

346.0 

334.1 

541 

389.2 

375.8 

02 

217.2 

209.8 

62 

260.4 

251.5 

22 

303.6 

293.2 

82 

346.7 

334.8 

42 

389.9 

376.5 

03 

218.0 

210.5 

63 

261.1 

252.2 

23 

304.3 

293.8 

83 

347.4 

335.5 

43 

390.6 

377.2 

04 

218.7 

211.2 

64 

261.8 

252.9 

24 

305.0 

294.5 

84 

348.2 

336.2 

44 

391.3 

377.9 

05 

219.4 

211.9 

65 

262.6 

253.6 

25 

305.7 

295.2 

85 

348.9 

336. 9 

45 

392.0 

378.6 

06 

220.1 

212.6 

66 

263.3 

254.3 

26 

306.4 

295.9 

86 

349.6 

337.6 

46 

392.8 

379.  3 

07 

220.8 

213.3 

67 

264.0 

254.9 

27 

307.2 

296.6 

87 

350.3 

338.3 

47 

393.5 

380.0 

08 

221.6 

214.0 

68 

264.7 

255.6 

28 

307.9 

297.3 

88 

351.0 

339.0 

48 

394.2 

380.7 

09 

222.3 

214.7 

69 

265.4 

256.3 

29 

308.6 

298.0 

89 

351.7 

339.7 

49 

394.9 

381.4 

10 

223.0 

215.4 

70 

266.2 

257.0 

30 

309.3 
310.0 

298.7 

90 

352.5 

340.4 

50 

396.6 

382.1 

311 

223.7 

216.0 

371 

266.9 

257.7 

431 

299.4 

491 

353.2 

341.1 

551 

396.4 

382.7 

12 

224.4 

216.7 

72 

267.6 

258.4 

32 

310.8 

300.1 

92 

353.9 

341.8 

52 

397.1 

383.4 

13 

225.2 

217.4 

73 

268.3 

259.1 

33 

311.5 

300.8 

93 

354.6 

342.5 

53 

397.8 

384.1 

14 

225.9 

218.1 

74 

269.0 

259.8 

34 

312.2 

301.5 

94 

355.3 

343.2 

54 

398.5 

384.8 

15 

226.6 

218.8 

75 

269.8 

260.5 

35 

312. 9 

302.  2 

95 

356.1 

343.9 

55 

399.2 

386.5 

16 

227.3 

219.5 

76 

270.5 

261.2 

36 

313. 6 

302. 9 

96 

356.8 

344.6 

56 

400.0 

386.2 

17 

228.0 

220.2 

77 

271.2 

261.9 

37 

314.4 

303.6 

97 

357.5 

346.2 

57 

400.7 

386.9 

18 

228.8 

220.9 

78 

271.9 

262.6 

38 

315.1 

304.3 

98 

358.2 

345.9 

58 

401.4 

387.6 

19 

229.5 

221.6 

79 

272.6 

263.3 

39 

315.8 

305. 0 

99 

358.9 

346. 6 

59 

402.1 

388.3 

20 

230.2 

222.3 

80 

273.4 

264.0 

40 

316.5 

305.7 

500 

359.7 

347.3 

60 

402.8 

389.0 

321 

230.9 

223.0 

381 

274.1 

264.7 

441 

317.2 

306.4 

501 

360.4 

348.0 

561 

403.6 

389.7 

22 

231.6 

223.7 

82 

274.8 

265.4 

42 

318.0 

307.0 

02 

361.1 

348.7 

62 

404.3 

390.4 

23 

232.3 

224.4 

83 

275.5 

266.1 

43 

318.7 

307.7 

03 

361.8 

349.4 

63 

406.0 

391.1 

24 

233.1 

225.1 

84 

276.2 

266.8 

44 

319.4 

308.4 

04 

362.5 

350.1 

64 

406.7 

391.8 

25 

233.8 

225.8 

85 

276.9 

267.5 

45 

320. 1 

309.1 

05 

363.3 

350.8 

65 

406.4 

392.6 

26 

234.5 

226.5 

86 

277.7 

268.1 

46 

320.8 

309.8 

06 

364.0 

351.5 

66 

407.2 

393.2 

27 

235.2 

227.2 

87 

278.4 

268.8 

47 

321.5 

310.5 

07 

364.7 

352.2 

67 

407.9 

393.9 

28 

235.9 

227.9 

88 

279.1 

269.5 

48 

322.3 

311.2 

08 

365.4 

352.9 

68 

408.6 

394.6 

29 

236.7 

228.6 

89 

279.8 

270.2 

49 

323.0 

311.9 

09 

366.1 

353.6 

69 

409.3 

396.3 

30 

237.4 

229.2 

90 

280.5 

270.9 

50 

323.7 

312.6 

10 

366.9 

354.3 

70 

410.0 

396.0 

331 

238.1 

229.9 

391 

281.3 

271.6 

451 

324.4 

313.3 

511 

367.6 

355.0 

571 

410.7 

396.7 

32 

238.8 

230.6 

92 

282.0 

272.3 

52 

325.2 

314.0 

12 

368.3 

355.7 

72 

411.5 

397.3 

33 

239.5 

231.3 

93 

282.7 

273.0 

53 

325.9 

314.7 

13 

369.0 

356.4 

73 

412.2 

398.0 

34 

240.3 

232.0 

94 

283.4 

273.7 

54 

326.6 

315.4 

14 

369.7 

357.1 

74 

412.9 

398.7 

35 

241.0 

232.7 

95 

284.1 

274.4 

55 

327.3 

316.1 

15 

.  370. 5 

357.8 

75 

413.6 

399.4 

36 

241.7 

233.4 

96 

284.9 

275.1 

56 

328.0 

316.8 

16 

371.2 

358.4 

76 

414.3 

400.1 

37 

242.4 

234.1 

97 

285.6 

275.8 

57 

328.7 

317.5 

17 

371.9 

359.1 

77 

415.1 

400.8 

38 

243.1 

234.8 

98 

286.3 

276.5 

58 

329.5 

318.2 

18 

372.6 

359.8 

78 

416.8 

401.5 

39 

243.9 

235.5 

99 

287.0 

277.2 

59 

330.2 

318.9 

19 

373.3 

360.5 

79 

416.5 

402.2 

40 

244.6 

236. 2 

400 

287.7 

277.9 

60 

330.9 

319.6 

20 

374.1 

361.2 

80 
581 

417.2 

402.9 
403.6 

341 

245.3 

236.9 

401 

288.5 

278.6 

461 

331.6 

320.2 

521 

374.8 

361.9 

417.9 

42 

246.0 

237.6 

02 

289.2 

279.3 

62 

332.3 

320.9 

22 

375. 5 

362.6 

82 

418.7 

404.3 

43 

246.7 

238.3 

03 

289.9 

280.0 

63 

333.1 

321.6 

23 

376.2 

363.3 

83 

419.4 

405.0 

44 

247.5 

239.0 

04 

290.6 

280.7 

64 

333.8 

322.3 

24 

376.9 

364.0 

84 

420.1 

405.7 

45 

248.2 

239.7 

05 

291.3 

281.3 

65 

334.5 

323.0 

25 

377.7 

364.7 

86 

420.8 

406.4 

46 

248.9 

240.4 

06 

292.1 

282.0 

66 

335.2 

323.7 

26 

378.4 

365.4 

86 

421.5 

407.1 

47 

249.6 

241.1 

07 

292.8 

282.7 

67 

335.9 

324.4 

27 

379.1 

366.1 

87 

422.3 

407.8 

48 

250.3 

241.7 

08 

293.5 

283.4 

68 

336.7 

325.1 

28 

379.8 

366.8 

88 

423.0 

408.5 

49 

251.1 

242.4 

09 

294.2 

284.1 

69 

337.4 

325.8 

29 

380.5 

367.5 

89 

423.7 

409.1 

50 

251.8 

243.1 

10 

294.9 

284.8 

70 

338.1 

326.  5 

30 

381.2 

368.2 

90 

424.4 

409.9 

351 

252.5 

243.8 

411 

295.7 

285.5 

471 

338.8 

327.  2 

531 

382.0 

368.9 

591 

426.1 

410.5 

52 

253.2 

244.5 

12 

296.4 

286.2 

72 

339.5 

327.9 

32 

382.7 

369.6 

92 

426.9 

411.2 

53 

253.9 

245.2 

13 

297.1 

286.9 

73 

340.3 

328.6 

33 

383.4 

370.3 

93 

426.6 

411.9 

54 

254.6 

245.9 

14 

297.8 

287.6 

74 

341.0 

329.3 

34 

384.1 

371.0 

94 

427.3 

412.6 

55 

255.4 

246.6 

15 

298.5 

288.3 

75 

341.7 

330.0 

35 

384.8 

371.7 

96 

428.0 

413.3 

56 

256.1 

247.3 

16 

299.2 

289.0 

76 

342.4 

330.7 

36 

385.6 

372.4 

96 

428.7 

414.0 

57 

256.8 

248.0 

17 

300.0 

289.7 

77 

343.1 

331.4 

37 

386.3 

373.1 

97 

429.5 

414.7 

58 

257.5 

248.7 

18 

300.7 

290.4 

78 

343.8 

332.1 

38 

387.0 

373.7 

98 

430.2 

415.4 

59 

258.2 

249.4 

19 

301.4 

291.1 

79 

344.6 

332.7 

39 

387.7 

374.4 

99 

430.9 

416.1 

60 

259.0 

250.1 

20 

302.1 

291.8 

80 

345.3 

333.4 

40 

388.4 

375.1 

600 

431.6 

416.8 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

46°  (134°,  226' 

,  314°). 

1 

Page  620] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  45°  (135°,  225°,  315' 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.1 

43.1 

121 

85.6 

85,6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

1.4 

1.4 

62 

43.8 

43.8 

22 

86.3 

86,3 

82 

128.7 

128.7 

42 

171.1 

171.1 

3 

2.1 

2.1 

63 

44.5 

44.5 

23 

87.0 

87.0 

83 

129.4 

129.4 

43 

171.8 

171.8 

4 

2.8 

2.8 

64 

45.3 

45.3 

24 

87.7 

87.7 

84 

130.1 

130.1 

44 

172.5 

172.5 

5 

3.5 

3.5 

65 

46.0 

46.0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

173.2 

173.2 

6 

4.2 

4.2 

66 

46.7 

46.7 

26 

89.1 

89.1 

86 

131.5 

131.5 

46 

173.9 

173.9 

7 

4.9 

4.9 

67 

47.4 

47.4 

27 

89.8 

89.8 

87 

132.2 

132.2 

47 

174.7 

174.7 

8 

5.7 

5.7 

68 

48.1 

48.1 

28 

90.5 

90,5 

88 

132.9 

132.9 

48 

175.4 

175.4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91,2 

89 

133.6 

133.6 

49 

176.1 

176.1 

10 

7.1 

7.1 

70 

49.5 

49.5 

30 

91.9 

91.9 

90 

134.4 

134.4 

50 

176.8 

176.8 

11 

7.8 

7.8 

71 

50.2 

50.2 

131 

92.6 

92.6 

191 

135.1 

135.1 

251 

177.5 

177.5 

12 

8.5 

8.5 

72 

50.9 

50.9 

32 

93.3 

93.3 

92 

135.8 

135,8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51.6 

51.6 

33 

94.0 

94.0 

93 

136,5 

136,5 

53 

178.9 

178.9 

14 

9.9 

9.9 

74 

52.3 

52.3 

34 

94,8 

94.8 

94 

137.2 

137,2 

54 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

35 

95.5 

95.5 

95 

137.9 

137,9 

55 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

36 

96.2 

96.2 

96 

138.6 

138.6 

56 

181.0 

181.0 

17 

12,0 

12.0 

77 

54.4 

54.4 

37 

96.9 

96.9 

97 

139.3 

139.3 

57 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

38 

97,6 

97.6 

98 

140.0 

140.0 

58 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

39 

98,3 

98.3 

99 

140.7 

140.7 

59 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 

141.4 

141,4 

60 

183.8 

183.8 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

99,7 

99.7 

201 

142.1 

142,1 

261 

184.6 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

43 

101.1 

101.1 

03 

143.5 

143.5 

63 

186.0 

186,0 

24 

17.0 

17.0 

84 

59.4 

59.4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186,7 

25 

17.7 

17.7 

85 

60.1 

60.1 

45 

102.5 

102.5 

05 

145.0 

145.0 

65 

187.4 

187,4 

26 

18.4 

18.4 

86 

60.8 

60.8 

46 

103.2 

103.2 

06 

145.7 

145.7 

66 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

48 

104.7 

104.7 

08 

147.1 

147.1 

68 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190.2 

190.2 

30 

21.2 

21.2 

90 

63.6 

63.6 

50 

106.1 

106.1 

10 

148.5 

148.5 

70 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.2 

149.2 

271 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

53 

108.2 

108.2 

13 

150.6 

150.6 

73 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

54 

108.9 

108.9 

14 

151.3 

151.3 

74 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109,6 

109.6 

15 

152.0 

152.0 

75 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

56 

110,3 

110.3 

16 

152.7 

152.7 

76 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

57 

111.0 

111.0 

17 

153.4 

153.4 

77 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

58 

111.7 

111.7 

18 

154.1 

154.1 

78 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

59 

112.4 

112.4 

19 

154.9 

154.9 

79 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

60 

113.1 

113.1 

20 

155.6 

155.6 

80 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

02 

72.1 

72.1 

62 

114.6 

114.6 

22 

157.0 

157.0 

82 

199.4 

199.4 

43 

30.4 

30.4 

03 

72.8 

72.8 

63 

115.3 

115.3 

23 

157.7 

157.7 

83 

200.1 

200.1 

44 

31.1 

31.1 

04 

73.5 

73.5 

64 

116.0 

116.0 

24 

158.4 

158.4 

84 

200.8 

200.8 

45 

31.8 

31.8 

05 

74.2 

74.2 

65 

116.7 

116.7 

25 

159.1 

159.1 

85 

201.5 

201.5 

46 

32.5 

32.5 

06 

75.0 

75.0 

66 

117.4 

117.4 

26 

159.8 

159.8 

86 

202.2 

202.2 

47 

33.2 

33.2 

07 

75.7 

75.7 

67 

118.1 

118.1 

27 

160.5 

160.5 

87 

202.9 

202.9 

48 

33.9 

33.9 

08 

76.4 

76.4 

68 

118.8 

118.8 

28 

161.2 

161.2 

88 

203.6 

203.6 

49 

34.6 

34.6 

09 

77.1 

77.1 

69 

119.5 

119.5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 

35.4 

35.4 

10 

77.8 

77,8 

70 

120.2 

120,2 

30 

162.6 

162,6 

90 

205.1 

205.1 

51 

36.1 

36.1 

111 

78.5 

78.5 

171 

120.9 

120,9 

231 

163.3 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79.2 

79.2 

72 

121.6 

121,6 

32 

164.0 

164,0 

92 

206.5 

206.5 

53 

37.5 

37.5 

13 

79.9 

79.9 

73 

122.3 

122,3 

33 

164.8 

164.8 

93 

207.2 

207. 2 

54 

38.2 

38.2 

14 

80.6 

80.6 

74 

123.0 

123,0 

34 

165.5 

165.5 

94 

207.9 

207.9 

55 

38.9 

38.9 

15 

81.3 

81.3 

75 

123.7 

123.7 

35 

166.2 

166.2 

95 

208.6 

208.6 

56 

39.6 

39.6 

16 

82.0 

82.0 

76 

124.5 

124.5 

36 

166.9 

166.9 

96 

209.3 

209.3 

57 

40.3 

40.3 

17 

82.7 

82.7 

77 

125.2 

125.2 

37 

167.6 

167.6 

97 

210.0 

210.0 

58 

41.0 

41.0 

18 

83.4 

83.4 

78 

125. 9 

125.9 

38 

168.3 

168.3 

98 

210.7 

210.7 

59 

41.7 

41.7 

19 

84.1 

84.1 

79 

126.6 

126.6 

39 

169.0 

169.0 

99 

211.4 

211,4 

60 

42.4 

42.4 

20 

84.9 

84.9 

80 

127.3 

127.3 

40 

169.7 

169.7 

300 

212.1 

212. 1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

4 

S°(K 

J5°,  225°,  815° 

). 

1 

TABLE  2. 

[Page  620a     | 

Difference  of  Latitude  and  Departure  for  45°  (135°,  225°,  315 

')• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

212.8 

212.8 

361 

255.3 

255.3 

421 

297.7 

297.7 

481 

340.1 

340.1 

541 

382.6 

382.5 

02 

213.5 

213.5 

62 

256.0 

256.0 

22 

298.4 

298.4 

82 

340.8 

340.8 

42 

383.2 

383.2 

03 

214.3 

214.3 

63 

256.7 

256.7 

23 

299.1 

299.1 

83 

341.6 

341.5 

43 

383.9 

383.9 

04 

215.0 

215.0 

64 

257.4 

257.4 

24 

299.8 

299.8 

84 

342.2 

342.2 

44 

384.7 

384.7 

05 

215.7 

215.7 

65 

258.1 

258.1 

25 

300.5 

300.5 

85 

342.9 

342.9 

45 

385.4 

386.4 

06 

216.4 

216.4 

66 

258.8 

258.8 

26 

301.2 

301.2 

86 

343.6 

343.6 

46 

386.1 

386.1 

07 

217.1 

217.1 

67 

259.5 

259.5 

27 

301.9 

301.9 

87 

344.3 

344.3 

47 

386.8 

386.8 

08 

217.8 

217.8 

68 

260.2 

260.2 

28 

302.6 

302.6 

88 

346.1 

345.1 

48 

387.5 

387.6 

09 

218.5 

218.5 

69 

260.9 

260.9 

29 

303.4 

303.4 

89 

345.8 

345.8 

49 

388.2 

388.2 

10 

219.2 

219.2 

70 

261.6 

261.6 

30 

304.1 

304.1 

90 

346.5 

346.5 

50 

388.9 

388.9 

311 

219.9 

219.9 

371 

262,3 

262.3 

431 

304.8 

304.8 

491 

347.2 

347.2 

561 

389.6 

389.6 

12 

220.6 

220.6 

72 

263.0 

263.0 

32 

306. 5 

305.6 

92 

347.9 

347.9 

62 

390.3 

390.3 

13 

221.3 

221.3 

73 

263.8 

263.8 

33 

306.2 

306.2 

93 

348.6 

348.6 

53 

391,0 

391.0 

14 

222.0 

222.0 

74 

264.5 

264.5 

34 

306.9 

306.9 

94 

349.3 

349.3 

54 

391.7 

391.7 

15 

222.7 

222.7 

75 

266.2 

265.2 

35 

307.6 

307.6 

95 

350.0 

360.0 

55 

392.4 

392.4 

16 

223.4 

223.4 

76 

265.9 

266.9 

36 

308.3 

308.3 

96 

350.7 

350.7 

56 

393.1 

393.1 

17 

224.2 

224.2 

77 

266.6 

266.6 

37 

309.0 

309.0 

97 

361.4 

351.4 

57 

393.9 

393.9 

18 

224.9 

224.9 

78 

267.3 

267.3 

38 

309.7 

309.7 

98 

352.1 

352.1 

58 

394.6 

394.6 

19 

225.6 

225.6 

79 

268.0 

268.0 

39 

310.4 

310.4 

99 

352.8 

352.8 

69 

396.3 

396.3 

20 

226.3 

226.3 

80 

268.7 

268.7 

40 

311.1 

311.1 

500 

353.5 

353.6 

60 

396.0 

396.0 

321 

227.0 

227.0 

381 

269.4 

269.4 

441 

311.8 

311.8 

501 

354.3 

354.3 

661 

396,7 

396.7 

22 

227.7 

227.7 

82 

270.1 

270.1 

42 

312.5 

312.6 

02 

365.0 

355.0 

62 

397.4 

397.4 

23 

228.4 

228.4 

83 

270.8 

270.8 

43 

313.3 

313.3 

03 

355.7 

366.7 

63 

398.1 

398.1 

24 

229.1 

229.1 

84 

271.5 

271.5 

44 

314.0 

314.0 

04 

356.4 

366.4 

64 

398.8 

398.8 

25 

229.8 

229.8 

85 

272.2 

272.2 

45 

314.7 

314.7 

05 

357.1 

357.1 

65 

399.6 

399.6 

26 

230.5 

230.5 

86 

272.9 

272.9 

46 

315.4 

315.4 

06 

367.8 

367.8 

66 

400.2 

400.2 

27 

231.2 

231.2 

87 

273.7 

273.7 

47 

316.1 

316.1 

07 

358.6 

358.5 

67 

400.9 

400.9 

28 

231.9 

231.9 

88 

274.4 

274.4 

48 

316.8 

316.8 

08 

359.2 

369.2 

68 

401.6 

401.6 

29 

232.6 

232.6 

89 

275.1 

275.1 

49 

317.5 

317.5 

09 

359.9 

369.9 

69 

402.3 

402.3 

30 

233.3 

233.3 

90 

275.8 

275.8 

50 

318.2 

318.2 

10 

360.6 

360.6 

70 

403,0 

403.0 

331 

234.1 

234.1 

391 

276.5 

276.5 

451 

318.9 

318.9 

511 

361.3 

361.3 

571 

403.8 

403,8 

32 

234.8 

234.8 

92 

277.2 

277.2 

52 

319.6 

319.6 

12 

362.0 

362.0 

72 

404.5 

404,5 

33 

235.5 

235.5 

93 

277.9 

277.9 

63 

320.3 

320.3 

13 

362.7 

362.7 

73 

405.2 

405.2 

34 

236.2 

236.2 

94 

278.6 

278.6 

54 

321.0 

321.0 

14 

363.5 

363.5 

74 

406.9 

406.9 

35 

236.9 

236.9 

95 

279.3 

279.3 

55 

321.7 

321.7 

15 

364.2 

364.2 

75 

406.6 

406.6 

36 

237.6 

237.6 

96 

280.0 

280.0 

56 

322.4 

322.4 

16 

364.9 

364.9 

76 

407.3 

407.3 

37 

238.3 

238.3 

97 

280.7 

280.7 

57 

323.2 

323.2 

17 

365.6 

365.6 

77 

408.0 

408.0 

38 

239.0 

239.0 

98 

281.4 

281.4 

58 

323.9 

323.9 

18 

366.3 

366.3 

78 

408.7 

408.7 

39 

239.7 

239.7 

99 

282.1 

282.1 

59 

324.6 

324.6 

19 

367.0 

367.0 

79 

409.4 

409,4 

40 

240.4 

240.4 

400 

282.8 

282.8 

60 

326.3 
326.0 

325.3 

20 

367.7 

367.7 

80 

410.1 

410,1 

341 

241.1 

241.1 

401 

283.6 

283.6 

461 

326.0 

521 

368.4 

368.4 

581 

410.8 

410.8 

42 

241.8 

241.8 

02 

284.3 

284.3 

62 

326.7 

326.7 

22 

369.1 

369.1 

82 

411.6 

411.6 

43 

242.5 

242.5 

03 

285.0 

286.0 

63 

327.4 

327.4 

23 

369.8 

369.8 

83 

412.2 

412.2 

44 

243.2 

243.2 

04 

285.7 

285.7 

64 

328.1 

328.1 

24 

370.5 

370.6 

84 

412.9 

412.9 

45 

244.0 

244.0 

05 

286.4 

286.4 

66 

328.8 

328.8 

25 

371.2 

371.2 

85 

413.7 

413.7 

46 

244.7 

244.7 

06 

287.1 

287.1 

66 

329.5 

329.5 

26 

371.9 

371.9 

86 

414.4 

414.4 

47 

245.4 

245.4 

07 

287.8 

287.8 

67 

330.2 

330.2 

27 

372.6 

372.6 

87 

415.1 

416.1 

48 

246.1 

246.1 

08 

288.5 

288.5 

68 

330.9 

330.9 

28 

373.4 

373.4 

88 

415.8 

415.8 

49 

246.8 

246.8 

09 

289.2 

289.2 

69 

331.6 

331.6 

29 

374.1 

374.1 

89 

416.5 

416.6 

50 

247.5 

247.5 

10 

289.9 

289.9 

70 

332.3 

332.3 

30 

374.8 

374.8 

90 

417.2 

417.2 

351 

248.2 

248.2 

411 

290.6 

290.6 

471 

333.1 

333.1 

631 

375.5 

375.6 

691 

417.9 

417.9 

52 

248.9 

248.9 

12 

291.3 

291.3 

72 

333.8 

333.8 

32 

376.2 

376.2 

92 

418.6 

418.6 

53 

249.6 

249.6 

13 

292.0 

292.0 

73 

334.5 

334.5 

33 

376.9 

376.9 

93 

419.3 

419.3 

54 

260.3 

250.3 

14 

292.7 

292.7 

74 

336.2 

335.2 

34 

377.6 

377.6 

94 

420.0 

420.0 

55 

251.0 

251.0 

15 

293.5 

293.5 

75 

335.9 

335.9 

35 

378.3 

378.3 

96 

420.7 

420,7 

56 

251.7 

251.7 

16 

294.2 

294.2 

76 

336.6 

336.6 

36 

379.0 

379.0 

96 

421.4 

421,4 

57 

252.4 

252.4 

17 

294.9 

294.9 

77 

337.3 

337.3 

37 

379.7 

379.7 

97 

422,1 

422,1 

58 

253.1 

253.1 

18 

295.6 

296.6 

78 

338.0 

338.0 

38 

380.4 

380.4 

98 

422,8 

422,8 

59 

253.9 

253.9 

19 

296.3 

296.3 

79 

338.7 

338.7 

39 

381.1 

381.1 

99 

423,6 

423.6 

60 

254.6 

254.6 

20 

297.0 

297.0 

80 

339.4 

339.4 

40 

381.8 

381.8 

600 

424.3 

424.3 

DIflt. 

Dep. 

Lat. 

Diat.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

45°  (135°,  225°,  315°).                                                                  1 

TABLE  3. 

[Page 

621 

Meridional  Parts,  or 

Increased  Latitadee. 

Comp 

1 

•  293.465 

M. 

0° 

1° 

go 

8° 

4° 

6° 

6° 

70 

8° 

90 

M. 

0 

0.0 

69.6 

119.2 

178.9 

238.6 

298.3 

368.2 

418.2 

478.3 

538.6 

0 

1 

1.0 

60.6 

20.2 

79.9 

39.6 

99.3 

69.2 

19.2 

79.3 

39.6 

1 

2 

2.0 

61.6 

21.2 

80.8 

40.6 

300.3 

60.2 

20.2 

80.3 

40.6 

2 

3 

3.0 

62.6 

22.2 

81.8 

41.6 

01.3 

61.2 

21.2 

81.3 

41.6 

3 

4 

4.0 

63.6 

23.2 

82.8 

42.5 

02.3 

62.2 

22.2 

82.3 

42.6 

4 

5 

5.0 

64.6 

124.2 

183.8 

243.5 

303.3 

363.2 

423.2 

483.3 

543.6 

6 

6 

6.0 

66.6 

25.2 

84.8 

44.5 

04.3 

64.2 

24.2 

84.3 

44.6 

6 

7 

7.0 

66.5 

26.2 

86.8 

46.6 

.     06.3 

65.2 

25.2 

85.3 

46.6 

7 

8 

7.9 

67.5 

27.2 

86.8 

46.5 

06.3 

66.2 

26.2 

86.3 

46.6 

8 

9 

8.9 

68.5 

28.2 

87.8 

47.5 

07.3 

67.2 

27.2 

87.3 

47.6 
548.6 

9 

10 

9.9 

69.6 

129.1 

188.8 

248.6 

308.3 

368.2 

428.2 

488.3 

10 

11 

10.9 

70.6 

30.1 

89.8 

49.5 

09.3 

69.2 

29.2 

89.3 

49.6 

11 

12 

11.9 

71.5 

31.1 

90.8 

50.5 

10.3 

70.2 

30.2 

90.4 

50.6 

12 

13 

12.9 

72.5 

32.1 

91.8 

51.6 

11.3 

71.2 

31.2 

91.4 

61.7 

13 

14 

13.9 

73.5 

33.1 

92.8 

52.6 

12.3 

T2.2 

32.2 

92.4 

52.7 

14 

15 

14.9 

74.5 

134.1 

193.8 

253.5 

313.3 

373.2 

433.2 

493.4 

553.7 

15 

16 

15.9 

75.5 

35.1 

94.8 

54.5 

14.3 

74.2 

34.2 

94.4 

54.7 

16 

17 

16.9 

76.5 

36.1 

95.8 

55.6 

16.3 

76.2 

35.2 

95.4 

55.7 

17 

18 

17.9 

77.5 

37.1 

96.8 

56.5 

16.3 

76.2 

36.2 

96.4 

66.7 

18 

19 

18.9 

78.5 

38.1 

97.8 

57.6 

17.3 

77.2 

37.2 

97.4 

67.7 

19 

20 

19.9 

79.6 

139.1 

198.8 

258.5 

318.3 

378.2 

438.2 

498.4 

658.7 

20 

21 

20.9 

80.5 

40.1 

99.7 

59.5 

19.3 

79.2 

39.2 

99.4 

59.7 

21 

22 

21.9 

81.5 

41.1 

200.7 

60.5 

20.3 

80.2 

40.2 

500.4 

60.7 

22 

23 

22.8 

82.4 

42.1 

01.7 

61.5 

21.3 

81.2 

41.2 

01.4 

61.7 

23 

24 

23.8 

83.4 

43.1 

02.7 

62.5 

22.3 

82.2 

42.2 

02.4 

62.7 

24 

25 

24.8 

84.4 

144.1 

203.7 

263.6 

323.3 

383.2 

443.2 

503.4 

563.7 

25 

26 

25.8 

85.4 

45.1 

04.7 

64.5 

24.3 

84.2 

44.2 

04.4 

64.7 

26 

27 

26.8 

86.4 

46.0 

06.7 

65.5 

25.3 

85.2 

45.2 

05.4 

65.7 

27 

28 

27.8 

87.4 

47.0 

06.7 

66.6 

26.3 

86.2 

46.2 

06.4 

66.8 

28 

29 

28.8 

88.4 

48.0 

07.7 

67.4 

27.3 

87.2 

47.2 

07.4 

67.8 

29 

30 

29.8 

89.4 

149.0 

208.7 

268.4 

328.3 

388.2 

448.2 

508.4 

568.8 

30 

31 

30.8 

90.4 

50.0 

09.7 

69.4 

29.3 

89.2 

49.2 

09.4 

69.8 

31 

32 

31.8 

91.4 

61.0 

10.7 

70.4 

30.3 

90.2 

50.2 

10.4 

70.8 

32 

33 

32.8 

92.4 

62.0 

11.7 

71.4 

31.3 

91.2 

61.2 

11.4 

71.8 

33 

34 

33.8 

93.4 

53.0 

12.7 

72.4 

32.3 

92.2 

52.2 

12.4 

72.8 

34 

35 

34.8 

94.4 

164.0 

213.7 

273.4 

333.3 

393.2 

453.2 

513.4 

673.8 

36 

36 

35.8 

96.4 

66.0 

14.7 

74.4 

34.3 

94.2 

54.3 

14.6 

74.8 

36 

37 

36.7 

96.4 

56.0 

16.7 

76.4 

36.3 

95.2 

55.3 

15.6 

75.8 

37 

38 

37.7 

97.3 

57.0 

16.7 

76.4 

36.2 

96.2 

66.3 

16.6 

76.8 

38 

39 

38.7 

98.3 

58.0 

17.7 

77.4 

37.2 

97.2 

57.3 

17.5 

77.8 

39 

40 

39.7 

99.3 

159.0 

218.7 

278.4 

338.2 

398.2 

458.3 

518.5 

578.8 

40 

41 

40.7 

100.3 

60.0 

19.7 

79.4 

39.2 

99.2 

59.3 

19.5 

79.9 

41 

42 

41.7 

01.3 

61.0 

20.6 

80.4 

40.2 

400.2 

60.3 

20.6 

80.9 

42 

43 

42.7 

02.3 

62.0 

21.6 

81.4 

41.2 

01.2 

61.3 

21.5 

81.9 

43 

44 
45 

43.7 

03.3 

63.0 

22.6 

82.4 

42.2 

02.2 

62.3 

22.5 

82.9 

44 

44.7 

104.3 

164.0 

223.6 

283.4 

343.2 

403.2 

463.3 

523.5 

583.9 

46 

46 

46.7 

05.3 

65.0 

24.6 

84.4 

44.2 

04.2 

64.3 

24.5 

84.9 

46 

47 

46.7 

06.3 

66.0 

25.6 

85.4 

45.2 

05.2 

65.3 

25.5 

85.9 

47 

48 

47.7 

07.3 

67.0 

26.6 

86.4 

46.2 

06.2 

66.3 

26.5 

86.9 

48 

49 

48.7 

08.3 

68.0 

27.6 

87.4 

47.2 

07.2 

67.3 

27.5 

87.9 

49 

50 

49.7 

109.3 

168.9 

228.6 

288.4 

348.2 

408.2 

468.3 

628.6 

688.9 

60 

51 

50.7 

10.3 

69.9 

29.6 

89.4 

49.2 

09.2 

69.3 

29.5 

89.9 

51 

52 

51.6 

11.3 

70.9 

30.6 

90.4 

50.2 

10.2 

70.3 

30.5 

90.9 

52 

53 

52.6 

12.3 

71.9 

31.6 

91.4 

51.2 

11.2 

71.3 

31.5 

91.9 

63 

54 

53.6 

13.2 

72.9 

32.6 

92.4 

52.2 

12.2 

72.3 

32.5 

93.0 

54 

56 

54.6 

114.2 

173.9 

233.6 

293.4 

363.2 

413.2 

473.3 

533.5 

594.0 

55 

56 

55.6 

16.2 

74.9 

34.6 

94.4 

54.2 

14.2 

74.3 

34.6 

95.0 

66 

57 

56.6 

16.2 

75.9 

36.6 

95.4 

65.2 

16.2 

75.3 

36.6 

96.0 

67 

58 

67.6 

17.2 

76.9 

36.6 

96.3 

66.2 

16.2 

76.3 

36.6 

97.0 

58 

59 

58.6 

18.2 

77.9 

37.6 

97.3 

67.2 

17.2 

77.3 

37.6 

98.0 

59 

M. 

0° 

1° 

go 

8° 

4° 

6° 

6° 

7° 

8° 

»o 

M. 

Page  622] 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp 

1 

2^3.466 

M. 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

M. 

0 

599.0 

659.6 

720.5 

781.5 

842.8 

904.4 

966.3 

1028. 5 

1091. 0 

1153. 9 

0 

1 

600.0 

60.6 

21.5 

82.5 

43.9 

05.4 

67.3 

29.5 

92.0 

54.9 

1 

2 

01.0 

61.7 

22.5 

83.6 

44.9 

06.5 

68.3 

30.5 

93.1 

56.0 

2 

3 

02.0 

62.7 

23.5 

84.6 

45.9 

07.5 

69.4 

31.6 

94.1 

57.0 

3 

4 

03.0 

63.7 

24.5 

85.6 

46.9 

08.5 

70.4 

32.6 

95.2 

58.1 

4 

5 

604.1 

664.7 

725.5 

786.6 

847.9 

909.6 

971.4 

1033.  7 

1096.  2 

1159. 1 

5 

6 

05.1 

65.7 

26.6 

87.6 

49.0 

10.6 

72.5 

34.7 

97.3 

60.2 

6 

7 

06.1 

66.7 

27.6 

88.7 

50.0 

11.6 

73.5 

35.7 

98.3 

61.2 

7 

8 

07.1 

67.7 

28.6 

89.7 

51.0 

12.6 

74.6 

36.8 

99.4 

62.3 

8 

9 

08.1 

68.7 

29.6 

90.7 

52.0 

13.7 

75.6 

37.8 

1100. 4 

63.3 

9 

10 

609.1 

669.8 

730.6 

791.7 

853.1 

914.7 

976.6 

1038. 9 

1101. 4 

1164. 4 

10 

11 

10.1 

70.8 

31.6 

92.7 

54.1 

15.7 

77.7 

39.9 

02.5 

65.4 

11 

12 

11.1 

71.8 

32.7 

93.8 

55.1 

16.8 

78.7 

40.9 

03.5 

66.5 

12 

13 

12.1 

72.8 

33.7 

94.8 

56.1 

17.8 

79.7 

42.0 

04.6 

67.5 

13 

14 
15 

13.1 

73.8 

34.7 

95.8 

57.2 

18.8 

80.8 

43.0 

05.6 

68.6 

14 

614.1 

674.8 

735.7 

796.8 

858.2 

919.8 

981.8 

1044.1 

1106. 7 

1169. 7 

15 

16 

15.2 

75.8 

36.7 

97.8 

59.2 

20.9 

82.8 

45.1 

07.7 

70.7 

16 

17 

16.2 

76.8 

37.7 

98.9 

60.2 

21.9 

83.9 

46.1 

08.8 

71.8 

17 

18 

17.2 

77.9 

38.8 

99.9 

.61.3 

22.9 

84.9 

47.2 

09.8 

72.8 

18 

19 

18.2 

78.9 

39.8 

800.9 

62.3 

24.0 

85.9 

48.2 

10.9 

73.9 

19 

20 

619.2 

679.9 

740.8 

801.9 

863.3 

925.0 

987.0 

1049. 3 

1111.9 

1174. 9 

20 

21 

20.2 

80.9 

41.8 

02.9 

64.3 

26.0 

88.0 

50.3 

13.0 

76.0 

21 

22 

21.2 

81.9 

42.8 

04.0 

65.4 

27.1 

89.0 

51.3 

14.0 

77.0 

22 

23 

22.2 

82.9 

43.8 

05.0 

66.4 

28.1 

90.1 

52.4 

15.0 

78.1 

23 

24 

23.2 

83.9 

44.9 

06.0 

67.4 

29.1 

91.1 

53.4 

16.1 

79.1 

24 

25 

624.2 

684.9 

745.9 

807.0 

868.5 

930.1 

992.1 

1054. 5 

1117. 1 

1180.  2 

25 

26 

25.3 

86.0 

46.9 

08.1 

69.5 

31.2 

93.2 

55.5 

18.2 

81.2 

26 

27 

26.3 

87.0 

47.9 

09.1 

70.5 

32.2 

94.2 

56.6 

19.2 

82.3 

27 

28 

27.3 

88.0 

48.9 

10.1 

71.5 

33.2 

95.3 

57.6 

20.3 

83.3 

28 

29 

28.3 

89.0 

49.9 

11.1 

72.6 

34.3 

96.3 

58.6 

21.3 

84.4 

29 

30 

629.3 

690.0 

751.0 

812.1 

873.6 

935.3 

997.3 

1059.  7 

1122. 4 

1185.5 

30 

31 

30.3 

91.0 

52.0 

13.2 

74.6 

36.3 

98.4 

60.7 

23.4 

86.5 

31 

32 

31.3 

92.0 

53.0 

14.2 

75.6 

37.4 

99.4 

61.8 

24.5 

87.6 

32 

33 

32.3 

93.1 

54.0 

15.2 

76.7 

38.4 

1000.4 

62.8 

25.5 

88.6 

33 

34 

33.3 

94.1 

55.0 

16.2 

77.7 

39.4 

01.5 

63.9 

26.6 

89.7 

34 

36 

634,3 

695.1 

756.0 

817.3 

878.7 

940.5 

1002.5 

1064. 9 

1127.  6 

1190.7 

35 

36 

35.4 

96.1 

57.1 

18.3 

79.7 

41.5 

03.6 

65.9 

28.7 

91.8 

36 

37 

36.4 

97.1 

58.1 

19.3 

80.8 

42.5 

04.6 

67.0 

29.7 

92.8 

37 

38 

37.4 

98.1 

59.1 

20.3 

81.8 

43.6 

05.6 

68.0 

30.8 

93.9 

38 

39 

38.4 

99.1 

60.1 

21.3 

82.8 

44.6 

06.7 

69.1 

31.8 

95.0 

39 

40 

639.4 

700.2 

761.1 

822.4 

883.8 

945.6 

1007.  7 

1070. 1 

1132. 9 

1196. 0 

40 

41 

40.4 

01.2 

62.2 

23.4 

84.9 

46.7 

08.7 

71.2 

33.9 

97.1 

41 

42 

41.4 

02.2 

63.2 

24.4 

85.9 

47.7 

09.8 

72.2 

35.0 

98.1 

42 

43 

42.4 

03.2 

64.2 

25.4 

86.9 

48.7 

10.8 

73.2 

36.0 

99.2 

43 

44 

43.4 

04.2 

65.2 

26.5 

88.0 

49.7 

11.8 

74.3 

37.1 

1200.2 

44 

45 

644.5 

705.2 

766.2 

827.5 

889.0 

950.8 

1012. 9 

1075. 3 

1138. 1 

1201. 3 

45 

46 

45.5 

06.2 

67.3 

28.5 

90.0 

51.8 

13.9 

76.4 

39.2 

02.3 

46 

47 

46.5 

07.3 

68.3 

29.5 

91.0 

52.8 

15.0 

77.4 

40.2 

03.4 

47 

48 

47.5 

08.3 

69.3 

30.5 

92.1 

53.9 

16.0 

78.5 

41.3 

04.5 

48 

49 

48.5 

09.3 

70.3 

31.6 

93.1 

54.9 

17.0 

79.5 

42.3 

05.5 

49 

50 

649.5 

710.3 

771.3 

832.6 

894.1 

955.9 

1018. 1 

1080. 5 

1143. 4 

1206.6 

50 

51 

50.5 

11.3 

72.3 

33.6 

95.2 

57.0 

19.1 

81.6 

44.4 

07.6 

51 

52 

51.5 

12.3 

73.4 

34.6 

96.2 

58.0 

20.2 

82.6 

45.5 

08.7 

52 

53 

52.5 

13.4 

74.4 

35.7 

97.2 

59.0 

21.2 

83.7 

46.5 

09.7 

53 

54 

53.6 

14.4 

75.4 

36.7 

98.2 

60.1 

22.2 

84.7 

47.6 

10.8 

54 

55 

664.6 

715.4 

776.4 

837.7 

899.3 

961.1 

1023. 3 

1085. 8 

1148. 6 

1211. 8 

55 

56 

55.6 

16.4 

77.4 

38.7 

900.3 

62.1 

24.3 

86.8 

49.7 

12.9 

56 

57 

56.6 

17.4 

78.5 

39.8 

01.3 

63.2 

25.3 

87.9 

50.7 

14.0 

57 

58 

57.6 

18.4 

79.5 

40.8 

02.3 

64.2 

26.4 

88.9 

51.8 

15.0 

58 

59 

58.6 

19.4 

80.5 

41.8 

03.4 

65.2 

27.4 

89.9 

52.8 

16.1 

59 

M. 

100 

11° 

12° 

18° 

14° 

16° 

16° 

17° 

18° 

19° 

M. 

TABLE  3. 

[Page  623 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp 

1 

293.465 

M. 

20° 

210 

ago 

2»o 

24° 

25° 

26° 

27° 

28° 

29° 

M. 

0 

1217. 1 

1280.8 

1344.9 

1409.5 

1474. 5 

1540.1 

1606.2 

1672. 9 

1740.2 

1808.1 

0 

1 

18.2 

81.9 

46.0 

10.6 

75.6 

41.2 

07.3 

74.0 

41.3 

09.2 

1 

2 

19.3 

82.9 

47.1 

11.6 

76.7 

42.3 

08.4 

75.1 

42.4 

10.4 

2 

3 

20.3 

84.0 

48.1 

12.7 

77.8 

43.4 

09.5 

76.2 

43.6 

11.5 

3 

4 

21.4 

85.1 

49.2 

13.8 

78.9 

44.5 

10.6 

77.4 

44.7 

12.6 

4 

5 

1222. 4 

1286. 1 

1350.3 

1414. 9 

1480.0 

1545.  6 

1611. 7 

1678. 5 

1745.8 

1813. 8 

5 

6 

23.5 

87.2 

51.4 

16.0 

81.1 

46.7 

12.9 

79.6 

46.9 

14.9 

6 

7 

24.5 

88.3 

52.4 

17.1 

82.2 

47.8 

14.0 

80.7 

48,1 

16.1 

7 

8 

25.6 

89.3 

53.5 

18.1 

83.3 

48.9 

15.1 

81.8 

49.2 

17.2 

8 

9 

26.7 

90.4 

54.6 

19.2 

84.3 

50.0 

16.2 

82.9 

50.3 

18.3 

9 

10 

1227. 7 

1291.5 

1355.7 

1420.3 

1485.4 

1551. 1 

1617. 3 

1684.1 

1751.5 

1819. 5 

10 

11 

28.8 

92.5 

56.7 

21.4 

86.5 

52.2 

18.4 

85.2 

52.6 

20.6 

11 

12 

29.8 

93.6 

57.8 

22.5 

87.6 

53.3 

19.5 

86.3 

53.7 

21.8 

12 

13 

30.9 

94.7 

58.9 

23.5 

88.7 

54.4 

20.6 

87.4 

54.8 

22.9 

13 

14 

32.0 

95.7 

59.9 

24.6 

89.8 

55.5 

21.7 

88.5 

56.0 

24.0 

14 

15 

1233. 0 

1296.8 

1361.0 

1425.  7 

1490.9 

1556.6 

1622. 8 

1689.7 

1757. 1 

1825.2 

15 

16 

34.1 

97.9 

62.1 

26.8 

92.0 

57.7 

23.9 

90.8 

58.2 

26.3 

16 

17 

35.1 

98.9 

63.2 

27.9 

93.1 

58.8 

25.0 

91.9 

59.4 

27.5 

17 

18 

36.2 

1300.0 

64.2 

29.0 

94.2 

59.9 

26.2 

93.0 

60,5 

28.6 

18 

19 

37.3 

01.1 

65.3 

30.0 

95.2 

61.0 

27.3 
1628,  4 

94.1 

61.6 

29.7 

19 

20 

1238.  3 

1302.1 

1366.4 

1431. 1 

1496. 3 

1562.1 

1695. 3 

1762.  7 

1830.9 

20 

21 

39.4 

03.2 

67.5 

32.2 

97.4 

63.2 

29.5 

96.4 

63.9 

32.0 

21 

22 

40.4 

04.3 

68.5 

33.3 

98.5 

64.3 

30.6 

97.5 

65.0 

33.2 

22 

23 

41.5 

05.3 

69.6 

34.4 

99.6 

65.4 

31,7 

98.6 

66.1 

34.3 

23 

24 

42.6 

06.4 

70.7 

35.4 

1500.7 

66.5 

32.8 

99.7 

67.3 

35.4 

24 

25 

1243. 6 

1307. 5 

1371. 8 

1436.  5 

1501.8 

1567.6 

1633.9 

1700.9 

1768.4 

1836.6 

25 

26 

44.7 

08.5 

72.8 

37.6 

02.9 

68.7 

35.0 

02.0 

69.5 

37,7 

26 

27 

45.7 

09.6 

73.9 

38.7 

04.0 

69.8 

36.1 

03.1 

70.7 

38,9 

27 

28 

46.8 

10.7 

75.0 

39.8 

05.1 

70.9 

37.3 

04.2 

71.8 

40.0 

28 

29 

47.9 

11.7 

76.1 

40.9 

06.2 

72.0 

38.4 

05.3 

72.9 

41.2 

29 

30 

1248. 9 

1312. 8 

1377. 1 

1442.0 

1507. 3 

1573. 1 

1639,5 

1706.5 

1774, 1 

1842.3 

30 

81 

50.0 

13.9 

78.2 

43.0 

08.4 

74.2 

40,6 

07.6 

75,2 

43.4 

31 

32 

51.0 

14.9 

79.3 

44.1 

09.4 

75.3 

41.7 

08.7 

76.3 

44.6 

32 

33 

52.1 

16.0 

80.4 

45.2 

10.5 

76.4 

42.8 

09.8 

77.4 

45.7 

33 

34 

53.2 

17.1 

81.5 

46.3 

11.6 

77.5 

43.9 

10.9 

78.6 

46.9 

34 

35 

1254. 2 

1318. 2 

1382. 5 

1447.4 

1512.  7 

1578, 6 

1645.0 

1712. 1 

1779, 7 

1848. 0 

36 

36 

55.3 

19.2 

83.6 

48.5 

13.8 

79.7 

46.2 

1.3.2 

80.8 

49.2 

36 

37 

56.4 

20.3 

84.7 

49.5 

14,9 

80.8 

47.3 

14.3 

82,0 

'     50.3 

37 

38 

57.4 

21.4 

85.8 

50.6 

16.0 

81.9 

48,4 

15.4 

83,1 

51.4 

38 

39 

58.5 

22.4 

86.8 

51.7 

17.1 

83.0 

49.5 

16.6 

84.2 

52.6 

39 

40 

1259. 5 

1323. 5 

1387. 9 

1452.8 

1518. 2 

1584.1 

1650.6 

1717. 7 

1785.4 

1853.7 

40 

41 

60.6 

24.6 

89.0 

53.9 

19.3 

86.2 

51.7 

18,8 

86.5 

54.9 

41 

42 

61.7 

25.6 

90.1 

55.0 

20.4 

86.3 

52.8 

19.9 

87.6 

56.0 

42 

43 

62.7 

26.7 

91.1 

56.1 

21.5 

87.4 

53.9 

21.1 

88.8 

57.2 

43 

44 

63.8 

27.8 

92.2 

57.1 

22.6 

88.5 

55.1 

22.2 

89.9 

58.3 

44 

45 

1264.9 

1328. 9 

1393.  3 

1458.2 

1523. 7 

1589. 6 

1656.2 

1723. 3 

1791. 1 

1859.5 

45 

46 

65.9 

29.9 

94.4 

59.3 

24.8 

90.7 

57.3 

24.4 

92.2 

60.6 

46 

47 

67.0 

31.0 

95.5 

60.4 

25.9 

91.8 

58.4 

25.5 

93.3 

61.8 

47 

48 

68.0 

32.1 

96.5 

61.5 

27.0 

92.9 

59.5 

26.7 

94.5 

62.9 

48 

49 

69.1 

33.1 

97.6 

62.6 

28.0 

94.1 

60.6 

27.8 

95.6 

64.0 

49 

50 

1270. 2 

1334. 2 

1398. 7 

1463.7 

1529.1 

1595.  2 

1661.7 

1728. 9 

1796.  7 

1865.2 

50 

51 

71.2 

35.3 

99.8 

64.8 

30.2 

96.3 

62.9 

30.0 

97.9 

66.3 

51 

52 

72.3 

36.3 

1400.9 

65.8 

31.3 

97.4 

64.0 

31.2 

99.0 

67.5 

52 

53 

73.4 

37.4 

01.9 

66.9 

32.4 

98.5 

65.1 

32.3 

1800.1 

68.6 

53 

54 

74.4 

38.5 

03.0 

68.0 

33.5 

99.6 

66.2 

33.4 

01.3 

69.8 
1870. 9 

54 

55 

1275. 5 

1339.6 

1404.1 

1469. 1 

1534. 6 

1600.7 

1667. 3 

1734.5 

1802. 4 

55 

56 

76.6 

40.6 

05.2 

70.2 

35.7 

01.8 

68.4 

35.7 

03.5 

72.1 

56 

57 

77.6 

41.7 

06.2 

71.3 

36.8 

02.9 

69.5 

36.8 

04.7 

73.2 

57 

58 

78.7 

42.8 

07.3 

72.4 

37.9 

04.0 

70.7 

37.9 

05.8 

74.4 

58 

59 

79.7 

43.8 

08.4 

73.5 

39.0 

05.1 

71.8 

39.1 

07.0 

75,5 

59 

M. 

20° 

210 

220 

28° 

24° 

25° 

26° 

27° 

28° 

29° 

M. 

21594°— 14- 


-33 


Page  624] 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp. 

1 

293.465 

M. 

80° 

81° 

82° 

88° 

84° 

36° 

86° 

87° 

88° 

89° 

M. 

0 

1876.  7 

1946. 0 

2016. 0 

2086. 8 

2158. 4 

2230. 9 

2304.2 

2378. 5 

2453. 8 

2530. 2 

0 

1 

77.8 

47.1 

17.2 

88.0 

59.6 

32.1 

05.5 

79.8 

55.1 

31.5 

1 

2 

79.0 

48.3 

18.3 

89.2 

60.8 

33.3 

06.7 

81.0 

56.4 

32.8 

2 

3 

80.1 

49.4 

19.5 

90.3 

62.0 

34.5 

07.9 

82.3 

57.6 

34.0 

3 

4 

81.3 

50.6 

20.7 

91.5 

63.2 

35.7 

09.2 

83.5 

58.9 

35.3 

4 

5 

1882. 4 

1951.  8 

2021.  9 

2092.7 

2164.4 

2236. 9 

2310. 4 

2384.  8 

2460.  2 

2536. 6 

5 

6 

83.6 

52.9 

23.0 

93.9 

65.6 

38.2 

11.6 

86.0 

61.4 

37.9 

6 

7 

84.7 

54.1 

24.2 

95.1 

66.8 

39.4 

12.9 

87.3 

62.7 

39.2 

7 

8 

85.9 

55.3 

25.4 

96.3 

68.0 

40.6 

14.1 

88.5 

64.0 

40.5 

8 

9 

87.0 

56.4 

26.6 

97.5 

69.2 

41.8 

15.3 

89.8 

65.2 

41.7 

9 

10 

1888. 2 

1957. 6 

2027.  7 

2098.  7 

2170. 4 

2243. 0 

2316. 5 

2391. 0 

2466. 5 

2543. 0 

10 

11 

89.3 

58.7 

28.9 

99.8 

71.6 

44.2 

17.8 

92.3 

67.8 

44.3 

11 

12 

90.5 

59.9 

30.1 

2101. 0 

72.8 

45.5 

19.0 

93.5 

69.0 

45.6 

12 

13 

91.6 

61.1 

31.3 

02.2 

74.0 

46.7 

20.3 

94.8 

70.3 

46.9 

13 

14 

92.8 

62.2 

32.4 

03.4 

75.2 

47.9 

21.5 

96.0 

71.6 

48.2 

14 

15 

1893. 9 

1963. 4 

2033.  6 

2104. 6 

2176. 4 

2249. 1 

2322.  7 

2397.  3 

2472.  8 

2549. 5 

15 

16 

95.1 

64.6 

34.8 

05.8 

77.6 

50.3 

24.0 

98.5 

74.1 

50.7 

16 

17 

96.2 

65.7 

36.0 

07.0 

78.8 

51.6 

25.2 

99.8 

75.4 

52.0 

17 

18 

97.4 

66.9 

37.1 

08.2 

80.0 

52.8 

26.4 

2401. 0 

76.6 

53.3 

18 

19 

98.5 

68.1 

38.3 

09.4 

81.2 

54.0 

27.7 

02.3 

77.9 

54.6 

19 

20 

1899.  7 

1969. 2 

2039. 5 

2110. 6 

2182. 5 

2255. 2 

2328. 9 

2403. 5 

2479. 2 

2555. 9 

20 

21 

1900.8 

70.4 

40.7 

11.8 

83.7 

56.4 

30.1 

04.8 

80.4 

57.2 

21 

22 

02.0 

71.5 

41.8 

12.9 

84.9 

57.7 

31.4 

06.0 

81.7 

58.5 

22 

23 

03.1 

72.7 

43.0 

14.1 

86.1 

58.9 

32.6 

07.3 

83.0 

59.8 

23 

24 

04.3 

73.9 

44.2 

15.3 

87.3 

60.1 

33.8 

08.5 

84.3 

61.0 

24 

25 

1905.5 

1975. 0 

2045.  4 

2116. 5 

2188. 5 

2261.  3 

2335. 1 

2409. 8 

2485.  5 

2562.  3 

25 

26 

06.6 

76.2 

46.6 

17.7 

89.7 

62.5 

36.3 

11.1 

86.8 

63.6 

26 

27 

07.8 

77.4 

47.7 

18.9 

90.9 

63.8 

37.6 

12.3 

88.1 

64.9 

27 

28 

08.9 

78.5 

48.9 

20.1 

92.1 

65.0 

38.8 

13.6 

89.3 

66.2 

28 

29 

10.1 

79.7 

50.1 

21.3 

93.3 

66.2 

40.0 

14.8 

90.6 

67.5 

29 

30 

1911.2 

1980.  9 

2051. 3 

2122. 5 

2194. 5 

2267. 4 

2341. 3 

2416. 1 

2491. 9 

2568. 8 

30 

31 

12.4 

82.0 

52.5 

23.7 

95.7 

68.7 

42.5 

17.3 

93.2 

70.1 

31 

32 

13.5 

83.2 

53.6 

24.9 

96.9 

69.9 

43.7 

18.6 

94.4 

71.4 

32 

33 

14.7 

84.4 

54.8 

26.1 

98.1 

71.1 

45.0 

19.8 

95.7 

72.7 

33 

34 

15.8 

85.5 

56.0 

27.3 

99.4 

72.3 

46.2 

21.1 

97.0 

73.9 

34 

35 

1917. 0 

1986.  7 

2057.2 

2128. 5 

2200.6 

2273. 5 

2347.  5 

2422.  3 

2498. 3 

2575. 2 

35 

36 

18.2 

87.9 

58.4 

29.6 

01.8 

74.8 

48.7 

23.6 

99.5 

76.5 

36 

37 

19.3 

89.1 

59.5 

30.8 

03.0 

76.0 

49.9 

24.9 

2500.8 

77.8 

37 

38 

20.5 

90.2 

60.7 

32.0 

04.2 

77.2 

51.2 

26.1 

02.1 

79.1 

38 

39 

21.6 

91.4 

61.9 

33.2 

05.4 

78.4 

52.4 

27.4 

03.4 

80.4 

39 

40 

1922.  8 

1992.6 

2063. 1 

2134. 4 

2206. 6 

2279. 7 

2353.  7 

2428.  6 

2504.6 

2581.  7 

40 

41 

23.9 

93.7 

64.3 

35.6 

07.8 

80.9 

54.9 

29.9 

05.9 

83.0 

41 

42 

26.1 

94.9 

65.5 

36.8 

09.0 

82.1 

56.1 

31.2 

07.2 

84.3 

42 

43 

26.3 

96.1 

66.6 

38.0 

10.2 

83.3 

57.4 

32.4 

08.5 

85.6 

43 

44 

27.4 

97.2 

67.8 

39.2 

11.5 

84.6 

58.6 

33.7 

09.7 

86.9 

44 

45 

1928.  6 

1998. 4 

2069. 0 

2140. 4 

^2212.  7 

2285. 8 

2359.  9 

2434. 9 

2511. 0 

2588.  2 

45 

46 

29.7 

99.6 

70.2 

41.6 

13.9 

87.0 

61.1 

36.2 

12.3 

89.5 

46 

47 

30.9 

2000.  7 

71.4 

42.8 

15.1 

88.3 

62.4 

37.4 

13.6 

90.8 

47 

48 

32.0 

01.9 

72.6 

44.0 

16.3 

89.5 

63.6 

38.7 

14.8 

92.1 

48 

49 

33.2 

03.1 

73.7 

45.2 

17.5 

90.7 

64.8 

40.0 

16.1 

93.4 

49 

50 

1984. 4 

2004.3 

2074. 9 

2146. 4 

2218. 7 

2291. 9 

2366. 1 

2441.2 

2517. 4 

2594. 7 

50 

51 

35.5 

05.4 

76.1 

47.6 

19.9 

93.2 

67.3 

42.5 

18.7 

96.0 

51 

52 

36.7 

06.6 

77.3 

48.8 

21.1 

94.4 

68.6 

43.7 

20.0 

97.3 

52 

53 

37.8 

07.8 

78.5 

50.0 

22.4 

95.6 

69.8 

45.0 

21.2 

98.5 

53 

54 

39.0 

08.9 

79.7 

51.2 

23.6 

96.9 

71.1 

46.3 

22.5 

99.8 

54 

55 

1940. 2 

2010. 1 

2080.  8 

2152. 4 

2224.  8 

2298. 1 

2372.  3 

2447. 5 

2523.  8 

2601. 1 

55 

56 

41.3 

11.3 

82.0 

53.6 

26.0 

99.3 

73.6 

48.8 

25.1 

02.4 

56 

57 

42.5 

12.5 

83.2 

54.8 

27.2 

2300. 5 

74.8 

50.1 

26.4 

03.7 

57 

58 

43.6 

13.6 

84.4 

56.0 

28.4 

01.8 

76.1 

51.3 

27.6 

05.0 

58 

59 

44.8 

14.8 

85.6 

57.2 

29.6 

03.0 

77.3 

£2.3 

28.9 

06.3 

59 

M. 

80° 

81° 

82° 

88° 

84° 

86° 

86° 

87° 

88° 

89° 

M. 

' 

• 

TABLE  3. 

[Page  625    { 

Meridional  Parte,  or 

Increased  Latitades. 

Comp 

1 

293.465 

M. 

40° 

41° 

48° 

48° 

44° 

46° 

46° 

47° 

48° 

49° 

M. 

0 

2607. 6 

2686.2 

2766.0 

2847.1 

2929.5 

3013.4 

3098.7 

3185.6 

3274. 1 

3364.4 

0 

1 

08.9 

87.6 

67.4 

48.5 

30.9 

14.8 

3100.1 

87.1 

75.6 

65.9 

1 

2 

10.2 

88.9 

68.7 

49.9 

32.3 

16.2 

01.6 

88.5 

77.1 

67.4 

2 

3 

11.5 

90.2 

70.1 

51.2 

33.7 

17.6 

03.0 

90.0 

78.6 

69.0 

3 

4 

12.8 

91.5 

71.4 

52.6 

35.1 
2936.5 

19.0 

04.4 

91.4 
3192. 9 

80.1 
3281. 6 

70.5 
3372.0 

4 
5 

5 

2614. 1 

2692. 8 

2772. 8 

2853.9 

3020. 4 

3105. 9 

6 

15.4 

94.2 

74.1 

55.3 

37.9 

21.8 

07.3 

94.4 

83.1 

73.5 

6 

7 

16.8 

95.5 

75.4 

56.7 

39.3 

23.3 

08.8 

95.8 

84.6 

75.1 

7 

8 

18.1 

96.8 

76.8 

58.0 

40.6 

24.7 

10.2 

97.3 

86.1 

76.6 

8 

9 

19.4 

98.1 

78.1 

59.4 

42.0 

26.1 

11.6  1      98.8 

87.6 

78.1 

9 

10 

2620.  7 

2699. 6 

2779. 5 

2860.8 

2943.4 

3027. 5 

3113. 1 

3200.2 

3289. 0 

3379.6 

10 

11 

22.0 

2700.8 

80.8 

62.1 

44.8 

28.9 

14.5 

01.7 

90.5 

81.2 

11 

12 

23.3 

02.1 

82.2 

63.5 

46.2 

30.3 

16.0 

03.2 

92.0 

82.7 

12 

13 

24.6 

03.4 

83.5 

64.9 

47.6 

31.7 

17.4 

04.6 

93.5 

84.2 

13 

14 

25.9 

04.8 

84.8 

66.2 

49.0 

33.2 

18.8 

06.1 

95.0 

85.7 

14 

15 
16 

2627. 2 
28.5 

2706.1 
07.4 

2786.2 
87.5 

2867. 6 
69.0 

2950.4 
51.8 

3034.6 
36.0 

3120.3 
21.7 

3207.6 
09.0 

3296.5 
98.0 

3387. 3 
88.8 

15 
16 

17 

29.8 

08.7 

88.9 

70.3 

53.2 

37.4 

23.2 

10.5 

99.5 

90.3 

17 

18 

31.1 

10.1 

90.2 

71.7 

54.5 

38.8 

24.6 

12.0 

3301.0 

91.8 

18 

19 
■    20 

32.4 

11.4 

91.6 

73.1 

55.9 

40.2 

26.0 

13.4 

02.5 

93.4 

19 

2633. 7 

2712.  7 

2792.9 

2874. 4 

2967.3 

3041.7 

3127. 5 

3214. 9 

3304.0 

3394.9 

20 

21 

35.0 

14.0 

94.3 

75.8 

58.7 

43.1 

28.9 

16.4 

05.5 

96.4 

21 

22 

36.3 

15.4 

95.6 

77.2 

60.1 

44.5 

30.4 

17.9 

07.0 

98.0 

22 

23 

37.6 

16.7 

97.0 

78.6 

61.5 

45.9 

31.8 

19.3 

08.5 

99.5 

23 

24 

25 

38.9 

18.0 

98.3 

79.9 

62.9 

47.3 

33.3 

20.8 

10.0 

3401.0 

24 

2640.2 

2719. 3 

2799.7 

2881.3 

2964.3 

3048.7 

3134.  7 

3222. 3 

3311.5 

3402.6 

26 

26 

41.6 

20.7 

2801. 0 

82.7 

65.7 

50.2 

36.2 

23.7 

13.0 

04.1 

26 

27 

42.9 

22.0 

02.4 

84.0 

67.1 

51.6 

37.6 

25.2 

14.5 

06.6 

27 

28 

44.2 

23.3 

03.7 

85.4 

68.5 

53.0 

39.0 

26.7 

16.0 

07.2 

28 

29 

45.5 

24.7 

05.1 

86.8 

69.9 

54.4 

40.5 

28.2 

17.5 

08.7 

29 

30 

2646.8 

2726. 0 

2806.4 

2888.2 

2971.3 

3055.9 

3141. 9 

3229.6 

3319.0 

3410.2 

30 

31 

48.1 

27.3 

07.8 

89.5 

72.7 

57.3 

43.4 

31.1 

20.5 

11.8 

31 

32 

49.4 

28.6 

09.1 

90.9 

74.1 

58.7 

44.8 

32.6 

22.1 

13.3 

32 

33 

50.7 

30.0 

10.5 

92.3 

75.5 

60.1 

46.3 

34.1 

23.6 

14.8 

33 

34 
35 

52.0 
~2653.  3 

31.3 

11.8 

93.7 

76.9 

61.5 

47.7 

35.6 

25.1 

16.4 

34 

2732. 6 

2813.  2 

2895. 0 

2978.3 

3063.0 

3149. 2 

3237. 0 

3326. 6 

3417. 9 

35 

36 

54.7 

34.0 

14.5 

96.4 

79.7 

64.4 

50.6 

38.5 

28.1 

19.5 

36 

37 

56.0 

35.3 

15.9 

97.8 

81.1 

65.8 

52.1 

40.0 

29.6 

21.0 

37 

38 

57.3 

36.6 

17.2 

99.2 

82.5 

67.2 

53.5 

41.5 

31.1 

22.5 

38 

39 
40 

58.6 

38.0 

18.6 

2900.5 

83.9 

68.7 

55.0 

42.9 

32.6 

24.1 

39 

2659.9 

2739. 3 

2820.0 

2901.9 

2985.3 

3070. 1 

3156. 4 

3244.4 

3334.1 

3425.6 

40 

41 

61.2 

40.6 

21.3 

03.3 

86.7 

71.5 

57.9 

45.9 

35.6 

27.2 

41 

42 

62.5 

42.0 

22.7 

04.7 

88.1 

72.9 

59.4 

47.4 

37.1 

28.7 

42 

43 

63.9 

43.3 

24.0 

06.1 

89.5 

74.4 

60.8 

48.9 

38.6 

30.2 

43 

44 

65.2 

44.6 

25.4 

07.4 

90.9 

75.8 

62.3 

50.3 

40.2 

31.8 

44 

45 

2666. 5 

2746. 0 

2826.  7 

2908.8 

2992.3 

3077.  2 

3163.7 

3251.8 

3341. 7 

3433.3 

46 

46 

67.8 

47.3 

28.1 

10.2 

93.7 

78.7 

65.2 

53.3 

43.2 

34.9 

46 

47 

69.1 

48.6 

29.4 

11.6 

95.1 

80.1 

66.6 

54.8 

44.7 

36.4 

47 

48 

70.4 

50.0 

30.8 

13.0 

96.5 

81.5 

68.1 

56.3 

46.2 

38.0 

48 

49 

71.7 

51.3 

32.2 

14.3 

97.9 

82.9 

69.5 

57.8 

47.7 

39.5 

49 

50 

2673. 1 

2752. 7 

2833. 5 

2915. 7 

2999.  3 

3084. 4 

3171.0 

3259. 3 

3349. 2 

3441.0 

50 

51 

74.4 

54.0 

34.9 

17.1 

3000.7 

85.8 

72.5 

60.7 

50.8 

42.6 

51 

52 

75.7 

55.3 

36.2 

18.5 

02.1 

87.2 

73.9 

62.2 

52.3 

44.1 

52 

53 

77.0 

56.7 

37.6 

19.9 

03.5 

88.7 

75.4 

63.7 

53.8 

45.7 

53 

54 

78.3 

58.0 

39.0 

21.2 

04.9 

90.1 

76.8 

65.2 

55.3 

47.2 

64 

55 

2679.  6 

2759.  3 

2840.3 

2922. 6 

3006.3 

3091.5 

3178. 3 

3266.7 

3356. 8 

3448.  8 

55 

56 

81.0 

60.7 

41.7 

24.0 

07.7 

93.0 

79.7 

68.2 

58.3 

50.3 

56 

57 

82.3 

62.0 

43.0 

25.4 

09.2 

94.4 

81.2 

69.7 

59.9 

51.9 

57 

58 

83.6 

63.4 

44.4 

26.8 

10.6 

95.8 

82.7 

71.1 

61.4 

53.4 

58 

59 

84.9 

64.7 

45.8 

28.2 

12.0 

97.3 

84.1 

72.6 

62.9 

55.0 

59 

M. 

40° 

41° 

42° 

48° 

44° 

46° 

46° 

47° 

48° 

49° 

M. 

Page  626] 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp. 

1 

293.465 

M. 

50* 

51° 

62° 

68° 

54° 

55° 

58° 

67° 

68° 

69° 

H. 

0 

3456.  5 

3550.6 

3646.  7 

3745.1 

3845.7 

3948.  8 

4054. 5 

4163. 0 

4274.  4 

4389. 1 

0 

1 

58.1 

52.2 

48.4 

46.7 

47.4 

50.5 

56.3 

64.8 

76.3 

91.0 

1 

2 

59.6 

53.8 

50.0 

48.4 

49.1 

52.3 

58.1 

66.6  1      78.2 

92.9 

2 

3 

61.2 

55.4 

51.6 

50.0 

50.8 

54.0 

59.8 

68.5 

80.1 

94.9 

3 

4 

62.7 

56.9 

53.2 
3654.8 

51.7 

52.5 

55.7 

61.6 

70.3 

82.0 

96.8 

4 

5 

3464. 3 

3558. 5 

3753. 4 

3854. 2 

3957. 5 

4063. 4 

4172. 1 

4283. 9 

4398. 8 

5 

6 

65.9 

60.1 

56.5 

55.0 

55.9 

59.2 

65.2 

74.0 

85.7 

4400.7 

6 

7 

67.4 

61.7 

58.1 

56.7 

57.6 

61.0 

67.0 

75.8 

87.6 

02.6 

7 

8 

69.0 

63.3 

59.7 

58.3 

59.3 

62.7 

68.8 

77.7 

89.5 

04.6 

8 

9 

70.5 

64.9 

61.3 

60.0 

61.0 

64.5 

70.6 

79.5 

91.4 

06.5 

9 

10 

3472. 1 

3566.5 

3663.0 

3761.  7 

3862.  7 

3966.  2 

4072. 4 

4181. 3 

4293.3 

4408. 5 

10 

11 

73.6 

68.1 

64.6 

63.3 

64.4 

68.0 

74.2 

83.2 

95.2 

10.4 

11 

12 

75.2 

69.7 

66.2 

65.0 

66.1 

69.7 

76.0 

85.0 

97.1 

12.4 

12 

13 

76.7 

71.3 

67.9 

66.7 

67.8 

71.5 

77.7 

86.9 

99.0 

14.3 

13 

14 

78.3 

72.8 

69.5 

68.3 

69.5 

73.2 

79.5 

88.7 

4300.9 

16.3 

14 

15 

3479. 9 

3574. 4 

3671. 1 

3770. 0 

3871.  2 

3975. 0 

4081. 3 

4190.6 

4302.  8 

4418.2 

15 

16 

81.4 

76.0 

72.7 

71.7 

72.9 

76.7 

83.1 

92.4 

04.7 

20.2 

16 

17 

83.0 

77.6 

74.4 

73.8 

74.6 

78.5 

84.9 

94.2 

06.6 

22.1 

17 

18 

84.5 

79.2 

76.0 

75.0 

76.3 

80.2 

86.7 

96.1 

08.5 

24.1 

18 

19 

86.1 

80.8 

77.6 

76.7 

78.1 

82.0 

88.5 

97.9 

10.4 

26.1 

19 

20 

3487. 7 

3582. 4 

3679. 3 

3778. 3 

3879.  8 

3983.  7 

4090.  3 

4199. 8 

4312.  3 

4428. 0 

20 

21 

89.2 

84.0 

80.9 

80.0 

81.5 

85.5 

92.1 

4201. 6 

14.2 

30.0 

21 

22 

90.8 

85.6 

82.5 

81.7 

83.2 

87.2 

93.9 

03.5 

16.1 

31.9 

22 

23 

92.4 

87.2 

84.2 

83.3 

84.9 

89.0 

95.7 

05.3 

18.0 

33.9 

23 

24 

93.9 

88.8 

85.8 

85.0 

86.6 

90.7 

97.5 

07.2 

19.9 

35.8 

24 

25 

3495. 5 

3590.4 

3687.  4 

3786.  7 

3888. 3 

3992. 5 

4099.3 

4209. 0 

4321. 8 

4437. 8 

25 

26 

97.1 

92.0 

89.1 

88.4 

90.0 

94.3 

4101. 1 

10.9 

23.7 

39.8 

26 

27 

98.6 

93.6 

90.7 

90.0 

91.8 

96.0 

02.9 

12.8 

25.6 

41.7 

27 

28 

3500.  2 

95.2 

92.3 

91.7 

93.5 

97.8 

04.8 

14.6 

27.5 

43.7 

28 

29 

01.8 

96.8 

94.0 

93.4 

95.2 

99.5 

06.6 

16.5 

29.4 

45.7 

29 

30 

3503.  3 

3598. 4 

3695.6 

3795. 1 

3896. 9 

4001.3 

4108. 4 

4218. 3 

4331. 3 

4447.6 

30 

31 

04.9 

3600. 0 

97.3 

96.8 

98.6 

03.1 

10.2 

20.2 

33.2 

49.6 

31 

32 

06.5 

01.6 

98.9 

98.4 

3900.4 

04.8 

12.0 

22.0 

35.2 

51.6 

32 

33 

08.0 

03.2 

3700.5 

3800.1 

02.1 

06.6 

13.8 

23.9 

37.1 

53.5 

33 

34 

09.6 

04.8 

02.2 

01.8 

03.8 

08.3 

15.6 

25.8 

39.0 

55.5 

34 

35 

3511.  2 

3606.4 

3703. 8 

3803. 5 

3905.  5 

4010. 1 

4117. 4 

4227. 6 

4340. 9 

4457. 5 

35 

36 

12.7 

08.0 

05.5 

05.1 

07.2 

11.9 

19.2 

29.5 

42.8 

59.4 

36 

37 

14.3 

09.6 

07.1 

06.8 

09.0 

13.6 

21.0 

31.3 

44.7 

61.4 

37 

38 

15.9 

11.2 

08.7 

08.5 

10.7 

15.4 

22.9 

33.2 

46.6 

63.4 

38 

39 

17.5 

12.8 

10.4 

10.2 

12.4 

17.2 

24.7 

35.1 

48.6 

65.4 

39 

40 

3519. 0 

3614. 5 

3712. 0 

3811. 9 

3914. 1 

4018.9 

4126. 5 

4236. 9 

4350. 5 

4467. 3 

40 

41 

20.6 

16.1 

13.7 

13.6 

15.9 

20.7 

28.3 

38.8 

52.4 

69.3 

41 

42 

22.2 

17.7 

15.3 

15.2 

17.6 

22.5 

30.1 

40.7 

54.3 

71.3 

42 

43 

23.7 

19.3 

17.0 

17.0 

19.3 

24.3 

31.9 

42.5 

56.2 

73.3 

43 

44 

25.3 

20.9 

18.6 

18.6 

21.0 

26.0 

33.8 

44.4 

58.2 

75.3 

44 

45 

3526. 9 

3622. 5 

3720. 3 

3820.  3 

3922.  8 

4027. 8 

4135.6 

4246. 3 

4360. 1 

4477.2 

45 

46 

28.5 

24.1 

21.9 

22.0 

24.5 

29.6 

37.4 

48.1 

62.0 

79.2 

46 

47 

30.1 

25.7 

23.6 

23.7 

26.2 

31.4 

39.2 

50.0 

63.9 

81.2 

47 

48 

31.6 

27.3 

25.2 

25.4 

28.0 

33.1 

41.0 

51.9 

65.9 

83.2 

48 

49 

33.2 

29.0 

26.9 

27.1 

29.7 

34.9 

42.9 

53.8 

67.8 

85.2 

49 

50 

3534. 8 

3630. 6 

3728. 5 

3828. 7 

3931.  4 

4036.  7 

4144. 7 

4255. 6 

4369.  7 

4487.2 

50 

51 

36.4 

32.2 

30.2 

30.4 

33.2 

38.5 

46.5 

57.5 

71.7 

89.1 

51 

52 

37.9 

33.8 

31.8 

32.1 

34.9 

40.2 

48.3 

59.4 

73.6 

91.1 

52 

53 

39.5 

35.4 

33.5 

33.8 

36.6 

42.0 

50.2 

61.3 

75.5 

93.1 

53 

54 

41.1 

37.0 

35.1 

35.5 

38.4 

43.8 

52.0 

63.1 

77.4 

95.1 

54 

55 

3542.  7 

3638.  6 

3736.  8 

3837.  2 

3940. 1 

4045.6 

4153.  8 

4265.0 

4379. 4 

4497. 1 

55 

56 

44.3 

40.3 

38.4 

38.9 

41.8 

47.4 

55.7 

66.9 

81.3 

99.1 

56 

57 

45.9 

41.9 

40.1 

40.6 

43.6 

49.1 

57.5 

68.8 

83.2 

4501. 1 

57 

58 

47.4 

43.5 

41.7 

42.3 

45.3 

50.9 

59.3 

70.7 

85.2 

03.1 

58 

59 

49.0 

45.1 

43.4 

45.0 

47.0 

52.7 

61.1 

72.5 

87.1 

05.1 

59 

M. 

50° 

61° 

62° 

58° 

54° 

66° 

66° 

67° 

58° 

69° 

M. 

TABLE  3.                                           [Page 

627 

Meridional  Parte,  or 

Increased  Latitudes. 

Comp 

1 

■  293.466 

M. 

60° 

61° 

62° 

68° 

64° 

66° 

66° 

67° 

68° 

69° 

M. 

0 

4507.1 

4628.  7 

4754.3 

4884.1 

5018. 4 

5157. 6 

5302. 1 

5452. 4 

5609.1 

6772. 7 

0 

1 

09.1 

30.8 

56.4 

86.3 

20.6 

59.9 

04.6 

55.0 

11.8 

75.5 

1 

2 

11.1 

32.9 

58.6 

88.5 

22.9 

62.3 

07.0 

57.6 

14.4 

78.3 

2 

3 

13.1 

34.9 

60.7 

90.7 

25.2 

64.7 

09.5 

60.1 

17.1 

81.1 

3 

4 

15.1 

37.0 

62.8 

92.9 

27.5 

67.0. 

11.9 

62.7 

19.8 

83.8 

4 

6 

4517. 1 

4639.  0 

4764.9 

4895. 1 

5029.8 

5169. 4 

5314. 4 

5465.2 

5622. 4 

5786. 6 

5 

6 

19.1 

41.1 

67.1 

97.3 

32.1 

71.8 

16.9 

67.8 

25.1 

89.4 

6 

7 

21.1 

43.2 

69.2 

99.5 

34.3 

74.2 

19.3 

70.4 

27.8 

92.2 

7 

8 

23.1 

45.2 

71.3 

4901. 7 

36.6 

76.5 

21.8 

72.9 

30.5 

95.1 

8 

9 

25.1 

47.3 

73.5 

03.9 

38.9 

78.9 

24.3 

75.5 

33.2 

97.9 

9 

10 

4527. 1 

4649.4 

4775. 6 

4906.1 

5041.2 

5181.3 

5326.  7 

5477.1 

5636.9 

5800.7 

10 

11 

29.1 

51.5 

77.8 

08.3 

43.5 

83.7 

29.2 

80.7 

38.5 

03.5 

11 

12 

31.1 

53.5 

79.9 

10.5 

45.8 

86.0 

31.7 

83.2 

41.2 

06.3 

12 

13 

33.1 

55.6 

82.0 

12.8 

48.1 

88.4 

34.2 

85.8 

43.9 

09.1 

13 

14 

35.1 

57.7 

84.2 

15.0 

50.4 

90.8 

36.6 

88.4 

46.6 

11.9 

14 

15 

4537. 1 

4659.7 

4786.  3 

4917.  2 

5052.7 

5193. 2 

5339. 1 

5491.0 

5649.3 

5814.  7 

16 

16 

39.2 

61.8 

88.5 

19.4 

55.0 

95.6 

41.6 

93.6 

52.0 

17.6 

16 

17 

41.2 

63.9 

90.6 

21.6 

57.3 

98.0 

44.1 

96.2 

54.7 

20.4 

17 

18 

43.2 

66.0 

92.8 

23.9 

59.6 

5200.4 

46.6 

98.7 

57.4 

23.2 

18 

19 
20 

45.2 

68.1 

94.9 

26.1 

61.9 

02.7 

49.1 

5501.3 

60.1 

26.0 

19 
20 

4547.2 

4670. 1 

4797. 1 

4928. 3 

5064.2 

5205.1 

5351.5 

5503. 9 

5662. 8 

5828. 9 

21 

49.2 

72.2 

99.2 

30.5 

66.5 

07.5 

54.0 

06.5 

65.5 

31.7 

21 

22 

51.3 

74.3 

4801. 4 

32.8 

68.8 

09.9 

56.5 

09.1 

68.2 

34.5 

22 

23 

53.3 

76.4 

03.5 

35.0 

71.1 

12.3 

59.0 

11.7 

70.9 

37.4 

23 

24 

55.3 

78.5 

05.7 

37.2 

73.4 

14.7 

61.5 

14.3 

73.7 
5676. 4 

40.2 

24 

25 

4557.3 

4680. 6 

4807. 8 

4939. 4 

5075.7 

5217. 1 

5364.0 

5516.9 

5843. 0 

25 

26 

59.3 

82.6 

10.0 

41.7 

78.1 

19.5 

66.5 

19.5 

79.1 

46.9 

26 

27 

61.4 

84.7 

12.1 

43.9 

80.4 

21.9 

69.0 

22.1 

81.8 

48.7 

27 

28 

63.4 

86.8 

14.3 

46.1 

82.7 

24.3 

71.5 

24.7 

84.5 

51.6 

28 

29 

65.4 

88.9 

16.5 

48.4 

85.0 

26.7 

74.0 

27.3 

87.3 

54.4 

29 

30 

4567. 4 

4691. 0 

4818. 6 

4950.6 

5087. 3 

5229.1 

5376. 5 

5529. 9 

5690.0 

5857.3 

30 

31 

69.5 

93.1 

20.8 

52.9 

89.6 

-31.6 

79.0 

32.5 

92.7 

60.1 

31 

32 

71.5 

95.2 

23.0 

55.1 

92.0 

34.0 

81.5 

36.2 

95.4 

63.0 

32 

33 

73.5 

97.3 

25.1 

57.3 

94.3 

36.4 

84.0 

37.8 

98.2 

65.9 

33 

34 

75.6 

99.4 

27.3 

59.6 

96.6 

38.8 

86.5 

40.4 

5700.9 
5703. 6 

68.7 

34 

35 

4577.6 

4701. 5 

4829.5 

4961.8 

5098.9 

5241. 2 

5389. 1 

5543. 0 

6871. 6 

36 

36 

79.6 

03.6 

31.6 

64.1 

5101.3 

43.6 

91.6 

45.6 

06.4 

74.4 

36 

37 

81.7 

05.7 

33.8 

66.3 

03.6 

46.0 

94.1 

48.3 

09.1 

77.3 

37 

38 

83.7 

07.8 

36.0 

68.6 

05.9 

48.5 

96.6 

50.9 

11.9 

80.2 

38 

39 

85.7 

09.9 

38.1 

70.8 

08.3 

50.9 

99.1 

53.5 

14.6 

83.1 

39 

40 

4587. 8 

4712. 0 

4840.3 

4973. 1 

5110. 6 

5253. 3 

5401. 6 

5556.1 

5717. 3 

6885.9 

40 

41 

89.8 

14.1 

42.5 

75.3 

12.9 

55.7 

04.2 

58.8 

20.1 

88.8 

41 

42 

91.8 

16.2 

44.7 

77.6 

15.3 

58.2 

06.7 

61.4 

22.8 

91.7 

42 

43 

93.9 

18.3 

46.8 

79.8 

17.6 

60.6 

09.2 

64.0 

25.6 

94.6 

43 

44 

95.9 

20.4 

49.0 

82.1 

19.9 

63.0 

11.8 

66.7 

28.3 

97.4 

44 

45 

4598. 0 

4722. 5 

4851.2 

4984.3 

5122. 3 

5265.4 

5414.3 

5569. 3 

5731. 1 

5900.3 

45 

46 

4600.0 

24.6 

53.4 

86.6 

24.6 

67.9 

16.8 

71.9 

33.9 

03.2 

46 

47 

02.1 

26.7 

55.6 

88.9 

27.0 

70.3 

19.3 

74.6 

36.6 

06.1 

47 

48 

04.1 

28.9 

57.8 

91.1 

29.3 

72.8 

21.9 

77.2 

39.4 

09.0 

48 

49 

06.1 

31.0 

59.9 
4862. 1 

93.4 

31.7 

75.2 
5277. 6 

24.4 

79.9 

42.1 

11.9 

49 

50 

4608. 2 

4733. 1 

4995. 6 

5134. 0 

5427.0 

5582. 5 

5744.9 

5914. 8 

60 

51 

10.2 

35.2 

64.3 

97.9 

36.4 

80.1 

29.5 

85.2 

47.7 

17.7 

61 

52 

12.3 

37.3 

66.5 

5000.2 

38.7 

82.5 

32.0 

87.8 

50.4 

20.6 

62 

53 

14.3 

39.4 

68.7 

02.4 

41.1 

85.0 

34.6 

90.5 

53.2 

23.5 

63 

54 

16.4 

41.6 

70.9 

04.7 

43.4 

87.4 

37.1 

93.1 

56.0 

26.4 

54 

55 

4618.  5 

4743.  7 

4873. 1 

5007.0 

5145. 8 

5289. 8 

5439.  7 

5595. 8 

5758. 8 

5929. 3 

56 

56 

20.5 

45.8 

75.3 

09.3 

48.1 

92.3 

42.2 

98.4 

61.5 

32,2 

66 

57 

22.6 

47.9 

77.5 

11.5 

50.5 

94.7 

44.8 

5601. 1 

64.3 

36.1 

67 

58 

24.6 

50.0 

79.7 

13.8 

52.8 

97.2 

47.3 

03.8 

67.1 

38.1 

58 

59 

26.7 

52.2 

81.9 

16.1 

55.2 

99.7 

49.9 

06.4 

69.9 

41.0 

59 

M. 

60° 

61° 

62° 

68» 

64° 

65° 

66° 

67° 

68° 

69° 

M. 

Page  628] 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp. 

1 

293.465 

M. 

70° 

71" 

72° 

78° 

74° 

75° 

78° 

77° 

78° 

7»° 

M. 

0 

5943. 9 

6123. 5 

6312.5 

6512.0 

6723. 2 

6947.  7 

7187. 3 

7444.4 

7721. 6 

8022. 7 

0 

1 

46.8 

26.6 

15.8 

15.4 

26.8 

51.6 

91.5 

48.8 

26.4 

27.9 

1 

2 

49.7 

29.7 

19.0 

18.9 

30.5 

55.4 

95.6 

53.3 

31.3 

33.2 

2 

3 

52.7 

32.8 

22.3 

22.3 

34.1 

59.3 

99.7 

57.7 

36.1 

38.5 

3 

4 

55.6 

35.8 

25.5 

25.7 

37.7 

63.2 

7203. 9 

62.2 

40.9 

43.7 

4 

5 

5958. 5 

6138. 9 

6328. 8 

6529.1 

6741. 4 

6967. 1 

7208. 0 

7466.  7 

7745.8 

8049.0 

5 

6 

61.5 

42.0 

32.0 

32.6 

45.0 

70.9 

12.2 

71.1 

50.6 

54.3 

6 

7 

64.4 

45.1 

35.3 

36.0 

48.7 

74.8 

16.4 

75.6 

55.5 

59.6 

7 

8 

67.3 

48.2 

38.5 

39.5 

52.3 

78.7 

20.5 

80.1 

60.3 

64.9 

8 

9 

70.3 

51.3 

41.8 

42.9 

56.0 

82.6 

24.7 

84.6 

65.2 

70.2 

9 
10 

10 

5973. 2 

6154. 4 

6345.0 

6546.4 

6759.  7 

6986.5 

7228. 9 

7489. 1 

7770. 1 

8075. 5 

11 

76.2 

57.5 

48.3 

49.8 

63.3 

90.4 

33.1 

93.6 

74.9 

80.8 

11 

12 

79.1 

60.6 

51.6 

53.3 

67.0 

94.3 

37.3 

98.1 

79.8 

86.1 

12 

13 

82.1 

63.7 

54.8 

56.7 

70.7 

98.3 

41.5 

7502.6 

84.7 

91.5 

13 

14 

85.0 

66.8 

58.1 

60.2 

74.3 

7002.2 

45.7 

07.1 

89.6 

96.8 

14 

15 

5988. 0 

6169. 9 

6361. 4 

6563.7 

6778. 0 

7006. 1 

7249. 9 

7511. 7 

7794. 5 

8102. 2 

15 

16 

90.9 

73.0 

64.7 

67.1 

81.7 

10.0 

54.1 

16.2 

99.4 

07.5 

16 

17 

93.9 

76.1 

67.9 

70.6 

85.4 

14.0 

58.3 

20.7 

7804. 3 

12.9 

17 

18 

96.9 

79.2 

71.2 

74.1 

89.1 

17.9 

62.5 

25.3 

09.3 

18.3 

18 

19 

99.8 

82.3 

74.5 

77.6 

92.8 

21.8 

66.7 

29.8 

14.2 

23.7 

19 

20 

6002.8 

6185. 5 

6377.  8 

6581. 0 

6796. 5 

7025. 8 

7270. 9 

7534. 4 

7819. 1 

8129.1 

20 

21 

05.8 

88.6 

81.1 

84.5 

6800.2 

29.7 

75.2 

38.9 

24.1 

34.5 

21 

22 

08.7 

91.7 

84.4 

88.0 

03.9 

33.7 

79.4 

43.5 

29.0 

39.9 

22 

23 

11.7 

94.8 

87.7 

91.5 

07.6 

37.7 

83.7 

48.1 

34.0 

45.3 

23 

24 

14.7 

98.0 

91.0 

95.0 

11.3 

41.6 

87.9 

52.7 

39.0 

50.8 

24 

25 

6017.7 

6201.1 

6394. 3 

6598.5 

6815. 0 

7045.6 

7292.2 

7557. 3 

7844. 0 

8156. 2 

25 

26 

20.7 

04.2 

97.6 

6602. 0 

18.8 

49.6 

96.4 

61.8 

48.9 

61.6 

26 

27 

23.6 

07.4 

6400.9 

05.5 

22.5 

53.5 

7300.7 

66.4 

53.9 

67.1 

27 

28 

26.6 

10.5 

04.3 

09.0 

26.2 

57.5 

05.0 

71.0 

58.9 

72.6 

28 

29 

29.6 

13.7 

07.6 

12.5 

30.0 

61.5 

09.2 

75.7 

63.9 

78.0 

29 
30 

80 

6032.  6 

6216.  8 

6410.9 

6616.1 

6833.  7 

7065.5 

7313.  5 

7580.  3 

7868.  9 

8183. 5 

31 

35.6 

20.0 

14.2 

19.6 

37.4 

69.5 

17.8 

84.9 

74.0 

89.0 

31 

32 

38.6 

23.1 

17.6 

23.1 

41.2 

73.5 

22.1 

89.5 

79.0 

94.5 

32 

33 

41.6 

26.3 

20.9 

26.6 

44.9 

77.5 

26.4 

94.2 

84.0 

8200.0 

33 

34 
35 

44.6 

29.4 

24.2 

30.2 

48.7 

81.5 

30.7 

98.8 

89.1 

05.5 

34 

6047.6 

6232.  6 

6427.6 

6633.  7 

6852.4 

7085. 5 

7335.0 

7603. 4 

7894. 1 

8211. 1 

35 

36 

50.6 

35.8 

30.9 

37.2 

56.2 

89.5 

39.3 

08.1 

99.2 

16.6 

36 

37 

53.6 

38.9 

34.2 

40.8 

60.0 

93.5 

43.6 

12.8 

7904.2 

22.1 

37 

38 

56.6 

42.1 

37.6 

44.3 

63.7 

97.6 

47.9 

17.4 

09.3 

27.7 

38 

39 

59.7 

45.3 

40.9 

47.9 

67.5 

7101.6 

52.3 

22.1 

14.4 

33.3 

39 

40 

6062.7 

6248. 4 

6444.3 

6651.4 

6871. 3 

7105. 6 

7356. 6 

7626.  8 

7919. 4 

8238.  8 

40 

41 

65.7 

51.6 

47.6 

55.0 

75.1 

09.7 

60.9 

31.4 

24.5 

44.4 

41 

42 

68.7 

54.8 

51.0 

58.5 

78.9 

13.7 

65.3 

36.1 

29.6 

50.0 

42 

43 

71.7 

58.0 

54.4 

62.1 

82.6 

17.8 

69.6 

40.8 

34.7 

55.6 

43 

44 

74.8 

61.2 

57.7 

65.7 

86.4 

21.8 

74.0 

45.5 

39.9 

61.2 

44 

45 

6077.  8 

6264.  4 

6461.1 

6669.2 

6890. 2 

7125. 9 

7378. 3 

7650. 2 

7945. 0 

8266.  8 

45 

46 

80.8 

67.6 

64.5 

72.8 

94.0 

29.9 

82.7 

55.0 

50.1 

72.4 

46 

47 

83.9 

70.8 

67.8 

76.4 

97.8 

34.0 

87.1 

59.7 

55.2 

78.1 

47 

48 

86.9 

74.0 

71.2 

80.0 

6901.7 

38.1 

91.4 

64.4 

60.4 

83.7 

48 

49 

89.9 

77.2 

74.6 

83.5 

05.5 

42.2 

95.8 

69.1 

65.5 

89.3 

49 

50 

6093.0 

6280.4 

6478.0 

6687. 1 

6909.  3 

7146. 2 

7400.  2 

7673. 9 

7970.  7 

8295.0 

50 

51 

96.0 

83.6 

81.4 

90.7 

13.1 

50.3 

04.6 

78.6 

75.9 

8300.7 

51 

52 

99.1 

86.8 

84.8 

94.3 

16.9 

54.4 

09.0 

83.4 

81.0 

06.4 

52 

53 

6102. 1 

90.0 

88.2 

97.9 

20.8 

58.5 

13.4 

88.1 

86.2 

12.0 

53 

54 

05.2 

93.2 

91.6 

6701. 5 

24.6 

62.6 

17.8 

92.9 

91.4 

17.7 
8323.  4 

54 

55 

6108. 2 

6296. 4 

6495.0 

6705. 1 

6928. 4 

7166.  7 

7422. 2 

7697.  7 

7996. 6 

55 

56 

11.3 

99.6 

98.4 

08.7 

32.3 

70.8 

26.6 

7702. 5 

8001.  8 

29.2 

56 

57 

14.3 

6302. 9 

6501.8 

12.4 

36.1 

75.0 

31.1 

07.2 

07.0 

34.9 

57 

58 

17.4 

06.1 

05.2 

16.0 

40.0 

79.1 

35.5 

12.0 

12.2 

40.6 

58 

59 

20.5 

09.3 

08.6 

19.6 

43.8 

83.2 

39.9 

16.8 

17.5 

46.4 

59 

H. 

70° 

71° 

72° 

73° 

74° 

76° 

76° 

77° 

78° 

79° 

M. 

TABLE  4. 

[Page  629    | 

Lenji^h  of 

a  Degree  in  Latitude  and 

Longitude. 

Degree  of  Long. 

Degree  of  Lat. 

Lat 

Lat. 

Naut.  miles. 

statute  miles. 

Meters. 

Naut.  miles. 

statute  miles. 

Meters. 

O 

0 

60.068 

69. 172 

Ill  321 

59.661 

68.704 

110  567 

o 

0 

1 

0.059 

9.162 

1  304 

.661 

.704 

568 

1 

2 

0.031 

9.130 

1  253 

.662 

.705 

669 

2 

3 

59. 986 

9.078 

1  169 

.663 

.706 

670 

3 

4 

9.922 

9.005 

1  061 

.664 

.708 

573 

4 

5 

59.840 

68.911 

110  900 

59.666 

68.710 

110  576 

6 

6 

9.741 

8.795 

0  715 

.668 

.712 

580 

6 

7 

9.622 

8.660 

0  497 

.670 

.715 

584 

7 

8 

9.487 

8.504 

0  245 

.673 

.718 

589 

8 

9 

9.333 

8.326 

109  959 

.676 

.721 

596 

9 

10 

59. 161 

68.129 

109  641 

59.680 

68.726 

110  601 

10 

11 

8.971 

7.910 

9  289 

.684 

.730 

608 

11 

12 

8.764 

7.670 

8  904 

.687 

.734 

616 

12 

13 

8.538 

7.410 

8  486 

.692 

.739 

624 

13 

14 

8.295 

7.131 

8  036 

.697 

.744 

633 

14 

15 

58.034 

66.830 

107  563 

59. 702 

68.761 

110  643 

16 

16 

7.756 

6.510 

7  036 

.707 

.757 

663 

16 

17 

7.459 

6.169 

6  487 

.713 

.764 

663 

17 

18 

7.146 

5.808 

5  906 

.719 

.771 

675 

18 

19 

6.816 

5.427 

5  294 

.726 

.778 

686 

19 

20 

56.468 

65.026 

104  649 

59. 732 

68.786 

110  699 

20 

21 

6.102 

4.606 

3  972 

.739 

.794 

712 

21 

22 

5.720 

4.166 

3  264 

.746 

.802 

726 

22 

23 

5.321 

3.706 

2  624 

.754 

.811 

739 

23 

24 

4.905 

3.228 

1  754 

.761 

.820 
68.829 

763 

24 

25 

54.473 

62.729 

100  952 

59. 769 

110  768 

25 

26 

4.024 

2.  212 

0  119 

.777 

.839 

783 

26 

27 

3.558 

1.676 

99  257 

.786 

.848 

799 

27 

28 

3.076 

1.122 

8  364 

.795 

.858 

816 

28 

29 

2.578 

0.548 

7  441 

.804 

.869 

832 

29 

30 

52.064 

59. 956 

96  488 

59. 813 

68.879 

110  849 

30 

31 

1.534 

9.346 

5  506 

.822 

.890 

866 

31 

32 

0.989 

8.716 

4  495 

.831 

.901 

883 

32 

33 

0.428 

8.071 

3  455 

.841 

.912 

901 

33 

34 

49.851 

7.407 

2  387 

.851 

.923 

919 

34 

36 

49. 259 

56.725 

91  290 

59. 861 

68.936 

110  938 

35 

36 

8.653 

6.027 

0  166 

.871 

.946 

956 

36 

37 

8.031 

5.311 

89  014 

.881 

.958 

975 

37 

38 

7.395 

4.579 

7  835 

.891 

.969 

994 

38 

39 

6.744 

3.829 

6  629 

.902 

.981 

111  013 

39 

40 

46.079 

53. 063 

86  396 

59. 912 

68.993 

111  033 

40 

41 

5.399 

2.281 

4  137 

.923 

69.006 

052 

41 

42 

4.706 

1.483 

2  853 

.933 

.018 

072 

42 

43 

4.000 

0.669 

1  543 

.944 

.030 

091 

43 

44 

3.280 

49.840 

0  208 

.954 

.042 

111 

44 

^^^^ 

45 

2.546 

8.995 

78  849 

.965 

.054 

131 

46 

Page  630] 

TABLE  4. 

1 

Length  of 

a  Degree  in  Latitude  and  Longitude. 

Lat. 

Degree  of  Long. 

Degree  of  Lat. 

Lat. 

Naut.  miles. 

statute  miles. 

Meters. 

Naut.  miles. 

Statute  miles. 

Meters. 

o 
45 

42.546 

48. 995 

78  849 

59.965 

69. 054 

Ill  131 

o 

45 

46 

1.801 

8.136 

7  466 

.976 

.066 

151 

46 

47 

1.041 

7.261 

6  058 

.987 

.079 

170 

47 

48 

0.268 

6.372 

4  628 

.997 

.091 

190 

48 

49 

39.484 

5.469 

3  174 

60. 008 

.103 

210 

49 

50 

88.  688 

44. 552 

71  698 

60. 019 

69. 115 

111  229 

50 

51 

7.880 

3.621 

0  200 

.029 

.127 

249 

51 

52 

7.060 

2.676 

68  680 

.039 

.139 

268 

52 

53 

6.229 

1.719 

7  140 

.050 

.151 

287 

53 

54 

5.386 

0.749 

5  578 

.060 

.163 

306 

54 

55 

34. 532 

39.  766 

63  996 

60.  070 

69. 175 

111  325 

55 

56 

3.668 

8.771 

2  395 

.080 

.086 

343 

56 

57 

2.794 

7.764 

0  774 

.090 

.197 

362 

57 

58 

1.909 

6.745 

59  135 

.100 

.209 

380 

58 

59 

1.015 

5.716 

7  478 

.109 

.220 

397 

59 

60 

30. 110 

34.  674 

55  802 

60. 118 

69. 230 

111  415 

60 

61 

29. 197 

3.623 

4  110 

.128 

.241 

432 

61 

62 

8.275 

2.560 

2  400 

.137 

.251 

448 

62 

63 

7.344 

1.488 

0  675 

.145 

.261 

464 

63 

64 

6.404 

0.406 

48  934 

.154 

.271 

480 

64 

65 

25. 456 

29. 315 

47  177 

60.162 

69. 281 

111  496 

65 

66 

4.501 

8.215 

5  407 

.170 

.290 

511 

66 

67 

3.538 

7.106 

3  622 

.178 

.299 

525 

67 

68 

2.567 

5.988 

1  823 

.186 

.308 

539 

68 

69 

1.590 

4.862 

0  012 

.193 

.316 

553 

69 

70 

20.  606 

23. 729 

38  188 

60.200 

69.  324 

111  566 

70 

71 

19. 616 

2.589 

6  353 

.207 

.332 

578 

71 

72 

8.619 

1.441 

4  506 

.213 

.340 

590 

72 

73 

7.617 

0.287 

2  648 

.220 

.347 

602 

73 

74 

6.609 

19. 127 

0  781 

.225 

.354 

613 

74 

75 

15. 596 

17. 960 

28  903 

60. 231 

69. 360 

111  623 

75 

76 

4.578 

6.788 

7  017 

.236 

.366 

633 

76 

77 

3.556 

5.611 

5  123 

.241 

.372 

642 

77 

78 

2.529 

4.428 

3  220 

.246 

.377 

650 

78 

79 

1.499 

3.242 

1  311 

.250 

.382 

658 

79 

80 

10.465 

12. 051 

19  394 

60.  254 

69.  386 

111  665 

80 

81 

9.428 

10.857 

7  472 

.257 

.390 

671 

81 

82 

8.388 

9.659 

5  545 

.260 

.394 

677 

82 

83 

7.345 

8.458 

3  612 

.263 

.397 

682 

83 

84 

6.300 

7.255 

1  675 

.265 

.400 

687 

84 

85 

5.253 

6.049 

9  735 

60.268 

69. 402 

111  691 

85 

86 

4.205 

4.842 

7  792 

.269 

.404 

694 

86 

87 

3.154 

3.632 

5  846 

.270 

.405 

696 

87 

88 

2.103 

2.422 

3  898 

.271 

.407 

698 

88 

89 

1.052 

1.211 

1  949 

.272 

.407 

699 

89 

90 

0 

0 

0 

.272 

.407 

699 

90 

TABLE  6A. 

[Page  631    | 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 
the  course 

Difference  between  the  course  and  first  bearing,  in  pointa 

and  second 
bearing,  in 

points. 

2/ 

2li 

2M 

iy* 

I 

8« 

8H              1 

3 

1.96 

1.09 

3i 

1.57 

0.94 

2.19 

1.31 

3i 

1.32 

0.84 

1.76 

1.12 

2.42 

1.53 

3f 

1.14 

0.76 

1.47 

0.99 

1.94 

1.30 

2.64 

1.77 

4 

1.00< 

.0.  71. 

1.27 

0.90 

1.62 

1.15 

2.12 

1.50 

2.85 

2.01 

4i 

0.90 

0.66 

1.12 

0.83 

1.40 

1.04 

1.77 

1.31 

2.29 

1.69 

3.05 

2.26 

^ 

0.81 

0.63 

1.00 

0.77 

1.23 

0.95 

1.53 

1.18 

1.91 

1.48 

2.45 

1.90 

3.25 

2.51 

4f 

0.74 

0.60 

0.91 

0.73 

1.10 

0.89 

1.34 

1.08 

1.65 

1.32 

2.05 

1.65 

2.61 

2.10 

5 

0.69 

0.57 

0.83 

0.69 

1.00 

0.83 

1.20 

1.00 

1.45 

1.21 

1.77 

1.47 

2.19 

1.82 

5J 

0.64 

0.55 

0.77 

0.66 

0.92 

0.79 

1.09 

0.94 

1.30 

1.11 

1.56 

1.34 

1.88 

1.62 

5i 

0.60 

0.53 

0.72 

0.63 

0.85 

0.75 

1.00 

0.88 

1.18 

1.04 

1.39 

1.23 

1.66 

1.46 

5f 

0.57 

0.52 

0.68 

0.61 

0.79 

0.72 

0.93 

0.84 

1.08 

0.98 

1.26 

1.14 

1.48 

1.34 

6 

0.54 

0.50 

0.64 

0.59 

0.74 

0.69 

0.86 

0.80 

1.00 

0.92 

1.16 

1.07 

1.35 

1.24 

6i 

0.52 

0.49 

0.60 

0.57 

0,70 

0.66 

0.81 

0.76 

0.93 

0.88 

1.07 

1.01 

1.23 

1.16 

6J 

0.50 

0.47 

0.58 

0.55 

0.67 

0.64 

0.77 

0.73 

0.88 

0.84 

1.00 

0.96 

1.14 

1.09 

6| 

0.48 

0.46 

0.55 

0.54 

0.64 

0.62 

0.73 

0.71 

0.83 

0.80 

0.94 

0.91 

1.06 

1.03 

7 

0.46 

0.45 

0.53 

0.52 

0.61 

0.60 

0.69 

0.68 

0.79 

0.77 

0.89 

0.87 

1.00 

0.98 

7i 

0.45 

0.44 

0.51 

0.51 

0.59 

0.58 

0.67 

0.66 

0.75 

0.74 

0.84 

0.83 

0.94 

0.93 

7i 

0.43 

0.43 

0.50 

0.50 

0.57 

0.56 

0.64 

0.64 

0.72 

0.72 

0.80 

0.80 

0.90 

0.89 

7f 

0.42 

0.42 

0.48 

0.48 

0.55 

0.55 

0.62 

0.62 

0.69 

0.69 

0.77 

0.77 

0.86 

0.86 

8 

0.41 

0.41 

0.47 

0.47 

0.53 

0.53 

0.60 

0.60 

0.67 

0.67 

0.74 

0.74 

0.82 

0.82 

8i 

0.41 

0.41 

0.46 

0.46 

0.52 

0.52 

0.58 

0.58 

0.65 

0.65 

0.72 

0.72 

0.79 

0.79 

8J 

0.40 

0.40 

0.45 

0.45 

0.51 

0.51 

0.57 

0.57 

0.63 

0.63 

0.69 

0.69 

0.76 

0.76 

81 

0.39 

0.39 

0.45 

0.44 

0.50 

0.50 

0.56 

0.55 

0.61 

0.61 

0.68 

0.67 

0.74 

0.73 

9 

0.39 

0.38 

0.44 

0.43 

0.49 

0.48 

0.55 

0.54 

0.60 

0.59 

0.66 

0.65 

0.72 

0.71 

9i 

0.39 

0.38 

0.44 

0.42 

0.49 

0.47 

0.54 

0.52 

0.59 

0.57 

0.64 

0.63 

0.70 

0.68 

9i 

0.38 

0.37 

0.43 

0.41 

0.48 

0.46 

0.53 

0.51 

0.58 

0.56 

0.63 

0.61 

0.69 

0.66 

9i 

0.38 

0.36 

0.43 

0.40 

0.48 

0.45 

0.52 

0.49 

0.57 

0.54 

0.62 

0.59 

0.67 

0.63 

10 

0.38 

0.35 

0.43 

0.40 

0.47 

0.44 

0.52 

0.48 

0.57 

0.52 

0.61 

0.57 

0.66 

0.61 

lOi 

0.38 

0.35 

0.43 

0.39 

0.47 

0.43 

0.52 

0.47 

0.56 

0.51 

0.61 

0.55 

0.65 

0.59 

lOJ 

0.38 

0.34 

0.43 

0.38 

0.47 

0.42 

0.51 

0.45 

0.56 

0.49 

0.60 

0.53 

0.65 

0.57 

lOf 

0.39 

0.33 

0.43 

0.37 

0.47 

0.40 

0.51 

0.44 

0.56 

0.48 

0.60 

0.51 

0.64 

0.55 

11 

0.39 

0.32 

0.43 

0.36 

0.47 

0.39 

0.61 

0.43 

0.56 

0.46 

0-60 

0.50 

0.64 

0.53 

lU 

0.39 

0.31 

0.44 

0.35 

0.48 

0.38 

0.52 

0.41 

0.56 

0.45 

0.60 

0.48 

0.64 

0.51 

Hi 

0.40 

0.31 

0.44 

0.34 

0.48 

0.37 

0.52 

0.40 

0.56 

0.43 

0.60 

0.46 

0.63 

0.49 

111 

0.41 

0.30 

0.45 

0.33 

0.49 

0.36 

0.52 

0.39 

0.56 

0.42 

0.60 

0.44 

0.64 

0.47 

12 

0.41 

0.29 

0.45 

0.32 

0.49 

0.35 

0.53 

0.37 

0.57 

0.40 

0.60 

0.43 

0.64 

0.45 

m 

0.42 

0.28 

0.46 

0.31 

0.50 

0.34 

0.54 

0.36 

0.57 

0.38 

0.61 

0.41 

0.64 

0.42 

m 

0.43 

0.28 

0.47 

0.30 

0.51 

0.32 

0.55 

0.35 

0.58 

0.37 

0.61 

0.39 

0.65 

0.41 

12f 

0.45 

0.27 

0.48 

0.29 

0.52 

0.31 

0.56 

0.33 

0.59 

0.35 

0.62 

0.37 

0.65 

0.39 

13 

0.46 

0.26 

0.50 

0.28 

0.53 

0.30 

0.57 

0.32 

0.60 

0.33 

0.63 

0.35 

0.66 

0.37 

13i 

0.48 

0.24 

0.51 

0.26 

0.55 

0.28 

0.58 

0.30 

0.61 

0.32 

0.64 

0.33 

0.67 

0.35 

13J 

0.50 

0.23 

0.53 

0.25 

0.57 

0.27 

0.60 

0.28 

0.63 

0.30 

0.66 

0.31 

0.69 

0.32 

131 

0.52 

0.22 

0.55 

0.24 

0.59 

0.25 

0.62 

0.26 

0.65 

0.28 

0.68 

0.29 

0.70 

0.30 

14 

0.54 

0.21 

0.58 

0.22 

0.61 

0.23 

0.64 

0.24 

0.67 

0.26 

0.69 

0.27 

0.72 

0.28 

/  f 


4-^^ 


p^> 


L 


ii 


h 


,/.. 


Page  632]                                        TABLE  5A. 

Distance  of  an  Object  by  Two  Bearinga. 

Difference 

between 
the  course 

Difference  between  the  course  and  first  bearing,  in  points. 

and  second 
bearing,  in 

points. 

m 

4 

4K 

*H 

iK 

i 

^v.        1 

4| 

3.44 

2.76 

5 

2.76 

2.30 

3.62 

3.01 

H 

2.31 

1.98 

2.91 

2.50 

3.80 

3.26 

5i 

1.99 

1.76 

2.44 

2.15 

3.05 

2.69 

3.96 

3.49 

51 

1.75 

1.59 

2.10 

1.90 

2.55 

2.31 

3.18 

2.88 

4.12 

3.72 

6 

1.57 

1.45 

1.85 

1.71 

2.20 

2.03 

2.66 

2.46 

3.31 

3.05 

4.26 

3.94 

6i 

1.42 

1.34 

1.65 

1.56 

1.94 

1.82 

2.29 

2.16 

2.77 

2.61 

3.42 

3.22 

4.40 

4.14 

6i 

1.31 

1.25 

1.50 

1.44 

1.73 

1.66 

2.02 

1.93 

2.38 

2.28 

2.86 

2.74 

3.53 

3.38 

61 

1.21 

1.17 

1.38 

1.33 

1.57 

1.52 

1.81 

1.75 

2.10 

2.04 

2.47 

2.39 

2.95 

2.87 

7 

1.13 

1.11 

1.27 

1.25 

1.44 

1.41 

1.64 

1.61 

1.88 

1.84 

2.17 

2.13 

2.55 

2.50 

7i 

1.06 

1.05 

1.19 

1.17 

1.33 

1.32 

1.50 

1.49 

1.70 

1.69 

1.94 

1.92 

2.24 

2.22 

7i 

1.00 

1.00 

1.11 

1.11 

1.24 

1.24 

1.39 

1.38 

1.56 

1.55 

1.76 

1.76 

2.01 

2.00 

71 

0.95 

0.95 

1.05 

1.05 

1.17 

1.17 

1.30 

1.30 

1.45 

1.44 

1.62 

1.62 

1.82 

1.82 

8 

0.91 

0.91 

1.00 

1.00 

1.10 

1.10 

1.22 

1.22 

1.35 

1.35 

1.50 

1.50 

1.67 

1.67 

8J 

0.87 

0.87 

0.95 

0.95 

1.05 

1.05 

1.15 

1.15 

1.27 

1.26 

1.40 

1.39 

1.54 

1.54 

8^ 

0.84 

0.83 

0.91 

0.91 

1.00 

1.00 

1.09 

1.09 

1.20 

1.19 

1.31 

1.30 

1.44 

1.43 

81 

0.81 

0.80 

0.88 

0.87 

0.96 

0.95 

1.04 

1.03 

1.14 

1.12 

1.24 

1.22 

1.35 

1.34 

9 

0.78 

0.77 

0.85 

0.83 

0.92 

0.90 

1.00 

0.98 

1.08 

1.06 

1.18 

1.15 

1.28 

1.25 

9i 

0.76 

0.74 

0.82 

0.80 

0.89 

0.86 

0.96 

0.93 

1.04 

1.01 

1.12 

1.09 

1.21 

1.18 

9i 

0.74 

0.71 

0.80 

0.77 

0.86 

0.83 

0.93 

0.89 

1.00 

0.96 

1.08 

1.03 

1.16 

1.11 

91 

0.73 

0.68 

0.78 

0.74 

0.84 

0.79 

0.90 

0.85 

0.97 

0.91 

1.04 

0.97 

1.11 

1.04 

10 

0.71 

0.66 

0.77 

0.71 

0.82 

0.76 

0.88 

0.81 

0.94 

0.87 

1.00 

0.92 

1.07 

0.99 

lOi 

0.70 

0.63 

0.75 

0.68 

0.80 

0.72 

0.86 

0.77 

0.91 

0.82 

0.97 

0.88 

1.03 

0.93 

10} 

0.69 

0.61 

0.74 

0.65 

0.79 

0.69 

0.84 

0.74 

0.89 

0.78 

0.94 

0.83 

1.00 

0.88 

101 

0.68 

0.59 

0.73 

0.63 

0.77 

0.66 

0.82 

0.70 

0.87 

0.75 

0.92 

0.79 

0.97 

0.83 

11 

0.68 

0.56 

0.72 

0.60 

0.76 

0.64 

0.81 

0.67 

0.85 

0.71 

0.90 

0.75 

0.95 

0.79 

Hi 

0.67 

0.54 

0.71 

0.57 

0.76 

0.61 

0.80 

0.64 

0.84 

0.67 

0.88 

0.71 

0.93 

0.75 

Hi 

0.67 

0.52 

0.71 

0.55 

0.75 

0.58 

0.79 

0.61 

0.83 

0.64 

0.87 

0.67 

0.91 

0.70 

llf 

0.67 

0.50 

0.71 

0.52 

0.74 

0.55 

0.78 

0.58 

0.82 

0.61 

0.86 

0.64 

0.90 

0.66 

12 

0.67 

0.48 

0.71 

0.50 

0.74 

0.52 

0.78 

0.55 

0.81 

0.57 

0.85 

0.60 

0.88 

0.63 

12i 

0.67 

0.45 

0.71 

0.48 

0.74 

0.50 

0.77 

0.52 

0.81 

0.54 

0.84 

0.56 

0.87 

0.59 

12} 

0.68 

0.43 

0.71 

0.45 

0.74 

0.47 

0.77 

0.49 

0.80 

0.51 

0.84 

0.53 

0.87 

0.55 

12f 

0.68 

0.41 

0.71 

0.43 

0.74 

0.44 

0.77 

0.46 

0.80 

0.48 

0.83 

0.50 

0.86 

0.51 

13 

0.69 

0.38 

0.72 

0.40 

0.75 

0.42 

0.78 

0.43 

0.80 

0.45 

0.83 

0.46 

0.86 

0.48 

13i 

0.70 

0.36 

0.73 

0.37 

0.76 

0.39 

0.78 

0.40 

0.81 

0.41 

0.83 

0.43 

0.86 

0.44 

13} 

0.71 

0.34 

0.74 

0.35 

0.76 

0.36 

0.79 

0.37 

0.81 

0.38 

0.84 

0.39 

0.86 

0.41 

131 

0.73 

0.31 

0.75 

0.32 

0.77 

0.33 

0.80 

0.34 

0.82 

0.35 

0.84 

0.36 

0.86 

0.37 

14 

0.74 

0.28 

0.77 

0.29 

0.79 

0.30 

0.81 

0.31 

0.83 

0.32 

0.85 

0.32 

0.87 

0.33 

&y2 

6K 

6 

eK 

6J^ 

6% 

'       1 

6} 

4.52 

4.33 

6| 

3.63 

3.52 

4.63 

4.49 

7 

3.04 

2.98 

3.72 

3.65 

4.74 

4.64 

7i 

2.62 

2.59 

3.11 

3.08 

3.80 

3.76 

4.83 

4.77 

7} 

2.30 

2.29 

2.68 

2.67 

3.18 

3.17 

3.87 

3.86 

4.91 

4.88 

7f 

2.06 

2.06 

2.36 

2.36 

2.74 

2.74 

3.24 

3.24 

3.94 

3.93 

4.97 

4.97 

8 

1.87 

1.87 

2.11 

2.11 

2.41 

2.41 

2.79 

2.79 

3.30 

3.30 

3.99 

3.99 

5.03 

5.03 

8* 

1.72 

1.71 

1.92 

1.92 

2.16 

2.16 

2.46 

2.46 

2.84 

2.84 

3.34 

3.34 

4.04 

4.03 

8} 

1.59 

1.58 

1.76 

1.75 

1.96 

1.95 

2.20 

2.19 

2.50 

2.49 

2.88 

2.87 

3.38 

3.36 

81 

1.48 

1.46 

1.63 

1.61 

1.80 

1.78 

2.00 

1.98 

2.24 

2.21 

2.53 

2.51 

2.91 

2.88 

9 

1.39 

1.36 

1.52 

1.49 

1.66 

1.63 

1.83 

1.80 

2.03 

1.99 

2.27 

2.23 

2.56 

2.51 

9J 

1.31 

1.27 

1.42 

1.38 

1.55 

1.50 

1.69 

1.64 

1.86 

1.81 

2.06 

2.00 

2.29 

2.23 

9} 

1.25 

1.19 

1.35 

1.29 

1.46 

1.39 

1.58 

1.51 

1.72 

1.65 

1.89 

1.81 

2.08 

1.99 

91 

1.19 

1.12 

1.28 

1.20 

1.38 

1.30 

1.48 

1.40 

1.61 

1.51 

1.75 

1.64 

1.91 

1.80 

10 

1.14 

1.05 

1.22 

1.13 

1.31 

1.21 

1.40 

1.30 

1.51 

1.39 

1.62 

1.50 

1.77 

1.63 

lOi 

1.10 

0.99 

1.17 

1.06 

1.25 

1.13 

1.33 

1.20 

1.42 

1.29 

1.53 

1.38 

1.65 

1.49 

10} 

1.06 

0.94 

1.13 

0.99 

1.20 

1.05 

1.27 

1.12 

1.35 

1.19 

1.44 

1.27 

1.55 

1.36 

lOf 

1.03 

0.88 

1.09 

0.93 

1.15 

0.99 

1.22 

1.04 

1.29 

1.11 

1.37 

1.18 

1.46 

1.25 

11 

1.00 

0.83 

1.05 

0.88 

1.11 

0.92 

1.17 

0.97 

1.24 

1.03 

1.31 

1.09 

1.39 

1.15 

lU 

0.98 

0.78 

1.03 

0.82 

1.08 

0.87 

1.13 

0.91 

1.19 

0.96 

1.25 

1.01 

1.32 

1.06 

11} 

0.95 

0.73 

1.00 

0.77 

1.05 

0.81 

1.10 

0.85 

1.15 

0.89 

1.21 

0.93 

1.27 

0.98 

111 

0.94 

0.69 

0.98 

0.72 

1.02 

0.76 

1.07 

0.79 

1.12 

0.83 

1.17 

0.86 

1.22 

0.90 

12 

0.92 

0.65 

0.96 

0.68 

1.00 

0.71 

1.04 

0.73 

1.09 

0.77 

1.13 

0.80 

1.18 

0.83 

12i 

0.91 

0.61 

0.94 

0.63 

0.98 

0.66 

1.02 

0.68 

1.06 

0.71 

1.10 

0.74 

1.14 

0.77 

12} 

0.90 

0.57 

0.93 

0.59 

0.97 

0.61 

1.00 

0.63 

1.04 

0.66 

1.07 

0.68 

1.11 

0.71 

12| 

0.89 

0.53 

0.92 

0.55 

0.95 

0.57 

0.98 

0.59 

1.02 

0.61 

1.05 

0.63 

1.08 

0.65 

13 

0.89 

0.49 

0.91 

0.51 

0.94 

0.52 

0.97 

0.54 

1.00 

0.56 

1.03 

0.57 

1.06 

0.59 

13J 

0.88 

0.45 

0.91 

0.47 

0.93 

0.48 

0.96 

0.49 

0.99 

0.51 

1.01 

0.52 

1.04 

0.54 

13} 

0.88 

0.42 

0.91 

0.43 

0.93 

0.44 

0.95 

0.45 

0.98 

0.46 

1.00 

0.47 

1.02 

0.48 

13i 

0.88 

0.38 

0.90 

0.39 

0.92 

0.40 

0.95 

0.41 

0.97 

0.41 

0.99 

0.42 

1.01 

0.43 

14 

0.89 

0.34 

0.91 

0.35 

0.92 

0.35 

0.94 

0.36 

0.90 

0.37 

0.98 

0.38 

1.00 

0.38 

TABLE  5A.                                         [Page  633 

Distance  of  an  Object  by  Tyro  Bearings. 

Difference 
between 

Difference  between  the  course  and  first  bearing,  in  points. 

the  course 

and second 

bearing,  in 
points. 

75i 

7H 

m 

8 

8K 

8J4 

8K 

9 

Si 

5.07 

5.06 

H 

4.07 

4.05 

5.10 

5.08 

8| 

3.41 

3.37 

4.10 

4.06 

5.12 

5.06 

9 

2.94 

2.88 

3.43 

3.36 

4.11 

4.03 

5.13 

5.03 

9k 

2.58 

2.51 

2.95 

2.87 

3.44 

3.34 

4.12 

3.39 

5.12 

4.97 

9J 

2.31 

2.21 

2.60 

2.49 

2.96 

2.84 

3.44 

3.30 

4.11 

3.93 

5.10 

4.88 

9J 

2.10 

1.98 

2.33 

2.19 

2.61 

2.46 

2.97 

2.79 

3.44 

3.24 

4.10 

3.86 

5.07 

4.77 

10 

1.92 

1.78 

2.11 

1.95 

2.34 

2.16 

2.61 

2.41 

2.96 

2.74 

3.43 

3.17 

4.07 

3.76 

5.03 

4.64 

lOJ 

1.78 

1.61 

1.93 

1.75 

2.12 

1.92 

2.34 

2.11 

2.61 

2.36 

2.95 

2.67 

3.41 

3.08 

4.04 

3.65 

lOJ 

1.66 

1.46 

1.79 

1.58 

1,94 

1.71 

2.12 

1.87 

2.34 

2.06 

2.60 

2.29 

2.94 

2.59 

3.38 

2.98 

lOJ 

1.56 

1.34 

1.67 

1.43 

1.80 

1.54 

1.95 

1.67 

2.12 

1.82 

2.33 

2.00 

2.58 

2.22 

2.91 

2.50 

11 

1.47 

1.22 

1.57 

1.30 

1.68 

1.39 

1.80 

1.50 

1.94 

1.62 

2.11 

1.76 

2.31 

1.92 

2.56 

2.13 

lli 

1.40 

1.12 

1.48 

1.19 

1.57 

1.26 

1.68 

1.35 

1.80 

1.44 

1.93 

1.55 

2.10 

1.69 

2.29 

1.84 

Hi 

1.34 

1.03 

1.41 

1.09 

1.49 

1.15 

1.58 

1.22 

1.68 

1.30 

1.79 

1.38 

1.92 

1.49 

2.08 

1.61 

iif 

1.28 

0.95 

1.34 

1.00 

1.41 

1.05 

1.49 

1.10 

1.57 

1.17 

1.67 

1.24 

1.78 

1.32 

1.91 

1.41 

12 

1.23 

0.87 

1.29 

0.91 

1.35 

0.95 

1.41 

1.00 

1.49 

1.05 

1.57 

1.11 

1.66 

1.17 

1.77 

1.25 

12i 

1.19 

0.80 

1.24 

0.83 

1.29 

0.87 

1.35 

0.91 

1.41 

0.95 

1.48 

1.00 

1.56 

1.05 

1.65 

1.11 

12} 

1.15 

0.73 

1.20 

0.76 

1.24 

0.79 

1.29 

0.82 

1.35 

0.86 

1.41 

0.89 

1.47 

0.93 

1.55 

0.98 

12f 

1.12 

0.67 

1.16 

0.69 

1.20 

0.72 

1.25 

0.74 

1.29 

0.77 

1.34 

0.80 

1.40 

0.83 

1.46 

0.87 

13 

1.09 

0.61 

1.13 

0.63 

1.16 

0.65 

1.20 

0.67 

1.24 

0.69 

1.29 

0.72 

1.34 

0.74 

1.39 

0.77 

13i 

1.07 

0.55 

1.10 

0.57 

1.13 

0.58 

1.17 

0.60 

1.20 

0.62 

1.24 

0.64 

1.28 

0.66 

1.32 

0.68 

13i 

1.05 

0.50 

1.08 

0.51 

1.10 

0.52 

1.13 

0.53 

1.16 

0.55 

1.20 

0.56 

1.23 

0.58 

1.27 

0.60 

13i 

1.03 

0.44 

1.06 

0.45 

1.08 

0.46 

1.11 

0.47 

1.13 

0.48 

1.16 

0.50 

1.19 

0.51 

1.22 

0.52 

14 

1.02 

0.39 

1.04 

0.40 

1.06 

0.41 

1.08 

0.41 

1.10 

0.42 

1.13 

0.43 

1.15 

0.44 

1.18 

0.45 

9y* 

»J^ 

»K 

10 

105i 

lOM 

lOK 

"     1 

10} 

4.97 

4.50 

lOi 

3.99 

3.52 

4.91 

4.33 

lOJ 

3.34 

2.87 

3.94 

3.38 

4.83 

4.14 

11 

2.88 

2.39 

3.30 

2.74 

3.87 

3.22 

4.74 

3.94 

lU 

2.53 

2.04 

2.84 

2.28 

3.24 

2.61 

3.80 

3.05 

4.63 

3.72 

in 

2.27 

1.75 

2.50 

1.93 

2.79 

2.16 

3.18 

2.46 

3.72 

2.88 

4.52 

3.49 

111 

2.06 

1.52 

2.24 

1.66 

2.46 

1.82 

2.74 

2.03 

3.11 

2.31 

3.63 

2.69 

4.40 

3.20 

12 

1.89 

1.33 

2.03 

1.44 

2.20 

1.56 

2.41 

1.71 

2.68 

1.90 

3.04 

2.15 

3.53 

2.50 

4.26 

3.01 

m 

1.75 

1.18 

1.86 

1.25 

2.00 

1.34 

2.16 

1.45 

2.36 

1.59 

2.62 

1.76 

2.95 

1.98 

3.42 

2.30 

12i 

1.62 

1.03 

1.72 

1.09 

1.83 

1.16 

1.96 

1.24 

2.11 

1.34 

2.30 

1.46 

2.55 

1.62 

2.86 

1.82 

12f 

1.53 

0.91 

1.61 

0.96 

1.69 

1.01 

1.80 

1.07 

1.92 

1.14 

2.06 

1.23 

2.24 

1.34 

2.47 

1.47 

13 

1.44 

0.80 

1.51 

0.84 

1.58 

0.88 

1.66 

0.92 

1.76 

0.98 

1.87 

1.04 

2.01 

1.11 

2.17 

1.21 

13} 

1.37 

0.71 

1.42 

0.73 

1.48 

0.76 

1.55 

0.80 

1.63 

0.84 

1.72 

0.88 

1.82 

0.94 

1.94 

1.00 

13J 

1.31 

0.62 

1.35 

0.64 

1.40 

0.66 

1.46 

0.69 

1.52 

0.72 

1.59 

0.75 

1.67 

0.79 

1.76 

0.83 

131 

1.25 

0.54 

1.29 

0.55 

1.33 

0.57 

1.38 

0.59 

1.42 

0.61 

1.48 

0.63 

1.54 

0.66 

1.62 

0.69 

14 

1.21 

0.46 

1.24 

0.47 

1.27 

0.49 

1.31 

0.50 

1.35 

0.52 

1.39 

0.53 

1.44 

0.55 

1.50 

0.57 

llJi 

n^A 

nK      1 

"    1 

125<         1 

12J^         1 

12)i        1 

n       1 

12} 

4.12 

2.77 

12i 

3.31 

2.10 

3.96 

2.51 

12| 

2.77 

1.65 

3.18 

1.90 

3.80 

2.26 

13 

2.38 

1.32 

2.66 

1.48 

3.05 

1.69 

3.62 

2.01 

13} 

2.10 

1.08 

2.29 

1.18 

2.55 

1.31 

2.91 

1.50 

3.44 

1.77 

13J 

1.88 

0.89 

2.02 

0.95    2.20 

1.04 

2.44 

1.15 

2.76 

1.30 

3.25 

1.53 

13| 

1.70 

0.73 

1.81 

0.77    1.94 

0.83 

2.10 

0.90 

2.31 

0.99 

2.61 

1.12 

3.05 

1.31 

14 

1.56 

0.60 

1.64 

0.63    1.73 

0.66 

1.85 

0.71    1.99 

0.76 

2.19 

0.84 

2.45 

0.94 

2.85 

1.09 

Page  634] 

TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

the  course 

and  second 

bearing. 

Difierence  between  the  course  and  first  bearing. 

20° 

22° 

24° 

26° 

28° 

30° 

82°            1 

30° 

1.97 

0.98 

32 

1.64 

0.87 

2.16 

1.14 

34 

1.41 

0.79 

1.80 

1.01 

2.34 

1.31 

36 

1.24 

0.73 

1.55 

0.91 

1.96 

1.15 

2.52 

1.48 

38 

1.11 

0.68 

1.36 

0.84 

1.68 

1.04 

2.11 

1.30 

2.70 

1.66 

40 

1.00 

0.64 

1.21 

0.78 

1.48 

0.95 

1.81 

1.16 

2.26 

1.45 

2.88 

1.85 

42 

0.91 

0.61 

1.10 

0.73 

1.32 

0.88 

1.59 

1.06 

1.94 

1.30 

2.40 

1.61 

3.05 

2.04 

44 

0.84 

0.58 

1.00 

0.69 

1.19 

0.83 

1.42 

0.98 

1.70 

1.18 

2.07 

1.44 

2.55 

1.77 

46 

0.78 

0.56 

0.92 

0.66 

1.09 

0.78 

1.28 

0.92 

1.52 

1.09 

1.81 

1.30 

2.19 

1.58 

48 

0.73 

0.54 

0.85 

0.64 

1.00 

0.74 

1.17 

0.87 

1.37 

1.02 

1.62 

1.20 

1.92 

1.43 

50 

0.68 

0.52 

0.80 

0.61 

0.93 

0.71 

1.08 

0.83 

1.25 

0.96 

1.46 

1.12 

1.71 

1.31 

52 

0.65 

0.51 

0.75 

0.59 

0.87 

0.68 

1.00 

0.79 

1.15 

0.91 

1.33 

1.05 

1.55 

1.22 

54 

0.61 

0.49 

0.71 

0.57 

0.81 

0.66 

0.93 

0.76 

1.07 

0.87 

1.23 

0.99 

1.41 

1.14 

56 

0.58 

0.48 

0.67 

0.56 

0.77 

0.64 

0.88 

0.73 

1.00 

0.83 

1.14 

0.95 

1.30 

1.08 

58 

0.56 

0.47 

0.64 

0.54 

0.73 

0.62 

0.83 

0.70 

0.94 

0.80 

1.07 

0.90 

1.21 

1.03 

60 

0.53 

0.46 

0.61 

0.53 

0.69 

0.60 

0.78 

0.68 

0.89 

0.77 

1.00 

0.87 

1.13 

0.98 

62 

0.51 

0.45 

0.58 

0.51 

0.66 

0.58 

0.75 

0.66 

0.84 

0.74 

0.94 

0.83 

1.06 

0.94 

64 

0.49 

0.44 

0.56 

0.50 

0.63 

C.57 

0.71 

0.64 

0.80 

0.72 

0.89 

0.80 

1.00 

0.90 

66 

0.48 

0.43 

0.54 

0.49 

0.61 

0.56 

0.68 

0.62 

0.76 

0.70 

0.85 

0.78 

0.95 

0.87 

68 

0.46 

0.43 

0.52 

0.48 

0.59 

0.54 

0.66 

0.61 

0.73 

0.68 

0.81 

0.75 

0.90 

0.84 

70 

0.45 

0.42 

0.50 

0.47 

0.57 

0.53 

0.63 

0.59 

0.70 

0.66 

0.78 

0.73 

0.86 

0.81 

72 

0.43 

0.41 

0.49 

0.47 

0.55 

0.52 

0.61 

0.58 

0.68 

0.64 

0.75 

0.71 

0.82 

0.78 

.    74 

0.42 

0.41 

0.48 

0.46 

0.53 

0.51 

0.59 

0.57 

0.65 

0.63 

0.72 

0.69 

0.79 

0.76 

76 

0.41    0.40 

0.46 

0.45 

0.52 

0.50 

0.57 

0.56 

0.63 

0.61 

0.70 

0.67 

0.76 

0.74 

78 

0.40 

0.39 

0.45 

0.44 

0.50 

0.49 

0.56 

0.54 

0.61 

0.00 

0.67 

0.66 

0.74 

0,72 

80 

0.39 

0.39 

0.44 

0.44 

0.49 

0.48 

0.54 

0.53 

0.60 

0.59 

0.65 

0.64 

0.71 

0.70 

82 

0.39 

0.38 

0.43 

0.43 

0.48 

0.47 

0.53 

0.52 

0.58 

0.57 

0.63 

0.63 

0.69 

0.69 

84 

0.38 

0.38 

0.42 

0.42 

0.47 

0.47 

0.52 

0.51 

0.57 

0.56 

0.62 

0.61 

0.67 

0.67 

86 

0.37 

0.37 

0.42 

0.42 

0.46 

0.46 

0.51 

0.51 

0.55 

0.55 

0.60 

0.60 

0.66 

0.65 

88 

0.37 

0.37 

0.41 

0.41 

0.45 

0.45 

0.50 

0.50 

0.54 

0.54 

0.59 

0.59 

0.64 

0.64 

90 

0.36 

0.36 

0.40 

0.40 

0.45 

0.45 

0.49 

0.49 

0.53 

0.53 

0.58 

0.58 

0.62 

0.62 

92 

0.36 

0.36 

0.40 

0.40 

0.44 

0.44 

0.48 

0.48 

0.52 

0.52 

0.57 

0.57 

0.61 

0.61 

94 

0.36 

0.35 

0.39 

0.39 

0.43 

0.43 

0.47 

0.47 

0.51 

0.51 

0.56 

0.55 

0.60 

0.60 

96 

0.35 

0.35 

0.39 

0.39 

0.43 

0.43 

0.47 

0.46 

0.51 

0.50 

0.55 

0.54 

0.59 

0.59 

98 

0.35 

0.35 

0.39 

0.38 

0.42 

0.42 

0.46 

0.46 

0.50 

0.50 

0.54 

0.53 

0.58 

0.57 

100 

0.35 

0.34 

0.38 

0.38 

0.42 

0.41 

0.46 

0.45 

0.49 

0.49 

0.53 

0.52 

0.57 

0.56 

102 

0.35 

0.34 

0.38 

0.37 

0.42 

0.41 

0.45 

0.44 

0.49 

0.48 

0.53 

0.51 

0.56 

0.55 

104 

0.34 

0.33 

0.38 

0.37 

0.41 

0.40 

0.45 

0.43 

0.48 

0.47 

0.52 

0.50 

0.56 

0.54 

106 

0.34 

0.33 

0.38 

0.36 

0.41 

0.39 

0.45 

0.43 

0.48 

0.46 

0.52 

0.50 

0.55 

0.53 

108 

0.34 

0.32 

0.38 

0.36 

0.41 

0.39 

0.44 

0.42 

0.48 

0.45 

0.51 

0.49 

0.55 

0.52 

110 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0.47 

0.44 

0.51 

0.48 

0.54 

0.51 

112 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0.47 

0.44 

0.50 

0.47 

0.54 

0.50 

114 

0.34 

0.31 

0.37 

0.34 

0.41 

0.37 

0.44 

0.40 

0.47 

0.43 

0.50 

0.46 

0.54 

0.49 

116 

0.34 

0.31 

0.38 

0.34 

0.41 

0.37 

0.44 

0.39 

0.47 

0.42 

0.50 

0.45 

0.53 

0.48 

118 

0.35 

0.31 

0.38 

0.33 

0.41 

0.36 

0.44 

0.39 

0.47 

0.41 

0.50 

0.44 

0.53 

0.47 

120 

0.35 

0.30 

0.38 

0.33 

0.41 

0.36 

0.44 

0.38 

0.47 

0.41 

0.50 

0.43 

0.53 

0,46 

122 

0.35 

0.30 

0.38 

0.32 

0.41 

0.35 

0.44 

0.37 

0.47 

0.40 

0.50 

0.42 

0.53 

0.45 

124 

0.35 

0.29 

0.38 

0.32 

0.41 

0.34 

0.44 

0.37 

0.47 

0.39 

0.50 

0.42 

0.53 

0.44 

126 

0.36 

0.29 

0.39 

0.31 

0.42 

0.34 

0.45 

0.36 

0.47 

0.38 

0.50 

0.41 

0.53 

0.43 

128 

0.36 

0.28 

0.39 

0.31 

0.42 

0.33 

0.45 

0.35 

0.48 

0.38 

0.50 

0.40 

0.53 

0.42 

130 

0.36 

0.28 

0.39 

0.30 

0.42 

0.32 

0.45 

0.35 

0.48 

0.37 

0.51 

0.39 

0.54 

0.41 

132 

0.37 

0.27 

0.40 

0.30 

0.43 

0.32 

0.46 

0.34 

0.48 

0.36 

0.51 

0.38 

0,54 

0.40 

134 

0.37 

0.27 

0.40 

0.29 

0.43 

0.31 

0.46 

0.33 

0.49 

0.35 

0.52 

0.37 

0.54 

0.39 

136 

0.38 

0.26 

0.41 

0.28 

0.44 

0.30 

0.47 

0.32 

0.49 

0.34 

0.52 

0.36 

0.55 

0.38 

138 

0.39 

0.26 

0.42 

0.28 

0.45 

0.30 

0.47 

0.32 

0.50 

0.33 

0.53 

0.36 

0.55 

0,37 

140 

0.39 

0.25 

0.42 

0.27 

0.45 

0.29 

0.48 

0.31 

0.51 

0.33 

0.53 

0.34 

0.56 

0,36 

142 

0.40 

0.25 

0.43 

0.27 

0.46 

0.28 

0.49 

0.30 

0.51 

0.32 

0.54 

0.33 

0.56 

0,35 

144 

0.41 

0.24 

0.44 

0.26 

0.47 

0.28 

0.50 

0.29 

0.52 

0.31 

0.55 

0.32 

0.57 

0,34 

146 

0.42 

0.24 

0.45 

0.25 

0.48 

0.27 

0.51 

0.28 

0.53 

0.30 

0.56 

0.31 

0.58 

0,32 

148 

0.43 

0  23 

0.46 

0.25 

0.49 

0.26 

0.52 

0.27 

0.54 

0.29 

0.57 

0.30 

0.59 

0.31 

150 

0.45 

0.22 

0.48 

0.24 

0.50 

0.25 

0.53 

0.26 

0.55 

0.28 

0.58 

0.29 

0.60 

0.30 

152 

0.46 

0.22 

0.49 

0.23 

0.52 

0.24 

0.54 

0.25 

0.57 

0.27 

0.59 

0.28 

0.61 

0.29 

154 

0.48 

0.21 

0.50 

0.22 

0.53 

0.23 

0.56 

0.24 

0.58 

0.25 

0.60 

0  26 

0.62 

0.27 

156 

0.49 

0.20 

0.52 

0.21 

0.55 

0.22 

0.57 

0.23 

0.60 

0.24 

0.62 

0  25 

0.64 

0.26 

158 

0.51 

0.19 

0.54 

0.20 

0.57 

0.21 

0.59 

0.22 

0.61 

0.23 

0.63 

0.24 

0.66 

0.25 

160 

0.53 

0.18 

0.56 

0.19 

0.59 

0.20 

0.61 

0.21 

0.63 

0.22 

0,65 

0.22 

0.67 

0.23 

TABLE  5B. 

[Page 

635 

Difference 

Distance  of  an  Object  by  Two  Bearings. 

Difference  between  the  course  and  first  bearing. 

between 

the  course 

1 

1 

md  second 
bearing. 

84° 

36° 

88° 

40° 

48°           1 

44° 

46°            1 

44° 

3.22 

2.24 

46 

2.69 

1.93 

3.39 

2.43 

48 

2.31 

1.72 

2.83 

2.10 

3.55 

2.63 

50 

2.03 

1.55 

2.43 

1.86 

2.96 

2.27 

3.70 

2.84 

52 

1.81 

1.43 

2.13 

1.68 

2.54 

2.01 

3.09 

2.44 

3.85 

3.04 

54 

1.63 

1.32 

1.90 

1.54 

2.23 

1.81 

2.66 

2.15 

3.22 

2.60 

4.00 

3.24 

56 

1.49 

1.24 

1.72 

1.42 

1.99 

1.65 

2.33 

1.93 

2.77 

2.29 

3.34 

2.77 

4.14 

3.43 

58 

1.37 

1.17 

1.57 

1.33 

1.80 

1.53 

2.08 

1.76 

2.43 

2.06 

2.87 

2.44 

3.46 

2.93 

60 

1.28 

1.10 

1.45 

1.25 

1.64 

1.42 

1.88 

1.63 

2.17 

1.88 

2.52 

2.18 

2.97 

2.57 

62 

1.19 

1.05 

1.34 

1.18 

1.51 

1.34 

1.72 

1.52 

1.96 

1.73 

2.25 

1.98 

2.61 

2.30 

64 

1.12 

1.01 

1.25 

1.13 

1.40 

1.26 

1.58 

1.42 

1.79 

1.61 

2.03 

1.83 

2.33 

2.09 

66 

1.06 

0.96 

1.18 

1.07 

1.31 

1.20 

1.47 

1.34 

1.65 

1.51 

1.85 

1.69 

2.10 

1.92 

68 

1.00 

0.93 

1.11 

1.03 

1.23 

1.14 

1.37 

1.27 

1.53 

1.42 

1.71 

1.58 

1.92 

1.78 

70 

0.95 

0.89 

1.05 

0.99 

1.16 

1.09 

1.29 

1.21 

1.43 

1..34 

1.58 

1.49 

1.77 

1.66 

72 

0.91 

0.86 

1.00 

0.95 

1.10 

1.05 

1.21 

1.15 

1.34 

1.27 

1.48 

1.41 

1.64 

1.56 

74 

0.87 

0.84 

0.95 

0.92 

1.05 

1.01 

1.15 

1.10 

1.26 

1.21 

1.39 

1.34 

1.53 

1.47 

76 

0.84 

0.81 

0.91 

0.89 

1.00 

0.97 

1.09 

1.06 

1.20 

1.16 

1.31 

1.27 

1.44 

1.40 

78 

0.80 

0.79 

0.88 

0.86 

0.96 

0.94 

1.04 

1.02 

1.14 

1.11 

1.24 

1.22 

1.36 

1.33 

80 

0.78 

0.77 

0.85 

0.83 

0.92 

0.91 

1.00 

0.98 

1.09 

1.07 

1.18 

1.16 

1.28 

1.27 

82 

0.75 

0.75 

0.82 

0.81 

0.89 

0.88 

0.96 

0.95 

1.04 

1.03 

1.13 

1.12 

1.22 

1.21 

84 

0.73 

0.73 

0.79 

0.79 

0.86 

0.85 

0.93 

0.92 

1.00 

0.99 

1.08 

1.07 

1.17 

1.16 

86 

0.71 

0.71 

0.77 

0.77 

0.83 

0.83 

0.89 

0.89 

0.96 

0.96 

1.04 

1.04 

1.12 

1.12 

88 

0.69 

0.69 

0.75 

0.75 

0.80 

0.80 

0.86 

0.86 

0.93 

0.93 

1.00 

1.00 

1.08 

1.07 

90 

0.67 

0.67 

0.73 

0.73 

0.78 

0.78 

0.84 

0.84 

0.90 

0.90 

0.97 

0.97 

1.04 

1.04 

92 

0.66 

0.66 

0.71 

0.71 

0.76 

0.76 

0.82 

0.82 

0.67 

0.87 

0.93 

0.93 

1.00 

1.00 

94 

0.65 

0.64 

0.69 

0.69 

0.74 

0.74 

0.79 

0.79 

0.85 

0.85 

0.91 

0.90 

0.97 

0.97 

96 

0.63 

0.63 

0.68 

0.67 

0.73 

0.72 

0.78 

0.77 

0.83 

0.82 

0.88 

0.88 

0.94 

0.93 

98 

0.62 

0.62 

0.67 

0.66 

0.71 

0.70 

0.76 

0.75 

0.81 

0.80 

0.86 

0.85 

0.91 

0.90 

100 

0.61 

0.60 

0.65 

0.64 

0.70 

0.69 

0.74 

0.73 

0.79 

0.78 

0.84 

0.83 

0.89 

0.88 

102 

0.60 

0.59 

0.64 

0.63 

0.68 

0.67 

0.73 

0.71 

0.77 

0.76 

0.82 

0.80 

0.87 

0.85 

104 

0.60 

0.58 

0.63 

0.61 

0.67 

0.65 

0.72 

0.69 

0.76 

0.74 

0.80 

0.78 

0.85 

0.82 

106 

0.59 

0.57 

0.63 

0.60 

0.66 

0.64 

0.70 

0.68 

0.74 

0.72 

0.79 

0.76 

0.83 

0.80 

108 

0.58 

0.55 

0.62 

0.59 

0.66 

0.62 

0.69 

0.66 

0.73 

0.70 

0.77 

0.74 

0.81 

0.77 

110 

0.58 

0.54 

0.61 

0.57 

0.65 

0.61 

0.68 

0.64 

0.72 

0.68 

0.76 

0.71 

0.80 

0.75 

112 

0.57 

0.53 

0.61 

0.56 

0.64 

0.59 

0.68 

0.63 

0.71 

0.66 

0.75 

0.69 

0.79 

0.73 

114 

0.57 

0.52 

0.60 

0.55 

0.63 

0.58 

0.67 

0.61 

0.70 

0.64 

0.74 

0.68 

0.78 

0.71 

116 

0.56 

0.51 

0.60 

0.54 

0.63 

0.57 

0.66 

0.60 

0.70 

0.63 

0.73 

0.66 

0.77 

0.69 

118 

0.56 

0.50 

0.59 

0.52 

0.63 

0.55 

0.66 

0.58 

0.69 

0.61 

0.72 

0.64 

0.76 

0.67 

120 

0.56 

0.49 

0.59 

0.51 

0.62 

0.54 

0.65 

0.57 

0.68 

0.59 

0.72 

0.62 

0.75 

0.65 

122 

0.56 

0.47 

0.59 

0.50 

0.62 

0.53 

0.65 

0.55 

0.68 

0.58 

0.71 

0.60 

0.74 

0.63 

124 

0.56 

0.46 

0.59 

0.49 

0.62 

0.51 

0.65 

0.54 

0.68 

0.56 

0.71 

0.58 

0.74 

0.61 

126 

0.56 

0.45 

0.59 

0.48 

0.62 

0.50 

0.64 

0.52 

0.67 

0.54 

0.70 

0.57 

0.73 

0.59 

128 

0.56 

0.44 

0.59 

0.46 

0.62 

0.49 

0.64 

0.51 

0.67 

0.53 

0.70 

0.55 

0.73 

0.57 

130 

0.56 

0.43 

0.59 

0.45 

0.62 

0.47 

0.64 

0.49 

0.67 

0.51 

0.70 

0.53 

0.72 

0.55 

132 

0.56 

0.42 

0.59 

0.44 

0.62 

0.46 

0.64 

0.48 

0.67 

0.50 

0.70 

0.52 

0.72 

0.54 

134 

0.57 

0.41 

0.59 

0.43 

0.62 

0.45 

0.64 

0.46 

0.67 

0.48 

0.69 

0.50 

0.72 

0.52 

136 

0.57 

0.40 

0.60 

0.41 

0.62 

0.43 

0.65 

0.45 

0.67 

0.47 

0.70 

0.48 

0.72 

0.50 

138 

0.58 

0.39 

0.60 

0.40 

0.63 

0.42 

0.65 

0.43 

0.67 

0.45 

0.70 

0.47 

0.72 

0.48 

140 

0.58 

0.37 

0.61 

0.39 

0.63 

0.40 

0.65 

0.42 

0.68 

0.43 

0.70 

0.45 

0.72 

0.46 

142 

0.59 

0.36 

0.61 

0.38 

0.63 

0.39 

0.66 

0.41 

0.68 

0.42 

0.70 

0.43 

0.72 

0.45 

144 

0.60 

0.35 

0.62 

0.36 

0.64 

0.38 

0.66 

0.39 

0.68 

0.40 

0.71 

0.41 

0.73 

0.43 

146 

0.60 

0.34 

0.63 

0.35 

0.65 

0.36 

0.67 

0.37 

0.69 

0.39 

0.71 

0.40 

0.73 

0.41 

148 

0.61 

0.32 

0.63 

0.34 

0.66 

0.35 

0.68 

0.36 

0.70 

0.37 

0.72 

0.38 

0.74 

0.39 

150 

0.62 

0.31 

0.64 

0.32 

0.66 

0.33 

0.68 

0.34 

0.70 

0.35 

0.72 

0.36 

0.74 

0.37 

152 

0.63 

0.30 

0.65 

0.31 

0.67 

0.32 

0.69 

0.33 

0.71 

0.33 

0.73 

0.34 

0.75 

0.35 

154 

0.65 

0.28 

0.67 

0.29 

0.68 

0.30 

0.70 

0.31 

0.72 

0.32 

0.74 

0.32 

0.76 

0.33 

156 

0.66 

0.27 

0.68 

0.28 

0.70 

0.28 

0.72 

0.29 

0.73 

0.30 

0.75 

0.30 

0.77 

0.31 

158 

0.67 

0.25 

0.69 

0.26 

0.71 

0.27 

0.73 

0.  27     0.  74 

0.28 

0.76 

0.28 

0.78 

0.29 

160 

0.69 

0.24 

0.71 

0.24 

0.73 

0.25 

0.74 

0.  25     0.  76 

0.26 

0.77 

0.26 

0.79 

0.27 

Page  636]                                          TABLE  6B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 

Difference  between  the  course  and  first  bearing. 

the  course 

I 

and  second 
bearing. 

48° 

50« 

52° 

64° 

56° 

68° 

60° 

68° 

4.28 

3.63 

• 

60 

3.57 

3.10 

4.41 

3.82 

62 

3.07 

2.71 

3.68 

3.26 

4.64 

4.01 

64 

2.70 

2.42 

3.17 

2.86 

3.79 

3.41 

4.66 

4.19 

66 

2.40 

2.20 

2.78 

2.54 

3.26 

2.98 

3.89 

3.55 

4.77 

4.36 

68 

2.17 

2.01 

2.48 

2.30 

2.86 

2.66 

3.34 

3.10 

3.99 

3.71 

4.88 

4.53 

70 

1.98 

1.86 

2.24 

2.10 

2.55 

2.39 

2.94 

2.76 

3.43 

3.22 

4.08 

3.83 

4.99 

4.69 

72 

1.83 

1.74 

2.04 

1.94 

2.30 

2.19 

2.62 

2.49 

3.01 

2.86 

3.51 

3.33 

4.17 

3.96 

74 

1.70 

1.63 

1.88 

1.81 

2.10 

2.02 

2.37 

2.27 

2.68 

2.58 

3.08 

2.96 

3.68 

3.44 

76 

1.58 

1.54 

1.75 

1.70 

1.94 

1.88 

2.16 

2.10 

2.42 

2.36 

2.74 

2.66 

3.14 

3.05 

78 

1.49 

1.45 

1.63 

1.60 

1.80 

1.76 

1.99 

1.95 

2.21 

2.16 

2.48 

2.43 

2.80 

2.74 

80 

1.40 

1.38 

1.53 

1.51 

1.68 

1.66 

1.86 

1.82 

2.04 

2.01 

2.26 

2.23 

2.63 

2.49 

82 

1.33 

1.32 

1.45 

1.43 

1.58 

1.56 

1.72 

1.71 

1.89 

1.87 

2.08 

2.06 

2.31 

2.29 

84 

1.26 

1.26 

1.37 

1.36 

1.49 

1.48 

1.62 

1.61 

1.77 

1.76 

1.93 

1.92 

2.13 

2.12 

86 

1.21 

1.20 

1.30 

1.30 

1.41 

1.41 

1.53 

1.62 

1.66 

1.65 

1.81 

1.80 

1.98 

1.97 

88 

1.16 

1.16 

1.24 

1.24 

1.34 

1.34 

1.46 

1.45 

1.56 

1.56 

1.70 

1.70 

1.84 

1.84 

90 

1.11 

1.11 

1.19 

1.19 

1.28 

1.28 

1.38 

1.38 

1.48 

1.48 

1.60 

1.60 

1.73 

1.73 

92 

1.07 

1.07 

1.14 

1.14 

1.23 

1.23 

1.31 

1.31 

1.41 

1.41 

1.62 

1.62 

1.63 

1.63 

94 

1.03 

1.03 

1.10 

1.10 

1.18 

1.17 

1.26 

1.26 

1.36 

1.34 

1.44 

1.44 

1.55 

1.54 

96 

1.00 

0.99 

1.06 

1.06 

1.13 

1.13 

1.21 

1.20 

1.29 

1.28 

1.38 

1.37 

1.47 

1.47 

98 

0.97 

0.96 

1.03 

1.02 

1.10 

1.08 

1.16 

1.15 

1.24 

1.23 

1.32 

1.31 

1.41 

1.39 

100 

0.94 

0.93 

1.00 

0.98 

1.06 

1.04 

1.12 

1.11 

1.19 

1.18 

1.27 

1.25 

1.35 

1.33 

102 

0.92 

0.90 

0.97 

0.95 

1.03 

1.01 

1.09 

1.06 

1.15 

1.13 

1.22 

1.19 

1.29 

1.27 

104 

0.90 

0.87 

0.95 

0.92 

1.00 

0.97 

1.06 

1.02 

1.12 

1.08 

1.18 

1.14 

1.25 

1.21 

106 

0.88 

0.84 

0.92 

0.89 

0.97 

0.94 

1.03 

0.99 

1.09 

1.04 

1.14 

1.10 

1.20 

1.16 

108 

0.86 

0.82 

0.90 

0.86 

0.95 

0.90 

1.00 

0.96 

1.05 

1.00 

1.11 

1.05 

1.17 

1.11 

110 

0.84 

0.79 

0.88 

0.83 

0.93 

0.87 

0.98 

0.92 

1.02 

0.96 

1.08 

1.01 

1.13 

1.06 

112 

0.83 

0.77 

0.87 

0.80 

0.91 

0.84 

0.95 

0.88 

1.00 

0.93 

1.05 

0.97 

1.10 

1.02 

114 

0.81 

0.74 

0.86 

0.78 

0.89 

0.82 

0.93 

0.86 

0.98 

0.89 

1.02 

0.93 

1.07 

0.98 

116 

0.80 

0.72 

0.84 

0.76 

0.88 

0.79 

0.92 

0.82 

0.96 

0.86 

1.00 

0.90 

1.04 

0.94 

118 

0.79 

0.70 

0.83 

0.73 

0.86 

0.76 

0.90 

0.79 

0.94 

0.83 

0.98 

0.86 

1.02 

0.90 

120 

0.78 

0.68 

0.82 

0.71 

0.86 

0.74 

0.89 

0.77 

0.91 

0.80 

0.96 

0.83 

1.00 

0.87 

122 

0.77 

0.66 

0.81 

0.68 

0.84 

0.71 

0.87 

0.74 

0.90 

0.77 

0.96 

0.80 

0.98 

0.83 

124 

0.77 

0.63 

0.80 

0.66 

0.83 

0.69 

0.86 

0.71 

0.90 

0.74 

0.93 

0.77 

0.96 

0.80 

126 

0.76 

0.61 

0.79 

0.64 

0.82 

0.66 

0.85 

0.69 

0.88 

0.71 

0.91 

0.74 

0.96 

0.77 

128 

0.75 

0.59 

0.78 

0.62 

0.81 

0.64 

0.84 

0.66 

0.87 

0.69 

0.90 

0.71 

0.93 

0.74 

130 

0.75 

0.57 

0.78 

0.60 

0.81 

0.62 

0.83 

0.64 

0.86 

0.66 

0.89 

0.68 

0.92 

0.71 

132 

0.75 

0.56 

0.77 

0.57 

0.80 

0.59 

0.83 

0.61 

0.86 

0.64 

0.88 

0.66 

0.91 

0.68 

134 

0.74 

0.54 

0.77 

0.56 

0.80 

0.57 

0.82 

0.59 

0.86 

0.61 

0.87 

0.63 

0.90 

0.65 

136 

0.74 

0.52 

0.77 

0.53 

0.80 

0.55 

0.82 

0.57 

0.84 

0.58 

0.87 

0.60 

0.89 

0.62 

138 

0.74 

0.50 

0.77 

0.51 

0.79 

0.53 

0.81 

0.54 

0.84 

0.56 

0.86 

0.58 

0.89 

0.59 

140 

0.74 

0.48 

0.77 

0.49 

0.79 

0.51 

0.81 

0.62 

0.83 

0.54 

0.86 

0.56 

0.88 

0.57 

142 

0.74 

0.46 

0.77 

0.47 

0.79 

0.49 

0.81 

0.50 

0.83 

0.61 

0.85 

0.62 

0.87 

0.54 

144 

0.75 

0.44 

0.77 

0.45 

0.79 

0.46 

0.81 

0.48 

0.83 

0.49 

0.86 

0.50 

0.87 

0.51 

146 

0.75 

0.42 

0.77 

0.43 

0.79 

0.44 

0.81 

0.46 

0.83 

0.46 

0.86 

0.47 

0.87 

0.49 

148 

0.76 

0.40 

0.77 

0.41 

0.79 

0.42 

0.81 

0.43 

0.83 

0.44 

0.85 

0.45 

0.87 

0.46 

150 

0.76 

0.38 

0.78 

0.39 

0.80 

0.40 

0.81 

0.41 

0.83 

0.42 

0.85 

0.42 

0.87 

0.43 

152 

0.77 

0.36 

0.78 

0.37 

0.80 

0.38 

0.82 

0.38 

0.83 

0.39 

0.85 

0.40 

0.87 

0.41 

154 

0.77 

0.34 

0.79 

0.36 

0.81 

0.35 

0.82 

0.36 

0.84 

0.37 

0.85 

0.37 

0.87 

0.38 

156 

0.78 

0.32 

0.80 

0.32 

0.81 

0.33 

0.83 

0.34 

0.84 

0..34 

0.86 

0.35 

0.87 

0.35 

158 

0.79 

0.30 

0.81 

0.30 

0.82 

0.31 

0.83 

0.31 

0.85 

0.32 

0.86 

0.32 

0.87 

0.33 

160 

0.80 

0.27 

0.82 

0.28 

0.83 

0.28 

0.84 

0.29 

0.85 

0.29 

0.86 

0.30 

0.88 

0.30 

TABLE  5B.                                          [Page  637 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

Difference  between  the  course  and  first  bearing. 

between 

the  course 

I 

md  second 
bearing. 

62° 

64° 

66° 

68° 

70° 

72° 

740 

76°          1 

72° 

6.08 

4.84 

74 

4.25 

4.08 

5.18 

4.98 

76 

3.&5 

3.54 

4.32 

4.19 

5.26 

5.10 

78 

3.20 

3.13 

3.72 

3.63 

4.39 

4.30 

5.34 

5.22 

80 

2.86 

2.81 

3.26 

3.21 

3.78 

3.72 

4.46 

4.39 

5.41 

5.33 

82 

2.58 

2.56 

2.91 

2.88 

3.31 

3.28 

3.83 

3.80 

4.52 

4.48 

5.48 

5.42 

84 

2.36 

2.34 

2.63 

2.61 

2.96 

2.94 

3.36 

3.35 

3.88 

3.86 

4.57 

4.55 

5.54 

5.51 

86 

2.17 

2.17 

2.40 

2.39 

2.67 

2.66 

3.00 

2.99 

3.41 

3.40 

3.93 

3.92 

4.62 

4.61 

5.59 

5.57 

88 

2.01 

2.01 

2.21 

2.21 

2.44 

2.44 

2.71 

2.71 

3.04 

3.04 

3.45 

3.45 

3.97 

3.97 

4.67 

4.66 

90 

1.88 

1.88 

2.05 

2.05 

2.25 

2.25 

2.48 

2.48 

2.75 

2.75 

3.08 

3.08 

3.49 

3.49 

4.01 

4.01 

92 

1.77 

1.76 

1.91 

1.91 

2.08 

2.08 

2.28 

2.28 

2.51 

2.51 

2.78 

2.78 

3.11 

3.11 

3.52 

3.52 

94 

1.67 

1.66 

1.80 

1.79 

1.95 

1.94 

2.12 

2.11 

2.31 

2.30 

2.54 

2.53 

2.81 

2.80 

3.14 

3.13 

96 

1.58 

1.57 

1.70 

1.69 

1.83 

1.82 

1.97 

1.96 

2.14 

2.13 

2.34 

2.33 

2.57 

2.55 

2.84 

2.82 

98 

1.50 

1.49 

1.61 

1.59 

1.72 

1.71 

1.85 

1.84 

2.00 

1.98 

2.17 

2.15 

2.36 

2.34 

2.59 

2.56 

100 

1.43 

1.41 

1.53 

1.51 

1.63 

1.61 

1.75 

1.72 

1.88 

1.85 

2.03 

2.00 

2.19 

2.16 

2.39 

2.35 

102 

1.37 

1.34 

1.46 

1.43 

1.55 

1.52 

1.66 

1.62 

1.77 

1.73 

1.90 

1.86 

2.05 

2.00 

2.21 

2.16 

104 

1.32 

1.28 

1.40 

1.36 

1.48 

1.44 

1.58 

1.53 

1.68 

1,63 

1.79 

1.74 

1.92 

1.87 

2.07 

2.01 

106 

1.27 

1.22 

1.34 

1.29 

1.42 

1.37 

1.51 

1.45 

1.60 

1.54 

1.70 

1.63 

1.81 

1.74 

1.94 

1.87 

108 

1.23 

1.17 

1.29 

1.23 

1.37 

1.30 

1.44 

1.37 

1.53 

1.45 

1.62 

1.54 

1.72 

1.63 

1.83 

1.74 

110 

1.19 

1.12 

1.25 

1.17 

1.32 

1.24 

1.39 

1.30 

1.46 

1.37 

1.54 

1.45 

1.64 

1.54 

1.74 

1.63 

112 

1.15 

1.07 

1.21 

1.12 

1.27 

1.18 

1.33 

1.24 

1.40 

1.30 

1.48 

1.37 

1.56 

1.45 

1.65 

1.53 

114 

1.12 

1.02 

1.17 

1.07 

1.23 

1.12 

1.29 

1.18 

1.35 

1.24 

1.42 

1.30 

1.50 

1.37 

1.58 

1.44 

116 

1.09 

0.98 

1.14 

1.03 

1.19 

1.07 

1.25 

1.12 

1.31 

1.17 

1.37 

1.23 

1.44 

1.29 

1.51 

1.36 

118 

1.07 

0.94 

1.11 

0.98 

1.16 

1.02 

1.21 

1.07 

1.26 

1.12 

1.32 

1.17 

1.38 

1.22 

1.45 

1.28 

120 

1.04 

0.90 

1.08 

0.94 

1.13 

0.98 

1.18 

1.02 

1.23 

1.06 

1.28 

1.11 

1.34 

1.16 

1.40 

1.21 

122 

1.02 

0.86 

1.06 

0.90 

1.10 

0.93 

1.15 

0.97 

1.19 

1.01 

1.24 

1.05 

1.29 

1.10 

1.35 

1.14 

124 

1.00 

0.83 

1.04 

0.86 

1.08 

0.89 

1.12 

0.93 

1.16 

0.96 

1.21 

1.00 

1.25 

1.04 

1.31 

1.08 

126 

0.98 

0.79 

1.02 

0.82 

1.05 

0.85 

1.09 

0.88 

1.13 

0.92 

1.18 

0.95 

1.22 

0.99 

1.27 

1.02 

128 

0.97 

0.76 

1.00 

0.79 

1.03 

0.82 

1.07 

0.84 

1.11 

0.87 

1.15 

0.90 

1.19 

0.94 

1.23 

0.97 

130 

0.95 

0.73 

0.98 

0.75 

1.02 

0.78 

1.05 

0.80 

1.09 

0.83 

1.12 

0.86 

1.16 

0.89 

1.20 

0.92 

132 

0.94 

0.70 

0.97 

0.72 

1.00 

0.74 

1.03 

0.77 

1.06 

0.79 

1.10 

0.82 

1.13 

0.84 

1.17 

0.87 

134 

0.93 

0.67 

0.96 

0.69 

0.99 

0.71 

1.01 

0.73 

1.04 

0.75 

1.08 

0.77 

1.11 

0.80 

1.14 

0.82 

136 

0.92 

0.64 

0.95 

0.66 

0.97 

0.68 

1.00 

0.69 

1.03 

0.71 

1.06 

0.74 

1.09 

0.76 

1.12 

0.78 

138 

0.91 

0.61 

0.94 

0.63 

0.96 

0.64 

0.99 

0.66 

1.01 

0.68 

1.04 

0.70 

1.07 

0.72 

1.10 

0.74 

140 

0.90 

0.58 

0.93 

0.60 

0.95 

0.61 

0.97 

0.63 

1.00 

0.64 

1.03 

0.66 

1.05 

0.68 

1.08 

0.70 

142 

0.90 

0.55 

0.92 

0.57 

0.94 

0.58 

0.96 

0.59 

0.99 

0.61 

1.01 

0.62 

1.04 

0.64 

1.06 

0.65 

144 

0.89 

0.52 

0.91 

0.54 

0.93 

0.55 

0.96 

0.56 

0.98 

0.57 

1.00 

0.59 

1.02 

0.60 

1.05 

0.62 

146 

0.89 

0.50 

0.91 

0.51 

0.93 

0.52 

0.95 

0.53 

0.97 

0.54 

0.99 

0.55 

1.01 

0.57 

1.03 

0.58 

148 

0.89 

0.47 

0.90 

0.48 

0.92 

0.49 

0.94 

0.50 

0.96 

0.51 

0.98 

0.52 

1.00 

0.53 

1.02 

0.54 

150 

0.88 

0.44 

0.90 

0.45 

0.92 

0.46 

0.94 

0.47 

0.95 

0.48 

0.97 

0.49 

0.99 

0.50 

1.01 

0.50 

152 

0.88 

0.41 

0.90 

0.42 

0.92 

0.43 

0.93 

0.44 

0.95 

0.45 

0.97 

0.45 

0.98 

0.46 

1.00 

0.47 

154 

0.88 

0.39 

0.90 

0.39 

0.91 

0.40 

0.93 

0.41 

0.94 

0.41 

0.96 

0.42 

0.98 

0.43 

0.99 

0.43 

156 

0.89 

0.36 

0.90 

0.37 

0.91 

0.37 

0.93 

0.38 

0.94 

0.38 

0.96 

0.39 

0.97 

0.39 

0.99 

0.40 

158 

0.89 

0.33 

0.90 

0.34 

0.91 

0.34 

0.93 

0.35 

0.94 

0.35 

0.95 

0.36 

0.97 

0.36 

0.98 

0.37 

160 

0.89 

0.30 

0.90 

0.31 

0.91 

0.31 

0.93 

0.32 

0.94 

0.32 

0.95 

0.33 

0.96 

0.33 

0.98 

0.33 

Page  638]                                          TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

the  course 

and  second 

bearing. 

Difference  between  the  course  and  first  bearing. 

78° 

80° 

82° 

84° 

86° 

88° 

90° 

92°          1 

88° 

5.63 

5.63 

90 

4.70 

4.70 

5.67 

5.67 

92 

4.04 

4.04 

4.74 

4.73 

5.70 

5.70 

94 

3.55 

3.54 

4.07 

4.06 

4.76 

4.75 

5.73 

5.71 

96 

3.17 

3.15 

3.57 

3.55 

4.09 

4.07 

4.78 

4.76 

5.74 

5.71 

98 

2.86 

2.83 

3.19 

3.16 

3.59 

3.56 

4.11 

4.07 

4.80 

4.75 

5.76 

5.70 

100 

2.61 

2.57 

2.88 

2.84 

3.20 

3.16 

3.61 

3.55 

4.12 

4.06 

4.81 

4.73 

5.76 

5.67 

102 

2.40 

2.35 

2.63 

2.57 

2.90 

2.83 

3.22 

3.15 

3.62 

3.54 

4.13 

4.04 

4.81 

4.70 

5.76 

5.63 

104 

2.23 

2.16 

2.42 

2.35 

2.64 

2.56 

2.91 

2.82 

3.23 

3.13 

3.63 

3.52 

4.13 

4.01 

4.81 

4.66 

106 

2.08 

2.00 

2.25 

2.16 

2.43 

2.34 

2.65 

2.55 

2.92 

2.80 

3.23 

3.11 

3.63 

3.49 

4.13 

3.97 

108 

1.96 

1.86 

2.10 

2.00 

2.26 

2.15 

2.45 

2.33 

2.66 

2.53 

2.92 

2.78 

3.24 

3.08 

3.63 

3.45 

110 

1.85 

1.73 

1.97 

1.85 

2.11 

1.98 

2.27 

2.13 

2.45 

2.31 

2.67 

2.51 

2.92 

2.75 

3.23 

3.04 

112 

1.75 

1.62 

1.86 

1.72 

1.98 

1.83 

2.12 

1.96 

2.28 

2.11 

2.46 

2.28 

2.67 

2.48 

2.92 

2.71 

114 

1.66 

1.52 

1.76 

1.61 

1.87 

1.71 

1.99 

1.82 

2.12 

1.94 

2.28 

2.08 

2.46 

2.25 

2.67 

2.44 

116 

1.59 

1.43 

1.68 

1.51 

1.77 

1.59 

1.88 

1.69 

2.00 

1.79 

2.13 

1.91 

2.28 

2.05 

2.46 

2.21 

118 

1.52 

1.34 

1.60 

1.41 

1.68 

1.49 

1.78 

1.57 

1.88 

1.66 

2.00 

1.76 

2.13 

1.88 

2.28 

2.01 

120 

1.46 

1.27 

1.53 

1.33 

1.61 

1.39 

1.69 

1.47 

1.78 

1.54 

1.89 

1.63 

2.00 

1.73 

2.13 

1.84 

122 

1.41 

1.19 

1.47 

1.25 

1.54 

1.31 

1.62 

1.37 

1.70 

1.44 

1.79 

1.52 

1.89 

1.60 

2.00 

1.70 

124 

1.36 

1.13 

1.42 

1.18 

1.48 

1.23 

1.55 

1.28 

1.62 

1.34 

1.70 

1.41 

1.79 

1.48 

1.89 

1.56 

126 

1.32 

1.06 

1..S7 

1.11 

1.43 

1.15 

1.48 

1.20 

1.55 

1.26 

1.62 

1.31 

1.70 

1.38 

1.79 

1.45 

128 

1.28 

1.01 

1.33 

1.04 

1.38 

1.08 

1.43 

1.13 

1.49 

1.17 

1.55 

1.23 

1.62 

1.28 

1.70 

1.34 

130 

1.24 

0.95 

1.29 

0.98 

1..33 

1.02 

1.38 

1.06 

1.44 

1.10 

1.49 

1.14 

1.56 

1.19 

1.62 

1.24 

132 

1.21 

0.90 

1.25 

0.93 

1.29 

0.96 

1.34 

0.99 

1.39 

1.03 

1.44 

1.07 

1.49 

1.11 

1.55 

1.16 

134 

1.18 

0.85 

1.22 

0.88 

1.26 

0.90 

1.30 

0.93 

1.34 

0.97 

1.39 

1.00 

1.44 

1.04 

1.49 

1.07 

136 

1.15 

0.80 

1.19 

0.83 

1.22 

0.85 

1.26 

0.88 

1.30 

0.90 

1.34 

0.93 

1.39 

0.97 

1.44 

1.00 

138 

1.13 

0.76 

1.16 

0.78 

1.19 

0.80 

1.23 

0.82 

1.27 

0.85 

1.30 

0.87 

1.35 

0.90 

1.39 

0.93 

140 

1.11 

0.71 

1.14 

0.73 

1.17 

0.75 

1.20 

0.77 

1.23 

0.79 

1.27 

0.82 

1.31 

0.84 

1.34 

0.86 

142 

1.09 

0.67 

1.12 

0.69 

1.14 

0.70 

1.17 

0.72 

1.20 

0.74 

1.24 

0.76 

1.27 

0.78 

1.30 

0.80 

144 

1.07 

0.63 

1.10 

0.64 

1.12 

0.66 

1.15 

0.67 

1.18 

0.69 

1.21 

0.71 

1.24 

0.73 

1.27 

0.75 

146 

1.05 

0.59 

1.08 

0.60 

1.10 

0.62 

1.13 

0.63 

1.15 

0.64 

1.18 

0.66 

1.21 

0.67 

1.24 

0.69 

148 

1.04 

0.55 

1.06 

0.56 

1.08 

0.57 

1.11 

0.59 

1.13 

0.60 

1.15 

0.61 

1.18 

0.62 

1.21 

0.64 

150 

1.03 

0.51 

1.05 

0.52 

1.07 

0.53 

1.09 

0.54 

1.11 

0.55 

1.13 

0.57 

1.15 

0.58 

1.18 

0.59 

152 

1.02 

0.48 

1.04 

0.49 

1.05 

0.49 

1.07 

0.50 

1.09 

0.51 

1.11 

0.52 

1.13 

0.53 

1.15 

0.54 

154 

1.01 

0.44 

1.02 

0.45 

1.04 

0.46 

1.06 

0.46 

1.08 

0.47 

1.09 

0.48 

1.11 

0.49 

1.13 

0.50 

156 

1.00 

0.41 

1.01 

0.41 

1.03 

0.42 

1.05 

0.43 

1.06 

0.43 

1.08 

0.44 

1.09 

0.45 

1.11 

0.45 

158 

0.99 

0.37 

1.01 

0.38 

1.02 

0.38 

1.03 

0.39 

1.05 

0.39 

1.06 

0.40 

1.08 

0.40 

1.09 

0.41 

160 

0.99 

0.34 

1.00 

0.34 

1.01 

0.35 

1.02 

0.35 

1.04 

0.35 

1.05 

0.36 

1.06 

0.36 

1.08 

0.37 

94° 

96° 

98° 

100° 

102° 

104° 

106° 

108°         1 

104° 

5.74 

5.57 

106 

4.80 

4.61 

5.78 

5.51 

108 

4.12 

3.92 

4.78 

4.55 

5.70 

5.42 

110 

3.62 

3.40 

4.11 

3.86 

4.76 

4.48 

5.67 

5.33 

112 

3.23 

2.99 

3.61 

3.35 

4.09 

3.80 

4.74 

4.40 

5.63 

5.22 

114 

2.92 

2.66 

3.22 

2.94 

3.59 

3.28 

4.07 

3.72 

4.70 

4.30 

5.59 

5.10 

116 

2.66 

2.39 

2.91 

2.61 

3.20 

2.88 

3.57 

3.21 

4.04 

3.63 

4.67 

4.19 

5.54 

4.98 

118 

2.45 

2.17 

2.65 

2.34 

2.90 

2.56 

3.19 

2.81 

3.55 

3.13 

4.01 

3.54 

4.62 

4.08 

5.48 

4.84 

120 

2.28 

1.97 

2.45 

2.12 

2.64 

2.29 

2.88 

2.49 

3.17 

2.74 

3.52 

3.05 

3.97 

3.44 

4.57 

3.96 

122 

2,12 

1.80 

2.27 

1.92 

2.43 

2.06 

2.63 

2.23 

2.86 

2.43 

3.14 

2.66 

3.49 

2.96 

3.93 

3.33 

124 

2.00 

1.65 

2.12 

1.76 

2.26 

1.87 

2.42 

2.01 

2.61 

2.16 

2.84 

2.35 

3.11 

2.58 

3.45 

2.86 

126 

1.88 

1.52 

1.99 

1.61 

2.11 

1.71 

2.25 

1.82 

2.40 

1.95 

2.59 

2.10 

2.81 

2.27 

3.08 

2.49 

128 

1.78 

1.41 

1.88 

1.48 

1.98 

1.56 

2.10 

1.65 

2.23 

1.76 

2.39 

1.88 

2.57 

2.02 

2.78 

2.19 

130 

1.70 

1.30 

1.78 

1.36 

1.87 

1.43 

1.97 

1.51 

2.08 

1.60 

2.21 

1.70 

2.36 

1.81 

2.54 

1.94 

132 

1.62 

1.20 

1.69 

1.26 

1.77 

1.32 

1.86 

1.38 

1.96 

1.45 

2.07 

1.54 

2.19 

1.63 

2.34 

1.74 

134 

1.55 

1.12 

1.62 

1.16 

1.68 

1.21 

1.76 

1.27 

1.85 

1.33 

1.94 

1.40 

2.05 

1.47 

2.17 

1.56 

136 

1.49 

1.04 

1.55 

1.07 

1.61 

1.12 

1.68 

1.16 

1.75 

1.22 

1.83 

1.27 

1.92 

1.34 

2.03 

1.41 

138 

1.44 

0.96 

1.49 

0.99 

1.54 

1.03 

1.60 

1.07 

1.66 

1.11 

1.74 

1.16 

1.81 

1.21 

1.90 

1.27 

140 

1.39 

0.89 

1.43 

0.92 

1.48 

0.95 

1.53 

0.98 

1.59 

1.02 

1.65 

1.06 

1.72 

1.10 

1.79 

1.15 

142 

1.34 

0.83 

1.38 

0.85 

1.43 

0.88 

1.47 

0.91 

1.52 

0.94 

1.58 

0.97 

1.64 

1.01 

1.70 

1.05 

144 

1.30 

0.77 

1.34 

0.79 

1.38 

0.81 

1.42 

0.83 

1.46 

0.86 

1.51 

0.89 

1.56 

0.92 

1.62 

0.95 

146 

1.27 

0.71 

1.30 

0.73 

1.33 

0.75 

1.37 

0.77 

1.41 

0.79 

1.45 

0.81 

1.50 

0.84 

1.54 

0.86 

148 

1.2* 

0.65 

1.26 

0.67 

1.29 

0.69 

1.33 

0.70 

1.36 

0.72 

1.40 

0.74 

1.44 

0.76 

1.48 

0.78 

150 

1.20 

0.60 

1.23 

0.61 

1.26 

0.63 

1.29 

0.64 

1.32 

0.66 

1.35 

0.67 

1.38 

0.69 

1.42 

0.71 

152 

1.18 

0.55 

1.20 

0.56 

1.22 

0.57 

1.25 

0.59 

1.28 

0.60 

1.31 

0.61 

1.34 

0.63 

1.37 

0.64 

154 

1.15 

0.50 

1.17 

0.51 

1.19 

0.52 

1.22 

0.53 

1.24 

0.54 

1.27 

0.56 

1.29 

0.57 

1.32 

0.58 

156 

1.13 

0.46 

1.15 

0.47 

1.17 

0.47 

1.19 

0.48 

1.21 

0.49 

1.23 

0.50 

1.25 

0.51 

1.28 

0.52 

158 

1.11 

0.42 

1.13 

0.42 

1.14 

0.43 

1.16 

0.44 

1.18 

0.44 

1.20 

0.45 

1.22 

0.46 

1.24 

0.47 

160 

1.09 

0.37 

1.11 

0.38 

1.12 

0.38 

1.14 

0.39 

1.15 

0.39 

1.17 

0.40 

1.19 

0.41 

1.21 

0.41 

TABLE  5B.                                           [Page  639 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 
the  course 
and  second 
bearing. 

Difference  between  the  course  and  first  bearin«r. 

110° 

112° 

114° 

116° 

118° 

120° 

122° 

120° 

5.41 

4.69 

122 

4.52 

3.83 

5.34 

4.53 

124 

3.88 

3.22 

4.46 

3.70 

5.26 

4.36 

126 

3.41 

2.76 

3.83 

3.10 

4.39 

3.55 

5.18 

4.19 

128 

3.04 

2.40 

3.36 

2.65 

3.78 

2.98 

4.32 

3.41 

5.08 

4.01 

130 

2.75 

2.10 

3.00 

2.30 

3.31 

2.54 

3.72 

2.85 

4.25 

3.25 

4.99 

3.82 

132 

2.51 

1.86 

2.71 

2.01 

2.96 

2.20 

3.26 

2.42 

3.65 

2.71 

4.17 

3.10 

4.88 

3.63 

134 

2.31 

1.66 

2.48 

1.78 

2.67 

1.92 

2.91 

2.09 

3.20 

2.30 

3.58 

2.57 

4.08 

2.93 

136 

2.14 

1.49 

2.28 

1.58 

2.44 

1.69 

2.63 

1.83 

2.86 

1.98 

3.14 

2.18 

3.51 

2.44 

138 

2.00 

1.34 

2.12 

1.42 

2.25 

1.50 

2.40 

1.61 

2.58 

1.73 

2.80 

1.88 

3.08 

2.06 

140 

1.88 

1.21 

1.97 

1.27 

2.08 

1.34 

2.21 

1.42 

2.36 

1.52 

2.53 

1.63 

2.74 

1.76 

142 

1.77 

1.09 

1.85 

1.14 

1.95 

1.20 

2.05 

1.26 

2.17 

1.34 

2.31 

1.42 

2.48 

1.53 

144 

1.68 

0.99 

1.75 

1.03 

1.83 

1.07 

1.91 

1.13 

2.01 

1.18 

2.13 

1.25 

2.26 

1.33 

146 

1.60 

0.89 

1.66 

0.93 

1.72 

0.96 

1.80 

1.01 

1.88 

1.05 

1.98 

1.10 

2.08 

1.17 

148 

1.53 

0.81 

1.58 

0.84 

1.63 

0.87 

1.70 

0.90 

1.77 

0.94 

1.84 

0.98 

1.93 

1.03 

150 

1.46 

0.73 

1.51 

0.75 

1.55 

0.78 

1.61 

0.80 

1.67 

0.83 

1.73 

0.87 

1.81 

0.90 

152 

1.40 

0.66 

1.44 

0.68 

1.48 

0.70 

1.53 

0.72 

1.58 

0.74 

1.63 

0.77 

1.70 

0.80 

154 

1.35 

0.59 

1.39 

0.61 

1.42 

0.62 

1.46 

0.64 

1.50 

0.66 

1.55 

0.68 

1.60 

0.70 

156 

1.31 

0.53 

1.33 

0.54 

1.37 

0.56 

1.40 

0.57 

1.43 

0.58 

1.47 

0.60 

1.52 

0.62 

158 

1.26 

0.47 

1.29 

0.48 

1.32 

0.49 

1.34 

0.50 

1.37 

0.51 

1. 41     0. 53 

1.44 

0.54 

160 

1.23 

0.42 

1.25 

0.43 

1.27 

0.43 

1.29 

0.44 

1.32 

0.45 

1.  35     0. 46 

1.38 

0.47 

124° 

126° 

128° 

180° 

182° 

184° 

186°           1 

134° 

4.77 

3.43 

136 

3.99 

2.77 

4.66 

3.23 

138 

3.43 

2.29 

3.89 

2.60 

4.54 

3.04 

140 

3.01 

1.93 

3.34 

2.15 

3.79 

2.44 

4.41 

2.84 

142 

2.68 

1.65 

2.94 

1.81 

3.26 

2.01 

3.63 

2.27 

4.28 

2.63 

144 

2.42 

1.42 

2.62 

1.54 

2.86 

1.68 

3.17 

1.86 

3.57 

2.10 

4.14 

2.43 

146 

2.21 

1.24 

2.37 

1.32 

2.55 

1.43 

2.78 

1.55 

3.07 

1.72 

3.46 

1.93 

4.00 

2.24 

148 

2.04 

1.08 

2.16 

1.14 

2.30 

1.22 

2.48 

1.31 

2.70 

1.43 

2.97 

1.58 

3.34 

1.77 

150 

1.89 

0.95 

1.99 

0.99 

2.10 

1.05 

2.24 

1.12 

2.40 

1.20 

2.61 

1.30 

2.87 

1.44 

152 

1.77 

0.83 

1.85 

0.87 

1.94 

0.91 

2.04 

0.96 

2.17 

1.02 

2.33 

1.09 

2.52 

1.18 

154 

1.66 

0.73 

1.72 

0.76 

1.80 

0.79 

1.88 

0.83 

1.98 

0.87 

2.10 

0.92 

2.25 

0.99 

156 

1.56 

0.64 

1.62 

0.66 

1.68 

0.68 

1.75 

0.71 

1.83 

0.74 

1.92 

0.78 

2.03 

0.83 

158 

1.48 

0.56 

1.53 

0.57 

1.58 

0.59 

1.63 

0.61 

1.70 

0.64 

1.77 

0.66 

1.85 

0.69 

160 

1.41 

0.48 

1.45 

0.49 

1.49 

0..51 

1.53 

0.52 

1.58 

0.54 

1.64 

0.56 

1.71 

0.58 

138° 

140° 

142°         1 

1*4°           1 

146°           1 

148° 

160°           1 

148° 

3.85 

2.04 

150 

3.22 

1.61 

3.70 

1.85 

152 

2.77 

1.30 

3.09 

1.45 

3.55 

1.66 

154 

2.43 

1.06 

2.66 

1.16 

2.96 

1.30 

3.38 

1.48 

156 

2.17 

0.88 

2.33 

0.95 

2.54 

1.04 

2.83 

1.15 

3.22 

1.31 

158 

1.96 

0.73 

2.08 

0.78 

2.23 

0.84 

2.43 

0.91 

2.69 

1.01 

3.05 

1.14 

160 

1.79 

0.61 

1.88 

0.64 

1.99 

0.68 

2.13 

0.73 

2.31 

0.79 

2.55 

0.87 

2.88 

0.98 

21594°— 14- 


-34 


Page  640] 

TABLE  6. 

1 

■Distance  of  Visibility  of  Objects  at  Sea. 

Height. 

Nautical 

statute 

Height, 

Nautical 

Statute 

Height, 

Nautical 

Statute 

feet. 

miles. 

miles. 

feet. 

miles. 

miles. 

feet. 

miles. 

miles. 

1 

1.1 

1.3 

100 

11.5 

13.2 

760 

31.6 

36.4 

2 

1.7 

1.9 

105 

11.7 

13.5 

780 

32.0 

36.9 

3 

2.0 

2.3 

110 

12.0 

13.8 

800 

32.4 

37.3 

4 

2.3 

2.6 

115 

12.3 

14.1 

820 

32.8 

37.8 

5 

2.5 

2.9 

120 

12.6 

14.5 

840 

33.2 

38.3 

6 

2.8 

3.2 

125 

12.9 

14.8 

860 

33.6 

38.7 

7 

2.9 

3.5 

130 

13.1 

15.1 

880 

34.0 

39.2 

8 

3.1 

3.7 

135 

13.3 

15.3 

900 

34.4 

39.6 

9 

3.5 

4.0 

140 

13.6 

15.6 

920 

34.7 

40.0 

10 

3.6 

4.2 

145 

13.8 

15.9 

940 

35.2 

40.5 

11 

3.8 

4.4 

150 

14.1 

16.2 

960 

35.5 

40.9 

12 

4.0 

4.6 

160 

14.5 

16.7 

980 

35.9 

41.3 

13 

4.2 

4.8 

170 

14.9 

17.2 

1,000 

36.2 

41.7 

14 

4.3 

4.9 

180 

15.4 

17.7 

1,100 

38.0 

43.8 

15 

4.4 

5.1 

190 

15.8 

18.2 

1,200 

39.6 

45.6 

16 

4.6 

6.3 

200 

16.2 

18.7 

1,300 

41.3 

47.6 

17 

4.7 

6.4 

210 

16.6 

19.1 

1,400 

42.9 

49.4 

18 

4.9 

6.6 

220 

17.0 

19.6 

1,500 

44.4 

51.1 

19 

5.0 

5.8 

230 

17.4 

20.0 

1,600 

45.8 

52.8 

20 

6.1 

6.9 

240 

17.7 

20.4 

1,700 

47.2 

54.4 

21 

5.3 

6.1 

250 

18.2 

20.9 

1,800 

48.6 

56.0 

22 

5.4 

6.2 

260 

18.5 

21.3 

1,900 

49.9 

57.5 

23 

5.5 

6.3 

270 

18.9 

21.7 

2,000 

51.2 

59.0 

24 

5.6 

6.5 

280 

19.2 

22.1 

2,100 

52.5 

60.6 

25 

6.7 

6.6 

290 

19.6 

22.5 

2,200 

63.8 

61.9 

26 

5.8 

6.7 

300 

19.9 

22.9 

2,300 

55.0 

63.3 

27 

6.0 

6.9 

310 

20.1 

23.2 

2,400 

56.2 

64,7 

28 

6.1 

7.0 

320 

20.5 

23.6 

2,500 

57.3 

66.0 

29 

6.2 

7.1 

330 

20.8 

24.0 

2,600 

58.5 

67.3 

30 

6.3 

7.2 

340 

21.1 

24.3 

2,700 

59.6 

68.6 

31 

6.4 

7.3 

350 

21.5 

24.7 

2,800 

60.6 

69.8 

32 

6.5 

7.5 

360 

21.7 

25.0 

2,900 

61.8 

71.1 

33 

6.6 

7.6 

370 

22.1 

25.4 

3,000 

62.8 

72.3 

34 

6.7 

7.7 

380 

22.3 

25.7 

3,100 

63.8 

73.6 

35 

6.8 

7.8 

390 

22.7 

26.1 

3,200 

64.9 

74.7 

36 

6.9 

7.9 

400 

22.9 

26.4 

3,300 

65.9 

75.9 

37 

6.9 

8.0 

410 

23.2 

26.7 

3,400 

66.9 

77.0 

38 

7.0 

8.1 

420 

23.5 

27.1 

3,500 

67.8 

78.1 

39 

7.1 

8.2 

430 

23.8 

27.4 

3,600 

68.8 

79.2 

40 

7.2 

8.3 

440 

24.1 

27.7 

3,700 

69.7 

80.3 

41 

7.3 

8.4 

450 

24.3 

28.0 

3,800 

70.7 

81.4 

42 

7.4 

8.5 

460 

24.6 

28.3 

3,900 

71.6 

82.4 

43 

7.5 

8.7 

470 

24.8 

28.6 

4,000 

72.5 

83.5 

44 

7.6 

8.8 

480 

25.1 

28.9 

4,100 

73.4 

84.6 

45 

7.7 

8.9 

490 

25.4 

29.2 

4,200 

74.3 

85.6 

46 

7.8 

9.0 

500 

25.6 

29.5 

4,300 

75.2 

86.6 

47 

7.9 

9.0 

520 

26.1 

30.1 

4,400 

76.1 

87.6 

48 

7.9 

9.1 

540 

26.7 

30.7 

4, 500 

76.9 

88.5 

49 

8.0 

9.2 

560 

27.1 

31.2 

4,600 

77.7 

89.6 

50 

8.1 

9.3 

580 

27.6 

31.8 

4,700 

78.6 

90.6 

55 

8.5 

9.8 

600 

28.0 

32.3 

4,800 

79.4 

91.4 

60 

8.9 

10.2 

620 

28.6 

32.9 

4,900 

80.2 

92.4 

65 

9.2 

10.6 

640 

29.0 

33.4 

5,000 

81.0 

93.3 

70 

9.6 

11.0 

660 

29.4 

33.9 

6,000 

88.8 

102.2 

75 

9.9 

11.4 

680 

29.9 

34.4 

7,000 

96.0 

110.6 

80 

10.3 

11.8 

700 

30.3 

34.9 

8,000 

102.6 

118.1 

85 

10.6 

12.2 

720 

30.7 

35.4 

9,000 

108.7 

125.2 

90 

10.9 

12.5 

740 

31.1 

35.9 

10,000 

114.6 

132.0 

95 

11.2 

12.9 

TABLE  7 

. 

[Page  641  | 

For  converting  Arc  into  Time 

and  the 

reverse. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

/ 

M.  S. 

/ 

M.  8. 

1 

M.  S. 

' 

M.  s. 

' 

M.  S. 

/ 

M.  S. 

H 

8.  A 

// 

R  A 

II 

8.  A 

II 

8.  A 

// 

8.  A 

" 

s.  A 

1 

0  4 

61 

4  4 

121 

8  4 

181 

12  4 

241 

16  4 

301 

20  4 

2 

0  8 

62 

4  8 

122 

8  8 

182 

12  8 

242 

16  8 

302 

20  8 

3 

0  12 

63 

4  12 

123 

8  12 

183 

12  12 

243 

16  12 

303 

20  12 

4 

0  16 

64 

4  16 

124 

8  16 

184 

12  16 

244 

16  16 

304 

20  16 

5 

0  20 

65 

4  20 

125 

8  20 

185 

12  20 

245 

16  20 

305 

20  20 

6 

0  24 

66 

4  24 

126 

8  24 

186 

12  24 

246 

16  24 

306 

20  24 

7 

0  28 

67 

4  28 

127 

8  28 

187 

12  28 

247 

16  28 

307 

20  28 

8 

0  32 

68 

4  32 

128 

8  32 

188 

12  32 

248 

16  32 

308 

20  32 

9 

0  36 

69 

4  36 

129 

8  36 

189 

12  36 

249 

16  36 

309 

20  36 

10 

0  40 

70 

4  40 

130 

8  40 

190 

12  40 

250 

16  40 

310 

20  40 

11 

0  44 

71 

4  44 

131 

8  44 

191 

12  44 

261 

16  44 

311 

20  44 

12 

0  48 

72 

4  48 

132 

8  48 

192 

12  48 

252 

16  48 

312 

20  48 

13 

0  52 

73 

4  52 

133 

8  52 

193 

12  52 

253 

16  52 

313 

20  52 

14 

0  56 

74 

4  66 

134 

8  56 

194 

12  56 

254 

16  66 

314 

20  56 

15 

1  0 

75 

5  0 

135 

9  0 

195 

13  0 

265 

17  0 

315 

21  0 

16 

1  4 

76 

5  4 

136 

9  4 

196 

13  4 

256 

17  4 

316 

21  4 

17 

1  8 

77 

5  8 

137 

9  8 

197 

13  8 

257 

17  8 

317 

21  8 

18 

1  12 

78 

5  12 

138 

9  12 

198 

13  12 

268 

17  12 

318 

21  12 

19 

1  16 

79 

5  16 

139 

9  16 

199 

13  16 

259 

17  16 

319 

21  16 

20 

1  20 

80 

5  20 

140 

9  20 

200 

13  20 

260 

17  20 

320 

21  20 

21 

1  24 

81 

5  24 

141 

9  24 

201 

13  24 

261 

17  24 

321 

21  24 

22 

1  28 

82 

5  28 

142 

9  28 

202 

13  28 

262 

17  28 

322 

21  28 

23 

1  32 

83 

5  32 

143 

9  32 

203 

13  32 

263 

17  32 

323 

21  32 

24 

1  36 

84 

5  36 

144 

9  36 

204 

13  36 

264 

17  36 

324 

21  36 

25 

1  40 

85 

5  40 

145 

9  40 

205 

13  40 

265 

17  40 

326 

21  40 

26 

1  44 

86 

5  44 

.  146 

9  44 

206 

13  44 

266 

17  44 

326 

21  44 

27 

1  48 

87 

5  48 

147 

9  48 

207 

13  48 

267 

17  48 

327 

21  48 

28 

1  52 

88 

5  52 

148 

9  52 

208 

13  52 

268 

17  52 

328 

21  52 

29 

1  56 

89 

5  56 

149 

9  56 

209 

13  56 

269 

17  56 

329 

21  56 

30 

2  0 

90 

6  0 

150 

10  0 

210 

14  0 

270 

18  0 

330 
331 

22  0 

31 

2  4 

91 

6  4 

151 

10  4 

211 

14  4 

271 

18  4 

22  4 

32 

2  8 

92 

6  8 

152 

10  8 

212 

14  8 

272 

18  8 

332 

22  8 

33 

2  12 

93 

6  12 

153 

10  12 

213 

14  12 

273 

18  12 

333 

22  12 

34 

2  16 

94 

6  16 

154 

10  16 

214 

14  16 

274 

18  16 

334 

22  16 

35 

2  20 

95 

6  20 

155 

10  20 

215 

14  20 

275 

18  20 

335 

22  20 

36 

2  24 

96 

6  24 

156 

10  24 

216 

14  24 

276 

18  24 

336 

22  24 

37 

2  28 

97 

6  28 

157 

10  28 

217 

14  28 

277 

18  28 

337 

22  28 

38 

2  32 

98 

6  32 

158 

10  32 

218 

14  32 

278 

18  32 

338 

22  32 

39 

2  36 

99 

6  36 

159 

10  36 

219 

14  36 

279 

18  36 

339 

22  36 

40 

2  40 

100 

6  40 

160 

10  40 

220 

14  40 

280 

18  40 

340 

22  40 

41 

2  44 

101 

6  44 

161 

10  44 

221 

14  44 

281 

18  44 

341 

22  44 

42 

2  48 

102 

6  48 

162 

10  48 

222 

14  48 

282 

18  48 

342 

22  48 

43 

2  52 

103 

6  52 

163 

10  52 

223 

14  52 

283 

18  52 

343 

22  52 

44 

2  56 

104 

6  56 

164 

10  56 

224 

14  56 

284 

18  56 

344 

22  56 

45 

3  0 

105 

7  0 

165 

11  0 

225 

15  0 

285 

19  0 

345 

23  0 

46 

3  4 

106 

7  4 

166 

11  4 

226 

15  4 

286 

19  4 

346 

23  4 

47 

3  8 

107 

7  8 

167 

11  8 

227 

15  8 

287 

19  8 

347 

23  8 

48 

3  12 

108 

7  12 

168 

11  12 

228 

15  12 

288 

19  12 

348 

23  12 

49 

3  16 

109 

7  16 

169 

11  16 

229 

15  16 

289 

19  16 

349 

23  16 

50 
51 

3  20 

110 

7  20 

170 

11  20 

230 

15  20 

290 

19  20 

350 

23  20 

3  24 

111 

7  24 

171 

11  24 

231 

15  24 

291 

19  24 

361 

23  24 

52 

3  28 

112 

7  28 

172 

11  28 

232 

15  28 

292 

19  28 

352 

23  28 

53 

3  32 

113 

7  32 

173 

11  32 

233 

15  32 

293 

19  32 

353 

23  32 

54 

3  36 

114 

7  36 

174 

11  36 

234 

15  36 

294 

19  36 

354 

23  36 

55 

3  40 

115 

7  40 

175 

11  40 

235 

15  40 

295 

19  40 

355 

23  40 

56 

3  44 

116 

7  44 

176 

11  44 

236 

15  44 

296 

19  44 

366 

23  44 

57 

3  48 

117 

7  48 

177 

11  48 

237 

15  48 

297 

19  48 

367 

23  48 

58 

3  52 

118 

7  52 

178 

11  52 

238 

15  52 

298 

19  62 

358 

23  62 

59 

3  56 

119 

7  56 

179 

11  56 

239 

15  56 

299 

19  66 

359 

23  56 

60 

4  0 

120 

8  0 

180 

12  0 

240 

16  0 

300 

20  0 

360 

24  0 

MoTK.— When  turning  seconds  of  arc  into  time,  and  vice  versa,  it  should  be  remembered  that  the  fractions  are  slxtiethar 
thus,  the  value  in  time  ol  42"  is  not  2*.48,  but  S^U-a^.S. 


Page  642] 

TABLE  8. 
Sidereal  into  Mean  Solar  Time. 

73 

To  be  subtracted  from  a  sidereal  time  interral. 

Ofc 

1" 

21. 

3t 

4h 

Sh 

Ok 

7h 

For  seconds. 

TO. 

0 

1 

2 
3 
4 

m.    «. 
0  0.000 
0  0.164 
0  0.  328 
0  0. 491 
0  0. 655 

m.   s. 
0  9.830 
0  9.993 
0  10. 157 
0  10.  321 
0  10.  485 

TO.    8. 

0  19. 659 
0  19. 823 
0  19.987 
0  20. 151 
0  20.  314 

TO.    «. 

0  29.  489 
0  29. 653 
0  29.  816 
0  29. 980 
0  30. 144 

TO.    S. 

0  39. 318 
0  39.482 
0  39. 646 
0  39. 810 
0  39. 974 

m.      s. 
0  49. 148 
0  49. 312 
0  49.  475 
0  49. 639 
0  49.  803 

m.  s. 
0  58. 977 
0  59. 141 
0  59. 305 
0  59.  469 
0  59. 633 

TO. 

8.807 
8.971 
9.135 
9.298 
9.462 

s. 

1 
2 
3 
4 

s. 

0.003 
.005 
.008 
.011 

5 
6 
7 
8 
9 

0  0.  819 
0  0. 983 
0  1. 147 
0  1.311 
0  1.474 

0  10.649 
0  10.813 
0  10.976 
0  11. 140 
0  11. 304 

0  20.  478 
0  20.  642 
0  20.  806 
0  20.  970 
0  21. 134 

0  30. 308 
0  30.  472 
0  30.  635 
0  30.  799 
0  30. 963 

0  40. 137 
0  40.  301 
0  40. 465 
0  40.  629 
0  40.  793 
0  40.  956 
0  41. 120 
0  41. 284 
0  41.  448 
0  41.612 

0  49. 967 
0  50. 131 
0  50.  295 
0  50. 458 
0  50. 622 

0  59.  796 

0  59. 960 

1  0.124 
1  0.288 
1  0.452 

9.626 

9.790 

9.954 

10. 118 

10.  281 

5 
6 

7 
8 
9 

.014 
.016 
.019 
.022 
.025 

10 
11 
12 
13 
14 

0  1.  638 
0  1.  802 
0  1.966 
0  2. 130 
0  2.  294 

0  11.  468 
0  11.  632 
0  11.  795 
0  11.  959 
0  12. 123 

0  21. 297 
0  21. 461 
0  21. 625 
0  21. 789 
0  21. 953 

0  31. 127 
0  31.  291 
0  31. 455 
0  31.  618 
0  31.  782 

0  50.  786 
0  50. 950 
0  51.114 
0  51. 278 
0  51. 441 

1  0.616 
1  0.779 
1  0.943 
1  1. 107 
1  1.271 

10.445 
10. 609 
10.  773 
10.  937 
11. 100 

10 
11 
12 
13 
14 

.027 
.030 
.033 
.035 
.038 

15 
16 
17 
18 
19 

0  2. 457 
0  2.  621 
0  2.  785 
0  2. 949 
0  3. 113 

0  12.  287 
0  12.  451 
0  12.  615 
0  12.  778 
0  12.  942 

0  22. 117 
0  22. 280 
0  22.  444 
0  22.  608 

0  22.  772 

0  31.  946 
0  32. 110 
0  32.  274 
0  32.  438 
0  32.  601 

0  41.  776 
0  41.  939 
0  42. 103 
0  42.  267 
0  42.  431 

0  51.605 
0  51.  769 
0  51. 933 
0  52. 097 
0  52. 260 

1  1. 435 
1  1. 599 
1  1.762 
1  1.926 
1  2. 090 

11.  264 
11. 428 
11. 592 
11. 756 
11.920 

15 
16 
17 
18 
19 

.041 
.044 
.046 
.049 
.052 
.055 
.057 
.060 
.063 
.066 

20 
21 
22 
23 
24 

0  3. 277 
0  3.440 
0  3. 604 
0  3.  768 
0  3. 932 

0  13. 106 
0  13.270 
0  13. 434 
0  13.598 
0  13. 761 

0  22. 936 
0  23. 099 
0  23.  263 
0  23.  427 
0  23. 591 

0  32. 765 
0  32. 929 
0  33. 093 
0  33. 257 
0  33.420 

0  42.  595 
0  42. 759 
0  42. 922 
0  43. 086 
0  43. 250 

0  52.  424 
0  52.  588 
0  52. 752 
0  52. 916 
0  53. 080 

1  2.254 
1  2.418 
1  2. 582 
1  2. 745 
1  2. 909 

12. 083 
12.  247 
12.411 
12. 575 
12.  739 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

0  4.096 
0  4.  259 
0  4. 423 
0  4. 587 
0  4.  751 

0  13.925 
0  14.089 
0  14. 253 
0  14.417 
0  14. 581 

0  23.  755 
0  23. 919 
0  24. 082 
0  24.  246 
0  24. 410 

0  33. 584 
0  33.  748 
0  33. 912 
0  34. 076 
0  34.  240 

0  43. 414 
0  43. 578 
0  43.  742 
0  43. 905 
0  44. 069 

0  53. 243 
0  53. 407 
0  53.  571 
0  53. 735 
0  53.  899 

1  3.073 
1  3.237 
1  3. 401 
1  3.564 
1  3.728 

12.  903 
13.066 
13. 230 
13. 394 

13.  558 

25 
26 

27 
28 
29 

.068 
.071 
.074 
.076 
.079 

30 
31 
32 
33 
34 

0  4. 915 
0  5.  079 
0  5.  242 
0  5. 406 
0  5. 570 

0  14.  744 
0  14.908 
0  15.072 
0  15.  236 
0  15.  400 

0  24.  574 
0  24.  738 
0  24. 902 
0  25.065 
0  25. 229 

0  34. 403 
0  34.  567 
0  34.  731 
0  34.  895 
0  35.  059 

0  44.  233 
0  44.  397 
0  44. 561 
0  44.  724 
0  44.  888 

0  54. 063 
0  54.  226 
0  54.  390 
0  54.  554 

0  54.  718 

1  3.892 
1  4.056 
1  4. 220 
1  4.384 
1  4.547 

13.  722 
13. 886 
14. 049 
14.213 

14.  377 

30 
31 
32 
33 
34 

.082 
.085 
.087 
.090 
.093 

35 
36 
37 
38 
39 

0  5.  734 
0  5. 898 
0  6. 062 
0  6. 225 
0  6.  389 

0  15.563 
0  15. 727 
0  15. 891 
0  16. 055 
0  16.  219 

0  25. 393 
0  25. 557 
0  25.  721 
0  25. 885 
0  26. 048 

0  35.  223 
0  35.  386 
0  35. 550 
0  35.  714 
0  35. 878 

0  45. 052 
0  45.  216 
0  45.  380 
0  45.  544 
0  45.  707 

0  54. 882 
0  55.  046 
0  55. 209 
0  55.  373 
0  55.  537 

1  4.711 
1  4. 875 
1  5.039 
1  5.203 
1  5.367 

14.  541 
14.  705 

14.  868 

15.  032 
15. 196 

35 
36 
37 
38 
39 

.096 
.098 
.101 
.104 
.106 

40 
41 
42 
43 
44 

0  6. 553 
0  6.  717 
0  6.  881 
0  7.045 
0  7.  208 

0  16.383 
0  16.546 
0  16.  710 
0  16.874 
0  17.  038 

0  26.  212 
0  26.  376 
0  26. 540 
0  26.  704 
0  26.  867 

0  36. 042 
0  36.  206 
0  36.  369 
0  36.  533 
0  36. 697 

0  45. 871 
0  46.035 
0  46. 199 
0  46.  363 
0  46.  527 

0  55. 701 
0  55. 865 
0  56. 028 
0  56. 192 
0  56. 356 

1  5.530 
1  5.694 
1  5.858 
1  6. 022 
i     6. 186 

15. 360 
15. 524 

15.  688 
15. 851 

16.  015 

40 
41 
42 
43 
44 

.109 
.112 
.115 
.117 
.120 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

0  7.372 
0  7.536 
0  7. 700 
0  7.864 
0  8.  027 

0  17.202 
0  17.366 
0  17.529 
0  17.693 
0  17.  857 

0  27. 031 
0  27. 195 
0  27. 359 
0  27.  523 
0  27.  687 

0  36.  861 
0  37. 025 
0  37. 188 
0  37.  352 
0  37.  516 

0  46.  690 
0  46. 854 
0  47.018 
0  47. 182 
0  47. 346 

0  56. 520 
0  56. 684 
0  56.  848 
0  57.  Oil 
0  57. 175 

1  6.350 
1  6. 513 
1  6.677 
1  6.841 
1  7.005 

-J- 

16. 179 
16.  343 
16.  507 
16.  671 
16.  834 

45 
46 

47 
48 
49 

.123 
.126 
.128 
.131 
.134 

0  8. 191 
0  8.  355 
0  8.519 
0  8.  683 
0  8.  847 

0  18.021 
0  18. 186 
0  18. 349 
0  18.  512 
0  18.676 

0  27. 850 
0  28.014 
0  28. 178 
0  28. 342 
0  28. 506 

0  37. 680 
0  37.  844 
0  38.  008 
0  38. 171 
0  38.  335 

0  47. 510 
0  47.  673 
0  47.  837 
0  48. 001 
0  48. 165 

0  57. 339 
0  57. 503 
0  57.  667 
0  57.  831 
0  57.  994 

1  7. 169 
1  7. 332 
1  7. 496 
1  7.660 
1  7.824 

16. 998 
17. 162 
17.  326 
17. 490 
17.  654 

50 
51 
52 
53 
54 

.137 
.139 
.142 
.145 
.147 

55 
56 
57 
58 
59 

0  9. 010 
0  9. 174 
0  9. 338 
0  9. 502 
0  9.  666 

0  18.840 
0  19.004 
0  19. 168 
0  19. 331 
0  19. 495 

0  28. 670 
0  28.  833 
0  28. 997 
0  29. 161 
0  29.  325 

0  38. 499 
0  38. 663 
0  38.  827 
0  38. 991 
0  39. 154 

0  48. 329 
0  48.  492 
0  48. 656 
0  48.  820 
0  48.  984 

0  58. 158 
0  58. 322 
0  58. 486 
0  58.  650 
0  58. 814 
1 . 

1  7. 988 
1  8.152 
1  8. 315 
1  8. 479 
1  8.643 

17.817 

17.  981 
18. 145 
18. 309 

18.  473 

55 
56 
57 
58 
59 

.150 
.153 
.156 
.158 
0.161 

TABLE  8.                  [Page  643 
Sidereal  into  Mean  Solar  Time. 

To  be  subtracted  from  a  sidereal  time  interval.                       ,  1 

SO 

9* 

10k 

llfc 

121. 

Igi- 

u^ 

15fc 

For  seconds.! 

m. 
0 

1 

2 
3 
4 

m.      «. 
1  18.636 
1  18.800 
1  18.964 
'  1  19.128 
1  19.292 

m.   «. 
1  28.466 
1  28.630 
1  28.  794 
1  28.958 
1  29. 121 

m.   «. 
1  38.  296 
1  38.459 
1  38.623 
1  38.787 
1  38.951 

■m.      8. 
1  48.125 
1  48.289 
1  48.453 
1  48.617 
1  48.  780 

m.      s. 
1   57.965 
1  58. 119 
1  58.282 
1  68.446 
1  58.610 

2  7.784 
2  7.948 
2  8.112- 
2  8.276 
2  8.440 

in.      t. 
2  17.614 
2  17.  778 
2  17.941 
2  18. 105 
2  18.  269 

m.      8. 
2  27.443 

2  27. 607 
2  27.  771 
2  27.  935 
2  28. 099 

8. 

1 
2 
3 
4 

0.003 
.005 
.008 
.011 

5;  1  19.456 

6  1  19.619 

7  1  19.783 

8  1  19.947 

9  1  20.  Ill 
10  1  20.275 
11 1  1  20.  439 

12  1  1  20. 602 

13  ;  1  20.  766 
141  1  20.930 

1  29.285 
1  29.449 
1  29.613 
1  29.  777 
1  29.940 
1  30. 104 
1  30.  268 
1  30.432 
1  30.696 
1  30.  760 

1  39.115 
1  39.279 
1  39.442 
1  39.606 
1  39. 770 

1  48.944 
1  49.  108 
1  49.272 
1  49.436 
1  49.600 

1  68.  774 
1  58.938 
1  69. 101 
1  69.  265 
1  59.429 

2  8.603 
2  8.767 
2  8.931 
2  9.095 
2  9.259 

2  18. 433  2  28.  263 
2  18. 597  2  28.  426 
2  18.  761  2  28. 590 
2  18. 924  2  28.  764 
2  19.  088  2  28. 918 

5 
6 

7 
8 
9 

.014 
.016 
.019 
.022 
.025 

1  39.934 
1  40.098 
1  40.  261 
1  40.425 
1  40.589 

1  49.  763 
1  49.927 
1  60.091 
1  50.256 
1  60.419 

1  69.593 
1  59. 757 

1  59.921 

2  0.084 
2  0.248 

2  9.423 
2  9.586 
2  9.760 
2  9.914 
2  10.078 
2  10.242 
2  10.405 
2  10.669 
2  10.  733 
2  10.897 

2  19.252 
2  19.416 
2  19.580 
2  19.  744 
2  19.907 

2  29. 082 
2  29.  245 
2  29.409 
2  29. 673 
2  29.  737 

10 
11 
12 
13 
14 

.027 
.030 
.033 
.036 
.038 

15 
16 
17 
18 
19 

1  21.094 
i  21.258 
i  21.422 
i  21.585 
1  21.749 

1  30.923 
1  31.087 
1  31.261 
1  31.415 
1  31.579 

1  40.  753 
1  40.917 
1  41.081 
1  41.244 
1  41.408 

1  50.583 
1  50.  746 
1  50.910 
1  51.074 
1  51.238 

2  0.412 
2  0.576 
2  0.740 
2  0.904 
2  1.067 

2  20.  071 
2  20.235 
2  20.  399 
2  20.563 
2  20. 727 

2  29.901 
2  30.  065 
2  30. 228 
2  30. 392 
2  30. 566 

16 
16 
17 
18 
19 

.041 
.044 
.046 
.049 
.052 
.055 
.057 
.060 
.063 
.066 

20 
21 
22 
23 
24 

1  21.913 
1  22.077 
1  22.241 
1  22.404 
1  22.568 

1  31.743 
1  31.906 
1  32.070 
1  32.234 
1  32.398 

1  41.672 
1  41.  736 
1  41.900 
1  42.064 
1  42.  227 

1  61.402 
1  51.665 
1  51.729 
1  51.893 
1  62.057 

2  1.231 
2  1.395 
2  1.569 
2  1.723 
2  1.887 

2  11.061 
2  11. 225 
2  11.388 
2  11.562 
2  11. 716 

2  20. 890 
2  21.064 
2  21.218 
2  21.  382 
2  21.646 

2  30.  720 
2  30.  884 
2  31. 048 
2  31.211 
2  31.  376 

20 
21 
22 
23 
24 

26 
26 

27 
28 
29 

1  22.  732 
1  22.896 
1  23.060 
1  23.224 
1  23,387 

1  32.562 
1  32.  726 
1  32.889 
1  33.053 
1  33.217 

1  42.391 
1  42.  665 
1  42.  719 
1  42.883 
1  43.047 

1  52.221 
1  62.385 
1  52.548 
1  52.  712 
1  52.876 

2  2.050 
2  2.214 
2  2.378 
2  2.642 
2  2.706 

2  11.880 
2  12.044 
2  12.208 
2  12.371 
2  12.535 

2  21.  709 
2  21.873 
2  22.037 
2  22.201 
2  22.365 

2  31. 539 
2  31.  703 
2  31.  867 
2  32. 031 
2  32. 194 

26 
26 
27 
28 
29 
30 
31 
32 
33 
34 

.068 
.071 
.074 
.076 
.079 
.082 
.085 
.087 
.090 
.093 

30 
31 
32 
33 
34 

1  23.551 
1  23.  715 
1  23.  879 
1  24.043 
1  24.207 

1  33.381 
1  33.545 
1  33.708 
1  33.872 
1  34.036 

1  43.210 
1  43.374 
1  43.638 
1  43. 702 
1  43.866 

1  53.040 
1  63.204 
1  63.  368 
1  53.531 
1  53.695 

2  2.869 
2  3.033 
2  3.197 
2  3.361 
2  3.525 

2  12.699 
2  12.863 
2  13. 027 
2  13.191 
2  13.354 

2  22. 629 
2  22.  692 
2  22.  856 
2  23. 020 
2  23. 184 

2  32.  358 
2  32.  622 
2  32. 686 
2  32. 860 
2  33.013 

35 
36 
37 
38 
39 

1  24.370 
1  24.534 
1  24.698 
1  24.862 
1  25.026 

1  34.200 
1  34.364 
1  34.528 
1  34.691 
1  34.855 

1  44.029 
1  44. 193 
1  44.357 
1  44.621 
1  44.686 

1  53.  859 
1  54.023 
1  54. 187 
1  54.351 
1  54.514 

2  3.689 
2  3.852 
2  4.016 
2  4.180 
2  4.344 

2  13.518 
2  13.682 
2  13. 846 
2  14.010 
2  14.173 

2  23.  348 
2  23.512 
2  23. 675 
2  23.  839 
2  24.003 

2  33. 177 
2  33.  341 
2  33.  506 
2  33. 669 
2  33.  833 

35 

36 
37 
38 
39 

.096 
.098 
.101 
.104 
.106 

40 
41 
42 
43 
44 

1  25.190 
1  26.353 
1  25.617 
1  25.681 
1  25.846 

1  35.019 
1  36. 183 
1  36.347 
1  35.511 
1  35.674 

1  44.849 
1  46.  012 
1  45. 176 
1  46.340 
1  45.  604 

1  54.678 
1  54.842 
1  55.006 
1  55. 170 
1  55.333 

2  4.608 
2  4.672 
2  4.835 
2  4.999 
2  6.163 

2  14.337 
2  14.501 
2  14.  665 
2  14.829 
2  14.993 

2  24. 167 
2  24. 331 
2  24. 495 
2  24. 668 
2  24.  822 

2  33.  996 
2  34. 160 
2  34.  324 
2  .34.  488 
2  34.652 

40 
41 
42 
43 
44 

.109 
.112 
.115 
.117 
.120 

45 
46 

47 
48 
49 

1  26.009 
1  26.172 
1  26.336 
1  26.500 
1  26.664 

1  35.838 
1  36.002 
1  36.166 
1  36.330 
1  36.493 

1  45.668 
1  45.  832 
1  46.995 
1  46. 169 
1  46.323 

1  65.497 
1  65.661 
1  55.825 
1  65. 989 
1  66. 163 

2  5.327 
2  5.491 
2  5.655 
2  5.818 
2  5.982 

2  15. 156 
2  15. 320 
2  15.484 
2  15.648 
2  15.812 

2  24. 986 
2  25. 150 
2  25.  314 
2  25.477 
2  26.641 

2  34.816 
2  34. 979 
2  35. 143 
2  35. 307 
2  35.471 
2  35. 635 
2  35.  798 
2  36.  962 
2  36. 126 
2  36.  290 
2  36. 454 
2  36.  618 
2  36.  781 
2  36.  945 
2  37. 109 

45 
46 
47 
48 
49 

.123 
.126 
.128 
.131 
.134 

50 
51 
52 
53 

54 

1  26.828 
1  26.992 
1  27.156 
1  27.319 
1  27.483 

1  36.  657 
1  36.821 
1  36.985 
1  37.149 
1  37.313 

1  46.487 
1  46.651 
1  46.816 
1  46.978 
1  47.142 

1  56.  316 
1  66.480 
1  66.644 
1  66.808 
1  66.972 

2  6.146 
2  6.310 
2  6.474 
2  6.637 
2  6.801 

2  16.976 
2  16. 139 
2  16.  303 
2  16.467 
2  16.631 

2  25. 805 
2  26.969 
2  26. 133 
2  26. 297 
2  26. 460 

50 
51 
62 
63 
54 

.137 
.139 
.142 
.145 
.147 

55 
56 
57 
58 
59 

1  27.647 
1  27.811 
1  27.975 
1  28. 138 
1  28.302 

1  37.476 
1  37.  640 
1  37.  804 
1  37.968 
1  38.132 

1  47.306 
1  47.470 
1  47.634 
1  47.  797 
1  47.961 

1  57. 136 
1  57.  299 
1  57.463 
1  57.627 
1  57. 791 

2  6.965 
2  7.129 
2  7.293 
2  7.467 
2  7.620 

2  16. 795 
2  16.969 
2  17. 122 
2  17.286 
2  17.460 

2  26.  624 
2  26. 788 
2  26. 962 
2  27. 116 
2  27.  280 

55 
56 
57 
68 
59 

.150 
.153 
.156 
.168 
0.161 

Page  644] 


TABLE  8. 
Sidereal  into  Mean  Solar  Time. 


To  be  subtracted  from  a  sidereal  time  interval. 


50 
51 
52 
53 
54 
55 
56 
57 
58 
69 


16k 


2  37.273 
2  37.  437 
2  37.  601 
2  37.  764 
2  37.  928 


38.092 
38. 256 
38. 420 
38. 584 
38.  747 


2  38.  911 
2  39.075 
2  39.  239 
2  39.403 
2  39. 566 


2  39.  730 
2  39. 894 
2  40.  058 
2  40.  222 
2  40.  386 


2  40.  549 
2  40.  713 
2  40.  877 
2  41.041 
2  41.  205 


2  41.369 
2  41. 532 
2  41.  696 
2  41.  860 
2  42. 024 


2  42. 188 
2  42.  352 
2  42. 515 
2  42.  679 
2  42. 843 


43.007 
43. 171 
43. 334 
43. 498 
43.  662 


43.  826 
43. 990 
44.154 
44. 317 
44. 481 


44.645 
44.809 
44.  973 
45. 137 
45. 300 


45.464 
45. 628 
45.  792 
45. 956 
46. 120 


46. 283 
46. 447 
46.611 
46. 755 
46.939 


170 


47. 102 
47.266 
47. 430 
47.  594 
47.  758 


2  47. 922 
2  48. 085 
2  48.  249 
2  48.413 
2  48. 577 


2  48.  741 
2  48. 905 
2  49. 068 
2  49.  232 
2  49. 396 


2  49. 560 
2  49.  724 
2  49. 888 
2  50.051 
2  50. 215 


2  50. 379 
2  50. 543 
2  50.  707 
2  50. 870 
2  51. 034 


2  51. 198 
2  51.  362 
2  51.526 
2  51. 690 
2  51.  853 


2  52. 017 
2  52. 181 
2  52.  345 
2  52. 509 
2  52.  673 


2  52. 836 
2  53.000 
2  53. 164 
2  53. 328 
2  53. 492 


2  53.  656 
2  53. 819 
2  53.983 
2  54. 147 
2  54. 311 


2  54. 475 
2  54.  638 
2  54. 802 
2  54. 966 
2  55. 130 


55.294 
55.458 
55. 621 
55.785 
55. 949 


2  56. 113 
2  56. 277 
2  56. 441 
2  56. 604 
2  56.  768 


ISO 


2  56. 932 
2  57. 096 
2  57.  260 
2  57.424 
2  57. 587 


57.  751 
57. 915 
58. 079 
58. 243 
58. 406 


2  58. 570 
2  58.  734 
2  58. 898 
2  59. 062 
2  59.  226 


2  59. 389 
2  59. 553 
2  59.  717 

2  59.  881 

3  0.045 


0.209 
0.372 
0.  536 
0.700 
0.864 
1.028 
1.192 
1.355 
1.519 
1.683 


1.847 
2.011 
2.174 
2.338 
2.502 


2.666 
2.830 
2.994 
3.157 
3.321 


3.485 
3.649 
3.813 
3.977 
4.140 


4.304 
4.468 
4.632 
4.796 
4.960 


5.123 
5.287 
5.451 
5.615 
5.779 


5.942 
6.106 
6.270 
6.434 
6.598 


ISfc 


6.762 
6.925 
7.089 
7.253 
7.417 


7.581 
7.745 
7.908 
8.072 
8.236 


8.400 
8.564 
8.728 
8.891 
9.055 


9.219 
9.383 
9.547 
9.710 
9.874 


10. 038 
10.  202 
10.  366 
10.  530 
10.  693 


3  10.857 
3  11.021 
3  11. 185 
3  11.349 
3  11.513 


3  11.676 
3  11.840 
3  12.004 
3  12.168 
3  12.  332 


12. 496 
12.659 
12. 823 
12. 987 
13. 151 


13.  315 
13. 478 
13.642 
13.806 
13. 970 


14. 134 
14.298 
14. 461 
14. 625 
14.  789 


14. 953 
15. 117 
15.  281 
15.444 
15.608 


3  15.  772 
3  15. 936 
3  16. 100 
3  16.264 
3  16.427 


20» 


3  16.591 
3  16.  755 
3  16.919 
3  17.083 
3  17.246 
3  17.410 
3  17.574 
3  17. 738 
3  17.902 
3  18.066 


3  18.229 
3  18.  .393 
3  18.557 
3  18.  721 
3  18.  885 


3  19.049 
3  19.212 
3  19.376 
3  19.540 
3  19.  704 


19. 868 
20. 032 
20. 195 
20. 359 
20. 523 


3  20. 687 
3  20.851 
3  21.014 
3  21. 178 
3  21.  342 


3  21.  506 
3  21.670 
3  21. 834 
3  21.997 
3  22. 161 


3  22. 325 
3  22. 489 
3  22. 653 
3  22.  817 
3  22.  980 


23. 144 
23. 308 
23. 472 
23. 636 
23.  800 


3  23. 963 
3  24. 127 
3  24.  291 
3  24.  455 
3  24. 619 


3  24.  782 
3  24.946 
3  25. 110 
3  25. 274 
3  25. 438 


3  25.602 
3  25.  765 
3  25.929 
3  26. 093 
3  26.257 


aih 


3  26.421 
3  26. 585 
3  26.  748 
3  26.  912 
3  27.076 


3  27.  240 
3  27.  404 
3  27. 568 
3  27. 731 
3  27. 895 


3  28.  059 
3  28. 223 
3  28.  387 
3  28.550 
3  28.  714 


28. 878 
29.042 
29.206 
29.  370 
29. 533 


3  29.  697 
3  29.  861 
3  30. 025 
3  30. 189 
3  30.  353 


3  30. 516 
3  30.  680 
3  30.844 
3  31. 008 
3  31. 172 


3  31.336 
3  31. 499 
3  31.  663 
3  31. 827 
3  31.991 


3  32. 155 
3  32. 318 
3  32. 482 
3  32.  646 
3  32. 810 


3  32.974 
3  33. 138 
3  33. 301 
3  33.465 
3  33. 629 


3  33.  793 
3  33.957 
3  34. 121 
3  34.284 
3  34. 448 


3  34. 612 
3  34.  776 
3  34.940 
3  35.104 
3  35. 267 


3  35. 431 
3  35.  595 
3  35.  759 
3  35.  923 
3  36.086 


22i> 


36. 250 
36.  414 
36. 578 
36. 742 
36. 906 


3  37.069 
3  37. 233 
3  37.  397 
3  37.  561 
3  37.  725 


3  37.  889 
3  38. 052 
3  38.  216 
3  38. 380 
3  38. 544 


3  38.  708 
3  38.  871 
3  39.035 
3  39. 199 
3  39. 363 


3  39.527 
3  39.  691 
3  39. 854 
3  40. 018 
3  40. 182 


3  40. 346 
3  40. 510 
3  40.674 
3  40.  837 
3  41. 001 


3  41. 165 
3  41. 329 
3  41. 493 
3  41. 657 
3  41.  820 


3  41. 984 
3  42. 148 
3  42. 312 
3  42. 476 
3  42. 639 


3  42.  803 
3  42. 967 
3  43. 131 
3  43. 295 
3  43. 459 


3  43.622 
3  43. 786 
3  43. 950 
3  44. 114 
3  44.  278 


3  44.442 
3  44.605 
3  44.  769 
3  44. 933 
3  45. 097 


3  45. 261 
3  45.425 
3  45. 588 
3  45.  752 
3  45. 916 


28'' 


46.  080 
46.  244 
46. 407 
46. 571 
46.  735 


3  46.  899 
3  47. 063 
3  47.  227 
3  47.  390 
3  47.  554 


3  47.  718 
3  47.  882 
3  48. 046 
3  48.210 
3  48.  373 


48. 537 
48.  701 
48.865 
49. 029 
49. 193 


3  49. 356 
3  49. 520 
3  49.  684 
3  49. 848 
3  50. 012 


3  50. 175 
3  50.  339 
3  50. 503 
3  50. 667 
3  50.  831 


50. 995 
51. 158 
51. 322 
51. 486 
51.650 


3  51.  814 
3  51. 978 
3  52. 141 
3  52.  305 
3  52. 469 


3  52. 633 
3  52.  797 
3  52.  961 
3  53. 124 
3  53. 288 


3  53. 452 
3  53. 616 
3  53. 780 
3  53.  943 
3  54. 107 


3  54. 271 
3  54. 435 
3  54. 599 
3  54.  763 
3  54. 926 


3  55. 090 
3  55. 254 
3  55. 418 
3  55. 582 
3  55, 746 


For  seconds. 


TABLE  9. 

[Page  646  | 

Mean  Solar  into  Sidereal  Time. 

s 

To  be  added  to  a  mean  time  interval.                           1 

Oh      1 

lb 

Sh 

3>> 

4h 

oh 

6h 

7h 

For  secondsJ 

m. 
0 

1 

2 
3 
4 

m. 
0 

0 
0 
0 
0 

0.000 
0.164 
0.329 
0.493 
0.657 

m.    t. 

0  9.856 
0  10.021 
0  10. 185 
0  10. 349 
0  10. 514 

m.  s. 

0   19.  713 
0  19. 877 
0  20. 041 
0  20.  206 
0  20. 370 
0  20. 534 
0  20.  699 
0  20.  863 
0  21. 027 
0  21. 191 

m.  s. 

0  29. 569 
0  29.  734 
0  29. 898 
0  30. 062 
0  30.  227 

m.  8. 

0  39.426 
0  39. 590 
0  39. 754 
0  39.  919 
0  40.  083 

m.  «. 
0  49.  282 
0  49. 447 
0  49.611 
0  49.  775 
0  49. 939 

m.  1. 
0  59. 139 
0  59.  303 
0  59. 467 
0  59. 632 
0  59.  796 

m.  s. 
1  8.995 
1  9.160 
1  9.324 
1  9.488 
1  9.652 

«. 

1 
2 
3 

4 

s. 

0.003 
.005 
.008 
.011 

5 
6 

7 
8 
9 

0 
0 
0 
0 
0 

0.821 
0.986 
1.150 
1.314 
1.478 

0  10.678 
0  10.  842 
0  11.006 
0  11.171 
0  11.335 

0  30.391 
0  30. 555 
0  30.  719 
0  30. 884 
0  31. 048 

0  40. 247 
0  40. 412 
0  40. 576 
0  40.  740 
0  40.904 

0  50. 104 
0  50.  268 
0  50.432 
0  50. 597 
0  50.  761 

0  59. 960 

1  0.124 
1  0.289 
1  0. 453 
1  0.617 

1  9.817 
1  9.981 
1  10.145 
1  10.310 
1  10.474 

5 
6 

7 
8 
9 

.014 
.016 
.019 
.022 
.025 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

0 
0 
0 
0 
0 

1.643 
1.807 
1.971 
2.136 
2.300 

0  11.  499 
0  11.663 
0  11. 828 
0  11.992 
0  12. 156 

0  21. 356 
0  21. 520 
0  21.  684 
0  21.8i9 
0  22. 013 

0  31.  212 
0  31. 376 
0  31. 541 
0  31.  705 
0  31. 869 

0  41.069 
0  41.  233 
0  41. 397 
0  41.561 
0  41.  726 

0  50.  925 
0  51. 089 
0  51.  254 
0  51.418 
0  51. 582 

0.782 
0.946 
1.110 
1.274 
1.439 

1  10.638 
1  10.802 
1  10.967 
1  11.131 
1  11.295 

10 
11 
12 
13 
14 

.027 
.030 
.033 
.036 
.038 

0 
0 
0 
0 
0 

2.464 
2.628 
2.793 
2.957 
3.121 

0  12.321 
0  12. 485 
0  12.649 
0  12.  813 
0  12.978 

0  22. 177 
0  22. 341 
0  22.506 
0  22.670 
0  22.  834 

0  32. 034 
0  32. 198 
0  32.  362 
0  32.526 
0  32. 691 

0  41.890 
0  42.054 
0  42. 219 
0  42.  383 
0  42. 547 

0  51.  746 
0  51.911 
0  52. 075 
0  52.  239 
0  52. 404 

1.603 
1.767 
1.932 
2.096 
2.260 

1  11.459 
1  11.624 
1  11.788 
1  11.952 
1  12.117 

15 
16 
17 
18 
19 

.041 
.044 
.047 
.049 
.052 

0 
0 
0 
0 
0 

3.285 
3.450 
3.614 
3.778 
3.943 

0  13. 142 
0  13. 306 
0  13. 471 
0  13. 636 
0  13.799 

0  22. 998 
0  23. 163 
0  23.  327 
0  23. 491 
0  23.656 

0  32. 855 
0  33. 019 
0  33.183 
0  33. 348 
0  33. 512 

0  42.711 
0  42. 876 
0  43. 040 
0  43.204 
0  43.368 

0  52. 568 
0  52.  732 
0  52.  896 
0  53. 061 
0  53. 225 

2.424 
2.589 
2.753 
2.917 
3.081 

1  12.281 
1  12.445 
1  12.609 
1  12.  774 
1  12.938 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

.055 
.067 
.060 
.063 
.066 
.068 
.071 
.074 
.077 
.079 

25 
26 
27 
28 
29 

0 
0 
0 
0 
0 

4.107 
4.271 
4.435 
4.600 
4.764 

0  13.963 
0  14. 128 
0  14. 292 
0  14.456 
0  14.620 

0  23. 820 
0  23.984 
0  24. 148 
0  24. 313 
0  24. 477 

0  33. 676 
0  33. 841 
0  34. 005 
0  34. 169 
0  34.  333 

0  43.  533 
0  43. 697 
0  43.  861 
0  44. 026 
0  44.190 

0  53. 389 
0  53. 554 
0  53.  718 
0  53.  882 
0  54.046 

3.246 
3.410 
3.574 
3.739 
3.903 

1  13.102 
1  13.266 
1  13.431 
1  13.595 
1  13.759 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

0 
0 
0 
0 
0 

4.928 
5.093 
5.257 
5.421 
5.585 

0  14.  785 
0  14.949 
0  15. 113 
0  15.  278 
0  15.  442 

0  24,  641 
0  24.  805 
0  24. 970 
0  25. 134 
0  25.  298 

0  34.  498 
0  34.662 
0  34. 826 
0  34.990 
0  35. 155 

0  44.  354 
0  44. 518 
0  44. 683 
0  44.  847 
0  45.  Oil 

0  54.  211 
0  54.  375 
0  54. 539 
0  54.  703 
0  54. 868 

4.067 
4.231 
4.396 
4.560 
4.724 

1  13.924 
1  14.088 
1  14.252 
1  14.416 
1  14.581 

30 
31 
32 
33 
34 
36 
36 
37 
38 
39 

.082 
.085 
.088 
.090 
.093 
.096 
.099 
.101 
.104 
.107 

0 
0 
0 
0 
0 

5.750 
5.914 
6.078 
6.242 
6.407 

0  15.606 
0  15.770 
0  15.935 
0  16.099 
0  16.  263 

0  25. 463 
0  25. 627 
0  25.  791 
0  25. 955 
0  26. 120 

0  35.  319 
0  35.483 
0  35.648 
0  35.  812 
0  35. 976 

0  45. 176 
0  45.340 
0  45. 504 
0  45.668 
0  45.833 

0  55. 032 
0  55.196 
0  55.  361 
0  55.  525 
0  55. 689 

4.888 
5.053 
5.217 
5.381 
5.546 

1  14.745 
1  14.909 
1  15.073 
1  15.238 
1  15.402 

40 
41 
42 
43 
44 

0 
0 
0 
0 
0 

6.571 
6.735 
6.900 
7.064 
7.228 

0  16.  427 
0  16.592 
0  16.  756 
0  16.920 
0  17.085 

0  26.  284 
0  26.  448 
0  26. 612 
0  26.  777 
0  26. 941 

0  36. 140 
0  36.  305 
0  36. 469 
0  36.633 
0  36. 798 

0  45.997 
0  46. 161 
0  46. 325 
0  46.490 
0  46. 654 

0  55.  853 
0  56. 018 
0  56. 182 
0  56.346 
0  56.  510 

5.710 

5.874 
6.038 
6.203 
6.367 

1  15.566 
1  15. 731 
1  15.895 
1  16.059 
1  16.223 

40 
41 
42 
43 
44 

.110 
.112 
.115 
.118 
.120 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

7.392 
7.557 
7.721 
7.885 
8.049 

0  17.249 
0  17.  413 
0  17. 577 
0  17. 742 
0  17.906 

0  27. 105 
0  27.  270 
0  27.  434 
0  27. 598 
0  27.  762 

0  36. 962 
0  37. 126 
0  37.290 
0  37.455 
0  37. 619 

0  46.  818 
0  46. 983 
0  47. 147 
0  47. 311 
0  47. 475 

0  56. 675 
0  56.  839 
0  57. 003 
0  57. 168 
0  57.  332 

T 

6.531 
6.695 
6.860 
7.024 
7.188 
7.353 
7.517 
7.681 
7.845 
8.010 

1  16.388 
1  16.552 
1  16.716 
1  16.881 
1  17.045 

45 
46 
47 
48 
49 

.123 
.126 
.129 
.131 
.134 

8.214 
8.378 
8.542 
8.707 
8.871 

0  18.070 
0  18.234 
0  18. 399 
0  18.563 
0  18.  727 

0  27. 927 
0  28. 091 
0  28.  255 
0  28.420 
0  28. 584 

0  37. 783 
0  37. 947 
0  38. 112 
0  38.  276 
0  38. 440 

0  47.640 
0  47.  804 
0  47. 968 
0  48. 132 
0  48.  297 

0  57.  496 
0  57.660 
0  57.  825 
0  57.  989 
0  58. 153 

1  17.209 
1  17.373 
1  17.538 
1  17.702 
1  17.866 

50 
51 
52 
53 
64 

.137 
.140 
.142 
.145 
.148 

55 
56 
57 
58 
59 

0 
0 
0 
0 
0 

9.035 
9.199 
9.364 
9.528 
9.692 

0  18.892 
0  19.056 
0  19.  220 
0  19.384 
0  19.549 

0  28.  748 
0  28.  912 
0  29.  077 
0  29.  241 
0  29.  405 

0  38.  605 
0  38.  769 
0  38.  933 
0  39.  097 
0  39.  262 

0  48.  461 
0  48. 625 
0  48. 790 
0  48. 954 
0  49. 118 

0  58. 317 
0  58.  482 
0  58. 646 
0  58.  810 
0  58. 975 

8.174 
8.338 
8.502 
8.667 
8.831 

1  18.030 
1  18.195 
1  18.359 
1  18.523 
1  18.688 

55 
56 
57 
58 
59 

.151 
.153 
.156 
.159 
0.162 

1 

Page  646] 

TABLE  9. 

Mean  Solar  into  Sidereal  Time. 

a 

To  be  added  to  a  mean  time  interval.                            1 

S*- 

91" 

10" 

Ilk 

121. 

Igi" 

14» 

IS" 

For  secondsJ 

TO. 

0 

1 

2 
3 
4 

m.     s. 
1   18.852 
1  19.016 
1  19.180 
1  19.345 
1  19.609 

m.  s. 
1   28.708 
1  28.873 
1  29.037 
1  29.201 
1  29.365 

m.     s. 
1  38.565 
1  38.  729 
1  38.893 
1  39.058 
1  39.222 

TO.  S. 

1  48.421 
1  48.585 
1  48. 750 
1  48.914 
1  49.078 

m.  s. 
1   58.278 
1  58. 442 
1  58.606 
1  58.771 
1  58.935 

TO.  S. 

2  8.134 
2  8.298 
2  8.463 
2  8.627 
2  8.791 

m.     s. 
2  17.  991 
2  18. 166 
2  18.319 
2  18.483 
2  18.648 

TO.   S. 

2  27. 847 
2  28.011 
2  28. 176 
2  28. 340 
2  28. 604 

8. 

1 
2 
3 
4 
5 
6 
7 
8 
9 

s. 

0.003 
.005 
.008 
.011 
.014 
.016 
.019 
.022 
.025 

5 

6 

7 
8 
9 

1  19.673 
1  19.837 
1  20.  002 
1  20. 166 
1  20.  330 

1  29.530 
1  29.694 
1  29.858 
1  30.022 
1  30.187 

1  39.386 
1  39.550 
1  39. 715 
1  39.879 
1  40. 043 

1  49.243 
1  49.407 
1  49.571 
1  49. 735 
1  49.900 

1  69.099 
1  59. 263 
1  59.428 
1  59.592 
1  59. 756 

2  8.956 
2  9.120 
2  9.284 
2  9.448 
2  9.613 

2  18.  812 
2  18.976 
2  19. 141 
2  19.306 
2  19.469 

2  28.668 
2  28. 833 
2  28. 997 
2  29. 161 
2  29. 326 

10 
11 
12 
13 
14 

1  20.495 
1  20.659 
1  20.823 
1  20.987 
1  21.152 

1  30.351 
1  30.515 
1  30.680 
1  30.844 
1  31.008 

1  40. 207 
1  40. 372 
1  40. 536 
1  40.  700 
1  40.  865 

1  50.064 
1  50.228 
1  50.  393 
1  50. 557 
1  50.  721 

1  59.920 

2  0.085 
2  0.249 
2  0.413 
2  0.578 

2  9.777 
2  9.941 
2  10. 105 
2  10. 270 
2  10.434 

2  19.633 
2  19. 798 
2  19.962 
2  20. 126 
2  20. 290 

2  29.490 
2  29. 664 
2  29.  818 
2  29. 983 
2  30. 147 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

.027 
.030 
.033 
.036 
.038 

15 
16 
17 
18 
19 

1  21.316 
1  21.480 
1  21.644 
1  21.809 
1  21.973 

1  31.172 
1  31.337 
1  31.501 
1  31.665 
1  31.829 

1  41.029 
1  41.193 
1  41. 357 
1  41.522 
1  41.686 

1  50.  885 
1  51.050 
1  51.214 
1  51.  378 
1  51.  542 

2  0.742 
2  0.906 
2  1.070 
2  1.235 
2  1. 399 

2  10.698 
2  10.763 
2  10.927 
2  11.091 
2  11.255 

2  20. 455 
2  20.  619 
2  20.  783 
2  20. 948 
2  21. 112 

2  30. 311 
2  30. 476 
2  30.  640 
2  30. 804 
2  30. 968 

.041 
.044 
.047 
.049 
.052 

20 
21 
22 
23 
24 

1  22.137 
1  22.302 
1  22,466 
1  22.630 
1  22. 794 

1  31.994 
1  32.158 
1  32.322 
1  32.487 
1  32. 651 

1  41.850 
1  42.015 
1  42.179 
1  42. 343 
1  42. 507 

1  51.  707 
1  51.871 
1  52.035 
1  52.200 
1  52.364 

2  1. 563 
2  1. 727 
2  1.892 
2  2.056 
2  2.220 

2  11. 420 
2  11.584 
2  11. 748 
2  11. 912 
2  12.077 

2  21. 276 
2  21.440 
2  21.  605 
2  21. 769 
2  21. 933 

2  31. 133 
2  31. 297 
2  31.461 
2  31.626 
2  31.  790 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

.066 
.067 
.060 
.063 
.066 

25 
26 
27 
28 
29 

1  22.959 
1  23. 123 
1  23.287 
1  23.  45] 
1  23.  616 

1  32.  815 
1  32.979 
1  33. 144 
1  33. 308 
1  33.472 

1  42.672 
1  42.  836 
1  43.000 
1  43. 164 
1  43.329 

1  52. 528 
1  52.  692 
1  52.  857 
1  53.021 
1  53. 185 

2  2.385 
2  2.549 
2  2.713 
2  2.877 
2  3.042 

2  12.241 
2  12.405 
2  12.570 
2  12.  734 
2  12. 898 

2  22. 098 
2  22. 262 
2  22.  426 
2  22. 590 
2  22. 766 

2  31. 964 
2  32. 118 
2  32. 283 
2  32. 447 
2  32. 611 

.068 
.071 
.074 
.077 
.079 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 

1  23.  780 
1  23.944 
1  24.109 
1  24.273 
1  24.437 

1  33.637 
1  33. 801 
1  33.965 
1  34. 129 
1  34. 294 

1  43. 493 
1  43.  657 
1  43.  822 
1  43.986 
1  44. 150 

1  53.  349 
1  53.514 
1  53.678 
1  53.  842 
1  54.007 

2  3.206 
2  3.370 
2  3.534 
2  3.699 
2  3.863 

2  13.062 
2  13.227 
2  13.391 
2  13. 555 
2  13. 720 

2  22.919 
2  23.  083 
2  23.  247 
2  23.412 
2  23. 676 

2  32.  776 
2  32.  940 
2  33. 104 
2  33. 268 
2  33. 432 

30 
31 
32 
33 
34 

.082 
.085 
.088 
.090 
.093 

1  24.601 
1  24.766 
1  24.930 
1  25.094 
1  25.259 

1  34. 458 
1  34.622 
1  34.  786 
1  34.  951 
1  35.115 

1  44. 314 
1  44.479 
1  44.643 
1  44.807 
1  44.971 

1  54. 171 
1  54. 335 
1  54.499 
1  54.  664 
1  54.828 

2  4.027 
2  4.192 
2  4.356 
2  4.520 
2  4.684. 

2  13.884 
2  14. 048 
2  14. 212 
2  14. 377 
2  14.541 

2  23. 740 
2  23.906 
2  24. 069 
2  24. 233 
2  24.  397 

2  33. 697 
2  33. 761 
2  33. 925 
2  34.  090 
2  34. 254 

35 
36 

37 
38 
39 

.096 
.099 
.101 
.104 
.107 

1  25.423 
1  25. 587 
1  25.751 
1  25.916 
1  26.080 

1  35.279 
1  35.444 
1  35.608 
1  35.  772 
1  35.936 

1  45. 136 
1  45.300 
1  45.  464 
1  45. 629 
1  45.  793 

1  54.  992 
1  55. 156 
1  55.321 
1  55.485 
1  55.  649 

2  4.849 
2  5.013 
2  6.177 
2  6.342 
2  5.606 

2  14.  705 
2  14. 869 
2  16.034 
2  15. 198 
2  15.  362 

2  24. 562 
2  24.  726 
2  24.  890 
2  25. 054 
2  25.  219 

2  34.418 
2  34. 582 
2  34.  747 
2  34.911 
2  35. 075 
2  35.  239 
2  35.  404 
2  35. 668 
2  35.  732 
2  35.  897 

40 
41 
42 
43 
44 

.110 
.112 
.115 
.118 
.120 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

1  26.  244 
1  26.408 
1  26.573 
1  26.737 
1  26.  901 
1  27.066 
1  27.230 
1  27.394 
1  27.558 
1  27.  723 

1  36. 101 
1  36.265 
1  36.429 
1  36.593 
1  36.758 
1  36.922 
1  37.086 
1  37.251 
1  37.  415 
1  37.579 

1  45. 957 
1  46. 121 
1  46.  286 
1  46.450 
1  46.614 

1  55. 814 
1  55. 978 
1  56. 142 
1  56. 306 
1  56.471 

2  5.670 
2  6.834 
2  5.999 
2  6.163 
2  6.327 

2  16.627 
2  15. 691 
2  15. 855 
2  16. 019 
2  16. 184 

2  26. 383 
2  26. 647 
2  25.  712 

2  25.  876 
2  26.  040 

46 
46 
47 
48 
49 
50 
51 
52 
53 
54 

.123 
.126 
.129 
.131 
.134 

1  46.  778 
1  46.  943 
1  47. 107 
1  47. 271 
1  47.436 

1  56.635 
1  56.  799 
1  56.964 
1  57. 128 
1  57.292 

2  6.491 
2  6.656 
2  6.820 
2  6.984 
2  7.149 

2  16. 348 
2  16.512 
2  16. 676 
2  16.  841 
2  17.005 

2  26. 204 
2  26. 369 
2  26.  633 
2  26.  697 
2  26.  861 

2  36.  061 
2  36. 225 
2  36. 389 
2  36.  554 
2  36.  718 

.137 
.140 
.142 
.145 
.148 

55 
56 
57 
58 
59 

1  27.887 
1  28.051 
1  28. 215 
1  28.380 
1  28.544 

1  37.  743 
1  37.908 
1  38.072 
1  38.236 
1  38.400 

1  47.  600 
1  47.  764 
1  47.928 
1  48.093 
1  48.257 

1  57.456 
1  57. 621 
1  57.  785 
1  57.949 
1  58. 113 

2  7.313 
2  7.477 
2  7.641 
2  7.806 
2  7.970 

2  17. 169 
2  17.334 
2  17. 498 
2  17.662 
2  17.  826 

2  27.  026 
2  27. 190 
2  27.354 
2  27. 5]  9 
2  27.683 

2  36.  882 
2  37. 047 
2  37.  211 
2  37. 375 
2  37.  539 

65 
66 
67 
68 
59 

.151 
.153 
.156 
.159 
0.162 

TABLE  9.                 [Page  647 
Mean  Solar  into  Sidereal  time. 

i 

To  be  added  to  a  mean  time  interval. 

16i> 

iJfc 

ISk 

19'' 

20'' 

ai* 

22b 

281' 

For  seconds. 

m. 
0 
1 
2 
3 
4 

m.   £. 
2  37.  704 
2  37.  868 
2  38.  032 
2  38. 196 
2  38.  361 

OT.   «. 

2  47. 560 
2  47.  724 
2  47.  889 
2  48.  053 
2  48.  217 

m.  «. 
2  57.417 
2  57.581 
2  57.  745 
2  57. 909 
2  68. 074 

»« 
3 
3 
3 
3 
3 

7.273 
7.437 
7.602 
7.766 
7.930 

m.  «. 
3  17.129 
3  17.294 
3  17.458 
3  17.622 
3  17.  787 

m.  «. 
3  26.  986 
3  27. 160 
3  27.  315 
3  27.  479 
3  27. 643 

m.      8. 
3  36.  842 
3  37. 007 
3  37.171 
3  37. 335 
3  37.500 

m.   d. 
3  46. 699 
3  46.  863 
3  47.027 
3  47. 192 
3  47.  356 

s. 

1 
2 
3 
4 

s. 

0.003 
.005 
.008 
.011 

5 
6 

7 
8 
9 

2  38.525 
2  38. 689 
2  38. 854 
2  39. 018 
2  39. 182 

2  48.  381 
2  48. 546 
2  48. 710 
2  48. 874 
2  49.  039 

2  58.  238 
2  58. 402 
2  58. 566 
2  58. 731 
2  58.  895 

3 
3 
3 
3 
3 

8.094 
8.269 
8.423 
8.587 
8.751 

3  17.951 
3  18. 116 
3  18.279 
3  18.444 
3  18.608 

3  27.  807 
3  27. 972 
3  28. 136 
3  28. 300 
3  28.464 

3  37. 664 
3  37.  828 
3  37.992 
3  38. 157 
3  38.  321 

3  47.520 
3  47.  685 
3  47.  849 
3  48. 013 
3  48. 177 

5 
6 

7 
8 
9 

.014 
.016 
.019 
.022 
.026 

10 
11 
12 
13 
14 

2  39.  346 
2  39. 511 
2  39.  675 
2  39.  839 
2  40. 003 

2  49. 203 
2  49.  367 
2  49.  531 
2  49.  696 
2  49.  860 

2  59. 059 
2  59. 224 
2  59. 388 
2  59. 552 
2  59. 716 

3 
3 
3 
3 
3 

8.916 
9.080 
9.244 
9.409 
9.573 

3  18.772 
3  18.937 
3  19.101 
3  19.265 
3  19.429 

3  28.  629 
3  28. 793 
3  28.967 
3  29. 122 
3  29.  286 

3  38.  485 
3  38.649 
3  38. 814 
3  38.  978 
3  39. 142 
3  39.307 
3  39. 471 
3  39.636 
3  39.  799 
3  39.  964 

3  48.  342 
3  48.606 
3  48. 670 
3  48.  834 
3  48.  999 
3  49.  163 
3  49.  327 
3  49.  492 
3  49. 666 
3  49.  820 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

.027 
.030 
.033 
.036 
.038 

15 
16 
17 
18 
19 

2  40. 168 
2  40. 332 
2  40. 496 
2  40. 661 
2  40.  825 

2  50. 024 
2  50. 188 
2  50.  353 
2  50. 517 
2  50. 681 

2  59.  881 

3  0.045 
3  0.209 
3  0.373 
3  0.638 

3 
3 
3 
3 
3 

9.737 

9.901 

10. 066 

10. 230 

10.  394 

3  19.594 
3  19.  758 
3  19.922 
3  20. 086 
3  20.  251 

3  29.  450 
3  29. 614 
3  29.  779 
3  29.943 
3  30. 107 

.041 
.044 
.047 
.049 
.052 

20 
21 
22 
23 
24 

2  40. 989 
2  41. 153 
2  41.318 
2  41. 482 
2  41. 646 

2  50. 846 
2  51.010 
2  51. 174 
2  51. 338 
2  51. 503 

3 
3 
3 
3 
3 

0.702 
0.866 
1.031 
1.195 
1.369 

3 
3 
3 
3 
3 

10. 569 
10.  723 

10.  887 
11. 061 

11.  216 

3  20.415 
3  20. 579 
3  20.  744 
3  20.908 
3  21.072 

3  30. 271 
3  30.436 
3  30. 600 
3  30.  764 
3  30.929 

3  40. 128 
3  40.292 
3  40. 456 
3  40.  621 

3  40.  785 

3  49.  984 
3  60. 149 
3  60. 313 
3  50. 477 
3  50. 642 

20 
21 
22 
23 
24 

.056 
.057 
.060 
.063 
.066 

25 
26 

27 
28 
29 

2  41.  810 
2  41.975 
2  42. 139 
2  42. 303 
2  42. 468 

2  51. 667 
2  51. 831 
2  51. 995 
2  52. 160 
2  52. 324 

3 
3 
3 
3 
3 

1.523 
1.688 
1.862 
2.016 
2.181 

3  11.  380 
3  11.644 
3  11.  708 
3  11.873 
3  12.037 

3  21. 236 
3  21.401 
3  21.566 
3  21.  729 
3  21. 893 

3  31.093 
3  31. 257 
3  31.421 
3  31.586 
3  31.  750 

3  40. 949 
3  41. 114 
3  41.278 
3  41.442 
3  41.606 

3  50.  806 
3  50. 970 
3  61. 134 
3  51. 299 
3  51.463 

25 
26 
27 
28 
29 

.068 
.071 
.074 
.077 
.079 

30 
31 
32 
33 
34 

2  42.  632 
2  42. 796 
2  42. 960 
2  43. 125 
2  43. 289 

2  52. 488 
2  52. 653 
2  52. 817 
2  52.981 
2  53. 145 

3 
3 
3 
3 
3 

2.345 
2.509 
2.673 
2.838 
3.002 

3 
3 
3 
3 
3 

12.  201 
12. 366 
12. 530 
12.  694 
12.858 

3  22. 058 
3  22.  222 
3  22.386 
3  22.561 
3  22.  715 

3  31.914 
3  32. 078 
3  32. 243 
3  32. 407 
3  32.571 

3  41.771 
3  41.936 
3  42.099 
3  42. 264 
3  42. 428 

3  51.627 
3  51. 791 
3  51. 966 
3  52. 120 
3  62. 284 

30 
31 
32 
33 
34 

.082 
.086 
.088 
.090 
.093 

35 
36 
37 
38 
39 

2  43. 453 
2  43. 617 
2  43.  782 
2  43.946 
2  44. 110 

2  53. 310 
2  53. 474 
2  53.  638 
2  53.  803 
2  53.967 

3 
3 
3 
3 
3 

3.166 
3.330 
3.495 
3.659 
3.823 

3 
3 
3 
3 
3 

13. 023 
13. 187 
13.351 
13. 616 
13.680 

3  22.  879 
3  23.043 
3  23.208 
3  23.  372 
3  23. 536 

3  32. 736 
3  32.900. 
3  33. 064 
3  33.  228 
3  33.393 

3  42. 592 
3  42.  756 
3  42. 921 
3  43.  085 
3  43.  249 

3  52. 449 
3  62. 613 
3  52. 777 
3  62. 941 
3  53. 106 

35 
36 
37 
38 
39 

.096 
.099 
.101 
.104 
.107 

40 
41 
42 
43 
44 

2  44. 275 
2  44.  439 
2  44.603 
2  44.  767 
2  44. 932 

2  54. 131 
2  54. 295 
2  54. 460 
2  54. 624 
2  54.  788 

3 
3 
3 
3 
3 

3.988 
4.162 
4.316 
4.480 
4.645 

3 
3 
3 
3 
3 

13.844 
14.008 
14. 173 
14. 337 
14.501 

3  23.  700 
3  23.  865 
3  24.029 
3  24. 193 
3  24. 368 

3  33.567 
3  33.  721 
3  33. 886 
3  34. 050 
3  34. 214 

3  43. 413 
3  43.578 
3  43.  742 
3  43.  906 
3  44. 071 

3  53. 270 
3  53. 434 
3  63.598 
3  53.  763 
3  53. 927 

40 
41 
42 
43 
44 

.110 
.112 
.116 
.118 
.120 

45 
46 
47 
48 
49 

2  45.  096 
2  45.  260 
2  45.  425 
2  45.589 
2  45.  753 

2  54. 952 
2  55.117 
2  55. 281 
2  55. 445 
2  55.  610 

3 
3 
3 
3 
3 

4.809 
4.973 
5.137 
5.302 
5.466 

3  14.666 
3  14.830 
3  14.994 
3  16. 158 
3  15.322 
3  15. 487 
3  15. 661 
3  16.  815 
3  16.980 
3  16. 144 

3  24.  622 
3  24.686 
3  24.  850 
3  25.015 
3  25. 179 

3  34.  378 
3  34. 543 
3  34.  707 
3  34. 871 
3  35. 036 

3  44.  236 
3  44.  399 
3  44. 563 
3  44. 728 
3  44. 892 

3  64.  091 
3  64. 256 
3  64.420 
3  54.  584 
3  54. 748 

45 
46 

47 
48 
49 

.123 
.126 
.129 
.131 
.134 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 

2  45.  917 
2  46. 082 
2  46.  246 
2  46.  410 
2  46.  574 

2  55. 774 
2  55. 938 
2  56. 102 
2  56. 267 
2  56. 431 

3 
3 
3 
3 
3 

5.630 
6.795 
5.969 
6.123 
6.287 

3  25.  343 
3  25.508 
3  25. 672 
3  25.  836 
3  26. 000 

3  35.  200 
3  36.364 
3  .35.  528 
3  35.  693 
3  35.  857 

3  45. 056 
3  45.  220 
3  46.  386 
3  46.549 
3  46.  713 

3  64. 913 
3  55. 077 
3  55. 241 
3  55.  405 
3  55. 570 

60 
51 
52 
53 
54 

.137 
.140 
.142 
.145 
.148 

2  46. 739 
2  46.  903 
2  47.  067 
2  47.  232 
2  47.  396 

2  56. 595 
2  56.  759 
2  56. 924 
2  57. 088 
2  57. 252 

3 
3 
3 

3 

6.452 
6.616 
6.780 
6.944 
7.109 

3  16.308 
3  16.472 
3  16.637 
3  16.801 
3  16.966 

3  26. 165 
3  26.329 
3  26.493 
3  26.  657 
3  26.822 

3  36.021 
3  36. 185 
3  36.  350 
3  36.  514 
3  36.  678 

3  45. 878 
3  46.  042 
3  46.  206 
3  46.  370 
3  46.  535 

3  65. 734 
3  55.  898 
3  66. 063 
3  56. 227 
3  56. 391 

55 
66 
57 
58 
59 

.151 
.153 
.156 
.169 
0.162 

Page  648] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


-^    a 


1 


S    -S 

"*^        on 


2  i 

o    a 


3 


,<i^ 


•loiddy 


pHO^ipCHCOPc^copejccpc^GO 


P^GGpCHCQp^GdP^CQpjoQ 


PchgqP^cqPchcjqPhcqPi^gq  0:^  co  Ph  ^  P^  oq  pj  :c  d  crj  oi :/; 


oicot^in^t^TfOiiMi-i 


t-»  1-H  COCO" 


5(Mr>.OOa 


COaiiOi-4  00COrHiCO4t 


iO00'»**OC^C^OCC0i»0 


(MOiCOQO»CKOi«Ot-'^a>COO.-lr-l 


O         rH         C^         « 


GOOtOC^li^'*CO':Or-tX) 


I— OOOO'^r-tOOCCi-tva 


COrHCOi-HCOrHCOC^COC^ 


COi-ICO»-(CCtHCCC^COC^ 


COrHCOi-iCOrHCOrHC055 


CO.-(COr-<CO.-ICO»HCOiH 


»OO«-H0iC0G0i0Ot0iCQ0 


oc^ajTt*ooicto-o»cao 


O^OiOCOO^iOCOlOO 


jtOt-^OOi-^OC^r 


■^i-l-^rHOOrHCOr-tCCrH 


XOt^t^-tOOiiOO" 


(Nr-.-(t>-OQ00V0100O 


OiOOiOOiOOlOtH 


codc^coi-'Tt*ai»j:?ooo 


iO<OiO':OiO?OiC'»iCO 


cot-ic^iC'ii-icooTfasio 


I>iH!£JC^iOCO^Tt*«iO 


Tf«a><MO»-lCNOCOCO'<1't^O 


5ao"*aicci-*(Nc^occaiio 


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r-( -rj*  ,-4  CO  ^ 


kOCO^^OCDOOiC^ 


r-lrHQlNaiC^aCCOCO"^ 


SiOOi^OiOOiOOiOO 


locc^oo-^aicoi^c^o 


(NrHr-tr-irHC^OCOaiCO 


i3o»00i00i00u30 


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£»QOOOOOOCOOQlOOi 

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feO.-lOrHOrHOrHOf-H 


OiOiOOOiOOOt^Ot^i-t 
lOOiOOiOrHiCt-HiOF-t 


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C0i-tC^r-tC^THC^r-4O»i-l 
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COr-ICOr-IMC^lMCJ— ICO 
lOcOtAcOiCcOt^COiOCO 


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5  lO  lO  iC 
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5  tOiOcOu 


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5  1/5  CO  lO 


5  r-H  uO  rH  IC  rH 
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^coilOcou::>coudcOiOco 


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50<0<i 


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to  to  CO  O  <o 


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5  to  10  to 


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TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  649 


5 


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tOCOtOCOtOCOtOCOtOCO 


iOi-(lOiH3rH-<»<rH'0"oS 
ItOCOiOCOtOCOtOCOtOcO 


rHioocoacogoctoooij 

tOCOtOCOtOCOtOCOtOCO 


iceog'-feC'^mtoc^io 
tOCOtOCOtOCOtOCOtOCO 


coooo 
to  CO  to 


r- t^  i-l  t^  M  CO  ff< 
H  •*  (N  -^  Jl  •♦  I'l 

CO  tO  CO  to  CO  to  CO 


St~qot^«t~coooc^oo 
rHtOi-*tOrHlOr-(iOf-t 

tOCOtOCOtOCOtOCOtOCO 


»0  rH  to 

lOCOiO 


coco  Cp^ 
to  CO  to  CO 


op  ^  l>  ^  t^  ■^ 

to  CO  to  <0  to  CO 


t^iOa>tocotoOcocoeo 
tOCOtOCOtOCOtOCOtOCO 


J^COt-IOOOCO 
i  O  rH  O  1-*  O  »H 

>  CO  CO  CO  CO  CO  CO 


CO  CO  O  CO  CO  CO  CO  CO  CO  CO 


MrHM>-l«r-lM<-(m<N 
-     HOr-IOrHOrHO>-l 

^cocococococococo 


Oi'^fiaiOicnBi'nX'Ji 


rHiO 
CO  CO  to 


eoo»eo!Ncoe<oo(N99e< 

OrHOrHO— lOrlOiH 

cocococococococococo 


pdtnO^crJMadoSGcOHCO 


SS23SSS 

CO  >S  CO  to  CO  to  CO 


SS3 

to  CO  to 


CO  lo  CO  [3 1^ -jr  t~ 

CO  tO  CO  to  CO  lO  CO 


^  0>  T)«  OtO  c 


>  CO  CO  CO  CO  CO  CO  CO 


S     C;     SS     S     S 

CO        OO        CO        CO        ^^ 


Page  650] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


o 

v 

»H 

'^ 

3 

v 

"m 

. 

T! 

> 

H 

00 

OS 

a 

S 

••1 

JS 

o 

X 

PI 

o 

» 

a 

<«» 


•a^Bp 
•xojddv 


•9JBP 

•xojady 


S  lO 


p^0QP^0Qp:icop<'aQpdcQ|Q[^cupia5p:jaipijcoda3b4QQ0^cQtf^ 


gC^CCC^-^tM^JfrH-^T-dCIOlCOOiCOlOOiCrH 

.■^c~-*i>'*c--^t>-'*t^-^t-Ti<Qocoooeoccwcc 


SC-ieoc^eooJeOrH-*!-!-* 


'.jH|-»Tri^'.j*i>cooDccoo 


JO^or^Oicoc^ocotoo 


"i-tCCIC^eOCOINKlT-HTr.t^iCOOiOO-Vr-lKKN 

ccooccoo»sooMQOcooo:ecoccccsc^o>e^o>iMO> 


lOeoooi'^iOoQi-i.-ioo 

O^OOCOQOCOOOCOOOCCX) 


kl<iOtOINt^>-lOOOmO> 

!i-l-*OlOlOOTI<r-ieOr-c 

icooocococm33c»cnc^ioj 


Mooecx«ooc^ooiNa» 


!MrHO 

:o5<NCO 


C^  IM  e^  iM  CO  c^  cc 

t>-  ^  l>»  TJ*  t"«  ^  t* 


^t^cot-*Ci^iOosr-tMsor».Hc^tot^i-(cc»oooo5'^(Ni-<»^Oir^t 


■"^  t^  -^  I^  -rtt  t^  -.J*  t^ 


»i>a5cce<5oomoc;ccoo 


TCXCOCOCCMCCOOeCOO 


:CCrt«lr-ICO<NC^IM'NC 


SaoiCcoocoiOcoo 
■^t~eot~«cocooo«oD 


:  l-H  T-H  OS  -^  CO  t-^ 


COPQM 


;ior*coa3  0c^t^i0-^oo 


I"  O  ■V  O  ■»»"  1-1 


M1-1M.-1 

-.*•  t^  ■■<}*  t^ 


-iOicOt^lCl/SaOC^IrHasCO 

g-<jio-*«5-<)io-».-'eort 


tOCOCOOiOCOCDtOCOO 

MC4cifj<Nco.-ieoi-i'<>< 


^Hi-Hco-n'iot^C4i-too-.*' 
ec<Nc-ic^r4c^CAosi-ico 


TtiO-^OiOiOu-SiOO 


t^iOi-KN-^COI^OOCO 


icr--oci5cco>t^'X>o« 

-U-OCCrHCOi-KNlNINCO 
COODCOQOCOQOCCOOCOOO 


lOOOi-llMt^tOOQOOira 
rHCOi-l'^O'^OiOiOlO 


COO«iCC^10tO-^0« 
iCO'*0-*i-iKii-l«liN 

CC0CMO0C<5  0O«0OMO0 


M.-ieOrtccc^(Nc^Mc'i 

T  l^  -»•  l^  f  I~  ^  I^  "tH^- 


oc^i'-or^QC^i'^coaico 
OiOiOiCiSO"9<oeoi-i 

■*C~COt~KloCCCOOMOO 


S-^OMCJOi'.J't^t 

:iOOiOOT(iO'fl'C 
i  ■«ji  t~  ■*  t^ -"ji  t^  ■^  t 


•  Oj'^r-icci-icomciSe^ecc-) 


r^co-siQOci5t^t>.cOf-i 


SiC-^QOSi^-^OoOiC 
■.^lOiCiCiOiOO-^O 


§  U3  iO  lO  iClS  O 

pfii  ^  to  ■.**  CO  "ij*  t^ 


C^C00siCl^r^iCOC4C00»iO«O00 


mi-iQ'^t^t^'VfHO'^ 


toooe'ic^t~t^e3C<ioot^ 

fHcoi-H'.ro-ii^OiOiOic 

■.S.l-T)it~iJit^-*t.Mt>- 


:  53  M  ©  Ifi  00  t^  CO 

:oidOio>OLOiO 

;i0C0i050-.«<C0'*< 


CO->»< 


>  O -^  O -^  .H  -.Ji  r-t 

1 1^  ■*  t^  Tf  r~ -.»' t^ 


OJlftcOOOCOrHQlCt^QO 

coi-ie<3iHeo?<wc5c^cs 


C^COr-ieOi-ICCTH'J<0^ 

■«ft~-cjir--.i<t>-o't>-9n> 


lOC^COCCiHOOil^   I^OiiOi-HWCOi-t 


fkOCOiOCOiCCOiC 


iCiCiOOiOCSiOO'^O 

■.JlCO-Wt^-^t^Tjlt^Tft^ 


corHeomocoi-~o>-*?) 

."Jir-ITJirHTrrHCOrHCCC^ 


ii-lt>"a>ODQpOCOr-t^CO 

ri-H'.j^O-^oiooiOOvO 

*tACDlCCOlOCOinCOLOCO 


eoiCHi^o>o>cOf-4'^co 

OiCOlCiCiOiOOlOO 
iC-^iOtO-^CO'^t^'«J<t~ 


SiOccfltioc^cOrtooe 


Joioooi-it^eoiC-V" 


CJCOOOOt^i-H'^COrHCO 


gi-itpeC''(<i053i^©0» 
lOO^O^OiCOiC 

iC.  cOiOCOiiSCOiC'^iCCO 


SiHlCCCCOlCi-lOOOOO 
OiOOiOOiOO^i-H 


^■.»<i-li»iOiOOiOCiO 
iC  CO  ifS  CO  iC  CO  lO  CO  lit  CO 


ICCCO.-iCQOiQt^CClOlC 

lo>oo>S>ao>Ao>co 
:iOcoioco'^t»'*r~i't^ 


.■■Vt^cOOOOJOi-liHOC^ 
fiOCOiOCOi/^COiCCOiCCO 


l»T)4<oiK)ir5t>-C<301r-( 


SloiNoO'^coco^iooe^o 


iC&iAOiCOiCO 
lOCOiOCOiOCOlOCOiCCOl^OCOiOCO^COiOCDiOt^lrft*'.*' 


00  Oi  IC  CC.H  CO  00 


I  CO  0>  0>  CD  Ci5  W  CO 
<  1-1  CC  r-l  CO  0>  CO  IM 

"  t^  •*  c^  ■.*<  t^ -^  t^ 


C^t^OiOt^CCTjlcOTHOO 


o>2J'~'*'Ot^i^o> 


SIN 


»oQ-***i^iccocoior*-^Oi 
:CHCcc*iccc^coc^»coc^cc 

AiCCOiCcOiOCOLOCOiOCO 


lOCOiOCOvCCOlCCOUDCO 


lOt^^OiMr-IOC^OO'J" 
i-<tJ1tHTJ.|H»Oi-(iOOiO 

tOCOlOCOii^cOiCCOiCCO 


8gS 


CO  C<l  O  O  CO  CO  >^ 

to  ic  r*  ic  c*  *t<  i> 


»c^rHc^c^.-(coO'*j*coicr-'X)tC'r-i/5Ci^oci'-"VHCooi'<!fco<cot^ioo5 


:cocoococoeccccccscc 


C^CCC^ICCWCO(NT}<C^Tt« 


lOcCiC^iOOiACOiOeO 


COQi-i 


c^  o  -^  t^  to  in  OO 

iC  O  iC  O  lO  O  lO 

to  ifl  to  iC  ^  lO  to 


sl:>-OStoaiiOO'^iMCC'CS 

:coc4coc4cocococccocc 

^iCtOkCtOiCtOiCtOiCtO 


C^CCi-(Tf<O^OitoaDt^r*0>?DO'**'-'C»3<MC^'* 


cocococccoccc^coc^co 
iritoictoiOtouotoiCto 


iCtOiCtOOtOiCtOirttO 


iC  tOiC 


t^  t^  OO  lO  Q  CC  CI 
Tf  i-H  -V  r-t  iO  r-1  lO 

CO  lO  to  lO  to  lO  to 


•  Or^  OioocoOi 


ItOiO  to 


CO  CS  CO  CM 
lO  tOiC  to 


l-*OI^i-(tOr-*iCC-l-rcO    CO-^C^vOr-II-^OCO 

cocococococococococo -  —  -* .^  — 

iCtOiOtOiOtOiCtOiCtO 


cocoeococococococ-jco 

iCtOiCOiOtOiOtOiCtO 


;  to  CO  lO  -^ 

»  iC  tOiO  ti 


■^^JiOCOtOiC^tOCMt^^t^OCOOO 


3iC  to  lO  to 


tCtOiCitOiOCOLOtOiCtO 


■  Sc^S 

iiCtOiO 


rH  OS  rH  05  <N  00  « 

C4  Tj*  CM -^  CM  Tj*  Csi 

to  lO  to  to  to  iC  tC 


00  CO  00  CO  Oi  CM  OS 

to  iC  to  lO  to  iC  to 


;oocor*cor^'^tDic»ciQ 

^CM^CM-VCM-^CM-^Csi 

ictou^itoirtitototoioto 


CMO>CMOi-iOi-l— ^i-*^ 
lOf-tiOCMiCC^iOCMiOCM 

iCtOiOtOiCCOtCtOiCtO 


.*qo  1,0  00 
:iOiHio 

»  lO  to  iO 


iC  C51  lO  00  <0  t;;  to  |l>  to  t^  tO  t^ 

to  lO  to 


HiOi-tlO 
3  iC  to  iC  to 


|iCi— tiOrHiOrHiOi—tiOrH 
iiCtOiOtOiOOiCtOiOtO 


^^i 


'^^ 


J^CMC^CMCMCMCMCOCMCO 

^cototototocototototo 


CMCOCMCOCMCOi-iCOtHCO 
~      ■*  O  rH  O  tH  O  r-t  O  r-( 

to  to  to  to  ^  <o  to  to  to  to 


2*  "^o]   to  r*  ,00  OS   Q 


©5^  ^  "lo  I 


OJOOOrHr^CMtOCOlO'^ 

cocococococococococo 

iCtOiOtOiCtOOtOLOtO 


iCtO'^tOcOt^COOOCMOl 
TjiCM-^CM'^CM'^CM'^CM 

lOtOtOtOiOtOiCtOiCtO 


SrHOCMOiCOOSCOOO^ 
C^«5  CM  -^  CM  rr  CM  -^  CM 

lOtOtOtOiOtOiOtOiOtO 


t>'OtOi-HvOCOCO'<J'CMtO 


CM-rr  c^ 

lO  tOiCi 


■^  CM -TT^  CM -^  C^  ^ 

to  tO  to  lO  to  lO  to 


•^iCcotpCMtrQOQ^o? 

lO  to  iC 


1-lOSOOOs— ^QOCMC^CO 
■^CM'^COCOCOCOCOCOCO 

LCtOiOtOiCtOiCtOiAtO 


00Tj«r*iOtoiOiOtotOt 


tTCMtJ* 
OtOiO 


lOiO  to  tO  t- 
to  iC  to  lO  to  lO  to 


toi>toooiccoioooicoi 

uii— (»Oi— (iOr-tl£if-liOi— t 
iCtOiCtOiOtOiOtOU^tO 


Oi-^OcOOOQi-<<NrH 


SS3 

lOcOi/t! 


(N  lO  IM  id  <N  lO  IN 

CO  lC  CO  iC  CO  lO  CO 


1-iMli-IWr-ieOiH'flli-lTjl 
Ol-lOr-tOTHOf-lOrH 

^  CO  CO  CO  CO  CO  CO  CO  CO  CO 


1-1  ■^p 

CO  CO  CO 


oiccf^ccCAixifii^cim 


Ml  p  ■<Ii  O  >0  p  lO 
CO  CO  CO  CO  CO  CO  CO 


tfQQP^OSP^cdPJQQOHCa 


iOiOlO         iCiOiCiCCO 


TABLE  10. 
Mean  Time  of  Sun'a  Visible  Rising  and  Setting. 


[Page  651 


B 
S 


S^ 


•xojdd 


dV 


•xoidd V 


.12; 


ii!z5 


O        IH        M 


SHcnQicQftSaitfGOP^ad  QjrnOiaQOiacOdsiO^gg 


O      i-(      ?i      w 


OncntfcoPji/jOjcnMcn 


e»9kt^O)t^O>t^0>t^9>t^   0>t^9kt^9>t^0kr«9)aQ  iCTkGO9>QQOkOO0)OO9^OO 


OJcnMcotfcDC^cfiS^cdQJai 


COOOSOCCaOCOOQOQaOCOCOGQ 


.-i.^.-irt^?is^3co  ocoo>s90>coo>3"o>5'  aoa>ooiet~ior-iOt^<ot>.o 


■OtOiOtO>OtO>0<i3>0<0>OtOiO<OiO<0>a<0>0<0>0<0 


SS8£8SgSSSS3SSS3SgS32|gSS?25S?253 


icoicoiooooi25p^ 


S      2 


SSSSSSSS2S3 


■<ri-c'j'pi'9"?i-*c»->»<M-<i<H 


lo  » <n  !0  >c  -^  lO  --o  lO  to 


tOfiftecf^coiSc^Oi-it- 


SCO  —  -^50»OC^*O  —  r* 


;'.s><:coic<ciaco>Aco 


■aeo-r-^cctoc^t^i-ioQpsi 


SSS82SS3S2B2 


vH  lO  ^H  lO  r^  U3  1^  U^  1-^ 


S3>o>poo^r^w«'^ 


SSS82S5S2SB2 

.^<o«o<oom«o>n<o>ot9 


p82S2SE:g2SS 


Ud<OiO<OtOCDiOCOtACOU3eO 


^:0:o<&cococOkO<OiCco 


kO<:OiO^OOOCOt.'tO 


^N^OCTTSOCOCOCOCCCOCQ 


5:£>r-(OrHS<-llO.-'lOrt 


■£^)S 


-OiOtO 


i/l  "^o  O  :0 


rf  C5  -"T  C^  •*  IN  ■«J'  M  ■*  «M 

ic  o  lO  to  lO  'O  ic  ^  i^  eo 


£j  a>  CO  00  lO  to '^  "I  f^ 

^CC'fCOCOCOCOCQCCCOCOCO 
intO^tOOtOkCtOlOtOiAtO 


Sg2SS82SSS2 


[g2s; 


SSS2 

>tO>A  to 


^tom 


tooto 


i/^  t^iO  to 


ac-»t--totor-Tj<oQMQ 

lOtOOtOLOtOirtltOIAtO 


i-I^OC<500i<5tOtOiCOQ«00» 
iCtO^tOiCtO^tOiAtOiCtO 


JCOCOOXM-J 


!  tOU3 


tOiOtO 


lO  to  ifl  to  ! 


-lOtOt-fOOMO-H-^ 

stoiotomtoustoioto 


eoQC'Ctoto^oQcoaJC-it-i 

COOtCCeOMCCCOSOCOM'J' 
lOtOtOeOiOtOtf^tOLCtOiCtO 


fg28 

•  to  to  to 


tOiOtOiO 


n-toto 

i-H  l5  p-( 

tOiCtO 


>toio 


1-1  lO  c^ 

to  in  to 


0>  Jl  00  -^  1 

-r -N  ■TC^  j 

xO  tOiO  O  I 


>inmt~OTooiNoocj 

^tOiCtOiCtO^tOiOtO 


intOtittOiCtOiOtOiCtOlOtO 


SSSS 

« to  to  to 


^  GO  C^  t^  -^  lO  to 
r^  lO  rH  IC  f-»  »C  r-l 

to  otoo  too  to 


0>Q'-1 
MiSlN 

tO>A  to 


lO  tOiO  to 


•OtOCOt^dOJOi-JOOIN 
iOtOUOtOir3tOiCtOU3tO 


tO'sf'^tOCCOOrHOiOSrHt^CO 

eococoeoMMcococ^'VC^M' 

lOtOiOtOiAtOiOtOiOtOiOtO 


OOOOCTH^i-liOMWJ" 


:  5ou5 
''  to  to  o 


oinSSS 
to  »r5  to  »c  t 


I  too 

StOiC 


00  OJ 

to>oo 


Or-liBrt  rr  rt 


lO  to  to  to 


.t>iOtor~'T'OOCMOi-iO) 


Jin  OiO 

"lOtom 


OtOOiOr 

toio  to  in  t 


MooKcQMcnOHOQQicn 


.  into  t~ 

)  to  lO  to 


in  to  u-:)  to 


Minr-lt-350Dt^OlOIN 

inointcintoioointo 


3  0»  to  iH  ■>»<  CO 


MCOCOCOCCC'SOlCOlM'^C^-T 

intointointoiotoiotoioto 


??3 


CXI  Tf  to  to  -^  00  N  o 

cocjcoc^coc^eoco 


intointointointointo 


KmeiiaifixiOixiaiwlcii'xiOitxiciaiKait^ai 


-s^^s-" 


c-      00      oa 


-^sr-^ 


QCJoQ'fl'totOTjiooiNOOej 
55co?Sco?Jcce<icoe^'«"(N'»" 
lotointointoiotointointo 


ojaJMccpHCC^jcopiHQQtfoQ 


Page  662] 


TABLE  10. 

Mean  Time  of  Sun's  "Visible  Rising  and  Setting. 


a 
s 


Q     "ffi 


!2;   g 


.•^J^; 


•xojddv 


•xojadv 


Oj  CQ  p4  a>  pj  OQ  pj  «}  P4  OQ 


CO        CO        CO 


^ 


p^OQe^COpf^OOP^tnplSaQ  PJCCpSCOp^iAQSOQpljCIQ 


p^ccp^xipi^izip^inci^cQ 


g'aOi©CO«0005000«000<0 


05  CO  oa  00  Oi  00  0> 
lO -.Jf  lO  Tj<  iC -^  »o 


-0-*0-*0-5'0 

tciC  «o  lO  to  la  <o 


oDtcoor-opr-cot^oDi^oct^oot~oot~oot^oot~. 


000it^CTil^QI>-Ol^Ot^Q«0QtC>Q^CH0C> 


t^lM50C)«5C0<OC0tOCClm'C0m'.!j'iOTjiiO'.1'T»i^ 


eCOtDr-iCOrHlO.-'lOrH 


-*-<j<^iO'«ineoiocoto 

■*0-*0'*0'*0-.J'0 
iC  CD  \C  <D  IC  O  lO  ?D  lO  !0 


<C  M"£l  •*  to  iC 
■  O-'J'O 

CO  to  CO 


icCCOCOCOCOt^iOt^lOOO 


Set?  CO  CO 


tOiOCOiC 


COiits  CO 


coiCiCiCiOcpi/s^M^cp 

tCCOiCCOiCCOlOcOiCCO 


|5oTtic>-*o^OT»ic5 

lOCOlCCOiCCOiOCOlCCO 


t~cor»cot^eoooc^oo  mooc^CTi-hoithooo 

1  CO  lO  CO  iC  CO  vO  CO 


90-^oo'»j'o>3;oJcog;coO(Noc-j.-ii-i.-i.Hc^oooeoo5coCTi'<j'oO'* 


kC  CO  iC  CO  kCCO 


^  Oi  CO  OS 


1  CO  rH  CO  rH  CO  rH 
S  CO  lO  CO  iC  CO  lO  CO 


JcD^vCCniOOTjiO 


5  COlCCOlC 


S5S 


^jiCcOiO 


.-i-*e^co 
to  in  CO  >o 


c^coco 

cOkO  CO 


C^COM-*ii-liOOiOOto 

—    •  —      —     ,J1  rt  .^ ._, 
IQ  to  U2  to 


lC  CO  iC  CO  kC  to  ii 


ostoost^opoot^Qor^cs 

COt^COi— (COr^CO.HCOi-1 
lOCOiOCOiCCOlCCOvOCO 


^■rfeO'^tjicofcoincjco 

S-^rH—       ■—      •—      ■—      ■ 
.cjkOCOkC 


StOiOtClO 


tOU5  to 


tomtoio 


00  .-to 

tOiOtO 


-.Jl  rH  CO  S^  CO  (N 
iC  to  iA  to  kO  to 


g'  CO  Oi  c^ 


to  tC  to  vC  c 


S-tflN-* 
<f  kO  cOiC 


i-ioc<oscoc 


<coi-(t~-ooocio>ooo> 


■^  rH -.f  tH -.Ji  r-t 
lO  to  1^5  to  kC  to 


CO  .H  CO  1-1 
iC  COlCCO 


CCOt-OCO.-ICOlMtQCO 
COI<1CONCOCJCOC^COC^ 

tCCOl/SCOiCCCk^cOkOCO 


l-»Nt~CO 

CO  6)  COIN 

lOtOift  to 


c5eoc^coc<> 

tc  to  kC  to  kC  to 


CO  r^ -^  to  iO  ic  to 


COC^COM 
iCtOiOtO 


JtOt^t^t^OOtOOOtOOi 


rlCO 
iC  CO  tC 


i-(  CO --*  CO  1-1  CO  r-i 
CO  kO  CO  iC  CO  kO  CO 


tooujT-iTjiiHcoc^eoc 


coc^co 
lOtOiiS 


C^  CO  iM  CO  C>4  CO  CJ 

to  IC  CO  iC  CO  IC  CO 


<-<J<cOiOC^iO.-(COOt^ 
SC^CO(NCOINCO?JCO<N 

:coiccoiocokCcokCco 


cp-»'i2TC"9<iO-*'.CC0t~lC<I00r-l5>OO0>-^00(N 


CO<Me4lMCOiNCOC-)COM 
iCCOOCOiOtOiCtOiOcO 


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liC  cOiC 


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■^t~COOOMO»rHOOi-l 


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CO  CM 

|u3tOiO 


CO  t^  M*  CO  lO  iC  CO 
CO  C-J  CO  O  CO  N  CO 

CO  >0  CD  IC  to  lO  to 


_   lOtotoic t^ 

eO(NooMcoM 

iO  tOkCtoiC  to 


300  CO  OS 
t/5  tOiO  to 


CT  O  T-J  .^  CM  —-  ?5  00  ■* 
COCOCOCOCOCO-MCOC^CO 

kCCOlOtOmcOiCtCiAtO 


t^iototxinoocooic^o 

C^eONCOlMCOMCOlM'* 
iCtOkCcOiOcOiCcOiOtO 


esi-^CSO-^OiiCOOtOt^t^ 
S-^cS-^M  CONCOCT  coc^ 

<*iCtOiCtOiOtOintOiCtO 


to  00  lO  g> -cc  o 
SSieowcoco 

lC  to  tC  to  iC  to 


CO  CO  CO  CO 
10  to  tA  CO 


cocococo?icoc^coc^eo 

lOCOiCCOiOCOkOCOiCCO 


10  05-* 
INCOCl 

llOCOiO 


■*  e< -.J"  c-» -ic  CM  •.»' 

CO  ift  CO  iC  CO  lO  CO 


S'gcco>t^ocoot-o>coo 
"Ji^COCMMINCOfjeOCO 

.C^if^cOiCCOiCtOiOtOtOCO 


S"oaQoooaawoco.-t»cco 
coiNcoficococoeococo 

rfjiftCOiOCOiOCOkCCOiCCD 


iftr^'^CMCOCOi-f^QlCast^OCQQCOaii/SO'^'ClCMCOrH 


CO  CO  CO  CO  CO  CO 
lO  to  iC  to  lO  CO 


coco 

iO  to  ire  CO 


T^cocMe<5cMcocM'*N-*f<| 

iCCOiOCOiACOiCCOiACO; 


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to  lO  CO  10  to  ifl  to 


■.((^•coiOi-itDOgoosos 

CO  CO  CO  CO  CO  CO  CO  Co  CM  CO 
'iretOiCtOiCtOiOCOiCtO 


p-oco.-i-.j'coeo-.jifico 

CM-*Cq'<X(Nr}(CM-.l<eM-* 
iCCOiOtOlCtOiOtOiOtOI 


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)  to  10  to  U5  to  iC  to 


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gcocococoeocococococo 

.cfiOtOiCtOiCtOiCcOiCtO 


^t^CMcocOinmcOtOCMOO 

acococococococoMcoco 
^tOCOiAcoiOcOiOCOiCco 


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COCOCOCOCOCOCOCOCO'.J' 

.^iCtOiCtOiCtOiCtOiOtO 


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:cococoeoco'*cO'«j'(M'j< 
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lOtOlQtOiOtOlCCO 


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lOtOiO 


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to  lO  to  lO  t^  m  t» 


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lor-iot- 


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f— HCr-tlOrHOi— 1000 


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COiO  COiC  CO 


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iccoiot^iOt^iot»irer* 


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iOr»io 


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H  ^  gj  CO  t~  to  lO  00 
KOOOOOOO 

5 1~  lO  t»  K5 1- lO  »»• 


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00  CO  to  lO  ■.# 

rHiO.-tirSiH 
ire  COiC  CO  lA 


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ire  rH  IC  1—*  o 

cOiOcOiO  t- 


5 -^  to  CD  CO  00  rH  r^  C 
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>  r»  ic  t^  lO  c~  lis  t~ ' 


COCDCOOOrHr-^OO-^iOCO 

iOrtirei-iirecM-*cM-«<c< 


tO  CO  iC  CO  iC 


ireooc 
toire  t^  u 


<mcoiocoio 


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r-(ire  T— ( »o 

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ire  CO  lO  CO  ire 


•  00  3;  CO  to-* 

•  to  CO  ire  CO  lO 


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•>i<  i-i  ire  1-1  ire 
CD  lO  to  in  to 


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CM        CM         CM         CM 


000 
r»irer~ 


ooiretpoO'i'O^c 


o  ire  o  ire  o 
10  to  ire  to  ire 


000 
r^ict^ 


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«5       r*       00       OS       Q 

CM         CM         CM         CM         CO 


sss 


■■*CO 

<ireT-( 


ggSSS; 


:  t^  Tt<  t^  "Tj*  r- "^  r* 


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OjadpfJcopijccpiJaSaJai 


'^sr^ 


t^  ire  ire  00  CM  o 


rHirer-l 


lO  CM  ire  CM 


CMOS<J3T-ICO'*COt>.00 


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■*CM-*CMtJ<CMCOC0C0C0 


co^O'Wr-i^-^o.-ico 

-»'CMTJ<CMCOCMCOCOCOeO 


oiwcAwpiixciiinoiK 


CO        CO         CO        CO 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  653 


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J  CO  M  CO  eo  CO  f»  tjl 

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i-iiOOOOO  *         —    " 

"J"  r- ^  00  ■»' CO 


cococoxcooocoooeoco 


:coco?» 


oiiccOfHt^-r^t-tcOkCOOs-^coQooinco 


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t»  T(<  r» -.!<  t- T»<  t~ 


800  lA  CO 
0>Om 

Tf  00  ■*  00  CO  00 


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iC^COCl-^M^i-l-^.-liO 


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•^jz; 


■.J"      »X^! 


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■-i^ciwfjcoeoc^-"}' 

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cocoeO'^c^^iHusoo 

cooocooocococooocoo) 


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f»T»<i^T>iH>nooiOi-i 

coooeoooeo»eoo»c^o> 


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■^i-Hcoc^cocorJWi-i^ 

CO00COXCO30CO00CO00 


MooPJaQp^GoMcnKod  p^cdPJaQpjcaPEiaoPjcQ 


C^C^'«1<Ok/3CS»C00i(5  0Q 
i-liOOOiOO'J'rHCOSi 
COOOCOOKNOINOC^O 


.-4      c^      CO    ^p      i6       to      »^      o6      o»      c? 

LO(/3^CUtO         kOir^iOtOtO 


Page  664} 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


S    "S 


5^' 


'xojdav 


a^GQa^cdpc^copiJGQttHQQ  p4c6tft»p4GQp:;a^PJQQCEHCOp:HcdMcAp:;a;pc^co 


QiHXp^HaQpHXp^GQp^a^pija:^ 


O-^OCOOCOr-tCOrHCO 


^^OO'^  t-cocOf-(0  0>  <M  00  eo  o  i/s  »c  r- CO  CO --* 
lO-^iO-^iO-^io-^ooo  ocoocoocooeooco 


5lWCSWC^COG^COC^<NCO(M 


u3CSt>.Q0iG0O':0(NTf-^C>) 
i-iC0rHCOr-t?S(NW5sC^IC>lC^ 


r-i6*rHC^rH<NiH(Ni-HC^f-tC^ 


iC'^iC'^»0^tO'^tOM.>OC0OC0O0QO00OC0]O(NOC^r-<C^r-tCSrHC^r-<^ 


-^lO-^iO-^iCCOiOCO 


t^-^CC^OCprHrHCOO^aQ^t^qplCaiCOTHCJfNO 

locoioeoocooccoco  o c>S o c^ o cs o 6i i-f  2s »-i ci 


gQ00r-t?pCSiOCO3*Tj<C0 


2»OOOi-^t*CmOCO»C*J<^ 


iOCQiOCO»OCOiOCOi055oC^O<MOCSOCSOCSOC^ 


tO!Nr-i-tQ0(3>O>0Qr-(r- 


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i/SCOOCOiCCOiOCOiOCO 


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lOCOOC^OC'lCXNOCMOC^ 


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iOLOiOiOiCiOiOOidO''-0  0 


a>aiOoQr-<t>.cstocoic  ■^'<fiOcotpcst^i-(GOQa>a> 

■^•WiOCOiCCOiOOOiOCO   lOCOOCOtOCOiOCOiOCCiOCS 
O  lO  tfti  lO  O  iO  O  O  tCO   lOO  »Oia  lO  lO  lO  O  »C  lO  >C  O 


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>rHa>CSQ0C0G0C0l^'^^*^O^OlCC0^t^'<1•00C0'a0C^C>rHO^-H^HOfH01,!^^0lC0QQCC^-■^C0lOl0C0»£5 


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pJGQpi^c»P^ciiQ^O3P^xQ<ci^p[{od0:jaQQ:^G6Q:2od|Q^c»aicfi2::^ 


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■^^-:^ 


'-ar 


TABLE  10. 
Mean  Time  of  Sun'a  Visible  Rising  and  Setting. 


[Page  655 


S 
B 


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3 

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CO^CO*<)<CO^CO^CO^ 


O  C<  i-l  r-l  rt  ,-(,-•  ,-1  rH  i-H    i-c  r1  .H  i-l  i-c  O  <N  O  Ci  O 
.^COtOCOiCCOiCCOiOCOtC   COiOcOiOCO>OCOOCOtC 


a « "-1 00 o g eo  1-1 1-- N X5  eo'soococo^oogog 
^  CO  kO  CO  tC  CO  kO  CO  in  CO  to   CO  lO  CO  *0  CO  iO  CO  lO  CO  tO 


ai005aS!Nr^Og>0>Ot~-UJCOCOin-»COCO<Nt^OO>5»Ot;?J«M5riON 
.^cOiOCOiOcOiOcOiOcoOCOiOcOOcOiAcOiOcOtO   cOiCCOtOCOiOCOiOcOiO 


•*2'C021QQOQO>ejt^ 

s^ocNofSoeoioSsiO 
co>aco>oco>ncoTfco'4i 


co^co^co^co^co^ 


cO>ACSiOCOtOCO>OcO^ 


goocjco'tl'ONOQO 
ra>Am>Aeoiacoon>o 

eO'«<«OT)<co^covcO'<i< 


c4  0?iian>ooo!Sm2 

IcOiOcOTfcO'J'CO'VCO'^ 


g«iOj('*g?»t-<-cgo»jgooor-e<coeO'»ioco 
•c^cokOcotccotccoiocotocoiocoiocoiocokacoio 


2S^22SSS?33 

COOCOiCCOtOcOtOCOiO 


74OC4OC4O6)>aMi0 

coiocomcO'Oco^co^ 


^CO>OCOiOCO>CCOiACO>0 


r^OQpo>a>«f-it^?^*oi'*'^»owcOF-iaooo4gp 

O  !?»  O  i-H  C>  1-1  .1  i-H  r-l  rH    r-1  f-1  r1  rt  rH  i-H  1-1  f-C  1-1  C5 

CO  iC  CO  lO  CO  lO  CO  O  CO  to  CO  tO  CO  10  CO  lO  CO  lO  CO  lO 


gSS8SS8SS22 


21594°— 14- 


-SJco 


-35 


S^SSS'-^oQS'f^tSco 
iO«5?<oSot<oc< 

,C*iCtOcOOcOLOCOiCOiO 


I3'ipi0'*co50t^c>)gpi-ilm©oo>.-<i^pjco-<»'i0 

!OeJt30«OCjO(NOirJjOSi-li-lrtr.(r1rHi-lr-l 
iCOtCcOkOcOiOcOiOCOiOcOiOCOiOCOkOCOiCCOlO 


S«ciopi-io>Qoo»rHor) 
SSeoaMioSoc^oc^ 

.^iOiOiOtOtOOCOtOcOtO 


^aoeoc-'fl'coiOxiO'.i' 
cOiOcOiOCOiOCOOCOiC 


ocoiac4>oco>oeooeo 

tCfOtOiOiCLOiCkOiOCOiO 


Scococoioi^irat— ^ooeo 


SiOop»cr*coi^cocot>.»o 


S?3S?!SS2SS2 


S22gSSa8SS 

COtOCOiOCOiOcOtOCOiO 


•o-»coe<c~i-«o>OQQp 

C0iOC0iC«0iOC0>OC0>0 


nt^cocO'^<oeo^t-M 
cOiOCOiOCOiOCOiOcOiO 


8Q-<<3>2)0QC<5t-5't- 
SOC^OMOC^O'N 

C0i0c0i0c0t0c0«0c0t0 


Scocpiot^^gpcoacJ 
(N  O  IN  O  <N  O  ci  O  61 

COiOcOtOCOtOCOtCCOiO 


0»«OC30<-I.-IO£!Q 
lOMOOTOmOCOOOT 

lOiOcOiOcOiCCOkOCOiO 


'"J*  0> -^  O  CO  O  N 
OOiOCOOOOOOO 

lO  t/d  tO  CO  tO  <o  o 


>  r^  r- r^  tN.  CO  CO  o 

J  CO  lO  CO  40  CO  lO  CO 


cOiAO 


00  lO  I^  »0  CO  CO  irt 
lO  CO  tO  CO  kO  CO  0 


5;S?3SSJ2Sa8 

COtOcOtOOOtOCOtO  cOlO 


ocoo 

COlOCO 


^^  CO  o  000*  ^  00 

lACOiACOlO  coo 


S558 

0*0  CO 


3;  r-(  05  i-l  CO  CJ  C^ 
CO  O  CO  O  CO  O  CO 

lOCOiOcOO  coo 


3'^O'fl'O'ViO'^iO^ 
30IOOICOOOOO 


ooco 

OtOO 


•rocoiccot 
o  000  Ou 


000 


r*  o»  tr  o»  CO  o  CO 

COiOOTOCOOCO 

00  00  icco  0 


8g 

^"5 


iOiMirae9'<>>cO'<»ie5co 
iOiOiOiOiO>0*CiOiC 


iOiOiO 


IN  ■5;  N  10  <N  lO  1-1 

^  lO^  10  ^  »o  ^ 
lO  tO  lO  lO  lO  lO  to 


S^fS 


O  I-  o  t^  o>  00  o» 

rji  u5  iji  lO  CO  i25  eo 


'i-jt^i-ir-Nr-iNcoNcomcomiOeoiO'j'io 


i  lO  rji  ic  *«!«  lO  Til 

^iniCiOiCtotOiCiOio 


to  tO  lO  u 


JiJiO 
"lO^ 

JiOiO 


lOiOiO 


•ci'io 


OOOSfHOSi— tOSt-100 
^lOTTiO'^iO'^iO'V 

tOiOiCtOiOtOiOtOiO 


-c;o 


tOOtOOOOOOO 


SQOCOOOCOOOCOQOCpOOCD 
*^0^iC^0'^O'^0 

iiCiOiCOiOOOOvCO 


rHO0*-4O0C^C»C^QO<N0O 


lOOOiOiOOOOLOiC 
iCOOiOOOiOiOlOO 


Oi  '(f  Oi  ^  0>  ^  0>  '^  04  ^ 
OOOiOiOOOOiOO 


CO  O  CO  tft  CO  o  cs 
^o  ^  o  ^  o  ^ 

lO  OiOO  O  tCO 


iO-<f  o 

000 


t^  CO  r*  CO  t^  CO  CO 

^  O  ^  lO  ^  10  ^ 

lO  O  iCOO  o  o 


000000 


O  O  o  o 
0000 


o^»-tQW04eooovt>» 

COOCOOCOOCOiOCOtO 


8S8K8 

CO  kO  CO  to  CO 


inomSS! 

10  CO  10  CO  10 


S  1-1 5205" 
MOCO© 

COlO  CO  10  CO 


88S8gS 

lO  COlO  COlO 


SlOrH-fllN 
eo©MO 

CO  lO  CO  10  CO 


o  coo  coo 


-_  -3  04Q0  04 
O  coo  CO  o 

00000 


l^Ot>-Ocp 

coocooco 

OCOOCOO 


flCOfHCp 

O  '*»"0^0 

00000 


■^o-^o^ 

00000 


00000 


o  '^  o  00 

t3«  O  "^  O  ^ 

00000 


C^OC^OC^OiC^OiNO* 


O  'VO 
00000 


^O  '^ij 
00000 


^  O  Tj<  o  ■^  o 
000000 


Oi  CO  O  CO 

-*j»ooo 
0000 


C30cooot>-oot^oor-oof- 
'«i'0'<T0-^O'«ro-n'o 

00000000  too 


rtcotf  cQtfajfticcaJco  aJcocuScoaiaJcicctf  cb  oi^coizacizQci'J^ciu^ 


00  r*  00  r- 00  r* 
'^  O  Tp  o  ^  o 

000000 


oor-oot^ 

^o-vo 

0000 


r-i         C^         CO 


'^K- 


OC^C^C^CJCM        c^c^c^c^co        cocococo 


SCOOCOQCOOepOOO 
OoOoOoiOOo 

0000000000 


■"  o  ^o  ■^  o 

)00000 


Cc^ccf^oda^ccpiHcnp^aQ 


"TX^ 


Page  666] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


2^ 


•xojadv 


•xoiddy    o 


^    ^ 


S 


(iiw(^w(Aaa(sinic^aa 


ojEAptjcop^GQpijaipjca 


SC-)«IN«>(NC4COiMC<5CN 


25QDCaT)<«00>-ltOiOr-l 

eoi-oj'.-i^iHiooioo 


OCOOTO.-INi-IC^>-l<N 


OCOOCOOCOOC^i-IIN 


OjCOPJQQp[jCCB[30QpjDQ 


rH(Ni-lr-l<SltHlNr-(SO 


lO<K>iOeOOeOOCOOC^O(NrHO»THr-ti-li-llNi-l 


S©r-l(NO»-*«5C~C»50i-teOOO«3>O^IM(NOOtO>0 
CTJl40CO>OM>OCOOCOOC40!NOC^rHT-liHi-l 


g<OrHOOO»Or^lMlO>OM    t^  1-1  0>  00  IN  «P  IC  CO  t»  o 
CO  »0  CO --^  TJ< -^  Tj*  Tp '^  TJH    -IS* -^ -^  CO  iC  CO  »C  CO  UD  CO 


t^C^QCSCOtOtOCOOO 
iOCOO<NO(MO(MOC< 

tO'^t~'«<t^'^t-'^t~T)< 


1-1      c^      o)      ■^      tn 
lO     ^     kc     >o     ko 


5tOiOiH^tO«>0(N-* 
SiOOkOTH-^rH-VC^CO 

oocooocococooocoooco 


lO^iOiOO'^OCOr-ICO 

t>-eor~cooocoooeoooeo 


OjcQpijccp^oop^aopi^aQ 


Cat^tOO-^COC^iOr^tO 
IM<NCO(M-*rHmOOiO 

aocoaocooocoaocood 


ot~t~0'>»<eoiNiCir-(«o 

(»IMOJC^COr-l-<tlOlO>5 

OOCOOOCOOOCOOOCOOOIM 


Wt-r^COC^OOt^COtNt^COr-t-^iOrHOOCOi-ltOCO 
■*  lO  •>Ji  lO  lO  ■*  lO  ■*  O  CO   O  CO  1-1  C^  (N  1-1  C^  i-l  CO  o 

t»  eo  t~  CO  t~  CO  t^  CO  00  CO  oo  eo  oo  co  oo  co  oo  co  oo  eo 


•<»|c^oot^cocooooococo 

COOCOiO'*1<iO*iS*'^lOi9« 

t-T»it^eot-eot~cot~eo 


<OtOO(N>CCOO»-*'^<3> 
(NOCOOCOU5COiCI'«I''<*i 

t~Tjlt»Tl<t~COC~COt~CO 


OSrHCOOOt^-^lrHO'OXS 
tHr-l(NOO<OCOOCOvO 

t~Trt»T)<t^Tj<t~i«<t^co 


(NtOtOCOOOCOiOt^i' 


COr~-S'rHOlOt^O>M>IN 
iOCOOeOlH(Ni-liHlMr-l 

t^cococooocooocoooeo 


a>T»<Tt<oDOco«ot»coo 

Tji-ifliiOCOOCOOdi-td 

r-eor-eooococoeoooco 


t~cot-cor~cot~coooco 


OJt~tOC^i-lt»t-(MC<ltO 


iH  r-i  1-1  i-i  o  e^  o  M  o  CO  lO  CO  lO  ■<}< -.jt  Tj< -^  io  CO 
t- "a"  t»  ■»"  t- T)<  t> -.ji  t»  T»<  t~  CO  r~  eo  t~  CO  t~  CO  t~  eo 


csi  to  ■*  eo  t^  1-1  o  00  CO  lO  to  (N  o>  00  eo  lO  to  1-1  p  00 

l0C0l0C0>ac0O?>O(N    0<N0rHrti-4i-lTH550 
to  ■*  to  tjl  to  ■^  t~  •^  t~  ■^   t~- «a<  t- Tjl  t».  Ti<  t»  ij<  t~  ■* 


■<}<Tjiooo>coiOQOOeoiO 

lMOiM>OCOiOeOiO'3<'<J< 

r--'»'r»cot~eot~cot~eo 


)r^co-*tDi-<oooeO'^ 


t-i-li-lt~iCCOCftOOT(<CO 


IM  O  <N  O  C4  i6  CO  lO 

t~is<t~Trt-'«i'i>03t»eo 


StNiCi^COtOr-ICOOiOl^ 
comeoiocoioco-*'*-* 

<;tO'<j<to-*tD'S<tOT("tot»< 


Sasosor«Nioi^-'^toc<i 
C^»OCOOCOiOCOiOOO»C 

,C*tO'^tO"i^tOTt<tOi!}<tO'^ 


T^iOTt<eOt^i-l(35«<NtOi5COI^OOI^CO'<}"t~i-IOt^-*i'^t-0'-<tOtOC< 

■^TP-t(<'T*iTji-i}i'^.  eoiocouScOiocooiNocaoc^iHiHi-ti-ii-ii-iojoe^o 

tOi#tO-^tO''#tO-^tO'^tO"^tO"^t^M*I^i1*C^"^t^"^t^TJt!>'i^t^-<Jit^id* 


OOOgoOCJtOrtlcOt^r-l 
tO-^tO"^tO*»4*tOi^tDTf* 


tftCeotOi-toooiOcOT-ttoco-^iOcot^iHasoi-ito 

ec50<MO<NlOeOiOCOiOCOiOCOiOCOiOCOTI<-»tl< 
,cftOiOtOiiDtO"^tOi^tO"^tO"^tO"<i<tO'^tO'^tOTf< 


gJ3tWldn-":)<tO<M00i-l 
rfStOiOtOiOtOiOtOiOtOiO 


aaO»HOOrHOOCOt^'rJ*lO 


((Nf-i 
rfjtOiCtOiO 


(NONOMO 
toiOtOiOtO»0 


g  lO  »C  to  -^ 
•citOiOtOiO 


OOCOCiiHOO 
1-1  rH  r-l  i-l(N  r-( 

tOiOtOiO  tOiO 


fiMOCOOO 
^(OiOtOiO 


ijl  t»  to  to  t~  lO 
tOiOtOiOtoiO 


COOC^r-li-IC>JOCOO> 


^jtOiOtOiO 


o^c»-^t^eotoiCTft*(N 
ojioeoiocoiocoiccoio 

tO"#tO"^tO'^tO'<J*tO*^ 


tOTi<t^(Ncni-(00>iM(— 

C^OlNOINOCOiOCOiO 
tO^tO^tOiOtO'^tO^ 


INOlCOt^iOtOtO'^OQCO 

toio  toio 


toiO  to 


oMOc 

lO  tOiO  t 


05rHiHOC000>0t0t^^    ^C^i-IO^COt^tOiCaOC<» 
(NOeOOCOiOCOiOCOiO   co  lO  ■**< -^ -^  ■'J* -^ -i^*  i^ -^ 

tOiO  tOiO  to  1*  to^  tO^  to  "^  tO'^  to  ^  to  ^  to  ^ 


OOrJiOl 
tOiOtO 


C^Or-l 
lOtOiO 


toio  toio 


■^OOiO 
iHr-lr-l 

tOiOtO 


t^toto 
lOtOiO 


OOiOcnrJ" 

1-(1-t1-*1-) 

tOiOtOiO 


»tOt^t^t^00tOO>iOC>'^ 


SO(NO(N 
rfjtoiOtOtO 


0(N0(M01N 

to>ato>atou3 


S-iJ<(M^»HiOOtOOtOO> 
ocoocooeoocoOfN 

^tOOtOOtOiOtOiCtO^ 


SrHtOiHiOdiQlN-^eOt' 
oeooeoocoocoooi 

^COiOtOiOtOiOtOiCtOiC 


I*00O00CJ>0at3iOCiO100 

Ro-Tjiioeoocoiocoiooo 


-  lO  t#l  to -^  to  Tj<  t 


«<aiOlOiit>iOU3kOiO^U3tO 


Seo^cooacoooeoooeooo 


e'2«2<5'^'5«^=>cOQeo 
•(•iCLOiCiOiCiOiCiOiOiO 


Sr^t^i-*t^t^t^t^QOt^oo 


.^^ 


Pi  OQ  Ph  CO  plH  cc  P4  cc  CtH  oi 


0<NOOIO(NO<N»H(N 


ocoocoocoocooco 


o5occocoocooco 


SCOQCOOCOQCOOCO 


OC^O(NrHi-lrHiHT-lTH 


lOCOOCSOdOCMr-lTH 


OC^*-trHOOO-^CO<Xir^ 


r^iooscoi-KMcooiOco 

(NOiMOWOCOOoOiO 


i-li-lrHrHr-*i-tl-tr-(<Nr-1 


'Mi-tiMi-f(NO(NOC>SO 


iH -^  <M  eo  CO  C^  Tf  r-l  iC  O  t— OS  CO  t^  OS  CO  1-H  tC  <N  CO 
-HC^rHC^rHCJiHCMi-t^N  rHrHrHi-ti-Ht-l(Nr-tlMrH 

COiOOiO«OiOCDiO(OiO   '^DiO^iCtOiO^OiOCOiO 


r--oacoo>asooosr^otD 

;OiOCOiCCOiOOiCCOtO 


..     5 -^  lO  "^  "^  >0 '<f  »0  CO 
OC00030COOCOOCO 


r-liC(N'^COCO'^iMtOtH 


ocoocoocoocoo?* 


'-tcr.r-ioooicoevir^coeo 
ocoocoocoocooco 

?OiC«OiCcOiCtO»CcD^ 


_  -  ift  r»  lO  CO  iO  CO  lO  CD  CO  ^  CO  1/3  CO  lO  r»  lO  t-- -^ 

iC  "^  lO  "^  lO  ^  lO  ■^  *0  ■^   lO  "^  »0  ^  iC ''I*  iC  Ti<  lO  ■^ 
lO  lO  lO  lO  lO  lO  O  1/3  iC  lO   lO  iC  lO  iC  lO  lO  lO  vO  iC  lO 


cOCOCOQOCOCOcOOCOOi   iOC1iCCTi»OO^i/30»jOO 
^  lO  ■^  u5   -^  lO  ^  lO  Tf  »C '^  O  ■^  1/3   TJ«  lO  "^  lO -^  lO -^  o -^  o 

1/3  i/t)  1/3  ^  ^  O  i/3  tO  tdO   1/3  U3  lO  1/3  lO  U3  lO  1/3  1/3  iO   O  t/3  t/3  i/3  i/3  \C  ^  CO  i/3  CO 


0(NOC^Q(Nr-l(NiHC^ 
i/3lOOuOiOlOU3iOl/3>/3 

LOO^^iOLOLO^tOL/3 


pHGQpC^OQP^GQp^CQpjcO 


Q^COp^CQP^cdp^OQpC^CO  plHCOpHCOPE^O^P^ODpi^CQ 


SiOt/3         kCioSlOCO 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  667 


I 


^  I 

^  s 

(-1  s 

^  a 


a 

r^ 

S 

3 

1 

II 
to 

1 

o 

g 

3 

-2 

(^ 

O 

." 

"^  10 

.•5  =1 

!^  DO 

I  I 

5^  g 


•xojddv 


•ajBp 
•xojddy 


.■SS; 


Or-tOCO'*        io«or~oo 


0»       OrHNOT'*       ic<ot-aoo>o 


pjoipjcoOi^ino^aDpijaiMaiPdaid^aQPi^aQe^od^P^aQedcnP^cdoi^ 


S^  CO  ^^  CO  r-(  CO  1^  CO  r^ 
i-HOr-tOrHOr-tOrH 


CO'HCO^HCO^^CO^HCOt^    CO^^COi-HCO^COrHCO^COFH 
OiHO^Or-(C5rtOi-t    0rH0»H0i-H0i-10i-l0lH 


CO  cO  CO  CO  CO  CO  CO  CO  CO  CO 


CO  CO  CO  CO  ^  CO  CO  CO  CO  CO 


sasasssasa 

CO  cO  CO  <0  CO  O  CO  CO  CO  CO 


P<  en  04  CO  tf*  CC  p^  QQ  P^  CO  P^  CQ 


rHOr-*OrHOiHOiHO?H 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


sasassssss 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


r^eoweor^dt^wtrCi  r*c<aoMgot-H©r-40?»H  osoojo^ogjooooo 

OrHOfHOi-HOHOiH    0t-»0»H0^0r-40fH    0»-^0rHO»HOfHiHfHiHiH 

cocococococococococo  cocococococo^cococo  cocococococococococococo 


^.r-tI>rH^*o^*o^ot«o 

OfHOi-tOrHOfHOiHOr^ 
COCOCOCOCOCOCOCOCOtOCOCO 


S"  to  '^  t^  ^  t^  ^  r^  so  r^  CO 
OrHOiHOrHOr-tOr-t 

^  CO  O  CO  CO  CO  CO  cO  CO  CO  CO 


«^cDcococococococococo 


jjoocOOOuoCgiCCJ-^Cft'^ 
t^cOcococOco^cOcOCOcO 


^oococ^co2*''50»coM* 

^  '"O  CO  O  CO  cO  CO  CO  CO  CO  CO 


g^t^-OCOOiCrHlCr-t^ 
f^cocOcOcOCOcDCOCOCOcO 


QOCOQOCOOOC^OOMgM 
COCOCOCOCOCOCOCOCOCO 


Sc^g>r-*o»Ho»-^oo»-tOi-HOi-^wi-t2ic*^c^2> 
cococDco^cococococo  'co cocococOcococococo^co 


>^0»C0OC0OC0OM— *Wi-*W^r^C<.-(WOCOOCOOC02aC0  24'*2>'^C 


COcOCOCOcOcDcOcOcOCOcOCOCOCOCOCOCOcOcOcCcOcOCOCOCOCOCOCOCOCOCOCO 


o-^oco^eoiHcoi-tcsc^c^Ni-tcoi-ieoO'^o 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  |cO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


t-t'^^COCSCO(NC^COC4!COi-('^TH'»<0»OOiO 


IcO  1-1 -^  tH 'J^  c 


CO  CO  CO  CO  CD  CO  CO  COcOCO  COCOCOcOcOcDCOcO  CO  CO  CO  CO  CO  ^  CO  CO  CO  CO  CO  CO  CO  CO 


COCOCOCDCOCOCOCOCOCOCOCO 


3SSSSSJ 


C<-^MCOCOCOCOC<^i-H|iOi-HiOOCDOcOgt^g|r-gOOgO>^OigOgOg 

cocococococococococo  !co  coco^cocococococDcocococococococococococo 


ggt*OcO»-tco»-tiOWiO 
*<£cOCOCOCOcOcOcOcOcOco 


^oao»-»r^^coc<coc<»o 
•^cOcOcOcOcOcOCOCOcocO 


S*OOQTHt*»-4COM<OCO»C 
^  COcO^OcOCOCOcOCOCOcO 


fcOooiHt^c^r^coco-^iO 


.{•COCOCOCOCOCOCOCOCOCO 


gO00rHt^C<r*C0<0'^»0 
^  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


JOCOrHt^WcOCOiO'^'^ 


^COcOCOcOcOcOcOCOcOCO 


»OCOrH 
:i-ti-<rH 

•COCOCO 


r^  cs  CO  CO  lO  "^  ■*>« 

iH  i-t  tH  r^  i-H  i-H  fH 
CO  CO  CO  CO  CO  CO  CO 


>oaoc» 
i  CO  CO  CO 


r>- CO  CO -^  iC  kO -^ 

tH  1-H  i-(  r-t  rH  iH  ^H 
CO  CO  CO  CO  CO  CO  CO 


;oooi-f 

*  CO  CO  CO 


CO  C^  iC  CO  M* '<**  CO 

f-4  1-1  i-H  r-trH  rH  fH 

CO  CO  CO  CO  CO  CO  CO 


;cotO<0 


to  w  lO  CO  eo  ■*  c» 
CO  CO  CO  CO  CO  CO  CO 


CO  CO  CO  CO  CO  ^  CO  CO  CO  CO 


CO'^'^'J'lOCOlOe^COrH 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


i-H  iH  rH  r-l  iH  rt  .H  .H  rH  r-l  lH  rH  rl  O  rH  S  S  O  N  © 

CO  O  CO  CO  CO  CO  CO  CO  CO  CO  COCOCOCOCOCOCOCOCOCO 


CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  COCOCOCOCOCOCOCOCO  CO  CO 


COCOCOCOCOCDCOCOCOCO 


iC^lOCOcOCJt^rHXO 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


iC^COeOt^C*OOr-40>0 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


OCOCOC^t^rHCOOOiC 


cOcocOcocOcocO'-OcOcO 


2SSS?5B?38?5S 

COCOcOcOcOcOcOcOCOCO 


S8SSS?J8?5gSS 


COCOcOcOcOcOcOCOcOcO  IcO  COCOCDCO'-OCOCOCOCO 


CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


CO  CO  CO  CO  ^  CO  CO  CO  CD  CO  CO  CO 


cocococococococococococo 


■«^lQMC0CJt^.H0QO0»0> 
C<l©S[«5MOMO?iO<SiO 

COCDCOCOCOCDCOCOCOCOCOlC 


CO  CO  CO  CO  CO  CO  CO  coco  kC  CO  lO 


'^SJr^aS^SSSS  S§?JS?5SSSS§  8gSSS8SSSSS3S 

cocococococococococo    CO  COCOCOCOCOCOCOCOCO    CO  COCOCOCOCOcO^COkACOiO 


COC<t*rHQOOO>©»-(gp 
rHr^r-*THr-)t-Hi-(OC^O 

COCO^COCOCOCOCOCOCD 


?5Sg58S5SS§8 

COCOCOCOCOCOCOCOCOCO 


cOcocoCOCOiOCOiOcOiOco^ 


coc^r>-i-Hco^<3igor-4r* 


cDi-Ht*oooopa>t*tHco 
cocococococococococo 


cocococococococococo   CO  kC  CO  iC  CO  ^  CO  lO  CO  lO  CO  U3 


tococococococococoic 


;OrHrH 
£  CO  CO  CO 


lO  iH -^t*  <N  (N -^  ^ 

rH  i-i  r-t  i-(  i-H  rH  r-t 

CO  CO  CO  CO  CO  CO  CO 


it^iCCi-^OiNC^^COOi 

:OrHOr-lT-liHTHiHi-HO 

»  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


-  C^  g  1-H  O  5^  <N  00 

>cococococococo 


isas 

» CO  CO  CO 


or^ooot^ocp 

T-tOOOOrH© 
CO  CO  CO  CO  CO  CO  CO 


>O00i-l 

:ooo 
» CO  CO  CO 


ggggggg 

CO  CO  CO  CO  CO  CO  CO 


lOOlcOcOcOr^OicpQ'^ 
COCOCOCOCOCOCOCOCOCO 


0«C0C0rHlftOC0  000Qt* 

cocococOcocOcoiOcOtC 


'■^Qocor-*r^*oa>"^oc^ 

rHOr-(Oi-<OrHO?5o 
COCOCOCOCOCOCOCOCOCO 


COcOiOjOCOCOOONOi© 
CO  CO  CO  CO  CO  CO  CO  ^  CO  CO 


e^^COC^iCHCOOSOOb* 
tHOrHOrHOrHiOrHiO 

COCOCOCOCOCOCOIOCOIC 


Mi-tCOOSiftCOCOCOQO»C 
cOcocOiCcOiCCO»CcOiO 


tHC>c^i^-^cDco'^r*c^ 

cOtOcOiOCOiOcOiOcOiC 


6iioco25o31r5coSwicco55 

COtCCOiCCOU^^OiACOiO'-O^ 


SScoScoiocoicSTfco^ 

COU^COlOcOlCcOtCCOiCCOUd 


isSjcoiocoSco^co-^cc"^ 

COiCcOiCcOiCCOi/iCOiCCOiC 


aa^-IQO>CSt^'^C0cO-^t>-(M 

c<noeo-^co^co^co-4coTj« 
cOkOCOUI^cOLCcOiOcOiOcOiO 


COiOCOiOCOiCCOiCCOiOCOiOcOiCCOiCCOiCCOi/^cOiO 


§8gS;:JS2SSS 

COCOcOiCcOiOCOiCCOiO 


•lOCOlO 


tH  r*  Oi  OS  I>-  »-H  cp 
CO  us  ^  UO  iC  CO  lO 


§SS28S§5S!J 

COiOCOiCcoUDCOtOcOiO 


dcodaapiaaoiisfiaa 


^^^ 


'^ir- 


IC        «3        t^        00        04 


CO  lO  CO  O  CO  lO  CO  lO  to  lO  CO  lO  CD  lO  CO  us  CO  iO  CO  iC  CO  lO 


COiOCOiOcOiOcOiOcOiC 


COLOcOkOCOiOCOiOcOiOcO^ 


(4  CO  0^  CO  p4  cc  p^  oD  p4  00 


O        —I        IN        CO 


C<  00  p$  OQ  P4  00  P4  CO  P4  00  P4  OQ 


1/5   CO 


oS"^S~^^"^ 


Page  658] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


B  a 


a  s 


^  I 


3 

o 


.=^^ 


•xoiddv    q"* 


•aj'Bp 
•xojddv 


<N        C^        IM       <M 


« 


P^aJOicQpiHaQPicnP^cc 


CfirflpHccrtodPiSccWaQ 


S  CO  rH  CO  rH  CO  r-4COi-l  CO  i-H 
O-HOi-IOrHOi-HOrH 


SSOOOqpOOOOOOOCQO 


?5 


IS 


CO        CO        CO        CO 


PhcqP^cqPchcoPchco^co 


^^CCO^COP^HCQP^X'P^CQ 


CO^COfHCOi-HCOi-4COM    COtNCOC^COfNCOC^COiM    C0!NC0iMC^01C^(NO»iM 
O  rH  Oi-H  Oi-HOi-iOfH    O  i-(  O  tH  O  i-i  O  i-(  O  iH    O  rH  O  i-H  O  r-l  O  *H  O  rH 


Oi-tOi-HOrHOi-HOrH 

CO  CO  ^  ^  to  ^  ^  ^  ^  ^ 


sss 


i-(S»-iOi-tO«-lO.HjO.-HOr-lOiHOt-tOiH 


oooooooooo 

OOOOCOOOOOO 


gOOiOOiOOir-iaiwMMOOrHCOCiQOC^XC^X 
i-tOiHOi-iOiHOrHOrHOi-HOWOrHOrHO 

^oooooooooooooooooooo 


<Nt>-(Nr-cot^coocooN?<o-^u^'^iCirt«inio»2 

■OrHOi-<Oi-tOTHOt-HO»-HOi-tOT-*Oi-HO 
OOOOOOOOOO  lOOOOOOOOOO 


rH0i-H0i-H0rH0i-t0r-(0i-*0-H0rH0r-(0 

^oooooooooooooooooooo 


»0^00»OOlOOTt^t^'*■^»COOOCOCOCOQO'^JO>M 
rHOiHOfHO»-HOr-(Ot-tOf-HOi-HOtHOrHO 

oooooooooo  oooooooooo 


g'OQOifttSOiOt^OI^OO 
r-10rHOT-lOi-HOr-tO 

^oooooooooo 


t^OI>iOt>iOQOiOGO-<^ 
i-tO.-HOr-lOrHOr-(0 

oooooooooo 


SI>l>t^O00O00i00i»0 
r-iOi-lOi-HOt-tOi-tO 

^OOOOOOOOOO 


ji a>oo>iO ovoo -^  1-H CO  (M co c^ <n co w co »-t tj< »h 

^oooooooooo  oooooooooo 


Ol^OlCOOCOOWt-tC^ 

o  o  o  o  o  o  o  o  o  o 


0>'^0-^OCOrHCOf-l<N 
r-(OC^O(NO<NOC^O 

OOOOOOOOOO 


*  (M  CO  CO  CO -^  CJ 


Scsjoc4oc^o6ioc^o 

^oooooooooo 


SCOCOrt^CO^I^C^iOC^OW 
<NOC^OCN)OC>»OC^O 

^  oooooooooo 


SiOC^O(Nr^rHI>OOOOl 
0JOcNO(NOCmOCS»0 

p^OOOOOOOOOjO 


OOOOOOOvOOiO 


oor^o>oooio>aooii:^ 

OOOiOOiCOtCO^ 


Oi'JiOGOrHt^'NOC^t 


cr>a»o>a>'3>oO(^GOOooocoot-*ot^ot^oi>' 

OOOOOOOOrHOi-HOi-lOr-lOr-lOrHO 

oooooooooo  'oooooooooo 


^i-(iMi-tciocoocoa» 

OOOOOOOOOiO 


C^  (N  C^  f-(  CO  rH  CO  O  "^  O    Tj<  C>  >C  00  O  CO  O  !>- t^  O 
oooooooooo   O  vO  O  lO  O  lO  O  lO  O  lO 


>iOi3>oo>ocoi>-t^iQOt^a>oaiioO'^r-ico 

><N^  (MiO<N  lOCJ  lO    C^  lO  (N  »0  (M  lO  CO  lO  CO  lO 
OOOiOOiCOiOOiO    OtOOiCOiCO»COiO 


C^SiO<NiO(M»5cOiOCOiO 
Oi00»00i00i00»0 


rH-^  C-JCOcOCC^C^iCt-H 
COiOCOiCCOiOCOiOCOO 

OiOOiCO»^OiOO»C 


OOTHiftC^'^CO'^'^OO    lOCNOi-HOOt^OlOOCO 
COiOCOiOCOiOCOtOCOiC    COiOCOiOCOiOCOTtfCO-^ 

OiOOiCOiOOiOOiO    OiCOiOOiCOiCOiO 


_  ^  _        »0   CO -^ -^  CO  lO  (N  O  r-(  t- Q   00  Ci  Oi  00  O  r- 1-1  O  CS  ift 

(NiOCOiOCOOCOiOCOift    OOiOCOiOCOiOCOiOCOiO    CO'^CO"^'^-^'«f'^'<1«'^ 

OiOOiOOiOOiOOiO    OiCOiOOiOOiCOiO    OiCOiOOiOOiOOiO 


SOOOiO  ooo  t^ 


St^  rH  GO  Q 

^OOOOOiOOiOOiC 


i-Hl-^C^OCQiO-^'^iCCO 
COiOCOiOCOiOCOiOCOiO 

OiCO»OOiCOiOO»^ 


O(Nt>-i-H00QO>O^Ot^   i-iOOJiOcO-^vOCOOrH 
OOlOCOlOCOiOCO'^'^Tr    -<^^Tf<-«J4-^'ie}*^TtTf<-^ 

O  »0  O  »0  O  »0  O  lO  OiO   O  lO  OiO  O  lO  OiC  OiO 


Sa>ooo>i-Hcc<Nt>-coo 
CSOCOtOCO*OCOiOCOiO 

^OOOtOOiOOiOOiO 


CO»OCO»OCOtOCOiOOOiO    OOiO^-^-^Tj^TjfTjtTt*^ 
OiOOiOOiOOiOOiO   O»00v00v0  0i00i0 


io-^oc^t^i-*a>ooao 


*OODi-HXNOCOiO»i 


, ,_ iiQ-^ocor^c^oOt-i^OQco 

-  CO  lO  CO  iC  CO  O  CO  lO  CO  lO  CO  lO  CO  O  COiO  CO  »o  ^ -^ 
^  O  lO  O  ^  O  iCi  O  iC  O  tO  O  »C  O  »C  O  O  O  iC  O  lO 


OiOOtOOiOOiOO»OOiOO»OOiOOvOOiO 


StNt-COtO-f^iOCOt^C^ 
CO»OCOiOCO»OCOiOCOiO 

^Olooioo^o^ou:^ 


SCOtOTf^OCOt^rHajQ 
COUttCOOCOiCCOiOCOiO 

^OiOOiOOiOOiOOO 


;iftCOOC^OOf-tOiC3>»-HCO 
;COlOCOiOCOiC00Tj<rrTj« 

•OOOiOOiCOiCOiO 


•0'-<OOOOCOi-lt>-<MiC    CO-^iOCOOi-HCOC^OOQ 
g  CO  O  CO  in  CO '^  Tj< -^ -^  Tt*    yji -^  ^  -^  ^ 'eS*  ^  CO  ilO  CO 

-OiOOiOOiCO'OOiO   OiOOiOOOOiOOO 


oorHa>QooirHr*coo 

COiOCOOTfTf'^Jf-^T**'^ 
OiOOUDOiOOiCOiO 


Tt<'*iOCOI>C^opQQ(3ii-H>COO-^-*fOCOt^f-< 
■^■^-^■^■^-^^■^iScOUCiCCiOCOiOCOiOCOiOCO 

o»oo»ootoo»oo»o  iOicoioovoo*noio 


00>r-iOOC^O-*»<iOiO« 
OiCOiOOtOOtOO^ 


t*C400.-HOSO>THGOOOO 


OiOOiOOiCOiOOiO 


St>.a><?n>'-HO(N-^Tf«co 
COT}«CO'^^Tjf'*3^T}*'^'^ 

^OtrtOiCOiCOiOOiC 


»O»-lt-*O000QQOC^»O 
^■^^■^•<J*CO«OCOiCCO 

OiOOiOOiOOiOOiO 


g  CO  O  O  1^1-4  COCO  (M»0  0 
^OiOOiCOiOOiOOiO 


OOOOOt^OiOC^COCOrH 
Tl«o5-<*<OOiCCOiOCOiOCO 

OiOO>/iOvOOiOOiO 


S*cr>cor-4c^(NOTj<osor-t^»oo>corHi-*cooiiOt^  i>.iooico»-4«-*coa>inr*  i^ioococ^oicoot^io 
COTi<Ti«rj<TjfTt«TrC0'^COr^CO-^C0iCCOidCNJlOC^    iOC^»0<NOC^Oi-40i— <    Ot-'i— li-HrH»— ii— fOT-*0 

^OiOOOOvCOiOOO   O  i0  0>00i00i£500    Oi00i01>i0t*»0t*»0  t>->Ct^iCr^iOt^»Ot^iO 


H-^focor^i-iaiaiwoo 


TJir^-^CbiOCOiOCO  OCOiOCOOCOiOC^OC^ 
OiCOiOO»OOiOOiC  OiCOiO  O  iC  o»oc*»o 


35  0>  «-<  CO  <>)  O  ■" 


CO    t-^f-tOiOSi-HCOCOOiC-^ 


Tt* CO »o CO »rt CO S CO S CO  tocoib(NO oi otNOC^ 
o ic o lO o lO o lO o o  o iC o o t^icr»ior*io 


T-tOOOidOCOO<-*OOOi    OoQ^lO^'^fOC^aOO 
lOCQiOCOiCCOiOCOiOCJ    0?iOC^OCJOC^O(N 

Oic o o o lO o vo o lO  r* ic r^ lO t^ tc t-* ic D» lO 


C0C0intHr*0*0l00rHOC0-^iD(Nt^OCll^i-<iC 
iOCOiOCOiOCMO(NOC^O(NOiNO(MOrHr-lrH 

oicoiooiOOiot^iot^'Ot-ict-ior-icc^io 


iOO»I>t^01iOi-HM'COCJ 
»0!NOC^iCC^OC^OC^ 

OiOOiOOiCt*vOI>»0 


iooi^r^giiC<Nco'<i<o 

OC^IOi-HOr-liHrHr-^r-l 


SaiOi-ia>cot^"«t<icoco 
COrjtTj^CO'^CO-^CO-^CO 

^OiOOiOOiOOiOOiO 


oO'-HOOic^r^'^tQ^co 

OtOOiOO'OOLAOO 


§r-(OOlCOr»tOtOt^CO    ^OC^OOTt*iOt--COCJQ 
dOi-HOi-tOr-lOi-H    0»-HrH0i-H0r-'0i-H0 


Sa>Oi-HiococoiOi— ii^o>  oat^r-tiococoiCi-Hr^o* 
CO  CO  Tji  CO -^  00  "*  CO  TJ<  CM    Tj*  C^  lO  04  O  CM  lO  CM  tO  iH 

^  O  lO  OiO  O  lO  O  tO  O  lO   O  lOO  lO  OiC  O  »CO  iC 


^r^comioco 


St-.-ia>05t-H,    ... 
COCOCOCM-^CM-^CMTfCM 

pcfOtOOiOOiAOiOOiO 


SCMTjf-^CMOOOOCOOO 
COCMCOCMCOCMCOrH-^r-i 

^OOOtOOiOOiOOiO 


P^COtfc^P^CfiP^COPiHCG 


-,       rH        CM        CO        Tf« 
O       CM        CM        CM        CM 


'T 


O  O  I-* -^  ^  CM  OO  00  t^  rH  lO  CO  CM  O  O  Oi  C^  f-H -^ 
lO  PH  O  rH  O  rH  O  •-<  O  O  iH  O  i-(  O  r-l  O  «— I  O  CM  lO 

o tO t*io t* o r»vc i> ic  r» »o t^o t> lO t> TT t> ^ 


_    00  i-l  O  CO  "^  lO  CM    QOOOr^COiCiCC^GOO 
TJ<  CM  TJ1  T-)  lO  *-l  lO  i-H  lO  rH    lOrHOOOOOOOO 

oo o»c o ic o ic o »o  o >o t* lO r* lO t^ lO r- »o 


CM'^iCCMt^OOit^i-HiQ 
OiOOOOkOOOOiO 


'<J«C00004GO<-HiO'^CO 
iOOtOOOiOOtOOiO 

OiOOiOO'^l>''«3*l>'^ 


S^COCtJodP^CGt^COP^GQ 


fO      r*      oQ      o>    ^5^ 

CM         CM         CM         CM         CO 


OI>C0iCOCMe7>ClCM<0 


^Q^t^CM-^iOr-tOOQO 


^oiP^coPtHxPtHCA'P^co  PehgoP^qqPhgqPhcqP^od 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  659 


S  -s 


-a  ' 

CD        t> 

Q     II 


.1^ 


■xojddv 


•»)BP 

xojddv 


.-I      e-j      cc 


pHodMcnC^copiHaiPiiaD 


EOi-lOi-lOrtOrHOrH 


Or-«0.-10r-IOlHOlH 

rf*  CC  to  to  to  to  to  to  to  to  to 


^  ?0  CO  <0  to  <0  <0  <0  to  CO  CO 


giOgio^ce^coMcom 

tti  to  CO  CO  CO  CO  CO  CO  CO  to  CO 


t^cototococototototoco 


^tOtCco^tOiOCOiAtOiO 


OdoQP^OQpHCCP^CAf^QQ  P^QdpEJcCp^QQP^odpciQd 


SccMcoMcoi-Hcoi-teo 
rlOi-lOi-lOi-lOi-l 

CO  totocotocotoco^to 


tfoQMoipjaQPgadpiiod 


rH  00  f^  CO  tH  CO  1— t  ^  ^^  Tf* 
Oi-iOf-iOi-iOf-<OrH 
tOtOCOCOCO'^tOCOtOtO 


OrHOriOf-HOi-fOi-HOOOOOOOOOO   OOOOOOOOOO 
CO  to  CO  CO  CO  CO  to  to  CO  to  CO  to  to  to  to  to  to  to  CO  CO  cotototototocotococo 


totototototototototo 


rHtpe<*e<go»«c<g 
to  to  to  to  to  to  to  to  to  to 


toeot»eot»c»ooiNoOiH 

i-HOr-IOr-IOr-IOiHO 

to  to  to  to  to  to  to  to  to  to 


rlOJCJOlMOOCOOCeOt^ 
tOtCtOkAtOiCtOiAtOiO 


tOiOtOiOtOtCtOiCtOtO 


•C^tOtOtOIOtOtCtOlCtOlO 


cotocoioniocoicco'.ti 

tOlOtOiOtOiAtOtOtOlO 


<to>OtO>OtOU3tOiOtO>0 


^lAtOiOtOiOtOiO^kO 


M'tOQt^O>CQaOO>t~QtQ 
rfftOiOtOlCtOtOtOiCtOlA 


tototototototovtoto 


totototototototototo 


t-iOi-iorH©«55e5io 
totototototototototo 


c^iisc<Se<Sw>o?5S 

tOiOtOtOtOtOtOOtOiO 


'Mto>oto>o>QtoiQt^^^-cQaQC4a>c40iH.-io 

tOiOtOlCtOiOtOiCtOlCtOiOtOtCtOtOtOiCtOiC 


oc<i-cMi-i.-ic<oe50i 
miocQ>cc4>ocoiAco'«< 

tOiOtOkOtOiOtOtOtOlO 


!SS!8G:C;2SS!222 

tOiOtotCtOiOtOiOtOiC 


i-Heoc^cjOT^^otoo 

^  ^  ^  ^  ^  ^  ^  ''t'  ^  CO 
cOiOtOtOtOiOtoiOtOiO 


^^^^^*^.T^^^  ■"^ c5 ^ rt ^ CO *o CO lO CO 

to  lO  to  to  to  iC  to  IC  to  lA  to  kO  to  iC  to  lO  to  lO  to  lO 


gS5;5J^g!g5555! 

.CftOlOtOiOtOiOtOiOtOiO 


iC'ar^QOOOJOJt^rHtD 
^^''It'T^CO^COlOCQ 

tOtOtOtOtOiOtOiOtOtO 


B'^tytOCQtOftcOOOaO 
■^^^^^^^.^■ItcO 

.citoiotoiotoiotoiotoia 


ioco>ccoioco>am£c^ 

tOtOtOiOtotOtOiOtOiO 


St^Ntocosi'^wtOi-i 
CQiOCOiOCCiOCOiOCO 

tOtOtOkOtO^tOtOtOiO 


sStocSotNOc^oSI 
toioto>ot«iat^ior«io 


^■"Ttrcoioeoiomioco 
^toiotototoiotoioto^ 


>OCOtOiHqOQC»OQ'^tOCOlQ>CeOt^l-IOO>f-ltO 
;><5cOiOCO><ScO>Oe^OC4   0C40C^OM0r-li-lrH 

to>oto>otoiotoior>io  t«>or>ior»iot^>ot^io 


S'e^tieoioio^'tDMooiH 
tOCOtOCQUScQiOOOlOCO 

^tOiOtOiOtOlOtOiOtOiO 


toiOt~>ot«iOt«ior>io 


SSeoioeoiOOToSSM 

tCJtOlOtOlOtOiOt-lOC^iO 


gO.HooeoiOioeo«>  — 
r-ioc*iot^»oi^iot*io 


SS8?3SS222i:;  SS22S2SSSS 

t^iOt~iOt>.iOt»iOt~iO   t»iOt~iOt~iO»^iOt^iO 


S"»O>^0QS0tO3'.9<^C^ 
iOC^oSlO<NO(NOC< 

,cito>ot~iot^iot^>ot~io 


gpO00NtDiC'*t~r-l 
J5rt.-,rtr-l.-liHi-li-> 

t*iOt^lOl^lOt^»Ot*iO 


g'eotoiO'>»;i--fio>Qr-ioo 
.Cjt^iOt^iOt^iOC^iOt^iO 


cotoi0^t^.-cpg>ri^ 

t^iOt^lOt^iOt^iOt^iO 


oNo?5o?»ocoi?5 

t~iOt~iOt^iOt~iOt^'W 


Sic5SSoco2eoiocou5 

t^iOt^iOt»^t~^t»"«< 


ONONrlrHrHrHr-trH 

■<!r»iot»ior-iot^iot»m 


gOt^CJiC'^cot^.-HOaap 


g-^eoco^Hoooci-Htococo 


S*r*oooicp*-(co^'Or*oo 


.cjt^iot^iot^'i't^-.jit*.^ 


gC^l^iOlCCOC-)rMO>Tj*tO 
C^4CC^USC^(OCO*^CO^ 


COiOCOtOCOiO^^T))'^ 


5J*Tf<cor»i-iQQOcoiO 
fJOc^oiNo553coio 

t~>Ot^iOt~iOt^Vt^'>»' 


tDC^<3>ooco>ototH<3aQi'«<^aQa>eOiOoOQeoio 
«ioco->»<t»'^-<f*oSS  iow3Noe<o«rti-( 

t^  ■*  t~  ■*  t^  Tf  t^  ■*  t»  ^  r,  ^  f  ■v  00  ■"C  00  ■*  00  ■»< 


tO<-IO>a0!N>O>OCM0QO> 

NOCiiraeoiocoiOco->»' 
r»iot^'»'r-'9't~Ti<r»T»< 


rtioiO«oqooc^ 
^  ^  ^  ^  ^  CO  *o 


SiOCOCJtooaOiOeoM 
uicoioco'.rco'*'^'^ 

i>.  ^  t**  .^  r*  ^  t»  ^  t*  ^ 


tocoo>o^i-icoc>c>?< 

"COiO«lOeOiONON 
l^^C^^t*^t*^O0^ 


■.j'ost^toocj'^OJaoira 

CO^CO^^^'^CO^CO 


COtJitCCOtTCO^C 


S;^*-J^.ooo»Ococ^r^oi  OiC-^csooooim 


eiNiOIN-<J<CO-*CO'»COCO 


■CO.a"<NiC 

"  r»  re  t^  •<(<  t^ 


■*too 

(NIC  IN 


S'lOCOOOO^Ht^TfcOOOO 
e^-^<N'*coccco«icoco 


■-itOiOc^o>ooeo-*QOO 


gooust^totot^iOCR'* 

co^co^co^co^co^ 

toioto>oto>oto>oto>o 


SlS2£20£22!2S2SS 

cOiOCOtOtOtCtOiCtOkC 


r-t^OaCOQ^CICO'^r-* 
^CO^CCiOCOiCCOiCCO 
COiOCOtOcOkCtOiOtOiO 


Sc^coor^oQoitOfH^ 
toiototototOtOiOr^kO 


t^iOt^tOt^kOt^kOt^iO 


I>pOOOMtO'<«<COt^O 

t^iOt^iot^ior*ior*»o 


i-lrtr-lr-li-l&C^OCSO 

t^ior*ioc*iot^»ot^»o 


^OOCOlOtOMOOlCltO 

cJOMOcJoNioeoiiS 

t~U5t^U5t»iOt>-'*t^* 


iSSSS 


-iOt^-«"r--*r»-<i«t^'* 


coSSeoio^f^'*^^ 


rHOQ'W^OOi-INt^tO'N 
'«<V'*-*TflT»<iOC010eO 


■«"lo«ioc?88oS 

t>-^r»'»'t»'^oo^oo'* 


^^tOiO^^OtOtOrHf-ttO 
OCJOMi-lrt-trHNO 

oot>«oo'<«'oO'*aO'>«<oo-* 


iH  1-1  lO  t~  O  CO  5< 
lO  CO  lO  CS  lO  c<  o 

t^  T><  r> -9 1^  ^  00 


■vcoyr 


t*  ^  00  ^  00  'tf'  00 


OiOg 

•«i<oo-* 


SiO  »0  »-l  O  to  lO 
i-H  O  1-1  i-H  O  .-H 

00  ■•1' 00  •<»<  00  ■<»' 00 


OMiO 

■o<ooeo 


00 -^  00 -^  00  CO  00 


CO  00  CO 


SrHlOTfMOOCTii-liOvC-. 
C^C0C^CO!NC^CO«C0C^ 


TfMOOCTii-liOvCINloQOOC^-'JItOOr-l 

t- '!}<  t".  •*  t~  Tji  r» 


rt  CO  P5  cert  00  PS  03  ft;  CO 


rt        C<         CO 


'~:x^ 


8SS 


siOi-ii-itotope>4'« 

3  0iOi-l-^i-(^CSCO 

cocooocooocooocoooco 


PjcOCtfCTpScOQ^ico'OScO 


to      r^      00      oi 


'-^r 


t;'~C<C<'^'^COC'9>'5 

Oi-iiH.-iiHoe<op<3 
oo'VoO'VoO'^oo'^iooco 


T»«00O>eOiOt»tHC»0QiO 

r^Oi-ic5e5ioeoio«S^ 
oo-otco^oocoaocoooco 


ootoTfc^r-oi-ite^ 
cjioeMioeo-^co-w^co 

oocooocooocooocoooco 


tOOSNCOOtOtOOi-^rH 
I"CO'^COCO'*(NiOC< 

ooeoooeoooeocccoooco 


ot»t^e5TfcoNiOi-i» 

COCOCOCO-^C^iOi-lOO 

oocooocooccooocooco 


o>r»toO'*eoN>Oi-ito 

flC<«(N'*i-HiOOOu5 

ooeooocooocooocoosiN 


CsScoo^oDOjocDSoopjco  QicoftScdoScoftSoopjai 


Page  660] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


J  i 


•xo  jdd  V 


fE^  02  P3  CO  p:5  ad  o4aQp3«i  cs^oQptJoQPi^aQrtcQpdaQ  oizcpi^pia^^a^pi^^ 


Cc!Mip:5«ip:HCBPc3aic^cQaHa!i 


-JOiCOi-^i-tCOCO^'^aiUot^QOCOO-'t'T-HfMCOO 


s£iocot^c3qoooa;»Ht>.  SOiCusTf-ErtNOQQgco  -ji^-,^-:,^^-,^-,^ 

.^  iC  CO  tO  ?D  iC  ^  CO  lO  O  lO  CO  tO  to  lO  CO  iC  iX>  vO  <0  lO  cO  lO  CD  lO  CO  lO  cO  iC  CO  lO 


c^t>Tt<iQiocot-»-Ha>o 


rtfOcOOOOOcOO-^C^OaTt^O 
COiCCOOcOiOcOiOcOiOCOtO 


tHGOCOCOiO-^COIMOOOQOO 
!M00(MCOCNCOtMC0(NC0CO(M 

fO»CCOiOCOiOcOiOcOiOCO»0 


S'-^c^iTiOt^aicor^Qco 

^lOcOiOCOiOiOiCiOcOiO 


S'COi-*'^OCDGOt^cOCs»C 
^SjiCcOiOOiOiCiOiCvCtO 


afNQ-^OSiCt^t^COQOiC 
iiCcOi-OiCiOOiCiOiOiO 


g'c^O'g«asicoococoGO»o 


(M"*C0C^i0rHCD0lQDI>O«0i-HTt<C0CCiOi-lcoa>00I^OC0(N'^00CMiOOt^Q0 
cOiOCOiOCOiOCOiOcOiCCOiOCOiOCOiOCOiCCDi^CDiOCOiOtOiCCOiOCOiOeOin 


WC^^COQiCOitOt*    ODCOai-^i-HCOCOi-H-Tt^OJ 
CO  iC  CO  la  CO  »0  CO  lO  CO  vO    CO  lO  CD  O  CO  iC  CO  O  CO  lO 


lOiCcOtOCDiCtOl^CDvO 


r*CDOO-^OOOr-li-HCOO 


OlCO  Q<M  (N  *H  rOQ-^  00    CD  t^  t^  »0  ^  "*  O  «  CSI  t-l 
lOiCOiOOiCOSOTj*    O  •*»<  O  ■«*<  O  Tj<  1-t  Tt<  iH  Tf 

lO  IC  CD  O  CO  lO  CO  lO  CD  1^2    CO  »0  CD  lO  CD  lO  CO  vO  CD  iC 


~:(rjO"g<oiirscocDOi^io  oi-^Qcoi-ii-ic^Q"^a>liooocDcDoo»cgicoiHOJ 

rfiiOcOiOiCiCiCiOiOtO»0   lOiOcOiCJCOiCCOiOCDiOCOvCCDiOcOtOcOiCOi^ 


S*C^JO*^'J>'Oopcpr^t^cD 
lOO'OiOiCiOiOiOlOiO 

^iCCD»OiOiOvCO>OiOiC 


-JWrH-g^CaiLOCOCOt-t^CD    QOiOQ'^i-ICOMCNCOQ 

$: ic o »o ut" lO ic i5 lO lO lo  iCiOOiOOiooiooio 

,^  iO  CO  UO  lO  lO  lO  lO  vO  >0  lO  lO  lO  CO  vO  CO  lO  CO  iC  CO  lO 


GO'^OCOi-t(M(NfHCOai!'»*<GO»'M>l:^CDQO^OCO 
iCOcOiOCDiOCDiOCDiOCOtOCO^CCDiOCOiOcOiC 


■«fOii«oo^r-*QOcocj»ic 


S"COt-i'«tQiOOs^00l>t^ 
,^iCCDiOcO»dCiOtOiOiLO 


2cOOiOrH'^C^COCO<N   -?fi-liOQCOO>l^t^COCD   aiCDO-^(N00C«0C^Tt<OiOa> 
OiCcOiOcOiO^OiOCDiO   COiOCDiCcO»C«0»CcOiC    '^lOCOiOCOiOCOiOcOiOCOiO 


^-^(NiCi-tCOQt^OiQOGO 
^i/^CDOcOiCtOiOiCiOiC 


a>t^ocpi-4ioc^'^coco 

vOiCO»OOiOOiOOiO 
lOvCCOUDCDiCCDiOcDiO 


S'-^oJliCi-icoot^oaoai 
10000100*0001^ 

^lOCOiOCOiOCOiOCOiOiO 


crscOOt^i-HCOtNiOCO-^ 
-  ^OiOOiOOiOOiO 

iOiOcOiO<XnOCDiOcDiO 


«a*iOCOCOC:i(COi-Ht^OOOaa 
S;iOO>OOtOOiOOiCiO 

,^iOCDiOCD»OCOiOCOiCvO 


_     O  O  CO  i-H  t*  (N  CO  CC  lO 
lOiCOtOOiCOiOOiO 

lOiOCOiOcOiOCDOCDiO 


•xoiddv     ft*^ 


giOOiCOiOOOOiOO 
^lOcOiOCOiOCDiOCDiOcD 


;  CO  ^  I-  CO  i>  c^  c 


giOOiOOibOuSOiOO 
^cjiOCOiOcOiOCOiOCDiOcD 


r-;i>iOGO*<i^ooeooicoai(N 

giOOiOOiOOiOOiCO 

^lOcOOcOiOCOiOCDiOCD 


-Jt^iOCO-^Ol^OiCCOCC 
S:tOOiOO»OOiOOOO 

^lOcOiOCOiCCDiOCDCDcD 


jQOcOOOiCas>OOlTfO'^    OeOiHCOTH(NC^^l(Ni-» 
;i00>0  OiOO  »00  OO    OOOOOOOOOO 

itOCDiOcOiCOiOCDCOCO   COCOCOCDCOCOCOCDCOCO 


:ooococoo-*ti-(coco.-i-«*<a> 

rHCOi-tCOCN|COCNCOC^CO(N(N 
CDiOcOiOCOiOcOiOCOiOcOiO 


-*COcot^COiC04COi-HM(NO 
r-ICOr-iCOrHCOi-(CO(MCO(N0O 

cOiOCOiOcOOcOiOcOiOcOtO 


COOliOOOCOCOOOiOOlCOi-HiN 

■C0i-ICCrHCOr-tC0rHCO(NCO 

COiOCOiOCD»OCDiOCDiOcO>0 


'Nt-HCOCliOOOCOcOOOvOaiCO 
rHTf<rHCOiHCOr-*COrHCOi-(CO 

CDiOcOiOCDiOtOiOcOiOCOiO 


OCOiH(NCOi-'Tj<OiOOOCOI> 
i-t'^rH'^rH-^.-HTr'rHCOr-tOO 

CDiOcOOCOiOCOiOCOlOtOiO 


^CMiOrHCOQt^^OOOp    Ol  t- O  CO  .H  g<  <N  CO  CO  C4 -^  T-4 
OiOOiOOlOOxt^O-^*    O'^rH'^iH^r^TjfrH'^rH^ 

CO  lO  CO  O  CO  lO  CD  lO  CD  lO  CO  lO  CO  »0  CO  lO  CO  lO  CD  lO  CO  lO 


COCO-^C-JiOrHOOt-Ol 
OiOOiOOiOOiOOTj< 

CDiOcOiOCDiOCDiOCD>C 


_,  _J^t>-OCOrHiOC^'rHCOCO 
0'^0'<J<rH'^rH'^rHTj«rHT}* 

COvOCDiOCOiCcOkOCOiOCO»0 


>aiOiOCOi-Ht*<NCO(NiO 
SO-^rH'^rHTfrH-'J'i-*^ 

COiOCDiOCOiOCDiOOiOcOiO 


OiOiOOii-HOOi-Ht^tNcpcOCO'TttiOiO-^CDCOcpC^ 
I0i00i00>00i0000i00i00i00»00i0 

lO  lO  CO  »0  CO  iC  CO  »0  CD  »0    CO  iC  CO  lO  CO  lO  ^  lO  CD  »0 


t'-CN  QO  tH  O^C 


)01r-1QOrH  t- 


a>OQQr-ia>r-IGO(NI> 
lOOOOOiOOiOOiO 

lOcOCOCOCOiOCOiOCOtO 


Mt'-'^'CD^OiO'^CO'^ 
O»00t00»00i00i0 

COiOCOOcOiOcOiCCDiO 


g,-H^r-t^OCJQCa(5 
00000000»0 

'^COCOCDCDCDCDCOCOiO 


OOOOOOOOOO 

^DcococDcocococococo 


ioOt^GSCOO^O'OOiO 
$iiOOiOOOOOOOO 

rf*iOCOiOCDCOCOCDCOCDCD 


OOOOOOOOOO   OOOOOOOOOO 

CDCOCDCDCOCOCOCOCDCD    COCOCOCDCOCDCDCOCOCO 


^OOOOt^Ot^i-tcpi— ICO 

goooooooooo 

^  CO  COCDCOCDCOCOCOCDCD 


i-ICOiMCOiNOC^iOCCiO 
OOOOOOOOOO 

COcOcOCOCDCOOCDCDCO 


^OX-i-^OOi-HOOi-Ht^fHt^ 

?=oooooooooo 

^  CDCDCOcDCDCOCDcOCOCD 


'Mr»-C?t~-^CDCNOCOCO 
OOOOOOOOOO 

COCDCOCDCOCOCOCDCOCO 


goooooooooo 

^COCOCOOCOCDCOCDCOCC 


SOOC^QpCOOOCOCOCOCO 
ooooooooo 

i:OCOCDCDCDCOCDCDCDCO 


g*C:JOMo>^ai(Ng?(N05 
OiHOOOOOOOO 

^CDCOCDCOCDCDCOCOCOCO 


g'eOrHCOOCOOCOOCOO 
0f-t0r-10r-t0rH0i-« 

fC^CDCOCDCDCOCDCOCDCDCD 


^COCOCOCO^OCOCDCOCOCO 


p;;xp^cQQ^cfip^cQp:jai 


Soc 

cOiOCDiOCDLO^iOcOiCCOiO 


5'*J*00"^l>tOcpcDCD 

SoooiooSoio 

CDiCcOiCcOiCCO»OCDiO 


cooi'^(3>*^oo\noo»oi> 

OiOOtOOiOOiOOiO 
CDiOCOiOCOiOCOiOCOlO 


COt^COCOt>CDCO»n00'^OS-^ 
O.iO  O»00i00t00i00i0 

CD»OcDiOCOiOCOiOCDiOCOiO 


,.  .HCOO^O-^aiiOOi 
OOOOOOOiOOiO 

COCOCDCDCDCOCD»OCO»0 


lOCO-^^Tl^-tJ^COiOOO 
OOOOOOOOO 

COCOCOCOCOCOCDCOCDCD 


C0cOC0»O"^iOxJ*'«:J<^-^ 
OOOOOOOOOO 
COCOCOCDCOCOCOCDCOCO 


.)COt--^t^-Tt<CO-<J<CD 

OOOOOOOOOO 

rQCDcOCDCDCDCOCDCOCO 


_5Ma>cooicoCT>coo> 

OOOOOOOOOO 

COCOCOCDCOCOCDCOsOCO 


COOfiOOCOOCOOCOO 
Oi-lO»-tOrHOi-tOrH 

CO  CO  cOCOCDCOcOCD^CO 


-,    .-tCOrHCOi-tCOfHCOi-i 
Oi-tOl-lOrHOfHOrH 

COCDCOCOCO^OOCDCO 


OCJGQQJCOp^OlpljCQpl^GQ 


lO        CO        l> 


oooicoooeooo-^oo^QO 

OOOOOOOOOO 
CDCOCOCOCDCOCOCOCOCO 


St^C^QOC^a>tHOQOO> 
OiOOiOOiOi-tiOi-H'i* 

COiOCOiOCOiiacDiOCDLOCOLO 


»Ot-'^CO-^OOCO^(NO(N 

lOOiOOiOOiOOiOi— ttO 

CD»OCD»OCDiO<OiOCD>OCD»0 


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OiOOOOiCOiOOiOOtO 

CDiOCOtOCOiOCDOcOUDcDiO 


COiHCOi-(COi-<COiHCOr-l 
OrHOr-lOrHO-HOiH 

CDCDcOcOCDCOCOCOCOCO 


p3coci:5a3p5cQpt5a2p^t/i 


r-H<MC^O'^aiiOCOcOcOI>'»0 
i-C^r-C^rHCOi-tOOrHCOr-fCO 

CD  lO  CO  iC  CO  lO  CO  lO  CD  lO  CO  lO   I 


ioo=oocDOcooi^-ait>-co 

OOOOOOOiOOiOOiO 
COcOCOcOCDCOCOUSCDtOCD'O 


l0(N»O(NCp<MC0r-(C0rHr*T-' 
OOOOOOOOOOOO 

CDCO^CDCDCDCOCDCDCOCOCD 


iOtt*iOtJ<»O'^iOCOCDC0COC0 
OOOOOOOOOOOO 

:dcdcdcdcocococococdcdo 


lO  CO  >0  ^  »0  CO  tO  iC  lO  lO  lO  >o 
OOOOOOOOOOOO 

5DCOCOCOCOCOCDCDCDCDCOO 


OOOOOOOOOOOO 
CDCOCOcOCOcOCDCOCDCDCOCO 


coocoocoo'^0"<*<o  ■^a>-vo-^o-^Q>^<yi'^g> 

OrHOrHOiHO—lOi-*    Oi-HOr-tOrHOOOOOO 
CDCOCDCDCDCOCOCOCOCO    CDCOOCOcOCDCOCDCOCOCDCD 


Sr-tCOrHCOi-HCOrHCOiHCOrH 
r-IOt-HOr-fOrHOf-)OrH 

COCDCDCDCDCOCOCDCDCOCO^ 


^a^^mp^mf^aip^oip^m 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  661 


2   I 
^  3 


.2  » 


cojddy 


•a;Bp 
xojdd V 


"Jz; 


5J!2i 


o   Si    gj    SJ    S    3 


OjCOpJQQpjCQMaQQjaS 


(NC^OOINCOlMOTNeOr-l 


S'tOC-OOtOO'O'r-ICiCOO 


S'T-IOJC).-C>»<O>iO00t^5O 


■-(•0<rHCOrHeOiHW«55 


r1'>«<r-(^f-l>«<iH^i-l^ 


C4      K      S      C4      n 


ajoipi^cnpEjcnaScQpjoQ  ojcotf  cnp^oipticDO^aQ 


V  iH  ^  rH  i  1-4  O  r-<  >0  O    lO  O  O  O  O  O  O  lO  O  S 

to  O  CO  tO  ^  lO  CO  lO  CO  lO  CO  to  t^  lO  C«  O  r* -^  t*  ^ 


(NC0>O'^t-IN0»Oi-l00 

■"iJlrHTHi-l^— tTjOHiOO 

coiocoiocoocoiacoio 


(3>  r- r-ltO  «  M  «0  » 


C0u3c0t0c0i0c0>0c0>0 


lOOOt^COOi^^NMO 

eoiHOOi-ieor-iTiii-i'^i-i 

COOCOlOCOOCOUdCOtO 


C^Og<aOCOcOOO'*QC* 
eoe<eoiHeOi-ieoi-i^i-( 

COiOCOiOCO^COtCCOiO 


lOOtOOiOOOiQOO 


CO  lO  ^  O  COiO  COtO  O  tO 


^tOCOiOO(0<0>CtOiO 


COiOCOiOtOiOCOiCCOtO 


Nc<e^c*6ie<eo6i coS  co i-i m r-i oo r-i eo ri ■^ fh 
CO  lO  CO  >0  CO  lO  CO  O  CO  tO   CO  lA  CO  tO  CO  to  CO  lO  CO  o 


COiOCOiOCOtOCOtOCOiO 


COiOCOtOcOtOcOtOCOtO 


OTCI0OC>100OI0OC4COrH 
cOtOcOtOcOtOCOiOCOtO 


r-i'*5)eococM'»ocoo> 
Oime<)eoc:coc4mc40i 

cOiOcOiOcOtOcOiOCOiO 


COtOcOkOcOkOcOtOcOiO 


00  gj  o»  00  p  r- 1-1  CO  fj  lO  eo -"i! -i<  eg  co  e<  t^ 'H  oo  o> 

CO  lO  CO  lO  CO  lO  O  lO  CO  lO  CO  lO  CO  lO  CO  tO  CO  lO  CO  lO 


COO*0QC^0Qi-fCQ-H0OrH 
cOOCOiOcOtOcOtOCOiO 


pjcotfoQOJcQp^aQpjaQ 


OtooiooSo-q<r-i3 


COt^m>Or-lNS"Qcpt>' 
lOUSiOiOOiOOiOO^ 

CO'<J"C3'*t-'*t»'^t^'* 


C<QiQ0Qt»iQQC9^Q 
lOOiOiOiOiOO^OiO 

COiOCO-<»'CO'Vt--*t»'* 


'VOiOOioioiAiaioia 

COiOcOiOCO<*4*CO^CO^ 


cot~ogiOoeoiNO'*QO 

•VO^OOOiOOiOO 
COlOCO^COkOCO^CO^ 


52!§§§8§SSg 

cOOOtOcOiOCOtOcOtO 


cOO^iOCOtOOiOCOiO 


CO  lO  CO  lO  CO  to  CO  O  CO  lO  CO  ^  CO  tO  CO  kO  CO  O  CO  kO 


>Oi-ICOOOOg>»t-rHCO 
COiOcOiOtO^COtOCOiO 


COCJt~i-iOOOO>0>000 
cOtOCOiOCOtOCOtOcOtO 


6'.-(QO(Nooeot~»coTfio 
r-(TjiH^rHVrH'*i-IT(< 

•cicoiocoiocoiocoiocoio 


iHiOr-li25i-<lO.-IT(>i-l^ 

.c;coiOco^O>OcOiOcOiO 


SOeOOC^rHlNi^HrHI^Q 
fHiOrHlOi-ttOfHlOrHlO 

.C^COtOCOiOcOtOCOiOCOkO 


gSSS3232SSS 

^COiO^tOCOOCOiOtOiO 


^COiOCOiOCOiOCOiOcOtO 


gssssssssss 

<*cocococo<o<ocotooia 


^0(0(OtOt05DtOtOCOtO 


OOOOcDOOOOO 


gSgSgggS§3g 

■c^cocococococococococo 


Seg.-iMi-(eOr-i«i-ieo>-i 
OrHOr-IOrHOr-IOrt 

^COCOCOCOCOCOCOCOCOCO 


pcioitfcopjaipiicoojco 


o  "S""^'^  S   "§" 


tOiOCO'^r^MOOCjjQOr-t 
COiOCOiOcOiOCOtOcOiO 


:OiC<OtCtO»OcOkO<OtO 


csico?3«SS<NwSS5 
C00:0t0c0i0cou3^i0 


i-(^c5coo«o5(Ncoc5eo 


COtOCO^<OOcOtOtOtO 


cOiOCOiOtOiOOiOcOiC 


gggggggggg 


oooooooo 


gggggggggg 


ooooooooo 


corHeorHco^cOl-HcO'^^ 

OrHOiHO»-HOi-tOrH 


pi^QQp^QOPE^cnpj'cQpcico  p^QQp[^a3p^'aQp:;cQp^aQ 


tO;DOcpt^iOQO'^0>00 


<<t<9)iO0>iCOQCOOQr>-r« 
eOtOCOiO<OiOCOiOCOiO 


<OtOO^COiOOiOOiO 


NC50OC^00C^55O40OCl 

<OtOCOiOCOLOCOtO<OtO 


C<ICOC4CQCieQC40OC40O 

COiOCOtOtOiOC&^OiO 


C40OC<lCQC40OCMeOCS0Q 

COkACOiOOiOCOtOCOiO 


tOiOcOiO(OiOCO»OCO*0 


cOiCCOiO^OiOcOtCcOiA 


cOLOCDiCCOtOtOOtOlO 


»OiO  a>oaoi-( 


SS2 

tOCOiO 


o^ggggg 

CD  O  CO  <0  O  CO  CO 


g§g 

CO  CO  CO 


>cococo^LOr*iot^iO 


oooooo 

CO  CO  CO  CO  CO  CO  CO 


Soo 

CO  CO  CO 


T*40>iOQ>iOO>iOC 
OOOOOOOC 

CO  CO  CO  CO  CO  CO  CO  c 


«C4eooJco(MeoNeoc>» 


O  i-t  O  11  O  rH  O 
CO  CO  CO  CO  CO  CO  CO 


r-iOr-l 

CO  CO  CO 


c^ciSiMrt       ooeoScooi 


co<3coaa(^O>t>0000t« 

i-(lO»-t^f-(^rH^fH^ 
COiOcOiOCOiOCOtOCOiO 


■^rresiocoiOocoN 
lOdiOf— tiOrHiOr-ciO 

COiOcOiOco^cOiOCOO 


i-it^pjt-.c^t^e<coeoco 

I— tiOr-ClOi-<*OrHlOiHlO 
COlOCOUSCO^^^COlO 


S?:;  5  ::^  2  ?:;  S  S  S  S 

<0  CO  CO  CO  CO  CO  CO  CO  CO  CO 


oooooooooo 
cocococococococococo 


CO  CO  ^  CO  <0  CO  CO  CO  CO  CO 


OTHOiHOrHOiHOr-l 
COCOCOCOCOCOCOCOCOCO 


Qc4GQpCHGO0c^cdpe4GQP4c& 


CO       r*    ^S^^^^g 

CO        00        OQ        CO        '^ 


Page  662] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


•xojadv 


S    S 


PjGQcdadP^QQMadpjcQ  cdoQPj'cdp^oQC^oQoiaQ  daafiwoiaaeiaDciaa  dwoimfimciaafiai 


S'ooocciocoiNOcncoire 
IM«CMCC(NMC0CM03<N 


O'^i-1'^i-IC0t-IC0<NC0 


MN'^rHT)<i-lTIli-llOO 


iOOOiCOiOt-''<g'iHCC 

r-Ti<oocooocoeoe<5ooeo 


(NlNC^C-tCOiNMrHCOi-l 


CCi-l-.l'r-l'^O-^OiOiO 


0>OOSO-*0-*rHTf< 


■.?^ait^^occccosr*cO;0(N-.j*cftoQicc^. 


TPCTitO-^IOl-fO^i-liOODOOiCrHjq 


0-<J<i^'^.-l»i-(CO(NCO 


lOOiOiOiOiOiOiCOiO 


R-*0>OOiOOiCiOiCiO 


833 


t-i  lo  o  go  to  o  M 

m  O  ■*  O  ■*  i-l  TT 

^  t>.  ^  t^  ^  t>.  Tj* 


lM<N(MO4CO(NMrtC0r-( 


i-ico6)«ic<i(Mc^e<copi 


oocoooOToocooocooooo 


cooiC<Joocitor^05>f5.-t 
ooeocccooocoooMooco 


t^tocCi-HaiTt*eDooc*Di-t 
oocooocooocooocoooco 


t^coaocoooccoocoooco 


^Ht-H(£Jto»-<^Ht^?OCOOS 

t>.-.jii>ccooccoomooco 


t-.TJH>TI't-COt^OT00CO 


t^tOi-KMiOr-QNiOt^ 


S<00>0Ct^O>O<MC0'^t-t 
rf£tOi05DiOO»0«OiC>tO»C 


&COCO-.1*«— <t00i0000O<:0 


JiOOiCC 


gsg 

iCtOiC 


»0  >0  O  lO 

to-oit--* 


0-*rH-*i-ITl<i-(COOJeO 


OiooiSo'<i<>-i-*i-i'.)< 


aO5I>f-HtDC<5*»#".J'(NCOrH00OiQt^C^iO'.f*CCtprH 


ScDiO<£)iO«DiCtOiCeC>iO 


CO  lO  to  L 


xioS 


:<OrHOOOa>OOT-lt~!NlO 


>COCO-^J<-^(OCOt— T-IOiO 
:COIMCO<NOT1NMINCO<M 

»CD»OC0iC<0iC50iOC0iC 


a"ooi-iaicsi>'*«oiCin 

;C0COMMCC!NCOCSICOlN 
»«0»CC0iOCDi0CD»OC0iO 


BCO»OCDiO?DiOCDiOtOiC 


CO  iCCO 


rHT)<i-l 

iCcOlC 


■*otno 
con  coo 


—       ■     ■■  —       ■  Tt<  tH  ■*  I-l 

COlOCOO 


CO  iC  CO  tJ 


ao»oco(W*iC^oooo 
io»oOicio»oo»no^ 

co'.}<t~-.lit>-vi>T(<r-.-.)i 


OiOOU^OOLOOiC 

cokCcoiocoiot^-^r^-^ 


QOOQCO(NCO'*'J't~C^ 
■.J'T-liCOiCOiCOiCO 

COvCCOlCCOiCCOiCCOlC 


O'cf-^OOOiCW'-lt^cO 


■^i-(r^t>"THccicoaiiO 


t~oo^in-*^oooo(NT)< 


TH>0'.J<(Nt-01.-ICOT>'(M 


lOiOOOOiOOiO.H'^ 

cO'*r--*t~-*t-T»<t--^ 


cOC<5CO?JOsO.-IOJINf»hrcom'.«>t^!NO>Oi-IOO!cO 


C001C064CO(MtI<i-IT)<i-( 
COLCCOiQCOiOCOlOCO^ 


COlOCOiOCO^CO^COlO 


«QC(MO<3lMt- 


COiOCOlOcO^cOiCCOlO 


JiOt^cOCDt^iOOOTjio>COO<N.-lrHCOO 


jeOCMCCMMNCO 
SiOCOiOCOiCCOiC 


coog"05 

COiOCOtCCOiOCO^COtO 


:iN-<)<iM    -  - 

»  CO  iC  CO 


SiOcOiO 


cOkCCOiO 


aOiW05COO>CTHlO^H".t* 

:rt  ■ci<rt    -         - 

jcOiOCO 


5  CDiC  COlO 


icoocor^t^coocicoa-^ 
cOiCcOiCCOiCCOiOcOi/5 


OC^t-'OCOCi'.l^t^COiO 
■«'C^T)<<N^rH.9'i-ITIIi-l 

coocoLocoiccotccoin 


iOt>-cOCOopiOO^CO»-tM 
cOiCCOtCcOiOcOiCCO^ 


-^MC^MCOrHTfOCOOD 

coMWMeocoeibcccoiN 

COiACO^CO^COiOCOiO 


(MC0CCC*5-^C^'.t<»-*iOO    CDOat^0000t^OiCO.HlC 


CDiOCOincOiOco^cOiC 


(MMCNMMmiNOTCOm 
COiCCO^COiCCOiCCOiO 


Sc 
lOOOiOOiO 

COiOCOiOCO»Ct^'^t*'<J* 


COiCcOiCCOiOCOtOCOiO 


■.rooco  t~ 

■.Ji  i-l  TJ<  rl 
CO  vn  COiO 


coioeoio 


co»cco»o 


cOOCOiO 


■*>-(  cootie 


cocomco 

CO  iC  CO  iC 


cc  coccus 
coiocotrs 


cOrHt^i-it^ocooocoilojooaioooi^^t^rH  CO  c^iOM-^-^  com  cocoes 


jcDiOCO 


)coic  co»o 


COOCOiOCOiCcOvCCCiO 


COiCCOiCcOiCCOiOcOiO 


•xojddv     P^ 


lO  CO  'X)  C*3  to  CS  t-  (M  ^-  r-l 
'cOiOtDiCcDiO«OiC?OU3 


s  CO  to  (O 


SrH  Oi  T-H  Oi -N  Ol 
f— t  lO  r-i  iO  i—t  lO 

(O  «0  lO  <0  iC  O  lO 


C^QOMoOOOOOMI^OOtO 


Sgo^co^oocoooccgoco 
:oooooooooo 

S(OcOtOtO«OOcOcOCOcO 


iCOOiCQOOCOiOQOiOOO 


:000 
;'0co<0 


ooooooo 

CO  O  CO  CO  O  '^  CO 


iCoOiAQOiOGOiCaOiCOO 

oooooooooo 

cOcOCOcOCOCOcOCOcOCO  CO  CO  CO  CO  CO  *0  CO  CO  CO  CO 


•  CO  CO  CO 


•N  C^l  04  (M  CC  Ol  CO 
T-*  O  Tl  O  i-t  O  r-1 

CO  CO  CO  CO  CO  CO  CO 


PC?  CO  Cc;  03  PCh  cc  tf  a5  pc;  cri 


g§s§sss§s§ 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


oOOCiOOsOiOCarHOO 
COifScOiCcOiOcOiCcOiO 


-fHQOOOlOiOCC'-HCO 


CM"<*C^CO 

cDiO  cOiC 


coco 

CO  iC  CO  lO 


i-it^c^t^cocO'<riOiC-^ 


■^  'O  -^  CO  iC  CO  .O  iC  CO  iC 
cOiCCO^co^c0^cO>^ 


2§2g2g2S::!o 

COCOcOCOcO^cOcOCOCO 


Icooocpoocpoocpcocpoo 
lOOOOOOOOOO 


co^t-'^r-cooocooiC^ 

T-HiOf-iiCt— •lOi-HiO'— <iO 
COiCcOiCcOiOCOiOcOiC 


.-•OrHOi-HOf-tOf-iiO 
COcOcOcOCOcOcOCOCOlO 


cococpoocp^-cpr^cpt^ 
oooooooooo 

CO  CO  cOcOCOCOCOcOCOcO 


CNCOC-ICOC^CC^^CCi-iCC 
Or-(O.-(0f-H0.-(0i-t 

cOcOcocOcOCOcOcOCOcO 


f-tCC^OO'-HCCi-tTJ'rH-^ 
Ol-tOr-iO-HOl-HOi-l 

cocococococococococo 


S28S8SS282 

cOcOCOcOcocOcOcOCOcO 


oc;  CO  p:2  CO  p:^  od  p^  OD  Qc^  OQ  p:^  CO  p:;  CO  pc^  OQ  P^H  CO  p:^  CO  pc^  co  P^h  co  P^  co  PCh  co  PCh  co 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  663 


a  " 


3  I 

CO     S 


iH        O        CO 


O        i-<        C^        « 


•xojddy 


^^ 


OHCGpHodP^QQpCHadO^aQ 


«;  0»  to  Ca  to  Ca  i:©  Ci  CO  O^  ^   Oi  CO  00  «  00  <0  QO  ?0  Op  tO 
^lOtOiOidCiCidOLOU^iC^tCCOiCUdiOiOtOiO 


pCS  CO  P^  :fi  Oh  CC  PiH  CQ  PlH  CO  P^  00  Ph  GQ  f^  CC  P^  QQ  OCh  CO 


P^co^QoQiaiP^coP^ccPc^co 


cpcooocoQOtoapcoopto 


S*QQO.-(COr-tCOiHOOi-HOO 


oc^cpcooocooocooocoooco 


St*QI>-Qt>-QCOQcp 


^^0Q'-(QOi-ir^i-'r>--Ht^  1— (r*c^t^c^t>-ococ^cD  c^coc^cococooptoeotococp 

'iO^^OUOiCiOLn^iC    lOiOiCOtOOuCiCidO    lCiClOiOiC^iOLOiQIOlO^ 
lO  lC  iC  tO  iC  iOiO  ^  ^  lO   lC  iC  lC^US  ^  ^O  iC  iC   lC  iCiO  lA  >0  iC  O  iC  iC  iO  iO  ^ 


S"i-i04MCic>oac^aiC^co  *N  GO  doocooo  coco  coco  coaoc5r^'«3*r^'^co-^coHl'(D»ocOiCcOintoiOiCiO*0 

^iC^iAiCtC^LO^iA^   kCi/SidQiOiOiOidCiC   iC^^^tC^iCiOkOiO  iCiOiOiCtA^iOiAiCiOiOiO 


^c^ocoQcoococacocs  h^OJ'TOi'^op'^apiooo  iOcOiQt>»or^:p«ocpto  Kocot^cot^iOt^iOcOiOooift 

^lOcOiCCO^COiCtOiOiC  uOiCiCtCiCiOLOiC^iC   LOtdO)>OLOiCidOtOiO   OlnU^lQtCiOkClOLdOlO^ 


f^CCi-''T''--'T*'-^*^Q-^Ql>COu0Cic0CiO04c0C5k0  00t^t>-00l^a0(0C0C0 

fciooiooiooiOoioOjU5oo»oiCkCiCiOiOioioicioiOioiOii5ira»i5»o 

^iO:OiOOiOtO»ft«0»CcoJu^COiOiOiOiOiOi0^iOi»OiCiCiOiO»OiOiCiO»0 


^lOcOiCCOUOCOi^COiOCO    iOeO^iO^OU^^iakO 


-alCC0U5M«OC^Cpr-(t^.-l   r*oooooooo»ososQO 
^iC<0^<0kAC0tO(0i<^c0>Ac0iOC0iOiOiOtOiOiO 


SSoiftOicoiooSoLcooSSooiooS 

^iCCOiOCOiCOkOCOiOCO  'iACO>OCDCOCOtOtCCOtO 


^lOCOtAcOtOtO^COtCCO 


•OCO<OCOtOCOCOCOtOiO 


(*t>"iOGO'3'©^oicoQco  •-'N<-ti-i^ocoo^04  '^oo»ftr^<or-t>-tot*»e 
5»oo25ofeoioooc5  oooooooooo  oiooiooiooicoS5 

^lOCO^  COiCCO  tOCOtOCO  CO  CO  CO  CO  CD  CO  CO  CO  CO  lO  CO  iO  CO  lO  CO  lO  CO  to  CO  ta 


GOcOOacOOiiCOs'OQiOO'^ 
iCiciCt/^kC40kOioOu50ira 

kOlCOUOU^tOlOiACOiCCOLO 


00  CO  CO  t^  0»  »-•  0»  CO  O  CD   OiC'-iuj^-^^'^CI^WCO 
iCtO  lO  lO  iO  O  iO  ^O  O   O  ^  OiC  O^C  O  iC  Oo  OtC 

iC  iO  lO  lO  kO  ^  to  lO  CO  iC   CO  tO  1^  tC  CO  tO  CO  to  CO  lO  CO  lO 


ScoQt>--^i--iHcDM<DNiccoioeC'3»^^^ccioeo 
tOOtOOtOOkOOiO   OiOOtootOOtOO^OtO 

C0tOc0tO(0tOc0t0COlOc0iOc0tO<0t0C0i0c0tOC0tO 


Moocir^cor*eocD2'cDt'j<iOiOiOO'<fcoeot;cot^M 
OtootooiootOOtO|OtootootoOtootOOto 

COiOCOtCCOtCcOtOcOtOjCOiOcOtOcOtOCOiOCOtOCOtO 


§ac^i^^r*iOcpcoco 
tOOtOO^OtOOtO 

cOtOCOtOCDtOCOtOCOtO 


S'ao^©»OQtO©^»-''»  ^^icoc^-^r-c^oioo  ^ooi--r*Qpr*^co^ic  o»o^'^cscococ^^i-t^o 
tOOtOOOOoOOO   £>OOOOOOOOtO   OiOOiOOiCOiOOtO   iitOr-ltOi-tiO^iOrHiOrHtO 

^tOCOtOCOCOCOCOCOCOCO   CDCOCOCOCOCOCOCOCOkO   C04OC0t0C0tOc0i0^tO   COtOCOtOCOiOCOtOcOiOcOiO 


iOOOOOOOOOOiOOOOOC.OOOinOiOO>COiOi-li(5.H>Oi-liA.--liO.-iiOi-llOi-liOfH^ 


Sooooooooo  ooooooooo>c  o>ni-ia.-nnrHi5r-iiA 

^COCOtOOCOCO<OCO<OcO   ^OCO^COCOCOCOtOCOkO  J(0»0^»0500tOiOtO»0 


OOOOOOOOOOjOOOOOOOOOiO 
^  CO^  CO  tOOtO  coco  V  CO   CO  CO  CO  CO  CO  CO  CO  CO  CO  1/5 


o  CO  >-i  r^  (N  CO  CO  lO 'j"^  lO  ro  CO  e^  00 1-1  o>  o  o  o> -^  00 

CO  lO  CO  lO  CO  lO  CO  iC  CO  iC  CO  lO  CO  iC  CO  iC  CO  iC  CO  IC  CO  IC 


Soooooooooo 

^COCOCOCOCOCOCOCO^CO 


^COCOCOCOCOCOCOCOCOCO 


-ic^ocooo-^r^iocptoio 

•^cococDcococococococo 


-oeot>-cjoo»-<osooa> 

OOOOOOOOriiO 
COCO^COCOOOCDCOtO 


'^■n'tOrtCOC^t^r^OCOOOi 

^HiOf^iOr-*iOrHtOf-HtO'-*^ 

OiOcOiOcOtOcOiOcOtOcOiO 


i-tooc^r*cocoiO»ocD'^r^«oowo>Qoa>5^cco2r* 

COtCcOtOcOtOcOtCCOtO  .COiOCOtOcOtOCOiOCOtOCOtO 


t^«OpMOii-HOOWCacCOO"*r*tOcOcO'-*'t>-COC^C^prH.-i^MQQ'fl'tr»OcD 
000000*HOrHtO^»OrHiOi-iiOf-HiOrHtOf-Hi0^tOW^C4^CS^6l'V 

COCOCOCOtOCOCOCOCOtO   OiCcDtOCDiOcOtOtOtO  {COtOCOtOcOiOCOtO<OtOCOtO 


cp-^^eoOr-d-tocooa 

OOOOi-tOrHOi-liO 

COcDCOcOCOCOCOCDcOtO 


Tj*oOtOr>-cOiOOO-^OacO 
i-HiOrHOi— «iO»-HiOi— tiO 

CDtOcOiOcOtOCOtOCOiO 


—  ■■♦5iQW<^'^<^<ocot^iO 

C^iOWiOcJ^C^^C^'^C^'^ 

cOtOcOtOcOtOCOiOcOtOcOtO 


C4tococo^r*io^-^occ»-*i-ic^O'^os 

^  CO  CD  CD  CO  CO  CO  CC  CO  lO 


io-rc4tocococp- 

ftOi-iOOOOOOOO 
^  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


iOCOCO«?COtOO»COQC** 

^lOCOtOCOiO^tCCOtO 


MQeQOiirir*cDcoooioa>co 

COkOcOtOcOtOCOtOcOtOCOtO 


xoaddv     q"^ 


j*S30'j'S?coooScooom 
eor-toooooooo 

^cococococococococDco 


OrHOrHOi-cOrnS 
COcOCOcOCOCOCOCOCOtO 


cor~t^mc»-^oc^?)i-H 

r-HlOi-llOr-(U5CliClMlO 
COlACOiCCOlCCOiOCOtO 


^^MO'^ouDi^r^cpoO'^ 

S0.-1000000  00 

^cocococococococococo: 


HO'-IOi-<Oi-(iOiHiO 
>COCOCDCOCOCOlCCOlC 


COiCCOiC 


.H—IMO 
COiOCOO 


eQO»icoococooo<io>c5.HCi 

COiOCOlCCOiCCOiCCOiCCOlO 


Tj'opcor-oQiooco-Heic^o 

iCOlCCOiACOiOCOt^cOiACOLO 


S'cjOMooiet^ccmoo^' 
OrHOOOOOOOO 

^cDcococococococococO 


iN-H.-(iNcn 


■^OOiCCO 
T-(  lO  rH  40 

coiacotc 


S'r-<OC<t^Tj'COCp»r:)t^CO 
oooooooooo 

^cocococococococococo 


S'OOprHCOWlCWJeOCOCJ 
00OOOOC5O0O 

^COCOCOCOCOCOCOCOCOCO 


iCOiOOOOOOOiC 

.fiocoiococococococom 


>r-l.-IO(M00 
>OrHO.-IU5 

>COCOCOCOiO 


rtiOiHiO 
CO  to  CO  iC 


>  cOCOlOCOtC 


i-tiOi-tO 
COiOcoiO 


.iCOOOOOIN 


cotOcoiO 


cOiCcOU^ 


mt-COiOOOMO(MC^OMOO 
COiCCOiOCOiCCOiCCOtCcOiC 


-coaiciOQ(Noo-i'coco>nr-eooi.-ii-io 


ji-doniot 
SCO  icco»o  t 


co>nr-eooi.-ii-iOMQO''Jco 

COiOCOtCCOiOCOlCCO^CCOO 


CO  rH  oooaooo 


COkOCOiO 


CDlOCOlO 


!t>.OOCOO-*. 
>iCO>OiHlOr 

>ioco>aco>oc 


pjOQP^QQMCQOiUitf  QQ  ^  QQ  pj  UQ  p^  <X)  pj  OQ  C<  OD  Sl^  OQ  p^  CO  3^  02  (^  CO  pi;  K 


CO  lO  COiC  c 


iCcjr*oa>oo.Ht^ccioicco 
o)'j'c<i«5»SS««>e<5OTo5co 

cOiOCOiOCOif^cOiOCOtACO^ 


■.»iocooooccoQtl^£J22 

C^ -^  C^  CO  C^  CO  CO  CO  CO  CO  COOT 
COlOCOiacOtACOiOcOiCcOiA 


O^COp^COpiJOQOjCCpjCfipJGQ 


Page  664] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


a<  3 
o     S 


o 

t« 

•* 

H 

o 

(/) 

p 

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r-(        fj        00        ■*        lO  50        t- 

e^     M     e5     (N     IN      (N     (N 


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(A^fAcapiixPiwA^ 


l^xfii^pitBP6aic:^m 


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S' 1-t  CO  1-i  to  T-l  CD  i-H  CO  i-H  (O    ft  CD  rH  Cp  i-l  to  »H  CO  «-H  CO 
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^  »0  »0  O  lO  lO  »0  lO  *0  »0  i^  iC  lO  lO  lO  »0  lO  idO  iO  lO 


s 


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CO        CO         CO        CO 


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P^a^p^c6;^c^^a2p^t:n  PhoqPhoqPhqqpc^cgPhcq 


00  r- oo  t^  00 1>  00  c- CO  r-  oo 


•^lO'Tj^iO'^iOTriO^iO  ■^iO-^iGriiiOTf^O'^iO    rj*inT}<iO'^iO'^i0^iO 
lO  lO  lO  lO  O  lO  tO  vO  lO  »0  lO  lO  lO  iC  lO  lO  lO  O  lO  lO  »C  »0  iC  vO  iC  lO  »^  lO  »0  lO 


.t-t-t^t>. 


_iCOrHCOrHiCt-iiOrHO 
LOiOtOiOiOiOiCkOtCiO 


;  CO  "C  CO  iC  CO  »0  CO 


■«}<lO'^»0'«?*'^'^'^Tj<'^H'-^'Tj<'rJ4trt-^i/t)-flCCO 
lOiCiOiniOOiOLOlOiOiCkOOiOtOiOtOUbiOLC 


S'cOiOcOiCCOincO"^I>'^  t^"«**t^'^t"*COt-COI:^CO00C0COCO00C400C^Oi(M 
lO  iO  lO  lO  lO  lO  lO  lO  lO  »0  lO  lO  iO  lO  lO  lO  »0  lO  lO  lO  lO  O  lO  lO  iO  lO  uO  lO  »o  o 


eOO'^OO'^Oa'^OiOOOCO 
S^iOiOOiOiOiOiOOOiO 

,^iOi/5iOiOiOOiOif^tOiO 


gi-Cflr-tCOfNCOMC^C^C^ 
OiOOiOOiOOiOOO 

^COiCcOiCcOvOCOiOCO^ 


QCOOC^O'Mi-t'Mi-KM 
Oi0  0u3  0»0  0u3  0i0 

COiCCOiOCOiOcOOCOiO 


COC^COrH00r-(^iH-^Q 
OtOOiOOOOiOOtO 

'-.OiOCOiOCOiOCOkOtOiA 


OOOiO 


^      (NocMoeoo 


CO  lO  to  lO  CO  lO  CO  lO  CO  tO  CO  to  CO  lO  to  lO  CO  kO  to  lO 


»OQiOo>toa»coooi>oo 

tOiOCOiCCOiOtOOCOiO 


Scocoeod'^iM'^r-iiOfH  >ootootoo>r^Oii:^QOoooooot^a>t^aicooto 

^COvOcOiO"OincDiOtOiO    tOiOtOiOCDiOCOiOtOiC    COiOtOiOtOiCCOiCtOiC 


girtC^tOfMCOt-T^i-IOOO 
^COiCtOiCtOiOCOiCeOiC 


si  00  i-<  Ci  >-<  O  O  O  O  i-H  Cl    1-1  00  Ol  00  <N  r*  CO  to '^  CO 
ft  O  lO  O  iC  oo  iH  iO  r-l  Tl*    1— I  ^  i-H  "<1<  i-H  ■^  iH -^  r-t  >*< 

^tOiOOiOCOiOtOuOCOiO  tOiOCOtOtOiOCOiOCOiO 


OOOiOOOiOOOOOOt^h-HtOCNCDtNtftCOiO-^"^ 
OiOCOiOtOiCCOtOtOiO   tOiOCOiftCOiCCOiCtOiO 


Si-ti-Hi-HQ'Mai  coo  coco 
i-HOi-<i5i-*'»1<rHTj<r-irj< 

^C0iOCOi/5t0iOc0iOC0»O 


S'c0QCOOlM<00iOQ0cOt^ 
^CDiOCOiOCOul^tOiO^iO 


giOOtOOQt^t^COCOOlcO 
^COiCtOiOCOiOtOiCtOvO 


^J5 


sa  i>  00  00  r-- a>  to  o  m  rH '^  c^  co  co  (N  Tt^  r-i  lo  o  to  o> 

^tOiOcOiOCOiOtOiCCOtO    'OkOCOtOCOtOtOkOtOO 


-^t^iOt^iCtOtOiOt^iC 
tOiOCOiCtOtOcOiOtOiO 


OtOt-i/SOO^JOCOOCO 
COiOtOiOtOiOtOiOtOO 


O^lCO-^i-HCO-MfNCOrH 
:OiCtOiacOiOtOiOtO>C 


So  00  rH  t*  C^l  CO  CO -T** 'Tj*  CO    lO  <M  CO  .H  r*  O  GO  Ol  O  OO 
C^^<N -^C^^tNTjfCM  ^    C^  Tjt  C>1 -^  <N  Tf  C^  CO  CO  CO 

^  to  lO  to  lO  to  iO  to  kO  CO  tO  to  lO  CO  lO  to  lO  to  lO  to  lO 


gc^t-coto^to»ncoi>-c^ 

^tOtCtOOtOtCtOLCtOiC 


g'^-rtfcpvOiOtOCOOOfMOiO 
^tOtOOLOCOiOtOiOtOiC 


OOrHO>OOai»HI>-COtp 
C^-*(Nt(<COCO00COCOCO 

tOiAtOiAtOiOtOiOtOlC 


oo>t-(oocor-"^iotO"<t' 

OOCO  coco  CO  CO  CO  CO  CO  CO 
(OiOtOiOtOiOCOiOCOiO 


SCO'^t^eOa»C^OO'MCiCOOQ-^COCOiOI— COOiC^ 
Wrf(NTj«C^-«^eOT^COCOCOCOCOCOCOOOCOCOCOCO 

^tOiOcOiOtOiOtOiOtOiCOiOtOiOtOiCtO»OtOiO 


»OOCOOC^f-(OCOO>'^t* 
:Cs|Tj*CO'^0Q't*<C'5COCOCO 

JtOiOtOiOtOiOOiCCOiC 


SO(N<NOCOO>iOI>-t--tO 
CO'^CO'^COCOCOCOCOCO 

^COiOtOiCCOlOtOiOtOlO 


S(NQTt*a>iOt^t^toa>Tp 
co-vcocococococococo 

^tOtCtOiOtOiOCOtOtOO 


S'^aotot^t*ioaiTt<rH(N 
coweocococococo-Tj^co 

^COiOtOiOtOiCtOLOtOkC 


SiQtOt'^iOaiCOOr-tC^CT* 
COCOCOCOCOCOtJ*cOtJ<CJ 

^tO»OtOiOCOiCtOiCtOiO 


COCOCOCO'^CO'Tj'C^'^C^ 
^tOtCtOiOtOiOtOiOCOiO 


CO  CO  CO  <N -^  (M -^  <N -^  <N    -^  WJ<  T-t  40  i-l  lO  i-t  lO  rH 
^  to  lO  CO  »0  to  »C  to  lO  to  lO  CO  lO  to  lO  to  tO  CO  lO  CO  lO 


lOtOOOOOCOOrHlMO 
o5cOCOC0C0C0tJiC0"<J'CO 

tOiOCOiOtOiOCDiOCOiO 


QO-^OfTiHr-teOOiiOOQ 
COCO'^CO'^CO"^<N-^o3 

coiotoiotoiotoirricoto 


OfNC^iH-^OiCOf-t-iO 

'^co-^cO'^c^'^c^-^ca 

tOkCtOiOtOLOtOiOtOiO 


CSO-'S'OQCOCOOO-^QC^ 
COiOtOiOtOOtOiOCOO 


"*t-tO»OOOCOOrH(NCT» 
■^C^'^(NtJ<CMU30iOt-' 

tOiOtOiOCOiCtOkOtOiO 


tO-^OOC^QOC^OO-^tO 
tOiOtOiCCOiOtOiOCOiO 


SCOOQCQtOO'**<Cl'NTfO 
CO(NCOC^'Tj<C^Tj<c^'^cN 

^4>iOCOtCtOOcOLOtOLO 


rtcdrtcotfcoPtSodrtoQ  PiicopJHcnrtcwtf oqPhqq 


tOOOCOiOOCOCOTHiOOS 
TrrH-^i-HiOi-tiOi-liOO 

COiOCOtOtOkQCOiOtOiO 


c^?i?3mS       <nSc3c^co 


u^iO»0'^tocor*cooocs 

COiOtOiOCOiOtOLOtOiC 


oo"^a>e»oc>iO'-'»-<o 

tOiOtOtOtOtOtOiOtCiC 


T-(<N2^i-tCOO'^Cfl»000 
CM'^CJ'^fiM'^C^COCSW 

tOLOCOiOtOiOtOLCtOiC 


Tj<OiCCitOOOI>r^OitO 


^•QOoor-otoi-fiQtNeo 

MCOC^COCOCOCOCOCOOO 
tOiOCOiOCOiOCOtOCOiO 


rHCOC^lOCO'<f»OCOtOrH 
CO  CO  COCO  CO  CO  CO  00  OOCO 

tOiOtOiOtOtOtOiOtOiLC 


Tf^iQCfjr-ciooooo 

COCOMCOCOCOCOOO^iM 
tOtOtOU3COU>tOkCtOLO 


T-tiOC^iOC^vOOiOdiO 
LOtCiOiQiOiCtOiOiOiQ 

iOiCOiOOiOiOidO»0 


vCCOtOCOtOeOCOCOCDCO 
lOi^iOiOtCOiOiOiOiO 


0>iMOi-hOt-(0'-<00 
lOiOOidOuOOiCoiC 

lOiOCOiOtOiOCOiOCOtO 


coo-^o>'^o>'^coinoo 

^-pO-^O'^O'^J^OTjt 


r*t^ooi>coto©cOQ>to 

0'^0'^0'«J<0"^0-^ 
COiOtOiCtOiOtOtCtOiO 


OlCrHTr(MT^COCOOO<N 


'^COiOlMtOWr-^ODQ 
tOiOtOtOtOiCtOiOtOtO 


OOt-tOlOpOr-lOC^CO 


C^OlCOOO'^J'll^ifttOCOvO 
C^CO(NOO(NCOC<ICOCSiCiO 

tOiOcOiOtOiOtOiOtOiO 


(Ot^t^tOOOiOO'^OCO 
!NCO(N00CJCOC^COCOC0 

tOiCcOiOtOiOtOiCcOtO 


OiOi-l'^C^OOCOrHTfO 
COCOCCCOCOCOCOCOCOCO 

tOiOtOiOtOtOtOiOtOiO 


■liO*-<tOOI:>-COOit:^ 

COCOCOOOCOCOCOC^COOl 

tOiOtOiOtOtOtOiOCOiO 


t^OO>OiOt-(MtOOO'«»t 
CO0O0O<Ntj»<N'^'M-^C^ 

tOiOtOiOtOiOtOiOtOiO 


FHr-cocO'rj<'<ttocot*^ 

tOtOtOOtOiCtOiOcOiO 


t>C^OOtHOO»-IOQCOtO    lOiOtOCOOOcNOOrHOO 
CO  00  CO  CO  T><  CO  Tt*  CS '^  (N    ^C^^^C^yrOi^OiiOyH 

to  to  to  tjO  CO  iO  CO  lO  CO  lO  ;o  ^  CO  tO  to  tc  to  tc  CO  lO 


OO(N0>C0t>-i0C0t-'^ 
^CO'^<N'^CJTt*<N'^(N 

tOiOtOiOcOLOcOtOtOiO 


oooQ»ot^r*iococooi-* 

tOiOtOiOtOiOtOLCCOiO 


QOMQOC^OlTt<t-tOiO 
"S^C^iOCOiOl-dOr-tiOi-l 

tOOCOLOcOtOCOtOtOLO 


<NO'^00C0C0C0'<i<O<N 
iOC^O.-HiOrH40iHOr-4 

tOiOtOiOtOiOtOOOiO 


t0t0Cp"«J*OC^C^TH-^a>t0l>00»CQC0C^O'3'C0 
■^(N-^<NiOMOlM»Oi-liLSrHOi-fOr-(Oi-)0  0 

COiOtOiOCOiOtOiOtOLOtOtOCOUDt>u^t^iOt»iO 


oico?-iiHeoo4iQooi>coa>"^t-ti-Hcoo>^r-.co^ 

Tj<  C^  U5  C*  iC  iH  lO  rH  lO  rl  lO  rH  O  r-(  O  O  O  O  O  O 
to  lO  to  iC  to  »0  CO  iO  to  lO  CO  to  t>  lO  l>  O  l>  lO  C^  lO 


CSO'^OOtOtOQO-^OC^ 
iOC^»Oi-n5iHiO.-HOi-l 

tOOcOiOtOiOCOiOt^iO 


^t^to»oa>coiHi-*cooi 

lOrHtOrHiOrHOrHOO 
tOkOOtOCOiOt^tOt^iO 


t^TfOiC^i-tOiCOt^-t 


gOOt^COtOtOC^OOO 
.-HOOOOOOOO 

cDiOt^iOt^tOt^iOt^iO 


tpO-^CMrHiOO>t--tp 
OOOOOOiOOiO 

tOiCt>-iOt>-iOt^'«*<t*'^ 


PCncdpiHGQpCHCQP^CAP^aD 


'^"i'x^ 


r^OiOoot^ioococ^Q 
OrHOOOOrtOi-lO 

r^iot>-iot^iOi>iOt*iO 


iOoco-<j*o»-Hcoa>tocp 

OOOOi-iOrllOi-liO 
t^iOt-lOt^iOt--T)'t-Tf 


00C-)rHOC0t^t0-^0><N 
OOrlOrHiOi-nOr-liO 

t~iot~ior»-^c--*t~Tj< 


r-ClOi-liOi-liOi-l^6j-<J< 


>-HOrtlOrH-3'i-l-»l<M-<)' 


Mqq(>hcqMcoP4c»Ce;qq 


TABLE  10. 

Mean  Time  of  Sun' a  Visible  Rieing  and  Setting. 


[Page  665 


M 


■2>    <u 


a    5 


S      bo 


o 

3 

P 
9 

5 

CD 

"^ 

TJ 

s 

cS 

*i  i 

hJ 

o 

-4^ 

0) 

s 

o 

ri 

tti 

at 

i'^ 


•xoiddy 


'xoaady 


^^ 


^     ^ 


5    !§ 


p:^  en  p<  X  fc;  en  tf  CO  p^  cQ 


ptHCGp^Gdtfodpi^cnpcJGd 


SrHOf-tOf-HOii-^OiC^Ci 


p:^  X  P:^  en  p^  QQ  p;  GQ  p^  GQ 


s  s 


C000000>00>00>0 


r-(COr-*COrHCOr-*0QiH00 


Ri-HeOr-cMe^WINOTINM 


6i>-'>l'0QC5a>«i-n-i(MO 
e^eoe5MfjMooeoco« 


c<«c5oO(M03ClcoNeo 


0QS4a><-IQQr-IOQe^C- 


o>c^i-ioeoo>Tj"t»to>(5 


«Or-i>op%aocoi>-o>a 


aQOOQtOt-l->»"«INiQO 

^f-*»i3fHlOiHii5rHiOt— 1 


a«OCJtO^OOO>OOOr-(tO 


■^i-HlOrHlOr-IOr-liOi-l 

^coiacotocoto^tocoiA 


S28S§88SSS 


S09tOtO'*t-(NO>Oi-lOO 
lOrHiOr-ltCrHiQt-tOO 


OOOOSOfllOrHlO 


t^  ^  t^  ^  t*  ^  t*  ^  t^  ^ 


i-lOi-IOi-(iOtHi4(NiO 


S&5 


•^OJ 


■  Tj<  t"»  ^  1^  ^  t*  ^ 


SOO  « -^  rl  Tf  00 


CO0QC0i-(O 


_. .  .  _  3;o 

■'T  CO  "^  CO  CO 
■<J|  t^  rf  t^ -It 


O  rH  r* -^  CO  00  o 
^  CO  CO  CO  CO  o5  CO 


■  iQO>oo(Orte^iQg>oo«o 
go>coc>ScOcoeoco6icoiM 


lOt^r-too-^r-ie^coo 

Ti-l'<ri-ITI'iHlOr-lu5iH 


rHeoeOf-i>o»h-tS'S 


s  s 


Qjcritfcnc^aiaiaQpicn 


gO*00>00»OTO'-<OQ 


S-^t-^-^I^COCCCOOCJ 


coo>'*oOinootot^t~to 

rlcOrlSSrlCOiHeOrH-O 


Srtcl§5?Jeo?3«8« 


M  f<  ?1  (M  fl  C^  CO  C<«3  C5 


SNM?Jeoortr-c«<S 
cOiOCOOcOiOcOiOcOiO 


r-(0>eOt— iriOCOOOOOrH 


OOCOOrHOm^C-COlO 
-^f-ttOr-llCO>OOtOO 


iQgot^«00>eo£ji-(5"oo 


SSSSBSSSSS 


OOOOOiOr-iOr-liO 


StOW^lCr-«eC00i-llO 


'^'-'S?SCOlOCOr-lo99 


O0»N«0lO-^00<Ht-(00 
r-<iOlHl5rHlOr-IOOI^ 


l«O^00.-li-iap'*iO0QC< 


coeoo5«c8eo5*S->><8 


^■^INr-li/JOOOQlQi-IM 

rtidcausiNfM-^co-* 


T}"o>r-tOOooeooit^«o 

c^-^ra-^co'^oicocoOT 


■^  ?i  ^  00  OT  o5  OT 

^  t^  ^  t^  ^  t^  "f 


S^eO' 


■CCC0C4Q 


■>»<C»OCl3r-( 
t^  ^  t^  ''J^  t^  ^ 


1-cOO 
OOtJIOO'C 


rH  1-1  ipt^Ol 


Sw^co 


OC^-^0000>nMr-l 


-S<CO'<J>C 


SCO 


0>T|<(NrHiqt^0>'*C0O 

oi-^cO'S'cococoeo^co 


>c^-*oo 


t^^r^-^oo-^ 


oO'«)<ooeo 


Or-loSrlO 

OO  •>!<  00 -}■  OO  •* 


00  CO  00  CO 


30  If  00  CO  CO  CO 


OI--C0O 

^  -^  CO  ^ 
00  CO  00  CO 


COQQt^iQOrHTJ'OOQO'* 

eoMcoeo-^co-^fS-^c^ 


C<IO«Old-Hi-*:OOrHrH 
lOCIiOrlOrHOOrHO 

r.Tft.Ttiooi^oO'^oO'^ 


5i-ig>iOioc 

CO  CO  ■>}•  Ol  ■'l' « ■> 

t~  ■<»•  t- ^  r- ■^  t 


?co5jooc:cOiMcoooco 

'00  CO  00  CO 


>OOOr 
J^OOtJIC 


1-1  <o  >g  5<  <3>  00 

—  (N  ^  64  ■»<  ■-( 
t^  ^  t^  ^  t^  "^ 


iar-liO.H 

t>- ■»)<  t^  ■<J' 


■«»"1M'»  i-liOr-l 
t- Td  t^  Tf  t~  rjl 


PJcfiPjQQpHoiP^aiP^cc  McnptjixiajaQPjoQMaQ  Ph  as  pj  as  P<aQ04CQ  PS  oo 


ooo 

OO'J'OO 


TIIOOCO 


r-1 -.J"  M  ■<»< 
00  CO  00  CO 


38S 

00->)<00 


CO  00  CO 


pTjltOOO 

cS-'j'c^co 

00  CO  00  CO 


t^        oS~    0»        O  rH         C^         CO         "J"        iS"^ 


cOlOC^QoocOlO^^'T^O 
i-iioc<«OMT)<cocoT>"eo 

oocoooeooocoooooooco 


'  r- o  r-(  r- f 

iTf^TfCOCO 

00  CO  00  CO  00  CO 


•*<NiClr-l 

CO  CO  00  oo 


or~t^O^c0CMir5r-ie 


CO  CO  CO  CO  ^  c^ 
00  CO  00  CO  00  CO 


lOrHOO 

CO  CO  Si  CO 


>  iH  O  ■*  t^  to  in  00 
1  CO -O"  04  ■*  1-1 

00  CO  00  CO  00  CO 


Sot 

OOCOOlM 


ediMCiicDpiaifiiaafiiad 


to      r^      a6      o»      C? 
lO       tO       u3       lO       ^ 


Page  666] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


•xoiddy 


a  s 

g    "S 

0)        <D 


*"         r-i 


Z 


00   a 

"3 

o 

II 

P3 


rtccQ3Kp4»rta!Jp^&Q!a5a}f<5a6o5a3Pi5Mcix',pJ33B5ccpi5oDp4 


DSaJrtcdaiaDWccrtaipicc 


ftiOOiOOiOO'^O-^O 


g^ 


i-<iOOr^CX)C3tOrH'^CO 


iOCOOCCOCCOCCO 


C^ffOCDOaCCt^OiOC^ 


CUNtNCOWCQC^COr-lCOT-iCC 


CStNCSCSiHCSi-tiMiHCOrHCO 


osooQc^<r)w^LOcoi> 


CD  Ol  »£)  i-H  CO  CO  T 


3COlOQI>-r^OiiCO'^(N(N'^ 


lOiCiC^OiOtOiO^iCCO  lOXiiOtOvCiCOiCCOiCCD 


g't^IOi-HC^OCOCOiOcOcOliCoOCOOiWrHOfNai-^ 
'"^ lO "^ lO '^ ic CO lO CO lO  co»o coiocoocoocao 

^  iC  lO  lO  Ut>  »0  lOiCiCiC  iC  tO  lO  iCiO  »0  to  iC  to  iC  CO 


g -^  Tj*  ^  lO  CO  lO  CO  lO  CO  iC   COiOCOiCCCiOOOOC^O 


g*O000iOQ0»-(I^C^iCC0l'^iCC0c0<— it^OascOQ   t^i-HCOCOiO-^COiitiC^r^ 
•<^TfC0iOC0iOC0iCc0iC|C0t0C0iOC0iCC0iOC4O   C^OC^OOIOC^OC^O 

^iOiC»OiOiOiCiO>dU5iC  ;iCiO»OiddCiOidOtO   iftl«OiC«OiCCOiCcOiCtO 


o»oosr»i>-Oiioococ^c^-^ 

CNrH,-l,-(i-ti-(i-)(Mr-*C^*i~iCl 
lOcDiOtOiOtOiCtDiOOiCtD 


t^iOtCt^iCCOCOOi-HTH 
iCCOiCCDxOCOiCCOiOtO 


OCOOa-<*«l:^CDiCOOCOC>C^i-H 
<NrHi-HT-irHr-(i-lTHr-H-fT-(C^ 

iCi«0»OtOiOCOiOtOiOtOiCCO 


t^COCOiCiCCDCOr-C^OS 
<NOC^O(NOCN|0<NO 

iCcOiOcOiOtOiCtOiOcO 


g*O000iOi0COI>i-HiC(N  ^Tt^-^COiCi-HCOOOCCiOi 
Tj«Tj(co-^coiccoiocoiO|coiocoiocou:5coiocsiC 


■t010:.0^*C<lcO'^'rfcOC<»C 


lOCOiCCOiOCOiCcOiCCOiOtO 


OOOCiOt^r-ICOCO'^-^COCO 

iivtoir:;otoco»ocoiccouti«o 


OOOtO.HiCC^rJ'-^cOiC    i— icpO0C000si>'i~IOC^iC-f 
C^OC^O(NOC>)OC^O    CSOCSIOrHOi-frHi-Hrlf^rH 

lOtOiCcOiCCOiCcOiCCO  lOtOiCCCiCcOiCcOiCOiOcO 


g^T^COTfCOiCCOiCCOlO 


COiCCOlCCOiCCQiCC^OjC^iOC^OC-JOC^OC^OC^OCSOC^OrHOi-Hi^T-ir-l 
iCiCiOiOiO>OiCiOiO*CiOiCiC«OiCtOiCcOiOCO  iCCOiCcOLCCOiOcOiCcOiCCO 


g'OODOldODOr^^tO'M 
'^Tt*cOT}«coiC»iCcou:2 


uticO'^^c^ii^i-Hcoot^asccoooir^Qcoc^iOco-Tf^'^^^'-Hcoor^OiOiooc) 

COiOCOiOCOiCCOiCCOiO    CS  iCi  WvO  C^  25  CS  t)  (N  O    (MOCMOcNOC^Or-iOr-irH 
iOiCiOiC»CiOiOiCiCiCiC»OiCiOiCcDiCCDiCCOiOCOiOcOiOCOiOCOiCcOiOCO 


g'OOOOiCsGCQt-^i-icDOJ   iCC0*f^-^C0iCC1cOi-4r^ 
Tt<  Tj«  CO  "«*<  CO  lO  CO  lO  CO  lO    CO  lO  CO  lO  CO  iC  CC  lO  CO  »c 

f^*  iC  1^  lO  iC  lO  vC  O  iC  lO  iC  tC  lO  iC  iC  iC  »dC  lO  »C  vC 


CCiO!MiOC^Oi>JO(NO 
iCiOidCiOtOiOcOiOCO 


'OOO-Tt^TfMiOi— *COOi>CiOO 
<NOCMOC^O{NO<NOi-(0 

lOCOiCCOiCtOiCtOiOCOiOco 


■^'^CO'^COTj^COiCCOiOCOiOCOiOCOlOCOiCCOiS    CO»OCO»Sc^iOC^OC-iO 
^lOUSiCiCiCOiOiCiOiOiCiOiCiOiCiOiOiCiOiOiCiCiCiCiCtOiCcDiOCD 


cOC^tCCO'#'rt*COlCf-lCD^^t^ 
LCCOiCcOiCCOiOCOu^COiCtO 


•^^■^■VCOTPCOiOCOiC 


^C)OC2i_C'^^iCCOCOC<)COi-tI^OCC050:'ODo|t^i-HCDC^iOCO'r*HTj*cOiC^)CO 
COUDCOUtlCOUicOiOCOlOCOiOCOiCCOiOC^iCC^OC^OC^OC^lOCJOC-lOC^O 

iCiOiCiOiCiCiO»OU3iOiOU0iOi^iC»OiCiOiCcOuCtDiOcOiCCOiCCOiOcOiCCO 


g*rHOlQClOOait-HCCi-^    t^MI"-C0<O'^*>fMC-1<«0    COtOC^t^daOi-iOOO 
■*  •<** -^  Tj< -^  to  CO  lO  CO  iC    CO  iC  CO  iC  CO  to  CO  lO  CO  lO    CO  lO  CO  iC  CO  io  CO  lO  CO  o 

rfjiOiCiC»CiC»dOiCiOiC  iCvCiCiOu^iC>OiO»0>0  iCiCiOiCiOiCuOiiliOCO 


<NO(MO!NOC^OiMOC^S 
iCcOiOCOtCCDiOCDiCcOtOCO 


•^M*'^iS'^iOCCiCCOiCCOiCCO"tiCOiOCOiCCOiC 
^iCiCiOiOiOiCiOi/OiOiOiOiCiOiOiCiOidOiOiC 


"tOoOt^COCCCNOiT-'Oi 
COiOCOiOCOiCCO^COOiO 

iCiCiOiCuCiCiddOiO 


n^MOrHQi-(i-IO.-(OM 
^iCiCiCiCiOiOiCiCiOiC 


ncooC'COGO'^i^'^coiC 

COiCCOOCOtCCOiOCOiO 
iCiCiOiOiCiCiiCiCiCiC 


^•,o»ct^'^t^cocococ:i 

COiOCOiOCOOCOiOCOiO 


COiOCOOCOOCOOC^O^O 
lOiCiCtOiOOiOcOiCcOiCsD 


S"^Q?3OCSi-Hi-H,-^.-HC^OC00iC0airt*00'^t^lO!t^CC'CDC0t0I^iC0C"*00 
'<^iO'^ic-^<>'^io-^iOTt*iocoicccicco»ocoic;coi?5coiccoiocoiccoio 

rfrjiCiCUSiOiCiCiOiCiOioKciCCOiCi^iCiOiOiCiCOiOiCiCiCiOiOiCiCiO 


^^^'^'Z^'^nt^'^  ^^  "^   T-HCOOCOO-^Ci-^OsiC 
&  Th  iC  •<*  lO '<^  lO -^  iC  TT  lO    Tj<  lO -*  lO  "^  t6  CO  iC  CO  iO 

^  lO  iC  iC  lO  lO  lO  lO  iCi  lO  iO   iO  iC  lO  »0  »C  »C  iC  ift  »0  lO 


tDI>CDt^t~^COr^COC0 
lOCOiOCOiOCOiOCOO 

iCiCiOiCiOiOiOOiOiC 


ja;T^C^Tt<<N'^(NCO(MCOCO 
^iCiCiOiOidCidOiCiO 


C^COfM'^rH-^THtCOiOfOcOCiOaar^OOI^OOGO 

TfiO'^iO'^in'^iCi^ioi'^iOcoiocoiocoiccoio 

lOiOiOidCiOiOiOiCi/OiOiOiCiOidOiOidOlO 


rJ'-t*C^'^C5-*(N'r^COT*<CO 


tOCOCO'^lM'^(MiOi-l>C    i-HCCrHtOOcOOt^Ot^ 

'^  lO  Tt<  lO  Tj*  lo  "Tj*  lO -^  ic  '^  lo '«rt  lO  "*:j<  ic  Tf<  lO -^  ic 

lOidOiOiCiCiOiOiCiC   iCiOiCiOiOiCiCiOiCUti 


•xojddv 


™;iCCOiOCOxCCOiCTt<iO'^' 


;^"^-^'^'*fiCcoiOcoiC  coco!^^toc^tO'^^I^'M^-  rnt^i-iococcooDOoiooi 
'^iorj<iC"^iC'<j'io-^ic  ■^iC'«r'»0'^iO'^iO"<!j'ic  Tfic-^iOTfiC'Tio^icrrio 

»OiCiit)»CiCiCiCiOiCiO   iOiO»OiCiCiCiOiCiCiC  lOiOiOiCiCiOiOiCiCiCiCiO 


OQOF-'C3'MOOC^I>.COr^Tf< 
COOcOOC^OC^OCnIOC^O 

iCCOiCCDiOCOiCtOiCtOiOCD 


■«^0iC00i(NO'Mi-(r-(r-(r-(O 
COiCCOiCCOOCOOCOOCOO 

iCiO^OiOiCCOiOtOiCtOvCcO 


lOOOiCOS-rfCl-^OCCOCOi-i 
COkCCOiOCOiOCOOCOOCOO 

iOiCidC»CiOiCCOiCCDiCCD 


r^oot^Oicocscoocoooo 

COUtiCOiC'COiOCOiCCOOCOO 
lOiCiCiOiCiOiCiOiCtCiOCC 


C0iCc0iOC0iCC0iOC0Li*C0»O 
iOiCiCidCiCiO>0»CiC»CiO 


'cc^co-fcococococolcor^cor-'Mt^Mr-.c^oO'Mc^ 
.  -    ..  -    ^  _    ..  I*,  P^J^^  ^  J^  ^  ^  _ ^ 

^lOiCiCiCiCiOidCiCiO   iCiCiC»CiOiCidO^>OliC>C>CiCiCiOtOidCiCiO»OiC»OiOuOu:)»OtO»OiOiit> 


^OiOiOuS»OiCiCiOiOiOOiOiOiCiC»OiCiCiCOuOiCUtiiOiCif3vCiC»OiCiCiO»OiCiCiCi^ 


rf*iOidC»OidOiCidCiCUCidOiC»dOidCiCUD   iO»OiCiCiCiCidOidO 


oscoQpcpoocpcotoooco 

iCiCiOiOiCiCiOidOiC 


goocooccp 
-^  lO  "^iC 


•sOCOCOcOcOOCOCOCDcoOCO 
iCiOiCiCiC»CiOvCiCiCi.OiC 


ooooOcooocooccooococcto 
■^iO'^iOTt«iOTt<iOTj<iCTriO 

vCiCiOiCiOiOiCvOiCUDiOiO 


p:^c/^p^copc^Qdp^QQp:)co,P4xP<odQ^cfipciccQdc>o 


i5r"'co   t-  ""oT*" 


OS  O  rH  C^l  CO 


pHdQfl^Gdpl^I^PC^CCpiH'cCCCH^ 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  667 


o 


tX     II 


T 


o     S 

cQ   a 


•  xo  J  ad  V 


■xoiddy 


OHGQpHodOHCCPJadPJcd 


P^aQP^odCdooPJcoPJud 


9<CGp4»iP4cfQpHCCp4<» 


ficDOiaioicaeiiaitAtji 


»i-'COeMCOOJCO(M(M(N 


■.JHt>-'^t^'^t^'^t^1'C^ 


coi-(Mi-ieor-ic^T-<cie< 

S'oO!>oc^<ff■^■^"■0'^J«lQOaoc^^P■^co<o•-<oo'o>.-lOc3'^'<o^-c»Olr"^omT»•«o.-lOl«:c^lClO 


.^iOOhO^iC^U^COiOCO  iO«D^CO'^<0^<0^sO'^«0^50'<S*«0'^«0'8'Ohj'tO'^t*^t*'^t>"'r<C* 


^  lO  -O  lO  to  O  -^  >n  <0  >0  CO 


^io;o>o«o>n<o>a<oiao 


:r.|i-l-Hr-li-(i-10iH0lN 
•  lO^^cOO'OkOCOO^ 


^■^coco-^rc^'^or-g^ov 


fkOOOOtOOiCCOlOCO 


oo53eooeij>0'fl'>0'<r|3- 


soeoeootn'ooco-co 


■rt  QCOCOO 


OC^S 


lOtO^tO'^tOfO'^tOj-'J'Or'OI'tOftO^tO 


•ijno-.j.to^O'<i<t~-<j'r» 


2J  00  rH  Q  0» 'M  t^  C5  vO  U5  CO  t- .H  C»  31  ■>»  t^ -T  lO  !0  CS  00  Q -J  Op  CO  (Q  >0  CC  OO 

lO  ^tO  CO  ^  ^^  ^  ^  O  ^  CO  ^  ^  ^  CO  *i*  CO  ^  CO  ^  CO  ^  CO  ^  CO  ^  co^  to 


SiQcjc-ooQQOQt^e<l>Q:i;?5cor-igooiQtcjlig-g!eocg>-<oogo.Hcpe5 
»Ocooco»OcO'^«0'<l<co^cO'*<cO'^co^co^cor^co*^cO'S"co^co^co 


lOcOtOCOtOCOtOcO^cO 


H  O  r-t  O  C^  O  N  O  04 


S*OOOt^rH»OC«"*COCOkO 


^iOCOtOCOU^COtO^iOcO 


iCcOU^COOCOi/SCOiOcO 


•*^MiO^COOOOgO> 
lOcOtOCOiOCO^COuOCO 


^iaco>Aco>aco>aco>aco 


^'lacotocovacoiocoioco 


^tCcOiOcOiAcO^CO^CO 


:coocoocco^omo 
:ocoocoLocoiOcoiOco 


^iflCOiO 


-H  •«<  2»  eo  c^  CO  CO 
oeoocoocoo 

:D  lA  CO  iC  CO  Ud  CO 


coe«>«eO'fl<'*eococ<t~ 

lOcOiOCOiOcOiOCOiOCO 


o>.Heooit»eoco^iOiO 
ioco>acoioco>ncoiaco 


rt©000>i-ICOC<t-CO 
C<05ii-lr-<i-(i-lrHrHi-l 

lOCOiACOtCCOiCCOi/^CO 


lOCOiOCOlCCOOCOtOCO 


•rtC0«C0iOC0»003iOCQ^'V'T'T^'<*^^C0^ 

■.j*co*a«co'*co^co'^co  l-^  co^co^cc^ce^co 


8oQ»ocO'H'Tcoeoinii-it~.o>o>t— r-iiftcoeoiq 
c*3eoi5eo>AeOi«o5  lOWfeo-*'*-*-*'-*^ 

lO  CO  ^  CO  "^l*  CO '^  CO  "^  CO  ^  CO  "^  CO '<f<  CO  ^  CO  ^  CO 


5iiQ-^t^<j>oQr-ococ3 
oiNo?<io55iOMi5co 

OcOiOcOTfcOTfcO-^CO 


iCCO^COOCOOCO-^CO 


•orfioeoi5eOTj<eo-*><< 

^CO^CO^CO^CO^^'CO 


iOn!noooni<3ASco 
■"J'cO-iI'cOtI'cO'^CO'J'CO 


t  ©  CO  i-l  lO  CO  CO  ■*  2!  CO   o  t^  o>  o>  t~  r-<  >Q  c^  ■v -^ 

incotoco'ocoiocoioco  >ocO'«co^co'4<cO'^co 


to-^^tiOiO'tf'coeot^c^QO 


lOcOiA'^iOCOtOCO^eO 


tO  CO  lO  CO  tA  CO  lA 


COtOcO 


HCO(N^r-<5'0 

coocoocoon 

lO  CO  iC  CO  ^  CO  iC 


CO  lO  CO 


tOCOcOCOiCcoiOCOiOCO 


S',0  i-H  kO  1-H  lO  N 
MOo5oo5o 

O  Ud  O  lO  'O  ^  CO 


j  CO  &  CO  o  CO  O  CO 

kC  O  ^  O  lO  CO  ^ 


COOCO 


rJ-J"MiOrtOQCOOt^ 

cooooocoocoocoo 
lAcOiCCOiOcO^coaOCO 


lOcoiocoiacoiocoioco 


iH3>O.Hg»Mt^COCO'<J< 

■   -ctHe-jOMocJoM 

iCCOiOCOiOcOiACOiOcO 


H  rt  .-,  r-1  iH  i-l  J5  t-l  IN 

tOcOtOCOkOCOiCCOiACO 


Q0'.*<t~incocoiOt~'*<» 

>-liH.-lr-(i-li-(i-liHr.|fH 
lOCOtOcOtCCOtOCOiOCO 


tocoiacotAOtocoiAco 


COOi«r^-9'rHCOC>)COCO 
C4i-l(NiHCSiH6ii-tMi-l 

(OCOtftcOtCCOiOcO^CO 


Sr^cooooDOii^ost^o 
tOCOO^>OCOiOcOtOCO 


SOOiOCS 


oa>o<»ooOi-i 

OCOOCO  OCOO 

O  lO  CO  O  CO  lO  CO 


i-Hr^rHr»c^coricpc^'cocoiOco«i5^'^ 


CO  o  CO  o  CO  o  CO 

lO  CO  ^  coo  CO  lO 


as 

:0  lO  o 


iOCO»0'^"f'^   -  — 

coocoocOoooocoo 

^COlOCOOCOiOCOiOO 


grHOOi-t^i-HaarHaiC 


^  TJ*  lO  -^ 


O  O  lO  iC  lO  O  lO 


Q  Oi  O  Q  Oi  O  OS 
lO  lO  ^  ^  tC  oo 


^  it5  iC  lO 


STj<  OO -^  GO  CO  op 
Tf  »3  -1<  lO  Tt*  l3 

lO  lO  lO  lO  iC  iCiO 


COGOCOOliMOiriOiC^OS 


»:Or^^r*cot>-':ot^Ot^ 


lO  '^  lO  ^  lO  "^  lO 
40  iO»0  O  O  »OiO 


^  tC  >0  lO 


too  iC^O  lO  lO 


P^cnP!HOQp!5cdP£5adrtaQ 


r-l         C^         CO 


Sa>*H  lai^HQQrHOOC^t^Cflt^CO 
cooicoocoooSocooooo 

cOlOcOiOcoiO<:oiOcOiAcO*AO 


COiOCOtOiMCO^t^r^r- 

coocoocoocooooo 

lOOLOCOtCcOiOOiOcO 


t^COeOCOCO'3«u5r-iOift 
COOCOOCQOCOOCOO 
lOOiOcOiCCOiOCOiOCO 


tOOvOcOiOCOiOCOiOCO 


i  -^  iC  "«J*  »o  -^  t 


lOoO'^oO'^aO'^co-^oo 


*>»•  iO '^  lO  Tf  »o -^ 
lO  lO  >CiO  lO  tO  iC 


>r>-aor^coi>  oot*-oor*oot^c30r>.ooi>' 


iCiOiC 


-rfno'^iO-^iO-^^'^ia 


i>      00      a>      Q 


pEHodP^cntfodP^aQpc^cn 


tHT-*Oi-HOtNOi^a>^ 

Tj*o^o-vocoocoo 

lOOiOOtCeOiOCOiCcO 


oot— cor*t>-r*t^r*r^t^ 


P^qoP^oqP^cqPhcqP^cq 


Page  668] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


Xi 

Jr 

Q 

P 

© 

o 

P 

0) 

n 

4^ 

53 

^ 

0 

^ 

fl 

z 

1 

S 

&, 

eg 

I 

o 

s 


^     .1 


•8JBp 

•xojddv 


•aiBp 
•xoaddy 


g 


QHtnpHcdpiHaipHasp^os 


s 


OiiacA(B(iimpiuifii<x 


iC<NO^tO.-(.-liO<00 


Si-HOOOQOT)<MO<OtOO 


SCvl  CO  Ol  i-t  iC 

JS  T><  t>  •*  t~  ■^ 


■^MOOOCIN 


Di-KNi-Crl 
,c*  ^  t^  ^  t*»  ^ 


gt~  (Q  ■f  aa  r^ 
,ei  ■*  t^  Tji  t^  •* 


t> -Jt  t^  T)«  t^ 


go  QOOCOvO 
COO(MOC3 

rfi  ■<*>  r~  ■^  t^  Tf 


tOOlOCOIN 

06lOi-lr-l 

C~  TJI  t>.  Tjl  t>. 


jgCOlCrHOOOOOlOCOC^C 


:  CO  U5  CO  li^  C^i 

.<S -^  O  ■^  to  T)l 


CMOC^ 


st^rHlOCOCliC^OOC^r-l 


feCOiOCOiO  CO 


locmcc^o 
to -^  to -*  t~ 


»^^t^OOStO^H'^'<^i-ltO 


K '* -^  CO  ■*  CO 

^  -^  -o  -^  to  '*< 


lO  CO  k/i  CO  lO 

to  ^  to  ■^  to 


»incOCOiOOt^QQt7stOW 


^'  ■*  to  Tj<  to  ■<}< 


"^COiO 
to  ■>!)<  to  Tjl  to 


lO       ^       U3       lC 


!8 


P<o30JcopjaQ^oQ&Jcn 


P^cAO^DOP^asPjodoiSoQ 


i-ttOkO^HOSt^CO-^tOi-f 
■*rHCOOld<N(NC0i-l'* 

cooocococoooeooocooo 


O'*m'«J<iii>Oi*'i0-*OC0OC0i-l(NrH<NC^i-IC0 

->»<t»eot^cot~eot-cococooocooc«oocoooeooo 


OOOOQtOt-liOC^iCi— (to 

0'*Oi25>oo-«<>-ieoiM 

CO00CO0O<NOi<Na>INO> 


OOOSOtOt-'lOC^^fHlO 

ocoo-«'iCiri-<»<oeOFH 
eoooeooO(Noo(NO>c>)0> 


!<tOpOt0'»'(Na0f-!N|c0t^r-<Ne<100t0'*OOC0t0t0C0C0r-lOOi-H01 
>COO->J"iO-*iOT)<'<a>ii5'*ir5COOeOO(Nr-i(NC<i-l(NOCO>0'<»'>0>Cl'Vi/3 

•  coc-coc-  cot»cooocooocoooeooo  COOOCO<»IMOO<NQONQO 


tP  t- -tji  t^  CO  t 


t^OO-*(NOintOO>IN'* 
OfNOCOOCOlOCOiO-^ 

tf<C^-^C*'^t^C0t*COt^ 


t^OOC^COt^OOtN-^tOCl 

cot~eot~eot-eooocoao 


i-l.-IOOlO^OOTH(Nt^tO 
rHCJOCNCXMOCOlOeO 

^t^T^t^-^t^^t^COC^ 


OlOCONtOOlCOr-r-llO 
C>*i->r-'<MOCJ*OCCli3'^ 

COOOCO0OCO(»C<OOC40O 


I^OOOlCCOOOOiOCOC 


i/DiCC^OOOiC^iOiClNOS   OOCOCOt^CiCS"^tOOit-l 
iH  rl  1-1  r-l  O  CM  O  (M  O  N    iC  CO  >0  CO  tt>  Tt* -^  •>!<  CO  lO 

tc  t~  Tji  t- -i*  f.  Tji  t- •<a<  t~  CO  r^  CO  i>  CO  t>- CO  r~  CO  t^ 


oa  ^  to  (N  CO  »o  o  OS  r^  (N  CO  to  a>oiOTf<oooto  CO 


O  r-l  rH  T-1  rH  r-1  i-l  O  04    O  Ot  lO  CO  lO  CO  ICI  CO -*  Tf    tjl  Tf  CO  O  CO  lO  CM  O  r-l  i-l 

•^  t^  ■<«<  t~ -^  i>  "if  t^  tc  t^  Uji  t~  CO  t~  CO  t^  CO  r~  CO  j>  co  t~  co  t~  co  i>  co  oo  co  oo 


r*iCr-(CM''!foor^icoco 

C^Oe^rHrHi-IOINOCO 

cocoeooocooocooocooo 


Tt<tooocjc^QOto-*a>M 

COiScNOINOrHrlOM 

cot-eooocoooeOQOcooo 


^OOtOCOOOi-^-^CCf-f 


■>l<-*r-ltO00OiiCCO(NtO00O>iOC0r-it^t~. 


coocoiraoooc-iiot^r 


C^tSNOi-HOrH^^i-llSi-iONOOjfecOuSSTfTf'^TjiTOiOcOiOCSO 

■<j(t^Tiit--<}"t>T)<t>'^t~'^t-'>ft~-t)<i>cot~cot^cot^cot~eot^cot~eoao 


o>ij>tOrHcO'*ot~r-o 

CmO(N000010i-l>H 
T(<tO-*t^'*t^-*t~-9't» 


■*COi-(f~t^O-*'*OOC 
f-liHi-liHOCMOOlOCM 


iOdi-(t^tOCMr-<I^lCC^ 


-t)<-*^toooo>to^eoinooot^'-iTf<'*or~r».-icoioooc»'<i"*'05(J)T»<co 

COOCOlOIMiOIMOOlO    IN  O  i-l  <H  rH  rH  i-l  rt  O  C-J    O  IM  lO  CJ  lO  CO  ■^  CO -VJ" 
■<•  to  •>S<  to -J<  to  1*  t- •*  t~   'f  t»  ■*  r~  •*  t»  rf  t^  Tj(  t-   "Jl  t^  CO  t~  CO  t"- CO  1>  CO  c~ 


g  oocitOi-H  ^e 
^ -"J"  to -S"  to -J' t 


'00CJ>tOdCO'<}'-JI>O0O> 
iCO-^COiOCOiOCOiOlMiO 

■*tOtJ'tO"«"tOT)<tO'«'tO 


>CMiCQt^O>0>t^»-liOCOCO>OT-lt^C>05tOC<)TfM* 


?=  lO  CO  »0  CO '<f  C 
rf;  "^  to -^  to -^  t 


etoc>jin"*coioiNt^ 

?:»ocoiccoiO"* 

rfi  ■*  to  "f  to  t(< 


coic  coioco 
to  ^  to  ^  to 


-q^^jf-^^CO-^COlOCOiC 
"»**tO-^tO"^tO"^tO'^tO 


tOMCOvCOCCr^THCO"*' 
rJOCMO(NOrHi-ti-Hi-t 


JtOCftOltOiMCOiOOQp 

'tOT)ttO-^t^T(lt~Tj<t~ 


00  O  to  IM  ■*■>«<  <N  t~  O  C5    t^  T-Hi3  •*  (M  to  O  Ol  t~  CJ 
-tfTjiTji-^-^-^-^-^'^Tf    COiOCOiOCOtOCOiO(NO 

■^  to  "tf  to -^  to  "^  to  tf  to  "^  to -^  to  1^  to -^  to  tf  c^ 


^OiOOOOC-ltOCOiCiC 


BOCMiOCOiO 
^lOtO^tO-*' 


COiO  COiO  CO 

tOTjHtO  tftO 


»lOtOT**t^CM00i— IOC*t-l 


ROCNOCMO 

rfjic  toic  toio 


CI  OCOiCCO 

to  lO  to  ti^  to 


(N  CO  CO  r»  uo  to  to 


SS>6joc^o 

rfjiCtOiO  to  lO 


3t~ 
(N 

to  iC  to  lO  to 


coa>f-ioo(Noo-*;oin 
"  (NOcoocomcoioco 

lOtOiOtOiOtO-^tOrftO 


acoon<iOi-i 

S  r-l  i-H  tH  O)  rl 

rfjiotoustoio 


<Nr-(I^OlM 

to  lO  to  >A  to 


oo»ctotoiooocoa>CMi-t 

0<NOC^O(NO<NOCO 
tCtOtOtOOtOOtOtOtO 


fft"-tot"-r^tooo»^a>coo 

Si-ti-lf-tiHi-HiHi-<rHi-iCM 

.cjiotomtoiotoicoicto 


SM  ■*  ,-1 -fl<  O 
CMr-l  C4rH(N 

rfS  lO  to  >0  to  lO 


lOOtO  COt^ 

to  vO  to  iC  to 


StoTHio>-imcM-<»<coco"i< 
(^^IHc^3r-<(^^■-^c<lr-lc^I-l 

.Cf^tO^tOiCtOiiDtOlOtO 


Si-i00OC0<3>0>OO00t-( 
COOCOO(NOlNi-l(NrH 

.ejictoictoiotoictoicto 


T^tO'^tOTfto-^tO^tO  pf*  tO"ft0^tO"^tO^tO 


GOCOto-1*'<J<tOlMaO»-tOO>CMt^''S<iCtOCOOOOO   OOCOiOtpCMOOOir-ir^-^ 

iocoiOcoiocoiOcoiOtr-^^-*T)<-*':)i-i<'^Tj<iocoiocoi5coiOiNONc6 
Tfto^to'^tO'^to^to  tr* totftO'^ftO'j^tot^to  "S^to^^to^to-^t^-^c— 


OOOtOO)(NtOt^.-ICOlt5 

rti-HOc^oiNiOcomco 
•*t--*t^-*t^cot^cot- 


t^i-HCOlCCiOatOCOi-lt^ 
rtrHrti-HOr-IOCMOC^ 


■^icoocr-c^icoiooo 

<NO(NOr-li-lr-li-lt-i.H 


i-ia><»e3iOirerHcc<».-i 

COiC<NOlMOCMOrHr-( 

»«'tO'<J<C-"!l<t-Tft^t}<t^ 


e^.-lr-IC^O'^OlOt^tO 
iHCar-IC->.HlNO<NOCM 

iltJtOlOtOlCtOlOtOlCtO 


lO  t^  CO  oi  i-i  i-H  o  CO  t^  m  lO  t~  (N  o>  o  d  r- -^  lO  t~ 

lO  CO  lO  CO  lO  Tf -^  Tf  Tf -^  -^  Tf -^ -^  Tf  lO  CO  ift  CO  o 
^  to  ■^  to  ^  to -^  to  ^  to  Tj*  to  ■'f  to  "^  to  "^  to  "*•  to 


SCM(T>-<»<i^totot>-cooa 
COiOCOiOCOlOCOlOCO 

i^tOTftC^tO'^tO^tO 


-  --(Oscot^iriicoocoQ 

tftO'^tOTt*tO'^tO"!ftO 


to  00  ^  05  CO  i-H  .H  N  O  ■r'  00  to  to  t^ -^  CJa  CM  i-l  Q  CO 

oc5oc^ocoocooco  lo CO iS CO lO CO lO ■>»< S T»i 

IC  to  »0  to  »0  to  lO  to  lO  to  ■'f  to -^  to -^  to -^  to -3<  to 


r-OOtOOSlOO-^r-^COC^    <NT)I.H>0»tOCOI^t-OS    lOO'^fC^CMCOOincCt^ 
1-H  i-l  rl  rH  1-1.  CM  iH  C-)  iH  e^    rHCMt-((N0040CMOCM    OCOOCOOCOOCOiOCO 

iCtOiCtOvOtOlOtOiCtO   lOtOl/StOiOasiOtOiOtO   lOtOiOtOiCtOiOtO'^tO 


cM-.j<.-iio.Htoor-o>oo 


ooo»i>oiOi-i-*CMcoeo 

■Hi-Ii-HCMiHCMt-ICMi-ICM 
lOtOLCtOlOtOlCtOiOtO 


t~-Ht^e^tOOlOCO>n'*    TflOCOtOCMt^rHOOOOO 


CMiOi-ltOO>t"-OOCJ5tOO 
iHCMi-ICMOCMOOOCO 

liStOiOtOiOtOiCtOiOtO 


OOOO— <t^NiOCO-^T»l 
THCMrHC^rHCMr-lCMi-(C<l 

icto»ctoiotoioto»cto 


S»o  lO  -^  lo  Tji 
COOCOOCO 

rf*  lO  to  ic  to  i/:i 


tOCOIr^COt^-ICMt^CMOO'-fOOOClOO 

ocoocoo 

to  U5  too  to 


coocoocoocooco 
lOtoiotoiotoictoioto 


lOOTi-HOQCMr-CMtOeO 
li^tOtOtOtOtOiCtOtOtO 


Sea  CO  31  CO  30 
ooocooco 

^intoiotoifs 


CO  00  "^  t^  ^ 

ocoocoo 
toLO  toio  to 


SCOOCOOCM 

rfi  lO  to  m  to  lO 


O'^O-'fO 

to  iO  to  iC  to 


t"»'5't^iCto»CtotptOtp 

coocoocoocooeoo 

lAtOiOtOOtOkOtOiCtO 


CM  ^  CM  i-l  ^  T-l  i-l  CM  r-l  CM  r-l  CM  O  CM  O  CO  O  CO  0>  CO 
TfO^O'^O-^O'^O  ■*0-*0"»<0-«'OCOO 

tf3  to  to  to  lO  to  »0  to  lO  to  ITD  to  lO  to  iC  to  iC  to  »c  to 


tD'*"n>o-*tocor~c^oo 

CMr-ICMi-<CMr-(CMrHCMrH 
iC  tOtCtOiCtOtOtOiOtO 


tpior^Tfi^-^qpcOQp 

OMOCOOCOOCOO 
iOtOiOtOlOtOlCtO>OtO 


COmCMOWOOr-igcM 
eOOeOTHCOr-(Mi-ICOF-l 

lOtOtCtOtCtOLOtOOtO 


cn^o0'2'ooicr»ict~o 
coocoocoocooeoo 

iOtO»CtOiCtOiOtOiOtO 


St^r"-r>-i>-t*t^t>-oot^op 


QOt~00t-00t^COtO00 

u5-'itiO'^iO-»fiO"tt»tc 

iCtCiCiOiOiCiCiOiCtC 


McOP^OSDhCOPIhCCP^CO 


aizaaixoixA-Mt:i<n 


toootoootocoto(7ito^ltQai>ociinaaiO 


inoi>OCiinoaiOOiOO 
■^O'^iO'VO'^rOT)!© 

inuoioiAtciOiCtoiOto 


a^ccC^QOtfasMccOHCO 


IC       kO        tO        to        to 


Q<cop4c»PdccpH<ntfca 


'T 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  669 


■^    'a 


s     a 


o 


xoaadv 


o 


•a^Bp 
•xoiddv 


pd  cc  K  oo  Ph  00  tf' CO  p4  00 


P^odpHodciHaQP^oopi^od 


PjodtfodCiiaQOdadpHod 


Sr-icOt-ieOi-ieor-ieor^ 
rlOi-IOi-IOi-lOrH 


CO  ^  ^  ^  ^  CO  to  CO  <0  to  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


O   .-I   N   CO   •* 
.H    rH    rH    iH    iH 


U3   CO   [~   00   o>   O 
rH   rH   rH   rH   iH   « 


P^odP^cdp^osoicdtfadpico 


§.-ieoi-i«Oi-(coi-ieOi-i  eOtH05r-ieO'-icoi-i«.-<eOr-i 
rH  O  1-1  ©  »-l  O  r-l  O  1-1  Or-(OrHO-HOiHOT-(Oi-l 

CO  COCOCOCOCOCOCOCO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


^COtOtO'-OtOCOOtO^CO  to  cococo<ot&to^o<o 


(O  (O  ^  <o  to  <o  to  to  ^  to 


-j^'^tO'^tO'^tO'^to-'j'uO'^io-^^iOiQiO-a'^Oi'g'ift^to-^tocotocgto 

SOr-tOi-tOi-HOi-tOfHO^HOf-HOf-lOi-tOr^OFHOrHOrHOrHOr-t 
^COtOtOtOtOtOtOtOtOtOtOtOtOtOtO^tOtOtOtO'tOtO^tOtOtOtO^tOtO 


'O'^tO^tO-^aPiOtOiOjSiOjOiCiOtOpiJ'tO^t^ 

^coto^tototototototo  to totototctototototo 


gC*ifli^»ot^»ct*tot^totptotor*^r*jooO'rpoo 

^totototototototototototototototototototo 


S'cotDqotOQptot^tor^r- 
a^totototototototototo 


tor-tooojooojco^oi 

tOtOtOtOtOtOtOtOtOtO 


(^totototototototototo 


^totototocotototototo 


(tftOtOtOtOtOtOtOtOtOCO 


gSSS2S2§SS§ 

i^tOtOtOtOtOtOtOtOtOtO 


S2S2g288SS 

to  to  to  to  CO  to  to  to  to  to 


totototototototototo 


to  to  to  to  to  CO  to  to  ^  to 


OC^oSSocJSc^OtN 

to  to  to  to  to  to  to  to  to  to 


6S2S2S2SSSS 

^totototototototototo 


CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


i-lrHi-li-l©i-IOC40(N 
.tfCOCOCOCOCOCOCOCOCOCO 


IcoMcosoin'^-fiomto  wco^t-ooooJOooQ 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  *0  CO  iO  CO 


r-IOi-IOi-IOi-lc5i-l 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


S2S2S2S8SS 

^  to  to  CO  to  to  to  ^  'O  to 


ScococccocococceoooOTco 
.-t0i-*0i-H0i-l0r-(0»-* 

to  to  tC  to  CO  to  to  to  ^  to  to  to 


OfHOr-tOr-iOrHOi-tOiH 
!0  to  CO  to  to  <D  to  to  CO  to  to  fO 


CO  to  to  CO  to  O  to  CO  CO  to  to  CO 


fHOr-lOr-(Oi-tO?5oc5 
to  to  to  to  CO  CO  to  CO  CO  CO  ^  CO 


to  CO  CO  to  to  to  to  CO  CO  to  CO  CO 


to  CO  to  to  to  to  to  to  CO  to 


|3?33g5ga8?J8SgS: 

[tOtOtOtOCOtOtOtOtOtOiCtO 


to  to  to  to  CO  to  CO  CO  CO  to 


COtOtOtO^tOiCcOtOCOtCCO 


CO  ^  CO  CD  CO  CO  CO  CO  CO  CO 


8iQOcOO»t^OOC-OOOQr~00 
SiocNiOMBMSeliioe'l 

cOCOcocOiOCOtOcOi/^COiAcO 


SCOM'^OliQi-ICOOCO 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


Sr»o>t~<iooor»o>t>.QcpQ 
MiONiOC5i06liO«iSc5 

COcotCcOtOcOOcoiACOiCCO 


ScnSSoSSSSS 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


0>gpC0O>t~-QC0i-liQ'-l>oe} 
kOcOiCcOtOcOiCco^cOiOcO 


5jJ5i-icOi-it^oaQo>o> 
cocOCOcOcOCOcocOiOCO 


S"O00OC3>0?Qe0^t^<N 
Si-hS?-ioSo<noc^ 

^cocococococococococo 


gS2g2S8SSS?J 

^COCOCOtOtOtOtOtOtOtO 


gSSS2g8SfJ8a 

•^tototocotocotocototo 


gSSg2§SSS8?3 

^cocococococococococo 


gCOiCCO^'J<MiQC^CO 
lNOeicScMO<NIO« 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


r-lt-OOQffiOiOOQl^iH 

oc<oc5i6N>oc5ioeo 
COcocOcOiOCCiOcOiOco 


iocoiOo5iCcoi/5eo>Scoiom 

cCCOiOcOiCCOiOCOOcOkCCO 


t^>-icoc^u5e5'fl<'<s<MU5iNco 
iCcoiAcQiocoiocoiacoiom 

iCCOiOcOiCCOU^COiCcOtACO 


iS  eo  >o  e<5  >4  05  55  55 

iCCOOCOiCCOiOCO 


NcOi-i  t^ 
Id  CO  to  CO 


iOc*5-^-^coiOCJcot-(t--Qccoac>ooor^i-icoc* 

'•OCOCOCOCOCOCOCOCOCO  (CO  COiOCOiOCOtCCOiOCO 


ujeC'^'^cocoiMt^ 
lOcoioeoicniaoo 

iOCOiCCOlOCOiOCO 


•HOOOO 
lOCOiOcO 


t^  CO  CO  CO  CO  CO  CO  CO  CO  CO 


80»0>O00r-tC0C^^?C0 
NioeoiBeoiOcoiOeo 

cOcoOcoiCCOk/^cOiOco 


'j'-feoirtoit^t-ioo 
>oco>acooco>om 

lOCOiCCOiOCOiOCO 


^  CO  ^  ^ 
lOcOlOCO 


S-^C^HQCJCOi-tt-OCS 
CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


o>  !5  00 1-"  i»  d 


CO  is  6q  >o  CO  is  m 

CO  lO  CO  lO  CO  lO  CO 


COiOPJt^CDOQOOJ 

lOeoioeoiOM^OT 

iQCOiOCOiCCOtACO 


OOrHCOM 

lacoiaco 


gS2S2SSSS§?5 

•^totototototococotoco 


SS§S3S8S5gg3 

CO  CO  CO  CO  CO  CO  CO  CO  lO  CO 


SnS 


niSmiSnSn 

CO  U3  CO  lO  CO  IC  CO 


S"®t^C»COt~OCOr-('J<5J 
Oi-IOr-IOtHOMOM 

tC^COCOCOCOCOCOcOcOCOCO 


CO'*CJinOCO<J>OQt^Ol 

oc<oc<ioe<iioe5ion 

CO  COCOCOCOCOiOcOiOCO 


iCCOiO 


gS2SJ^82S§§?3 

»tf  CO  CO  to  to  to  to  to  «D  CO  CO 


rHcoO'^oitor^r-cpoi 

tOtOtOCOtCtO^tOiOtO 


g't^ictor*'3»oocoo«-*f-i 
Oi-(OrHO»HOC5o<N 

i^tocococotocotototoco 


tOtOiCtOLCtOiOtOiOcO 


gSSS 

^cococo 


i-lOi-t 
CO  CO  CO 


CO  CO  CO  CO 


gSSS 

^cococo 


CO  i-»  ifl  O  CO  I^  X 


lOcou^coiAcotacOi/^co 


M  ■^  CO  CI  ■^  1-1  CO 

CO  >o  CO  la  CO  >o  CO 

CO  iC  CO  kC  CO  lO  CO 


Scoio 

to  CO  CO 


C<  (N  CO  Q -Ji  0>  CO 

CO  >o  CO  iS  CO  ^  CO 
CO  to  CO  to  CO  lO  CO 


c-i  o  1-1  e<  o»  CO 


CO  ^*  CO  ^  CO  ^  CO 
CO  to  CO  to  CO  to  CO 


go  a>  rH  t^  O  CO  ■* 

lOcoio 


-    -  -  _    -  3!  CO 

CO  ^  CO  ^  CO  *g*  CO 
CO  to  CO  tO  CO  tO  CO 


lOOOtOCQ^OO^'^ 
iOCOiOCOtOcOtOCO 


to  CO  lO  CO 


o>r»coo>cooiQi-i 
^co^oo^^^^ 

tOCOtOcOiOcOiOCO 


lOtOiOtO 


t^t^tOO-^i-HC^WrH-^OiiO 
^  CO  ^  CO  ^  ^  ^  ^  ^  ^  00  ^ 

iOtOiOtO»OtOiOCOiOtOiOtO 


ioooeoa>f-ii-HOcoQO'^t;tp 

^  CO  M*  CO  ^  ^  TT  ^  CO  Tl*  CO  ^ 

iOcOiOtOiOtOiOtOiOtOiOtO 


c^r-i-iOiOSf-ir*Mu5^^cQ 

^  CO  ^  CO  CO  ^  CO  Tj*  CO  ^  CO  ^ 
lOtOtCtOiCtOOtO^cOiCcO 


tOO'^t-HCSCOOiOOSI-* 
lOtOiOtOLOtDOCOiOtO 


lO  tOUD 


CO  lO  to  iC  CO  iO  to 


COCOCOCOCO'^CO^OO'^CO'^ 
LOtOiOtOiOtOOtOiOcO^tO 


g8gS 

^cOcOtO 


gt^l-l 
lOi-l 

COiOCO 


lOrHiOi-l 

.O  CO  to  CO 


CNCOOt^OQOJCOrHlOCO 
iOi-liOi-l^i-tTj<cl'^<N 

lOcOvOcOtOcOtOcOtOCO 


gSoio 

^lOCOtO 


OiOO 
COlOCO 


Tjio-*0 
to  COlOCO 


cO^HitfiC^M'^— ^COOiOO 
pJii-H^i-Hijli— 1^1— 1  CO  1—1 

lOCOtOcotOCOtOcCiOco 


p4QQp<aQpi;aop4aQpjaQ  pc^aspEjaopijaQpi^cop^ao 


■V         lO        CO        C~        so       C3> 


■flilM-* 

lOCOiO 


C-0>0Qt~Ot0dC0'^IMC0O000Q0JC0rH-«e0 
C<COf)COeOci5cOCOCOCOCOCOCOC5cO<N'*CS'^ 

COtOCOtOCOiOCOtOCOtOCOtOcOtOCOtOCOtOCO 


t^cftiOi-icocoi-i>oc»t~ 


«>i-lCO 

to  CO  to 


IM  CO  ei  CO  CQ  OJ  (N 

CD  lO  CO  lO  CO  to  CO 


CE^OQpjCCB^OQajaO^OO 


'-3-'- 


-"iT'^r' 


I^OiiO»-lCOCOi-nOO»t^t^O» 

e^e^NcoMcoocor-icOi-ieo 

tOcOtOcOlOCOtOCOtOCOiOCO 


PE^OQPljQQp^aQPI^CCP^aQp^OQ 


-sr-z^- 


-^sr-^ 


Page  670] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


-2   a 


I   i 


2 


•xojddv 


WW 


•xoiddy 


i^tn 


PdQQSJCOQjcxipI^OQPlHCIS 


pjoQP^cdP^'cdP^cdtfai 


g'C2rHCOi-l«lrHOTi-ICO.H 
OiHOi-IOrHOr-IOi-l 


Oi-IOiHOr-IOrHOrM    OrHOi-HOi-IO— 'Oi-H 
^0000000000   0000000000 


M        <N        CJ        CO 


S 


C>r-tOrHO.-lOrHO»-H 


P^copHcdP^cdPtHcdP^cn 


O^oqPh'^P^oqP^cqCehcq 


OiHOr-(Ot-HO'-^  OrH    C5  .-(  O  rH  O  r-t  O  iH  O  i-H 

(^^  O  CO  ^  O  '.O  'O  O  -^  O    C  O  'O  O  CO  'O  O  -o  o  -o 


S*  21  CO  ^J  '-0  -M  O  C^  CO  i-KD 

^-^cocococococococo^o 


OrlO^Or-IOiHOrH    Or-t'SC^iOC^idMiO'N 
^  CO  CO  CO  CO  CO  O  CO  CO  ?0  CO   CO  CO  CO  CO  iC  CO  lO  CO  lO  CO 


i-lcOTHt>Qr^Qt^Q00 

O.-HOi-HO^Or-)0rH 

COCOOCOCOCOCOCOCOCO 


JOOSOOOOirH 


O^iOrHlCi— llOf-HiCi-HLCt-HiOrHCOQcOQcOQcO 
COCOCOOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO 


>aooiaoo5oOdo0050i 


cocoio?OiOcoiCcou:^co 


OcOiOcOvCcOiOCOiOCO 


^COCOCOCOCO^COCOlCCo'ocOiOCOiOCOiOCOlOCD 


S"Ocooco<r>cooi'^aO'^botOt>»cr^cocpcocpi:^ 

fCJcOCOCOCOiOcOiOcOOcokocOiOCOi/iCOiOtOiCCO 


S'aiioooi^GOcot^cor^r" 

^lOcOiCcOiOcOOCOUTiCO 


^iCCOiOCOiOcOiOcOiOcO   lOCOiOCDii^cOvOcOiOCD 


iQCOtOCOiOCOiCCOiOcO 


t^'^cp-^cpiCiOiOiOco 
lOcOiOCOiCcOiOCOiOCO 


lAcOiOcO^COiOCOiOco 


lOcOOcOiCCOU^cOiOCO 


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di^Piwtsii^Piwciiix 


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oococooot^c 
CO  e^  CO  ?<  CO  M  oi  c 


t>.  Tt<  C- -*  t~ 


QjcopiHOSP^ccQjoQOjcn 


I 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  671 


O 


^  a 


a 

O       OS 


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rH      N      eo 


5 


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6'Qcoo>r~oooot^a>iOQ  ■«)<i-iMcOtH-*ocoopr»it>'0>iooc02jr}^0'S  ocigpcoO'*(Ni-i'*mco 
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21594°— 14- 


-36 


Page  672]                                          TABLE  11. 

For  reducing  the  Time  of  the  Moon's  passage  over  the  Meridian  of  Greenwich  to  the  Time  of  its  pass- 
age over  any  other  Meridian.     The  numbers  taken  from  this  Table  are  to  be  added  to  the  Time  at 
Greenwich  in  West  Longitude,  subtracted  in  Kast  Longitude. 

Longi- 
tude. 

Daily  variation  of  the  moon's  passing  the  meridian. 

Longi- 
tude. 

40" 

42m 

44m 

46m 

48" 

60" 

52" 

54" 

66" 

68" 

60" 

62" 

64" 

66" 

O 

0 
5 
10 
15 
20 
25 
30 

m. 
0 
1 
1 
2 
2 
3 
3 

m. 
0 
1 
1 
2 
2 
3 
3 

m. 

0 

1 

1 

2 
2 
3 
4 

TO.' 

0 

1 
1 

3 
2 
3 
4 

m. 
0 

1 
1 

2 
3 
3 

4 

m. 
0 
1 
1 
2 
3 
3 
4 

m. 

0 

1 

1 

2 
3 
4 
4 

m. 
0 

1 
1 

2 
3 
4 
4 

m. 
0 
1 
2 
2 
3 
4 
5 

TO. 

0 

1 

2 
2 
3 
4 
5 

TO. 

0 

1 

2 
2 
3 
4 
5 

TO. 

0 

1 

2 
3 
3 
4 
5 

m. 
0 
1 
2 
3 
4 
4 
5 

TO. 

0 

1 

2 
3 
4 
5 
5 

o 

0 

5 

10 

15 
20 
25 
30 

35 
40 
45 
50 
55 

4 
4 

5 
6 
6 

4 
5 

I 

6 

4 
5 
5 
6 

7 

4 
5 
6 
6 

7 

5 
5 
6 

7 
7 
8 
9 
9 
10 
11 

5 
6 
6 

7 
8 

5 
6 
6 

7 
8 

5 
6 

7 
7 
8 

5 
6 

7 
8 
9 

6 
6 

7 
8 
9 

6 

7 
7 
8 
9 

6 
7 
8 
9 
9 

6 

7 

8 

9 

10 

6 
7 
8 
9 
10 

35 
40 
45 
50 
55 

60 
65 
70 
75 
80 

7 
7 
8 
8 
9 

7 
8 

8 
9 
9 

7 
8 
9 
9 
10 

8 

8 

9 

10 

10 

8 
9 
10 
10 
11 
12 
12 
13 
14 
15 

9 

9 

10 

11 

12 

9 
10 
10 
11 
12 

9 
10 
11 
12 
12 

10 
10 
11 
12 
13 

10 
11 
12 
12 
13 

10 
11 
12 
13 
14 

11 
12 
12 
13 
14 

11 
12 
13 
14 
15 

60 
65 
70 

75 
80 

85 

90 

95 

100 

105 

9 
10 
11 
11 
12 

10 
10 
11 
12 
12 

10 
11 
12 
12 
13 

11 
11 
12 
13 
13 

11 

12 
13 
13 
14 

12 
13 
14 
14 
15 

13 
13 
14 
15 
16 

13 
14 
15 
16 
16 

14 
14 
15 
16 
17 

14 
15 
16 
17 
17 

15 
15 
16 
17 
18 

15 
16 
17 
18 
19 

16 
16 
17 
18 
19 

85 

90 

95 

100 

105 

110 
115 
120 
125 
130 

12 
13 
13 
14 
14 

13 
13 
14 
15 
15 

13 

14 
15 
15 
16 

14 
15 
15 
16 
17 

15 
15 
16 

17 
17 

15 
16 
17 
17 
18 

16 
17 
17 
18 
19 

16 
17 
18 
19 
19 

17 
18 
19 
19 
20 

18 
19 
19 
20 
21 

18 
19 
20 
21 

22 

19 
20 
21 
22 
22 

20 
20 
21 
22 
23 

20 
21 
22 
23 
24 

110 
115 
120 
125 
130 

135 
140 
145 
150 
155 

15 
16 
16 
17 
17 

16 
16 
17 
17 
18 

16 
17 
18 
18 
19 

17 
18 
19 
19 
20 

18 
19 
19 
20 
21 

19 
19 
20 
21 

22 

19 
20 
21 
22 

22 

20 
21 
22 
22 
23 

21 
22 
23 
23 
24 

22 
23 
23 
24 
25 

22 
23 
24 
25 
26 

23 
24 
25 
26 

27 

24 
25 
26 
27 
28 

25 
26 
27 
27 
28 

135 
140 
145 
150 
155 

160 
165 
170 
175 
180 

18 
18 
19 
19 
20 

19 
19 
20 
20 
21 

20 
20 

21 
21 
22 

20 
21 
22 
22 
23 

21 
22 
23 
23 
24 

22 
23 
24 
24 
25 

23 
24 
25 
25 
26 

24 
25 

25 
26 
27 

25 
26 
26 
27 
28 

26 
27 
27 
28 
29 

27 
27 
28 
29 
30 

28 
28 
29 
30 
31 

28 
29 
30 
31 
32 

29 
30 
31 
32 
33 

160 
165 
170 
175 
180 

40" 

42" 

44m 

46" 

48m 

50" 

52" 

64" 

56m 

68" 

60" 

62" 

64" 

66" 

TABLE  12.                                          [Page  673 

For  finding  the  Variation  of  the  Sun'B  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.     Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

1" 

2" 

8" 

4" 

6" 

6" 

7" 

8" 

9" 

10" 

11" 

12" 

18" 

14" 

15" 

16" 

17" 

18" 

19" 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 
0 

0 

0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

0 
0 
0 
0 

0 
0 
0 
0 

0 
0 
0 

1 

2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
5 
6 

0 
0 
0 

J 

2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 

0 
0 

0 
0 

0 
0 

0 
0 

1 
1 
1 

0 
0 

1 

1 
1 

0 
1 
1 
1 
1 

0 
1 
1 

1 
1 

0 
1 
1 
1 
1 

0 
1 
1 

1 
2 

0 

1 

1 
1 

2 

1 
2 
3 
4 
5 

2 
2 

2 
2 

2 
2 
2 

1 

2 
2 
2 
2 

1 

2 
2 
2 
2 

2 
2 
2 
2 
3 

2 
2 
2 
2 
3 

2 
2 
2 
3 
3 

2 
2 
2 
3 
3 

2 
2 
3 
3 
3 

6 
7 
8 
9 
10 

0 
0 
0 
0 
0 

0 
0 
0 
0 

1 
1 

-^ 

•*■ 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 

2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 

2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
6 
6 
6 

2 
2 
2 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 
6 

2 
2 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 
7 
7 
7 

2 
3 
3 
3 
3 
3 
4 
4 
4 
4 

3 
3 
3 
3 
4 
4 
4 
4 
4 
5 

3 
3 
3 
4 
4 
4 
4 
5 
5 
6 

3 
3 
3 

4 

4 

3 
3 

4 
4 
4 

3 
4 
4 
4 
5 

3 
4 
4 
4 
5 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

4 
5 
5 
5 
5 

5 
5 
5 
5 
6 

5 
5 
5 
6 
6 

5 
5 
6 
6 
6 

16 
17 
18 
19 
20 

21 
22 
23 
24 
26 

5 
6 
5 
5 
5 
6 
6 
6 
6 
7 
7 
7 
7 
7 
8 

t 

5 
6 
6 
6 
6 
7 
7 
7 
7 
7 
8 
8 
8 

5 
6 
6 
6 
6 
7 
7 
7 
7 
8 
8 
8 
8 
9 
9 

6 
6 
6 
6 
7 
7 
7 
7 
8 
8 
8 
9 
9 
9 
9 

6 
6 

7 
7 
7 

6 

7 
7 
7 
8 

7 
7 
7 
8 
8 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

0 
0 
0 
0 

—J- 

2 
2 
2 
2 
2 
2 

7 
8 
8 
8 
9 

8 
8 
8 
9 
9 

8 
9 
9 
9 
10 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

9 

9 

9 

10 

10 

9 
10 
10 
10 

11 

10 
10 
10 
11 
11 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

■l 

2 
2 
2 

1 

2 
2 
3 
3 
3 

3 
3 
3 
3 
3 

4 
4 
4 
4 
4 

4 
4 
4 
5 

5 

5 
6 
5 
5 
5 

5 
6 
6 
6 
6 

6 
6 
6 

7 
7 

7 

7 
7 
7 
7 

7 
7 
8 
8 
8 

8 
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8 
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9 

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10 

10 

10 
10 
10 
10 
11 

10 
10 
11 
11 
11 

11 
11 
11 
12 
12 

11 
12 
12 
12 
13 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

2 
2 
2 
2 
2 
2 

2 
2 
2 
2 
2 
2 
2 
2 
2 
3 

3 
3 
3 
3 
3 
3 
3 
3 
3 
3 

3 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 

4 

4. 

4 

4 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

5 
5 
5 
6 
5 
5 
5 
6 
6 
6 
6 
6 
6 
6 
6 
7 
7 
7 
7 
7 

5 
6 
6 
6 
6 
6 
6 
6 

8 
8 
8 
8 

6 
6 
6 

7 
7 
7 
7 
7 
7 
8 
8 
8 
8 
8 
8 
8 
9 
9 
9 
9 

7 
7 
7 
7 
8 
8 
8 
8 
8 
8 
9 
9 
9 
9 
9 
9 
10 
10 
10 
10 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

12 

12 

12 

9 
9 
9 
10 
10 
10 
10 
10 
11 
11 
11 
11 
11 
12 
12 
12 
12 
13 
13 
13 

10 
10 
10 
10 
11 
11 
11 
11 
11 
12 
12 
12 
12 
13 
13 
13 
13 
14 
14 
14 

10 
11 
11 
11 
11 

11 
11 
11 
12 
12 

12 
12 
12 
12 
13 

12 
13 
13 
13 
14 

13 
13 
14 

14 
14 

41 
42 
43 
44 
45 

46 

47 
48 
49 
50 

12 
12 
12 
12 
13 

12 
13 
13 
13 
13 

13 
13 

14 
14 
14 

14 
14 
14 
15 
15 

15 
15 
15 
16 
16 

46 

47 
48 
49 
50 

51 
52 
53 
54 
55 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 

3 
3 
3 
3 
3 
3 
3 
3 
3 
3 

3 
3 
4 
4 
4 
4 
4 
4 
4 
4 

13 
13 
13 
14 
14 

14 
14 
14 
14 
15 

14 
15 
15 
15 
16 

15 
16 
16 
16 
17 

16 
16 

17 
17 
17 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

14 
14 
15 
15 
15 

15 
15 
15 
16 
16 

16 
16 
16 
17 
17 

17 
17 
17 
18 
18 

18 
18 
18 
19 
19 

56 
57 
58 
59 
60 

Page  674]                                        TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.     Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

20" 

21" 

22" 

23" 

0 
1 
1 
2 
2 
2 
3 
3 
3 
4 

24" 

25" 

26" 

27" 

28" 

29" 

80" 

31" 

32" 

33" 

84" 

86" 

36" 

1 
2 
3 
4 
5 

0 

1 
1 
1 
2 

0 
1 
1 
1 
2 

0 

1 
1 

1 

2 

2 
3 
3 
3 
4 

0 

1 
1 

2 
2 
2 
3 
3 
4 
4 

0 

1 
1 

2 
2 
3 
3 
3 
4 
4 

0 
1 
1 
2 
2 
3 
3 
3 
4 
4 

0 

1 
1 

2 
2 

0 

1 

1 

2 
2 

0 
1 
1 
2 
2 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 

1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

2 
2 
3 
3 
3 

2 
2 
3 
3 

4 

3 
3 
4 
4 
5 

3 
3 
4 
4 
5 

3 
3 
4 
4 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
6 

3 
4 
5 
5 
6 

4 
4 
5 
5 
6 

4 
4 
5 
5 
6 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

4 
4 
4 
5 
5 
5 
6 
6 
6 
7 

4 
4 
5 
5 
5 
6 
6 
6 
7 
7 

4 
4 
5 
5 
6 
6 
6 
7 
7 
7 

4 
5 
5 
5 
6 

4 
5 
5 
6 
6 

5 
5 
5 
6 
6 

5 
5 
6 
6 

7 

5 
5 
6 
6 

7 

5 
6 
6 

7 
7 

5 
6 
6 

7 
7 

6 
6 

7 
7 
8 

6 
6 

7 
7 
8 

6 
6 

7 
7 
8 

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7 
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8 
8 

6 

7 

If 

i 

8 
9 

6 

7 
8 
8 
9 

7 
7 
8 
8 
9 

11 
12 
13 
14 
15 

16 
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18 
19 
20 

6 

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1 

8 
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9 
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11 
11 
12 

10 
10 
11 
11 
12 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

7 
7 
8 
8 
8 

7 
8 
8 
8 
9 

8 
8 
8 
9 
9 

8 
8 
9 
9 
10 

8 

9 

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10 

10 

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10 

9 
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14 
15 

13 
13 
14 
14 
15 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

9 

9 

9 

10 

10 

9 

9 

10 

10 

11 

10 
10 
10 
11 
11 

10 
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11 
11 
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21 
21 
22 
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23 
23 

10 
11 
11 
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18 
18 
18 
19 
19 
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20 
20 
21 
21 
22 
22 

11 
11 
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11 
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12 
13 
13 
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14 
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15 

15 

13 
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16 

14 
14 
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15 
16 

14 
15 
15 
16 

17 

15 
15 
16 
16 

17 

15 
16 
16 
17 
18 

16 
16 
17 
17 
18 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

10 
11 
11 
11 
12 

11 
11 
12 
12 
12 
13 
13 
13 
14 
14 

11 
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12 
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17 
18 
18 
18 
19 
19 
19 
20 
20 
21 
21 
21 
22 
22 

13 
13 
14 
14 
15 
15 
15 
16 
16 
17 
17 
18 
18 
18 
19 

13 
14 
14 
15 
15 
16 
16 
16 
17 
17 

14 
14 
15 
15 
16 

14 
15 
15 
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15 
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16 
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17 
18 
18 
19 
19 

16 
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18 

16 
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17 
18 
18 
19 

17 
18 
18 
19 
19 

18 
18 
19 
19 
20 

18 
19 
19 
20 
20 

19 
19 
20 
20 
21 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

12 
12 
13 
13 
13 

16 
17 
17 
18 
18 

17 
17 
18 
18 
19 

18 
19 
19 
20 
20 

19 
19 
20 
20 
21 

19 
20 
20 
21 
21 

20 
20 
21 
21 
22 

20 
21 
22 
22 
23 

21 
22 
22 
23 
23 

22 

22 
23 
23 

24 

36 
37 
38 
39 
40 

41 
42 
43 
44 

45 

14 
14 
14 
15 
15 

14 
15 
15 
15 
16 
16 
16 
17 
17 
18 

18 
18 
19 
19 
20 

18 
19 
19 
20 
20 

19 
20 
20 
21 
21 

20 
20 
21 
21 
22 

21 
21 
22 
22 
23 

21 
22 
22 
23 
23 

22 
22 
23 
23 
24 

23 
23 
24 
24 
25 
25 
26 
26 
27 
28 

23 

24 
24 
25 
26 

24 
25 
25 
26 
26 

25 
25 
26 
26 
27 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

15 
16 
16 
16 

17 

19 
20 
20 
20 
21 
21 
22 
22 
23 
23 

20 
20 
21 
21 
22 
22 
23 
23 
23 
24 

21 
21 
22 
22 
23 

21 
22 
22 
23 
23 

22 
23 
23 
24 
24 

23 
24 
24 
25 
25 

24 
24 
25 
25 
26 

25 
25 
26 
26 
27 

26 

27 
27 
28 
28 

27 
27 
28 
29 
29 

28 
28 
29 
29 
30 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

17 
17 
18 
18 
18 

18 
18 
19 
19 
19 
20 
20 
20 
21 
21 

23 
23 
24 
24 
25 

24 
24 
25 
25 
26 

25 
25 
26 

26 
27 

26 
26 

27 
27 
28 

26 

27 
27 
28 
28 

27 
28 
28 
29 
29 

28 
29 
29 
30 
30 

29 
29 
30 
31 
31 

30 
30 
81 
32 
32 

31 
31 
32 
32 
33 

51 
52 
53 
54 

55 

56 

57 
58 
59 
60 

19 
19 
19 
20 
20 

22 
23 
23 
24 
24 

23 
24 
24 
25 
25 

24 
25 
25 
26 
26 

25 
26 
26 

27 
27 

26 
27 

27 
28 
28 

27 
28 
28 
29 
29 

28 
29 
29 
30 
30 

29 
29 
30 
30 
31 

30 
30 
31 
31 
32 

31 
31 
32 
32 
33 

32 
32 
33 
33 
34 

33 
33 
34 
34 
35 

34 
34 
35 
35 
36 

56 
57 
58 
59 
60 

TABLE  12.                 [Page  676 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

87" 

88" 

89" 

40" 

41" 

42" 

48" 

44" 

45" 

46" 

47" 

48" 

49" 

50" 

51" 

62" 

68" 

1 

2 
3 
4 
5 

1 
1 
2 
2 
3 

1 
1 
2 
3 
3 

1 
1 
2 
3 
3 

1 
1 
2 
3 
3 

1 
1 
2 
3 
3 

1 
1 
2 
3 
4 

1 
1 
2 
3 
4 

1 
1 
2 
3 
4 

1 
2 
2 
3 
4 

1 
2 
2 
3 
4 

1 
2 
2 
3 
4 

1 
2 
2 
3 

4 

1 
2 
2 
3 

4 

1 
2 
3 
3 
4 

1 
2 
3 
3 
4 

1 
2 
3 
3 
4 

1 
2 
3 
4 
4 

1 

2 
3 
4 
5 

6 
7 
8 
9 
10 

4 

4 
5 
6 
6 

7 
7 
8 
9 
9 

4 
4 
5 
6 
6 
7 
8 
8 
9 
10 

4 
5 
5 
6 

7 
7 
8 
8 
9 

10 
10 
11 
12 
12 
13 
14 
14 
15 
16 
16 
17 
18 
18 
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20 
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21 
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26 
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28 
29 
29 
30 
31 
31 
32 
33 
33 
34 
34 
35 
36 
36 
37 
38 
38 
39 

4 
5 
5 
6 

7 
7 
8 
9 
9 
10 
11 
11 
12 
13 
13 
14 
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Page  676]                TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Eight  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion.                                1 

M. 

54" 

56" 

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TABLE  12.                 [Page  677 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

71" 

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74"  76" 

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Page  678]                TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension,  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

88" 

89" 

90" 

91" 

92" 

93" 

94" 

96" 

96" 

97" 

98" 

99" 

100" 

101" 

102" 

103" 

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TABLE  12.                 [Page  679 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variatior  of  the 
Moon's  Declination  or  Right  Ascension,  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

106" 

106" 

107" 

108" 

109" 

110" 

111" 

112" 

118" 

114" 

116" 

116" 

117" 

118" 

1 

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84 
86 

79 

81 
82 
84 
86 

79 

81 
83 
85 
87 

80 
82 
84 
86 
88 

81 
83 

85 
87 
89 

41 

42 
43 
44 
45 

81 
83 

85 
87 
88 

82 
84 
86 
87 
89 

83 
85 
86 
88 
90 

84 
85 
87 
89 
91 

84 
86 
88 
90 
92 

85 
87 
89 
91 
93 

86 
88 
90 
91 
93 

87 
89 
90 
92 
94 

87 
89 
91 
93 
95 

88 
90 
92 
94 
96 

89 
91 
93 
95 
97 

90 
92 
94 
96 
98 

90 
92 
94 
96 
98 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

89 
91 
93 
95 
96 

90 
92 
94 
95 
97 

91 
93 
95 
96 
98 

92 
94 
95 
97 
99 

93 
94 
96 
98 
100 

94 
95 
97 
99 
101 

94 

96 

98 

100 

102 

95 

97 

99 

101 

103 

96 

98 

100 

102 

104 

97 

99 

101 

103 

105 

98 
100 
102 
104 
105 

99 
101 
102 
104 
106 

99 
101 
103 
105 
107 

100 
102 
104 
106 
108 

51 
52 
53 
54 
55 

56 
57 
58 
59 
1  60 

98 
100 
102 
103 
105 

99 
101 
102 
104 
106 

100 
102 
103 
105 
107 

101 
103 
104 
106 
108 

102 
104 
105 
107 
109 

103 
105 
106 
108 
110 

104 
105 
107 
109 
111 

105 
106 
108 
110 
112 

105 
107 
109 
111 

113 

106 
108 
110 
112 

114 

107 
109 
111 
113 
115 

108 
110 
112 
114 
116 

109 
111 
113 
115 
117 

110 
112 
114 
116 
118 

56 
57 
58 
59 
60 

Page  680]                 TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

119" 

120" 

121" 

122" 

123" 

124" 

126" 

126" 

127" 

128" 

129" 

130" 

131" 

132" 

1 
2 
3 
4 
5 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
11 

2 
4 
6 
8 
11 

2 
4 
6 
9 
11 

2 
4 

11 

2 
4 
7 
9 
11 

2 
4 

7 

9 

11 

2 
4 
7 
9 
11 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

6 
7 
8 
9 
10 

12 

14 
16 
18 
20 

12 

14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
21 

12 
14 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
21 

13 

15 
17 
19 
21 

13 
15 
17 
19 
22 

13 
15 
17 
20 
22 

13 
15 
17 
20 
22 

13 
15 
18 
20 
22 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

22 
24 
26 
28 
30 

22 
24 
26 
28 
30 

22 
24 
26 
28 
30 

22 
24 
26 
28 
31 

23 
25 
27 
29 
31 

23 
25 
27 
29 
31 

23 
25 
27 
29 
31 

23 
25 
27 
29 
32 

23 
25 
28 
30 
32 

23 
26 
28 
30 
32 

24 
26 
28 
30 
32 

24 
26 
28 
30 
33 

24 
26 
28 
31 
33 

24 
26 
29 
31 
33 

11 
12 
13 
14 
15 

32 
34 
36 
38 
40 
42 
44 
46 
48 
50 

32 
34 
36 
38 
40 

32 
34 
36 
38 
40 

33 
35 
37 
39 
41 

33 
35 
37 
39 
41 

33 
35 
37 
39 
41 

33 
35 
38 
40 
42 

34 
36 
38 
40 
42 

34 
36 
38 
40 

42 

34 
36 
38 
41 
43 

34 
37 
39 
41 
43 

35 
37 
39 
41 
43 

35 
37 
39 
41 

44 

35 
37 
40 
42 
44 

16 
17 
18 
19 
20 

42 
44 
46 
48 
50 

42 
44 
46 
48 
50 

43 
45 
47 
49 
51 

43 
45 
47 
49 
51 

43 

45 
48 
50 
52 

44 
46 
48 
50 
52 

44 
46 
48 
50 
53 

44 
47 
49 
51 
53 

45 
47 
49 
51 
53 

45 
47 
49 
52 
54 

46 
48 
50 
52 
54 

46 
48 
50 
52 
55 

46 
48 
51 
53 
55 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 

52 
54 
56 
58 
60 

52 
54 
56 
58 
60 

52 
54 
56 
58 
61 

53 
55 
57 
59 
61 

53 
55 
57 
59 
62 

54 
56 
58 
60 
62 

54 
56 
58 
60 
63 

55 
57 
59 
61 
63 

55 
57 
59 
61 
64 

55 
58 
60 
62 
64 

56 
58 
60 
62 
65 

56 
59 
61 
63 
65 

57 
59 
61 
63 
66 

57 
59 
62 
64 
66 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

61 
63 
65 
67 
69 

62 
64 
66 
68 
70 

63 
65 
67 
69 
71 

63 
65 
67 
69 

71 

64 
66 
68 
70 
72 

64 
66 
68 
70 
72 

65 
67 
69 
71 
73 

65 
67 
69 
71 
74 

66 
68 
70 

72 
74 

66 
68 
70 
73 
75 

67 
69 
71 
73 
75 

67 
69 
72 
74 
76 

68 
70 
72 
74 
76 

68 
70 
73 
75 

77 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

71 
73 

75 

77 
79 

72 
74 
76 
78 
80 

73 
75 

77 
79 
81 

73 

75 
77 
79 
81 

74 
76 
78 
80 
82 

74 
76 
79 
81 
83 

75 

77 
79 
81 
83 

76 
78 
80 
82 
84 

76 

78 
80 
83 
85 

77 
79 
81 
83 
85 

77 
80 
82 
84 
86 

78 
80 
82 
85 
87 
89 
91 
93 
95 
98 

79 
81 
83 
85 
87 

79 
81 

84 
86 
88 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

81 
83 

85 
87 
89 

82 
84 
86 
88 
90 

83 
85 
87 
89 
91 

83 
85 
87 
89 
92 

84 
86 
88 
90 
92 

85 
87 
89 
91 
93 

85 
88 
90 
92 
94 

86 
88 
90 
92 
95 

87 
89 
91 
93 
95 

87 
90 
92 
94 
96 

88 
90 
92 
95 
97 

90 
92 
94 
96 
98 

90 
92 
95 
97 
99 

41 
42 
43 
44 
45 

46 

47 
48 
49 
50 

91 
93 
95 
97 
99 

92 
94 
96 
98 
100 

93 
95 
97 
99 
101 

94 

96 

98 

100 

102 

94 

96 

98 

100 

103 

95 

97 

99 

101 

103 

96 

98 

100 

102 

104 

97 

99 

101 

103 

105 

97 

99 

102 

104 

106 

98 
100 
102 
105 
107 

99 
101 
103 
105 
108 

100 
102 
104 
106 
108 

100 
103 
105 
107 
109 

101 
103 
106 
108 
110 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

101 
103 
105 
107 
109 

102 
104 
106 
108 
110 

103 
105 
107 
109 
111 

104 
106 
108 
110 
112 

105 
107 
109 
111 
113 

105 
107 
110 
112 
114 

106 
108 
110 
113 
115 

107 
109 
111 
113 
116 

108 
110 
112 
114 
116 

109 
111 
113 
115 
117 

110 
112 
114 
116 
118 

111 
113 
115 
117 
119 

111 
114 
116 
118 
120 

112 
114 
117 
119 
121 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

111 
113 
115 
117 
119 

112 
114 
116 
118 
120 

113 
115 
117 
119 
121 

114 
116 
118 
120 
122 

115 
117 
119 
121 
123 

116 
118 
120 
122 
124 

117 
119 
121 
123 
125 

118 
120 
122 
124 
126 

119 
121 
123 
125 
127 

119 
122 
124 
126 
128 

120 
123 
125 
127 
129 

121 
124 
126 
128 
130 

122 
124 
127 
129 
131 

123 
125 
128 
130 
132 

56 
57 
58 
59 
60 

TABLE  12.                  [Page  681 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  %t  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  findmg  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

138" 

184" 

185" 

186" 

137" 

188" 

139" 

140" 

141" 

142" 

148" 

144" 

145" 

146" 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

2 
4 
7 
9 
11 

2 

4 

7 

9 

11 

2 
5 
7 
9 
11 

2 
5 

7 

9 

11 

2 
5 

7 

9 

11 

2 
5 
7 
9 
12 

2 
5 
7 
9 
12 

2 
5 
7 
9 
12 

2 
5 
7 
9 
12 

2 

5 

7 

9 

12 

2 
5 
7 

10 
12 

2 
5 
7 

10 
12 

2 
5 
7 

10 
12 

2 

5 
7 

10 
12 

1 
2 
3 
4 
5 

13 
16 
18 
20 
22 

13 
16 
18 
20 
22 

14 
16 
1* 
20 
23 

14 
16 
18 
20 
23 

14 
16 
18 
21 
23 

14 
16 
18 
21 
23 

14 
16 
19 
21 
23 

14 
16 
19 
21 
23 

14 
16 
19 
21 
24 

14 
17 
19 
21 
24 

14 
17 
19 
21 
24 
26 
29 
31 
33 
36 

14 
17 
19 
22 
24 

15 
17 
19 
22 
24 

15 
17 
19 
22 
24 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

11 
12 
13 
14 
15 

24 
27 
29 
31 
33 

25 
27 
29 
31 
34 

'  25 
27 
29 
32 
34 

25 
27 
29 
32 
34 

25 
27 
30 
32 
34 

25 
28 
30 
32 
35 

25 
28 
30 
32 
36 

26 
28 
30 
33 
35 

26 
28 
31 
33 
35 

26 
28 
31 
33 
36 

26 
29 
31 
34 
36 

27 
29 
31 
34 
36 

27 
29 
32 
34 
37 

16 
17 
18 
19 
20 

35 
38 
40 
42 
44 

36 
38 
40 
42 
45 

36 
38 
41 
43 
45 

36 
39 
41 
43 
45 

37 
39 
41 
43 
46 

37 
39 
41 
44 
46 

37 
39 
42 
44 
46 

37 
40 
42 
44 
47 

38 
40 

42 
45 
47 

38 
40 
43 
45 
47 

38 
41 
43 
45 

48 

38 
41 
43 
46 
48 

39 
41 
44 
46 
48 

39 
41 
44 
46 
49 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

47 
49 
51 
53 
55 

47 
49 
51 
54 
56 

47 
50 
52 
54 
56 

48 
50 
52 
54 
57 

48 
50 
53 
55 
57 

48 
51 
53 
55 

58 

49 
51 
53 
56 
58 

49 
51 
54 
56 

58 

49 
52 
54 
56 
59 

50 
52 
54 
57 
59 

50 
52 
55 
57 
60 

60 
53 
55 
58 
60 

61 
53 

56 
68 
60 

61 

54 
56 
58 
61 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

58 
60 
62 
64 
67 

58 
60 
63 
65 
67 

59 
61 
63 
65 
68 

59 
61 
63 
66 
68 

59 
62 
64 
66 
69 

60 
62 
64 
67 
69 

60 
63 
65 
67 
70 

61 
63 
65 
68 
70 

61 
63 
66 
68 
71 

62 
64 
66 
69 
71 

62 
64 
67 
69 
72 

62 
65 
67 
70 
72 

63 
65 
68 
70 
73 

63 
66 
68 
71 
73 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

69 
71 
73 
75 

78 

69 
71 
74 
76 

78 

70 
72 
74 

77 
79 

70 
73 

75 

77 
79 

71 
73 
75 

78 
80 

71 

74 
76 
78 
81 

72 
74 
76 
79 
81 

72 
75 

77 
79 
82 

73 
75 

78 
80 
82 

73 

76 
78 
80 
83 

74 
76 
79 
81 
83 

74 
77 
79 
82 
84 

75 

77 
80 
82 
85 

76 
78 
80 
83 
85 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

80 
82 
84 
86 
89 

80 
83 
85 
87 
89 

81 
83 
86 
88 
90 
92 
95 
97 
99 
101 

82 
84 
86 
88 
91 

82 
84 
87 
89 
91 

83 
85 
87 
90 
92 

83 
86 
88 
90 
93 

84 
86 
89 
91 
93 

85 
87 
89 
92 
94 

85 
88 
90 
92 
95 

86 
88 
91 
93 
95 

86 
89 
91 
94 
96 

87 
89 
92 
94 
97 

88 
90 
92 
95 
97 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

91 
93 
95 
98 
100 

92 
94 
96 
98 
101 

93 

95 

97 

100 

102 

94 

96 

98 

100 

103 

94 

97 

99 

101 

104 

95 

'  97 

100 

102 

104 

96 

98 

100 

103 

105 

96 

99 

101 

103 

106 

97 

99 

102 

104 

107 

98 
100 
102 
105 
107 

98 
101 
103 
106 
108 

99 
102 
104 
106 
109 

100 
102 
105 
107 
110 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

102 
104 
106 
109 
111 

103 
105 
107 
109 
112 

104 
106 
108 
110 
113 

104 
107 
109 
111 
113 

105 
107 
110 
112 
114 

106 
108 
110 
113 
115 

107 
109 
111 
114 
116 

107 
110 
112 
114 
117 

108 
110 
113 
115 
118 

109 
111 
114 
116 
118 

110 
112 
114 
117 
119 

110 
113 
115 
118 
120 

111 
114 
116 
118 
121 

112 
114 
117 
119 
122 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

113 
115 
117 
120 
122 

114 
116 
118 
121 
123 

115 
117 
119 
122 
124 

116 
118 
120 
122 
125 

116 
119 
121 
123 
126 

117 
120 
122 
124 
127 

118 
120 
123 
125 
127 

119 
121 
124 
126 
128 

120 
122 
125 
127 
129 

121 
123 
125 
128 
130 

122 
124 
126 
129 
131 

122 
125 
127 
130 
132 

123 
126 
128 
131 
133 

124 
127 
129 
131 
134 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

124 
126 
129 
131 
133 

125 
127 
130 
132 
134 

126 
128 
131 
133 
135 

127 
129 
131 
134 
136 

128 
130 
132 
135 
137 

129 
131 
133 
136 
138 

130 
132 
134 
137 
139 

131 
133 
135 
138 
140 

132 
134 
136 
139 
141 

133 
135 
137 
140 
142 

133 
136 
138 
141 
143 

134 
137 
139 

142 
144 

135 
138 
140 
143 
146 

136 
139 
141 
144 
146 

56 
57 
58 
59 
60 

Page  682]                 TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Eight  Ascension,  or  Dechnation,  or  of  the  Equation  of  Time  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

147" 

148" 

149" 

160" 

161" 

152" 

163" 

164" 

165" 

166" 

157" 

168" 

169" 

160" 

1 
2 
3 
4 
5 

2 

5 

7 

10 

12 

2 

5 

7 

10 

12 

2 
5 

7 
10 
12 

3 

5 

8 

10 

13 

3 
5 
8 

10 
13 

3 

5 
8 

10 
13 

3 
5 
8 

10 
13 

3 

5 

8 

10 

13 

3 
5 

8 
10 
13 

3 

5 

8 

10 

13 

3 
5 
8 

10 
13 

3 

5 

8 

11 

13 

3 

5 

8 

11 

13 

3 

5 

8 

11 

13 

1 
2 
3 
4 
5 

6 
7 
8 
9 

10 
11 
12 
13 
14 
15 

15 
17 
20 
22 
25 

15 
17 
20 
22 
25 

15 
17 
20 
22 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
26 

15 
18 
21 
23 
26 

16 

18 
21 
23 
26 

16 
18 
21 
23 
26 

16 
18 
21 
24 
26 

16 
18 
21 
24 
26 

16 
19 
21 
24 
27 

16 
19 
21 
24 
27 

6 

7 

8 

9 

10 

27 
29 
32 
34 
37 

27 
30 
32 
35 
37 
39 
42 
44 
47 
49 

27 
30 
32 
35 
37 

28 
30 
33 
35 
38 

28 
30 
33 
35 
38 

28 
30 
33 
35 
38 

28 
31 
33 
36 
38 

28 
31 
33 
36 
39 

28 
31 
34 
36 
39 

29 
31 
34 
36 
39 

29 
31 
34 
37 
39 

29 
32 
34 
37 
40 

29 
32 
34 
37 
40 

29 
32 
35 
37 
40 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

39 
42 
44 
47 
49 

40 
42 
45 
47 
50 

40 
43 

45 
48 
50 

40 
43 
45 
48 
50 

41 
43 
46 
48 
51 

41 
43 
46 
48 
51 

41 
44 
46 
49 
51 

41 
44 
47 
49 
52 

42 

44 
47 
49 
52 

42 
44 
47 
50 
52 

42 
45 
47 
50 
53 

42 
45 
48 
50 
53 

43 

45 
48 
51 
53 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

51 
54 
56 
59 
61 

52 
54 
57 
59 
62 

52 

55 
57 
60 
62 

53 
55 
58 
60 
63 

53 
55 
58 
60 
63 

53 
56 
58 
61 
63 

54 
56 
59 
61 
64 

54 
56 
59 
62 
64 

54 
57 
59 
62 
65 

55 
57 
60 
62 
65 

55 
58 
60 
63 
65 

55 
58 
61 
63 
66 

56 
68 
61 
64 
66 

56 
59 
61 
64 
67 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

64 
66 
69 
71 

74 

64 

67 
69 
72 
74 

65 
67 
70 
72 
75 

65 
68 
70 
73 

75 

65 
68 
70 
73 
76 

66 
68 
71 
73 
76 

66 
69 
71 
74 

77 

67 
69 

72 
74 

77 

67 
70 

72 
76 
78 

68 
70 
73 

75 
78 

68 
71 
73 
76 

79 

68 
71 
74 
76 
79 

69 

■  72 

74 

77 
80 

69 
72 
75 

77 
80 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

76 
78 
81 
83 
86 

76 
79 
81 
84 
86 

77 
79 
82 
84 
87 

78 
80 
83 
85 
88 

78 
81 
83 
86 
88 

79 
81 
84 
86 
89 

79 
82 
84 
87 
89 

80 
82 
85 
87 
90 

80 
83 
85 
88 
90 

81 
83 
86 
88 
91 

81 
84 
86 
89 
92 

82 
84 
87 
90 
92 

82 
85 
87 
90 
93 

83 
85 
88 
91 
93 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

88 
91 
93 
96 
98 

89 
91 
94 
96 
99 

89 
92 
94 
97 
99 

90 

93 

95 

98 

100 

103 

105 

108 

110 

113 

91 

93 

96 

98 

101 

103 

106 

108 

111 

113 

91 
94 
96 
99 
101 

92 
94 
97 
99 
102 

92 

95 

98 

100 

103 

93 

96 

98 

101 

103 

94 

96 

99 

101 

104 

94 

97 

99 

102 

105 

.  95 

97 

100 

103 

105 

95 

98 

101 

103 

106 

96 

99 

101 

104 

107 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

100 
103 
105 
108 
110 

101 
104 
106 
109 
111 

102 
104 
107 
109 
112 

104 
106 
109 
111 
114 

105 
107 
110 
112 
115 

105 
108 
110 
113 
116 

106 
109 
111 
114 
116 

107 
109 
112 
114 
117 

107 
110 
113 
115 
118 

108 
111 
113 
116 

119 

109 
111 
114 
117 
119 

109 
112 
115 

117 
120 

41 
42 
43 

44 

45 

46 
47 
48 
49 
50 

113 
115 
118 
120 
123 

113 
116 
118 
121 
123 

114 
117 
119 
122 
124 

115 
118 
120 
123 
125 

116 
118 
121 
123 
126 

117 
119 
122 

124 
127- 

117 
120 
122 
125 
128 

118 
121 
123 
126 
128 

119 
121 
124 
127 
129 

120 
122 
125 
127 
130 

120 
123 
126 
128 
131 

121 
124 
126 
129 
132 

122 
125 
127 
130 
133 

123 
125 
128 
131 
133 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

125 
127 
130 
132 
135 

126 
128 
131 
133 
136 

127 
129 
132 
.134 
137 

128 
130 
133 
135 
138 

128 
131 
133 
136 
138 

129 
132 
134 
137 
139 

130 
133 
135 
138 
140 

131 
133 
136 
139 
141 

132 
134 
137 
140 
142 

133 
135 
138 
140 
143 

133 
136 
139 
141 
144 

134 
137 
140 
142 
145 

135 
138 
140 
143 
146 

136 
139 
141 
144 
147 

61 
62 
63 
54 
65 

56 
57 
58 
59 
60 

137 
140 
142 
145 
147 

138 
141 
143 
146 
148 

139 
142 
144 
147 
149 

140 
143 
145 
148 
150 

141 
343 
146 
148 
151 

142 
144 
147 
149 
152 

143 
145 
148 
150 
153 

144 
146 
149 
151 
154 

146 
'147 
150 
152 

155 

146 
148 
151 
153 
156 

147 
149 
162 
154 
157 

147 
150 
153 
155 

158 

148 
151 
154 
166 
159 

149 
162 
155 
157 
160 

56 
57 
58 
59 
60 

TABLE   13. 

[Page  683    1 

For  finding  the  Sun's  change  of  Right  Ascension  for  any  given  number  of  hours.                 1 

Hourly 

Number  of  hours. 

Hourly 
varia- 
tion. 

tion. 

1 

2 

s 

4 

5 

6 

7 

8 

9 

10 

11 

IS 

$. 

8. 

«. 

8. 

s. 

s. 

8. 

8. 

8. 

3. 

8. 

8. 

8. 

8. 

8.50 

8.5 

17.0 

25.5 

34.0 

42.5 

51.0 

59.5 

68.0 

76.5 

85.0 

93.5 

102.0 

8.50 

8.55 

8.6 

17.1 

25.7 

34.2 

42.8 

51.3 

59.9 

68.4 

77.0 

85.5 

94.1 

102.6 

8.55 

8.60 

8.6 

17.2 

25.8 

34.4 

43.0 

51.6 

60.2 

68.8 

77.4 

86.0 

94.6 

103.2 

8.60 

8.65 

8.7 

17.3 

26.0 

34.6 

43.3 

51.9 

60.6 

69.2 

77.9 

86.5 

95.2 

103.8 

8.65 

8.70 

8.7 

17.4 
17.5 

26.1 
26.3 

34.8 
35.0 

43.5 
43.8 

52.2 

60.9 

69.6 

78.3 

87.0 

95.7 

104.4 
105.0 

8.70 

8.75 

8.8 

52.5 

61.3 

70.0 

78.8 

87.5 

96.3 

8.75 

8.80 

8.8 

17.6 

26.4 

35.2 

44.0 

52.8 

61.6 

70.4 

79.2 

88.0 

96.8 

105.6 

8.80 

8.85 

8.9 

17.7 

26.6 

35.4 

44.3 

53.1 

62.0 

70.8 

79.7 

88.5 

97.4 

106.2 

8.85 

8.90 

8.9 

17.8 

26.7 

35.6 

44.5 

53.4 

62.3 

71.2 

80.1 

89.0 

97.9 

106.8 

8.90 

8.95 

9.0 

17.9 
18.0 

26.9 
27.0 

35.8 
36.0 

44.8 

53.7 

62.7 

71.6 

80.6 
81.0 

89.5 

98.5 

107.4 

8.95 

9.00 

9.0 

45.0 

54.0 

63.0 

72.0 

90.0 

99.0 

108.0 

9.00 

9.05 

9.1 

18.1 

27.2 

36.2 

45.3 

54.3 

63.4 

72.4 

81.5 

90.5 

99.6 

108.6 

9.05 

9.10 

9.1 

18.2 

27.3 

36.4 

45.5 

54.6 

63.7 

72.8 

81.9 

91.0 

100.1 

109.2 

9.10 

9.15 

9.2 

18.3 

27.5 

36.6 

45.8 

54.9 

64.1 

73.2 

82.4 

91.5 

100.7 

109.8 

9.15 

9.20 

9.2 

18.4 

27.6 

27.8 

36.8 

46.0 

55.2 

64.4 
64.8 

73.6 

82.8 

92.0 

101.2 

110.4 

9.20 
9.25 

9.25 

9.3 

18.5 

37.0 

46.3 

55.5 

74.0 

83.3 

92.5 

101.8 

111.0 

9.30 

9.3 

18.6 

27.9 

37.2 

46.5 

55.8 

65.1 

74.4 

83.7 

93.0 

102.3 

111.6 

9.30 

9.35 

9.4 

18.7 

28.1 

37.4 

46.8 

56.1 

65.5 

74.8 

84.2 

93.5 

102.9 

112.2 

9.35 

9.40 

9.4 

18.8 

28.2 

37.6 

47.0 

56.4 

65.8 

75.2 

84.6 

94.0 

103.4 

112.8 

9.40 

9.45 

9.5 

18.9 

28.4 

37.8 
38.0 

47.3 
47.5 

56.7 

66.2 
66.5 

75.6 

85.1 

94.5 

104.0 
104.5 

113.4 

9.45 

9.50 

9.5 

19.0 

28.5 

57.0 

76.0 

85.5 

95.0 

114.0 

9.50 

9.55 

9.6 

19.1 

28.7 

38.2 

47.8 

57.3 

66.9 

76.4 

86.0 

95.5 

105.1 

114.6 

9.55 

9.60 

9.6 

19.2 

28.8 

38.4 

48.0 

57.6 

67.2 

76.8 

86.4 

96.0 

105.6 

115.2 

9.60 

9.65 

9.7 

19.3 

29.0 

38.6 

48.3 

57.9 

67.6 

77.2 

86.9 

96.5 

106.2 

115.8 

9.65 

9.70 

9.7 
9.8 

19.4 
19.5 

29.1 

38.8 

48.5 

58.2 
58.5 

67.9 

77.6 

87.3 

97.0 

106.7 

116.4 

9.70 

9.75 

29.3 

39.0 

48.8 

68.3 

78.0 

87.8 

97.5 

107.3 

117.0 

9.75 

9.80 

9.8 

19.6 

29.4 

39.2 

49.0 

58.8 

68.6 

78.4 

88.2 

98.0 

107.8 

117.6 

9.80 

9.85 

9.9 

19.7 

29.6 

39.4 

49.3 

59.1 

69.0 

78.8 

88.7 

98.5 

108.4 

118.2 

9.85 

9.90 

9.9 

19.8 

29.7 

39.6 

49.5 

59.4 

69.3 

79.2 

89.1 

99.0 

108.9 

118.8 

9.90 

9.95 

10.0 

19.9 
20.0 

29.9 

39.8 

49.8 

59.7 

69.7 

79.6 
80.0 

89.6 
90.0 

99.5 
100.0 

109.5 

119.4 

9.95 

10.00 

10.0 

30.0 

40.0 

50.0 

60.0 

70.0 

110.0 

120.0 

10.00 

10.05 

10.1 

20.1 

30.2 

40.2 

50.3 

60.3 

70.4 

80.4 

90.5 

100.5 

110.6 

120.6 

10.05 

10.10 

10.1 

20.2 

30.3 

40.4 

50.5 

60.6 

70.7 

80.8 

90.9 

101.0 

111.1 

121.2 

10.10 

10.15 

10.2 

20.3 

30.5 

40.6 

50.8 

60.9 

71.1 

81.2 

91.4 

101.5 

111.7 

121.8 

10.15 

10.20 

10.2 
10.3 

20.4 

30.6 

40.8 

51.0 

61.2 

71.4 
71.8 

81.6 

91.8 
92.3 

102.0 

112.2 

122.4 

10.20 

10.25 

20.5 

30.8 

41.0 

51.3 

61.5 

82.0 

102.5 

112.8 

123.0 

10.25 

10.30 

10.3 

20.6 

30.9 

41.2 

51.5 

61.8 

72.1 

82.4 

92.7 

103.0 

113.3 

123.6 

10.30 

10.35 

10.4 

20.7 

31.1 

41.4 

51.8 

62.1 

72.5 

82.8 

93.2 

103.5 

113.9 

124.2 

10.35 

10.40 

10.4 

20.8 

31.2 

41.6 

52.0 

62.4 

72.8 

83.2 

93.6 

104.0 

114.4 

124.8 

10.40 

10.45 

10.5 

20.9 

31.4 

41.8 

52.3 

62.7 

73.2 

83.6 

94.1 
94.5 

104.5 
105.0 

115.0 

125.4 

10.45 

10.50 

10.5 

21.0 

31.5 

42.0 

52.5 

63.0 

73.5 

84.0 

115.5 

126.0 

10.50 

10.55 

10.6 

21.1 

31.7 

42.2 

52.8 

63.3 

73.9 

84.4 

95.0 

105.5 

116.1 

126.6 

10.55 

10.60 

10.6 

21.2 

31.8 

42.4 

53.0 

63.6 

74.2 

84.8 

95.4 

106.0 

116.6 

127.2 

10.60 

10.65 

10.7 

21.3 

32.0 

42.6 

53.3 

63.9 

74.6 

85.2 

95.9 

106.5 

117.2 

127.8 

10.65 

10.70 

10.7 

21.4 

32.1 

42.8 

53.5 

64.2 

74.9 

85.6 
86.0 

96.3 

107.0 

117.7 

128.4 

10.70 

10.75 

10.8 

21.5 

32.3 

43.0 

53.8 

64.5 

75.3 

96.8 

107.5 

118.3 

129.0 

10.75 

10.80 

10.8 

21.6 

32.4 

43.2 

54.0 

64.8 

75.6 

86.4 

97.2 

108.0 

118.8 

129.6 

10.80 

10.85 

10.9 

21.7 

32.6 

43.4 

54.3 

65.1 

76.0 

86.8 

97.7 

108.5 

119.4 

130.2 

10.85 

10.90 

10.9 

21.8 

32.7 

43.6 

54.5 

65.4 

76.3 

87.2 

98.1 

109.0 

119.9 

130.8 

10.90 

10.95 

11.0 

21.9 

32.9 
33.0 

43.8 
44.0 

54.8 

65.7 
66.0 

76.7 
77.0 

87.6 

98.6 

109.5 

120.5 

131.4 
132.0 

10.95 

11.00 

11.0 

22.0 

55.0 

88.0 

99.0 

110.0 

121.0 

11.00 

11.05 

11.1 

22.1 

33.2 

44.2 

55.3 

66.3 

77.4 

88.4 

99.5 

110.5 

121.6 

132.6 

11.05 

11.10 

11.1 

22.2 

33.3 

44.4 

55.5 

66.6 

77.7 

88.8 

99.9 

111.0 

122.1 

133.2 

11.10 

11.15 

11.2 

22.3 

33.5 

44.6 

55.8 

66.9 

78.1 

89.2 

100.4 

111.5 

122.7 

133.8 

11.15 

11.20 

11.2 
11.3 

22.4 

33.6 
33.8 

44.8 

56.0 

67.2 

78.4 

89.6 

100.8 

112.0 

123.2 

134.4 

11.20 

11.25 

22.5 

45.0 

56.3 

67.5 

78.8 

90.0 

101.3 

112.5 

123.8 

135.0 

11.25 

11.30 

11.3 

22.6 

33.9 

45.2 

56.5 

67.8 

79.1 

90.4 

101.7 

113.0 

124.3 

135.6 

11.30 

11.35 

11.4 

22.7 

34.1 

45.4 

56.8 

68.1 

79.5 

90.8 

102.2 

113.5 

124.9 

136.2 

11.35 

11.40 

11.4 

22.8 

34.2 

45.6 

57.0 

68.4 

79.8 

91.2 

102.6 

114.0 

125.4 

136.8 

11.40 

11.45 

11.5 

22.9 

34.4 

45.8 

57.3 

68.7 

80.2 

91.6 

103. 1 

114.5 

126.0 

137.4 

11.45 

Page  684]                                          TABLE  13.             .                                               1 

For  finding  the  Sun's  change  of  Right  Ascension  for  any  given  number  of  hours.                    | 

Hoxurly 

Number  of  hours. 

Hourly 

tion. 

18 

14 

15 

161 

17 

18 

19 

20 

21 

22 

28 

24 

tion. 

«. 

«. 

«. 

s. 

fi. 

s. 

s. 

«. 

«. 

8. 

g. 

«. 

s. 

«. 

8.50 

110.5 

119.0 

127.5 

136.0 

144.5 

153.0 

161.5 

170.0 

178.5 

187.0 

195.5 

204.0 

8.50 

8.55 

111.2 

119.7 

128.3 

136.8 

145.4 

153.9 

162.5 

171.0 

179.6 

188.1 

196.7 

205.2 

8.55 

8.60 

111.8 

120.4 

129.0 

137.6 

146.2 

154.8 

163.4 

172.0 

180.6 

189.2 

197.8 

206.4 

8.60 

8.65 

112.5 

121.1 

129.8 

138.4 

147.1 

155.7 

164.4 

173.0 

181.7 

190.3 

199.0 

207.6 

8.65 

8.70 

113.1 

121.8 
122.5 

130.5 

139.2 

147.9 

156.6 

165.3 

174.0 

182.7 

191.4 

200.1 

208.8 

8.70 

8.75 

113.8 

131.3 

140.0 

148.8 

157.5 

166.3 

175.0 

183.8 

192.5 

201.3 

210.0 

8.75 

8.80 

114.4 

123.2 

132.0 

140.8 

149.6 

158.4 

167.2 

176.0 

184.8 

193.6 

202.4 

211.2 

8.80 

8.85 

115.1 

123.9 

132.8 

141.6 

150.5 

159.3 

168.2 

177.0 

185.9 

194.7 

203.6 

212.4 

8.85 

8.90 

115.7 

124.6 

133.5 

142.4 

151.3 

160.2 

169.1 

178.0 

186.9 

195.8 

204.7 

213.6 

8.90 

8.95 

116.4 
117. 0 

125.3 

134.3 

143.2 

152.2 
153.0 

161.1 
162.0 

170.1 

179.0 

180.0 

188.0 

196.9 
198.0 

205.9 

214.8 

8.95 

9.00 

126.0 

135. 0 

144.0 

171.0 

189.0 

207.0 

•216. 0 

9.00 

9.05 

117.7 

126.7 

135.8 

144.8 

153.9 

162.9 

172.0 

181.0 

190.1 

199.1 

208.2 

217.2 

9.05 

9.10 

118.3 

127.4 

136.5 

145.6 

154.7 

163.8 

172.9 

182.0 

191.1 

200.2 

209.3 

218.4 

9.10 

9.15 

119.0 

128.1 

137.3 

146.4 

155.6 

164.7 

173.9 

183.0 

192.2 

201.3 

210.5 

219.6 

9.15 

9.20 

119.6 
120.3 

128.8 

138.0 

147.2 

156.4 

165.6 

174.8 

184.0 

193.2 

202.4 

211.6 

220.8 
222.0 

9.20 

9.25 

129.5 

138.8 

148.0 

157.3 

166.5 

175.8 

185.0 

194.3 

203.5 

212.8 

9.25 

9.30 

120.9 

130.2 

139.5 

148.8 

158.1 

167.4 

176.7 

186.0 

195.3 

204.6 

213.9 

223.2 

9.30 

9.35 

121.6 

130.9 

140.3 

149.6 

159.0 

168.3 

177.7 

187.0 

196.4 

205.7 

215.1 

224.4 

9.35 

9.40 

122.2 

131.6 

141.0 

150.4 

159.8 

169.2 

178.6 

188.0 

197.4 

206.8 

216.2 

225.6 

9.40 

9.45 

122.9 

132.3 

141.8 

151.2 

160.7 

170.1 

179.6 

189.0 

198.5 

207.9 

217.4 

226.8 

9.45 
9.50 

9.50 

123.5 

133.0 

142.5 

152.0 

161.5 

171.0 

180.5 

190.0 

199.5 

209.0 

218.5 

228.0 

9.55 

124.2 

133.7 

143.3 

152.8 

162.4 

171.9 

181.5 

191.0 

200.6 

210.1 

219.7 

229.2 

9.55 

9.60 

124.8 

134.4 

144.0 

153.6 

163.2 

172.8 

182.4 

192.0 

201.6 

211.2 

220.8 

230.4 

9.60 

9.65 

125.5 

135.1 

144.8 

154.4 

164.1 

173.7 

183.4 

193.0 

202.7 

212.3 

222.0 

231.6 

9.65 

9.70 

126.1 

135.8 
136.5 

145.5 

155.2 
156.0 

164.9 
165.8 

174.6 
175.5 

184.3 

194.0 

203.7 

213.4 

223.1 

232.8 

9.70 

9.75 

126.8 

146.3 

185.3 

195.0 

204.8 

214.5 

224.3 

234.0 

9.75 

9.80 

127.4 

137.2 

147.0 

156.8 

166.6 

176.4 

186.2 

196.0 

205.8 

215.6 

225.4 

235.2 

9.80 

9.85 

128.1 

137.9 

147.8 

157.6 

167.5 

177.3 

187.2 

197.0 

206.9 

216.7 

226.6 

236.4 

9.85 

9.90 

128.7 

138.6 

148.5 

158.4 

168.3 

178.2 

188.1 

198.0 

207.9 

217.8 

227.7 

237.6 

9.90 

9.95 

129.4 
130.0 

139.3 
140.0 

149.3 

159.2 

169.2 

179.1 

189.1 

199.0 

209.0 
210.0 

218.9 

228.9 
230.0 

238.8 
240.0 

9.95 

10.00 

150.0 

160.0 

170.0 

180.0 

190.0 

200.0 

220.0 

10.00 

10.05 

130.7 

140.7 

150.8 

160.8 

170.9 

180.9 

191.0 

201.0 

211.1 

221.1 

231.2 

241.2 

10.05 

10.10 

131.3 

141.4 

151.5 

161.6 

171.7 

181.8 

191.9 

202.0 

212.1 

222.2 

232.3 

242.4 

10.10 

10.15 

132.0 

142.1 

152.3 

162.4 

172.6 

182.7 

192.9 

203.  0 

213.2 

223.3 

233.5 

243.6 

10.15 

10.20 

132.6 

142.8 
143.5 

153.0 

163.2 

173.4 
174.3 

183.6 
184.5 

193.8 

204.0 
205.0 

214.2 
215.3 

224.4 

234.6 

244.8 

10.20 

10.25 

133.3 

153.8 

164.0 

194.8 

225.5 

235.8 

246.0 

10.25 

10.30 

133.9 

144.2 

154.5 

164.8 

175.1 

185.4 

195.7 

206.0 

216.3 

226.6 

236.9 

247.2 

10.30 

10.35 

134.6 

144.9 

155.3 

165.6 

176.0 

186.3 

196.7 

207.  0 

217.4 

227.7 

238.1 

248.4 

10.35 

10.40 

135.2 

145.6 

156.0 

166.4 

176.8 

187.2 

197.6 

208.0 

218.4 

228.8 

239.2 

249.6 

10.40 

10.45 

135.9 

146.3 

156.8 

167.2 

177.7 

188.1 

198.6 
199.5 

209.0 

219.5 

229.9 

240.4 

250.8 

10.45 

10.50 

136.5 

147.0 

157.5 

168.0 

178.6 

189.0 

210.0 

220.5 

231.0 

241.5 

252.0 

10.50 

10.55 

137.2 

147.7 

158.3 

168.8 

179.4 

189.9 

200.5 

211.0 

221.6 

232.1 

242.7 

253.2 

10.55 

10.60 

137.8 

148.4 

159.0 

169.6 

180.2 

190.8 

201.4 

212.0 

222.6 

233.2 

243.8 

254.4 

10.60 

10.65 

138.5 

149.1 

]59.8 

170.4 

181.1 

191.7 

202.4 

213.0 

223.7 

234.3 

245.0 

255.6 

10.66 

10.70 

139.1 

149.8 

160.5 

171.2 

181.9 
182.8 

192.6 

203.3 
204.3 

214.0 
215.0 

224.7 
225.8 

235.4 

246.1 

256.8 

10.70 

10.75 

139.8 

150.5 

161.3 

172.0 

193.5 

236.5 

247.3 

258.0 

10.75 

10.80 

140.4 

151.2 

162.0 

172.8 

183.6 

194.4 

•205. 2 

216.0 

226.8 

237.6 

248.4 

259.2 

10.80 

10.85 

141.1 

151.9 

162.8 

173.6 

184.5 

195.3 

206.2 

217.0 

227.9 

238.7 

249.6 

260.4 

10.85 

10.90 

141.7 

152.6 

163.5 

174.4 

185.3 

196.2 

207.1 

218.0 

228.9 

239.8 

250.7 

261.6 

10.90 

10.95 

142.4 

153.3 

164.3 

175.2 

186.2 

197.1 

208.1 

219.0 
220.0 

230.0 

240.9 
242.0 

251.9 

262.8 

10.95 

11.00 

143.0 

154.0 

165.0 

176.0 

187.0 

198.0 

209.0 

231.0 

253.0 

264.0 

11.00 

11.05 

143.7 

154.7 

165.8 

176.8 

187.9 

198.9 

210.0 

221.0 

232.1 

243.1 

254.2 

265.2 

11.05 

11.10 

144.3 

155.4 

166.5 

177.6 

188.7 

199.8 

210.9 

222.0 

233.1 

244.2 

255.3 

266.4 

11.10 

11.15 

145.0 

156.1 

167.3 

178.4 

189.6 

200.7 

211.9 

223.0 

234.2 

245.3 

256.5 

267.6 

11.15 

11.20 

145.6 

156.8 

168.0 

179.2 

190.4 

201.6 

212.8 
213.8 

224.0 
225.0 

235.2 

246.4 
247.5 

257.6 
258.8 

268.8 

11.20 

11.25 

146.3 

157.5 

168.8 

180.0 

191.3 

202.5 

236.3 

270.0 

11.25 

11.30 

146.9 

158.2 

169.5 

180.8 

192.1 

203.4 

214.7 

226.0 

237.3 

248.6 

259.9 

271.2 

11.30 

11.35 

147.6 

158.9 

170. 3 

181.6 

193.0 

204.3 

215.7 

227.0 

238.4 

249.7 

261.1 

272.4 

11.35 

11.40 

148.2 

159.6 

171.0 

182.4 

193.8 

205.2 

216.6 

228.0 

239.4 

250.8 

262.2 

273.6 

11.40 

11. 45  1 148. 9 

160.3 

171.8 

183.2 

194.7 

206.1 

217.6 

229.0 

240.5 

251.9 

263.4 

274.8 

11.45 

TABLES  14,  15,  16.                                   [Page  686 

TABLE  14. 

TABLE  15. 

Dip  of  the  Sea 
Horizon. 

Dip  of  the  Sea  at  different  Distances  from  the  Observer. 

Dist.  of 

Height  of  the  Eye  above  the  Sea  in  Feet. 

Height  of 

Dip  of  the 

the  Eye. 

Horizon. 

Land  in 
Sea  Miles. 

5 

10 

16 

20 

25 

30 

85 

40 

Feet. 

/     II 

/ 

/ 

1 

/ 

/ 

/ 

/ 

/ 

1 

0  59 

i 

11 

23 

34 

45 

57 

68 

79 

91 

2 

1  23 

i 

6 

12 

17 

23 

28 

34 

40 

45 

3 

1  42 

f 

4 

8 

12 

15 

19 

23 

27 

30 

4 
5 
6 
7 
8 
9 
10 

1  58 

2  11 
2  24 
2  36 
2  46 

2  56 

3  06 

1 

3 

6 

9 

12 

15 

17 

20 

23 

2 

3 
3 

2 

5 
4 
4 

7 
6 
5 

10 

8 

7 

12 

10 

8 

14 

12 

9 

16 
14 
11 

19 
16 
12 

2J 

2 

3 

4 

6 

7 

8 

9 

10 

3 

2 

3 

4 

5 

6 

7 

8 

9 

11 

3  15 

3i 

2 

3 

4 

5 

6 

6 

7 

8 

12 
13 
14 

3  24 
3  32 
3  40 

4 
6 

2 
2 

3 

4 
4 

5 
4 

5 
5 

6 
6 

7 
6 

7 
7 

S 

6 

2 

3 

4 

4 

5 

5 

6 

6 

15 
16 
17 
18 
19 
20 

3  48 

3  55 

4  02 
4  09 
4  16 
4  23 

Note  to  Table  15. — The  numbers  of  this  Table  below  the  black  lines 

are  the  same  as  are  given  in  Table  14,  the  visible  horizon  corres 
to  those  heights  not  being  so  far  distant  as  the  land. 

ponding 

21 

4  29 

22 

4  36 

23 

4  42 

24 

4  48 

25 

4  54 

26 

5  00 

27 

5  06 

28 

5  11 

29 

5  17 

30 
31 

5  22 
5  27 

32 

5  33 

TABLE  16. 

33 

5  38 

The  Sun's  Parallax 

34 

5  43 

in  Altitude. 

36 

5  48 

36 
37 

5  53 
5  58 

Altitude. 

Parallax. 

38 

6  02 

o 

II 

39 

6  07 

0 

9 

40 

6  12 

10 

9 

45 

6  36 

20 

8 

50 

6  56 

30 

8 

55 

7  16 

40 

7 

60 

7  35 

50 

6 

65 

7  54 

55 

5 

70 

8  12 

60 

4 

75 

8  29 

65 

4 

80 

8  46 

70 

3 

85 

9  02 

75 

2 

90 

9  18 

80 

2 

95 

9  33 

85 

1 

• 

100 

9  48 

90 

0 

Page  686] 


TABLE  17. 

Parallax  in  Altitude  of  a  Planet. 


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TABLES  18 

,19. 

[Page  687 

TABLE  18. 

TABLE  19. 

Augmentation  of  the  Moon's  Semidiameter. 

Augmentation  of  the  Mocm's 
Horizontal  Parallax. 

v   0) 

})'8  Semidiameter. 

O  St 

•< 

5-°  .2 

ya 

Hor.  Parallax.              1 

14' 

1 

5' 

16' 

17' 

58' 

67' 

61' 

80" 

0" 

80" 

0" 

80" 

0" 

II 

// 

n 

// 

// 

// 

0 

1/ 

1/ 

II 

0 

0.1 

0.1 

0.1 

0.1 

0.2 

0.2 

0 

0.0 

0.0 

0.0 

2 

0.6 

0.6 

0.7 

0.7 

0.8 

0.8 

2 

0.0 

0.0 

0.0 

4 

1.0 

1.1 

1.2 

1.3 

1.4 

1.5 

4 

0.1 

0.1 

0.1 

6 

1.5 

1.6 

1.7 

1.9 

2.0 

2.1 

6 

0.1 

0.1 

0.1 

8 

2.0 

2.1 

2.3 

2.4 

2.6 

2.7 

8 

0.2 

0.2 

0.2 

10 

2.4 

2.6 

2.8 

3.0 

3.2 

3.4 

10 

0.3 

0.3 

0.4 

12 

2.9 

3.1 

3.3 

3.6 

3.8 

4.0 

12 

0.5 

0.5 

0.5 

14 

3.4 

3.6 

3.9 

4.1 

4.4 

4.7 

14 

0.6 

0.7 

0.7 

16 

3.8 

4.1 

4.4 

4.7 

5.0 

5.3 

16 

0.8 

0.9 

0.9 

18 

4.3 

4.6 

4.9 

5.2 

5.6 

5.9 

18 

1.0 

1.1 

1.1 

20 

4.7 

5.1 

5.4 

5.8 

6.1 

6.5 

20 

1.2 

1.3 

1.4 

22 

5.2 

5.5 

5.9 

6.3 

6.7 

7.1 

22 

1.5 

1.6 

L7 

24 

5.6 

6.0 

6.4 

6.8 

7.3 

7.7 

24 

1.7 

L9 

2.0 

26 

6.0 

6.5 

6.9 

7.4 

7.8 

8.3 

26 

2.0 

2.2 

2.3 

28 

6.5 

6.9 

7.4 

7.9 

8.4 

8.9 

28 

2.3 

2.5 

2.6 

30 

6.9 

7.3 

7.9 

8.4 

8.9 

9.5 

30 

2.6 

2.8 

3.0 

32 

7.3 

7.8 

8.3 

8.9 

9.4 

10.0 

32 

2.9 

3.1. 

3.4 

34 

7.7 

8.2 

8.8 

9.4 

10.0 

10.6 

34 

3.3 

3.5 

3.8 

36 

8.1 

8.6 

9.2 

9.8 

10.5 

11.1 

36 

3.6 

3.9 

4.1 

38 

8.4 

9.0 

9.7 

10.3 

10.9 

11.6 

38 

4.0 

4.3 

4.6 

40 

8.8 

9.4 

10.1 

10.7 

11.4 

12.1 

40 

4.3 

4.6 

5.0 

42 

9.2 

9.8 

10.5 

11.2 

11.9 

12.6 

42 

4.7 

5.0 

5.4 

44 

9.5 

10.2 

10.9 

11.6 

12.3 

13.1 

44 

5.0 

5.4 

5.8 

46 

9.8 

10.5 

11.3 

12.0 

12.8 

13.6 

46 

5.4 

5.8 

6.2 

48 

10.2 

10.9 

11.6 

12.4 

13.2 

14.0 

48 

5.8 

6.2 

6.6 

50 

10.5 

11.2 

12.0 

12.8 

13.6 

14.4 

50 

6.1 

6.6 

7.1 

52 

10.8 

11.5 

12.3 

13.1 

14.0 

14.9 

52 

6.5 

7.0 

7.5 

54 

11.1 

11.8 

12.7 

13.5 

14.4 

15.3 

54 

6.8 

7.4 

7.9 

56 

11.3 

12.1 

13.0 

13.8 

14.7 

15.6 

56 

7.2 

7.7 

8.3 

58 

11.6 

12.4 

13.3 

14.1 

15.1 

16.0 

58 
60 

7.5 

8.1 

8.6 

60 

11.8 

12.7 

13.5 

14.4 

15.4 

16.3 

7.8 

8.4 

9.0 

62 

12.1 

12.9 

13.8 

14.7 

15.7 

16.6 

62 

8.1 

8.8 

9.4 

64 

12.3 

13.2 

14.1 

15.0 

16.0 

16.9 

64 

8.4 

9.1 

9.7 

66 

12.5 

13.4 

14.3 

15.2 

16.2 

17.2 

66 

8.7 

9.4 

10.0 

68 

12.7 

13.6 

14.5 

15.5 

16.5 

17.5 

68 

9.0 

9.7 

10.3 

70 

12.9 

13.8 

14.7 

15.7 

16.7 

17.7 

70 

9.2 

9.9 

10.6 

72 

13.0 

13.9 

14.9 

15.9 

16.9 

17.9 

72 

9.5 

10.2 

10.9 

74 

13.1 

14.1 

15.0 

16.0 

17.1 

18.1 

74 

9.7 

10.4 

11.1 

76 

13.3 

14.2 

15.2 

16.2 

17.2 

18.3 

76 

9.8 

10.6 

11.3 

78 
80 

13.4 

14.3 

15.3 

16.3 

17.4 

18.4 

78 

10.0 

10.8 

11.5 

13.5 

14.4 

15.4 

16.4 

17.5 

18.6 

80 

10.1 

10.9 

11.7 

82 

13.5 

14.5 

15.5 

16.5 

17.6 

18.7 

82 

10.3 

11.0 

11.8 

84 

13.6 

14.6 

15.6 

16.6 

17.6 

18.7 

84 

10.3 

11.1 

11.9 

86 

13.6 

14.6 

15.6 

16.6 

17.7 

18.8 

86 

10.4 

U.2 

12.0 

88 

13.7 

14.6 

15.6 

16.7 

17.7 

18.8 

88 

10.4 

n.2 

12.0 

90 

18.7 

14.6 

15.6 

16.7 

17.7 

18.8 

90 

10.5 

11.3 

12.0 

21594°— 14- 


-37 


Page  688] 

TABLE  20A. 

Mean  Refraction. 

[Barometer,  30  inches.    Fahrenheit's  Thermometer, 

50°.J 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

o       / 

'         " 

o       / 

9  30 

5  35.1 

o         / 

15  00 

/       II 
3  34.1 

o        / 

25  00 

2     4.4 

o        / 

42  00 

1  04.7 

0  00 

36  29.  4 

35 

5  32.4 

10 

3  31.7 

10 

2    3.4 

20 

1  03.9 

1  00 

24  53.  6 

40 

5  29.6 

20 

3  29.4 

20 

2     2.5 

40 

1  03.2 

2  00 

18  25. 5 

45 

5  27.0 

30 

3  27.1 

30 

2     1.6 

43  00 

1  02.4 

3  00 

14  25. 1 

50 

5  24.3 

40 

3  24.8 

40 

2    0.7 

20 

1  01.7 

4  00 

11  44.4 

55 

5  21.7 

50 

3  22.6 

50 

1  59.8 

40 

1  01.0 

5  00 

9  52. 0 

10  00 

5  19.2 

16  00 

3  20.5 

26  00 

1  58.9 

44  00 

1  00.3 

05 

9  44.0 

05 

5  16.7 

10 

3  18.4 

10 

1  58.1 

20 

0  59.6 

10 

9  36.2 

10 

5  14.2 

20 

3  16.3 

20 

1  57.2 

40 

0  58.9 

15 

9  28.6 

15 

5  11.7 

30 

3  14.2 

30 

1  56.4 

45  00 

0  58.2 

20 

9  21.2 

20 

5    9.3 

40 

3  12.2 

40 

1  55.5 

20 

0  57.6 

25 

9  14.0 

25 

5    6.9 

50 

3  10.3 

50 

1  54.7 

40 

0  56.9 

5  30 

9    7.0 

10  30 

5    4.6 

17  00 

3    8.3 

27  00 

1  53.9 

46  00 

0  56.2 

35 

9    0.1 

35 

5    2.3 

10 

3    6.4 

10 

1  53.1 

20 

0  55.6 

40 

8  53.4 

40 

5    0.0 

20 

3    4.6 

20 

1  52.3 

40 

0  55.0 

45 

8  46.8 

45 

4  57.8 

30 

3    2.8 

30 

1  51.5 

47  00 

0  54.3 

50 

8  40.4 

50 

4  55.6 

40 

3    1.0 

40 

1  50.7 

20 

0  53.7 

55 

8  34.2 

55 

4  53.4 

50 

2  59.2 

50 

1  50.0 

40 

0  53.1 

6  00 

8  28.0 

11  00 

4  51.2 

18  00 

2  57.5 

28  00 

1  49.2 

48  00 

0  52.5 

05 

8  22.1 

05 

4  49.1 

10 

2  55.8 

20 

1  47.7 

49  00 

0  50.6 

10 

8  16.2 

10 

4  47.0 

20 

2  54.1 

40 

1  46.2 

50  00 

0  48.9 

15 

8  10.5 

15 

4  44.9 

30 

2  52.4 

29  00 

1  44.8 

51  00 

0  47.2 

20 

.     8    4.8 

20 

4  42.9 

40 

2  50.8 

20 

1  43.4 

52  00 

0  45.5 

25 

7  59.3 

25 

4  40.9 

50 

2  49.2 

40 

1  42.0 

53  00 

0  43.9 

6  30 

7  53.9 

11  30 

4  38.9 

19  00 

2  47.7 

30  00 

1  40.6 

54  00 

0  42.3 

35 

7  48.7 

35 

4  36.9 

10 

2  46.1 

20 

1  39.3 

55  00 

0  40.8 

40 

7  43.5 

40 

4  35.0 

20 

2  44.6 

40 

1  38.0 

56  00 

0  39.3 

45 

7  38.4 

45 

4  33.1 

30 

2  43.1 

31  00 

1  36.7 

57  00 

0  37.8 

50 

7  33.5 

50 

4  31.2 

40 

2  41.6 

20 

1  35.5 

58  00 

0  36.4 

55 

7  28.6 

55 

4  29.4 

50 

2  40.2 

40 

1  34.2 

59  00 

0  35.0 

7  00 

7  23.8 

12  00 

4  27.5 

20  00 

2  38.8 

32  00 

1  33.0 

60  00 

0  33.6 

05 

7  19.2 

05 

4  25.7 

10 

2  37.4 

20 

1  31.8 

61  00 

0  32.3 

10 

7  14.6 

10 

4  23.9 

20 

2  36.0 

40 

1  30.7 

62  00 

0  31.0 

15 

7  10.1 

15 

4  22.2 

30 

2  34.6 

33  00 

1  29.5 

63  00 

0  29.7 

20 

7    5.7 

20 

4  20.4 

40 

2  33.3 

20 

1  28.4 

64  00 

0  28.4 

25 

7     1.4 

25 

4  18.7 

50 

2  32.0 

40 

1  27.3 

65  00 

0  27.2 

7  30 

6  57.1 

12  30 

4  17.0 

21  00 

2  30.7 

34  00 

1  26.2 

66  00 

0  25.9 

35 

6  53.0 

35 

4  15.3 

10 

2  29.4 

20 

1  25.1 

67  00 

0  24.7 

40 

6  48.9 

40 

4  13.6 

20 

2  28.1 

40 

1  24.1 

68  00 

0  23.6 

45 

6  44.9 

45 

4  12.0 

30 

2  26.9 

35  00 

1  23.1 

69  00 

0  22.4 

50 

6  41.0 

50 

4  10.4 

40 

2  25.7 

20 

1  22.0 

70  00 

0  21.2 

55 

6  37.1 

55 

4     8.8 

50 

2  24.5 

40 

1  21.0 
1  20.1 

71  00 

72  00 

0  20.1 

8  00 

6  33.3 

13  00 

4    7.2 

22  00 

2  23.3 

36  00 

0  18.9 

05 

6  29.6 

05 

4    5.6 

10 

2  22.1 

20 

1  19.1 

73  00 

0  17.8 

10 

6  25.9 

10 

4    4.1 

20 

2  20.9 

40 

1  18.2 

74  00 

0  16.7 

15 

6  22.3 

15 

4    2.6 

30 

2  19.8 

37  00 

1  17.2 

75  00 

0  15.6 

20 

6  18.8 

20 

4    1.0 

40 

2  18.7 

20 

1  16.3 

76  00 

0  14.5 

25 

6  15.3 

25 

3  59.6 

50 

2  17.5 

40 

1  15.4 

77  00 

0  13.5 

8  30 

6  11.9 

13  30 

3  58.1 

23  00 

2  16.4 

38  00 

1  14.5 

78  00 

0  12.4 

35 

6    8.5 

35 

3  56.6 

10 

2  15.4 

20 

1  13.6 

79  00 

0  11.3 

40 

6    5.2 

40 

3  55.2 

20 

2  14.3 

40 

1  12.7 

80  00 

0  10.3 

45 

6    2.0 

45 

3  53.7 

30 

2  13.3 

39  00 

1  11.9 

81  00 

0    9.2 

50 

5  58.8 

50 

3  52.3 

40 

2  12.2 

20 

1  11.0 

82  00 

0    8.2 

55 

5  55.7 

55 

3  50.9 

50 

2  11.2 

40 

1  10.2 

83  00 

0    7.2 

9  00 

5  52.6 

14  00 

3  49.5 

24  00 

2  10.2 

40  00 

1     9.4 

84  00 

0    6.1 

05 

5  49.6 

10 

3  46.8 

10 

2    9.2 

20 

1    8.6 

85  00 

0    5.1 

10 

5  46.6 

20 

3  44.2 

20 

2    8.2 

40 

1     7.8 

86  00 

0    4.1 

15 

5  43.6 

30 

3  41.6 

30 

2    7.2 

41  00 

1    7.0 

87  00 

0    3.1 

20 

5  40.7 

40 

3  39.0 

40 

2    6.2 

20 

1     6.2 

88  00 

0    2.0 

25 

5  37.9 

50 

3  36.5 

50 

2    5.3 

40 

1    5.4 

89  00 

0    1.0 
0    0.0 

9  30 

5  35.1 

15  00 

3  34.1 

25  00 

2    4.4 

42  00 

1     4.7 

90  00 

TABLE  20B. 

[Page  689 

Correction  of  the  Sun's  Apparent  Altitude  for  Refraction  and  Parallax. 

[Barometer,  30  Inches.    Fahrenheit's  Thermometer, 

50°.] 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax©. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

o       / 

'     // 

O         ' 

/     II 

o         / 

/     II 

O          1 

1     II 

o        / 

1     II 

9  30 

5  26 

15  00 

3  25 

25  00 

1  56 

42  00 

0  58 

0  00 

36  20 

35 

5  23 

10 

3  24 

10 

1  55 

20 

0  57 

1  00 

24  45 

40 

5  21 

20 

3  21 

20 

1  55 

40 

0  56 

2  00 

18  17 

45 

5  18 

30 

3  19 

30 

1  54 

43  00 

0  55 

3  00 

14  16 

50 

5  15 

40 

3  17 

40 

1  53 

20 

0  55 

4  00 

11  35 

55 

5  13 

50 

3  15 

50 

1  52 

40 

0  54 

5  00 

9  43 

10  00 

5  10 

16  00 

3  13 

26  00 

1  51 

44  00 

0  53 

05 

9  35 

05 

5    8 

10 

3  10 

10 

1  50 

20 

0  53 

10 

9  27 

10 

5    5 

20 

3    8 

20 

1  49 

40 

0  52 

15 

9  20 

15 

5    3 

30 

3    6 

30 

1  48 

45  00 

0  52 

20 

9  12 

20 

5    0 

40 

3    4 

40 

1  48 

20 

0  52 

25 

9    5 

25 

4  58 

50 

3    2 

50 

1  47 

40 

0  51 

5  30 

8  58 

10  30 

4  56 

17  00 

3    0 

27  00 

1  46 

46  00 

0  50 

35 

8  51 

35 

4  53 

10 

2  58 

10 

1  45 

20 

0  50 

40 

8  44 

40 

4  51 

20 

2  57 

20 

1  44 

40 

0  49 

45 

8  38 

45 

4  49 

30 

2  55 

30 

1  44 

47  00 

0  48 

50 

8  31 

50 

4  47 

40 

2  53 

40 

1  43 

20 

0  48 

55 

8  25 

55 

4  44 

50 

2  51 

50 

1  42 

40 

0  47 

6  00 

8  19 

11  00 

4  42 

18  00 

2  50 

28  00 

1  41 

48  00 

0  47 

05 

8  13 

05 

4  40 

10 

2  48 

20 

1  40 

49  00 

0  45 

10 

8    7 

10 

4  38 

20 

2  46 

40 

1  38 

50  00 

0  43 

15 

8    2 

15 

4  36 

30 

2  44 

29  00 

1  37 

51  00 

0  41 

20 

7  56 

20 

4  34 

40 

2  43 

20 

1  35 

52  00 

0  40 

25 

7  50 

25 

4  32 

50 

2  41 

40 

1  34 

53  00 

0  39 

6  30 

7  45 

11  30 

4  30 

19  00 

2  40 

30  00 

1  33 

54  00 

0  37 

35 

7  40 

35 

4  28 

10 

2  38 

20 

1  31 

55  00 

0  36 

40 

7  35 

40 

4  26 

20 

2  37 

40 

1  30 

56  00 

0  34 

45 

7  29 

45 

4  24 

30 

2  35 

31  00 

1  29 

57  00 

0  33 

50 

7  25 

50 

4  22 

40 

2  34 

20 

1  28 

58  00 

0  32 

55 

7  20 

55 

4  20 

50 

2  32 

40 

1  26 

59  00 

0  31 

7  00 

7  15 

12  00 

4  19 

20  00 

2  31 

32  00 

1  25 

60  00 

0  30 

05 

7  10 

05 

4  17 

10 

2  29 

20 

1  24 

61  00 

0  28 

10 

7    6 

10 

4  15 

20 

2  28 

40 

1  23 

62  00 

0  27 

15 

7    1 

15 

4  13 

30 

2  27 

33  00 

1  22 

63  00 

0  26 

20 

6  57 

20 

4  11 

40 

2  25 

20 

1  20 

64  00 

0  24 

25 

6  52 

25 

4  10 

50 

2  24 

40 

1  19 

65  00 

0  23 

7  30 

6  48 

12  30 

4    8 

21  00 

2  23 

34  00 

1  18 

66  00 

0  22 

35 

6  44 

35 

4    6 

10 

2  21 

20 

1  17 

67  00 

0  21 

40 

6  40 

40 

4    5 

20 

2  20 

40 

1  16 

68  00 

0  21 

45 

6  36 

45 

4    3 

30 

2  19 

35  00 

>    1  15 

69  00 

0  19 

50 

6  32 

50 

4     1 

40 

2  18 

20 

1  15 

70  00 

0  18 

55 

6  28 

55 

4    0 

50 

2  17 

40 

1  14 

71  00 

0  17 

8  00 

6  24 

13  00 

3  58 

22  00 

2  15 

36  00 

1  13 

72  00 

0  16 

05 

6  21 

05 

3  57 

10 

2  14 

20 

1  12 

73  00 

0  16 

10 

6  17 

10 

3  55 

20 

2  13 

40 

1  11 

74  00 

0  15 

15 

6  13 

15 

3  54 

30 

2  12 

37  00 

1  10 

75  00 

0  14 

20 

6  10 

20 

3  52 

40 

2  11 

20 

1     9 

76  00 

0  13 

25 

6    6 

25 

3  51 

50 

2  10 

40 

1     8 

77  00 

0  12 

8  30 

6    3 

13  30 

3  49 

23  00 

2    8 

38  00 

1    8 

78  00 

0  10 

35 

6    0 

35 

3  48 

10 

2    7 

20 

1     7 

79  00 

0    9 

40 

5  56 

40 

3  46 

20 

2    6 

40 

1     6 

80  00 

0    8 

45 

5  53 

45 

3  45 

30 

2    5 

39  00 

1     5 

81  00 

0    7 

50 

5  50 

50 

3  43 

40 

2    4 

20 

1    4 

82  00 

0    6 

55 

5  47 

55 

3  42 

50 

2    3 

40 

1     3 

83  00 

0    6 

9  00 

5  44 

14  00 

3  41 

24  00 

2    2 

40  00 

1     2 

84  00 

0    5 

05 

5  41 

10 

3  38 

10 

2    1 

20 

1     2 

85  00 

0    4 

10 

5  38 

20 

3  35 

20 

2    0 

40 

1     1 

86  00 

0    3 

15 

5  35 

30 

3  33 

30 

1  59 

41  00 

1    0 

87  00 

0    2 

20 

5  32 

40 

3  30 

40 

1  58 

20 

0  59 

88  00 

0    2 

25 

5  29 

50 

3  28 

50 

1  57 

40 

0  58 

89  00 

0    1 

9  30 

5  26 

15  00 

3  25 

25  00 

1  56 

42  00 

0  58 

90  00 

0    0 

Page  690] 

TABLE  21.                                                            1 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Barometer. 

Barom. 

Subtract. 

Mean  refraction. 

Barom. 

0' 

1' 

2' 

8' 

4' 

6' 

«' 

V 

8' 

9'        1 10' 

0" 

30" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

II 

,, 

„ 

II 

II 

„ 

„ 

// 

II 

„ 

/' 

// 

„ 

II 

/' 

II 

II 

II 

// 

II 

// 

27.50 

0 

2 

5 

7 

10 

12 

15 

17 

20 

23 

25 

28 

30 

33 

35 

38 

40 

43 

45 

48 

51 

27.55 

0 

2 

5 

7 

10 

12 

15 

17 

20 

22 

25 

27 

30 

32 

35 

37 

40 

42 

45 

47 

50 

27.60 

0 

2 

5 

7 

10 

12 

14 

17 

19 

22 

24 

27 

29 

31 

34 

36 

39 

41 

44 

46 

49 

27.65 

0 

2 

5 

7 

9 

12 

14 

16 

19 

21 

24 

26 

28 

31 

33 

36 

38 

40 

43 

45 

48 

27.70 

0 
0 

2 
2 

5 
4 

7 
7 

9 
9 

11 
11 

14 
13 

16 
16 

18 
18 

21 
20 

23 
23 

25 
26 

28 

27 

30 

29 

32 
32 

35 
34 

37 
36 

39 
39 

42 
41 

44 
43 

47 

27.75 

46 

27.80 

0 

2 

4 

7 

9 

11 

13 

15 

18 

20 

22 

24 

27 

29 

31 

33 

35 

38 

40 

42 

45 

27.85 

0 

2 

4 

6 

9 

11 

13 

15 

17 

19 

22 

24 

26 

28 

30 

32 

35 

37 

39 

41 

44 

27.90 

0 

2 

4 

6 

8 

10 

13 

15 

17 

19 

21 

23 

25 

27 

30 

32 

34 

36 

38 

40 

43 

27.95 
28.00 

0 
0 

2 
2 

4 
4 

6 
6 

8 
8 

10 
10 

12 
12 

14 
14 

16 
16 

18 
18 

21 
20 

23 
22 

25 
24 

27 
26 

29 

28 

31 
30 

33 
32 

35 
34 

37 
36 

39 

42 

38 

41 

28.05 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

25 

27 

29 

31 

33 

35 

37 

89 

28.10 

0 

2 

4 

6 

8 

9 

11 

13 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

34 

36 

38 

.  28.15 

0 

2 

4 

6 

7 

9 

11 

13 

15 

17 

19 

20 

22 

24 

26 

28 

30 

32 

34 

36 

37 

28.20 

0 
0 

2 
2 

4 
3 

5 

5 

7 
7 

9 
9 

11 
10 

13 
12 

14 
14 

16 
16 

18 

18 

20 
19 

22 
21 

24 
23 

25 
25 

27 
26 

29 

28 

31 
30 

33 
32 

35 
34 

36 
35 

28.25 

28.30 

0 

2 

3 

5 

7 

8 

10 

12 

14 

15 

17 

19 

21 

22 

24 

26 

27 

29 

31 

33 

34 

28.35 

0 

2 

3 

5 

7 

8 

10 

12 

13 

15 

17 

18 

20 

22 

23 

25 

27 

28 

30 

32 

33 

28.40 

0 

2 

3 

5 

6 

8 

10 

11 

13 

14 

16 

18 

19 

21 

23 

24 

26 

27 

29 

31 

32 

28.45 

0 
0 

2 

3 
3 

5 
4 

6 
6 

8 

7 

9 
9 

11 
10 

12 
12 

14 
14 

16 
15 

17 

17 

19 

18 

20 
20 

22 
2f 

23 
23 

25 
24 

27 
26 

28 

30 

31 

28.50 

27 

29 

30 

31.50 

28.55 

0 

3 

4 

6 

7 

9 

10 

12 

13 

15 

16 

17 

19 

20 

22 

23 

25 

26 

28 

29 

31.  45 

28.60 

0 

3 

4 

6 

7 

8 

10 

11 

13 

14 

15 

17 

18 

20 

21 

23 

24 

25 

27 

28 

31.  40 

28.65 

0 

3 

4 

5 

7 

8 

9 

11 

12 

14 

15 

16 

18 

19 

20 

22 

23 

25 

26 

27 

31.35 

28.70 

0 
0 

3 
2 

4 
4 

5 
5 

6 
6 

8 

7 

9 
9 

10 
10 

12 
11 

13 
13 

14 
14 

16 
15 

17 
16 

18 
18 

20 
19 

21 
20 

22 
21 

24 

25 

26 

31.30 

28.75 

23 

24 

25 

31.25 

28.80 

0 

2 

4 

5 

6 

7 

8 

10 

11 

12 

13. 

14 

16 

17 

18 

19 

21 

22 

23 

24 

31.20 

28.85 

0 

2 

3 

5 

6 

7 

8 

9 

10 

12 

13 

14 

15 

16 

17 

19 

20 

21 

22 

23 

31.15 

28.90 

0 

2 

3 

4 

5 

7 

8 

9 

10 

11 

12 

13 

14 

16 

17 

18 

19 

20 

21 

22 

31.10 

28.95 

0 

2 

3 

4 

5 

6 

7 

8 

9 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

31.05 

29.00 

0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

31.00 

29.05 

0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

11 

12 

13 

14 

15 

16 

17 

18 

19 

30.95 

29.10 

0 

2 

3 

4 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

15 

16 

17 

18 

30.90 

29.15 

0 

2 

3 

3 

4 

5 

6 

7 

8 

9 

9 

10 

11 

12 

13 

14 

15 

15 

16 

17 

30.85 

29.20 

0 

2 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

10 

11 

12 

13 

14 

15 

15 

16 

30.80 
30.  % 

29.25 

0 

2 

3 

4 

4 

5 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

14 

14 

15 

29.30 

0 

2 

3 

3 

4 

5 

6 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

13 

14 

30.70 

29.35 

0 

2 

3 

3 

4 

5 

5 

6 

7 

7 

8 

9 

9 

10 

10 

11 

12 

13 

13 

30.65 

29.40 

0 

2 

2 

3 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

10 

10 

11 

12 

12 

30.60 

29.45 

0 

2 

2 

3 
2 

3 
3 

4 
3 

4 
4 

5 
5 

6 
5 

6 

7 

7 

8 

8 

9 

9 

10 

11 

11 

30.  55 

29.50 

0 

0 

2 

6 

6 

7 

7 

8 

8 

9 

9 

10 

10 

30.50 

29.55 

0 

0 

2 

2 

3 

3 

4 

4 

5 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

30.  45 

29.60 

0 

0 

2 

2 

2 

3 

3 

4 

4 

4 

5 

5 

6 

6 

6 

7 

7 

8 

8 

30.40 

29.65 

0 

0 

2 

2 

2 

3 

3 

4 

4 

4 

5 

5 

5 

6 

6 

6 

7 

7 

30.35 

29.70 

0 

0 
0 

~0" 

-j- 

1 
1 

2 

2 
2 

2 
2 

3 

2 

3 

3 

4 

4 

4 

5 

5 

5 

5 

6 

6 

30.  30 

29.75 

0 

3 

3 

3 

3 

4 

4 

4 

4 

5 

5 

5 

30.  25 

29.80 

0 

0 

0 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

4 

4 

4 

30.20 

29.85 

0 

0 

0 

0 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

30.15 

29.90 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

30.10 

29.95 

0 
0 

0 

0 

0 
0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

30.05 

30.00 

0     0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

30.00 

Subtract. 
Barom. 

0" 

30"    0" 

80" 

0" 

80" 

0" 

80"   0" 

80" 

0" 

80"   0" 

80" 

0"  1  80"    0" 

80" 

0" 

80" 

0" 

Add. 
Barom. 

0' 

V 

2' 

3'        i        \ 

i' 

6'       1        6' 

V              %' 

9' 

10' 

Mean  refraction. 

TABLE  22. 

[Page 

691 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Thermometer. 

Mean  refraction. 

Ther. 

Ther. 

Add. 

0' 

1' 

a' 

8' 

V 

o' 

6' 

V 

8' 

9' 

10' 

Add. 

0" 

30" 

0" 

// 

80" 

II 

0" 

;/ 

80" 

II 

0" 

// 

30" 

// 

0" 

80" 

II 

0" 

// 

30" 

II 

0' 

II 

80" 

II 

0" 

II 

80" 

II 

0" 

II 

80" 

II 

0" 

30" 

0" 

o 

// 

II 

II 

II 

II 

o 

—10 

0 

4 

8 

12 

16 

20 

24 

28 

33 

37 

41 

46 

50 

55 

60 

65 

70 

75 

80 

85 

90 

—10 

—  8 

0 

4 

8 

12 

15 

19 

23 

27 

31 

36 

40 

44 

48 

53 

58 

62 

67 

72 

77 

82 

87 

—  8 

—  6 

0 

4 

7 

11 

15 

19 

22 

26 

30 

34 

38 

42 

47 

51 

55 

60 

64 

69 

74 

79 

84 

-  6 

—  4 

0 

4 

7 

11 

14 

18 

22 

25 

29 

33 

37 

41 

45 

49 

53 

57 

62 

66 

71 

76 

80 

—  4 

—  2 

0 

3 

7 

10 

14 

17 

21 

24 

28 

31 

35 

39 

43 

47 

51 

55 

59 

64 

68 

72 

77 

-  2 

0 

0 

3 

7 

10 

13 

16 

20 

23 

27 

30 

34 

37 

41 

45 

49 

53 

57 

61 

65 

69 

74 

0 

2 

0 

3 

6 

9 

12 

16 

19 

22 

25 

29 

32 

36 

39 

43 

47 

50 

54 

58 

62 

66 

70 

2 

4 

0 

3 

6 

9 

12 

15 

18 

21 

24 

28 

31 

34 

37 

41 

44 

48 

52 

55 

59 

63 

67 

4 

6 

0 

3 

6 

8 

11 

14 

17 

20 

23 

26 

29 

32 

36 

39 

42 

46 

49 

53 

56 

60 

64 

6 

8 
10 

0 
0 

3 
3 

5 

5 

8 
8 

11 
10 

14 
13 

16 
15 

19 
18 

22 
21 

25 
24 

28 
26 

31 
29 

34 
32 

37 
35 

40 
38 

43 

41 

47 
44 

50 
48 

54 
51 

57 
54 

61 

58 

8 

10 

11 

0 

2 

5 

7 

10 

13 

15 

18 

20 

23 

26 

28 

31 

34 

37 

40 

43 

46 

49 

53 

56 

11 

12 

0 

2 

5 

7 

10 

12 

15 

17 

20 

22 

25 

28 

30 

33 

36 

39 

42 

45 

48 

51 

54 

12 

13 

0 

2 

5 

7 

9 

12 

14 

17 

19 

22 

24 

27 

30 

32 

35 

38 

41 

44 

47 

50 

53 

13 

14 
15 

0 
0 

2 
2 

5 
4 

7 
7 

9 
9 

11 
11 

14 
13 

16 
16 

19 
18 

21 
20 

24 
23 

26 
25 

29 
28 

31 
30 

34 
33 

37 
36 

40 
38 

42 
41 

45 
44 

48 

47 

51 
50 

14 

15 

16 

0 

2 

4 

6 

9 

11 

13 

15 

18 

20 

22 

25 

27 

29 

32 

35 

37 

40 

43 

45 

48 

16 

17 

0 

2 

4 

6 

8 

10 

13 

15 

17 

19 

21 

24 

26 

29 

31 

33 

36 

39 

41 

44 

47 

17 

18 

0 

2 

4 

6 

8 

10 

12 

14 

16 

19 

21 

23 

25 

28 

30 

32 

35 

37 

40 

43 

45 

18 

19 

0 

2 

4 

6 

8 

10 

12 
11 

14 
13 

16 
15 

18 
17 

20 
"19 

22 
22 

24 
24 

27 
26 

29 
28 

31 
30 

34 
33 

36 
35 

39 
37 

41 
40 

44 
42 

19 

20 

0 

2 

4 

6 

8 

9 

20 

21 

0 

2 

4 

6 

7 

9 

11 

13 

15 

17 

19 

21 

23 

25 

27 

29 

31 

34 

36 

38 

41 

21 

22 

0 

2 

3 

5 

7 

9 

11 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

35 

37 

39 

22 

23 

0 

2 

3 

5 

7 

8 

10 

12 

14 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

36 

38 

23 

24 

0 

2 

3 

5 

6 

8 

10 

11 

13 
13 

15 
14 

17 
16 

18 
18 

20 
19 

22 
21 

24 
23 

26 
25 

28 
27 

30 
29 

32 
31 

34 
33 

36 
35 

24 

25 

0 

2 

3 

5 

6 

8 

9 

11 

25 

26 

0 

3 

4 

6 

7 

9 

11 

12 

14 

15 

17 

19 

20 

22 

24 

26 

28 

29 

31 

33 

26 

27 

0 

3 

4 

6 

7 

9 

10 

12 

13 

15 

16 

18 

19 

21 

23 

25 

26 

28 

30 

32 

27 

28 

0 

3 

4 

5 

7 

8 

10 

11 

12 

14 

15 

17 

19 

20 

22 

23 

25 

27 

29 

30 

28 

29 
30 

0 
0 

3 
2 

4 

•4 

5 
5 

6 
6 

8 

7 

9 
9 

11 
10 

12 
11 

13 
13 

15 
14 

16 
15 

18 
17 

19 
18 

21 
20 

22 
21 

24 
23 

26 
24 

27 

29 

29 

26 

28 

30 

31 

0 

2 

3 

5 

6 

7 

8 

9 

11 

12 

13 

15 

16 

17 

19 

20 

22 

23 

25 

26 

31 

32 

0 

2 

3 

4 

6 

7 

8 

9 

10 

11 

13 

14 

15 

16 

18 

19 

20 

22 

23 

25 

82 

33 

0 

2 

3 

4 

5 

6 

7 

8 

10 

11 

12 

13 

14 

15 

17 

18 

19 

21 

22 

23 

33 

34 

0 

2 

3 

4 

4 

5 
5 

6 
6 

7 
6 

8 
7 

9 

8 

10 
9 

11 
10 

12 
11 

13 
13 

14 
14 

16 
15 

17 
16 

18 
17 

19 
18 

21 
19 

22 

34 

35 

0 

2 

3 

20 

35 

36 

0 

2 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

36 

37 

0 

2 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

37 

38 

0 

2 

3 

4 

4 

5 

6 

7 

7 

8 

9 

10 

11 

12 

13 

13 

14 

15 

16 

38 

39 

0 

2 

3 

3 

4 

5 

5 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

14 

15 

39 

40 

0 

2 

2 

3 

4 

4 

5 

6 

6 

7 

8 

8 

9 

10 

10 

11 

12 

13 

13 

40 

41 

0 

2 

2 

3 

3 

4 

4 

5 

6 

6 

7 

7 

8 

9 

() 

10 

11 

11 

12 

41 

42 

0 

0 

2 

2 

3 

3 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

S 

10 

11 

42 

43 

0 

0 

2 

2 

3 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

43 

44 

0 

0 

1 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

44 

45 

0 

0 

1 

1 

2 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

6 

6 

6 

7 

45 

46 

0 

0 

0 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

4 

4 

4 

4 

5 

5 

5 

46 

47 

0 

0 

0 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

3 

3 

4 

4 

4 

47 

48 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

3 

48 

49 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

49 

50 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

50 

0" 

30" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

SO" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

Add. 

Add. 

0' 

1' 

V 

V 

4' 

6' 

6' 

V 

8'    1    9' 

10' 

Ther 

Ther. 

Mean  refraction. 

Page  692]                 TABLE  22. 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Thermometer. 

Ther. 
Subt. 

Mean  refraction. 

Ther. 
Subt. 

0' 

V 

2' 

8' 

4' 

6' 

6' 

V 

8' 

9' 

10' 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

o 

50 
51 
52 
53 
54 

II 

0 
0 
0 
0 
0 

II 

0 
0 
0 
0 
0 

tt 

0 
0 
0 
0 
0 

II 

0 
0 
0 

II 

0 
0 
0 

1 
1 

II 
0 
0 

1 
1 
1 

II 

0 
0 
1 
1 

1 

n 

0 
0 

1 

1 

2 

n 

0 
0 

1 
1 

2 

II 
0 
1 
1 
2 
2 

// 
0 

1 

1 

2 
2 

II 
0 
1 

1 
2 
3 

0 
1 
1 
2 
3 

II 
0 
1 
2 
2 
3 

// 

0 

1 

2 
2 
3 

II 
0 
1 
2 
3 
4 

II 

0 
1 
2 
3 
4 

II 
0 

1 

2 
3 
4 
5 
6 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

II 
0 
1 
2 
3 
5 
6 
7 
8 
9 
10 
11 
12 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 

II 

0 

1 

2 
4 
5 
6 
7 
8 
10 
11 
12 
13 
15 
16 
17 
18 
19 
20 
22 
23 
24 
25 
26 
27 
28 
29 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 

II 

0 
1 
3 
4 
5 

o 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 

2 

2 
2 
2 
2 
2 
2 

1 
1 

2 
2 
2 
2 
3 
3 
3 
3 

1 

2 
2 
2 
3 
3 
3 
3 
4 
4 

2 
2 
2 
3 
3 
3 
4 
4 
5 
5 

2 
2 
3 
3 
4 
4 
4 
5 
5 
6 

2 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

7 

8 

8 

9 

9 

10 

10 

11 

11 

11 

12 

12 

13 

13 

14 

14 

14 

15 

15 

3 
3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

10 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

15 

16 

16 

17 

17 

3 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

9 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

16 

16 

17 

17 

18 

18 

19 

19 

3 

4 

5 

5 

6 

7 

7 

8 

8 

9 

10 

10 

11 

11 

12 

12 

13 

14 

14 

15 

16 

16 

17 

18 

18 

19 

20 

20 

21 

21 

4 
4 
5 
6 
6 
7 
8 
9 
9 
10 
11 
11 
12 
13 
13 
14 
15 
16 
16 
17 
18 
18 
19 
20 
20 
21 
21 
22 
23 
23 
24 
25 
25 
26 
27 
27 
28 
29 
29 
30 
30 
31 
32 
32 
33 
34 

4 
5 
6 
6 
7 
8 
9 
9 
10 
11 
12 
12 
13 
14 
15 
16 
16 
17 
18 
18 
19 
20 
21 
21 
22 
23 
24 
24 
25 
26 
26 
27 
28 
28 
29 
30 
31 
31 
32 
33 
33 
34 
35 
35 
36 
37 

4 
5 
6 

7 
8 
9 
9 
10 
11 
12 
13 
14 
14 
15 
16 
17 
18 
18 
19 
20 
21 
22 
22 
23 
24 
25 
26 
26 
27 
28 
29 
29 
30 
31 
32 
32 
33 
34 
35 
35 
36 
37 
38 
38 
39 
40 

5 
6 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
16 
17 
18 
19 
20 
21 
22 
22 
23 
24 
25 
26 
27 
28 
28 
29 
30 
31 
32 
32 
33 
34 
35 
36 
37 
37 
38 
39 
40 
41 
41 
42 
43 

5 

6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
31 
32 
33 
34 
35 
36 
37 
38 
39 
39 
40 
41 
42 
43 
44 
44 
45 
46 

6 
8 
9 

10 
12 
13 
14 
15 
17 
18 
19 
20 
22 
23 
24 
25 
27 
28 
29 
30 
31 
32 
34 
35 
36 
37 
38 
40 
41 
42 

55 
56 

57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

0 
0 
0 
0 
0 

2 
2 
2 
2 
2 

3 
3 
3 
o 

3 

3 

4 
4 
4 
4 

4 
5 
5 
5 
5 

5 
6 
6 

6 

7 

6 
6 

7 
7 
8 

65 
66 
67 
68 
69 

70 
71 

72 
73 

74 

0 
0 
0 
0 
0 

2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 

3 

4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
6 

5 
6 
5 
5 
5 
6 
6 
6 
6 
6 
7 
7 
7 
7 
8 

6 
6 
6 
7 
7 
7 
7 
8 
8 
8 
8 
9 
9 
9 
9 

7 

7 

8 

8 

8 

8 

9 

9 

9 

10 

10 

10 

11 

11 

11 

8 

8 

9 

9 

10 

10 

10 

11 

11 

11 

12 

12 

13 

13 

13 

70 
71 
72 
73 
74 

75 
76 

77 
78 
79 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

80 
81 
82 
83 
84 

86 
86 
87 
88 
89 

0 
0 
0 
0 
0 

2 
2 
2 
2 
2 

4 
4 
4 
4 
4 

6 
6 
6 
6 
6 

8 
8 
8 
8 
9 

10 
10 
10 
10 
11 

12  1  14 
12;  14 
12!  14 

13  1  15 
13;  15 

16 
16 
17 
17 
17 

18 
18 
19 
19 
20 

20 
20 
21 
21 
22 

22 
23 
23 
24 
24 

43 
44 
45 
46 
48 
49 
50 
51 
52 
53 
54 
55 
56 
58 
59 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 
95 
96 
97 
98 
99 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
3 
3 
3 

4 
4 
5 
5 
5 
6 
5 
5 
5 
5 
5 

7 
7 
7 
7 
7 
7 
7 
8 
8 
8 
8 

9 

9 

9 

9 

10 

10 

10 

10 

10 

11 

11 

11 
11 
11 
12 
12 
12 
12 
13 
13 
13 
13 

13 
14 
14 
14 
14 
15" 
15 
15 
16 
16 

16 
16 
16 
17 
17 
17 
18 
18 
18 
19 

18 
18 
19 
19 
19 
20 
20 
21 
21 
21 
22 

20 
21 
21 
22 
22 
22 
23 
23 
24 
24 
25 

23 
23 
24 
24 
25 
25 
26 
26 
27 
27 
28 

25 
25 
26 
27 
27 
28 
28 
29 
29 
30 
31 

90 
91 
92 
93 
94 

95 
96 
97 

98 
99  . 

100 

0 

3 

16  19 

53 

56 

60 

100 

Subt. 
Ther. 

0" 

80" 

0" 

80" 

0" 

80" 

0"  1  80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80» 

0" 

80" 

0" 

Subt. 
Ther. 

0' 

1' 

2' 

8' 

4' 

6' 

6' 

V       j 

8' 

9' 

10' 

Mean  refraction. 

TABLES  23,  24. 

[Page  693 

TABLE  23.                                       1 

Correction  of  the  Moon's  Altitude  for  parallax  and  re- 

fraction corresponding  to  a  mean  value  of  the  hori- 

zontal parallax,  57'  SO'-'. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

C!orr. 

Moon's 
alt. 

Corr. 

o 

, 

o 

1 

o 

, 

o 

/ 

10 

51 

31 

48 

51 

35 

71 

18 

11 

52 

32 

47 

52 

35 

72 

17 

12 

52 

33 

47 

53 

34 

73 

17 

13 

52 

34 

46 

54 

33 

74 

16 

14 

52 

35 

46 

55 

32 

75 

15 

15 

52 

36 

45 

56 

32 

76 

14 

16 

52 

37 

45 

57 

31 

77 

13 

17 

52 

38 

44 

58 

30 

78 

12 

18 

52 

39 

44 

59 

29 

79 

11 

19 

52 

40 

43 

60 

28 

80 

10 

20 

51 

21 

51 

41 

42 

61 

27 

81 

9 

22 

51 

42 

42 

62 

26 

82 

8 

23 

51 

43 

41 

63 

26 

83 

7 

24 

50 

44 

40 

64 

25 

84 

6 

25 

50 

45 

40 

65 

24 

85 

5 

26 

50 

46 

39 

66 

23 

86 

4 

27 

49 

47 

38 

67 

22 

87 

3 

28 

49 

48 

38 

68 

21 

88 

2 

29 

49 

49 

37 

69 

20 

89 

1 

30 

48 

50 

36 

70 

19 

90    1      0 

i 

TABLE  24. 

Correction  of  tl 

18  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer,  30  Inches.— Fahrenheit's  Thermometer,  50°.] 

H 

orizontal  parallax. 

Correction  for  seconds  of 
parallax.— Add. 

Corr.  for 

Moon's 

minutes 
of  alt. 

app.  alt. 

54' 

&6' 

66' 

67' 

58' 

69' 

60' 

61' 

oB 
1- 

0" 

8" 

4" 

V 

8" 

O        1 

/      // 

/      II 

/      // 

1      II 

'      II 

1     II 

/     // 

/    // 

II 

// 

n 

It 

n 

n 

5    0 

43  56 

44  56 

45  56 

46  56 

47  56 

48  55 

49  55 

50  55 

0 

0 

2 

4 

6 

8 

10 

44  11 

45  11 

46  11 

47  11 

48  11 

49  10 

50  10 

5110 

10 

10 

12 

14 

16 

18 

20 

25 

25 

25 

25 

25 

24 

24 

24 

20 

20 

22 

24 

26 

28 

30 

39 

39 

38 

38 

38 

38 

37 

37 

30 

30 

32 

34 

36 

38 

40 

52 

51 

51 

51 

51 

51 

5^ 

51 

40 

40 

42 

44 

46 

48 

50 

45    4 

46    3 

47    3 

48    3 

49    3 

50    3 

51     6 

52    3 

50 
0 

50 
0 

52 
2 

54 
4 

56 

58 

6    0 

45  15 

46  15 

47  14 

48  14 

49  14 

50  13 

51  13 

52  13 

6 

8 

10 

26 

26 

25 

25 

25 

25 

25 

25 

10 

10 

12 

14 

16 

18 

20 

36 

36 

36 

35 

35 

34 

34 

34 

20 

20 

22 

24 

26 

28 

30 

46 

46 

45 

45 

45 

44 

44 

44 

30 

30 

32 

34 

36 

38 

40 

55 

55 

55 

54 

54 

54 

53 

53 

40 

40 

42 

44 

46 

48 

50 

46    4 

47    3 

48    3 

49    3 

50    3 

51     2 

52    1 

53    1 

50 

50 

52 
2 

54 
4 

56 
6 

58 
8 

7    0 

46  12 

47  12 

48  12 

49  12 

50  12 

51  11 

52  11 

53  10 

0 

0 

10 

21 

20 

20 

20 

19 

18 

18 

18 

10 

10 

12 

14 

16 

18 

20 

29 

28 

28 

27 

27 

26 

25 

25 

20 

20 

22 

24 

26 

28 

30 

36 

36 

35 

35 

34 

34 

34 

33 

30 

30 

32 

34 

36 

38 

40 

43 

42 

42 

41 

41 

40 

40 

40 

40 

40 

42 

44 

46 

48 

50 

50 

49 

48 

48 

48 

47 

46 

46 

50 

50 
0 

52 
2 

54 
4 

56 
6 

58 
8 

Add. 

8    0 

46  56 

47  56 

48  55 

49  54 

50  54 

51  54 

52  53 

53  53 

0 

10 

47    2 

48    2 

49    1 

50    0 

51    0 

59 

59 

58 

10 

10 

12 

14 

16 

18 

2    1 

20 

8 

7 

7 

6 

6 

52    5 

53    4 

54    4 

20 

20 

22 

24 

26 

28 

3    2 

30 

13 

13 

12 

11 

11 

10 

10 

9 

30 

30 

32 

34 

36 

38 

4    2 

40 

19 

18 

17 

17 

16 

16 

15 

14 

40 

40 

42 

44 

46 

48 

5    3 

50 

24 

23 

22 

22 

21 

20 

19 

19 

50 

50 

52 

54 

4 

56 
6 

58 
8 

6  4 

7  4 

9    0 

47  28 

48  27 

49  26 

50  26 

51  25 

52  24 

53  24 

54  23 

0 

0 

2 

10 

33 

32 

31 

30 

30 

29 

28 

27 

10 

10 

12 

14 

16 

18 

8    5 

20 

37 

36 

35 

34 

34 

33 

32 

32 

20 

20 

22 

24 

26 

28 

9    5 

30 

41 

41 

40 

39 

38 

37 

37 

36 

30 

30 

32 

34 

36 

38 

40 

45 

44 

43 

43 

42 

41 

40 

39 

40 

40 

42 

44 

46 

48 

50 

49 

48 

47 

46 

46 

45 

44 

44 

50 

49 

51 

53 

55 

57 

Page  604] 

TABLE  24.  • 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon'8 

Horizontal  parallax. 

1^" 

Correction  for  seconds  of 
parallax. — Add. 

Corr. 
for 

app.  alt 

minutes 
of  alt. 

64' 

56' 

66' 

67'   1   58' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

O     / 

'  // 

'   // 

/   // 

'   // 

/  // 

'  II 

'  II 

/  II 

II 

// 

II 

II 

II 

„ 

Add 

10  0 

47  63 

48  52 

49  51 

50  50 

51  50 

52  48 

63  48 

64  47 

0 

0 

2 

4 

6 

8 

V 

^' 

10 

56 

55 

54 

53 

62 

51 

60 

60 

10 

10 

12 

14 

16 

18 

2 

1 

20 

59 

58 

57 

56 

65 

56 

54 

63 

20 

20 

22 

24 

26 

28 

8 

1 

30 

48  2 

49  1 

50  0 

59  1   58 

57 

66 

55 

30 

29 

31 

33 

36 

37 

4 

1 

40 

5 

4 

2 

51  2  ;  52  1 

53  0 

59 

58 

40 

39 

41 

43 

46 

47 

6 

2 

50 

7 

6 

5 

4  1    4 

2 

54  1 
54  4 

55  0 

50 
0 

49 
0 

61 
2 

63 
4 

55 
6 

67 
8 

.6 

7 

2 
2 

11  0 

48  10 

49  9 

50  8 

51  7  {  62  7 

53  5 

56  3 

10 

12 

11 

10 

9  1    9 

7 

6 

6 

10 

10 

12 

14 

16 

18 

8 

2 

20 

15 

14 

12 

12  i   11 

9 

8 

7 

20 

20 

22 

24 

26 

28 

9 

8 

30 

17 

16 

14 

13    13 

11 

10 

9 

30 

29 

31 

33 

35 

87 

40 

19 

18 

17 

15    15 

13 

12 

11 

40 

39 

41 

43 

45 

47 

50 

21 

20 

18 

17 

17 

15 

14 

13 

50 

49 
0 

51 
2 

53 
4 

55 
6 

67 
8 

12  0 

48  22 

49  21 

50  19 

51  18 

52  17 

53  17 

54  16 

66  14 

0 

10 

24 

23 

21 

20 

19 

18 

16 

15 

10 

10 

12 

14 

16 

18 

20 

26 

25 

23 

22    21 

20 

18 

17 

20 

20 

22 

24 

26 

27 

30 

27 

26 

24 

23 

22 

20 

19 

18 

30 

29 

31 

33 

35 

37 

40 

28 

27 

25 

24 

23 

21 

20 

19 

40 

39 

41 

43 

46 

47 

50 

29 

28 

26 

25 

24 
62  25 

22 
53  23 

21 

20 

60  49 
0   0 

51 
2 

53 

4 

55 
6 

57 
8 

1 

0 

13  0 

48  30 

49  29 

50  27 

51  26 

64  22 

55  20 

10 

31 

30 

28 

27 

26 

24 

22 

21 

10  10 

12 

14 

16 

18 

2 

0 

20 

32 

31 

29 

27 

26 

24 

23 

21 

20 

19 

21 

23 

25 

27 

8 

0 

30 

33 

32 

30 

28 

27 

25 

23 

22 

30 

29 

31 

33 

35 

37 

4 

0 

40 

34 

32 

30 

29 

28 

26 

24 

22 

40 

39 

41 

43 

46 

47 

6 

0 

50 

35 

33 

31 

30 

28 

26 

25 

23 

60 
0 

49 
0 

51 

2 

53 

4 

55 
6 

57 

8 

6 

7 

0 
0 

14  0 

48  35 

49  33 

50  31 

51  30 

52  28 

53  26 

54  25 

56  23 

10 

35 

34 

32 

30 

28 

26 

25 

23 

10 

10 

12 

14 

16 

18 

8 

0 

20 

36 

34 

32 

30 

29 

27 

26 

24 

20 

19 

21 

23 

25 

27 

9 

0 

30 

36 

34 

32 

30 

29 

27 

25 

23 

30 

29 

31 

33 

35 

37 

40 

36 

34 

32 

30 

29 

27 

25 

23 

40 

39 

41 

43 

46 

47 

50 

36 

34 

32 

30 

29 

27 
53  27 

25 

23 

60 

49 
0 

61 
2 

53 

4 

55 
6 

57 
8 

15  0 

48  36 

49  35 

50  33 

51  31 

52  29 

64  25 

55  23 

0 

10 

36 

35 

32 

30 

28 

26 

24 

22 

10 

10 

12 

14 

16 

18 

20 

36 

35 

32 

30 

28 

26 

24 

22 

20 

19 

21 

23 

25 

27 

30 

36 

34 

31 

29 

28 

25 

23 

21 

30 

29 

31 

33 

35 

87 

40 

36 

34 

31 

29 

27 

25 

23 

21 

40 

39 

41 

43 

45 

47 

50 

35 

48  35 

33 

30 

28 

26 

24 

21 
54  20 

19 

50 
0 

49 
0 

61 
2 

53 

4 

66 
6 

57 
8 

16  0 

49  32 

50  29 

51  27 

52  26 

53  23 

55  18 

10 

34 

32 

29 

27 

25 

23 

20 

18 

10 

10 

12 

13 

15 

17 

20 

34 

32 

29 

27 

25 

22 

20 

17 

20 

19 

21 

23 

26 

27 

30 

33 

31 

28 

26 

24 

21 

19 

16 

30 

29 

31 

33 

36 

86 

40 

33 

31 

28 

25 

23 

21 

18 

16 

40 

38 

40 

42 

44 

46 

50 

32 

30 

27 

24 
51  23 

22 

20 

17 

15 

50 

48 
0 

50 
2 

62 
4 

64 
6 

56 
8 

Sub. 

17  0 

48  31 

49  29 

50  26 

52  21 

63  18 

54  16 

56  13 

0 

10 

30 

28 

25 

22 

20 

17 

14 

12 

10 

10 

12 

13 

15 

17 

2 

0 

20 

28 

26 

23 

20 

18 

16 

12 

10 

20 

19 

21 

23 

25 

27 

3 

0 

30 

27 

25 

22 

19 

17 

14 

11 

9 

30 

29 

31 

33 

34 

36 

4 

0 

40 

26 

24 

21 

18 

16 

13 

10 

7 

40 

38 

40 

42 

44 

46 

5 

50 

26 

23 

20 

17 

15 

12 

9 

6 

50 
0 

48 
0 

60 
2 

62 
4 

53 
6 

55 
8 

6 

7 

18  0 

48  24 

49  21 

50  18 

61  15 

52  13 

63  10 

54  7 

55  4 

10 

23 

20 

17 

14 

12 

9 

6 

3 

10 

10 

11 

13 

15 

17 

8 

20 

22 

19 

16 

13 

11 

8 

5 

2 

20 

19 

21 

23 

25 

27 

9 

30 

21 

18 

15 

12 

10 

6 

3 

0 

30 

29 

30 

32 

34 

36 

40 

20 

17 

14 

10 

8 

4 

1 

54  58 

40 

38 

40 

42 

44 

46 

50 

18 

15 

12 

9 

6 

2 

53  59 
53  57 

66 

50 
0 

48 
0 

60 
2 

51 
4 

53 
6 

66 

8 

19  0 

48  16 

49  13 

50  10 

51  7 

52  4 

63  0 

54  55 

10 

15 

12 

8 

5 

2 

52  59 

65 

53 

10 

10 

11 

13 

15 

17 

20 

13 

10 

6 

3 

0 

67 

63 

51 

20 

19 

21 

23 

25 

27 

30 

12 

8 

5 

2 

61  58 

65 

51 

49 

30 

29 

30 

32 

34 

36 

40 

10 

6 

3 

0 

56 

53 

49 

47 

40 

38 

40 

42 

44 

46 

50 

9 

5 

2 

60  68    55 

51 

48 

45 

60 

48 

60 

61 

53 

55 

TABLE  2L                                           [Page  696  ] 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer  30  inches. — Fahrenheit's  Thermometer  50°.] 

Moon's 

Horizontal  parallax. 

Ox" 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

app.  alt. 

minutes 
of  alt. 

64' 

66' 

66' 

57' 

58' 

69' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

o    / 

/   // 

'   // 

'  n 

/   // 

'  n 

'   // 

>      II 

'  II 

II 

II 

II 

II 

II 

„ 

Snh. 

20  0 

48  6 

49  3 

49  69 

50  56 

51  52 

52  49 

53  45 

54  42 

0 

0 

2 

4 

6 

8 

V 

(y 

10 

5 

2 

58 

55 

51 

47 

43 

40 

10 

9 

11 

13 

15 

17 

2 

0 

20 

3 

0 

56 

52 

49 

45 

41 

37 

20 

19 

21 

23 

24 

26 

3 

30 

1 

48  58 

53 

50 

46 

42 

38 

35 

30 

28 

30 

32 

34 

36 

4 

40 

59 

56 

52 

48 

44 

40 

36 

33 

40 

38 

39 

41 

43 

4o 

5 

50 

57 

54 

50 

46 

42 
51  39 

38 

34 
53  31 

30 

50 
0 

47 
0 

49 
2 

51 
4 

53 
6 

54 

7 

6 

7 

21  0 

47  55 

48  51 

49  47 

50  43 

52  35 

54  28 

10 

53 

49 

45 

41 

37 

33 

29 

26 

10 

9 

11 

13 

15 

17 

8 

20 

51 

47 

43 

39 

35 

31 

27 

23 

20 

19 

21 

22 

24 

26 

9 

2 

30 

48 

44 

40 

36 

32 

28 

24 

20 

30 

28 

30 

32 

34 

35 

40 

46 

42 

38 

33 

29 

25 

21 

17 

40 

37 

39 

41 

43 

45 

50 

43 

39 

35 

31 

27 

22 

18 
53  16 

14 

50 

47 
0' 

49 
2 

50 
4 

52 
6 

54 
7 

22  0 

47  42 

48  37 

49  33 

50  29 

51  25 

52  20 

54  11 

0 

10 

40 

35 

30 

26 

22 

17 

13 

8 

10 

9 

11 

13 

15 

17 

20 

37 

32 

27 

23 

19 

14 

10 

5 

20 

19 

20 

22 

24 

26 

30 

34 

30 

25 

20 

16 

11 

7 

3 

30 

28 

30 

31 

33 

35 

40 

32 

27 

22 

18 

13 

9 

4 

0 

40 

37 

39 

41 

43 

45 

50 

29 
47  27 

25 

20 

15 

11 

6 

1 
52  58 

53  57 

50 
0 

46 
0 

48 
2 

50 

4 

52 
6 

54 

7 

23  0 

48  22 

49  17 

50  13 

51  8 

52  3 

53  54 

10 

25 

20 

15 

10 

5 

0 

55 

51 

10 

9 

11 

13 

15 

17 

20 

22 

17 

12 

7 

2 

51  57 

52 

48 

20 

18 

20 

22 

24 

26 

30 

19 

14 

9 

4 

0 

54 

49 

45 

30 

28 

29 

31 

33 

35 

40 

16 

11 

6 

1 

50  57 

51 

46 

42 

40 

37 

39 

40 

42 

44 

50 

13 

8 

3 

49  58 
49  55 

54 
50  50 

48 

43 

38 

50 

46 
0 

48 
2 

50 
4 

51 
5 

53 

7 

1 

0 

24  0 

47  10 

48  5 

49  0 

51  45 

52  40 

53  35 

0 

10 

8 

3 

48  57 

52 

47 

42 

37 

32 

.10 

9 

11 

13 

15 

16 

2 

1 

20 

5 

0 

54 

49 

44 

39 

33 

28 

20 

18 

20 

22 

24 

26 

3 

1 

30 

2 

47  57 

51 

46 

41 

35 

30 

24 

30 

27 

29 

30 

32 

34 

4 

1 

40 

46  59 

54 

48 

43 

38 

32 

27 

21 

40 

36 

38 

40 

42 

44 

5 

2 

50 
25  0 

56 
46  53 

51 
47  48 

45 

40 

35 

29 

23 
52  20 

18 

50 

46 

47 
2 

49 
4 

51 
5 

53 

7 

6 

7 

2 
2 

48  42 

49  37 

50  31 

51  26 

53  14 

0 

0 

10 

50 

45 

39 

33 

28 

22 

16 

10 

10 

9 

11 

13 

14 

16 

8 

2 

20 

46 

41 

35 

29 

24 

18 

12 

6 

20 

18 

20 

22 

24 

25 

9 

3 

30 

43 

38 

32 

26 

20 

14 

8 

3 

30 

27 

29 

31 

33 

34 

40 

40 

34 

28 

23 

17 

11 

5 

52  59 

40 

36 

38 

40 

42 

43 

50 
26  0 

37 

31 

25 

19 

14 
50  10 

7 

1 

56 

50 

45 
0 

47 
2 

49 

4 

51 
5 

52 

7 

46  34 

47  28 

48  22 

49  16 

51  4 

51  58 

52  52 

0- 

10 

31 

25 

19 

13 

7 

1 

54 

48 

10 

9 

11 

13 

14 

16 

20 

27 

21 

15 

9 

3 

50  57 

50 

44 

20 

18 

20 

22 

23 

25 

30 

24 

18 

12 

6 

49  59 

53 

46 

40 

30 

27 

29 

31 

32 

34 

40 

20 

14 

8 

2 

55 

49 

42 

36 

40 

36 

38 

39 

41 

43 

50 

17 
46  14 

11 

4 

48  58 

51 

45 

38 

32 
"52  28 

50 
0 

45 
0 

47 
2 

48 
4 

50 
5 

52 

7 

1 

0 

27  0 

47  7 

48  1 

48  54 

49  48 

50  41 

51  35 

10 

11 

4 

47  58 

51 

44 

37 

31 

24 

10 

9 

11 

12 

14 

16 

2 

1 

20 

7 

1 

54 

47 

40 

33 

27 

20 

20 

18 

20 

21 

23 

25 

3 

1 

30 

3 

46  57 

50 

43 

36 

29 

23 

16 

30 

27 

28 

30 

32 

34 

4 

1 

40 

45  59 

53 

46 

39 

32 

25 

19 

12 

40 

36 

37 

39 

41 

43 

5 

o 

50 

56 
45  53 

49 
46  46 

42 
47  38 

35 

28 
49  24 

21 

15 

8 

50 
0 

44 
0 

46 
2 

48 
4 

50 
5 

52 

7 

6 

7 

2 
3 

28  0 

48  31 

50  17 

51  11 

52  4 

10 

49 

42 

34 

27 

20 

13 

6 

5159 

10 

9 

11 

12 

14 

16 

8 

3 

20 

45 

38 

30 

23 

16 

9 

2 

55 

20 

18 

19 

21 

23 

,25 

9 

3 

30 

41 

34 

26 

19 

12 

5 

50  57 

50 

30 

26 

28 

30 

:32 

33 

40 

37 

30 

23 

15 

8 

1 

54 

46 

40 

35 

37 

39 

41 

42 

50 

34 

45  30 

26 

19 
47  15 

11 

4 

49  57 

49 

42 

50 

44 
0 

46 
2 

48 
4 

49 
5 

51 

7 

29  0 

46  22 

48  7 

49  0 

49  53 

50  45 

5138 

0 

10 

26 

18 

11 

3 

48  56 

49 

40 

34 

10 

9 

10 

12 

14 

16 

20 

22 

14 

7 

47  59 

52 

44 

36 

29 

20 

17 

19 

21 

23 

24 

30 

18 

10 

2 

55 

47 

39 

31 

24 

30 

26 

28 

30 

31 

33 

40 

14 

6 

46 

58 

51 

43 

35 

27 

20 

40 

35  ;  37 

38 

40 

42 

50 

11 

3 

55 

47 

39 

31 

23 

15 

50 

44  45 

47 

49 

51 

Page  696] 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction.          | 

[Barometer 

30  inches.— Fahrenheit's  Thermometer  50°.] 

1 

Moon's 

Horizontal  parallax. 

^5 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

app.  alt. 

minutes 
of  alt. 

54' 

66' 

56' 

67' 

58' 

59' 

ec 

61' 

0" 

2" 

4" 

II 

6" 

II 

8" 

O   / 

/  // 

/  // 

/  // 

/  It 

/  // 

/  II 

1    II 

/  II 

II 

II 

// 

II 

Sub. 

30  0 

45  6 

45  57 

46  50 

47  42 

48  34 

49  26 

50  18 

61  10 

0 

0 

2 

3 

6 

7 

V  Q" 

10 

2 

64 

46 

38 

30 

22 

13 

6 

10 

9 

10 

12 

14 

16 

2  1 

20 

44  58 

50 

42 

34 

26 

18 

9 

1 

20 

17 

19 

21 

23 

24 

3  1 

30 

54 

46 

37 

29 

21 

13 

4 

50  56 

30 

26 

28 

29 

31 

33 

4  2 

40 

50 

42 

33 

25 

17 

8 

0 

52 

40 

35 

36 

38 

40 

42 

6  2 

50 

45 

38 

29 

21 

12 

4 

49  65 
49  50 

47 
50  42 

50 
0 

43 
0 

45 
2 

47 
3 

49 
5 

50 

7 

6  3 

7  3 

31  0 

44  41 

45  33 

46  24 

47  16 

48  7 

48  59 

10 

37 

29 

20 

12 

2 

54 

45 

37 

10 

9 

10 

12 

14 

15 

8  4 

20 

33 

24 

15 

7 

47  58 

49 

40 

32 

20 

17 

19 

21 

22 

24 

9  4 

30 

28 

20 

11 

2 

54 

46 

36 

27 

30 

26 

27 

29 

31 

32 

40 

24 

16 

7 

46  58 

49 

40 

31 

22 

40 

34 

36 

38 

39 

41 

50 

20 

11 

2 

53 

44 

35 

26 

17 

50 

43 

44 
2 

46 
3 

48 
5 

50 

7 

32  0 

44  15 

45  7 

45  58 

46  49 

47  40 

48  31 

49  22 

50  13 

0 

0 

10 

11 

3 

53 

44 

35 

26 

17 

8 

10 

8 

10 

12 

14 

15 

20 

7 

44  58 

48 

39 

30 

21 

11 

2 

20 

17 

19 

20 

22 

24 

30 

3 

53 

44 

34 

25 

16 

6 

49  57 

30 

26 

27 

29 

30 

32 

40 

43  58 

48 

39 

29 

20 

11 

1 

52 

40 

34 

35 

37 

39 

41 

50 

54 

44 

34 

24 

15 

6 

48  56 

47 

50 

42 
0 

44 
2 

46 
3 

47 
5 

49 

7 

1  0 

33  0 

43  48 

44  39 

45  29 

46  19 

47  10 

48  0 

48  50 

49  41 

0 

10 

44 

34 

26 

15 

5 

47  55 

45 

36 

10 

8 

10 

12 

13 

15 

2  1 

20 

40 

30 

20 

10 

0 

50 

40 

31 

20 

17 

18 

20 

22 

23 

3  1 

30 

35 

25 

15 

5 

46  55 

45 

35 

25 

30 

25 

27 

28 

30 

32 

4  2 

40 

30 

20 

10 

0 

60 

40 

30 

20 

40 

33 

35 

37 

38 

40 

5  2 

50 

25 

15 

6 

45  55 

45 
46  40 

36 

24 

14 

50 

42 
0 

43 

2 

45 
3 

47 
5 

48 

7 

6  3 

7  3 

34  0 

43  21 

44  11 

45  0 

45  50 

47  30 

48  19 

49  9 

0 

10 

16 

6 

44  55 

45 

34 

24 

14 

3 

10 

8 

10 

12 

13 

15 

8  4 

20 

11 

1 

50 

40 

29 

19 

9 

48  58 

20 

17 

18 

20 

21 

23 

9  4 

30 

6 

43  66 

45 

35 

24 

13 

3 

52 

30 

25 

26 

28 

30 

31 

40 

1 

61 

40 

30 

19 

8 

47  58 

47 

40 

33 

35 

36 

38 

40 

50 

42  56 

46 

35 

24 

14 

3 

52 

42 

50 

41 

43 

44 
3 

46 
5 

48 

7 

35  0 

42  52 

43  41 

44  30 

45  19 

46  9 

46  58 

47  47 

48  36 

0 

0 

2 

10 

47 

36 

25 

14 

3 

52 

41 

30 

10 

8 

10 

11 

13 

15 

20 

42 

31 

20 

9 

45  58 

47 

36 

25 

20 

16 

18 

20 

21 

23 

30 

37 

26 

15 

3 

52 

41 

30 

19 

30 

24 

26 

28 

29 

31 

40 

32 

21 

10 

44  58 

47 

36 

26 

14 

40 

33 

34 

36 

38 

39 

50 

27 

16 

4 

53 

42 

30 

19 

8 

50 

41 

42 

2 

44 
3 

46 
5 

47 
6 

36  0 

42  22 

43  11 

43  69 

44  48 

45  37 

46  25 

47  14 

48  2 

0 

0 

10 

17 

5 

54 

42 

31 

19 

8 

47  56 

10 

8 

10 

11 

13 

14 

1  1 

20 

12 

0 

48 

37 

25 

14 

2 

50 

20 

16 

18 

19 

21 

23 

2  1 

30 

7 

42  55 

43 

31 

20 

8 

46  56 

44 

30 

24 

26 

27 

29 

31 

3  2 

40 

1 

50 

38 

26 

14 

2 

50 

39 

40 

32 

34 

35 

37 

39 

4  2 

50 

41  56 

44 

32 

20 

8 

45  56 

44 

33 

60 

40 
0 

42 
2 

43 
3 

45 
6 

47 
6 

5  3 

6  3 

37  0 

41  51 

42  39 

43  27 

44  15 

45  3 

45  51 

46  39 

47  27 

0 

10 

46 

34 

21 

9 

44  67 

46 

33 

21 

10 

8 

10 

11 

13 

14 

7  4 

20 

41 

29 

16 

4 

52 

40 

27 

15 

20 

16 

17 

19 

21 

22 

8  4 

30 

35 

23 

11 

43  58 

46 

34 

21 

9 

30 

24 

25 

27 

29 

30 

9  5 

40 

30 

18 

5 

53 

40 

28 

16 

3 

40 

32 

33 

35 

37 

38 

50 

25 

12 

42  59 

47 

34 
44  29 

22 

9 
46  3 

46  57 

50 
0 

40 
0 

41 
2 

43 
3 

46 
5 

46 
6 

38  0 

41  19 

42  7 

42  54 

43  41 

46  16 

46  51 

10 

14 

2 

49 

36 

23 

10 

45  57 

45 

10 

8 

9 

11 

13 

14 

20 

.  8 

41  56 

43 

30 

17 

4 

51 

38 

20 

16 

17 

19 

20 

22 

30 

3 

■   51 

38 

24 

12 

44  58 

46 

32 

30 

23 

25 

27 

28 

30 

40 

40  58 

45 

32 

18 

6 

52 

39 

26 

40 

31 

33 

35 

36 

38 

50 

52 

39 

26 

13 

43  7 

0 

46 

33 

20 

50 

39 

41 
2 

42 
3 

44 

5 

46 
6 

39  0 

40  47 

41  33 

42  20 

43  54 

44  40 

45  27 

46  13 

0 

0 

10 

42 

28 

15 

1 

48 

34 

21 

7 

10 

8 

9 

11 

12 

14 

1  1 

20 

36 

23 

9 

42  55 

42 

28 

15 

1 

20 

16 

17 

19 

20 

22 

2  1 

30 

30 

17 

3 

49 

36 

22 

8 

45  54 

80 

23 

25 

26 

28 

29 

3  2 

40 

26 

11 

41  57 

43 

30 

16 

2 

48 

40 

31 

32 

34 

36 

37 

4  2 

50 

19 

5 

51 

37 

23 

9 

44  56 

42 

50 

39 

40 

42 

43 

45 

5  3 

I 

TABLE  24. 

[Page  697  1 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction.          | 

[Barometer 

30  inches.— Fahrenheit's  Thermometer  60°.] 

Horizontal  parallax. 

B  OS 

Correction  for  seconds  of 
parallax. — Add. 

Corr. 

Moon's 
app.  alt. 

Si 

for 
minutes 

64' 

56' 

66' 

57' 

58' 

69' 

ec 

61' 

9.  ss 

0" 

•ill 

4" 

6" 

8" 

of  alt. 

o   / 

1      II 

/  II 

/   // 

/  II 

/  II 

/  II 

1      n 

'  II 

II 

n 

II 

II 

II 

II 

Sub. 

40  0 

40  14 

41  0 

41  46 

42  32 

43  18 

44  4 

44  50 

45  36 

0 

0 

2 

3 

5 

6 

&    Z" 

10 

8 

40  54 

39 

25 

11 

43  57 

43 

29 

10 

8 

9 

11 

12 

14 

7     4 

20 

2 

48 

33 

19 

5 

50 

36 

22 

20 

15 

17 

18 

20 

21 

8  5 

30 

39  56 

42 

28 

13 

42  59 

44 

30 

16 

30 

23 

24 

26 

27 

29 

9  5 

40 

50 

36 

22 

7 

53 

38 

24 

9 

40 

30 

32 

34 

36 

37 

50 

45 

30 

16 

1 

47. 

32 

18 

3 
44  56 

50 
0 

38 
0 

40 
2 

41 
3 

43 

5 

44 
6 

41  0 

39  39 

40  24 

41  10 

41  55 

42  41 

43  26 

44  11 

10 

33 

18 

4 

49 

34 

19 

4 

49 

10 

8 

9 

11 

12 

14 

20 

27 

12 

40  58 

43 

28 

13 

43  58 

43 

20 

15 

17 

18 

20 

21 

30 

21 

6 

51 

36 

22 

7 

51 

37 

30 

23 

24 

26 

27 

29 

40 

16 

0 

45 

30 

16 

0 

45 

30 

40 

30 

32 

33 

35 

36 

50 

10 

39  54 
39  48 

39 

24 

9 
42  2 

42  53 

38 

23 

50 
0 

38 
0 

39 

1 

41 
3 

42 
4 

44 
6 

42  0 

39  4 

40  33 

41  17 

42  47 

43  31 

44  16 

10 

38  58 

42 

27 

11 

41  56 

41 

25 

10 

10 

7 

9 

10 

12 

13 

1  1 

20 

52 

36 

21 

5 

50 

34 

18 

3 

20 

15 

16 

18 

19 

21 

2  1 

30 

46 

30 

14 

40  68 

43 

27 

11 

43  56 

30 

22 

24 

25 

27 

28 

3  2 

40 

40 

24 

8 

52 

36 

21 

5 

49 

40 

30 

31 

33 

34 

36 

4  2 

50 

34 

18 

2 

46 

30 

14 

42  58 

42 

50 

37 
0 

38 

1 

40 
3 

41 
4 

43 
6 

6  3 
6  4 

43  0 

38  28 

39  12 

39  56 

40  40 

41  24 

42  8 

42  52 

43  36 

0 

10 

22 

6 

50 

34 

18 

1 

46 

29 

10 

7 

9 

10 

12 

13 

7  4 

20 

16 

38  59 

43 

27 

11 

41  54 

38 

22 

20 

15 

16 

18 

19 

20 

8  5 

30 

10 

53 

37 

20 

5 

48 

31 

15 

30 

22 

23 

25 

26 

28 

9  5 

40 

4 

47 

30 

14 

40  58 

41 

24 

8 

40 

29 

31 

32 

34 

36 

50 

37  57 

41 

24 

7 

51 

34 

17 

1 

50 

37 
0 

38 

1 

39 
3 

41 
4 

42 
6 

44  0 

37  51 

38  35 

39  18 

40  1 

40  44 

41  27 

42  10 

42  54 

0 

10 

45 

28 

11 

39  54 

37 

20 

3 

46 

10 

7 

9 

10 

11 

13 

20 

38 

21 

4 

47 

30 

13 

41  56 

39 

20 

14 

16 

17 

19 

20 

30 

32 

15 

38  58 

41 

24 

7 

49 

32 

30 

21 

23 

24 

26 

27 

40 

26 

9 

51 

34 

17 

0 

42 

26 

40 

29 

30 

31 

33 

34 

50 

20 

2 

44 

27 

10 
40  3 

40  53 

35 

18 

50 

36 

37 

1 

39 
3 

40 
4 

41 
6 

1  1 

45  0 

37  14 

37  56 

38  38 

39  21 

40  46 

41  28 

42  11 

0 

0 

10 

7 

49 

31 

14 

39  56 

39 

21 

3 

10 

7 

8 

10 

11 

13 

2  1 

20 

0 

43 

25 

7 

49 

32 

14 

41  56 

20 

14 

15 

17 

18 

20 

3  2 

30 

36  54 

37 

18 

1 

43 

25 

7 

49 

30 

21 

23 

24 

25 

27 

4  3 

40 

48 

30  1   11 

38  54 

36 

18 

0 

42 

40 

28 

30 

31 

32 

34 

5  3 

50 

41 

23 

4 

47 

29 

11 

40  52 

34 

50 

35 

37 
1 

38 
3 

39 
4 

41 
6 

6  4 

7  5 

46  0 

36  35 

37  17 

37  58 

38  40 

39  22 

40  4 

40  46 

41  27 

0 

0 

10 

29 

10 

51 

33 

15 

39  57 

38 

20 

10 

7 

8 

10 

11 

12 

8  6 

20 

22 

3 

44 

26 

8 

49 

31 

12 

20 

14 

15 

17 

18 

19 

9  6 

30 

16 

36  57 

38 

20 

1 

42 

24 

5 

30 

21 

22 

23 

25 

26 

40 

9 

50 

32 

13 

38  54 

35 

17 

40  58 

40 

28 

29 

30 

32 

33 

50 

2 

43  1   25 

6 

47 

28 

9 

50 

50 

35 

36 
1 

37 
3 

39 
4 

40 
6 

47  0 

35  56 

36  37 

37  18 

37  59 

38  40 

39  21 

40  2 

40  43 

0 

0 

10 

49 

30 

11 

52 

34 

14 

39  55 

36 

10 

7 

8 

10 

11 

12 

20 

42 

23 

4 

45 

26 

6 

47 

28 

20 

14 

15 

16 

18 

19 

30 

36 

17 

36  57 

38 

19 

38  59 

40 

21 

30 

20 

22 

23 

24 

26 

40 

30 

10 

50 

31 

12 

52 

32 

13 

40 

27 

29 

30 

31 

33 

50 

23 

3 

43 

24 

5 

45 

25 

5 

50 

34 
0 

35 

1 

37 
3 

38 
4 

39 
5 

1  1 

48  0 

35  16 

35  56 

36  36 

37  17 

37  57 

38  37 

39  17 

39  58 

0 

10 

10 

50 

30 

10 

50 

30 

10 

50 

10 

7 

8 

9 

11 

12 

2  1 

20 

3 

43 

23 

2 

43 

22 

2 

42 

20 

13 

15 

16 

17 

19 

3  2 

30 

34  56 

36 

16 

36  55 

35 

15 

38  55 

34 

30 

20 

21 

23 

24 

25 

4  3 

40 

49 

29 

9 

48 

28 

8 

48 

27 

40 

27 

28 

29 

31 

32 

5  3 

50 

42 

22 
35  15 

1 

41 

21 

0 

40 

19 

50 

33 

36 

1 

36 
3 

37 

4 

39 
5 

6  4 

7  6 

49  0 

34  35 

35  54 

36  34 

37  13 

37  53 

38  32 

39  11 

0 

0 

10 

29 

8 

47 

27 

6 

46 

25 

4 

10 

7 

8 

9 

10 

12 

8  5 

20 

22 

1 

40 

20 

36  59 

38 

17 

38  56 

20 

13 

14 

16 

17 

18 

9  6 

30 

15 

34  54 

33 

12 

51 

30 

9 

48 

30 

20 

21 

22 

23 

25 

40 

8 

47 

26 

5 

44 

23 

2 

41 

40 

26 

27 

29 

30 

31 

50 

1 

40 

19 

35  58 

36 

15 

37  54 

33 

50 

33 

34 

35 

36 

38 

Page  698] 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction.           | 

[Baremeter  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 

for 

minutes 

64' 

66' 

66' 

67' 

58' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

of  alt. 

O    ' 

'   // 

»  II 

>      II 

'  II 

1     II 

»  II 

'  II 

'  II 

II 

// 

II 

II 

II 

II 

50  0 

33  54 

34  33 

35  11 

35  50 

36  29 

37  8 

37  46 

38  25 

0 

0 

1 

3 

4 

5 

10 

47 

26 

4 

43 

21 

0 

38 

17 

10 

6 

8 

9 

10 

12 

20 

40 

19 

84  57 

36 

14 

36  53 

31 

9 

20 

13 

14 

15 

17 

18 

30 

33 

11 

49 

28 

6 

45 

23 

1 

30 

19 

20 

22 

23 

24 

40 

26 

4 

42 

20 

35  58 

37 

15 

37  53 

40 

26 

27 

28 

29 

31 

50 

19 

33  57 

35 
34  28 

13 
35  6 

51 

29 

7 

45 

50 

32 

33 

35 

36 
4 

37 
5 

Sub. 

51  0 

33  12 

33  50 

35  44 

36  22 

36  59 

37  37 

0 

0 

1 

3 

10 

5 

43 

21 

34  58 

36 

14 

51 

29 

10 

6 

8 

9 

10 

11 

2  1 

20 

32  58 

36 

13 

50 

28 

6 

43 

21 

20 

13 

14 

15 

16 

18 

3  2 

30 

51 

29 

6 

43 

21 

35  58 

36 

13 

30 

19 

20 

21 

23 

24 

4  3 

40 

44 

22 

33  59 

36 

14 

50 

28 

5 

40 

25 

26 

28 

29 

30 

6  4 

50 

37 

14 
33  7 

51 

28 

6 

42 

20 

36  57 

50 

31 

33 

1 

34 

2 

35 
4 

36 
5 

6  4 

7  5 

52  0 

32  50 

33  44 

34  21 

34  58 

36  35 

36  12 

36  49 

0 

0 

10 

23 

0 

36 

13 

50 

27 

4 

41 

10 

6 

7 

9 

10 

11 

8  6 

20 

15 

32  52 

29 

6 

43 

19 

35  56 

33 

20 

12 

13 

15 

16 

17 

9  6 

30 

8 

45 

21 

33  58 

35 

11 

48 

24 

30 

18 

20 

21 

22 

23 

40 

1 

38 

14 

50 

27 

3 

40 

16 

40 

24 

26 

27 

28 

29 

50 

31  54 

31 

7 

43 
33  35 

19 
34  11 

34  55 

32 

8 
36  0 

50 
0 

31 
0 

32 

1 

33 
2 

34 
4 

35 
5 

53  0 

31  47 

32  23 

32  59 

34  47 

35  24 

10 

39 

15 

51 

27 

3 

39 

15 

35  51 

10 

6 

7- 

8 

10 

11 

20 

32 

8 

44 

20 

33  56 

31 

7 

43 

20 

12 

13 

14 

16 

17 

30 

25 

0 

36 

12 

48 

23 

34  59 

35 

30 

18 

19 

20 

22 

23 

40 

17 

31  53 

28 

4 

40 

15 

51 

27 

40 

24 

25 

26 

28 

29 

50 

10 

46 

21 

32  57 

32 
33  24 

7 

43 

34  35 

19 

50 

30 

31 

32 
2 

34 
4 

35 
6 

54  0 

31  3 

31  38 

32  13 

32  49 

33  59 

35  10 

0 

0 

1 

10 

30  55 

30 

5 

41 

16 

51 

26 

1 

10 

6 

7 

8 

9 

11 

20 

48 

22 

31  57 

33 

8 

43 

18 

34  53 

20 

12 

13 

14 

15 

16 

30 

40 

15 

49 

25 

0 

35 

10 

45 

30 

18 

19 

20 

21 

22 

40 

33 

8 

42 

17 

32  52 

27 

1 

37 

40 

23 

25 

26 

27 

28 

50 

26 

0 

35 

9 

44 

19 

33  53 

28 

50 

29 
0 

30 
1 

32 
2 

33 
3 

34 

5 

55  0 

30  18 

30  52 

31  27 

32  1 

32  36 

33  10 

33  45 

34  19 

0 

10 

10 

45 

19 

31  53 

28 

2 

36 

11 

10 

6 

7 

8 

9 

10 

20 

3 

38 

12 

46 

20 

32  54 

28 

3 

20 

11 

13 

14 

15 

16 

30 

29  55 

30 

4 

38 

12 

46 

20 

33  54 

30 

17 

18 

19 

20 

22 

40 

48 

22 

30  56 

30 

4 

37 

11 

45 

40 

23 

24 

25 

26 

27 

50 
66  0 

40 

14 

48 

22 

31  55 

29 

3 

37 

50 

28 

30 
1 

31 
2 

32 
3 

33 
4 

29  33 

30  7 

30  40 

31  14 

31  47 

32  21 

32  55 

33  28 

0 

0 

10 

25 

29  59 

32 

6 

39 

13 

46 

20 

10 

6 

7 

8 

9 

10 

20 

18 

51 

24 

30  58 

31 

4 

37 

11 

20 

11 

12 

13 

14 

16 

30 

10 

43 

16 

60 

23 

31  56 

29 

2 

30 

17 

18 

19 

20 

21 

1  1 

40 

3 

36 

9 

42 

16 

48 

21 

32  64 

40 

22 

23 

24 

25 

27 

2  2 

50 

28  55 

28 

1 

34 

7 

40 

12 
32  3 

46 

50 

28 
0 

29 
1 

30 
2 

31 
3 

32 
4 

3  2 

4  3 

57  0 

28  47 

29  20 

29  53 

30  25 

30  58 

31  31 

32  36 

0 

10 

39 

12 

45 

17 

50 

22 

31  55 

27 

10 

6 

6 

7 

9 

10 

5  4 

20 

32 

5 

37 

9 

42 

14 

47 

19 

20 

11 

12 

13 

14 

16 

6  6 

30 

24 

28  57 

29 

1 

33 

6 

38 

10 

30 

16 

17 

18 

19 

21 

7  5 

40 

17 

49 

21 

29  53 

25 

30  67 

29 

1 

40 

22 

23 

24 

25 

26 

8  6 

50 

9 

41 

13 

45 

17 

49 

21 

3162 

50 
0 

27 
0 

28 
1 

29 
2 

30 
3 

31 
4 

9  7 

58  0 

28  1 

28  33 

29  5 

29  37 

30  9 

30  41 

31  12 

3144 

10 

27  53 

25 

28  57 

28 

0 

32 

4 

35 

10 

5 

6 

7 

8 

9 

20 

45 

17 

49 

20 

29  52 

23 

30  55 

26 

20 

10 

12 

13 

14 

16 

30 

38 

9 

41 

12 

44 

15 

46 

17 

30 

16 

17 

18 

19 

20 

40 

30 

1 

33     4  1 

35 

6 

38 

9 

40 

21 

22 

23 

24 

26 

50 

.22 
27  14 

27  53 

24 

28  55 

27 

29  58 

29 
30  20 

0 
30  61 

60 
0 

26 
0 

27 

1 

28 
2 

29 
3 

30 
4 

59  0 

27  45 

28  16 

28  47 

29  18 

29  49 

10 

6 

37 

7 

38 

9 

40 

11 

42 

10 

5 

6 

7 

8 

9 

20 

26  58 

29 

27  59 

30 

1 

31 

2 

33  20  1 

10 

11 

12 

13 

14 

30 

51 

21 

51 

22 

28  53 

23 

29  54 

24 

30  15 

16 

17 

18 

19 

40 

43 

13 

43 

14 

44 

14 

45 

16 

40  20 

21 

22 

23 

24 

50 

35 

5 

35 

5 

36 

6    36     6| 

50  25 

26 

27 

29 

30 

TABLE  24. 

[Page 

699 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction, 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
spp.  alt. 

Horizontal  parallax. 

§2 

Correction  for  seconds  of 
parallax. — Add. 

Corr. 

for 

minutes 

54' 

65' 

56' 

57' 

58' 

59' 

60' 

61' 

1^ 

0" 

2" 
II 

4" 
II 

6" 

II 

8" 
n 

of  alt. 

0   / 

'  n 

/  // 

t      II 

'   // 

1     II 

1      II 

'  II 

r       II 

II 

60  0 

26  26 

26  57 

27  27 

27  57 

28  27 

28  57 

29  27 

29  57 

0 

0 

1 

2 

3 

4 

10 

19 

49 

19 

49 

19 

49 

18 

48 

10 

5 

6 

7 

8 

9 

20 

11 

41 

11 

40 

10 

40 

9 

39 

20 

10 

11 

12 

13 

14 

30 

3 

32 

2 

31 

1 

31 

0 

30 

30 

15 

16 

17 

18 

19 

40 

25  55 

24 

26  53 

23 

27  53 

22 

28  51 

21 

40 

20 

21 

22 

23 

24 

50 

47 

16 

45 

14 

44 

13 

42 

12 

50 

25 
0 

26 
1 

27 
2 

28 
3 

29 
4 

61  0 

25  39 

26  8 

26  37 

27  6 

27  36 

28  5 

28  34 

29  3 

0 

10 

31 

0 

29 

26  58 

27 

27  56 

25 

28  54 

10 

5 

6 

7 

8 

9 

20 

23 

25  52 

20 

49 

18 

47 

16 

45 

20 

10 

11 

12 

12 

13 

30 

15 

43 

12 

40 

10 

38 

7 

35 

30 

14 

15 

16 

17 

18 

40 

7 

35 

4 

32 

1 

29 

27  58 

26 

40 

19 

20 

21 

22 

23 

50 

24  59 

27 

25  55 

24 

26  52 

20 

49 

17 
28  8 

50 
0 

24 
0 

25 
1 

26 
2 

27 
3 

28 
4 

62  0 

24  50 

25  19 

25  47 

26  15 

26  43 

27  11 

27  40 

10 

42 

10 

38 

6 

34 

2 

30 

27  58 

10 

5 

6 

6 

7 

8 

20 

34 

2 

29 

25  57 

25 

26  53 

21 

49 

20 

9 

10 

11 

12 

12 

30 

26 

24  54 

21 

49 

17 

45 

12 

40 

30 

14 

15 

16 

17 

18 

40 

18 

46 

13 

41 

8 

36 

3    31 

40 

19 

19 

20 

21 

22 

50 

10 

37 

4 

32 

25  59 

27 

26  54 

21 

50 

23 

24 

1 

25 
2 

26 
3 

27 
4 

63  0 

24  2 

24  29 

24  56 

25  23 

25  51 

26  18 

26  45 

27  12 

0 

0 

10 

23  54 

21 

48 

15 

42 

9 

36 

3 

10 

4 

5 

6 

7 

8 

20 

46 

13 

39 

6 

33 

0 

27 

26  54 

20 

9 

10 

11 

12 

13 

30 

37 

4 

31 

24  58 

24 

25  51 

18 

45 

30 

13 

14 

15 

16 

17 

40 

29 

23  55 

22 

49 

15 

42 

8 

35 

40 

18 

19 

20 

21 

22 

50 

20 

47 

13 

40 

6 

33 

25  59 

26 

50 

22 
0 

23 

1 

24 
2 

25 

26 

64  0 

23  12 

23  39 

24  5 

24  32 

24  58 

25  24 

25  50 

26  17 

0 

3 

3 

10 

4 

31 

23  57 

23 

49 

15 

41 

8 

10 

4 

5 

6 

7 

8 

20 

22  56 

22 

48 

14 

40 

6 

32 

25  58 

20 

9 

10 

10 

11 

12 

30 

47 

13 

39 

5 

31 

24  57 

22 

48 

30 

13 

14 

15 

16 

16 

40 

39 

5 

30 

23  56 

22 

48 

13 

39 

40 

17 

18 

19 

20 

21 

50 

31 

22  57 

22 

48 

13 
24  4 

39 

4 

30 

50 

22 
0 

23 

1 

23 
2 

24 
2 

25 
3 

Sub. 

65  0 

22  23 

22  48 

23  13 

23  39 

24  30 

24  55 

25  21 

0 

10 

14 

40 

5 

30 

23  55 

20 

46 

11 

10 

4 

5 

6 

7 

7 

V  V 

20 

6 

31 

22  56 

21 

46 

11 

36 

1 

20 

8 

9 

10 

11 

12 

2  2 

30 

21  58 

23 

48 

13 

37 

2 

27 

24  52 

30 

13 

13 

14 

15 

16 

3  3 

40 

49 

14 

39 

4 

28 

23  53 

18 

43 

40 

17 

18 

18 

19 

20 

4  4 

50 
66  0 

41 

6 

30 

22  55 

19 
23  10 

44 

8 

33 

50 

21 

22 

23 
2 

23 
2 

24 
3 

5  5 

6  5 

21  32 

21  57 

22  21 

22  46 

23  35 

23  59 

24  23 

0 

0 

1 

10 

24 

48 

12 

37 

1 

25 

49 

14 

10 

4 

5 

6 

7 

7 

7  6 

20 

15 

39 

3 

28 

22  52 

15 

40 

4 

20 

8 

9 

10 

11 

11 

8  7 

30 

7 

31 

21  55 

19 

43 

6 

31 

23  55 

30 

12 

13 

14 

15 

16 

9  8 

40 

20  59 

22 

46 

10 

34 

22  57 

21 

45 

40 

16 

17 

18 

19 

20 

50 

50 

14 

37 

1 

25 

48 

12 

36 

50 

20 
0 

21 

1 

22 
2 

23 
2 

24 
3 

67  0 

20  41 

21  5 

21  28 

21  52 

22  15 

22  39 

23  2 

23  26 

0 

10 

33 

20  56 

19 

43 

6 

29 

22  52 

16 

10 

4 

5 

5 

6 

7 

20 

25 

48 

11 

34 

21  57 

20 

43 

7 

20 

8 

8 

9 

10 

11 

30 

16 

39 

2 

25 

48 

11 

34 

22  57 

30 

12 

12 

13 

14 

15 

40 

8 

30 

20  53 

16 

39 

2 

24 

47 

40 

15 

16 

17 

18 

18 

50 

19  59 

21 

44 

7 

30 

21  52 

15 

37 

50 

19 

20 
1 

21 
1 

22 
2 

22 
3 

68  0 

19  50 

20  13 

20  35 

20  58 

21  21 

21  43 

22  5 

22  28 

0 

0 

10 

42 

4 

27 

49 

12 

34 

21  56 

19 

10 

4 

4 

5 

6 

7 

20 

33 

19  56 

18 

40 

2 

24 

47 

9 

20 

7 

8 

9 

9 

10 

30 

25 

47 

9 

31 

20  53 

15 

37 

21  59 

30 

11 

12 

13 

13 

14 

40 

16 

38 

0 

22 

44 

5 

27 

49 

40 

15 

16 

16 

17 

18 

50 

7 

29 

19  51 

13 

34 

20  56 

17 
21  8 

39 

50 
0 

18 
0 

19 
1 

20 
1 

21 
2 

21 
3 

69  0 

18  59 

19  21 

19  42 

20  4 

20  25 

20  47 

21  30 

10 

50 

12 

33 

19  55 

16 

37 

20  59 

20 

10 

4 

4 

5 

6 

6 

r          20 

42 

3 

24 

45 

7 

28 

49 

10 

20 

7 

8 

8 

9 

10 

30 

33 

18  54 

15 

36 

19  57 

18 

39 

0 

30 

11 

11 

12 

13 

13 

40 

24    45 

6 

27 

48 

9 

29 

20  50 

40 

14 

15 

15 

16 

17 

50 

16    37 

18  57 

18 

39 

0 

20 

41 

50 

18 

18 

19 

20 

20 

Page  700] 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Kefraction. 

[Barometer  30  inches. — Fahrenheit's  Thermometer  50°.] 

Moon's 

Horizontal  parallax. 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

app.  alt. 

minutes 
of  alt. 

64' 

65' 

66' 

67' 

68' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

o  / 

/  // 

/  II 

'  II 

'  II 

/   // 

/  // 

'  II 

II 

// 

II 

II 

II 

II 

70  0 

18  7 

18  28 

18  48 

19  9 

19  30 

19  60 

20  11 

20  31 

0 

0 

1 

1 

2 

3 

10 

17  58 

19 

39 

0 

20 

41 

1 

21 

10 

3 

4 

5 

5 

6 

20 

50 

10 

30 

18  50 

11 

31 

19  61 

11 

20 

7 

7 

8 

9 

9 

30 

41 

1 

21 

41 

1 

21 

41 

1 

30 

10 

11 

11 

12 

13 

40 

32 

17  53 

12 

32 

18  52 

12 

32 

19  52 

40 

13 

14 

15 

15 

16 

50 

24 

44 
17  35 

3 

23 

43 

3 

18  53 

22 
19  12 

42 

50 

17 
0 

17 

1 

18 
1 

19 
2 

19 
3 

71  0 

17  15 

17  54 

18  14 

18  34 

19  32 

0 

10 

6 

26 

45 

5 

24 

43 

3 

22 

10 

3 

4 

4 

5 

6 

20 

16  57 

17 

36 

17  55 

14 

33 

18  53 

12 

20 

6 

7 

8 

8 

9 

30 

48 

8 

27 

46 

5 

24 

43 

2 

30 

10 

10 

11 

12 

12 

40 

40 

16  59 

18 

37 

17  56 

15 

34 

18  52 

40 

13 

13 

14 

16 

16 

50 

31 

50 

9 

28 

47 

5 

24 

42 

50 

16 

17 

17 

18 

19 

72  0 

16  22 

16  41 

17  0 

17  18  17  37 

17  55 

18  14 

18  32 

0 

0 

1 

1 

2 

2 

10 

13 

32 

16  50 

9 

27 

46 

4 

22 

10 

3 

4 

4 

6 

6 

.  20 

5 

23 

41 

16  59 

18 

36 

17  54 

12 

20 

6 

7 

7 

8 

8 

30 

15  57 

14 

32 

50 

9 

27 

46 

3 

30 

9 

10 

10 

11 

n 

40 

48 

5 

23 

41 

16  59 

17 

35 

17  63 

40 

12 

13 

13 

14 

14 

50 

39 

15  56 

14 

32 

50 
16  40 

7 

25 

43 

50 

16 
0 

16 
1 

16 
1 

17 
2 

18 
2 

73  0 

15  30 

15  47 

16  5 

16  22 

16  58 

17  16 

17  33 

0 

10 

21 

38 

15  56 

13 

30 

48 

6 

23 

10 

3 

3 

4 

6 

5 

20 

12 

29 

47 

4 

21 

39 

16  66 

13 

20 

6 

6 

7 

7 

8 

30 

3 

20 

37 

15  55 

12 

29 

46 

3 

30 

9 

9 

10 

10 

11 

40 

14  54 

11 

28 

45 

2 

19 

36 

16  63 

40 

11 

12 

13 

13 

14 

50 

45 

2 

19 

35 

15  52 

9 

26 
16  16 

42 

50 

14 

15 

15 

16 
2 

17 
2 

Sub. 

74  0 

14  36 

14  53 

15  9 

15  26 

15  42 

15  59 

16  32 

0 

0 

1 

1 

10 

28 

44 

0 

17 

33 

49 

6 

22 

10 

3 

3 

4 

4 

5 

V  V 

20 

19 

35 

14  51 

8 

24 

40 

16  66 

12 

20 

6 

6 

6 

7 

8 

2  2 

30 

10 

26 

42 

14  58 

14 

30 

46 

2 

30 

8 

9 

9 

10 

11 

3  3 

40 

1 

17 

33 

49 

5 

20 

36 

15  62 

40 

11 

11 

12 

12 

13 

4  4 

50 

13  52 

8 

23 

39 

14  65 

10 

26 

42 

50 

13 

14 
1 

14 
1 

15 
2 

16 
2 

5  6 

6  6 

75  0 

13  43 

13  59 

14  14 

14  29 

14  45 

16  1 

15  ]6 

15  32 

0 

0 

10 

34 

50 

5 

20 

36 

14  52 

7 

22 

10 

3 

3 

4 

4 

5 

7  7 

20 

25 

41 

13  56 

11 

27 

42 

14  57 

12 

20 

6 

6 

6 

7 

7 

8  8 

30 

16 

32 

46 

1 

17 

32 

47 

2 

30 

8 

8 

9 

9 

10 

9  9 

40 

7 

22 

37 

13  52 

7 

22 

37 

14  51 

40 

10 

11 

11 

12 

12 

50 

12  58 

13 

28 

42 

13  67 

12 

27 

41 

50 

13 
0 

13 
0 

14 

1 

14 
1 

16 
2 

76  0 

12  49 

13  4 

13  18 

13  33 

13  47 

14  2 

14  17 

14  31 

0 

10 

41 

12  55 

9 

24 

38 

13  53 

7 

21 

10 

2 

3 

3 

4 

4 

20 

32 

46 

0 

14 

28 

43 

13  57 

11 

20 

6 

6 

6 

6 

7 

30 

23 

37 

12  51 

5 

19 

33 

47 

1 

30 

7 

8 

8 

8 

9 

40 

14 

27 

41 

12  55 

9 

23 

36 

13  50 

40 

9 

10 

10 

n 

11 

50 

5 

18 

32 

45 

12  69 

13 

26 

40 

60 

12 
0 

12 
0 

13 
1 

13 

1 

14 
2 

77  0 

11  56 

12  9 

12  22 

12  36 

12  49 

13  3 

13  16 

13  30 

0 

10 

47 

0 

13 

27 

40 

12  63 

7 

20 

10 

2 

3 

3 

4 

4 

20 

38 

11  51 

4 

17 

30 

43 

12  57 

10 

20 

4 

5 

6 

6 

6 

30 

29 

42 

11  55 

8 

21 

33 

47 

0 

30 

7 

7 

7 

8 

8 

40 

19 

32 

45 

11  58 

11 

23 

36 

12  49 

40 

9 

9 

9 

10 

10 

50 

10 

23 

35 

48 

1 

13 

26 
12  16 

39 

50 

11 

11 

12 

12 

13 
2 

78  0 

11  1 

11  14 

11  26 

11  39 

11  52 

12  4 

12  29 

0 

0 

0 

1 

1 

10 

10  52 

5 

17 

30 

42 

11  54 

6 

19 

10 

2 

2 

3 

3 

4 

20 

43 

10  65 

8 

20 

32 

44 

11  66 

8 

20 

4 

4 

5 

5 

6 

30 

34 

46 

10  58 

10 

22 

34 

46 

11  58 

30 

6 

6 

7 

7 

8 

40 

25 

37 

48 

0 

12 

24 

36 

48 

40 

8 

8 

9 

9 

10 

50 

16 

28 

39 

10  51 

3 

15 

26 

38 

50 

10 

10 

11 

11 

12 

79  0 

10  7 

10  19 

10  30 

10  42 

10  63 

11  5 

11  16 

11  28 

0 

0 

0 

1 

1 

1 

10 

9  58 

9 

21 

32 

43 

10  66 

6 

17 

10 

2 

2 

3 

3 

3 

20 

49 

0 

11 

22 

33 

44 

10  56 

7 

20 

4 

4 

4 

5 

5 

30 

40 

9  50 

1 

12 

23 

34 

45 

10  66 

30 

6 

6 

6 

7 

7 

40 

31 

41 

9  52 

3 

13 

24 

35 

46 

40 

7 

8 

8 

8 

9 

50 

22 

32 

43 

9  54 

4 

15 

25 

36 

50 

9 

10 

10 

10 

11 

TABLE  24. 

[Page  701   1 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer 

30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

Is 
11 

Correction  for  seconds  of 
parallax. — Add. 

Corr. 

for 

minutes 

54' 

65' 

56' 

57' 

58' 

6^ 

ec 

61' 

0" 

2" 

4" 

6" 

8" 

of  alt. 

O          / 

'     n 

/     // 

/     n 

/     // 

t     II 

/      // 

/    II 

'     II 

II 

II 

II 

u 

II 

II 

80    0 

9  13 

9  23 

9  34 

9  44 

9  55 

10    5 

10  15 

10  26 

0 

0 

0 

1 

1 

1 

10 

3 

14 

24 

34 

45 

9  55 

5 

15 

10 

2 

2 

2 

3 

3 

20 

8  54 

4 

14 

24 

35 

45 

9  65 

5 

20 

3 

4 

4 

4 

5 

30 

45 

8  55 

5 

15 

25 

35 

45 

9  54 

30 

5 

6 

6 

6 

6 

40 

36 

46 

8  55 

5 

15 

25 

35 

44 

40 

7 

7 

7 

8 

8 

50 

27 

37 

46 

8  56 

6 

15 

26 

34 

50 

8 

9 

9 
1 

9 

1 

10 
1 

81    0 

8  18 

8  27 

8  37 

8  46 

8  56 

9    5 

9  14 

9  24 

0 

0 

0 

10 

9 

18 

27 

36 

46 

8  55 

4 

13 

10 

1 

2 

2 

2 

3 

20 

7  59 

8 

17 

26 

36 

45 

8  54 

3 

20 

3 

3 

4 

4 

4 

30 

50 

7  59 

8 

17 

26 

35 

44 

8  52 

30 

4 

6 

5 

6 

6 

40 

41 

50 

7  59 

8 

17 

25 

34 

42 

40 

6 

6 

6 

7 

7 

50 

32 

41 
7  31 

49 

7  58 

7 

15 

24 

32 

50 

7 
0 

8 
0 

8 
1 

8 

1 

9 

1 

82    0 

7  23 

7  40 

7  48 

7  57 

8    5 

8  13 

8  22 

0 

10 

14 

22 

30 

38 

47 

7  55 

3 

11 

10 

1 

2 

2 

2 

2 

20 

4 

12 

20 

28 

37 

46 

7  62 

0 

20 

3 

3 

3 

3 

4 

30 

6  55 

3 

11 

19 

27 

36 

42 

7  60 

30 

4 

4 

6 

5 

6 

40 

46 

6  54 

2 

10 

17 

25 

32 

40 

40 

6 

6 

6 

6 

6 

50 

37 

45 

6  52 

0 

7 

15 

22 

30 

60 

7 

7 
0 

7 
0 

7 
1 

8 
1 

Sub. 

83    0 

6  28 

6  35 

6  43 

6  50 

6  57 

7    6 

7  12 

7  20 

0 

0 

10 

19 

26 

33 

40 

47 

6  64 

2 

9 

10 

1 

1 

2 

2 

2 

V  V' 

20 

9 

16 

23 

30 

37 

44 

6  61 

6  68 

20 

2 

3 

3 

3 

3 

2    2 

30 

0 

7 

13 

20 

27 

34 

41 

48 

30 

3 

4 

4 

4 

4 

3    3 

40 

5  51 

5  58 

4 

11 

18 

24 

31 

38 

40 

5 

6 

5 

5 

6 

4    4 

50 

42 

49 

5  55 

1 

8 

14 

21 

27 

60 

6 

6 

6 
0 

6 
1 

7 

1 

5  5 

6  6 

84    0 

5  33 

5  39 

5  45 

5  52 

5  58 

6    4 

6  10 

6  17 

0 

0 

0 

10 

23 

30 

36 

42 

48 

5  54 

0 

6 

10 

1 

1 

1 

2 

2 

7    7 

20 

14 

20 

26 

32 

38 

44 

5  60 

6  55 

20 

2 

2 

2 

3 

3 

8    8 

30 

5 

10 

16 

22 

28 

34 

39 

45 

30 

3 

3 

3 

3 

4 

9    9 

40 

4  56 

1 

7 

13 

18 

24 

29 

35 

40 

4 

4 

4 

4 

5 

50 

47 

4  52 

4  58 

3 

8 

14 

19 

26 

60 

5 

6 

6 

5 

6 

85    0 

4  37 

4  43 

4  48 

4  53 

4  58 

5    4 

5    9 

6  14 

0 

0 

0 

0 

0 

1 

10 

28 

33 

38 

43 

48 

4  53 

4  68 

3 

10 

1 

1 

1 

1 

1 

20 

18 

24 

28 

33 

38 

43 

48 

4  53 

20 

2 

2 

2 

2 

2 

30 

9 

14 

19 

23 

28 

33 

38 

43 

30 

2 

3 

3 

3 

3 

40 

0 

5 

10 

14 

19 

23 

28 

33 

40 

3 

3 

4 

4 

4 

50 

3  51 

3  56 

0 

5 

9 

13 

18 

22 

50 

4 
0 

4 
0 

4 
0 

6 
0 

5 

1 

86    0 

3  42 

3  46 

3  50 

3  55 

3  59 

4    3 

4    7 

4  11 

0 

10 

33 

37 

41 

45 

49 

3  53 

3  67 

1 

10 

1 

1 

1 

1 

1 

20 

23 

27 

31 

35 

39 

43 

46 

3  60 

20 

1 

1 

2 

2 

2 

30 

14 

18 

21 

25 

29 

33 

36 

40 

30 

2 

2 

2 

2 

2 

40 

5 

9 

12 

16 

19 

23 

26 

30 

40 

3 

3 

3 

3 

3 

50 

2  56 

2  59 

3 

6 

9 

13 

16 

19 

50 

3 

3 

3 
0 

4 
0 

4 
0 

87    0 

2  47 

2  50 

2  53 

2  56 

2  59 

3    2 

3    5 

3    9 

0 

0 

0 

10 

37 

40 

43 

46 

49 

2  52 

2  55 

2  58 

10 

0 

1 

1 

1 

1 

20 

28 

31 

33 

36 

39 

42 

45 

47 

20 

1 

1 

1 

1 

1 

30 

19 

21 

24 

26 

29 

32 

34 

37 

30 

1 

1 

2 

2 

2 

40 

10 

12 

15 

17 

19 

22 

24 

27 

40 

2 

2 

2 

2 

2 

50 

1 

3 

5 

7 

9 

12 

14 

16 

50 

2 

2 
0 

2 
0 

3 
0 

3 
0 

88    0 

1  51 

1  53 

1  55 

1  67 

1  59 

2    2 

2    4 

2    6 

0 

0 

10 

42 

43 

45 

47 

49 

1  61 

1  63 

1  55 

10 

0 

0 

0 

0 

0 

20 

32 

34 

36 

38 

39 

41 

43 

44 

20 

1 

1 

1 

1 

1 

30 

23 

25 

26 

28 

29 

31 

32 

34 

30 

1 

1 

1 

1 

1 

40 

14 

15 

16 

19 

20 

21 

22 

24 

40 

1 

1 

1 

1 

1 

50 

5 

6 

7 

9 

10 

11 

12 

13 

60 

1 

1 

1 

2 

2 

89    0 

0  56 

0  57 

0  58 

0  59 

1    0 

1     1 

1    2 

1    3 

0 

0 

0 

0 

0 

0 

10 

46 

47 

48 

49 

0  50 

0  51 

0  51 

0  52 

10 

0 

0 

0 

0 

0 

20 

37 

37 

38 

39 

40 

40 

41 

42 

20 

0 

0 

0 

0 

0 

30 

28 

28 

28 

29 

30 

30 

31 

31 

30 

0 

0 

0 

0 

0 

40 

19 

19 

19 

19 

20 

20 

21 

21 

40 

0 

0 

0 

0 

0 

50 

9 

10 

10 

10 

10 

10 

10 

10 

60 

1 

1 

1 

1 

1 

Page  702] 

TABLE  25. 

Table  showing  the  variation  of  the  altitude  of  an  object  arising  from  a  change  of  100  seconds  in  the 
declination.     Unmarked  quantities  in  the  Table  are  positive.     If  the  change  move  the  body  toward 
the  elevated  pole,  apply  the  correction  to  the  altitude  with  the  signs  m  the  Table;  otherwise, 

change  the 

Signs. 

a 
o 

'S 

.g 
1 

o 

3 

< 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

% 

< 

d 
o 

.g 
1 

70° 

60° 

50° 

40° 

30° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

50° 

60° 

70° 

0 

o 

„ 

// 

II 

„ 

II 

„ 

II 

II 

„ 

„ 

„ 

II 

II 

II 

„ 

0 

o 

0 

94 

87 

76 

64 

50 

34 

17 

0 

17 

34 

50 

64 

76 

87 

94 

0 

10 

95 

88 

78 

65 

51 

35 

18 

0 

18 

35 

51 

65 

78 

88 

95 

10 

20 

100 

92 

82 

68 

53 

36 

18 

0 

18 

36 

53 

68 

82 

92 

100 

20 

30 

100 

88 

74 

57 

39 

20 

0 

20 

39 

57 

74 

88 

100 

30 

0 

40 

100 

84 

65 

45 

22 

0 

22 

45 

65 

84 

100 

40 

0 

50 

100 

78 

53 

27 

0 

27 

53 

78 

100 

50 

60 

100 

68 

35 

0 

35 

68 

100 

60 

70 

100 

51 

0 

51 

100 

70 
0 

0 

94 

87 

77 

64 

50 

34 

17 

0 

17 

34 

50 

64 

77 

87 

94 

10 

95 

87 

77 

65 

50 

34 

17 

-  1 

18 

35 

51 

66 

78 

88 

96 

10 

20 

99 

91 

81 

67 

52 

35 

17 

-  1 

19 

37 

54 

69 

83 

93 

101 

20 

30 

107 

98 

87 

73 

56 

38 

18 

-  2 

22 

41 

59 

76 

90 

102 

30 

2 

40 

111 

98 

82 

63 

42 

20 

-  2 

25 

47 

68 

86 

102 

40 

2 

50 

116 

97 

74 

50 

24 

-  3 

30 

57 

81 

103 

50 

60 

124 

95 

64 

30 

-  5 

40 

73 

103 

60 

70 

139 

92 
34 

43 

17 

-  8 
0 

59 

108 

70 
0 

0 

94 

87 

77 

64 

50 

17 

34 

50 

64 

77 

87 

94 

10 

94 

87 

77 

64 

50 

34 

16 

—  1 

19 

36 

52 

67 

79 

89 

97 

10 

20 

98 

90 

79 

66 

51 

34 

16 

-  3 

21 

39 

56 

71 

84 

95 

103 

20 

30 

105 

96 

85 

70 

54 

36 

16 

-  4 

24 

44 

62 

78 

93 

104 

• 

30 

4 

40 

107 

94 

78 

59 

39 

17 

-  6 

29 

51 

71 

90 

106 

40 

4 

50 

111 

92 

70 

45 

19 

-  8 

35 

62 

86 

109 

50 

1  60 

117 

88 

56 

23 

-12 

47 

81 

112 

60 

70 

127 

81 

32 

-19 
0 

70 

17 

119 

65 

70 

0 

94 

87 

77 

65 

50 

34 

17 

34 

50 

77 

87 

94 

0 

10 

94 

87 

76 

64 

49 

33 

16 

-  2 

20 

37 

53 

67 

80 

90 

98 

10 

20 

97 

89 

78 

65 

50 

33 

15 

-  4 

22 

40 

57 

73 

86 

96 

104 

20 

30 

103 

94 

83 

69 

52 

34 

14 

-  6 

26 

46 

64 

81 

95 

107 

30 

6 

40 

105 

92 

76 

57 

36 

14 

-  9 

32 

54 

74 

93 

109 

40 

6 

50 

107 

88 

66 

41 

15 

-13 

40 

66 

91 

113 

50 

60 

111 

82 

51 

17 

-18 

53 

87 

119 

60 

70 

118 

72 

22 

-29 

80 

129 

70 

0 

95 

87 

77 

65 

50 

35 

18 

0 

18 

35 

50 

65 

77 

87 

95 

0 

10 

94 

86 

76 

63 

49 

33 

15 

-  3 

20 

38 

54 

68 

81 

91 

99 

10 

20 

96 

88 

77 

64 

49 

32 

14 

-  5 

24 

40 

59 

74 

87 

98 

106 

20 

30 

101 

93 

81 

67 

50 

32 

12 

-  8 

28 

48 

66 

83 

97 

109 

30 

8 

40 

102 

89 

73 

54 

33 

11 

-12 

35 

57 

78 

97 

113 

40 

8 

50 

104 

84 

62 

37 

11 

-17 

44 

70 

95 

118 

50 

60 

105 

77 

45 

11 

-24 

59 

93 

125 

60 



70 

109 

62 

13 

-39 

90 

140 

70 

0 

95 

88 

78 

65 

51 

35 

18 

0 

18 

35 

51 

65 

78 

88 

'95 

0 

10 

94 

86 

75 

63 

48 

32 

15 

-  3 

21 

38 

55 

69 

82 

92 

100 

10 

20 

95 

87 

76 

63 

48 

31 

12 

-  6 

25 

43 

60 

76 

89 

100 

20 

30 

100 

91 

80 

65 

49 

30 

10 

-10 

30 

50 

69 

86 

100 

30 

10 

40 

100 

87 

70 

51 

31 

8 

-15 

38 

60 

81 

100 

40 

10 

50 

. 

100 

81 

58 

33 

6 

-21 

48 

75 

100 

50 

60 

100 

71 

39 

5 

-31 

66 

100 

60 

70 

66 

100 
51 

53 
35 

3 

18 

-48 

100 

18 

35 

51 

96 

70 
0 

0 

96 

89 

78 

0 

66 

78 

89 

10 

94 

86 

76 

63 

48 

32 

14 

—  4 

22 

39 

56 

70 

83 

94 

101 

10 

20 

94 

86 

76 

62 

47 

29 

11 

-  8 

27 

45 

62 

78 

91 

102 

20 

30 

99 

90 

78 

64 

47 

28 

8 

-12 

33 

53 

71 

88 

103 

30 

12 

40 

108 

98 

84 

68 

49 

28 

5 

-18 

41 

63 

85 

104 

40 

12 

50 

112 

97 

77 

54 

29 

2 

-25 

53 

80 

105 

50 

60 

120 

95 

65 

33 

—1 

-37 

72 

107 

60 

70 

134 

91 

44 

-6 

-58 

110 

70 

j 

0) 

3 
3 

70° 

60° 

50° 

40= 

80° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

50° 

60° 

70° 

3 

o 
1 

I 

latitude  of  same  nam 

e  as  c 

ecllnal 

ion. 

Latitude  of  differen 

t  name  from  < 

leclina 

tion. 

< 

< 

o 

TABLE  25.                                            [Page  703    1 

Table  showing  the  variation  of  the  altitude  of  an  object  arising  from  a  change  of  100  seconds  in  the 

declination.     Unmarked  quantities  in  the  Table  are  positive.     If  the  change  move  the  body  toward 

the  elevated  pole,  apply  the  correction  to  the  altitude  with  the  signs  in  the  Table;  otherwise, 

c 

bange  the  signs. 

1 

§ 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

a 
o 

1 
ft 

•0 

1 

i 

a 

< 

70° 

60° 

60° 

40° 

80° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

50° 

60° 

70° 

^ 

ft 

o 

o 

H 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

o 

o 

0 

97 

89 

79 

66 

52 

35 

18 

0 

18 

36 

62 

66 

79 

89 

97 

0 

10 

94 

86 

76 

63 

48 

31 

14 

-     4 

23 

40 

57 

72 

85 

95 

103 

10 

20 

94 

86 

75 

61 

46 

27 

10 

-     9 

28 

45 

64 

80 

93 

104 

20 

30 

97 

89 

77 

62 

45 

26 

6 

-  14 

35 

55 

74 

91 

106 

30 

14 

40 

106 

96 

82 

66 

46 

25 

2 

-  21 

44 

67 

88 

107 

40 

14 

50 

109 

93 

73 

50 

25 

-  2 

-  30 

58 

85 

110 

50 

60 

115 

89 

60 

27 

-  7 

-  43 

79 

114 

60 

70 

125 

82 

35 

-16 

-  69 
0 

121 

18 

36 

70 

0 

98 

90 

80 

67 

52 

36 

18 

52 

67 

80 

90 

98 

0 

10 

94 

86 

76 

63 

48 

31 

13 

-     5 

23 

41 

68 

73 

86 

97 

104 

10 

20 

94 

85 

74 

61 

45 

27 

9 

-  10 

30 

48 

66 

82 

96 

106 

20 

80 

96 

87 

75 

61 

44 

25 

4 

-  17 

37 

58 

77 

94 

109 

30 

16 

40 

104 

94 

80 

63 

44 

22 

0 

-  24 

48 

70 

92 

111 

40 

16 

50 

106 

90 

70 

47 

21 

-  6 

-  34 

62 

90 

115 

50 

60 

110 

84 

54 

21 

-14 

-  50 

86 

121 

60 

70 

117 

73 

25 

-26 

-  79 

132 
18 

36 

70 
0 

0 

99 

91 

81 

68 

53 

36 

18 

0 

53 

68 

81 

91 

99 

10 

95 

87 

76 

63 

48 

31 

13 

-     6 

24 

42 

59 

74 

88 

98 

106 

10 

20 

93 

85 

74 

60 

44 

26 

8 

-  12 

31 

50 

68 

84 

98 

109 

20 

30 

95 

86 

74 

59 

42 

23 

2 

-  19 

40 

60 

79 

97 

112 

30 

18 

40 

102 

92 

78 

61 

41 

20 

-  3 

-  27 

51 

74 

96 

116 

40 

18 

50 

103 

87 

66 

43 

17 

-10 

-  39 

67 

96 

121 

50 

60 

106 

79 

49 

16 

-20 

-  56 

93 

128 

60 

70 
0 

100 

108 

64 

16 

-36 

-  89 

143 

70 

92 

82 

68 

53 

36 

18 

0 

18 

36 

53 

68 

82 

92 

100 

0 

10 

95 

87 

76 

63 

48 

31 

12 

-     6 

25 

43 

60 

76 

89 

100 

10 

20 

93 

85 

74 

60 

43 

25 

6 

-  13 

33 

52 

70 

86 

100 

20 

30 

94 

85 

73 

58 

40 

21 

0 

-  21 

42 

63 

82 

100 

30 

20 

40 

100 

90 

76 

59 

39 

17 

-  6 

-  31 

55 

78 

100 

40 

20 

50 

100 

83 

63 

39 

13 

-15 

-  43 

72 

100 

50 

60 

100 

74 

43 

10 

-26 

-  63 

100 

60 

70 

100 

56 

6 

-46 

-100 

69 

70 

0 

93 

83 

69 

54 

37 

19 

0 

19 

37 

64 

83 

93 

101 

0 

10 

96 

88 

77 

63 

48 

30 

12 

-     7 

26 

45 

62 

78 

91 

102 

10 

20 

93 

85 

73 

59 

43 

25 

5 

-  15 

35 

54 

72 

88 

103 

20 

30 

94 

85 

72 

57 

39 

19 

-  2 

-  23 

46 

66 

86 

103 

30 

22 

40 

98 

88 

74 

57 

36 

14 

-  9 

-  34 

58 

82 

104 

40 

22 

50 

110 

97 

80 

60 

36 

9 

-19 

-  48 

77 

106 

bO 

60 

117 

95 

68 

38 

4 

-33 

-  70 

107 

60          1 



70 

131 

92 

47 

-  3 

-56 

-111 

70 

0 

95 

84 

70 

55 

37 

19 

0 

19 

37 

56 

70 

84 

96 

103 

0 

10 

97 

88 

77 

64 

48 

30 

11 

-     8 

27 

46 

63 

79 

93 

104 

10 

20 

93 

85 

73 

59 

42 

24 

4 

-  16 

36 

56 

74 

91 

106 

20 

30 

93 

84 

71 

56 

38 

18 

-  4 

-  26 

48 

69 

89 

107 

30 

24 

40 

97 

86 

72 

54 

34 

12 

-12 

-  37 

62 

86 

109 

40 

24 

50 

107 

93 

77 

56 

32 

5 

-23 

-  53 

83 

111 

50 

60 

112 

91 

64 

32 

-  2 

-39 

-  77 

115 

60 

70 

123 

83 

38 

-13 

-67 

-122 

vo 

0 

96 

85 

72 

56 

38 

19 

0 

19 

38 

66 

72 

85 

96 

105 

0 

10 

98 

89 

78 

64 

48 

30 

11 

-     9 

28 

47 

66 

81 

96 

106 

10 

20 

95 

85 

73 

59 

41 

23 

3 

-  18 

38 

68 

77 

94 

108 

20 

30 

93 

83 

70 

54 

36 

16 

-  6 

-  28 

50 

72 

92 

111 

30 

26 

40 

96 

85 

70 

52 

32 

9 

-16 

-  41 

66 

91 

114 

40 

26 

50 

105 

92 

74 

53 

28 

1 

-28 

-  58 

88 

117 

bO 

60 

108 

86 

58 

27 

-  8 

-46 

-  84 

123 

60 

70 

115 

75 

29 

-23 

-78 

-134 

VO 

1 

B 

"3 

§ 

a 

1 

70° 

60° 

50° 

40° 

80° 

20° 

10° 

0° 

10° 

20° 

30° 

40° 

60° 

60° 

70° 

•3 

declinatioa. 

Latitude  of  dififerent  name  from  declination. 

ft 

< 

< 

ft 

21594°— 14- 


-38 


Page  704] 

TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian 

passage 

Lati- 
tude. 

Declination  of  the 

same  name  as  the  latitude; 

upper  transit;  reduction  additlre. 

Lati- 
tude. 

0° 

1° 

2° 

8° 

4° 

6° 

6° 

JO 

8° 

9° 

\W> 

11° 

o 

II 

;/ 

II 

II 

II 

II 

II 

// 

n 

// 

II 

II 

o 

0 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

11.1 

10.1 

0 

1 

28.0 

22.4 

18.6 

16.0 

13.9 

12.4 

11.1 

1 

2 

28.0 

22.3 

18.6 

15.9 

13.9 

12.3 

2 

3 

27.9 

22.3 

18.6 

15.8 

13.8 

3 

4 

28.1 

27.8 

22.2 

18.5 

15.8 

4 

5 

22.4 

28.0 

27.7 

22.1 

18.4 

5 

6 

18.7 

22.4 

28.0 

27.6 

22.0 

6 

7 

16.0 

18.6 

22.3 

27.9 

27.4 

7 

8 

14.0 

16.0 

18.6 

22.3 

27.8 

8 

9 

12.4 

13.9 

15.9 

18.5 

22.2 

27.7 

9 

10 

11.1 

12.4 

13.9 

15.8 

18.6 

22.1 

27.6 

10 

11 

10.1 

11.1 

12.3 

13.8 

16.8 

18.4 

22.0 

27.4 

11 

12 

9.2 

10.1 

11.1 

12.3 

13.8 

16.7 

18.3 

21.9 

27.3 

12 

13 

8.5 

9.2 

10.0 

11.0 

12.2 

13.7 

15.6 

18.2 

21.7 

27.1 

13 

14 

7.9 

8.6 

9.2 

10.0 

10.9 

12.1 

13.6 

15.6 

18.0 

21.6 

26.9 
21.4 

14 

15 

7.3 

7.8 

8.4 

9.1 

9.9 

10.9 

12.1 

13.6 

16.4 

17.9 

26.7 

15 

16 

6.8 

7.3 

7.8 

8.4 

9.1 

9.8 

10.8 

12.0 

13.4 

16.3 

17.8 

21.3 

16 

17 

6.4 

6.8 

7.2 

7.8 

8.3 

9.0 

9.8 

10.7 

11.9 

13.3 

15.2 

17.6 

17 

18 

6.0 

6.4 

6.8 

7.2 

7.7 

8.3 

8.9 

9.7 

10.6 

11.8 

13.2 

16.0 

18 

19 

5.7 

6.0 

6.3 

6.7 

7.2 

7.6 

8.2 

8.9 

9.6 

10.6 

11.7 

13.1 

19 

20 

6.4 

6.7 

6.0 

6.3 

6.7 

7.1 

7.6 

8.1 

8.8 

9.5 

10.5 

11.6 

20 

21 

6.1 

5.4 

6.6 

6.9 

6.3 

6.6 

7.0 

7.6 

8.1 

8.7 

9.5 

10.4 

21 

22 

4.9 

5.1 

5.3 

6.6 

6.9 

6.2 

6.6 

7.0 

7.5 

8.0 

8.6 

9.4 

22 

23 

4.6 

4.8 

6.0 

5.3 

6.5 

6.8 

6.1 

6.5 

6.9 

7.4 

7.9 

8.6 

23 

24 

4.4 

4.6 

4.8 

5.0 

5.2 

6.5 

5.8 

6.1 

6.4 

6.8 

7.3 

7.8 

24 

25 

4.2 

4.4 

4.6 

4.7 

6.0 

5.2 

5.4 

6.7 

6.0 

6.4 

6.8 

7.2 

26 

26 

4.0 

4.2 

4.3 

4.5 

4.7 

4.9 

6.1 

6.4 

5.7 

6.0 

6.3 

6.7 

26 

27 

3.9 

4.0 

4.1 

4.3 

4.6 

4.7 

4.9 

5.1 

5.3 

5.6 

5.9 

6.2 

27 

28 

3.7 

3.8 

4.0 

4.1 

4.3 

4.4 

4.6 

4.8 

6.0 

5.3 

6.5 

5.8 

28 

29 

3.5 

3.7 

3.8 

3.9 

4.1 

4.2 

4.4 

4.2 

4.6 

4.7 

5.0 

5.2 

5.5 

29 

30 

3.4 

3.5 

3.6 

3.7 

3.9 

4.0 

4.3 

4.6 

4.7 

4.9 

5.1 

30 

31 

3.3 

3.4 

3.5 

3.6 

3.7 

3.8 

4.0 

4.1 

4.3 

4.4 

4.6 

4.8 

31 

32 

3.1 

3.2 

3.3 

3.4 

3.5 

3.7 

3.8 

3.9 

4.1 

4.2 

4.4 

4.6 

32 

33 

3.0 

3.1 

3.2 

3.3 

.3.4 

3.5 

3.6 

3.7 

3.9 

4.0 

4.2 

4.3 

33 

34 

2.9 

3.0 

3.1 

3.2 

3.2 

3.3 

3.4 

3.6 

3.7 

3.8 

3.9 

4.1 
3.9 

34 
35 

35 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

3.3 

3.4 

3.6 

3.6 

3.7 

36 

2.7 

2.8 

2.8 

2,9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

36 

37 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

37 

38 

2.6 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3.0 

3.0 

3.2 

3.2 

3.3 

38 

39 

2.4 

2.5 

2.5 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3.0 

3.1 

3.2 

39 

40 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.7 

2.8 

2.9 

3.0 

3.0 

40 

41 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

41 

42 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.6 

2.5 

2.6 

2.6 

2.7 

2.8 

42 

43 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.7 

43 

44 

2.0 

2.1 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

44 

45 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

46 

46 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.2 

2.3 

2.3 

46 

47 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.1 

2.2 

2.2 

47 

48 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.1 

48 

49 

1.7 

1.7 

1.8 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.1 

49 

50 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

60 

51 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

51 

62 

1.5 

1.6 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

52 

53 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.7 

53 

54 

1.4 

1.4 

1.6 

1.5 

1.6 

1.6 

1.6 

1.6 

1.6 

1.6 

1.6 

1.7 

54 

55 

1.4 

1.4 

1.4 

1.4 

1.5 

1.6 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

65 

56 

1.3 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.6 

1.6 

1.6 

1.5 

56 

57 

1.3 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

67 

58 

1.2 

1.2 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

68 

59 

1.2 

1.2 

1.2 

1.2 

1.2 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

69 

60 

1.1 

1.1 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.3 

1.3 

60 

0° 

1° 

2° 

8° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

De 

clinatioi 

1  of  the 

same  nan 

le  as  the 

latitude; 

upper  tra 

asit;  redu 

ction  add 

Itlre. 

TABLE  26. 

(Page  706 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tade. 

Declination  of  the 

same  name  aa  the  latitude;  upper  transit 

;  reduction  additive. 

Lati- 
tude. 

12° 

18° 

14° 

16° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

28° 

24° 

o 

// 

H 

„ 

// 

// 

II 

II 

// 

// 

// 

II 

It 

„ 

o 

0 

9.2 

8.5 

7.9 

7.3 

6.8 

6.4 

6.0 

5.7 

5.4 

5.1 

4.9 

4.6 

4.4 

0 

1 

10.1 

9.2 

8.5 

7.8 

7.3 

6.8 

6.4 

6.0 

5.7 

5.4 

5.1 

4.8 

4.6 

1 

2 

11.1 

10.0 

9.2 

8.4 

7.8 

7.2 

6.8 

6.3 

6.0 

5.6 

5.3 

5.0 

4.8 

2 

3 

12.3 

11.0 

10.0 

9.1 

8.4 

7.8 

7.2 

6.7 

6.3 

5.9 

5.6 

5.3 

5.0 

3 

4 

13.8 

12.2 

10.9 

9.9 

9.1 

8.3 

7.7 

7.2 

6.7 

6.3 

5.9 

5.5 

5.2 

4 

5 

15.7 

13.7 

12.1 

10.9 

9.8 

9.0 

8.3 

7.6 

7.1 

6.6 

6.2 

5.8 

5.5 

5 

6 

18.3 

15.6 

13.6 

12.1 

10.8 

9.8 

8.9 

8.2 

7.6 

7.0 

6.6 

6.1 

5.8 

6 

7 

21.9 

18.2 

15.5 

13.5 

12.0 

10.7 

9.7 

8.9 

8.1 

7.5 

7.0 

6.5 

6.1 

7 

8 

27.3 

21.7 

18.0 

15.4 

13.4 

11.9 

10.6 

9.6 

8.8 

8.1 

7.5 

6.9 

6.4 

8 

9 

27.1 

21.6 

17.9 

15.3 

13.3 

11.8 

10.6 
11.7 

9.5 

8.7 

8.0 

7.4 

6.8 

9 
10 

10 

26.9 

21.4 

17.8 

15.2 

13.2 

10.5 

9.5 

8.6 

7.9 

7.3 

11 

26.7 

21.3 

17.6 

15.0 

13.1 

11.6 

10.4 

9.4 

8.5 

7.8 

11 

12 

26.5 

21.1 

17.5 

14.9 

13.0 

11.5 

10.3 

9.3 

8.4 

12 

13 

26.2 

20.9 

17.3 

14.8 

12.8 

11.3 

10.1 

9.2 

13 

14 

26.0 

20.7 

17.1 

14.6 

12.7 

11.2 

10.0 

14 

15 

25.7 

20.4 

16.9 

14.4 

12.5 

11.1 

15 

16 

26.5 

25.4 

20.2 

16.7 

14.3 

12.4 

16 

17 

21.1 

26.2 

25.1 

20.0 

16.5 

14.1 

17 

18 

17.5 

20.9 

26.0 

24.8 

19.7 

16.3 

18 

19 

14.9 

17.3 

20.7 

25.7 

24.5 

19.5 

19 

20 

13.0 

14.8 

17.1 

20.4 

25.4 

24.2 

20 

21 

11.5 

12.8 

14.6 

16.9 

20.2 

25.1 

21 

22 

10.3 

11.3 

12.7 

14.4 

16.7 

20.0 

24.8 

22 

23 

9.3 

10.1 

11.2 

12.5 

14.3 

16.5 

19.7 

24.5 

23 

24 

8.4 

9.2 

10.0 

11.1 

12.4 

14.1 

16.3 

19.5 

24.2 

24 

25 

7.7 

8.3 

9.0 

9.9 

10.9 

12.2 

13.9 

16.1 

19.2 

23.8 

25 

26 

7.1 

7.6 

8.2 

8.9 

9.8 

10.8 

12.1 

13.7 

15.9 

18.9 

23.5 

26 

27 

6.6 

7.0 

7.5 

8.1 

8.8 

9.6 

10.6 

11.9 

13.5 

15.6 

18.6 

23.1 

27 

28 

6.2 

6.5 

7.0 

7.4 

8.0 

8.7 

9.5 

10.5 

11.7 

13.3 

15.4 

18.3 

22.7 

28 

29 

5.7 

6.1 

6.4 

6.9 

7.3 

7.9 

8.6 

9.4 

10.3 

11.5 

13.1 

15.1 

18.0 

29 

30 

5.4 

5.7 

6.0 

6.4 

6.8 

7.2 

7.8 

8.4 

9.2 

10.1 

11.3 

12.8 

14.9 

30 

31 

5.1 

5.3 

5.6 

5.9 

6.3 

6.7 

7.1 

7.7 

8.3 

9.0 

10.0 

11.1 

12.6 

31 

32 

4.8 

5.0 

5.2 

5.5 

5.8 

6.2 

6.5 

7.0 

7.5 

8.1 

8.9 

9.8 

10.9 

32 

33 

4.5 

4.7 

4.9 

5.1 

5.4 

5.7 

6.1 

6.4 

6.9 

7.4 

8.0 

8.7 

9.6 

33 

34 

4.3 

4.4 

4.6 

4.8 

5.1 

5.3 

5.6 

5.9 

6.3 

6.8 

7.3 

7.8 

8.6 

34 

35 

4.0 

4.2 

4.4 

4.5 

4.7 

5.0 

5.2 

5.5 

5.8 

6.2 

6.6 

7.1 

7.7 

35 

36 

3.8 

4.0 

4.1 

4.3 

4.5 

4.7 

4.9 

5.1 

5.4 

5.7 

6.1 

6.5 

7.0 

36 

37 

3.6 

3.8 

3.9 

4.0 

4.2 

4.4 

4.6 

4.8 

5.0 

5.3 

5.6 

6.0 

6.4 

37 

38 

3.4 

3.6 

3.7 

3.8 

4.0 

4.1 

4.3 

4.5 

4.7 

4.9 

5.2 

5.5 

5.8 

38 

39 

3.3 

3.4 

3.5 

3.6 

3.8 

3.9 

4.0 

4.2 

4.4 

4.6 

4.8 

5.1 

5.4 

39 

40 

3.1 

3.2 

3.3 

3.4 

3.6 

3.7 

3.8 

4.0 

4.1 

4.3 

4.5 

4.7 

5.0 

40 

41 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

3.9 

4.0 

4.2 

4.4 

4.6 

41 

42 

2.9 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.7 

3.8 

4.0 

4.1 

4.3 

42 

43 

2.7 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

3.3 

3.5 

3.6 

3.7 

3.9 

4.0 

43 

44 

2.6 

2.7 

2.7 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.8 

44 

45 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

45 

46 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

46 

47 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.9 

2.9 

3.0 

3.1 

47 

48 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.9 

3.0 

48 

49 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

49 

50 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

50 

51 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

51 

52 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.1 

2.1 

2.1 

2.2 

2.2 

2.3 

2.4 

52 

53 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

53 

54 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.1 

2.1 

54 

55 

55 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

56 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

56 

57 

1.5 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

67 

58 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

58 

59 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

59 

60 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

60 

12° 

18° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

28° 

24° 

De< 

3UnatioE 

t  of  the  f 

une  nai 

neasth 

i  latitude;  appei 

transit- 

reducti 

on  addit 

iTC. 

1 

Page  706]                                            TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  the  same  name  as  the  latitude;  npper  transit;  reduction  addltlre. 

.  Lati- 
tude. 

26° 

26° 

27° 

28° 

29° 

80° 

31° 

32° 

88° 

34° 

36° 

86° 

87° 

0 
1 
2 
3 
4 

// 

4.2 
4.4 
4.6 
4.7 
5.0 

n 

4.0 
4.2 
4.3 
4.5 
4.7 

It 

3.9 
4.0 
4.1 
4.3 
4.5 

» 

3.7 

3.8 

4.0 

4.1 

4.3 

3.5 
3.7 
3.8 
3,9 
4.1 

II 

3.4 

3.5 

3.6 

3.7 

3.9 

II 

3.3 

3.4 

3.5 

3.6 

3.7 

II 

3.1 

3.2 

3.3 

3.4 

3.5 

II 

3.0 

3.1 

3.2 

3.3 

3.4 

II 

2.9 
3.0 
3.1 
3.2 
3.3 

II 

2.8 
2.9 
3.0 
3.0 
3.1 

2.7 
2.8 
2.8 
2.9 
3.0 

2.6 
2.7 
2.7 

2.8 
2.9 

o 

0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

5.2 
5.4 
5.7 
6.0 
6.4 

4.9 
5.1 
5.4 
5.7 
6.0 

4.7 
4.9 
5.1 
5.3 
5.6 

4.4 
4.6 
4.8 
5.0 
5.3 

4.2 
4.4 
4.6 
4.8 
5.0 

4.0 
4.2 
4.3 
4.5 
4.7 

3.8 
4.0 
4.1 
4.3 
4.4 

3.7 
3.8 
3.9 
4.1 
4.2 

3.5 
3.6 
3.7 
3.9 
4.0 

3.3 
3.5 
3.6 
3.7 
3.8 

3.2 
3.3 
3.4 
3.5 
3.6 

3.1 
3.2 
3.3 
3.4 
3.5 

3.0 
3.0 
3.1 
3.2 
3.3 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

6.8 
7.2 
7.7 
8.3 
9.1 

6.3 
6.7 
7.1 
7.6 

8.2 

5.9 
6.2 
6.6 
7.1 
7.6 

5.5 
5.8 
6.2 
6.5 
7.0 

5.2 
5.5 

5.8 
6.1 
6.4 

4.9 
5.1 
5.4 
5.7 
6.0 

4.6 
4.8 
5.1 
5.3 
5.6 

4.4 
4.6 
4.8 
5.0 
5.2 

4.2 
4.3 
4.5 
4.7 
4.9 

3.9 
4.1 
4.3 
4.4 
4.6 

3.8 
3.9 
4.0 
4.2 
4.4 

3.6 
3.7 
3.8 
4.0 
4.1 

3.4 
3.5 
3.6 
3.8 
3.9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

9.9 
10.9 
12.2 
13.9 
16.1 

8.9 

9.8 

10.8 

12.1 

13.7 

8.1 

8.8 

9.6 

10.6 

11.9 

7.4 
8.0 
8.7 
9.5 
10.5 

6.9 
7.3 
7.9 
8.6 
9.4 

6.4 
6.8 
7.2 
7.8 
8.4 

5.9 
6.3 
6.7 
7.1 

7.7 

5.5 
5.8 
6.2 
6.6 
7.0 

5.2 
5.4 
5.7 
6.1 
6.4 

4.8 
5.1 
5.3 
5.6 
6.0 

4.5 
4.8 
5.0 
5.2 
5.5 

4.3 
4.5 
4.7 
4.9 
5.1 

4.0 
4.2 
4.4 
4.6 
4.8 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

19.2 
23.8 

15.9 
18.9 
23.5 

13.5 
15.6 
18.6 
23.1 

11.7 
13.3 
15.4 
18.3 
22.7 

10.3 
11.5 
13.1 
15.1 
18.0 

9.2 
10.2 
11.3 
12.8 
14.9 

8.3 

9.1 

10.0 

11.1 

12.6 

7.5 
8.2 
8.9 
9.8 
10.9 

6.9 
7.4 
8.0 
8.7 
9.6 

6.3 
6.8 
7.3 
7.9 

8.6 

5.8 
6.2 
6.6 

7.1 
7.7 

5.4 
5.7 
6.1 
6.5 
7.0 

5.0 
5.3 
5.6 
6.0 
6.4 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

22.3 

22.3 

17.7 
21.9 

14.6 
17.4 
21.5 

12.4 
14.3 
17.0 
21.1 

10.7 
12.1 
14.0 
16.7 
20.6 

9.4 
10.5 
11.9 
13.8 
16.3 

8.4 

9.2 

10.3 

11.7 

13.5 

7.5 

8.2 

9.1 

10.1 

11.4 

6.8 
7.4 
8.1 
8.9 
9.9 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

17.7 
14.6 
12.4 
10.7 
9.4 

21.9 
17.4 
14.3 
12.1 
10.5 

21.5 
17.0 
14.0 
11.9 

21.1 
16.7 
13.8 

20.6 
16.3 

20.2 

20.2 

16.0 
19.8 

13.2 
15.6 
19.3 

y.i 

12.9 
15.3 
18.9 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

8.4 
7.5 
6.8 
6.2 
5.7 

9.2 
8.2 
7.4 
6.7 
6.1 

10.3 
9.1 
8.1 
7.2 
6.5 

11.7 

10.1 

8.9 

7.9 

7.1 

13.5 

11.4 

9.9 

8.7 
7.7 

16.0 

13.2 

11.1 

9.6 

8.5 

19.8 
15.6 
12.9 
10.9 
9.4 

19.3 
15.3 
12.6 
10.6 

18.9 
14.9 
12.2 

18.4 
14.5 

17.9 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

5.3 
4.9 
4.5 
4.2 
3.9 

5.6 
5.2 
4.8 
4.4 
4.1 

6.0 
5.5 
5.0 
4.6 
4.3 

6.4 
5.8 
5.3 
4.9 
4.5 

6.9 
6.2 
5.7 
5.2 
4.8 

7.5 
6.7 
6.1 
5.5 
5.1 

8.2 
7.3 
6.6 
5.9 
5.4 

9.2 

8.0 
7.1 
6.4 
5.8 

10.4 
8.9 
7.8 
6.9 
6.2 

11.9 

10.1 

8.7 

7.6 

6.7 

14.1 

11.6 

9.8 

8.5 
7.4 

17.4 

13.8 

11.3 

9.5 

8.2 

17.0 

13.4 

11.0 

9.3 

40 
41 
42 
43 
44 

45 
46 
47 

48 
49 

3.7 
3.5 
3.3 
3.1 
2.9 

3.8 
3.6 
3.4 
3.2 
3.0 

4.0 
3.7 
3.5 
3.3 
3.1 

4.2 
3.9 
3.6 
3.4 
3.2 

4.4 
4.1 
3.8 
3.5 
3.3 

4.7 
4.3 
4.0 
3.7 
3.4 

4.9 
4.5 
4.2 
3.9 
3.6 

5.2 
4.8 
4.4 
4.0 
3.7 

5.6 
5.1 
4.6 
4.3 
3.9 

6.0 
5.4 
4.9 
4.5 
4.1 

6.6 
5.9 
5.3 
4.8 
4.4 

7.2 
6.4 
5.7 
5.1 
4.6 

8.0 
7.0 
6.2 
5.5 
5.0 

45 

46 
47 
48 
49 

50 
51 
52 
53 
54 

2.7 
2.6 
2.4 
2.3 
2.2 

2.8 
2.6 
2.5 
2.3 
2.2 

2.9 
2.7 
2.6 
2.4 
2.3 

3.0 
2.8 
2.6 
2.5 
2.3 

3.1 
2.9 
2.7 
2.5 
2.4 

3.2 
3.0 
2.8 
2.6 
2.5 

3.3 
3.1 

2.9 
2.7 
2.5 

3.5 
3.2 
3.0 
2.8 
2.6 

3.6 
3.4 
3.1 
2.9 

2.7 

3.8 
3.5 
3.2 
3.0 
2.8 
2.6 
2.4 
2.3 
2.1 
2.0 
1.9 

4.0 
3.7 
3.4 
3.1 
2.9 
2.7 
2.5 
2.3 
2.2 
2.0 
1.9 

4.2 
3.9 
3.6 
3.3 
3.0 

4.5 
4.1 
3.7 
3.4 
3.2 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 

2.0 
1.9 
1.8 
1.7 
1.6 
1.6 

2.1 
2.0 
1.9 
1.8 
1.7 
1.6 

2.1 
2.0 
1.9 
1.8 
1.7 
1.6 

2.2 
2.1 
2.0 
1.8 
1.7 
1.6 

2.3 
2.1 
2.0 
1.9 
1.8 
1.7 

2.3 
2.2 
2.0 
1.9 
1.8 
.    1.7 

2.4 
2.2 

2.1 
2.0 
1.9 
1.7 

2.4 
2.3 
2.2 
2.0 

1.9 
1.8 

2.5 
2.4 
2.2 
2.1 
1.9 
1.8 

2.8 
2.6 
2.4 
2.3 
2.1 
2.0 

2.9 
2.7 
2.5 
2.3 
2.2 
2.0 

55 
56 
57 
58 
59 
60 

'26° 

26° 

27° 

28° 

29° 

80° 

81° 

32° 

38° 

84° 

85°i 

36° 

37° 

Declination  of  the  same  name  as  the  latitude;  upper  transit;  reduction  addltlre. 

TABLE  26. 

[Page 

707 

Vajiation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  the 

same  name  as  the  latitude;  upper  transit 

reduction  addltlre. 

Lati- 
tude. 

38° 

89° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

60° 

o 

0 

2.5 

2.4 

2.3 

II 
2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

o 

0 

1 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

1.7 

1 

2 

2.6 

2.5 

2.4 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

2 

3 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

3 

4 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

4 

5 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

5 

6 

2.9 

2.8 

2.7 

2.6 

2.6 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

6 

7 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.8 

7 

8 

3.1 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

1.9 

8 

9 

3.2 

3.0 

2.9 

2.8 
2.8 

2.7 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

9 

10 

3.3 

3.1 

3.0 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

10 

11 

3.4 

3.2 

3.1 

2.9 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

2.1 

2.1 

2.0 

11 

12 

3.5 

3.3 

3.1 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

12 

13 

3.6 

3.4 

3.2 

3.1 

2.9 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

2.1 

2.0 

13 

14 

3.7 

3.5 

3.3 

3.2 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

14 

15 

3.8 

3.6 

3.4 

3.3 

3.1 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

2.1 

15 

16 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

2.9 

2.8 

2.6 

2.5 

2.4 

2.3 

2.2 

16 

17 

4.1 

3.9 

3.7 

3.5 

3.3 

3.1 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

17 

18 

4.3 

4.1 

3.8 

3.6 

3.4 

3.2 

3.1 

2.9 

2.8 

2.6 

2.6 

2.4 

2.3 

18 

19 

4.5 

4.2 

4.0 

3.7 

3.5 

3.3 

3.2 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

19 
20 

20 

4.7 

4.4 

4.1 

3.9 

3.7 

3.5 

3.3 

3.1 

2.9 

2.8 

2.6 

2.6 

2.4 

21 

4.9 

4.6 

4.3 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

2.9 

2.7 

2.6 

2.4 

21 

22 

5.2 

4.8 

4.5 

4.2 

4.0 

3.7 

3.6 

3.3 

3.1 

2.9 

2.8 

2.6 

2.5 

22 

23 

5.5 

5.1 

4.7 

4.4 

4.1 

3.9 

3.6 

3.4 

3.2 

3.0 

2.9 

2.7 

2.6 

23 

24 

5.8 

5.4 

5.0 

4.6 

4.3 

4.0 

3.8 

3.5 

3.3 

3.1 

3.0 

2.8 

2.6 

24 

25 

6.2 

5.7 

5.3 

4.9 

4.5 

4.2 

3.9 

3.7 

3.5 

3.3 

3.1 

2.9 

2.7 

26 

26 

6.7 

6.1 

5.6 

5.2 

4.8 

4.4 

4.1 

3.8 

3.6 

3.4 

3.2 

3.0 

2.8 

26 

27 

7.2 

6.5 

6.0 

5.5 

5.0 

4.6 

4.3 

4.0 

3.7 

3.5 

3.3 

3.1 

2.9 

27 

28 

7.9 

7.1 

6.4 

5.8 

5.3 

4.9 

4.5 

4.2 

3.9 

3.6 

3.4 

3.2 

3.0 

28 

29 

8.7 

7.7 

6.9 

6.2 

5.7 

5.2 

4.8 

4.4 

4.1 

3.8 

3.6 

3.3 

3.1 

29 

30 

9.6 

8.5 

7.5 

6.7 

6.1 

5.5 

5.1 

4.7 

4.3 

4.0 

3.7 

3.4 

3.2 

30 

31 

10.9 

9.4 

8.2 

7.3 

6.6 

5.9 

5.4 

4.9 

4.6 

4.2 

3.9 

3.6 

3.3 

31 

32 

12.6 

10.6 

9.2 

8.0 

7.1 

6.4 

5.8 

5.2 

4.8 

4.4 

4.0 

3.7 

3.5 

32 

33 

14.9 

12.2 

10.4 

8.9 

7.8 

6.9 

6.2 

5.6 

5.1 

4.6 

4.3 

3.9 

3.6 

33 

34 

18.4 

14.5 

11,9 

10.1 

8.7 

7.6 

6.  7       6. 0 

5.4 

4.9 

4.5 

4.1 

3.8 

34 

35 

17.9 

14.1 

11.6 

9.8 

8.5 

7. 4       6. 6 

5.9 

5.3 

4.8 

4.4 

4.0 

35 

36 

17.4 

13.8 

11.3 

9.5 

8.2 

7.2 

6.4 

5.7 

5.1 

4.6 

4.2 

36 

37 

17.0 

13.4 

11.0 

9.3 

8.0 

7.0 

6.2 

6.6 

5.0 

4.6 

37 

38 

16.5 

13.0 

10.7 

9.0 

7.7 

6.8 

6.0 

6.3 

4.8 

38 

39 

16.0 

12.6 

10.3 

8.7 

7.6 

6.5 

5.8 

6.1 

39 

40 

15.6 

12.2 

10.0 

8.4 

7.2 

6.3 

5.6 

40 

41 

15.0 

11.8 

9.7 

8.1 

7.0 

6.1 

41 

42 

16.5 

14.5 

11.4 

9.3 

7.9 

6.7 

42 

43 

13.0 

16.0 

14.0 

11.0 

9.0 

7.6 

43 

44 

10.7 

12.6 

15.5 

13.6 

10.6 

8.7 

44 

45 

9.0 

10.3 

12.2 

15.0 

13.1 

10.2 

45 

46 

7.7 

*8.7 

10.0 

11.8 

14.5 

12.6 

46 

47 

6.8 

7.5 

8.4 

9.7 

11.4 

14.0 

47 

48 

6.0 

6.5 

7.2 

8.1 

9.3 

11.0 

13.6 

48 

49 

5.3 

5.8 

6.3 

7.0 

7.9 

9.0 

10.6 

13.1 

49 
50 

50 

4.8 

5.1 

5.6 

6.1 

6.7 

7.6 

8.7 

10.2 

12.6 

51 

4.3 

4.6 

5.0 

5.4 

5.9 

6.6 

7.3 

8.4 

9.9 

12.1 

1 

51 

52 

3.9 

4.2 

4.5 

4.8 

5.2 

5.7 

6.3 

7.0 

8.0 

9.5 

11.6 

52 

53 

3.6 

3.8 

4.0 

4.3 

4.6 

5.0 

5.4 

6.0 

6.7 

7.7 

9.1 

11.1 

63 

54 

3.3 

3.5 

3.7 

3.9 

4.1 

4.4 

4.8 

5.2 

5.8 

6.6 

7.4 

8.7 

10.6 

54 

55 

3.0 

3.2 

3.3 

3.5 

3.7 

4.0 

4.3 

4.6 

5.0 

5.5 

6.2 

7.1 

8.3 

55 

56 

2.8 

2.9 

3.1 

3.2 

3.4 

3.6 

3.8 

4.1 

4.4 

4.8 

5.3 

5.9 

6.8 

56 

57 

2.6 

2.7 

2.8 

2.9 

3.1 

3.2 

3.4 

3.6 

3.9 

4.2 

4.6 

6.0 

5.6 

57 

58 

2.4 

2.5 

2.6 

2.7 

2.8 

2.9 

3.1 

3.3 

3.5 

3.7 

4.0 

4.4 

4.8 

58 

59 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

3.0 

3.1 

3.3 

3.6 

3.8 

4.2 

59 

60 

2.1 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

3.0 

3.2 

3.4 

3.6 

60 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

60° 

De 

clinatioi 

1  of  the 

same  na 

me  as  the  latitude;  uppei 

r  transit 

reducti 

on  addil 

iTe, 



Page  708] 

TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  the  f 

same  name  as  the  latitude:  nppei 

transit 

reduction  addltlre. 

Lati- 
tude. 

Lati- 
tude. 

51° 

52° 

68° 

64° 

55° 

56° 

57° 

68° 

59° 

60° 

61° 

62° 

68° 

0 

II 

// 

II 

11 

u 

II 

II 

11 

II 

1/ 

. 

II 

II 

o 

0 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

0 

1 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1 

2 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

2 

3 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

3 

4 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

4 

5 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

1.1 

5 

6 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

6 

7 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

7 

8 

1.8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

1.1 

1.1 

8 

9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

9 

10 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

10 

11 

1.9 

1.8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

11 

12 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

1.1 

12 

13 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

13 

14 

2.0 
2.0 

1.9 

1.8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

14 

15 

1.9 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

15 

16 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

16 

17 

2.1 

2.0 

1.9 

1.8 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

17 

18 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

18 

19 
20 

2.2 
2.3 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

19 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

20 

21 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.2 

21 

22 

2.4 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.3 

1.3 

22 

23 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

1.3 

23 

24 

2.5 

2.4 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

24 

25 

2.6 

2.4 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.3 

25 

26 

2.6 

2.5 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.3 

26 

27 

2.7 

2.6 

2.4 

2.3 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

27 

28 

2.8 

2.6 

2.5 

2.3 

2.2 

2.1 

2.0 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

28 

29 

2.9 

2.7 

2.5 

2.4 

2.3 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

29 

80 

3.0 

2.8 

2.6 

2.5 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

30 

31 

3.1 

2.9 

2.7 

2.5 

2.4 

2.2 

2.1 

2.0 

1.9 

1.7 

1.6 

1.5 

1.4 

31 

32 

3.2 

3.0 

?.8 

2.6 

2.4 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

32 

33 

3.4 

3.1 

2.9 

2.7 

2.5 

2.4 

2.2 

2.1 

1.9 

1.8 

1.7 

1.6 

1.5 

33 

34 

3.5 

3.2 

3.0 

2.8 

2.6 

2.4 

2.3 

2.1 

2.0 

1.9 

1.7 

1.6 

1.5 

34 

35 

3.7 

3.4 

3.1 

2.9 

2.7 

2.5 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

35 

36 

3.9 

3.6 

3.3 

3.0 

2.8 

2.6 

2.4 

2.3 

2.1 

2.0 

1.8 

1.7 

1.6 

36 

37 

4.1 

3.7 

3.4 

3.2 

2.9 

2.7 

2.5 

2.3 

2.2 

2.0 

1.9 

1.7 

1.6 

37 

38 

4.3 

3.9 

3.6 

3.3 

3.0 

2.8 

2.6 

2.4 

2.2 

2.1 

1.9 

1.8 

1.7 

38 

39 

4.6 

4.2 

3.8 

3.5 

3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

2.0 

1.8 

1.7 

39 

40 

5.0 

4.5 

4.0 

3.7 

3.3 

3.1 

2.8 

2.6 

2.4 

2.2 

2.0 

1.9 

1.8 

40 

41 

5.4 

4.8 

4.3 

3.9 

3.5 

3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

1.9 

1.8 

41 

42 

5.9 

5.2 

•1.6 

4.1 

3.7 

3.4 

3.1 

2.8 

2.6 

2.4 

2.2 

2.0 

1.9 

42 

43 

6.5 

5.7 

5.0 

4.4 

4.0 

3.6 

3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

1.9 

43 

44 

7.3 

6.3 

5.4 

4.8 

4.3 

3.8 

3.4 

3.1 

2.8 

2.6 

2.3 

2.2 

2.0 

44 

45 

8.4 

7.0 

6.0 

5.2 

4.6 

4.1 

3.6 

3.3 

3.0 

2.7 

2.4 

2.2 

2.0 

45 

46 

9.9 

8.0 

6.7 

5.8 

5.0 

4.4 

3.9 

3.5 

3.1 

2.8 

2.6 

2.3 

2.1 

46 

47 

12.1 

9.5 

7.7 

6.5 

5.5 

4.8 

4.2 

3.7 

3.3 

3.0 

2.7 

2.4 

2.2 

47 

48 

11.6 

9.1 

7.4 

6.2 

5.3 

4.6 

4.0 

3.6 

3.2 

2.8 

2.6 

2.3 

48 

49 

11.1 

8.7 

7.1 

5.9 

5.0 

4.4 

3.8 

3.4 

3.0 

2.7 

2.4 

49 

50 

10.6 

8.3 

6.8 

5.6 

4.8 

4.2 

3.6 

3.2 

2.9 

2.6 

50 

51 

10.2 

7.9 

6.4 

5.4 

4.6 

4.0 

3.5 

3.0 

2.7 

51 

52 

9.7 

7.6 

6.1 

5.1 

4.3 

3.8 

3.3 

2.9 

52 

53 

9.2 

7.2 

5.9 

4.9 

4.1 

3.6 

3.1 

53 

54 

8.8 

6.8 

5.5 

4.6 

3.9 

3.4 

54 

55 

10.2 

8.3 

6.5 

5.3 

4.3 

3.7 

55 

56 

7.9 

9.7 

7.9 

6.1 

5.0 

4.1 

56 

57 

6.4 

7.6 

9.2 

7.4 

5.8 

4.7 

57 

58 

5.4 

6.1 

7.2 

8.8 

7.0 

5.4 

58 

59 

4.6 

5.1 

5.9 

6.8 

8.3 

6.6 

59 

60 

4.0 

4.3 

4.9 

5.5 

6.5 

7.9 

60 

51° 

520 

580 

54° 

55° 

56° 

57° 

68° 

59° 

60° 

61° 

62° 

68° 

De 

clinatio 

Q  of  the 

same  na 

me  as  th 

e  latitude;  uppe 

r  transit 

;  reduct 

ion  addl 

tire. 

TABLE  26. 

[Page 

709 

Variation  of  Altitude  in  one  minute  from  meridian 

passage 

• 

Declination  of  a  different  name  from  the  latitude 

;  apper  transit:  reduction  addltlre. 

Lati- 
tnde. 

Lati- 
tude. 

0° 

1° 

2° 

3° 

4" 

6° 

6° 

7° 

8° 

»° 

10° 

11° 

O 

H 

» 

« 

u 

H 

n 

H 

» 

K 

II 

n 

II 

o 

0 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

11.1 

10.1 

0 

1 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

11.2 

10.1 

9.3 

1 

2 

28.1 

22.4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

2 

3 

28.1 

22.4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

3 

4 

28.1 

22.4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

7.4 

4 

5 

22,4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

7.4 

7.0 

6 

6 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

7.6 

7.0 

6.6 

6 

7 

16.0 

14.0 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6.2 

7 

8 

14.0 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6.2 

5.9 

8 

9 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 
6.2 

6.2 

5.9 

5.6 

9 

10 

11.1 

10.1 

9.3 

8.6 

8.0 

7.4 

7.0 

6.6 

5.9 

5.6 

6.3 

10 

11 

10.1 

9.3 

8.6 

8.0 

7.4 

7.0 

6.6 

6.2 

6.9 

5.6 

5.3 

5.1 

11 

12 

9.2 

8.5 

7.9 

7.4 

7.0 

6.5 

6.2 

5.9 

6.6 

5.3 

6.0 

4.8 

12 

13 

8.5 

7.9 

7.4 

6.9 

6.5 

6.2 

5.8 

5.6 

5.3 

5.0 

4.8 

4.6 

13 

14 

7.9 

7.4 

6.9 

6.5 

6.2 

5.8 

5.5 

5.3 

6.0 

4.8 

4.6 

4.4 

14 

15 

7.3 

6.9 

6.5 

6.1 

5.8 

5.5 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

15 

16 

6.8 

6.5 

6.1 

5.8 

5.5 

5.2 

5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

16 

17 

6.4 

6.1 

5.8 

5.5 

5.2 

5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

17 

18 

6.0 

5.7 

5.5 

5.2 

5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

3.8 

18 

19 

5.7 

5.4 

5.2 

4.9 

4.7 

4.5 

4.4 

4.2 

4.0 

3.9 

3.8 

3.6 

19 

20 

5.4 

5.1 

4.9 

4.7 

4.5 

4.3 

4.2 

4.0 

3.9 

3.8 

3.6 

3.5 

20 

21 

5.1 

4.9 

4.7 

4.5 

4.3 

4.2 

4.0 

3.9 

3.7 

3.6 

3.5 

3.4 

21 

22 

4.9 

4.7 

4.6 

4.3 

4.1 

4.0 

3.9 

3.7 

3.6 

3.6 

3.4 

3.3 

22 

23 

4.6 

4.4 

4.3 

4.1 

4.0 

3.8 

3.7 

3.6 

3.6 

3.4 

3.3 

3.2 

23 

24 

4.4 

4.2 

4.1 

3.9 

3.8 

3.7 

3.6 

3.5 
3.3 

3.4 

3.3 

3.2 

3.1 

24 

25 

4.2 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.2 

3.1 

3.1 

3.0 

25 

26 

4.0 

3.9 

3.8 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

3.0 

2.9 

26 

27 

3.9 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

27 

28 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

28 

29 

3.5 

3.4 

3.3 

3.2 

3.1 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

29 

30 

3.4 

3.3 

3.2 

3.1 

3.0 

3.0 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

30 

31 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

2.5 

31 

32 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.6 

2.5 

2.4 

32 

33 

3.0 

2.9 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

2.6 

2.4 

2.4 

2.3 

33 

34 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

34 

35 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

35 

36 

2.7 

2.6 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

36 

37 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.2 

2.1 

2.1 

37 

38 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

38 

39 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

2.0 

39 

40 

2.3 

2.3 

2.2 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

40 

41 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

41 

42 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

42 

43 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

43 

44 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

44 

45 

2.0 

1.9 

1.9' 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

45 

46 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

46 

47 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.6 

47 

48 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.6 

1.5 

1.6 

48 

49 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 
1.5 

1.5 

1.6 

49 

50 

1.6 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

50 

51 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

51 

52 

1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

52 

53 

1.5 

1.5 

1.4 

1.4 

1.4 

\A 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

53 

54 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

54 

55 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

55 

56 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

56 

57 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

57 

58 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

58 

59 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

59 

60 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1  0 

1.0 

1.0 

60 

0° 

1° 

2° 

8° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

Declii 

lation  o 

a  differ 

ent  name 

from  th 

e  latitude 

;  upper  ti 

ansit;  rec 

luction  a( 

Idltire. 

Page  710] 

TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  additive. 

Lati- 
tude. 

12° 

18° 

14° 

16° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

o 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

o 

0 

9.2 

8.5 

7.9 

7.3 

6.8 

6.4 

6.0 

5.7 

5.4 

5.1 

4.9 

4.6 

4.4 

0 

1 

8.5 

7.9 

7.4 

6.9 

6.5 

6.1 

5.7 

5.4 

5.1 

4.9 

4.7 

4.4 

4.2 

1 

2 

7.9 

7.4 

6.9 

6.5 

6.1 

5.8 

5.5 

5.2 

4.9 

4.7 

4.5 

4.3 

4.1 

2 

3 

7.4 

6.9 

6.5 

6.1 

5.8 

5.5 

5.2 

4.9 

4.7 

4.5 

4.3 

4.1 

3.9 

3 

4 

7.0 

6.5 

6.2 

5.8 

5.5 

5.2 

5.0 

4.7 

4.5 

4.3 

4.1 

4.0 

3.8 

4 

5 

6.5 

6.2 

5.8 

5.5 

5.2 

5.0 

4.8 

4.5 

4.3 

4.2 

4.0 

3.8 

3.7 

6 

6 

6.2 

5.8 

5.5 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

4.0 

3.9 

3.7 

3.6 

6 

7 

5.9 

5.6 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

4.0 

3.9 

3.7 

3.6 

3.5 

7 

8 

5.6 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

4.0 

3.9 

3.7 

3.6 

3.5 

3.4 

8 

9 
10 

5.3 

6.0 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

3.8 

3.6 

3.5 

3.4 

3.3 

9 

5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

3.8 

3.6 

3.5 

3.4 

3.3 

3.2 

10 

11 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

3.8 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

11 

12 

4.6 

4.4 

4.3 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

12 

13 

4.4 

4.3 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

13 

14 

4.2 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

14 

15 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

15 

16 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

16 

17 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

17 

18 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.5 

18 

19 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

19 

20 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

20 

21 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

2.4 

21 

22 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

2.4 

2.3 

22 

23 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

2.4 

2.3 

2.3 

23 

24 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

24 

25 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

25 

26 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.1 

2.1 

26 

27 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

27 

28 

2.6 

2.6 

2.5 

2.5 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

28 

29 

2.6 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

29 

30 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

30 

31 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

31 

32 

2.3 

2.3 

2.2 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

32 

33 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

33 

34 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

34 

35 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

35 

36 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

36 

37 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

37 

38 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

38 

39 
40 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

39 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

40 

41 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.6 

41 

42 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.6 

42 

43 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

43 

44 

1.7 

1.6 
1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.5 

,1.4 

1.4 

1.4 

44 

45 

45 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

46 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

46 

47 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

47 

48 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

48 

49 
50 

1.4 
1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

49 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

60 

51 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

61 

52 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

52 

53 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

53 

54 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

54 

55 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

66 

56 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

66 

57 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

57 

58 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

58 

59 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

59 

60 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

60 

12° 

18° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

Decl 

ination 

3f  a  diffe 

rent  nai 

ne  from 

the  latit 

ude;  up 

per  trans 

it;  redu 

ction  ad 

dltlve. 

TABLE  26. 

[Page  711 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  additire. 

tude. 

Lati- 
tude. 

26° 

26° 

27° 

28° 

29° 

30° 

81° 

82° 

83° 

84° 

86° 

36° 

87° 

0 

II 

// 

n 

II 

u 

II 

n 

II 

II 

II 

II 

II 

// 

0 

0 

4.2 

4.0 

3.9 

3.7 

3.5 

3.4 

3.3 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

0 

1 

4.1 

3.9 

3.7 

3.6 

3.4 

3.3 

3.2 

3.1 

2.9 

2.8 

2.7 

2.6 

2.6 

1 

2 

3.9 

3.8 

3.6 

3.5 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2 

3 

3.8 

3.6 

3,5 

3.4 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

3 

4 

3.7 

3.5 

3.4 

3.3 

3.2 

3.0 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

4 

5 

3.6 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

5 

6 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.4 

2.3 

6 

7 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.5 

2.4 

2.3 

2.2 

7 

8 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

2.4 

2.3 

2.3 

2.2 

8 

9 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.4 

2.3 

2.2 

2.2 

9 
10 

10 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

11 

3.0 

2.9 

2.8 

2.7 

2.6 

2.5 

2.5 

2.4 

2.3 

2.3 

2.2 

2.1 

2.1 

11 

12 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.0 

12 

13 

2.8 

2.7 

2.7 

2.6 

2.5 

2.4 

2.4 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

13 

14 

2.7 

2.7 

2.6 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.1 

2.1 

2,0 

2.0 

14 

15 

2.7 

2.6 

2.5 

2.5 

2.4 

2.3 

2.3 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

15 

16 

2.6 

2.5 

2.6 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.0 

2.0 

1.9 

1.9 

16 

17 

2.5 

2.5 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

17 

18 

2.5 

2.4 

2.4 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

18 

19 

2.4 

2.4 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

19 

20 

2.4 

2.3 

2.3 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

20 

21 

2.3 

2.3 

2.2 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

21 

22 

2.3 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

22 

23 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

23 

24 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.6 

24 

25 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.8 

1,7 

1.7 

1.6 

1.6 

25 

26 

2.1 

2.0 

2.0 

1.9 

•  1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

26 

27 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

27 

28 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

28 

29 

1.9 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

29 

30 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

30 

31 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

31 

32 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1,4 

32 

33 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1,4 

33 

34 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 
1.5 

1.5 

1.5 

1.4 

1.4 

1,4 

34 

35 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1,4 

35 

36 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1,3 

36 

37 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

37 

38 

1.6 

1.5 

1.5 

1.5 

1.5- 

1.5 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

38 

39 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

39 

40 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

40 

41 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

41 

42 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

42 

43 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

43 

44 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1,2 

44 

45 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

45 

46 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

46 

47 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

47 

48 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

48 

49 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

49 

50 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

50 

51 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

51 

52 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

52 

53 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

53 

54 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

54 

55 

1.0 

1.0 

1.0 

1.0 

1.0 

55 

56 

1.0 

1.0 

1.0 

1.0 

56 

57 

1.0 

1.0 

1.0 

57 

58 
59 
60 

1.0 
0.9 

0.9 

58 
59 
60 

6.8 
0.8 

0.^ 

26° 

26° 

27° 

28° 

29° 

S0° 

Sl° 

82° 

88° 

84° 

86° 

36° 

87° 

Dec] 

ination 

of  the  8 

tmenan 

le  as  the 

latitud* 

3;  lower 

transit; 

reductic 

)n  snbtr 

Mtire. 

Page  712]                                         TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  a  different  name  from  tlie  latitude;  upper  transit;  reduction  addltire.                    1 

Lati- 
tude. 

88° 

89° 

40° 

41° 

42° 

48° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

o 

0 
1 
2 
3 
4 

// 

2.5 
2.5 
2.4 
2.4 
2.3 

2.4 
2.4 
2.3 
2.3 
2.2 

II 

2.3 
2.3 
2.3 
2.2 

2.2 

II 

2.3 
2.2 
2.2 
2.1 
2.1 

n 

2.2 
2.1 
2.1 
2.1 
2.0 

II 

2.1 
2.1 
2.0 
2.0 
2.0 

// 

2.0 
2.0 
2.0 
1.9 
1.9 

II 

2.0 
1.9 
1.9 
1.9 
1.8 

II 

1.9 
1.9 
1.8 
1.8 
1.8 

II 

1.8 
1.8 
1.8 
1.8 
1.7 

II 

1,8 
1.7 

1.7 
1.7 
1.7 

II 

1.7 
1.7 
1.7 
1.6 
1.6 

II 

1.7 
1.6 
1.6 
1.6 
1.6 

o 

0 
1 

2 
3 
4 

5 
6 

7 
8 
9 

2.3 
2.2 
2.2 
2.1 
2.1 

2.2 
2.2 
2.1 
2.1 
2.0 

2.1 
2.1 
2.0 
2.0 
2.0 

2.1 
2.0 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.9 

1.9 
1.9 
1.9 
1.8 
1.8 

1.9 
1.8 
1.8 
1.8 
1.8 

1.8 
1.8 
1.8 
1.7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.6 

1.7 
1.7 
1.6 
1.6 
1.6 

1.6 
1.6 
1.6 
1.6 
1.6 

1.6 
1.6 
1.5 
1.5 
1.5 

1.5 
1.5 
1.5 
1.5 
1.5 

5 
6 

7 
8 
9 

10 
11 
12 
13 

14 

2.1 
2.0 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.9 

1.9 
1.9 
1.9 
1.8 
1.8 

1.9 
1.8 
1.8 
1.8 
1.8 

1.8 
1.8 
1.8 
1.7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.7 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.6 
1.6 
1.6 
1.6 

1.6 
1.6 
1.6 
1.6 
1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.5 
1.5 
1.5 
1.5 
1.4 

1.5 
1.5 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.4 
1.4 

10 
11 
12 
13 
14 

15 
16 
17 

18 
19 

1.9 
1.8 
1.8 
1.8 
1.7 

1.8 
1.8 
1.8 
1.7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.7 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.7 
1.6 
1.6 
1.6 

1.6 
1.6 
1.6 
1.6 

1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.6 
1.5 
1.5 
1.5 

1.5 

1.5 
1.5 

1.5 
1.4 
1.4 

1.5 
1.4 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.3 
1.3 
1.3 
1.3 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.6 
1.6 
1.6 
1.6 

1.6 
1.6 
1.6 
1.6 
1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.6 
1.5 
1.5 
1.5 

1.5 

1.5 
1.5 
1.5 
1.4 
1.4 

1.5 
1.5 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.3 
1.3 
1.3 
1.3 
1.3 

1.3 
1.3 
1.3 
1.3 

1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

1.6 
1.6 
1.5 
1.5 
1.5 

1.5 
1.5 
1.5 
1.5 
1.4 

1.5 
1.5 
1.5 
1.4 
1.4 

1.5 
1.5 

1.4 
1.4 
1.4 

1.4 
1.4 
1.4 

1.4 
1.4 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.3 
1.3 
1.3 
1.3 
1.3 

1.3 
1.3^ 
1.3 
1.3 

1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 
1.2 

1.2 

1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.1 
1.1 

25 
26 

27 
28 
29 

30 
31 
32 
33 
34 

1.5 
1.4 
1.4 
1.4 
1.4 

1.4 
1.4 
1.4 
1.4 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.4 
1.3 
1.3 
1.3 
1.3 

1.3 
1.3 
1.3 
1.3 
1.3 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 

1.2 

1.2 
1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.1 
1.1 

1.2 
1.2 
1.1 
1.1 
1.1 

1.1 
1.1 
1.1 
1.1 
1.1 

1.1 
1.1 
1.1 
1.1 
1.1 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

1.3 
1.3 
1.3 
1.3 

1.2 

1.3 
1.3 
1.3 
1.2 

1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.3 
1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 
1.1 

1.2 
1.2 
.    1.2 
1.1 
1.1 

1.2 
1.1 
1.1 
1.1 
1.1 

1.1 
1.1 
1.1 
1.1 

1.1 
1.1 
1.1 

1.1 
1.1 

1.1 

35 
36 

37 
38 
39 

40 
41 
42 
43 
44 

1.2 
1.2 
1.2 
1.2 
1.1 

1.2 
1.2 
1.2 
1.1 
1.1 

1.2 
1.2 
1.1 
1.1 
1.1 

1.2 
1.1 
1.1 
1.1 

1.1 
1.1 
1.1 

1.1 
1.1 

1.1 

40 
41 
42 
43 
44 

45 
46 

47 
48 
49 

1.1 
1.1 

1.1 

45 
46 
47 
48 
49 

0.9 
0.9 
0.9 
0.8 

0.9 
0.9 
0.9 

0.9 
0.9 

0.9 

50 
51 
52 
53 
54 

0.9 
0.9 
0.9 
0.8 
0.8 

0.9 
0.9 
0.8 
0.8 
0.8 

0.9 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

50 
51 
52 
53 
54 

0.9 
0.9 
0.8 
0.8 

0.9 
0.9 
0.8 

0.9 
0.9 

0.9 

55 
56 
57 
58 
59 
60 

0.9 
0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 
0.7 

0.8 
0.8 
0.8 
0.8 
0.8 
0.7 

0.8 
0.8 
0.8 
0.8 
0.7 
0.7 

0.8 
0.8 
0.8 
0.8 
0.7 
0.7 

0.8 
0.8 
0.8 
0.7 
0.7 
0.7 

0.8 
0.8 
0.7 
0.7 
0.7 
0.7 

0.8 
0.7 
0.7 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 
0.7 

55 
56 
57 
58 
59 
60 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 

88° 

89° 

40° 

41° 

42° 

48° 

44° 

43° 

46° 

47° 

48° 

49° 

50° 

Declination  of  the  same  name  as  the  latitude;  lower  transit;  reduction  snbtractlre. 

TABLE  26. 

[Page 

713 

Variation  of  Altitude  in  one  minute  from  meridian  passj^e. 

Lati- 
tude. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  addltlre.                 1 

Lati- 
tude. 

51° 

520 

58° 

54° 

55° 

56° 

57° 

68° 

59° 

60° 

61° 

62° 

68° 

o 

„ 

„ 

II 

II 

„ 

„ 

II 

„ 

„ 

„ 

II 

II 

II 

o 

0 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

0 

1 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1 

2 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

2 

3 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

3 

4 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

4 

5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

5 

6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

'l.l 

1.0 

1.0 

1.0 

6 

7 

1.4 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

7 

8 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

8 

9 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

9 

10 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

10 

11 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

11 

12 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

0.9 

12 

13 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

13 

14 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

14 

15 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

15 

16 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

16 

17 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

17 

18 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

18 

19 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

19 

20 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

0.8 

20 

21 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

0.8 

21 

22 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

22 

23 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

23 

24 

1.2 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

24 

25 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

25 

26 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

26 

27 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

27 

28 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

28 

29 

1.1 

1.1 

1.0 

1.0 

1.0 

29 

30 

1.1 

1.1 

1.0 

1.0 

30 

31 

1.1 

1.0 

1.0 

31 

32 
33 
34 

1.1 
1.1 

1.0 

32 
33 
34 

6.8 
0.7 

6.6 

35 
36 
37 
38 
39 

6.^ 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

35 
36 
37 
38 
39 
40 
41 
42 
43 
44 

6.8 
0.8 
0.8 
0.8 

6.^ 

0.8 
0.8 

0.8 
0.8 

6.^ 

40 
41 
42 
43 
44 

6.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0,8 
0.7 
0.7 

0.8 
0.7 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

0.9 
0.8 
0.8 
0.8 

0.9 
0.9 
0.8 

0.9 
0.9 

0.9 

45 

0.9 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

45 

46 

0.9 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

46 

47 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

47 

48 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

48 

49 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

49 

50 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

50 

51 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

51 

52 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

52 

53 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

53 

54 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

54 

55 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

55 

56 

0.7 

0.7 

•0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

56 

57 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

57 

58 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

58 

59 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.5 

59 

60 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.5 

60 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

68° 

69° 

60° 

61° 

62° 

68° 

D 

eclinati( 

)n  of  the 

same  nt 

ime  as  t 

tie  latitu 

de;  lone 

r  transit 

;  reduct 

ion  Bttbt 

ractire. 

Page  714] 

TABLE  27. 

Reduction  to  be  applied 

to  Altitudes  near  the  Meridian. 

Var. 

Time  from  meridian  passage.                                                                  1 

Var. 
1  min. 
(Table 

(Table 

m.  s. 

m.  s. 

TO.  8. 

7».  S. 

m.  s. 

TO.  S. 

TO.  8. 

TO.  8. 

TO.  «. 

TO.  8. 

TO.  «. 

TO.  «. 

TO.  i. 

26.) 

0  80 

1  0 

1  30 

2  0 

2  30 

S  0 

3  80 

4  0 

4  80 

5  0 

5  30 

6  0 

6  30 

26.) 

// 

/     n 

1    II 

/    // 

1    n 

I    II 

'     n 

1    II 

/     II 

/     // 

1     II 

/     // 

/    // 

'     // 

II 

0.1 

00 

0    0 

0    0 

0    0 

0    1 

0    1 

0    1 

0    2 

0    2 

0    2 

0    3 

0    4 

0    4 

0.1 

0.2 

00 

0    0 

0    0 

0    1 

0    1 

0    2 

0    3 

0    3 

0    4 

0    5 

0    6 

0    7 

0    8 

0.2 

0.3 

0  0 

0    0 

0    1 

0    1 

0    2 

0    3 

0    4 

0    5 

0    6 

0    7 

0    9 

0  11 

0  13 

0.3 

0.4 

0  0 

0    0 

0    1 

0    2 

0    2 

0    4 

0    5 

0    6 

0    8 

0  10 

0  12 

0  14 

0  17 

0.4 

0.5 

0  0 

0    0 

0    1 

0    2 

0    3 

0    4 

0    6 

0    8 

0  10 

0  12 

0  15 

0  18 

0  21 

0.5 

0.6 

0  0 

0    1 

0    1 

0    2 

0    4 

0    5 

0    7 

0  10 

0  12 

0  15 

0  18 

0  22 

0  25 

0.6 

0.7 

0  0 

0    1 

0    2 

0    3 

0    4 

0    6 

0    9 

0  11 

0  14 

0  17 

0  21 

0  25 

0  30 

0.7 

0.8 

0  0 

0    1 

0    2 

0    3 

0    5 

0    7 

0  10 

0  13 

0  16 

0  20 

0  24 

0  29 

0  34 

0.8 

0.9 

0  0 

0    1 

0    2 

0    4 

0    6 

0    8 

0  11 

0  14 

0  18 

0  22 

0  27 

0  32 

0  38 

0.9 

1.0 

0  0 

0    1 

0    2 

0    4 

0    6 

0    9 

0  12 

0  16 

0  20 

0  25 

0  30 

0  36 

0  42 

1.0 

2.0 

00 

0    2 

0    4 

0    8 

0  12 

0  18 

0  24 

0  32 

0  41 

0  50 

1    0 

1  12 

1  24 

2.0 

3.0 

0  1 

0    3 

0    7 

0  12 

0  19 

0  27 

0  37 

0  48 

1     1 

1  15 

1  31 

1  48 

2    6 

3.0 

4.0 

0  1 

0    4 

0    9 

0  16 

0  25 

0  36 

0  49 

1    4 

1  21 

1  40 

2    1 

2  24 

2  49 

4.0 

5.0 

0  1 

0    5 

0  11 

0  20 

0  31 

0  45 

1     1 

1  20 

1  41 

2    5 

2  31 

3    0 

3  31 

5.0 

6.0 

0  1 

0    6 

0  13 

0  24 

0  37 

0  54 

1  13 

1  36 

2    1 

2  30 

3    1 

3  36 

4  13 

6.0 

7.0 

0  2 

0    7 

0  16 

0  28 

0  44 

1    3 

1  26 

1  52 

2  22 

2  55 

3  32 

4  12 

4  56 

7.0 

8.0 

0  2 

0    8 

0  18 

0  32 

0  50 

1  12 

1  38 

2    8 

2  42 

3  20 

4    2 

4  48 

5  38 

8.0 

9.0 

0  2 

0    9 

0  20 

0  36 

0  56 

1  21 

1  50 

2  24 

3    2 

3  45 

4  32 

5  24 

6  20 

9.0 

10.0 

0  2 

0  10 

0  22 

0  40 

1    2 

1  30 

2    3 

2  40 

3  23 

4  10 

5    2 

6    0 

7    2 

10.0 

11.0 

0  3 

0  11 

0  25 

0  44 

1    9 

1  39 

2  15 

2  56 

3  43 

4  35 

5  32 

6  36 

7  45 

11.0 

12.0 

0  3 

0  12 

0  27 

0  48 

1  15 

1  48 

2  27 

3  12 

4    3 

5    0 

6    3 

7  12 

8  27 

12.0 

13.0 

0  3 

0  13 

0  29 

0  52 

1  21 

1  57 

2  39 

3  28 

4  23 

5  25 

6  33 

7  48 

9    9 

13.0 

14.0 

0  3 

0  14 

0  31 

0  56 

1  27 

2    6 

2  51 

3  44 

4  43 

5  50 

7    4 

8  24 

9  51 

14.0 

15.0 

0  4 

0  15 

0  34 

1    0 

1  34 

2  15 

3    4 

4    0 

5    3 

6  15 

7  34 

9    0 

10  34 

11  16 

15.0 

16.0 

0  4 

0  16 

0  36 

1    4 

1  40 

2  24 

3  16 

4  16 

5  24 

6  40 

8    4 

9  36 

16.0 

17.0 

0  4 

0  17 

0  38 

1    8 

1  46 

2  33 

3  28 

4  32 

5  44 

7    5 

8  34 

10  12 

11  58 

17.0 

18.0 

0  4 

0  18 

0  40 

1  12 

1  52 

2  42 

3  40 

4  48 

6    4 

7  30 

9    4 

10  48 

12  40 

18.0 

19.0 

0  5 

0  19 

0  43 

1  16 

1  59 

2  51 

3  53 

5    4 

6  25 

7  55 

9  35 

11  24 

13  23 

19.0 

20.0 

0  5 

0  20 

0  45 

1  20 

2    5 

3    0 

4    5 

5  20 

6  45 

8  20 

10    5 

12    0 

14    5 

20.0 

21.0 

0  5 

0  21 

0  47 

1  24 

2  11 

3    9 

4  17 

5  36 

7    5 

8  45 

10  35 

12  36 

14  47 

21.0 

22.0 

0  5 

0  22 

0  49 

1  28 

2  17 

3  18 

4  30 

5  52 

7  25 

9  10 

11    5 

13  12 

15  29 

22.0 

23.0 

0  6 

0  23 

0  52 

1  32 

2  24 

3  27 

4  42 

6    8 

7  46 

9  35 

11  36 

13  48 

16  12 

23.0 

24.0 

0  6 

0  24 

0  54 

1  36 

2  30 

3  36 

4  54 

6  24 

8    6 

10    0 

12    6 

14  24 

16  54 

24.0 

25.0 

0  6 

0  25 

0  56 

1  40 

2  36 

3  45 

5    6 

6  40 

8  26 

10  25 

12  36 

15    0 

25.0 

26.0 

0  6 

0  26 

0  58 

1  44 

2  42 

3  54 

5  18 

6  56 

8  46 

10  50 

13    6 

26.0 

27.0 

0  7 

0  27 

1     1 

1  48 

2  49 

4    3 

5  30 

7  12 

9    7 

11  15 

27.0 

28.0 

0  7 

0  28 

1     3 

1  52 

2  55 

4  12 

5  43 

7  28 

9  27 

11  40 

28.0 

TABLE  2T. 

[Page  715  | 

Reduction  to  be  applied  to  Altitudes  near  the  Meridian. 

Var. 

Time  from  meridian  passage. 

Var. 

(Table 

m.  s. 

m.  8. 

m.  s. 

m.  s. 

m.  s. 

m.  8. 

m.  8. 

m.  8. 

m.  8. 

m.  s. 

m.  8. 

m.  8. 

m.  8. 

(Table 

26.) 

7  0 

7  SO 

80 

8  30 

9  0 

9  80 

10  0 

10  80 

11  0 

11  80 

12  0 

12  80 

18  0 

26.) 

„ 

'  n 

/  // 

e     n 

t     It 

/  // 

/  // 

f      tr 

/  // 

/  // 

t     II 

»  II 

/  II 

1    II 

II 

0.1 

0  5 

0  6 

0  6 

0  7 

0  8 

0  9 

0  10 

0  11 

0  12 

0  13 

0  14 

0  16 

0  17 

0.1 

0.2 

0  10 

0  11 

0  13 

0  14 

0  16 

0  18 

0  20 

0  22 

0  24 

0  26 

0  29 

0  31 

0  34 

0.2 

0.3 

0  15 

0  17 

0  19 

0  22 

0  24 

0  27 

0  30 

0  33 

0  36 

0  40 

0  43 

0  47 

0  51 

0.3 

0.4 
0.5 

0  20 

0  23 

0  26 

0  29 

0  32 

0  36 

0  40 

0  44 

0  48 

0  53 

0  58 

1  2 

1  8 

0.4 

0  24 

0  28 

0  32 

0  36 

0  40 

0  45 

0  50 

0  55 

1  0 

1  6 

1  12 

1  18 

1  24 

0.5 

0.6 

0  29 

0  34 

0  38 

0  43 

0  49 

0  54 

1  0 

1  6 

1  13 

1  19 

1  26 

1  34 

1  41 

0.6 

0.7 

0  34 

0  39 

0  45 

0  51 

0  57 

1  3 

1  10 

1  17 

1  25 

1  33 

1  41 

1  49 

1  58 

0.7 

0.8 

0  39 

0  45 

0  51 

0  58 

1  5 

1  12 

1  20 

1  28 

1  37 

1  46 

1  55 

2  5 

2  15 

0.8 

0.9 

0  44 

0  51 

0  57 

1  5 

1  13 

1  21 

1  30 

1  39 

1  49 

1  59 

2  10 

2  21 

2  32 

0.9 

1.0 

0  49 

0  56 

1  4 

1  12 

1  21 

1  30 

1  40 

1  50 

2  1 

2  12 

2  24 

2  36 

2  49 

1.0 

2.0 

1  38 

1  52 

2  8 

2  24 

2  42 

3  0 

3  20 

3  40 

4  2 

4  24 

4  48 

5  12 

5  38 

2.0 

3.0 

2  27 

2  49 

3  12 

3  37 

4  3 

4  30 

5  0 

5  31 

6  3 

6  37 

7  12 

7  49 

8  27 

3.0 

4.0 

3  16 

3  45 

4  16 

4  49 

5  24 

6  1 

6  40 

7  21 

8  4 

8  49 

9  36 

10  25 

11  16 

4.0 

5.0 

4  5 

4  41 

5  20 

6  1 

6  45 

7  31 

8  20 

9  11 

10  5 

11  1 

12  0 

13  1 

14  5 

5.0 

6.0 

4  54 

5  37 

6  24 

7  14 

8  6 

9  1 

10  0 

11  1 

12  6 

13  13 

14  24 

15  37 

16  54 

6.0 

7.0 

5  43 

6  34 

7  28 

8  26 

9  27 

10  32 

11  40 

12  52 

14  7 

15  26 

16  48 

18  14 

19  43 

7.0 

8.0 

6  32 

7  30 

8  32 

9  38 

10  48 

12  2 

13  20 

14  42 

16  8 

17  38 

19  12 

20  50 

22  32 

8.0 

9.0 

7  21 

8  26 

9  36 

10  50 

12  9 

13  32 

15  0 

16  32 

18  9 

19  50 

21  36 

23  26 

25  21 

9.0 

10.0 

8  10 

9  22 

10  40 

12  2 

13  30 

15  2 

16  33 

16  40 
18  20 

18  22 
20  13 

20  10 
22  11 

22  2 

24  0 

26  2 

28  10 

10.0 
11.0 

11.0 

8  59 

10  19 

11  44 

13  15 

14  51 

24  15 

26  24 

28  39 

12.0 

9  48 

11  15 

12  48 

14  27 

16  12 

18  3 

20  0 

22  3 

24  12 

26  27 

28  48 

12.0 

13.0 

10  37 

12  11 

13  52 

15  39 

17  33 

19  33 

21  40 

23  53 

26  13 

28  39 

13.0 

14.0 

11  26 

13  7 

14  56 

16  51 

18  54 

21  3 

23  20 

25  43 

28  14 

14.0 

15.0 

12  15 

14  4 

16  0 

18  14 

20  15 

22  34 

25  0 

27  34 

15.0 

16.0 

13  4 

15  0 

17  4 

19  16 

21  36 

24  4 

26  40 

16.0 

17.0 

13  53 

15  56 

18  8 

20  28 

22  57 

25  34 

17.0 

18.0 

14  42 

16  52 

19  12 

21  40 

24  18 

18.0 

19.0 

15  31 

17  49 

20  16 

19.0 

20.0 

16  20 

18  45 

20.0 

21.0 

17  9 

21.0 

Page  716 

TABLE  27. 
Reduction  to  be  applied  to  Altitudes  near  the  Meridian 

Var. 
Imin. 
(Table 

26.) 

Time  from  meridian  passage. 

Var. 
1  min. 
(Table 

26.) 

m.  t. 
18  80 

m.  8. 
14  0 

wi.  a. 
14  80 

m.  8. 
15  0 

TO.    8. 

15  80 

TO.  8. 

16  0 

TO.    «. 

16  80 

TO.  8. 

17  0 

TO.    8. 

17  80 

TO.  8. 

18  0 

TO.    8. 

18  80 

TO.  8. 

19  0 

TO.    8. 

19  80 

// 
0,1 
0.2 
0.3 
0.4 

'    // 
018 
0  36 
0  55 
113 

/    // 
0  20 
0  39 
0  59 
118 

1    II 
0  21 

0  42 

1  3 
124 

1    II 
0  22 

0  45 

1  7 
130 

1    II 
0  24 
0  48 
112 
136 

/    II 
0  26 
0  51 
117 
142 

/    II 
0  27 
0  54 
122 
149 

/    II 
0  29 
0  58 
127 
166 

1    II 

0  31 

1  1 
132 

2  2 

/    // 

0  32 

1  5 
137 
210 

/    // 

0  34 

1  8 
143 

2  17 

/    // 
0  36 
112 
148 
2  24 

1  II 

0  38 
116 
154 

2  32 

II 

0.1 
0.2 
0.3 
0.4 

0.6 
0.6 
0.7 
0.8 
0.9 

131 
149 
2    8 
2  26 
244 

138 
158 
2  17 
2  37 
2  56 

145 
2    6 
2  27 

2  48 

3  9 

152 
2  15 

2  37 

3  0 
3  22 

2    0 
2  24 

2  48 
312 

3  36 

2    8 
2  34 

2  59 

3  25- 
3  50 

2  16 

2  43 

3  11 

3  38 

4  5 

2  24 

2  53 

3  22 

3  61 

4  20 

2  33 

3  4 

3  34 

4  5 
4  36 

2  42 
314 

3  47 
419 

4  62 

2  51 

3  25 

4  0 

4  34 

5  8 

3    1 

3  37 
413 

4  49 
6  26 

3  10 

3  48 

4  26 
6    4 

5  42 

0.5 
0.6 
0.7 
0.8 
0.9 

' 

1.0 
2.0 
3.0 
4.0 
5.0 

3    2 

6    4 

9    7 

12    9 

15  11 

3  16 
6  32 

9  48 
1314 
16  20 

3  30 

7    0 

10  30 

14    1 

17  31 

3  45 

7  30 

1115 

15    0 

18  45 

4    0 

8    0 

12    1 

16    1 

20    1 

416 

8  32 
12  48 
17    4 
2120 

4  32 

9    4 

13  38 

18    9 

22  41 

4  49 

9  38 

14  27 

19  16 

24    5 

5    6 
1012 
1519 
20  25 
25  31 

5  24 

10  48 
1612 
2136 
27    0 

5  42 
1124 
17    7 
22  49 
28  31 

6    1 
12    2 
18    3 
24    4 

6  20 
12  40 
19    1 
25  21 

1.0 
2.0 
3.0 
4.0 
5.0 

; 

6.0 
7.0 
8.0 
9.0 

Var. 

Imin. 

(Table 

26.) 

18  13 
21  16 
2418 
27  20 

19  36 
22  52 
26    8 

21    2 
24  32 
28    2 

22  30 
26  15 

24    1 

28    1 

25  36 

27  13 

6.0 
7.0 
8.0 
9.0 

; 

T 

ime  from  meridi 

an  passage. 

Var. 
Imin. 
(Table 

26.) 

m.  8. 
20  0 

m.  s. 
20  30 

m.  s. 
21  0 

TO.    «. 

21  80 

m.  8. 
22  0 

m.  8. 
22  30 

TO.  ». 

23  0 

TO.    8. 

23  30 

TO.  8. 

24  0 

TO.    8. 

24  80 

TO.  8. 

25  0 

TO.    8. 

25  80 

m.  8. 
26  0 

// 
0.1 
0.2 
0.3 
0.4 
0.6 
0.6 
0.7 
0.8 
0.9 

t    u 
0  40 
120 
2    0 
2  40 

0  42 
124 
2    6 
2  48 

'    II 
044 
128 
212 
2  56 

1  II 

0  46 
132 

2  19 

3  5 

0  48 
137 

2  25 

3  14 

/    II 

0  51 
141 

2  32 

3  22 

/    II 

0  53 
146 

2  39 

3  32 

/    // 

0  65 
150 

2  46 

3  41 

/    // 

0  58 
155 

2  53 

3  50 

/    II 

1  0 

2  0 

3  0 

4  0 

1    II 

1  2 

2  5 

3  7 

4  10 

1    II 

1  6 

2  10 

3  15 

4  20 

'    // 

1    8 
215 

3  23 

4  30 

II 

0.1 
0.2 
0.3 
0.4 

< 

3  20 

4  0 
440 

5  20 

6  0 

3  30 

4  12 
454 

5  36 
618 

3  41 

4  25 

5  9 

5  53 

6  37 

3  51 

4  37 

5  24 

6  10 
6  56 

4    2 

4  50 

5  39 

6  27 
716 

4  13 

5  4 
554 

6  45 

7  36 

4  24 
517 
610 
7    3 
7  66 

4  36 

5  31 

6  27 

7  22 

8  17 

4  48 

5  46 

6  43 

7  41 

8  38 

5  0 

6  0 

7  0 

8  0 

9  0 

5  12 
615 

7  17 

8  20 

9  22 

5  25 

6  30 

7  35 

8  40 

9  45 

5  38 

6  46 

7  53 
9    1 

10    8 

0.5 
0.6 
0.7 
0.8 
0.9 

1.0 
2.0 
3.0 
4.0 

6  40 
13  20 
20    0 
26  40 

7    0 
14    0 
21    0 

28    1 

7  21 
14  42 
22    3 
29  24 

7  42 
15  24 
23    7 

8    4 
16    8 
2412 

8  26 
16  52 
2519 

8  49 
17  38 
26  27 

912 
18  24 
27  37 

9  36 
1912 

28  48 

10    0 
20    0 
30    0 

10  25 
20  50 

10  50 
2140 

1116 
22  32 

1.0 
2.0 
3.0 
4.0 

' 

Note. — Tlie  pages  formerly  occupied  with  Tables  28A,  %8B,  28C,  and  /S8D  liave  been  dropped,  and 
consecutive  page  numbering  iK  tliereby  broken. 


TABLE  29.                                         [Page  725    I 

Conversion  Tables  for  Nautical  and  Statute  Miles. 

Nautical  miles  into  statute  miles. 

statute  miles  into  nautical  miles. 

1  nautical  mile  or  knot=  6,080.20  feet. 

1  statute  mile               =  5,280  feet 

1  statute  mUe               -=5,280  feet. 

1  nautical  mile  or  knot=  6,080.20  feet. 

Nautical 

Statute 

Nautical 

Statute 

Statute 

Nautical 

Statute 

Nautical 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

1 

1.15 

51 

58. 729 

1 

0.87 

61 

44.288 

2 

2.30 

52 

59. 881 

2 

1.74 

52 

45. 156 

3 

3.45 

53 

61. 032 

3 

2.61 

53 

46. 025 

4 

4.61 

54 

62. 184 

4 

3.47 

54 

46. 893 

5 

5.76 

55 

63. 335 

5 

4.34 

55 

47. 762 

6 

6.91 

56 

64.487 

6 

5.21 

56 

48.  630 

7 

8.06 

57 

65.  639 

7 

6.08 

57 

49. 498 

8 

9.21 

58 

66.  790 

8 

6.95 

58 

50. 367 

9 

10.36 

59 

67. 942 

9 

7.82 

59 

51. 235 

10 

11.52 

60 

69. 093 

10 

8.68 

60 

52. 104 

11 

12.  667 

61 

70. 245 

11 

9.552 

61 

52. 972 

12 

13. 819 

62 

71.396 

12 

10. 421 

62 

53. 840 

13 

14. 970 

63 

72.548 

13 

11.289 

63 

54.  709 

14 

16. 122 

64 

73. 699 

14 

12. 158 

64 

55. 577 

15 

17. 273 

65 

74. 851 

15 

13. 026 

65 

56. 445 

16 

18. 425 

66 

76.003 

16 

13. 894 

66 

57. 314 

17 

19.  576 

67 

77. 154 

17 

14.  763 

67 

58. 182 

18 

20.  728 

68 

78. 306 

18 

15. 631 

68 

59. 051 

19 

21. 880 

69 

79.457 

19 

16.499 

69 

59.  919 

20 

23. 031 

70 

80.  609 

20 

17.  368 

70 

60.  787 

21 

24.183 

71 

81.  760 

21 

18. 236 

71 

61. 656 

22 

25. 334 

72 

82. 912 

22 

19. 105 

72 

62. 524 

23 

26. 486 

73 

84.063 

23 

19. 973 

73 

63. 393 

24 

27. 637 

74 

85. 215 

24 

20. 841 

74 

64. 261 

25 

28.  789 

75 

86. 366 

25 

21.  710 

75 

65. 129 

26 

29. 940 

76 

87. 518 

26 

22. 578 

76 

65. 998 

27 

31. 092 

77 

88. 670 

27 

23. 447 

77 

66.  866 

28 

32. 243 

78 

89. 821 

28 

24. 315 

78 

67.  735 

29 

33. 395 

79 

90. 973 

29 

25. 183 

79 

68.  603 

30 

34. 547 

80 

92. 124 

30 

26. 052 

80 

69. 471 

31 

35. 698 

81 

93. 276 

31 

26. 920 

81 

70. 340 

32 

36. 850 

82 

94. 427 

32 

27. 789 

82 

71.  208 

33 

38.001 

83 

95. 579 

33 

28. 657 

83 

72. 077 

34 

39.153     i 

84 

96. 730 

34 

29. 525 

84 

72. 945 

35 

40. 304 

85 

97. 882 

35 

30. 394 

85 

73.  813 

36 

41.456 

86 

99. 034 

36 

31. 262 

86 

74. 682 

37 

42. 607 

87 

100. 185 

37 

32. 131 

87 

75. 550 

38 

43. 759 

88 

101. 337 

38 

32. 999 

88 

76.419 

39 

44. 911     1 

89 

102. 488 

39 

33. 867 

89 

77. 287 

40 

46.062    i 

90 

103.  640 

40 

34.736 

90 

78. 155 

41 

47.214 

91 

104.  791 

41 

35. 604 

91 

79. 024 

42 

48. 365 

92 

105. 942 

42 

36. 473 

92 

79. 892 

43 

49.  517 

93 

107.  094 

43 

37.  341 

93 

80.  760 

44 

50.668 

94 

108.  246 

44 

38.  209 

94 

81.  629 

45 

51.  820 

95 

109.  397 

45 

39.  078 

95 

82.  497 

46 

52.  971 

96 

110.  549 

46 

39.  946 

96 

83.  366 

47 

54.123 

97 

111.  701 

47 

40.  814 

97 

84.234 

48 

55.  275 

98 

112.  852 

48 

41.  683 

98 

85. 102 

49 

56. 426 

99 

114.004 

49 

42.  551 

99 

85.  971 

50 

57.  578 

100 

115. 155 

50 

43.  420 

100 

86.  839 

I 


Page  726]                                         TABLE  30. 

Conversion  Tables  for  Metric  and  English  Linear  Measure. 

Metric  to  English. 

Meters. 

Feet. 

Yards. 

Statute  miles. 

Nautical  miles. 

1 
2 
3 

4 

3.280    833    3 

6.561     666    7 

9.842    500    0 

13.123    333     3 

1.093     611     1 
2.187    222    2 
3.280    833    3 
4.374    444    4 

0.000    621     369 
.001     242    738 
. 001     864     106 
.002    485    475 

0.000    539    593 
.001     079     185 
.001    618    778 
.002    158    .370 

5 

6 
7 
8 
9 

16.404    166    7 
19.685    000    0 
22.965    833    3 
26.246    666    7 
29.527    500    0 

5.468    055    6 
6.561     666    7 
7.655    277    8 
8.748    888    9 
9.842    500    0 

.003    106    844 
.003    728    213 
.004    349    582 
.004    970    950 
.005    592    319 

.002    697    963 
.003    237    556 
.003    777     148 
.004    316    741 
.004    856    333 

English  to  metric. 

No. 

Feet  to  meters. 

Yards  to  meters. 

Statute  miles  to  meters. 

Nautical  miles  to  meters. 

1 
2 
3 
4 

0.304    800     6 
0.609     601     2 
0.914    401     8 
1.219'  202    4 

0.914     401     8 
1.828     803     7 
2.743    205    5 
3.657    607    3 

1, 609. 35 
8, 218.  70 
4, 828. 05 
6, 437. 40 

1, 853.  25 
3,  706. 50 
5, 559.  75 
7,413.00 

5 
6 

7 
8 
9 

1.524    003    0 
1.828    803    7 
2.133    604    3 
2.438    404    9 
2.743    205    5 

4.572    009     1 
5.486    411     0 
6.400    812    8 
7.315    214    6 
8.229    616    5 

8, 046.  75 

9, 656. 10 

11, 265. 45 

12,  874. 80 

14, 484. 15 

9, 266. 25 
11, 119. 50 
12, 972.  75 
14,  826. 00 
16, 679.  25 

TABLE  31.                                            (Page  727   1 

Conversion  Tables  for  Thermometer  Scales. 

[po^ Fahrenheit  temperature;  C°=Centlgrade  temperature;  R«>=R6aumur  temperature.] 

Equivalent  temj>erature»—Fahr.,  CetU.,  Riau 

RO=J  c°=J  (F°- 
Co={RO=j(FO- 

-32°). 

-32°). 

F°. 

C°. 

R°. 

F°. 

C°. 

R°. 

1 

-17.2 

-13.8 

51 

+10.6 

+  8.4 

2 

16.7 

13.3 

52 

11.1 

8.9 

EquivcUetU  temperatures — Centigrade  and  FhhrenheiL 

3 
4 
5 

16.1 
15.6 
15.0 

12.9 
12.4 
12.0 

53 
54 
55 

11.7 
12.2 
12.8 

9.3 

9.8 

10.2 

F°=|C°+32°. 

C°. 

F°. 

c°. 

F°. 

c°. 

F°. 

c°. 

F°. 

C°. 

F°. 

6 

7 
g 

14.4 
13.9 
13.3 

11.6 
11.1 
10.7 

56 

57 
58 

13.3 
13.9 
14.4 

10.7 
11.1 
11.6 

-10 

14.0 

0 

32.0 

10 

50.0 

20 

68.0 

30 

86.0 

9 

12.8 

10.2 

59 

15.0 

12.0 

-  9 

15.8 

1 

33.8 

11 

51.8 

21 

69.8 

31 

87.8 

10 

12.2 

9.8 

60 

15.6 

12.4 

-  8 

17.6 

2 

35.6 

12 

53.6 

22 

71.6 

32 

89.6 

11 

11.7 

9.3 

61 

16.1 

12.9 

-  7 

19.4 

3 

37.4 

13 

55.4 

23 

73.4 

33 

91.4 

12 

ll!l 

8.9 

62 

16.7 

13.3 

-  6 

21.2 

4 

39.2 

14 

57.2 

24 

75.2 

34 

93.2 

13 

10.6 

8.4 

63 

17.2 

13.8 

-  5 

23.0 

5 

41.0 

15 

59.0 

25 

77.0 

35 

95.0 

14 

10.0 

8.0 

64 

17.8 

14.2 

-  4 

24.8 

6 

42.8 

16 

60.8 

26 

78.8 

36 

96.8 

15 

9.4 

7.6 

65 

18.3 

14.7 

-  3 

26.6 

7 

44.6 

17 

62.6 

27 

80.6 

37 

98.6 

16 

8  9 

7.1 

66 

18.9 

15.1 

-  2 

28.4 

8 

46.4 

18 

64.4 

28 

82.4 

38 

100.4 

17 

8.3 

6.7 

67 

19.4 

15.6 

-  1 

30.2 

9 

48.2 

19 

66.2 

29 

84.2 

39 

102.2 

18 
19 

7.8 
7.2 

6.2 
5.8 

68 
69 

20.0 
20.6 

16.0 
16.4 

1 

20 

6.7 

5.3 

70 

21.1 

16.9 

21 

6.1 

4.9 

71 

21.7 

17.3 

22 

5.6 

4.4 

72 

22.2 

17.8 

23 

5.0 

4.0 

73 

22.8 

18.2 

24 

4.4 

3.6 

74 

23.3 

18.7 

25 

3.9 

3.1 

75 

23.9 

19.1 

26 

3.3 

2.7 

76 

24.4 

19.6 

27 

2.8 

2.2 

77 

25.0 

20.0 

Equivalent  temperatures— JUaumur  and  Fahrenheit 

28 

2.2 

1.8 

78 

25.6 

20.4 

F°=|  R°+32°. 

29 
30 

1.7 
1.1 

1.3 
0.9 

79 
80 

26.1 
26.7 

20.9 
21.3 

E°. 

F°. 

R°. 

F°. 

Ro. 

F<>. 

R°. 

F". 

31 

—  0.6 

—  04 

81 

27.2 

21.8 

32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 

o!o 

+  0.6 
1.1 
1.7 
2.2 
2.8 
3.3 
3.9 
4.4 
5.0 
5.6 

olo 

+  0.4 
0.9 
1.3 
1.8 
2.2 
2.7 
3.1 
3.6 
4.0 
4.4 

82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 

27.8 
28.3 
28.9 
29.4 
30.0 
30.6 
31.1 
31.7 
32.2 
32.8 
33.3 

22.2 
22.7 
23.1 
23.6 
24.0 
24.4 
24.9 
25.3 
25.8 
26.2 
26.7 

-10 

-  9 

-  8 

-  7 

-  6 

-  5 

-  4 

-  3 

-  2 

-  1 

9.5 
11.8 
14.0 
16.2 
18.5 
20.8 
23.0 
25.2 
27.5 
29.8 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

32.0 
34.2 
36.5 
38.8 
41.0 
43.2 
45.5 
47.8 
50.0 
52.2 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

54.5 
56.8 
59.0 
61.2 
63.5 
65.8 
68.0 
70.2 
72.5 
74.8 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

77.0 
79.2 
81.5 
83.8 
86.0 
88.2 
90.5 
92.8 
95.0 
97.2 

43 

6. 1 

4  9 

93 

33.9 

27. 1 

44 

a? 

5.3 

94 

34!  4 

27.6 

45 

7.2 

5.8 

95 

35.0 

28.0 

46 

7.8 

6.2 

96 

35.6 

28.4 

47 

8.3 

6.7 

97 

36.1 

28.9 

48 

8.9 

7.1 

98 

36.7 

29.3 

49 

9.4 

7.6 

99 

37.2 

29.8 

50 

+10.0 

+  8.0 

100 

+37.8 

+  30.2 

21594°— 14 39 


Page  728]                                        TABLE  32. 

To  obtain  the  True  Force  and  Direction  of  the  Wind  from  its  Apparent  Force  and  Direction  on  a 

Moving  Vessel. 

1 

"§ 

1 

1 

■s 

g 

< 

•8JB0B  ^jojnBag  'aojoj  arux 

Neisioe>5-*io->}(ictoio«2j>tot-eo 

t^OOQOaOOC09CCa>0030rHOrHrH 

rHrH01(N(NCs>CJe<eq 

•Ak.oq  8qi  50  sjuiod  'uotpojip  ami 

«DtO«D<DCOCOeOtO«O^O^tO^<OtO 

toto*o<o<oto«o*co«cnDto«o<oto 

tOCOCD^COc^cOtOCO 

•81B08  :)jojnB8a  '80JOJ  anjx 

cjMioe<s->*<ic-*iotoiratct-tor-oo 

t~"OOODOOOOOJOCCSOOiOrHOrHr— 

rHrH(N(M01C^<Ne^(N 

•Aioq  9q4  BO  sjuiod  'nojjoaaip  orux 

(C(OCO«£>«OCD»/5<DtOiftii5«£>vCiOtC 

iOLOiCiOiOi^lO»OtO»C>OiOiO»Ci^ 

iClO«0»OiOiOiOlOLO 

;Jl 

•ajBos  jjojnBag  'aojtoj  arux 

e«ooioeo««<iO'»i<io«oio«ot<.tor»eO 

t»000000000>00roO0»OOOrHrH 
rH       rH  rHrHrHrH 

rHrHNC^(N(NNCJ(N 

•M.oq  9X1%  jjo  sjuiod  'uotjoaitp  anjx 

i/5<C«OiOiOUt»lCtOiO»OlOlOlQ»0»C 

iniOiO.*lO"#r)<iolO-<JllOlOTJ<Tjtifl 

■>JI'<J<>0-<jC<}<T}<Tf"TjlHj( 

•siBos  ^jAjnTOa:  '9oaoj  anjx 

cjeouseo-^ic^ioioiCKDOtot-oo 

l>t»OOJ>OCO>00090>05000rHr- 

rHrH<N«<Ne4«OJC-< 

•Aoq  aq;  go  sjuiod  'uopoajip  anix 

lOtOtOiClOiCTj<iOiO-<»'-*U5->JI-*-* 

■0<-<><-«<-*-*-*Tfl-*.OlTI.-«'-*00-*-<}< 

CC-<»'-*CO-*TjlCO«>-<* 

•aiBos  jjojnBag  'aojoj  anjx 

Neo-^eo'^ic-'fiintoiotoixor-i^ 

t*l~-0DI>00000005O0SOOOOrH 

rHrHIN(NN(N<NINN 

•Aioq  aq;  go  ffjuiod  'uonaajip  anJX 

in>ntO'<j'ioio-*->j'io->*i-*-<((co-*-* 

cc^-jeoTO^TOcoeoMCOTOcoeoTO 

COCOCCtNTOTOC^TOCC 

•aiBos  ^ojnBag  'aojoj  anjx 

INM-^MTfliC-fliiOtDiCOtOiCtOt^ 

^Ct^OCt^OOODODOOOSOsOSOOOO 

rHrHrHrH(N(N<NC^C^ 

•Aioq  aqj  go  sjaiod  'uoijoaiip  on  jx 

iomic-<j<TjiineO'*i)<Med<«m-* 

(NCOeOOTOCOCJCMTOCKMTONINN 

(Ne<lNOJ(N(NlM!Ne^ 

e 

•ai^os  jjojnBag  'aojoj  anJX 

NM-^WrfioeO-^iO-^intovOcOt- 

!Ot~t~t^t^ooooooo>o>cnoooo 

rHrHrHrHCi<N(N(NC^ 

■Avoq  Qvi%  go  s^uiod  'uoi;oajip  amx 

io>oiOTC-*K5eoc<5-*iN«j«)e^c->ro 

MC4MrH(MC<lrHN<NrHrHINrHrH(M 

e» 

•ajBos  iJojnBag  'aojoj  anJX 

<Neo-<ji(Neo-*eo->»'in-<(<iO«oi050to 

<otot»r»t~t~i>ooooooosO!Oioo 

OrHrHrHrHlNeMC^IN 

•Aioq  amsosjniod'uopoajtp  amx 

lOiOiOM-*-rl<(NKl-<)<(NC^eCi-H(NeQ 

rHCJNrHrHNOrHrHOrHrHOOrH 

OOrHOOOOOC 

00 

•aXBOs  wojnBag  'aojoj  anjx 

<N«T(ilMM'^W<*lm'<KI-*iO-0<iOU5 

lCHO<OtOt>t^l>t^OOeOOOC»OlCVOV    OOOrHrHrH«(M!N         1 

•Aioq  aqj  50  ejoiod  'aopoaiip  amx 

lC»ClOCC'*T}<(NCCCCrHC^ICOOT-tC^ 

OrH<NOOrHOJO.H05000»00 

OSCJOOS^OOSOSOl 

- 

•aiBos  jjojnBag  'aojoj  anjx 

MCO-*fqcC-^TOCC'^CO-*La-<f<mio|iOlO«0!0«>t^t-r»l>WOOOOO>0»Oo|oOOrHr-lr-IC^(NCl        1 

•Aioqaq^  go  ffjuiod  'uonoajip  anjx 

lOiOlOCO-a<-«.-llN«iO.-l(NOrH(N 

OSOrHO>OOCeOaOOOOS(»000»0> 

QOOOOlQOOOOiOOOOOC 

« 

•axB08  ^jojnBag  'aojoj  anJX 

r-1              THr-ir-(!Hr-(r-^        1 

•Moq  aqj  go  Rioiod  'uotjoajip  amx 

iOiome<i->t"*<0(Neoo5r-i(NOsOTW 

aoosooooioi>oc>cii^ocoat>oooc 

t>  I:~  «  C~  t^  00  l>  t^  t>       1 

>s 

•aiBOS  jjojnBag  'aoioj  anJX 

i-iiN-<j<r-ic^«iNiNeoc^roei3eoeo-*  "3'-tj'tciOiCiCnD<o<ot>.t-i~-cooooocnaiO>c>oo<NtH.-i      1 

•Aioq  aqj  go  s^uiod  'noijoajip  anjx 

iOiO>CN-<C-*OMM0001NOOOJO 
?H  1-H  r-1  iH  rH  rH  f-l  r-(  iH        tH  iH             r-t 

i>ooot^ooo:^l>oocot^oototoi> 

5 

■* 

•aiBOs  iiojnBag  'aojoj  anjx 

•Aioq  aqj  go  ffjntod  'uoi^oajip  anJX 

iOmiO<N-^-<flO>M«lCOO(NI>000 
rH  r-1  i-H  rH  l-H  rH        rH  rH        rH  rH               rH 

COt*O55Ot^00iOt£>l>iC^^^»OeO   lOiOOiCiOiO-^lOiC       1 

09 

•aiBOs  iiojnBag  'aojoj  amx 

rHCq  ■*  rH  C^  CO  rH  rH  Ca  t^.rH  C^  N  (N  M  |tOTOeOT("HJleCHOlCl-fl'r^tO<OOOI>l>|oiOOaOOOO>rHrHrH        1 

•Moq  aqj  jgosjuiod  'uotjoajip  anjx 

miotoc^-*ici»<NM<cai(Ntot^o 

rH-HrHrHrHrH        rH  rH              rH               rH 

io<oooHi<iot>.*iotD-*-Ti<in->j<-*io 

rJ<-rj'*<J<Tj*-^Tj<CO"Tf?' 

ei 

•aiBos  jjojuBaa  'aojoj  anJX 

rHC^COOC^MOrHlNrHrHrHlNrHrH 

CO c^ w^ CO N iC -^ -^ t- ^ ic 00 r^ «o  oaooooooioi rHrHo     1 

•Moq  aqj  go  sjutod  'uopoajip  amx 

u5tD<oeo-*iot~e^-<i<iOooe^->jitoos 

eoiot~eo->}(irieoTO.9<TOTOT)<<NeOTO 

C^TOCC(NCOTOC^OJTO 

TH 

•aXBOs  jjojnBaa  'aojoj  anjx 

rHe)«0rH(N00IMrH0rHIMrH0| 

OOC»rH-<)<CCC^lCl->><CCHOtOlOOOt^5D 

»  00 1~  O  0»  0>  rH  rH  O 
rH             rHrHrH 

•Moqaq^  go  s^uiod  'nopoajip  amx 

<otocOT)iioi05DMioeocceoMHi(os 

NeOiCC»C<mirH(N(NrH(NINrHr-l<N 

■ 

e 

•9XB0S  jjojnBag  'aojoj  amx 

i-H(N(»OrH(NOOi-HrHOO<NrHo| 

•OC^OTfcOWlO-^CO^OlC-^OOt^cO    OSOOt^OOiOrHrHO        1 

rH               rHrHi-l        1 

•Aioqaq^  goKjmod  'uopoajipamx 

(05COtOtOCOO<D<000<000     '• 
rHrHrHrHrHrH        rH  rH              y-*                  • 

OOOOOOOOOOOOOOO 

ooooooooo 

•Kjonii  'ias88A  JO  paadg 

rHrHf5rHrH(NrHrHINrHrH<NrHrHIM 

DUiOOiOOOiOOOiOOOi^O 
-HrH(NrHrHC^>-lrH01rHrH(NrHrH!M 

DiOOOiOOOiOO 
-HrH<NrHrH(NrHrtC<l 

Appar- 
ent 
force 
of  the 
wind 
(Beau- 
fort 
scale). 

O               rH               N               TO              -"J" 

u5            «6            ti            00            di 

""o     '~^     "~?5 

TABLE  33. 

Distance  by  Vertical  Angle. 

[Page  729 

1 

a 

s 

Q  cot* ^ CO 

■*SoSto 

^ssgg 

t^eoot^ic 
OOOOO 

OOOOO 

StototoS 

OOOOO 

OOOOO 

ocoooo 

^rHi-lTHrH 

5 

iHiHOOlO 

iHlHrHiHO 

OOOOO 

^  COTO  coco 
OOOOO 

TOmSScs 

OOOOO 

OOOOO 

f5  r-l  rt -(  rH  tH 

oooooo 

s 

1-4 

-S8SS 

0    ««•*« 

s^gissa 

SBSSS 

OOOOO 

CO  CO  TO  TO  TO 
OOOOO 

OOOOO 

ScSSSS 

oct»t^;cmio 

OOOOO 

oooooo 

1 

0  jHU3«e< 

sssas 

SSBS^ 

OOOOO 

SStoSS 

OOOOO 

OOOOO 

g5c3§SS 

OOOOO 

oooooo 

e 

0  oioecN 

S5SS§ 

Sioioir?' 

^  CC  TO  TO  05 
OOOOO 

toSScSS 

OOOOO 

OOOOO 

rHO>oct^<o  «o le Til ■* re c» 

""^  ^^„^„_ 

s 

o  o»-*eON 

Stomih© 

r-  rl  t-  •<»  o 
ooooe 

TOCO  CQ  coco 

OOOOO 

00  t~  «0  IC  If! 
OOOOO 

gsasss 

OOOOO 

cioot^tem 

OOOOO 

J<-*TO«Mi-c 

oooooo 

JJgSSS 

OOOOO 

CO  WTOCcS 
OOOOO 

ooooe 

rH  rH  O0»O3 
(NMINr-lr-l 

OOOOO 

0Ct~<OiO«»" 
OOOOO 

CO  CO  PJ  CJ  1-1  r- 

oooooo 

s 

*    Hr-I'VO 
0   OC^MCJ 

iHi-Hrlr-IO 

1-HOOOXO 
OOOOO 

■*  e-i  o  «  r- 

eoroeoc^c^ 

OOOOO 

OOOOO 

O  O  0%  CC  00 
OOOOO 

t^  <0  lO  •«•  TO 
OOOOO 

COC^C<>-i.-iO 

oooooo 

00 

0  r^-^e^iN 

S§g8S 

OOOOO 

OOOOO 

OOOOO 

OOOOO  t*  t^ 

JDiC'VTOTO 

N.-1-^OOO 

OOOOO 

OOOOO 

oooooo 

s 

0    t-TOMlH 

gssss 

l-lTHt-lOO 

OOOOO 

OOOOO 

OOOOO 

00 1~  t~  <o  «e 

lOTfrereci 

rt 

OOOOO 

OOOOO 

o 

^SS255 

rHlH.HOO 

OOOOO 

OOOOO 

538S2S 

r^tctoioio 

■«>«e<pi.M 

rt 

OOOOO 

OOOOO 

OOOOO 

o 

e 

TOiHi-HTO 

0  <cece^.-i 

iHtHOOO 

OOOOO 

OOOOO 

ooioor-t^ 

tomiOif-v 

TO  «■»  e^  r-  o 

o 
o 

OOOOO 

OOOOO 

OOOOO 

"    OOOTO 
0   <CTOM  i-H 

^rtOOO 

tootSSS 

OOOOO 

OOOOO 

OOODt-^loliO'.rrJ'TOTO 

CI 

OOOOO 

OOOOO 

o 

s 

0   tONrHiH 

i-lOOO© 

OOOOO 

OOOOO 

iH  >H  r-l  tH  r-( 
OOOOO 

eocoddiH 

OOOOO 

o 
o 

to 

^    O  »C  -v  » 
O    iCOi-HrH 

oio-*toS 

rHOOOO 

OOOOO 

IM.T-lrtrHr-l 
OOOOO 

;OiOtJ1t)<to 
OOOOO 

C^  C^  ^^  r-H  O 

OOOOO 

o 
o 

g 

■fliOQCClT-l 
0    '9' I^  r-l  t-( 

l>r*OlO  rH 

iO  ^  "^  TO  TO 

OOOOO 

OOOOO 

OiCCt^^Oift   Tjt -^t*  CO  Ci  M 

t-c.-(000 

o 
o 

OOOOO  OOOOO 

OOOOO 

0    -^Ni-trH 

S^cSSS 

sssss 

t^tClO-<f  TO 

meoiN«rt 

rHOO0>0» 

o 

OOOOO 

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o 
>* 

0    TOr-lrHO 

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10-*TOCON 

1-H^OOO 

o  o>  Oft  00  00 

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00 

o 

OOOOO 

OOOOO 

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5ai 

i-IC^eO'* 

iO«Ot^00Oi 

OiHMTO-* 

lotot^aaoi 

Or-KMCO-* 

•OtOt^oOO) 

oe<'*<coo 

oo-vtoooo 

o 

d 

<N 

(N 

re 

^   •   •   •   -uS 

Page  730] 


TABLE  33. 

Distance  by  Vertical  Angle. 


55 


otoNooo 


«D  iH  O  «  » 


T»<ococOTHaoo>c»eoo 


eoOMr;r-i 
^-((^^■-(eoc^ 


8S 


<OQt 

>ooe 


o       oooeo 


O         OOIN3> 


■<1<0r-l>0 


r-i«?ii-ci-(  e^eoiocjS 


toioeoc^r-i 


■<l<COMtHO 


^  00>  O^  00 


-     JOOOl-* 

o>o>oooot^ 


Tl<rHCOt~iO 
■<J<  iH  •*  rH  iS 

OOOOt-t-tO 


mo  COO'* 

OlOOOOOOt- 


i-HO-^IN 

t-t~tototo 


oooot-t~t» 


(OiO  lOO  lO 


eoiHio^c*) 


o>aot»t»«o 


lOC^Ncor- 
iHioeoiHirj 


tOCOrHOOl 


V5  o  e<  o  53 
iM-^oeoo 

aor»t~to«D 


iCift  ^  ■*  ^ 


■"S"  f)  CO  C<  rH 
tfllNOOlOO 


T)<iH'<J'!N 
t^*0  OiCiO 


C)00>OOC- 


sssss 

I-*  0>  00  t^  o 


00(NO2j 

0->S<lMC> 

lO  in -*■*■* 


OOOiMINCO 

(M -sjl  Tjl  o  .-( 

a>  i>  'o  in  lO 


0>n<NC<r-l 

r-  'O  lO  ■*  ■* 


"■  r-(ioe5o 


QQOej(N00 

co-^ocoo 
lO  *  "^  CO  CO 


Q    CO  9)  CO  ^ 


CO  CO  INN 


e^ioiofS 

Q   t»00iO  * 


O    COCOiO^ 


o  •«*"t~ioeo 


OtXC^t-iiO 

»n  "^  ■*  Tj*  CO 


(N  o>  r»  >o  lO 

Tllc^rHOlO 
■*  ^  ^  ^  CO 


fHOm-S'eO 
^  ^  CO  CO  CO 


i-iioeoi-<>o 
(O  tO  vo  »n  ■* 


Tj<cOi-i©3 
^to'-o  :oiO 


iH(M«O<-l0O 
OT)<(Mr-llO 

lO  ^  ^  ^  CO 


rioio^eo 
u3>n  ■*■*■* 


COlNiHOlO 

*  ■*  *  ^  CO 


«0t^05  C<liO 

-^eofac^r-i 

CO  CO  CO  CO  CO 


e5iHOOio 

CO  CO  cocoes 


;OlOu3eO00  U-f-itffr-^HCO 
■<JICOOJi-IO|OiO-<»<T)<CO 

COCOCOCOCO   COC,  MiMIM 


<NOiO^?S 

^  ^  CO  CO  CO 


ooooOMiq 

rHOOlO-"* 
COCOCOC^N 


•<l<COiHOS 
CO  CO  00  CO  o 


(N  t^in  t--c^ 

^iHiOCO(M 
•"J"'*  CO  CO  CO 


oor^eor*04 

OiO-«<C0C4 


«PiO00-*r-l 
^INOiOtJI 

COCOCOIMC^ 


t-if-Hco^  a> 


01-*rHO.-l 
— -^<Nt-IO 


StOQ-*0> 
'j'^coiN 


CO  CO  ^  t*"  tH 
iO-*cOC^<N 


>0  O  CO  ''J*  o» 
COiOCOrHlO 

CO'NCJOJrt 


COI^ClC^rH 


5JSS22 


COCie<<Nr-( 


oeooioS 

eOlMINiHiH 


iotoc~wa> 


•  OOQCOC- 

^eoeoc>»r-i 


OOC^t-'-l'O 
COCOMINrH 


■>)lcONC^ 
<NC<NC^C< 


r-(rHOO>0 

(^^l^^o^<N^H 


«i-(OOi6 

IM(NC<C^rH 


COOiiO  1-1  t* 
lO  T)l  TJI  rJH  CO 


lOiHt-tOQ 
tHi-IOOO 


-  lOlO-<»lTl< 

OOOOO 


iHOoom 


OOOOO 


SS8S3 

rHrHrHOO 


SS;SSS 


OMinoio 

«NrHi-lc3 


OiHMCO'* 


O  O  kO  lO  tO 
-lOOO 


rHOOOO 

>atac~aoo> 


CO(MIMC^r-( 


-    -5  <g  ^  cj 

iQ  Tj*  *  TJ4  ^ 

OOOOO 


OOOOO 


>neoiHO>oo 

*  ■*  ^  CO  00 
OOOOO 


**  ^  ■*  ^  CO  CO 


eoi^(NOoo 

C^O>0-<)<<M 

■*  ^  CO  CO  CO 


0-<J'COCJ 
COS^O«INOJ 


■<)>  C^  ^  r-(  e^  CO 
OiO-<)<C0(N 

^  *  CO  CO  CO  oo 


OiOiO  tOQp*-« 

■a-coiMi-ioo 

CO  CO  CO  CO  CO  CO 


oooooiMiOog 
i-toom'fM 

CO  CO  CO  c-i  o  N 


a>  i-H  ■»!<  i>  >-i  :0 
■*  ■*  CO  <M  (N  iH 

C»l  CI  I^  ?»  f1  C^ 


iHlOOOCOOOCO 
(MrHOOBiO 

IM  O  <N  ?»  rH  r-( 


CftOlOtH-S* 
Tj<COCOC^r-l 


t~  r-l  O  i-(  to  M 
CTOOiO-^Tjl 

*4  C<1  rH  i-<  rH  f( 


i-ti-ICO  too^ 
C0<Mr-IOlO 


00  CQCOC*  C4  iH 


OOOOO 


5^§co 
OOOOO 


^  ^1  ^  CO  CO 
OOOOO 


^  oo  o5  CO  CO 
OOOOO 


9Qt~tO3<c0 

CO  CO  CO  CO  CO 
OOOOO 


■ocot^cooi 


in  r-(  t^  T>"  rH  00 
lNlMiHrHi-(0 


)  1-1 1- coo 
<>-lOOO 


-  lA  in  ■*  ■*  T* 

OOOOOO 


OOinCOrHO 
COCOCOCOCO 

OOOOO 


tOTfc^OOO 
CO  CO  CO  CO  CN 

OOOOO 


eocococ>Sc^ 
OOOOO 


COCOfSMlN 
OOOOO 


OOOOO 
OIN-^fOOO 


(oooinio 

(r-liH-HOO 


^  ^  CO  CO  CO  CO 
OOOOOO 


00  t- CO  lO  Tjl  CO 
OOOOOO 


t- to-*co<Mri 
IN<MC^CJ(Mf« 

OOOOOO 


iC-^COflrHO 
OOOOOO 


Sc5?J(NSrH 
OOOOOO 


COlNiHOOlOO 
CN  CI  e>^  <N  rH  rH 

OOOOOO 

oc^-mtoooo 


TABLE  34.                                          [Page  731 

For  finding  the  distance  of  an  object  by  an  angle,  measured  from  an  elevated  position,  between  the 

object  and  the  horizon  beyond. 

Dist, 
yards. 

Height  of  the  Eye  Above  the  Level  of  the  Sea,  in  Feet. 

Diet., 
yards. 

20 

30 

40 

50 

60 

70 

80 

90 

lOO 

110 

ISO 

100 
200 
300 
400 
500 

0  / 

3  44 

1  50 
1  12 

52 
41 

0  / 

5  37 
2  46 

1  49 
1  21 
1  03 

0  < 

7  29 
3  43 
2  26 

1  48 
1  25 

0  / 

9  21 
4  39 
3  04 
2  16 

1  48 

o     / 
11   11 

5  35 
3  41 
2  44 
2  10 

o       t 

13  00 
6  31 
4  19 
3  12 
2  32 

o       / 

14  47 
7  27 
4  66 
3  40 
2  64 

o       / 

16  34 
8  23 
6  33 
4  08 
3  17 

O        ) 

18  16 
9  18 
6  11 
4  36 
3  39 

o       / 

19  58 

10  13 

6  48 

&  04 

4  01 

0       / 

21  37 

11  08 

7  26 

5  32 

4  24 

100 
200 
300 
400 
500 

600 
700 
800 
900 
1,000 

34 
28 
24 
21 
18 

52 
44 
38 
33 
29 

1  10 

1  01 

51 

46 

40 

1  29 

1  15 

1  05 

57 

50 

1  47 
1  31 
1  18 
1  09 
1  01 

2  05 
1  46 
1  32 
1  22 
1  12 

2  24 
2  01 
1  46 
1  33 
1  23 

2  42 
2  18 
2  00 
1  45 
1  34 

3  01 
2  34 
2  13 
1  67 
1  45 

3  20 

2  50 
2  27 
2  10 
1  56 

3  38 
3  05 
2  41 
2  22 
2  07 

600 
700 
800 
900 
1,000 

1,100 
1,200 
1,300 
1,400 
1,500 

16 
16 
13 
12 
11 

26 
23 
21 
19 
18 

35 
32 

29 
27 
24 

45 
41 
37 
34 
31 

65 
50 
45 
41 
38 

1  06 
69 
53 
49 
46 

1  16 

1  08 

1  02 

57 

52 

1  24 
1  17 
1  10 
1  04 
59 

1  34 
1  26 
1  18 
1  12 
1  07 

1  44 
1  35 
1  27 
1  20 
1  14 

1  54 
1  44 
1  36 
1  27 
1  21 

1,100 
1,200 
1,300 
1,400 
1,600 

1,600 
1,700 
1,800 
1,900 
2,000 

10 

16 
15 
14 
13 
12 

22 
21 
19 
18 
17 

29 

27 
25 
23 
22 

36 
33 
31 
29 

27 

42 
39 
36 
34 
32 

48 
46 
42 
39 
37 

55 
51 
48 
46 
42 

1  02 
58 
54 
50 
47 

1  08 

1  04 

1  00 

56 

53 

1  16 
1  10 
1  06 
1  02 
68 

1,600 
1,700 
1,800 
1,900 
2,000 

2,100 
2,200 
2,300 
2,400 
2,500 

11 
10 

16 
15 
14 
13 
12 

20 
19 
18 
17 
16 

25 
24 
22 
21 
20 

30 

28 
27 
26 
24 

36 
33 
31 
29 
28 

40 
38 
36 
34 
32 

46 
42 
40 
38 
36 

60 
47 
46 
42 
40 

66 
62 
49 

47 
44 

2,100 
2,200 
2,300 
2,400 
2,600 

2,600 
2,700 
2,800 
2,900 
3,000 

11 
11 
10 

15 
14 
14 
13 
12 

19 

18 

17. 

16 

15 

23 
22 
20 
19 
19 

26 
25 
24 
23 
22 

30 
29 
28 
26 
26 

34 
33 
31 
30 

28 

38 
36 
36 
33 
32 

42 
40 
38 
37 
36 

2,600 
2,700 
2,800 
2,900 
3,000 

3,100 
3,200 
3,300 
3,400 
3,500 

12 
11 
10 

16 
14 
13 
13 
12 

18 
17 
16 
15 
15 

21 
20 
19 
18 
17 

24 
23 
22 
21 
20 

27 
26 
25 
24 
23 

30 
29 
28 
27 
26 

34 
32 
31 
30 
29 

3,100 
3,200 
3,300 
3,400 
3,600 

3,600 
3,700 
3,800 
3,900 
4,000 

12 
11 
11 
10 

14 
13 
13 
12 
12 

17 
16 
16 
16 
14 

19 
19 
18 
17 
16 

22 
21 
20 
20 
19 

25 
24 
23 
22 
21 

27 
26 
25 
26 
24 

3,600 
3,700 
3,800 
3,900 
4,000 

4,100 
4,200 
4,300 
4,400 
4,600 

11 
11 
10 

14 
13 
■       13 
12 
12 

16 
15 
16 
14 
14 

18 
17 
17 
16 
16 

20 
20 
19 
18 
18 

23 
22 
21 
21 
20 

4,100 
4,200 
4,300 
4,400 
4,500 

4,600 
4,700 
4,800 
4,900 
5,000 

11 
11 
10 

13 
13 
12 
12 
11 

15 
15 
14 
14 
13 

17 
17 
16 
16 
15 

19 
19 
18 
17 

17 

4,600 
4,700 
4,800 
4,900 
5,000 

Page  732] 

TABLE  3.5. 

Speed  in  knots  per  hour  developed  by  a 

vessel 

traversing  a  measured  nautical  mile  in  any  given  1 

number  of  minutes  and  seconds.                                                           1 

■dumber  of  minutes 

1 

2 

3 

4 

o 

G 

4 

8 

9 

10       j       11 

12 

KnoU. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

1    Knots. 

Knots. 

Knots. 

Knots,  i  Knots. 

Knots. 

0 

60.  000 

30.000 

20.000 

15.000 

12. 000 

10.000 

8.571 

7.500 

6.666 

6.000 

5.455 

5.000 

0 

1 

59. 016 

29. 752 

19. 890 

14. 938 

11.960 

9.972 

8.551 

7.484 

6.654 

5.990 

5.446 

4.993 

1 

2 

58.  065 

29. 508 

19.  780 

14. 876 

11. 920 

9.944 

8.530 

7.468 

6.642 

5.980 

5. 438  i  4. 986 

2 

3 

57. 143 

29. 268 

19.  672 

14.815 

11.880 

9.917 

8.510 

7.453 

6.629 

5.970 

5.429 

4.979 

3 

4 
5 

56. 250 

55.  385 

29. 032 

19.565 

14.  754 

11.841 
11. 803 

9.890 

8,490 

7.438 
7.422 

6.617 
6.605 

5.960 
5.950 

5.421 

4.972 

4 

28. 800 

19. 460 

14.694 

9.863 

a  470 

5.413 

4.965 

5 

6 

54. 545 

28. 571 

19. 355 

14.634 

11.764 

9.836 

8.450 

7.407 

6.593 

5.940 

5.405 

4.958 

6 

7 

53.731 

28.346 

19. 251 

14. 575 

11. 726 

9.809 

8.430 

7.392 

6.581 

5.930 

5.397 

4.951 

7 

8 

52.  941 

28. 125 

19. 149 

14. 516 

11. 688 

9.783 

8.411 

7.377 

6.569 

5.921 

5.389 

4.945 

8 

9 

52. 174 

27.907 

19.048 

14. 458 

11. 650 

9.756 

8.392 

7.362 

6.557 

5.911 

5.381 

4.938 

9 

10 

51. 429 

27. 692 

18. 947 

14. 400 

11. 613 

9.729 

8.372 

7.346 

6.545 

5.902 

5.373 

4.932 

10 

11 

50.704 

27. 481 

18.848 

14.342 

11. 575 

9.703 

8.353 

7.331 

6.533 

5.892 

5.365 

4.924 

11 

12 

50.000 

27. 273 

18. 750 

14. 286 

11. 538 

9.677 

8.334 

7.317 

6.521 

5.882 

5.357 

4.918 

12 

13 

49.  315 

27. 068 

18. 652 

14.  229 

11. 501 

9.651 

8.315 

7.302 

6.509 

5.872 

5.349 

4.911 

13 

14 

48.649 

26. 866 

18. 556 

14. 173 

11.465 

9.625 

8.295 

7.287 

7.272 

6.498 
6.486 

5.863 

5.341 

4.904 

4.897 

14 

15 

15 

48.  000 

26.  667 

18. 461 

14. 118 

11. 428 

9.600 

8.276 

5.853 

5.333 

16 

47.  368 

26. 471 

18. 367 

14. 063 

11.  392 

9.574 

8.257 

7.258 

6.474 

5.844 

5.325 

4.891 

16 

17 

46.  753 

26.  277 

18. 274 

14. 008 

11. 356 

9.549 

8.238 

7.243 

6.463 

5.834 

5.317 

4.884 

17 

18 

46. 154 

26.  087 

18. 182 

13.  953 

11.  321 

9.524 

8.219 

7.229 

6. 451 

5.825 

5.309 

4.878 

18 

19 
20 

45. 570 

25.  899 

18. 090 

13.900 

11.  285 

9.499 

8.200 

7.214 

6.440 

5.815 

5.301 

4.871 

19 

45.000 

25.  714 

18.000 

13. 846 

11.  250 

9.473 

8.181 

7.200 

6.428 

5.806 

5.294 

4.865 

20 

21 

44.444 

25.  532 

17. 910 

13.  793 

11. 214 

9.448 

8.163 

7.185 

6.417 

5.797 

5.286 

4.858 

21 

22 

43. 902 

25.352 

17.  822 

13. 740 

11. 180 

9.424 

8.144 

7.171 

6.405 

5.787 

5.278 

4.851 

22 

23 

43.  373 

25. 175 

17.734 

13.  688 

11. 146 

9.399 

8.126 

7.157 

6.394 

5.778 

5.270 

4.845 

23 

24 

42.  857 

25.000 

17.647 
17. 560 

13. 636 

11. Ill 
11.077 

9.375 
9.350 

8.108 

7.142 

6.383 
6.371 

5.769 

5.263 

4.838 

24 

25 

42.  353 

24. 828 

13.584 

8.090 

7.128 

5.760 

5. 255 

4.832 

25 

26 

41.  860 

24. 658 

17. 475 

13. 533 

11.043 

9.326 

8.071 

7.114 

6.360 

5.750 

5.247 

4.825 

26 

27 

41.379 

24. 490 

17.  391 

13. 483 

11. 009 

9.302 

8.053 

7.100 

6.349 

5.741 

5.240 

4.819 

27 

28 

40. 909 

24. 324 

17.  307 

13. 433 

10. 975 

9.278 

8.035 

7.086 

6.338 

5.732    5.232 

4.812 

28 

29 
30 

40.449 

24. 161 

17.  225 
17. 143 

13.  383 

10. 942 

9.254 

8.017 

7.072 

6.327 

5.723    5.224 

4.806 

29 

40. 000 

24.000 

13.  333 

10.  909 

9.230 

8.000 

7.059 

6.315 

5.714 

5.217 

4.800 

30 

31 

39. 560 

23.841 

17. 061 

13.284 

10. 876 

9.207 

7.982 

7.045 

6.304 

5.  705 

5.210 

4.793 

31 

32 

39. 130 

23.  684 

16. 981 

13. 235 

10.843 

9.183 

7.964 

7.031 

6.293 

5.696 

5.202 

4.787 

32 

33 

38. 710 

23.529 

16. 901 

13. 186 

10.  810 

9.160 

7.947 

7.017 

6.282 

5.687 

5.195 

4.780 

33 

34 
35 

38.298 

23. 377 

16. 822 

13. 138 

10.  778 

9. 137 

7.929 

7.004 
6.990 

6.  271  1  5.  678 

5.187 
5.179 

4.774 
4.768 

34 
35 

37.  895 

23.  226 

16.744 

13. 091 

10.  746 

9.113 

7.912 

6.260 

5.669 

36 

37.500 

26.077 

16. 667 

13.043 

10.  714 

9.090 

7.895 

6.977 

6.250 

5.660 

5.172 

4.761 

36 

37 

37. 113 

22. 930 

16.  590 

12. 996 

10.  682 

9.068 

7.877 

6.963 

6.239 

5.651 

5.164 

4.755 

37 

38 

36.  735 

22.  785 

16. 514 

12.  950 

10. 651 

9.045 

7.860 

6.950 

6.228 

5.642 

5.157 

4.749 

38 

39 
40 

36.364 

22.642 

16. 438 

12. 903 

10. 619 

9.022 

7.843 

6.936 
6.923 

6.217 
6.207 

5.633 

5.150 

4.743 

39 
40 

36.  000 

22. 500 

16.  363 

12.  857 

10.  588 

9.000 

7.826 

5.625 

5.143 

4.737 

41 

35.644 

22.  360 

16. 289 

12.  811 

10. 557 

8.977 

7.809 

6.909 

6.196 

5.616 

5.135 

4.731 

41 

42 

35. 294 

22. 222 

16.  216 

12. 766 

10.  526 

8.955 

7.792 

6.896 

6.185 

5.607 

5.128 

4.724 

42 

43 

34. 951 

22. 086 

16. 143 

12.  721 

10. 495 

8.933 

7.  775 

6.883 

6.174 

5.598 

5.121 

4.718 

43 

44 
45 

34. 615 

21. 951 

16. 071 

12. 676 

10.465 

8.911 

7.758 

6.870 

6.164 

5.590 

5.114 

4.712 

44 
45 

34.286 

21. 818 

16.000 

12. 631 

10.434 

8.889 

7.741 

6.857 

6.153 

5.581 

5. 106  . 

4.706 

46 

33. 962 

21. 687 

15. 929 

12. 587 

10.404 

8.867 

7.725 

6.844 

6.143 

5.572 

5.099 

4.700 

46 

47 

33.645 

21. 557 

15. 859 

12. 543 

10.  375 

8. 845 

7.708 

6.831 

6.132 

5.564 

5.091 

4.693 

47 

48 

33.  333 

21. 429 

15.  789 

12.500 

10.345 

8.823 

7.692 

6.818 

6.122 

5.555 

5.084 

4.687 

48 

49 
50 

33. 028 

21. 302 

15.  721 

12. 456 

10.  315 

8.801 

7.  675 

6.805 

6.112 

5.  547 

5.077 

4.681 

49 

32.  727 

21. 176 

15.  652 

12. 413 

10.  286 

8.780 

7.659 

6.792 

6.101 

5.538 

5.070 

4.675 

50 

51 

32. 432 

21. 053 

15. 584 

12. 371 

10. 256 

8.759 

7.643 

6.779 

6.091 

5.530 

5.063 

4.669 

51 

52 

32. 143 

20. 930 

15. 517 

12. 329 

10. 227 

8.737 

7.627 

6.766 

6.081 

5.521 

5.056 

4.663 

52 

53 

31.858 

20.  809 

15. 450 

12.  287 

10. 198 

8.716 

7.611 

6.754 

6.071 

5.513 

5.049 

4.657 

53 

54 
55 

31, 579 

20.690 

15.384 

12. 245 

10. 169 

8.695 

7.595 

6.  741 

6.060 

5.504 
5.496 

5.042 

4.651 

54 

55 

31.304 

20. 571 

15.  319 

12. 203 

10. 140 

8.675 

7.579 

6.739 

6.050 

5. 035 

4.  645 

56 

31.034 

20.455 

15. 254 

12. 162 

10. 112 

8.654 

7.563 

6.716 

6.040 

5.487 

5.028 

4.639 

56 

57 

30.  769 

20.  339 

15. 190 

12. 121 

10. 084 

8.633 

7.547 

6.704 

6.030 

5.479 

5.  020 

4.633 

57 

58 

30. 508 

20. 225 

15. 126 

12. 080 

10.055 

8.612 

7.531 

6.691 

6.020 

5.471 

5.013 

4.627 

58 

59 

30.252 

20.112 

15. 062 

12.040 

10. 027 

8.591 

7.515 

6.679 

6.010 

9 

5.463 
10 

5.006 

4.621 

59 

Sec. 

Sec. 

1 

2 

3 

4               5 

6 

7 

8 

11 

12 

4 


TABLE  36.                                           [Page  733 

Reduction  of  Local  Mean  Time  to  Standard  Meridian  Time,  and  the  reverse. 

[If  local  meridian  is  east  of  standard  meridian,  subtract  from  local  mean  time,  or  add  to  standard  meridian  time.   If  local 

meridian  is  west  of  standard  meridian,  add  to  local  mean  time,  or  subtract  from  standard  meridian  time.] 

Difference  of  longitude  be- 

Reduction to 

be  applied 

to  local  mean 

time. 

Difference  of   longitude  be- 

Reduction to 

be  applied 

to  local  mean 

time. 

tween  local  meridian  and 
standard  meridian. 

tween  local  meridian  and 
standard  meridian. 

0      /             o      / 

Minutes. 

o      /              o      / 

Minvteii. 

0  00  to  0  07 

0 

7  23  to    7  37 

30 

0  08  to  0  22 

1 

7  38  to    7  52 

31 

0  23  to  0  37 

2 

7  53  to    8  07 

32 

0  38  to  0  52 

3 

8  08  to    8  22 

33 

0  53  to  1  07 

4 

8  23  to    8  37 

34 

1  08  to  1  22 

5 

8  38  to    8  52 

35 

1  23  to  1  37 

6 

8  53  to    9  07 

36 

1  .38  to  1  52 

7 

9  08  to    9  22 

37 

1  53  to  2  07 

8 

9  23  to    9  37 

38 

2  08  to  2  22 

9 

9  38  to    9  52 

39 

2  23  to  2  37 

10 

9  53  to  10  07 

40 

2  38  to  2  52 

11 

10  08  to  10  22 

41 

2  53  to  3  07 

12 

10  23  to  10  37 

42 

3  08  to  3  22 

13 

10  38  to  10  52 

43 

3  23  to  3  37 

14 

10  53  to  11  07 

44 

3  38  to  3  52 

15 

11  08  to  11  22 

45 

3  53  to  4  07 

16 

11  23  to  11  37 

46 

4  08  to  4  22 

17 

11  38  to  11  52 

47 

4  23  to  4  37 

18 

11  53  to  12  07 

48 

4  38  to  4  52 

19 

12  08  to  12  22 

49  • 

4  53  to  5  07 

20 

12  23  to  12  37 

50 

5  08  to  5  22 

21 

12  38  to  12  52 

51 

5  23  to  5  37 

22 

12  53  to  13  07 

52 

5  38  to  5  52 

23 

13  08  to  13  22 

53 

5  53  to  6  07 

24 

13  23  to  13  37 

54 

6  08  to  6  22 

25 

13  38  to  13  52 

55 

6  23  to  6  37 

26 

13  53  to  14  07 

56 

6  38  to  6  52 

27 

14  08  to  14  22 

57 

6  53  to  7  07 

28 

14  23  to  14  37 

58 

7  08  to  7  22 

29 

U  38  to  14  52 

59 

!Note.— The  pageti  formerly  occupied  with  Tablen  .'?7  and  37  A  have  beeu  4ropped,  and  coiisecutiTe  page 
nuiubering  is  thereby  broken. 


TABLE  38.                                         [Page  739 

Error  in  Longitude  due  to  one  minute  Error  of  Latitude. 

-a 

(0*0 
OQ 

Latitude. 

2 

00*0 
OQ 

0° 

6° 

10° 

16° 

20° 

25° 

80° 

86° 

40° 

46° 

60° 

66° 

60° 

66° 

70° 

76° 

O 

10 
20 
30 
40 
50 
60 
10 
20 
30 
40 
50 
60 
15 
20 
30 
40 
50 
60 

o 

110 

f 

.4 
.4 
.4 

.5 
.7 
.9 

/ 
4 
4 
6 
6 
9 

1 

.4 
6 
6 
8 
2 

/ 

.5 

.6 

.7 

1.0 

/ 

.5 

.7 

.9 

1.3 

/ 

.6 

.8 

1.1 

.7 
1.0 
1.5 

/ 

.8 
1.2 
2.3 

/ 

1.0 
L6 

1.3 
2.6 

.9 
1.6 

.8 
1.1 
2.4 

.6 

.8 

L5 

.6 
1.0 
2.2 

.3 

.7 

L3 

.1 
.4 
.9 

.0 

.2 

.6 

1.1 

.2* 

.0 

.3 

.7 

L8 

172" 
2.7 

1.1 
1.6 

.8 
LI 
2.5 

.7 
L5 

.5 
LO 
2.3 

.2 

.6 

L3 

To" 

.4 
.8 

.2* 
.1 
.5 
LI 

2.9 
1.8 

L6 

2.7 

LI 
L6 

LI 

2.7 

.7 
1.5 

.4 

.9 

2.4 

.1 

.6 

L3 

72* 
.2 
.8 

3.0 

2.9 

L7 
2.8 

L6 

1.0 
2.7 

.5 
1.5 

.2 

.9 

2.5 

.2* 
.6 
L3 

f 

3.0 
3.0 
L6 

.9 

2.8 

.3 
1.5 

.2* 
.8 
2.6 

/ 

/ 

o 

110 

0 

10 
20 
30 
40 
50 
60 

105 

.3 
.3 
.3 
.4 
.4 
.6 

3 
3 
4 
5 
6 
9 

3 
4 
5 
6 

8 

1 

.3 
.4 
.6 

.7 
2 

.4 

.5 

.7 

1.0 

.4 

.6 

.8 

1.3 

.6 

.7 

1.1 

.6 

.9 

1.5 

.8 
1.2 
2.4 

105 

10 
20 
30 
40 
50 
60 

100 

.2 
.2 
.2 
.2 
.3 
.3 

2 
2 
3 
3 
4 
6 

2 
3 
3 
4 

6 
9 

3 

.3 

4 

6 

8 

.3 
.4 
.5 
.7 
1.2 

.4 
.5 
.6 
.9 

.4 

.6 

.8 

1.3 

.5 

.7 

1.1 

2.1 

.6 

.9 

1.6 

.5 
.6 

1.0 

2.1 

.4 

.7 

1.3 

.3 
.5 
.9 

.1 

.3 

.6 

1.1 

.1* 

.1 

.4 

.7 

.2* 

.0 

.2 

.4 

.9 

3.1 

L5 

.6 
3.0 

.2* 
L5 

100 

15 
20 
30 
40 
50 
60 

15 
20 
30 
40 
60 
60 

95 

'.2 

1 

1 
2 
2 
3 
3 

1 
2 
2 
3 
4 
6 

2 
2 
3 
4 
6 
9 

.2 
.3 
.4 
.6 

.8 

.3 
.3 
.5 
.7 
1.1 

.3 
.4 
.6 
.9 

.4 

.5 

.8 

1.3 

96 

15 
20 
30 
40 
50 
60 

20 
30 
40 
50 
60 
70 

90 

.0 
.0 
.0 
.0 
.0 
.0 

0 
1 
1 
1 
2 
2 

1 
1 
2 
2 
3 
6 

1 

1 
2 
3 
4 
6 
1 

.1 
.2 
.3 
.6 
.9 

.2 
.3 
.5 

.8 

.2 

.4 

.6 

1.1 

.3 
.5 
.9 

.2 

.4 

.6 

1.1 

3.1 
L2 

90 
85 
80 

20 
30 
40 
50 
60 
70 
20 
30 
40 
50 
60 
70 
20 
30 
40 
50 
60 
70 

20 
30 
40 
50 
60 
70 

86 

.1* 
.1* 
.1* 
.1* 

.2* 
.3* 

1* 

0 

0 

0 

0 

0 

0 
0 
0 
1 
1 
2 

0 
1 

1 
2 
3 
6 

.0 
.1 
.2 
.3 

.1 
.2 
.3 
.5 
.9 

.1 
.2 
.4 

.7 

20 
30 
40 
50 
60 
70 

80 

.2* 
.2* 
.2* 
.3* 
.4* 
.6* 

2* 
2* 
2* 
2* 
2* 
3* 

1* 

1* 

1* 

1* 

0 

0 

1* 

0 

0 

1 
1 
2 

A* 

.0 

.1 

.2 

.3 

.6 

.0 
.1 
.2 
.3 
.5 
1.2 

.0 

:l 

.5 
.9 

.0 
.2 
.4 

.7 

20 
30 
40 
50 
60 
70 

75 

.3* 
.3* 
.4* 
.4* 
.6* 
1.2* 

3* 
3* 
3> 
3* 
4* 
6* 

2* 
2* 
2* 
2* 
2* 
3* 

2* 
2* 
1* 
1* 
1* 
0 

.2* 

.1* 

.1* 

.0 

.1 

.2 

.1* 

.1* 

.0 

.1 

.3 

.6 

.1* 
.0 
.1 
.3 
.5 
1.2 

.1* 

.1 

.2 

.5 

.9 

75 

20 
30 
40 
50 
60 
70 

20 
30 
40 
50 
60 
70 

70 

.4* 
.4* 
.5* 
.6* 
.9* 

1 

4* 
4* 
4* 
5* 
6* 
2* 

3* 
3* 
3* 
3* 
4* 
6* 

3* 
3* 
3* 
2* 
3* 
3* 

.3* 
.2* 
.2* 
.2* 
.1* 
.1* 

.3* 

.2* 

.1* 

.0 

.1 

.2 

.2* 

.1* 

.0 

.1 

.2 

.6 

.2* 
.1* 
.1 
.3 
.5 
L2 

.2* 
3.1 

70 

20 
30 
40 
50 
60 
70 

i' 

P 

GO 

P 

OQ 

0° 

6° 

10° 

16° 

20° 

26° 

80° 

86° 

40° 

46° 

60° 

66° 

•0° 

66° 

70° 

76° 

^s 

Latitude. 

Page  740] 

TABLE  39. 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

o°.o 

0°.6 

1°.0 

10.5 

2<^.0 

2°.  6 

s°.o 

8°.  6 

4°.0 

4°.  5 

6°.0 

5°.  6 

6°.0 

o 

0 

0 

0 

o 

o 

o 

o 

o 

o 

o 

o 

0 

o 

0 

0 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

4.5 

5.0 

5.5 

6.0 

0 

10 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.1 

4.6 

5.1 

5.6 

6.1 

10 

15 

0.0 

0.5 

1.0 

1.5 

2.1 

2.6 

3.1 

3.6 

4.2 

4.7 

5.2 

5.7 

6.2 

15 

20 

0.0 

0.5 

1.1 

1.6 

2.1 

2.7 

3.2 

3.7 

4.3 

4.8 

5.3 

5.8 

6.4 

20 

25 

0.0 

0.5 

1.1 

1.6 

2.2 

2.8 

3.3 

3.8 

4.4 

5.0 

5.5 

6.0 

6.6 

25 

30 

0.0 

0.6 

1.2 

1.7 

2.3 

2.9 

3.4 

4.0 

4.6 

5.2 

5.8 

6.3 

6.9 

30 

32 

0.0 

0.6 

1.2 

1.8 

2.4 

2.9 

3.5 

4.1 

4.7 

5.3 

5.9 

6.5 

7.0 

32 

34 

0.0 

0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.2 

4.8 

5.4 

6.0 

6.6 

7.2 

34 

36 

0.0 

0.6 

1.2 

1.8 

2.5 

3.1 

3.7 

4.3 

4.9 

5.6 

6.1 

6.8 

7.4 

36 

38 

0.0 

0.6 

1.3 

1.9 

2.5 

3.2 

3.8 

4.4 

5.1 

5.7 

6.3 

7.0 

7.6 

38 

40 

0.0 

0.7 

1.3 

2.0 

2.6 

3.3 

3.9 

4.6 

5.2 

5.9 

6.5 

7.2 

7.8 

40 

42 

0.0 

0.7 

1.3 

2.0 

2.7 

3.4 

4.0 

4.7 

5.4 

6.1 

6.7 

7.4 

8.0 

42 

44 

0.0 

0.7 

1.4 

2.1 

2.8 

3.5 

4.2 

4.9 

5.6 

6.3 

6.9 

7.6 

8.3. 

44 

46 

0.0 

0.7 

1.4 

2.2 

2.9 

3.6 

4.3 

5.0 

5.8 

6.5 

7.2 

7.9 

8.6 

46 

48 

0.0 

0.7 

1.5 

2.2 

3.0 

3.7 

4.5 

5.2 

6.0 

6.7 

7.5 

8.2 

9.0 

48 

50 

0.0 

0.8 

1.5 

2.3 

3.1 

3.9 

4.7 

5.4 

6.2 

7.0 

7.8 

8.6 

9.3 

50 

51 

0.0 

0.8 

1.6 

2.4 

3.2 

4.0 

4.8 

5.6 

6.4 

7.2 

8.0 

8.8 

9.5 

51 

52 

0.0 

0.8 

1.6 

2.4 

3.3 

4.1 

4.9 

5.7 

6.5 

7.3 

8.1 

9.0 

9.7 

52 

53 

0.0 

0.8 

1.6 

2.5 

3.3 

4.2 

5.0 

5.8 

6.7 

7.5 

8.3 

9.2 

10.0 

53 

54 

0.0 

0.9 

1.7 

2.5 

3.4 

4.3 

5.1 

6.0 

6.8 

7.7 

8.5 

9.4 

0.2 

54 

55 

0.0 

0.9 

1.7 

2.6 

3.5 

4.4 

5.2 

6.1 

7.0 

7.9 

8.7 

9.6 

10.5 

55 

56 

0.0 

0.9 

1.8 

2.7 

3.6 

4.5 

5.4 

6.3 

7.2 

8.1 

9.0 

9.9 

0.8 

56 

57 

0.0 

0.9 

1.8 

2.7 

3.7 

4.6 

5.5 

6.4 

7.4 

8.3 

9.2 

10.1 

1.1 

57 

58 

0.0 

0.9 

1.9 

2.8 

3.8 

4.7 

5.7 

6.6 

7.6 

8.5 

9.5 

0.4 

1.4 

58 

59 

0.0 

1.0 

1.9 

2.9 

3.9 

4.9 

5.8 

6.8 

7.8 

8.8 

9.7 

0.7 

1.7 

59 

60 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

8.0 

9.0 

10.0 

11.0 

12.1 

60 

61 

0.0 

1.0 

2.1 

3.1 

4.1 

5.2 

6.2 

7.2 

8.3 

9.3 

0.3 

1.4 

2.5 

61 

62 

0.0 

1.1 

2.1 

3.2 

4.3 

5.3 

6.4 

7.5 

8.5 

9.6 

0.7 

1.8 

2.9 

62 

63 

0.0 

1.1 

2.2 

3.3 

4.5 

5.5 

6.6 

7.7 

8.8 

9.9 

1.1 

2.2 

3.4 

63 

64 

0.0 

1.1 

2.3 

3.4 

4.6 

5.7 

6.9 

8.0 

9.2 

10.3 

1.5 

2.6 

3.9 

64 

65.0 

0.0 

1.2 

2.4 

3.5 

4.8 

5.9 

7.1 

8.3 

9.5 

10.7 

11.9 

13.1 

14.4 

65.0 

5.5 

0.0 

1.2 

2.4 

3.6 

4.8 

6.0 

7.2 

8.5 

9.7 

0.9 

2.1 

3.4 

4.6 

5.5 

6.0 

0.0 

1.2 

2.5 

3.7 

4.9 

6.1 

7.4 

8.6 

9.9 

1.1 

2.4 

3.6 

4.9 

6.0 

6.5 

0.0 

1.2 

2.5 

3.8 

5.0 

6.3 

7.5 

8.8 

10.1 

1.3 

2.6 

3.9 

5.2 

6.5 

7.0 

0.0 

1.3 

2.6 

3.8 

5.1 

6.4 

7.7 

9.0 

0.3 

1.6 

2.9 

4.2 

5.5 

7.0 

67.5 

0.0 

1.3 

2.6 

3.9 

5.2 

6.5 

7.9 

9.2 

10.5 

11.8 

13.2 

14.5 

15.9 

67.5 

8.0 

0.0 

1.3 

2.7 

4.0 

5.3 

6.7 

8.0 

9.4 

0.7 

2.1 

3.5 

4.8 

6.2 

8.0 

8.5 

0.0 

1.4 

2.7 

4.1 

5.4 

6.8 

8.2 

9.6 

1.0 

2.4 

3.8 

5.2 

6.6 

8.5 

9.0 

0.0 

1.4 

2.8 

4.2 

5.5 

7.0 

8.4 

9.8 

1.2 

2.6 

4.1 

5.5 

7.0 

9.0 

9.5 

0.0 

1.4 

2.9 

4.3 

5.7 

7.2 

8.6 

10.0 

1.5 

2.9 

4.4 

5.9 

7.4 

9.5 

70.0 

0.0 

1.5 

2.9 

4.4 

5.8 

7.3 

8.8 

10.3 

11.8 

13.3 

14.8 

16.3 

17.8 

70.0 

0.5 

0.0 

1.5 

3.0 

4.5 

6.0 

7.5 

9.0 

0.5 

2.1 

3.6 

5.1 

6.7 

8.2 

0.5 

1.0 

0.0 

1.5 

3.1 

4.6 

6.2 

7.7 

9.3 

0.8 

2.4 

3.9 

5.5 

7.1 

8.7 

1.0 

1.5 

0.0 

1.6 

3.2 

4.7 

6.3 

7.9 

9.5 

1.1 

2.7 

4.3 

5.9 

7.8 

9.2 

1.5 

2.0 

0.0 

1.6 

3.2 

4.9 

6.5 

8.1 

9.8 

1.4 

3.0 

4.7 

6.4 

8.1 

9.8 

2.0 

72.5 

0.0 

1.7 

3.3 

5.0 

6.7 

8.3 

10.0 

11.7 

13.4 

15.1 

16.9 

18.6 

20.3 

72.5 

3.0 

0.0 

1.7 

3.4 

5.1 

6.9 

8.6 

0.3 

2.0 

3.8 

5.5 

7.4 

9.1 

0.9 

3.0 

3.5 

0.0 

1.8 

3.5 

5.2 

7.1 

8.8 

0.6 

2.4 

4.2 

6.0 

7.9 

9.7 

1.6 

3.5 

4.0 

0.0 

1.8 

3.6 

5.4 

7.3 

9.1 

0.9 

2.8 

4.6 

6.5 

8.4 

20.3 

2.3 

4.0 

4.5 

0.0 

1.9 

3.7 

5.6 

7.5 

9.4 

1.3 

3.2 

5.1 

7.1 

9.0 

1.0 

3.0 

4.5 

75.0 

0.0 

1.9 

3.8 

5.8 

7.7 

9.7 

11.7 

13.6 

15.6 

17.7 

19.7 

21.7 

23.8 

75.0 

5.5 

0.0 

2.0 

3.9 

6.0 

8.0 

10.0 

2.1 

4.1 

6.2 

8.3 

20.4 

2.5 

4.7 

5.5 

6.0 

0.0 

2.1 

4.0 

6.2 

8.3 

0.4 

2.5 

4.6 

6.8 

8.9 

1.1 

3.3 

5.6 

6.0 

6.5 

0.0 

2.1 

4.2 

6.4 

8.6 

0.8 

3.0 

5.2 

7.4 

9.6 

1.9 

4.2 

6.6 

6.5 

7.0 

0.0 

2.2 

4.4 

6.6 

8.9 

1.2 

3.5 

5.8 

8.1 

20.4 

2.8 

5.2 

7.7 

7.0 

TABLE  39. 

[Page  741 

Amplitudes. 

Lati- 
tude. 

Decimation.                                                                               1 

Lati- 
tude. 

6°.0 

«°.5 

;°.o 

7°.  5 

8°.0 

8°.  5 

9°.0   1    9°.  5 

10°.0 

10°.  5 

11°.0 

11°.6 

li°.0 

o 

o 

o 

o 

o 

o 

o 

o                o 

o 

o 

o 

0 

0 

o 

0 

6.0 

6.5 

7.0 

7.5 

8.0 

8.5 

9.0  1    9.5 

10.0 

10.5 

11.0 

11.5 

12.0 

0 

10 

6.1 

6.6 

7.1 

7.6 

8.1 

8.6 

9.1  1    9.7 

0.1 

0.7 

1.2 

1.7 

2.2 

10 

15 

6.2 

6.7 

7.2 

7.8 

8.3 

8.8 

9.3 

9.8 

0.4 

0.9 

1.4 

1.9 

2.5 

15 

20 

6.4 

6.9 

7.4 

8.0 

8.5 

9.1 

9.6 

10,1 

0.7 

1.2 

1.7 

2.3 

2.8 

20 

25 
30 

6.6 

7.1 

7.7 

8.3 

8.8 

9.4 

9.9 

0.5 

1.1 

1.6 

2.2 

2.8 

3.3 

25 

6.9 

7.5 

8.1 

8.7 

9.3 

9.8 

10.4  1 

11.0 

11.5 

12.1 

12.7 

13.3 

13.9 

30 

32 

7.0 

7.7 

8.3 

8.8 

9.5 

10.0 

0.6  i     1.2 

1.8 

2.4 

3.0 

3.6 

4.2 

32 

34 

7.2 

7.8 

8.5 

9.0 

9.7 

0.3 

0.8  1    1.5 

2.1 

2.7 

3.3 

8.9 

4.5 

34 

36 

7.4 

8.0 

8.7 

9.3 

9.9 

0.5 

1.1  !    1.8 

2.4 

3.0 

3.6 

4.3 

4.9 

36 

38 

7.6 

8.2 

8.9 

9.5 

10.2 

0.8 

1.4  !    2.1 

2.7 

3.4 

4.0 

4.7 

5.3 

38 

40 

7.8 

8.5 

9.1 

9.8 

10.5 

11.1 

11.7 

12.4 

13.1 

13.8 

14.4 

15.1 

15.7 

40 

42 

8.0 

8.8 

9.4 

10.1 

0.8 

1.5 

2.1 

2.8 

3.5 

4.2 

4.8 

5.6 

6.2 

42 

44 

8.3 

9.1 

9.7 

0.5 

1.1 

1.9 

2.5 

3.3 

4.0 

4.7 

5.3 

6.1 

6.8 

44 

46 

8.6 

9.4 

10.1 

0.8 

1.5 

2.3 

3.0 

3.8 

4.5 

5.2 

5.9 

6.7 

7.4 

46 

48 

9.0 

9.7 

0.5 

1.2 

2.0 

2.8 

3.5 

4.3 

5.0 

5.8 

6.6 

7.3 

8.1 

48 

50 

9.3 

10.1 

10.9 

11.7 

12.5 

13.3 

14.1 

14.9 

15.7 

16.5 

17.3 

18.1 

18.9 

50 

51 

9.5 

0.4 

1.2 

2.0 

2.8 

3.6 

4.4 

5.2 

6.0 

6.8 

7.7 

8.5 

9.3 

51 

52 

9.7 

0.6 

1.4 

2.2 

3.1 

3.9 

4.  7       5. 6 

6.4 

7.2 

8.1 

8.9 

9.7 

52 

53 

10.0 

0.8 

1.7 

2.5 

3.4 

4.2 

5.1 

5.9 

6.8 

7.6 

8.5 

9.4 

20.2 

53 

54 

0.2 

1.1 

2.0 

2.8 

3.7 

4.6 

5.4 

6.3 

7.2 

8.1 

8.9 

9.8 

0.7 

54 

55 

10.5 

11.4 

12.3 

13.1 

14.0 

14.9 

15.8 

16.7 

17.6 

18.5 

19.4 

20.3 

21.2 

55 

56 

0.8 

1.7 

2.6 

3.5 

4.4 

5.3 

6.2 

7.2 

8.1 

9.0 

9.9 

0.9 

1.8 

56 

57 

1.1 

2.0 

2.9 

3.9 

4.8 

5.8 

6.7 

7.7 

8.6 

9.6 

20.5 

1.5 

2.4 

57 

58 

1.4 

2.3 

3.3 

4.3 

5.2 

6.2 

7.2 

8.2 

9.1 

20.1 

1.1 

2.1 

3.1 

58 

59 

1.7 

2.7 

3.7 

4.7 

5.7 

6.7 

7.7 

8.7 

9.7 

0.7 

1.7 

2.8 

3.8 

59 

60 

12.1 

13.1 

14.1 

15.1 

16.2 

17.2 

18.2 

19.3 

20.3 

21.4 

22.4 

23.5 

24.6 

60 

61 

2.5 

3.5 

4.6 

5.6 

6.7 

7.8 

8.8 

9.9 

1.0 

2.1 

3.1 

4.3 

5.4 

61 

62 

2.9 

3.9 

5.1 

6.1 

7.3 

8.4 

9.4 

20.6 

1.7 

2.9 

3.9 

5.2 

6.3 

62 

63 

3.4 

4.4 

5.6 

6.7 

7.9 

9.0 

20.1 

1.3 

2.5 

3.7 

4.8 

6.1 

7.2 

63 

64 

3.9 

5.0 

6.2 

7.3 

8.5 

9.7 

0.9 

2.1 

3.3 

4.6 

5.7 

7.1 

8.3 

64 

65.0 

14.4 

15.5 

16.8 

18.0 

19.3 

20.5 

21.7 

23.0 

24.2 

25.6 

26.8 

28. 2     29. 5 

65.0 

5.5 

4.6 

5.8 

7.1 

8.3 

9.6 

0.9 

2.2 

3.5 

4.7 

6.1 

7.4 

8.  7     30. 1 

5.5 

6.0 

4.9 

6.2 

7.4 

8.7 

20.0 

1.3 

2.6 

3.9 

5.3 

6.6 

8.0 

9. 3       0.  7 

6.0 

6.5 

5.2 

6.5 

7.8 

9.1 

0.4 

1.8 

3.1 

4.4 

5.8 

7.2 

8.6 

30.0       1.4 

6.5 

7.0 

5.5 

6.8 

8.2 

9.5 

0.9 

2.2 

3.6 

5.0 

6.4 

7.8 

9.2 

0.  7       2. 1 

7.0 

67.5 

15.9 

17.2 

18.6 

19.9 

21.3 

22.7 

24.1 

25.5 

27.0 

28.4 

29.9 

31. 4  1  32. 9 

67.5 

8.0 

6.2 

7.6 

9.0 

20.4 

1.8 

3.2 

4.7 

6.1 

7.6 

9.1 

30.6 

2.  2  1    3.  7 

8.0 

8.5 

6.6 

8.0 

9.4 

0.9 

2.3 

3.8 

5.3 

6.8 

8.3 

9.8 

1.4 

3.0 

4.6 

8.5 

9.0 

7.0 

8.4 

9.9 

1.4 

2.8 

4.4 

5.9 

7.4 

9.0 

30.6 

2.2 

3.8 

5.5 

9.0 

9.5 

7.4 

8.9 

20.4 

1.9 

3.4 

5.0 

6.5 

8.1 

9.7 

1.4 

3.0 

4.7 

6.4 

9.5 

70.0 

17.8 

19.3 

20.9 

22.4 

24.0 

25.6 

27.2 

28.8 

30.5 

32.2 

33.9 

35.7 

37.4 

70.0 

0.5 

8.2 

9.8 

1.4 

3.0 

4.6 

6.3 

7.9 

9.6 

1.3 

3.1 

4.9 

6.7 

8.5 

0.5 

1.0 

8.7 

20.3 

2.0 

3.6 

5.3 

7.0 

8.7 

30.5 

2.2 

4.0 

5.9 

7.8 

9.7 

1.0 

1.5 

9.2 

0.9 

2.6 

4.3 

6.0 

7.8 

9.5 

1.4 

3.2 

5.0 

7.0 

8.9 

40.9 

1.5 

2.0 

9.8 

1.5 

3.2 

5.0 

6.8 

8.6 

30.4 

2.3 

4.2 

6.1 

8.1 

40.2 

2.3 

2.0 

72.5 

20.3 

22.1 

23.9 

25.7 

27.6 

29.5 

31.4 

33.3 

35.3 

37.3 

39.4 

41.5 

43.7 

72.5 

3.0 

0.9 

2.8 

4.6 

6.5 

8.4 

30.4 

2.4 

4.4 

6.5 

8.6 

40.8 

3.0 

5.3 

3.0 

3.5 

1.6 

3.5 

5.4 

7.4 

9.3 

1.4 

3.4 

5.5 

7.7 

9.9 

2.2 

4.6 

7.0 

3.5 

4.0 

2.3 

4.3 

6.2 

8.3 

30.3 

2.5 

4.6 

6.8 

9.1 

41.4 

3.8 

6.3 

8.9 

4.0 

4.5 

3.0 

5.1 

7.1 

9.3 

1.4 

3.6 

5.8 

8.2 

40.5 

3.0 

5.6 

8.2 

51.1 

4.5 

75.0 

23.8 

26.0 

28.1 

30.3 

32.5 

34.8 

37.2 

39.6 

42.1 

44.8 

47.5 

50.4 

53.5 

75.0 

5.5 

4.7 

6.9 

9.1 

1.4 

3.8 

6.2 

8.7 

41.2 

3.9 

6.7 

9.6 

2.8 

6.2 

5.5 

6.0 

5.6 

7.9 

30.2 

2.6 

5.1 

7.7 

40.3 

3.0 

5.9 

8.9 

52.1 

5.5 

9.3 

6.0 

6.5 

6.6 

9.0 

1.4 

4.0 

6.6 

9.3 

2.1 

5.0 

8.1 

51.3 

4.8 

8.7 

63.0 

6.5 

7.0 

7.  7 

30.2 

2.8 

5.5 

8.2 

41.1 

4.1 

7.2 

50.5 

4.1 

8.0 

62.4 

7.6 

7.0 

Page  742; 

TABLE  39. 

Amplitudes. 

Lati- 
tude. 

Declination. 

Lati- 
tude. 

12°.0 

12°.  5 

13°.0 

18°.  6 

14°.  0 

14°.  5 

16°.0 

16°.  5 

16°.  0 

16°.  5 

17°.0 

17°.  5 

18°.o 

o 

0 

c 

o 

o 

o 

0 

o 

o 

o 

o 

o 

o 

o 

o 

0 

12.0 

12.5 

13.0 

13.6 

14.0 

14.5 

15.0 

15.6 

16.0 

16.5 

17.0 

17.5 

18.0 

0 

10 

2.2 

2.7 

3.2 

3.7 

4.2 

4.7 

5.3 

6.8 

6.3 

6.8 

7.3 

7.9 

8.3 

10 

15 

2.5 

2.9 

3.6 

4.0 

4.5 

6.0 

5.6 

6.1 

6.6 

7.1 

7.7 

8.2 

8.7 

15 

20 

2.8 

3.3 

3.8 

4.4 

4.9 

6.6 

6.0 

6.5 

7.1 

7.6 

8.1 

8.7 

9.2 

20 

25 

3.3 

3.8 

4.4 

4.9 

5.6 

6.1 

6.6 

7.1 

7.7 

8.3 

8.8 

9.4 

9.9 

25 

30 

13.9 

14.6 

16.0 

15.6 

16.2 

16.8 

17.4 

18.0 

18.6 

19.2 

19.7 

20.3 

20.9 

30 

32 

4.2 

4,8 

6.3 

6.0 

6.6 

7.2 

7.8 

8.4 

9.0 

9.6 

20.2 

0.8 

1.4 

32 

34 

4.5 

5.1 

5.7 

6.4 

7.0 

7.6 

8.2 

8.8 

9.5 

20.0 

0.7 

1.3 

1.9 

34 

36 

4.9 

5.6 

6.1 

6.8 

7.4 

8.0 

8.7 

9.3 

20.0 

0.6 

1.2 

1.8 

2.5 

36 

38 

5.3 

6.0 

6.6 

7.2 

7.9 

8.6 

9.2 

9.8 

0.6 

1.1 

1.8 

2,4 

3.1 

38 

40 

15.7 

16.4 

17.1 

17.8 

18.4 

19.1 

19.7 

20.4 

21.1 

21.8 

22.4 

23.1 

23.8 

40 

41 

6.0 

6.7 

7.3 

8.0 

8.7 

9.4 

20.0 

0.8 

1.4 

2.1 

2.8 

3.5 

4.2 

41 

42 

6.2 

6.9 

7.6 

8.3 

9.0 

9.7 

0.4 

1.1 

1.8 

2.5 

3.2 

3.9 

4.6 

42 

43 

6.5 

7.2 

7.9 

8.6 

9.3 

20.0 

0.7 

1.4 

2.2 

2.9 

3.6 

4.3 

6.0 

43 

44 

6.8 

7.6 

8.2 

8.9 

9.6 

0.4 

1.1 

1.8 

2.6 

3.3 

4.0 

4.7 

6.4 

44 

45 

17.1 

17.8 

18.5 

19.3 

20.0 

20.7 

21.6 

22.2 

23.0 

23.7 

24.4 

26.2 

26.9 

45 

46 

7.4 

8.2 

8.9 

9.6 

0.4 

1.1 

1.9 

2.6 

3.4 

4.1 

4.9 

6.7 

6.4 

46 

47 

7.7 

8.5 

9.3 

20.0 

0.8 

1.5 

2.3 

3.1 

3.8 

4.6 

5.4 

6.2 

6.9 

47 

48 

8.1 

8.9 

9.7 

0.4 

1.2 

2.0 

2.8 

3.6 

4.3 

6.1 

5.9 

6.7 

7.5 

48 

49 

8.5 

9.3 

20.1 

0.8 

1.6 

2.4 

3.2 

4.1 

4.9 

6.7 

6.6 

7.3 

8.1 

49 

50 

18.9 

19.7 

20.6 

21.3 

22.1 

22.9 

23.7 

24.6 

26.4 

26.2 

27.0 

27.9 

28.7 

50 

51 

9.3 

20.1 

0.9 

1.8 

2.6 

3.5 

4.3 

5.1 

6.0 

6.8 

7.6 

8.5 

9.4 

61 

52 

9.7 

0.6 

1.4 

2.3 

3.1 

4.0 

4.9 

5.7 

6.6 

7.6 

8.3 

9.2 

30.1 

62 

53 

20.2 

1.1 

1.9 

2.8 

3.7 

4.6 

5.6 

6.4 

7.3 

8.2 

9.0 

30.0 

0.9 

63 

54 

0.7 

1.6 

2.5 

3.4 

4.3 

5.2 

6.1 

7.1 

8.0 

8.9 

9.8 

0.8 

1.7 

54 

55 

21.2 

22.2 

23.1 

24.0 

24.9 

25.9 

26.8 

27.8 

28.7 

29.7 

30.6 

31.6 

32.6 

55 

56 

1.8 

2.8 

3.7 

4.7 

5.6 

6.6 

7.6 

8.6 

9.5 

30.6 

1.6 

2.5 

3.6 

56 

57 

2.4 

3.4 

4.4 

6.4 

6.4 

7.4 

8.4 

9.4 

30.4 

1.4 

2.5 

3.5 

4.6 

57 

58 

3.1 

4.1 

6.1 

6.1 

7.2 

8.2 

9.2 

30.3 

1.3 

2.4 

3.5 

4.6 

6.7 

58 

59 

3.8 

4.8 

6.9 

6.9 

8.0 

9.1 

30.2 

1.3 

2.3 

3.5 

4.6 

6.7 

6.9 

59 

60 

24.6 

25.6 

26.7 

27.8 

28.9 

30.1 

31.2 

32.3 

33.4 

34.6 

36.8 

36.9 

38.2 

60 

61 

5.4 

6.6 

7.6 

8.8 

9.9 

1.1 

2.2 

3.5 

4.6 

5.8 

7.1 

8.3 

9.6 

61 

62 

6.3 

7.6 

8.6 

9.8 

31.0 

2.2 

3.4 

4.7 

5.9 

7.2 

8.5 

9.8 

41.2 

62 

63 

7.2 

8.5 

9.7 

31.0 

2.2 

3.6 

4.7 

6.1 

7.4 

8.7 

40.1 

41.5 

2.9 

63 

64 

8.3 

9.6 

30.9 

2.2 

3.6 

4.8 

6.2 

7.6 

9.0 

40.4 

1.8 

3.3 

4.8 

64 

65.0 

29.5 

30.8 

32.2 

33.6 

34.9 

36.3 

37.8 

39.2 

40.7 

42.2 

43,8 

46.4 

47.0 

65.0 

5.5 

30.1 

1.6 

2.9 

4.3 

5.7 

7.1 

8.6 

40.1 

1.6 

3.2 

4.8 

6.6 

8.2 

5.5 

6.0 

0.7 

2.2 

3.6 

5.0 

6.6 

8.0 

9.6 

1.1 

2.7 

4.3 

6.9 

7.7 

9.4 

6.0 

6.5 

1.4 

2.9 

4.3 

5.8 

7.3 

8.9 

40.6 

2.1 

3.8 

5.4 

7.1 

8.9 

60.8 

6.5 

7.0 

2.1 

3.6 

5.1 

6.7 

8.2 

9.8 

1.6 

3.2 

4.9 

6.6 

8.4 

50.3 

2.3 

7.0 

67.5 

32.9 

34.4 

36.0 

37.6 

39.2 

40.8 

42.6 

44.3 

46.1 

47.9 

49.8 

61.8 

53.9 

67.5 

8.0 

3.7 

6.3 

6.9 

8.6 

40.2 

1.9 

3.7 

6.6 

7.4 

9.3 

51.3 

3.4 

6.6 

8.0 

8.5 

4.6 

6.2 

7.9 

9.6 

1.3 

3.1 

4.9 

6.8 

8.8 

60.8 

2.9 

5.1 

7.5 

8.5 

9.0 

5.6 

7.2 

8.9 

40.7 

2.5 

4.3 

6.2 

8.2 

50.3 

2.4 

4.6 

7.0 

9.6 

9.0 

9.5 

6.4 

8.2 

40.0 

1.8 

3.7 

5.6 

7.6 

9.7 

1.9 

4.2 

6.5 

9.1 

61.9 

9.5 

70.0 

37.4 

39.3 

41.1 

43.0 

45.0 

47.0 

49.2 

61.4 

53.7 

66.1 

68.7 

61.5 

64.6 

70.0 

0.5 

8.5 

40.4 

2.4 

4.4 

6.4 

8.6 

50.8 

3.2 

5.7 

8.3 

61.1 

4.3 

7.8 

0.5 

1.0 

9.7 

1.7 

3.7 

5.8 

8.0 

60.3 

2.6 

5.2 

7.9 

60.7 

3.9 

7.5 

71.7 

1.0 

1.5 

40.9 

3.0 

5.1 

7.4 

9.7 

2.1 

4.6 

7.4 

60.3 

3.6 

7.1 

71.4 

6.9 

1.5 

2.0 

2.3 

4.4 

6.7 

9.1 

51.5 

4.1 

6.9 

9.9 

3.1 

6.8 

71.1 

6.7 

90.0 

2.0 

72.5 

43.7 

46.0 

48.4 

50.9 

53.6 

56.4 

59.4 

62.7 

66.4 

70.9 

76.5 

90.0 

72.5 

3.0 

6.3 

7.7 

50.3 

3.0 

6.9 

8.9 

62.2 

6.1 

70.6 

6.3 

90.0 

3.0 

3.5 

7.0 

9.6 

2.3 

6.3 

8.4 

61.8 

6.6 

70.3 

6.1 

90.0 

3.5 

4.0 

8.9 

51.7 

4.7 

7.9 

61.4 

5.3 

9.8 

75.9 

90.0 

4.0 

4.5 

51.1 

4.1 

7.3 

60.9  1    4.9 

1 

9.6 

76.5 

90.0 

4.5 

TABLE  39. 

[Page  743    | 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

18°.0 

18°.  6 

19°.0 

19°.  5 

20°.0 

20°.  6 

21°.0 

21°.  6 

22°.0 

22°.  6 

28°.  0 

28°.  6 

24°.0 

0 

o 

o 

o 

o 

o 

o 

o 

0 

o 

o 

0 

o 

o 

0 

0 

18.0 

18.5 

19.0 

19.5 

20.0 

20.5 

21.0 

21.5 

22.0 

22.5 

23.0 

23.5 

24.0 

0 

10 

8.3 

8.8 

9.3 

9.8 

0.3 

0.8 

1.3 

1.8 

2.3 

2.9 

3.4 

3.9 

4.4 

10 

15 

8.7 

9.2 

9.7 

20.2 

0.7 

1.3 

1.8 

2.3 

2.8 

3.3 

3.9 

4.4 

4.9 

15 

20 

9.2 

9.7 

20.3 

0.8 

1.4 

1.9 

2.4 

3.0 

3.5 

4.0 

4.6 

5.1 

5.7 

20 

25 

9.9 

20.5 

1.1 

1.6 

2.2 

2.7 

3.3 

3.9 

4.4 

5.0 

5.5 

6.1 

6.7 

25 

30 

20.9 

21.5 

22.1 

22.7 

23.3 

23.8 

24.4 

25.0 

25.6 

26.2 

26.8 

27.4 

28.0 

30 

32 

1.4 

2.0 

2.6 

3.2 

3.8 

4.4 

5.0 

5.6 

6.2 

6.8 

7.4 

8.0 

8.7 

32 

34 

1.9 

2.5 

3.1 

3.8 

4.4 

5.0 

5.6 

6.2 

6.9 

7.5 

8.1 

8.7 

9.4 

34 

36 

2.5 

3.1 

3.7 

4.4 

5.0 

5.7 

6.3 

6.9 

7.6 

8.2 

8.9 

9.5 

30.2 

36 

38 
40 

3.1 

3.8 

4.4 

5.1 

5.7 

6.4 

7.0 

7.7 

8.4 

9.1 

9.7 

30.4 

1.1 

38 

23.9 

24.4 

25.1 

25.8 

26.5 

27.2 

27.9 

28.6 

29.3 

30.0 

30.7 

31.3 

32.1 

40 

41 

4.2 

4.8 

5.5 

6.2 

6.9 

7.7 

8.3 

9.1 

9.8 

0.5 

1.2 

1.8 

2.6 

41 

42 

4.6 

5.3 

6.0 

6.7 

7.4 

8.1 

8.8 

9.6 

30.3 

1.0 

1.7 

2.4 

3.2 

42 

43 

5.0 

5.7 

6.4 

7.2 

7.9 

8.6 

9.3 

30.1 

0.8 

1.6 

2.3 

3.0 

3.8 

43 

44 

5.4 

6.2 

6.9 

7.7 

8.4 

9.1 

9.8 

0.6 

1.4 

2.2 

2.9 

3.6 

4.4 

44 

45 

25.9 

26.7 

27.4 

28.2 

28.9 

29.7 

30.4 

31.2 

32.0 

32.8 

33.5 

34.3 

36.1 

45 

46 

6.4 

7.2 

7.9 

8.7 

9.6 

30.3 

1.0 

1.8 

2.6 

3.4 

4.2 

5.0 

5.8 

46 

47 

6.9 

7.7 

8.5 

9.3 

30.1 

0.9 

1.7 

2.5 

3.3 

4.1 

4.9 

5.7 

6.6 

47 

48 

7.5 

8.3 

9.1 

9.9 

0.7 

1.6 

2.4 

3.2 

4.0 

4.9 

5.7 

6.5 

7.4 

48 

49 

8.1 

8.9 

9.7 

30.6 

1.4 

2.3 

3.1 

4.0 

4.8 

5.7 

6.5 

7.4 

8.3 

49 

50 

28.7 

29.6 

30.4 

31.3 

32,1 

33.0 

33.9 

34.8 

35.6 

36.5 

37.4 

38.3 

39.2 

50 

51 

9.4 

30.3 

1.1 

2.0 

2.9 

3.8 

4.7 

5.6 

6.5 

7.4 

8.4 

9.3 

40.2 

51 

52 

30.1 

1.0 

1.9 

2.8 

3.7 

4.7 

5.6 

6.5 

7.5 

8.4 

9.4 

40.3 

1.3 

62 

53 

0.9 

1.8 

2.7 

3.7 

4.6 

5.6 

6.6 

7.5 

8.5 

9.5 

40.5 

1.4 

2.5 

53 

54 

1.7 

2.7 

3.6 

4.6 

5.6 

6.6 

7.6 

8.6 

9.6 

40.6 

1.7 

2.6 

3.8 

64 

55 

32.6 

33.6 

34.6 

35.6 

36.6 

37.6 

38.7 

39.7 

40.8 

41.9 

42.9 

44.0 

45.2 

56 

56 

3.6 

4.6 

5.6 

6.7 

7.7 

8.8 

9.8 

41.0 

2.1 

3.2 

4.3 

5.4 

6.7 

56 

57 

4.6 

5.6 

6.7 

7.8 

8.9 

40.0 

41.1 

2.3 

3.5 

4.6 

5.8 

7.0 

8.3 

57 

58 

5.7 

6.8 

7.9 

9.1 

40.2 

1.4 

2.5 

3.8 

5.0 

6.2 

7.5 

8.8 

50.1 

58 

59 

6.9 

8.0 

9.2 

40.4 

1.6 

2.8 

4.1 

5.4 

6.7 

8.0 

9.3 

50.7 

2.2 

59 

60.0 

38.2 

39.4 

40.6 

41.9 

43.2 

44.5 

45.8 

47.2 

48.6 

49.9 

51.4 

52.9 

54.4 

60.0 

0.5 

8.9 

40.1 

1.4 

2.7 

4.0 

5.4 

6.7 

8.1 

9.6 

51.0 

2.5 

4.1 

5.7 

0.5 

1.0 

9.6 

0.9 

2.2 

3.5 

4.9 

6.3 

7.7 

9.1 

50.6 

2.1 

3.7 

5.3 

7.0 

1.0 

1.5 

40.4 

1.7 

3.0 

4.4 

5.8 

7.3 

8.7 

50.2 

1.7 

3.3 

5.0 

6.7 

8.5 

1.5 

2.0 

1.2 

2.5 

3.9 

5.3 

6.8 

8.3 

9.8 

1.3 

2.9 

4.6 

6.3 

8.1 

60.0 

2.0 

62.5 

42.0 

43.4 

44.9 

46.3 

47.8 

49.4 

51.0 

52.6 

54.2 

56.0 

57.8 

59.7 

61.7 

62.5 

3.0 

2.9 

4.3 

5.9 

7.4 

8.9 

50.5 

2.2 

3.9 

5.6 

7.5 

9.4 

61.4 

3.6 

3.0 

3.5 

3.8 

5.3 

6.9 

8.5 

50.1 

1.7 

3.5 

5.3 

7.1 

9.1 

61.1 

3.4 

5.7 

3.5 

4.0 

4.8 

6.4 

8.0 

9.7 

1.3 

3.0 

4.9 

6.7 

8.7 

60.7 

3.0 

5.5 

8.1 

4.0 

4.5 

5.9 

7.5 

9.2 

50.9 

2.6 

4.5 

6.4 

8.4 

60.5 

2.8 

5.2 

7.8 

70.9 

4.5 

65.0 

47.0 

48.7 

50.4 

52.2 

54.0 

56.0 

58.0 

60.2 

62.5 

64.9 

67.6 

70.6 

74.4 

65.0 

5.5 

8.2 

50.0 

1.8 

3.6 

5.6 

7.6 

9.8 

2.2 

4.7 

7.3 

70.4 

4.1 

8.9 

5.5 

6.0 

9.4 

1.3 

3.2 

5.1 

7.3 

9.4 

61.8 

4.4 

7.1 

70.2 

3.8 

8.6 

90.0 

6.0 

6.5 

50.8 

2.7 

4.7 

6.8 

9.1 

61.4 

4.0 

6.8 

70.0 

3.7 

8.4 

90.0 

6.5 

7.0 

2.3 

4.3 

6.4 

8.7 

61.1 

3.7 

6.5 

9.8 

3.5 

8.3 

90.0 

7.0 

67.5 

53.9 

56.0 

58.3 

60.7 

63.4 

66.2 

69.5 

73.3 

78.2 

90.0 

67.5 

8.0 

5.6 

7.9 

60.3 

3.0 

5.9 

9.2 

73.0 

8.1 

90.0 

8.0 

8.5 

7.5 

60.0 

2.6 

5.6 

8.9 

72.8 

7.9 

90.0 

8.5 

9.0 

9.6 

2.3 

5.3 

8.7 

72.7 

7.7 

90.0 

9.0 

9.5 

61.9 

5.0 

8.4 

72.4 

7.6 

90.0 

■     9.5 

70.0 

64.6 

69.1 

72.2 

77.4 

90.0 

70.0 

0.5 

7.8 

71.9 

7.2 

90.0 

0.5 

1.0 

71.7 

7.1 

90.0 

1.0 

1.5 

6.9 

90.0 

1.6 

2.0 

90.0 

2.0 

Page  744] 

TABLE  39. 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

24°.0 

24°.  6 

25°.0 

25°.  6 

26°.  0 

26°.  5 

27°.0 

27°.5 

28°.0 

28°.  5 

29°.  0 

29°.6 

80°.  0 

o 

o 

0 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

0 

24.0 

24.5 

25.0 

25.5 

26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5 

30.0 

0 

4 

4.1 

4.6 

5.1 

5.6 

6.1 

6.6 

7.1 

7.6 

8.1 

8.6 

9.1 

9.6 

0.1 

4 

8 

4.3 

4.8 

5.3 

5.8 

6.3 

6.8 

7.3 

7.8 

8.3 

8.8 

9.3 

9.8 

0.3 

8 

12 

4.6 

5.1 

5.6 

6.1 

6.6 

7.1 

7.6 

8.1 

8.7 

9.2 

9.7 

30.2 

0.7 

12 

16 

5.0 

5.6 

6.1 

6.6 

7.1 

7.6 

8.2 

8.7 

9.2 

9.8 

30.3 

0.8 

1.3 

16 

20 

25.7 

26.2 

26.7 

27.3 

27.8 

28.3 

28.9 

29.4 

30.0 

30.5 

31.1 

31.6 

32.1 

20 

22 

6.0 

6.6 

7.1 

7.7 

8.2 

8.8 

9.3 

9.9 

0.4 

1.0 

1.5 

2.1 

2.6 

22 

24 

6.4 

7.0 

7.6 

8.1 

8.7 

9.2 

9.8 

30.4 

0.9 

1.5 

2.0 

2.6 

3.2 

24 

26 

6.9 

7.5 

8.1 

8.6 

9.2 

9.7 

30.3 

0.9 

1.5 

2.1 

2.6 

3.2 

3.8 

26 

28 
30 

7.4 

8.0 

8.6 

9.2 

9.8 

30.3 

0.9 

1.5 

2.1 

2.7 

3.3 

3.9 

4.5 

28 

28.0 

28.6 

29.2 

29.8 

30.4 

31.0 

31.6 

32.2 

32.8 

33.4 

34.0 

34.7 

35.3 

30 

31 

8.3 

8.9 

9.5 

30.1 

0.8 

1.4 

2.0 

2.6 

3.2 

3.8 

4.5 

5.1 

5.7 

31 

32 

8.7 

9.3 

9.9 

0.5 

1.1 

1.7 

2.4 

3.0 

3.6 

4.2 

4.9 

5.5 

6.1 

32 

33 

9.0 

9.6 

30.2 

0.9 

1.5 

2.1 

2.8 

3.4 

4.0 

4.7 

5.3 

6.0 

6.6 

33 

34 

9.4 

30.0 

0.6 

31.3 

1.9 

2.6 

3.2 

3.8 

4.5 

5.1 

5.8 

6.4 

7.1 

34 

35 

29.8 

30.4 

31.1 

31.7 

32.3 

33.0 

33.6 

34.3 

35.0 

35.6 

36.3 

36.9 

37.6 

35 

36 

30.2 

0.8 

1.5 

2.1 

2.8 

3.5 

4.1 

4.8 

5.5 

6.1 

6.8 

7.5 

8.2 

36 

37 

0.6 

1.3 

1.9 

2.6 

3.3 

4.0 

4.6 

5.3 

6.0 

6.7 

7.4 

8.1 

8.8 

37 

38 

1.1 

1.7 

2.4 

3.1 

3.8 

4.5 

5.2 

5.9 

6.6 

7.3 

8.0 

8.7 

9.4 

38 

39 

1.6 

2.2 

2.9 

3.6 

4.3 

5.0 

5.7 

6.5 

7.2 

7.9 

8.6 

9.3 

40.0 

39 

40 

32.1 

32.8 

33.5 

34.2 

34.9 

35.6 

36.3 

37.1 

37.8 

38.5 

39.3 

40.0 

40.7 

40 

41 

2.6 

3.3 

4.1 

4.8 

5.5 

6.2 

7.0 

7.7 

8.5 

9.2 

40.0 

0.7 

1.5 

41 

42 

3.2 

3.9 

4.7 

5.4 

6.1 

6.9 

7.7 

8.4 

9.2 

9.9 

0.7 

1.5 

2.3 

42 

43 

3.8 

4.5 

5.3 

6.1 

6.8 

7.6 

8.4 

9.2 

9.9 

40.7 

1.5 

2.3 

3.1 

43 

44 

4.4 

5.2 

6.0 

6.8 

7.5 

8.3 

9.1 

40.0 

40.7 
41.6 

1.6 

2.4 

3.2 

4.0 

44 

45 

35.1 

35.9 

36.7 

37.5 

38.3 

39.1 

39.9 

40.8 

42.5 

43.3 

44.1 

45.0 

45 

46 

5.8 

6.6 

7.5 

8.3 

9.1 

40.0 

40.8 

1.7 

2.5 

3.4 

4.3 

5.1 

6.0 

46 

47 

6.6 

7.4 

8.3 

9.1 

40.0 

0.9 

1.7 

2.6 

3.5 

4.4 

5.3 

6.2 

7.1 

47 

48 

7.4 

8.3 

9.2 

40.0 

0.9 

1.8 

2.7 

3.6 

4.6 

5.5 

6.4 

7.4 

8.3 

48 

49 

8.3 

9.2 

40.1 

1.0 

1.9 

2.8 

3.8 

4.7 

5.7 

6.7 

7.6 

8.6 

9.6 

49 

50 

39.2 

40.2 

41.1 

42.0 

43.0 

43.9 

44.9 

45.9 

46.9 

47.9 

48.9 

50.0 

51.1 

50 

51 

40.2 

1.2 

2.2 

3.2 

4.1 

5.1 

6.2 

7.2 

8.2 

9.3 

50.4 

1.5 

2.6 

51 

52 

1.3 

2.3 

3.3 

4.4 

5.4 

6.4 

7.5 

8.6 

9.7 

50.8 

2.0 

3.1 

4.3 

52 

53 

2.5 

3.5 

4.6 

5.7 

6.7 

7.8 

9.0 

50.1 

51.3 

2.5 

3.7 

4.9 

6.2 

53 

54 

3.8 

4.9 

6.0 

7.1 

8.2 

9.4 

50.6 

1.8 

3.0 

4.3 

5.6 

6.9 

8.3 

54 

55.0 

45.2 

46.3 

47.5 

48.6 

49.8 

51.1 

52.3 

53.6 

54.9 

56.3 

57.7 

59.1 

60.7 

55.0 

5.5 

5.9 

7.1 

8.3 

9.5 

50.7 

2.0 

3.3 

4.6 

6.0 

7.4 

8.9 

60.4 

2.0 

5.5 

6.0 

6.7 

7.9 

9.1 

50.4 

1.6 

2.9 

4.3 

5.7 

7.1 

8.6 

60.1 

1.7 

3.4 

6.0 

6.5 

7.5 

8.8 

50.0 

1.3 

2.6 

3.9 

5.4 

6.8 

8.3 

9.9 

1.5 

3.2 

5.0 

6.5 

7.0 

8.3 

9.6 

0.9 

2.2 

3.6 

5.0 

6.5 

8.0 

9.5 

61.2 

2.9 

4.7 

6.6 

7.0 

57.5 

49.2 

50.5 

51.9 

53.2 

54.7 

56.2 

57.7 

59.3 

60.9 

62.6 

64.5 

66.4 

68.5 

57.5 

8.0 

50.1 

1.5 

2.9 

4.3 

5.8 

7.4 

8.9 

60.6 

2.4 

4.2 

6.2 

8.3 

70.7 

8.0 

8.5 

1.1 

2.5 

4.0 

5.5 

7.0 

8.6 

60.3 

2.1 

3.9 

6.0 

8.1 

70.4 

3.1 

8.5 

9.0 

2.2 

3.6 

5.1 

6.7 

8.3 

60.0 

1.8 

3.7 

5.7 

7.9 

70.3 

3.0 

6.2 

9.0 

9.5 

3.3 

4.8 

6.4 

8.0 

9.7 

1.5 

3.4 

5.5 

7.7 

70.1 

2.8 

5.9 

80.1 

9.5 

60.0 

54.4 

56.0 

67.7 

59.4 

61.2 

63.2 

65.2 

67.4 

69.9 

72.6 

75.8 

80.0 

90.0 

60.0 

0.5 

5.7 

7.4 

9.1 

61.0 

2.9 

5.0 

7.2 

9.6 

72.4 

5.8 

9.9 

90.0 

0.5 

1.0 

7.0 

8.8 

60.7 

2.6 

4.7 

7.0 

9.5 

72.3 

5.5 

9.8 

90.0 

1.0 

1.5 

8.5 

60.3 

2.3 

4.4 

6.7 

9.2 

72.0 

5.4 

9.7 

90.0 

1.5 

2.0 

60.0 

2.0 

4.2 

6.5 

9.0 

71.9 

5.2 

9.6 

90.0 

2.0 

62.5 

61.7 

63.9 

66.2 

68.8 

71.7 

75.1 

9.5 

90.0 

62.5 

3.0 

3.6 

6.0 

8.6 

71.5 

4.9 

9.4 

90.0 

3.0 

3.5 

5.7 

8.3 

71.3 

4.8 

9.3 

90.0 

3.5 

4.0 

8.1 

71.1 

4.6 

9.2 

90.0 

4.0 

4.5 

70.9 

4.4 

9.0 

90.0 

4.5 

TABLE  40. 

[Page  746    j 

Correction  of  the  Amplitude  as  observed  on 

the  Apparent  Horizon, 

Declination. 

Lati- 
tude. 

o 

Lati- 
tude. 

0° 

5° 

10° 

12° 

14° 

1«° 

18° 

20° 

22° 

24° 

2«° 

28° 

80° 

o 

o 

o 

o 

0 

0 

o 

o 

o 

o 

o 

o 

. 

o 

0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0 

5 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

5 

10 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

10 

15 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

15 

20 

.2 

.2 

_  2 

.2 

.2 

.2 

.3 

.3 

.3 

.3 

.3 

.3 

.3 
0.4 

20 
24 

24 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.4 

28 

.3 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

28 

32 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.5 

.5 

.5 

.5 

.5 

.5 

32 

36 

.5 

.5 

.5 

.5 

.5 

.5 

.5 

.5 

.6 

.6 

.6 

.6 

.6 

36 

38 

.5 

.5 

.5 

.5 

.6 

.6 

.6 

.6 

.6 

.6 

.6 

.7 

.7 

38 

40 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.7 

0.7 

0.7 

40 

42 

.6 

.6 

.6 

.6 

.6 

.7 

.7 

.7 

.7 

.7 

.8 

.8 

.8 

42 

44 

.6 

.6 

.7 

.7 

.7 

.7 

.7 

.7 

.8 

.8 

.8 

.9 

.9 

44 

46 

.7. 

.7 

.7 

.7 

.7 

.8 

.8 

.8 

.8 

.9 

.9 

.9 

1.0 

46 

48 

.7 

.8 

.8 

.8 

.8 

.8 

.8 

.9 

.9 

1.0 

1.0 

1.0 

.1 

48 

50 

0.8 

0.8 

0.8 

0.8 

0.9 

0.9 

0.9 

0.9 

1.0 

1.1 

1.1 

1.1 

1.3 

50 

52 

.8 

.9 

.9 

.9 

.9 

1.0 

1.0 

1.0 

.1 

.2 

.2 

.3 

.5 

52 

54 

.9 

.9 

1.0 

1.0 

1.0 

.1 

.1 

.1 

.2 

.3 

.4 

.5 

.8 

54 

56 

1.0 

1.0 

.1 

.1 

.1 

.2 

.2 

.2 

.3 

.5 

.6 

.8 

2.2 

56 

68 

.1 

.1 

.2 

.2 

.2 

.3 

.3 

.4 

.5 

.7 

.9 

2.3 

3.2 

58 

60 

1.2 

1.2 

1.3 

1.3 

1.3 

1.4 

1.5 

1.6 

1.7 

2.0 

2.4 

3.4 

60 

62 

.3 

.3 

.4 

.4 

.4 

.6 

.7 

.8 

2.1 

.5 

3.5 

62 

64 

.4 

.4 

.5 

.5 

.6 

.8 

.9 

2.2 

.6 

3.7 

64 

66 

.5 

.5 

.7 

.7 

.9 

2.0 

2.3 

.8 

3.8 

66 

68 

.6 

.7 

.9 

2.0 

2.2 

.4 

.9 

4.0 

68 

70 

1.8 

1.9 

2.1 

2.3 

2.6 

3.1 

4.3 

70 

72 

2.0 

2.1 

.5 

.8 

3.3 

4.6 

72 

74 

.2 

.5 

3.0 

3.5 

4.8 

74 

76 

.6 

3.0 

.8 

5.2 

76 

78 

3.1 

.6 

5.7 

78 

80 

3.8 

4.4 

80 

I 


Page  746] 

TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

OO 

1 

D 

2° 

S° 

4 

o 

Prop. 

parts 
29 

0 

parts 
2 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine 

N.  COS. 

0 

00000 

100000 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

60 

2 

0 

1 

00029 

100000 

01774 

99984 

03519 

99938 

05263 

99861 

07005 

99754 

59 

2 

1 

2 

00058 

100000 

01803 

99984 

03548 

99937 

05292 

99860 

07034 

99752 

58 

2 

1 

3 

00087 

100000 

01832 

99983 

03577 

99936 

05321 

99858 

07063 

99750 

57 

2 

2 

4 

00116 

100000 

01862 

99983 

03606 

99935 

05350 

99857 

07092 

99748 

56 

2 

2 

5 

00145 

100000 

01891 

99982 

03635 

99934 

05379 

99855 

07121 

99746 

55 

2 

3 

6 

00175 

100000 

01920 

99982 

03664 

99933 

05408 

99854 

07150 

99744 

54 

2 

3 

7 

00204 

100000 

01949 

99981 

03693 

99932 

05437 

99852 

07179 

99742 

53 

2 

4 

8 

00233 

100000 

01978 

99980 

03723 

99931 

05466 

99851 

07208 

99740 

52 

2 

4 

9 

00262 

100000 

02007 

99980 

03752 

99930 

05495 

99849 

07237 

99738 

51 

2 

5 

10 

00291 

100000 

02036 

99979 

03781 

99929 

05524 

99847 

07266 

99736 

50 

2 

5 

11 

00320 

99999 

02065 

99979 

03810 

99927 

05553 

99846 

07295 

99734 

49 

2 

6 

12 

00349 

99999 

02094 

99978 

03839 

99926 

05582 

99844 

07324 

99731 

48 

2 

6 

13 

00378 

99999 

02123 

99977 

03868 

99925 

05611 

99842 

07353 

99729 

47 

2 

7 

14 

00407 

99999 

02152 

99977 

03897 

99924 

05640 

99841 

07382 

99727 

46 

2 

7 

15 

00436 

99999 

02181 

99976 

03926 

99923 

05669 

99839 

07411 

99725 

45 

2 

8 

16 

00465 

99999 

02211 

99976 

03955 

99922 

05698 

99838 

07440 

99723 

44 

8 

17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

9 

18 

00524 

99999 

02269 

99974 

04013 
04042 

99919 

05756 

99834 
99833 

07498 

99719 

42 

9 

19 

00553 

99998 

02298 

99974 

99918 

05785 

07527 

99716 

41 

10 

20 

00582 

99998 

02327 

99973 

04071 

99917 

05814 

99831 

07556 

99714 

40 

10 

21 

00611 

99998 

02356 

99972 

04100 

99916 

05844 

99829 

07585 

99712 

39 

11 

22 

00640 

99998 

02385 

99972 

04129 

99915 

05873 

99827 

07614 

99710 

38 

11 

23 

00669 

99998 

02414 

99971 

04159 

99913 

05902 

99826 

07643 

99708 

37 

12 

24 

00698 

99998 

02443 

99970 
99969 

04188 

99912 

05931 
05960 

99824 

07672 

99705 

36 

12 

25 

00727 

99997 

02472 

04217 

99911 

99822 

07701 

99703 

35 

13 

26 

00756 

99997 

02501 

99969 

04246 

99910 

05989 

99821 

07730 

99701 

34 

13 

27 

00785 

99997 

02530 

99968 

04275 

99909 

06018 

99819 

07769 

99699 

33 

14 

28 

00814 

99997 

02560 

99967 

04304 

99907 

06047 

99817 

07788 

99696 

32 

14 

29 

00844 

99996 

02589 

99966 

04333 

99906 

06076 

99815 

07817 

99694 

31 

15 

30 

00873 

99996 

02618 

99966 

04362 
04391 

99905 

06105 

99813 

07846 

99692 

30 

15 

31 

00902 

99996 

02647 

99965 

99904 

06134 

99812 

07875 

99689 

29 

15 

32 

00931 

99996 

02676 

99964 

04420 

99902 

06163 

99810 

07904 

99687 

28 

16 

33 

00960 

99995 

02705 

99963 

04449 

99901 

06192 

99808 

07933 

99685 

27 

16 

34 

00989 

99995 

02734 

99963 

04478 

99900 

06221 

99806 

07962 

99683 

26 

17 

35 

01018 

99995 

02763 

99962 

04507 

99898 

06250 

99804 

07991 

99680 

25 

17 

36 

01047 

99995 

02792 

99961 

04536 

99897 

06279 

99803 

08020 

99678 
99676 

24 
23 

18 

37 

01076 

99994 

02821 

99960 

04565 

99896 

06308 

99801 

08049 

18 

38 

01105 

99994 

02850 

99959 

04594 

99894 

06337 

99799 

08078 

99673 

22 

19 

39 

01134 

99994 

02879 

99959 

04623 

99893 

06366 

99797 

08107 

99671 

21 

19 

40 

01164 

99993 

02908 

99958 

04653 

99892 

06395 

99795 

08136 

99668 

20 

20 

41 

01193 

99993 

02938 

99957 

04682 

99890 

06424 

99793 

08165 

99666 

19 

20 

42 

01222 

99993 

02967 

99956 
99955 

04711 

99889 

06453 

99792 

08194 

99664 

18 

21 

43 

01251 

99992 

02996 

04740 

99888 

06482 

99790 

08223 

99661 

17 

21 

44 

01280 

99992 

03025 

99954 

04769 

99886 

06511 

99788 

08252 

99659 

16 

22 

45 

01309 

99991 

03054 

99953 

04798 

99885 

06540 

99786 

08281 

99657 

15 

22 

46 

01338 

99991 

03083 

99952 

04827 

99883 

06569 

99784 

08310 

99654 

14 

0 

23 

47 

01367 

99991 

03112 

99952 

04856 

99882 

06598 

99782 

08339 

99652 

13 

0 

23 

48 

01396 

99990 

03141 

99951 

04885 

99881 

06627 

99780 

08368 

99649 
99647 

12 

11 

0 

24 

49 

01425 

99990 

03170 

99950 

04914 

99879 

06656 

99778 

08397 

0 

24 

50 

01454 

99989 

03199 

99949 

04943 

99878 

06685 

99776 

08426 

99644 

10 

0 

25 

51 

01483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

08455 

99642 

9 

0 

25 

52 

01513 

99989 

03257 

99947 

05001 

99875 

06743 

99772 

08484 

99639 

8 

0 

26 

53 

01542 

99988 

03286 

99946 

05030 

99873 

06773 

99770 

08513 

99637 

7 

0 

26 

54 

01571 

99988 

03316 

99945 

05059 

99872 

06802 

99768 

08542 

99635 

6 

0 

27 

55 

01600 

99987 

03345 

99944 

05088 

99870 

06831 

99766 

08571 

99632 

5 

0 

27 

56 

01629 

99987 

03374 

99943 

05117 

99869 

06860 

99764 

08600 

99630 

4 

0 

28 

57 

01658 

99986 

03403 

99942 

05146 

99867 

06889 

99762 

08629 

99627 

3 

0 

28 

58 

01687 

99986 

03432 

99941 

05175 

99866 

06918 

99760 

08658 

99625 

2 

0 

29 

59 

01716 

99985 

03461 

99940 

05205 

99864 

06947 

99758 

08687 

99622 

1 

0 

29 

60 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

08716 

99619 

0 

0 

N.  COB. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

__ 

89° 

88° 

87° 

8 

8° 

86° 

TABLE  41. 

[Page  747 

Natural  Sines  and  Coeinea. 

Prop, 
parts 

29 

6 

o 

6< 

> 

7° 

- 

- 

Prop, 
parts 

4 

M. 

N.sina 

N.cos. 

N.sine. 

N.cos. 

N.  sine. 

N.cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  coa. 

0 

0 

08716 

99619 

10453 

99452 

12187 

99255 

13917 

99027 

15643 

98769 

60 

4 

0 

1 

08745 

99617 

10482 

99449 

12216 

99251 

13946 

99023 

15672 

98764 

59 

4 

1 

2 

08774 

99614 

10511 

99446 

12245 

99248 

13975 

99019 

15701 

98760 

58 

4 

1 

3 

08803 

99612 

10540 

99443 

12274 

99244 

14004 

99015 

15730 

98755 

57 

4 

2 

4 

08831 

99609 

10569 

99440 

12302 

99240 

14033 

99011 

15758 

98751 

56 

4 

2 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

15787 

98746 

55 

4 

3 

6 

08889 

99604 

10626 

99434 

12360 

99233 
99230 

14090 

99002 

15816 

98741 

54 

4 

3 

7 

08918 

99602 

10655 

99431 

12389 

14119 

98998 

15845 

98737 

53 

4 

4 

8 

08947 

99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

3 

4 

9 

08976 

99596 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

98728 

51 

3 

5 

10 

09005 

99594 

10742 

99421 

12476 

99219 

14205 

98986 

15931 

98723 

50 

3 

6 

11 

09034 

99591 

10771 

99418 

12504 

99215 

14234 

98982 

15959 

98718 

49 

3 

6 

12 

09063 

99588 
99586 

10800 

99415 
99412 

12533 

99211 

14263 

98978 

15988 

98714 

48 

3 

6 

13 

09092 

10829 

12562 

99208 

14292 

98973 

16017 

98709 

47 

3 

7 

14 

09121 

99583 

10858 

99409 

12591 

99204 

14320 

98969 

16046 

98704 

46 

3 

7 

15 

09150 

99580 

10887 

99406 

12620 

99200 

14349 

98965 

16074 

98700 

45 

3 

8 

16 

09179 

99578 

10916 

99402 

12649 

99197 

14378 

98961 

16103 

98695 

44 

3 

8 

17 

09208 

99575 

10945 

99399 

12678 

99193 

14407 

98957 

16132 

98690 

43 

3 

9 

18 

09237 

99572 

10973 

99396 

12706 

99189 

14436 

98953 

16160 

98686 

42 

3 

9 

19 

09266 

99570 

11002 

99393 

12735 

99186 

14464 

98948 

16189 

98681 

41 

3 

10 

20 

09295 

99567 

11031 

99390 

12764 

99182 

14493 

98944 

16218 

98676 

40 

3 

10 

21 

09324 

995M 

11060 

99386 

12793 

99178 

14522 

98940 

16246 

98671 

39 

3 

11 

22 

09353 

99562 

11089 

99383 

12822 

99175 

14551 

98936 

16275 

98667 

38 

3 

11 

23 

09382 

99559 

11118 

99380 

12851 

99171 

14580 

98931 

16304 

98662 

37 

2 

12 
12 

24 

09411 

99556 

11147 

99377 

12880 

99167 

14608 

98927 

16333 

98657 

36 

2 

25 

09440 

99553 

11176 

99374 

12908 

99163 

14637 

98923 

16361 

98652 

35 

2 

13 

26 

09469 

99551 

11205 

99370 

12937 

99160 

14666 

98919 

16390 

98648 

34 

2 

13 

27 

09498 

99548 

11234 

99367 

12966 

99156 

14695 

98914 

16419 

98643 

33 

2 

14 

28 

09527 

99545 

11263 

99364 

12995 

99152 

14723 

98910 

16447 

98638 

32 

2 

14 

29 

09556 

99542 

11291 

99360 

13024 

99148 

14752 

98906 

16476 

98633 

31 

2 

15 

30 

09585 

99540 

11320 

99357 

13053 

99144 

14781 

98902 

16505 
16533 

98629 

30 

2 

15 

31 

09614 

99537 

11349 

99354 

13081 

99141 

14810 

98897 

98624 

29 

2 

15 

32 

09642 

99534 

11378 

99351 

13110 

99137 

14838 

98893 

16562 

98619 

28 

2 

16 

33 

09671 

99531 

11407 

99347 

13139 

99133 

14867 

98889 

16591 

98614 

27 

2 

16 

34 

09700 

99528 

11436 

99344 

13168 

99129 

14896 

98884 

16620 

98609 

26 

2 

17 

35 

09729 

99526 

11465 

99341 

13197 

99125 

14925 

98880 

16648 

98604 

25 

2 

17 

36 
37 

09758 
09787 

99523 

11494 

99337 

13226 

99122 

14954 
14982 

98876 

16677 

98600 

24 

2 

18 

99520 

11523 

99334 

13254 

99118 

98871 

16706 

98595 

23 

2 

18 

38 

09816 

99517 

11552 

99331 

13283 

99114 

15011 

98867 

16734 

98590 

22 

19 

39 

09845 

99514 

11580 

99327 

13312 

99110 

15040 

98863 

16763 

98585 

21 

19 

40 

09874 

99511 

11609 

99324 

13341 

99106 

15069 

98858 

16792 

98580 

20 

20 

41 

09903 

99508 

11638 

99320 

13370 

99102 

15097 

98854 

16820 

98575 

19 

20 
21 

42 

09932 

99506 

11667 

99317 

13399 

99098 

15126 

98849 

16849 

98570 

18 

43 

09961 

99503 

11696 

99314 

13427 

99094 

15155 

98845 

16878 

98565 

17 

21 

44 

09990 

99500 

11725 

99310 

13456 

99091 

15184 

98841 

16906 

98561 

16 

22 

45 

10019 

99497 

11754 

99307 

13485 

99087 

15212 

98836 

16935 

98556 

15 

22 

46 

10048 

99494 

11783 

99303 

13514 

99083 

15241 

98832 

16964 

98551 

14 

23 

47 

10077 

99491 

11812 

99300 

13543 

99079 

15270 

98827 

16992 

98546 

13 

23 

48 

10106 

99488 

11840 

99297 

13572 

99075 

15299 

98823 

17021 

98541 

12 

24 

49 

10135 

99485 

11869 

99293 

13600 

99071 

15327 

98818 

17050 

98536 

11 

24 

50 

10164 

99482 

11898 

99290 

13629 

99067 

15356 

98814 

17078 

98531 

10 

25 

51 

10192 

99479 

11927 

99286 

13658 

99063 

15385 

98809 

17107 

98526 

9 

25 

52 

10221 

99476 

11956 

99283 

13687 

99059 

15414 

98805 

17136 

98521 

8 

26 

53 

10250 

99473 

11985 

99279 

13716 

99055 

15442 

98800 

17164 

98516 

7 

0 

26 

54 

10279 

99470 

12014 

99276 

13744 

99051 

15471 

98796 

17193 

98511 

6 

0 

27 

55 

10308 

99467 

12043 

99272 

13773 

99047 

15500 

98791 

17222 

98506 

5 

0 

27 

56 

10337 

99464 

12071 

99269 

13802 

99043 

15529 

98787 

17250 

98501 

4 

0 

28 

57 

10366 

99461 

12100 

99265 

13831 

99039 

15557 

98782 

17279 

98496 

3 

0 

28 

58 

10395 

99458 

12129 

99262 

13860 

99035 

15586 

98778 

17308 

98491 

2 

0 

29 

59 

10424 

99455 

12158 

99258 

13889 

99031 

15615 

98773 

17336 

98486 

1 

0 

29 

60 

10453 

99452 

12187 

99255 

13917 

99027 

15643 

98769 

17365 

98481 

0 

0 

N.cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

N.  Bine. 

N.  coa. 

N.  sine. 

M. 

84° 

83 

o 

82° 

8 

lo 

80° 

21594°— 14- 


-40 


Page  748] 

TABLE  41. 

Natural  Sines  and  Cosinee, 

Prop. 

parte 

28 

lOO       1 

11 

o 

12°      1 

18°      1 

14°      1 

Prop. 

parte 

6 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 

0 

17365 

98481 

19081 

98163 

20791 

97815 

22495 

97437 

24192 

97030 

60 

6 

0 

1 

17393 

9M76 

19109 

98157 

20820 

97809 

22623 

97430 

24220 

97023 

69 

6 

1 

2 

17422 

98471 

19138 

98162 

20848 

97803 

22562 

97424 

24249 

97015 

68 

6 

1 

3 

17451 

98466 

19167 

98146 

20877 

97797 

22580 

97417 

24277 

97008 

57 

6 

2 

4 

17479 

98461 

19195 

98140 

20905 

97791 

22608 

97411 

24305 

97001 

66 

6 

2 

5 

17508 

98456 

19224 

98136 

20933 

97784 

22637 

97404 

24333 

96994 

65 

6 

3 

6 

17537 

98450 

19252 

98129 

20962 

97778 

22665 

97398 

24362 

96987 

54 

5 

3 

7 

17565 

98445 

19281 

98124 

20990 

97772 

22693 

97391 

24390 

96980 

63 

5 

4 

8 

17594 

98440 

19309 

98118 

21019 

97766 

22722 

97384 

24418 

96973 

62 

5 

4 

9 

17623 

98435 

19338 

98112 

21047 

97760 

22750 

97378 

24446 

96966 

51 

5 

5 

10 

17661 

98430 

19366 

98107 

21076 

97764 

22778 

97371 

24474 

96959 

50 

5 

5 

11 

17680 

98426 

19396 

98101 

21104 

97748 

22807 

97365 

24503 

96952 

49 

5 

6 
6 

12 
13 

17708 

98420 

19423 

98096 

21132 

97742 

22835 

97358 

24531 

96945 

48 

5 

17737 

98414 

19462 

98090 

21161 

97735 

22863 

97351 

24559 

96937 

47 

5 

7 

14 

17766 

98409 

19481 

98084 

21189 

97729 

22892 

97346 

24587 

96930 

46 

5 

7 

15 

17794 

98404 

19509 

98079 

21218 

97723 

22920 

97338 

24616 

96923 

45 

5 

7 

16 

17823 

98399 

19638 

98073 

21246 

97717 

22948 

97331 

24644 

96916 

44 

4 

8 

17 

17852 

98394 

19666 

98067 

21275 

97711 

22977 

97325 

24672 

96909 

43 

4 

8 

18 

17880 

98389 

19596 

98061 

21303 

97705 

23006 

97318 

24700 

96902 

42 
41 

4 

9 

19 

17909 

98383 

19623 

98056 

21331 

97698 

23033 

97311 

24728 

96894 

4 

9 

20 

17937 

98378 

19662 

98050 

21360 

97692 

23062 

97304 

24766 

96887 

40 

4 

10 

21 

17966 

98373 

19680 

98044 

21388 

97686 

23090 

97298 

24784 

96880 

39 

4 

10 

22 

17995 

98368 

19709 

98039 

21417 

97680 

23118 

97291 

24813 

96873 

38 

4 

11 

23 

18023 

98362 

19737 

98033 

21445 

97673 

23146 

97284 

24841 

96866 

37 

4 

11 
12 

24 
25 

18052 

98367 

19766 

98027 

21474 

97667 

23175 

97278 

24869 

96868 

36 

4 

18081 

98352 

19794 

98021 

21502 

97661 

23203 

97271 

24897 

96861 

35 

4 

12 

26 

18109 

98347 

19823 

98016 

21530 

97655 

23231 

97264 

24926 

96844 

34 

3 

13 

27 

18138 

98341 

19861 

98010 

21659 

97648 

23260 

97257 

24964 

96837 

33 

3 

13 

28 

18166 

98336 

19880 

98004 

21587 

97642 

23288 

97261 

24982 

96829 

32 

3 

14 

29 

18195 

98331 

19908 

97998 

21616 

97636 

23316 

97244 

26010 

96822 

31 

3 

14 

30 

18224 

98325 

19937 

97992 

21644 

97630 
97623 

23345 

97237 

26038 

96816 

30 

3 

14 

31 

18252 

98320 

19966 

97987 

21672 

23373 

97230 

25066 

96807 

29 

3 

15 

32 

18281 

98315 

19994 

97981 

21701 

97617 

23401 

97223 

25094 

96800 

28 

3 

15 

33 

18309 

98310 

20022 

97975 

21729 

97611 

23429 

97217 

25122 

96793 

27 

3 

16 

34 

18338 

98304 

20051 

97969 

21758 

97604 

23458 

97210 

25151 

96786 

26 

3 

16 

35 

18367 

98299 

20079 

97963 

21786 

97598 

23486 

97203 

26179 

96778 

26 

3 

17 

36 

18396 

98294 

20108 

97958 

21814 

97692 

23614 

97196 

26207 

96771 

24 

2 

17 

37 

18424 

98288 

20136 

97952 

21843 

97585 

23542 

97189 

26235 

96764 

23 

2 

18 

38 

18452 

98283 

20165 

97946 

21871 

97679 

23571 

97182 

25263 

96756 

22 

2 

18 

39 

18481 

98277 

20193 

97940 

21899 

97573 

23599 

97176 

25291 

96749 

21 

2 

19 

40 

18509 

98272 

20222 

97934 

21928 

97566 

23627 

97169 

26320 

96742 

20 

2 

19 

41 

18538 

98267 

20250 

97928 

21966 

97560 

23656 

97162 

26348 

96734 

19 

2 

20 

42 

18567 

98261 

20279 

97922 

21986 

97663 

23684 

97155 

25376 

96727 

18 

2 

20 

43 

18596 

98256 

20307 

97916 

22013 

97547 

23712 

97148 

25404 

96719 

17 

2 

21 

44 

18624 

98260 

20336 

97910 

22041 

97641 

23740 

97141 

25432 

96712 

16 

2 

21 

45 

18652 

98246 

20364 

97906 

22070 

97634 

23769 

97134 

25460 

96705 

16 

2 

21 

46 

18681 
18710 

98240 

20393 

97899 

22098 

97528 

23797 

97127 

25488 

96697 

14 

22 

47 

98234 

20421 

97893 

22126 

97521 

23825 

97120 

25516 

96690 

13 

22 
23 

48 
49 

18738 

98229 

20460 

97887 

22165 

97516 

23863 

97113 

26646 

96682 

12 

18767 

98223 

20478 

97881 

22183 

97508 

23882 

97106 

25573 

96676 

11 

23 

50 

18795 

98218 

20507 

97876 

22212 

97502 

23910 

97100 

26601 

96667 

10 

24 

51 

18824 

98212 

20535 

97869 

22240 

97496 

23938 

97093 

26629 

96660 

9 

24 

52 

18862 

98207 

20563 

97863 

22268 

97489 

23966 

97086 

26667 

96653 

8 

1 

25 

53 

18881 

98201 

20592 

97867 

22297 

97483 

23995 

97079 

25686 

96645 

7 

25 

54 

18910 

98196 

20620 

97851 

22325 

97476 

24023 

97072 

25713 

96638 

6 

26 

55 

18938 

98190 

20649 

97845 

22353 

97470 

24051 

97066 

26741 

96630 

6 

26 

56 

18967 

98186 

20677 

97839 

22382 

97463 

24079 

97068 

25769 

96623 

4 

0 

27 

57 

18995 

98179 

20706 

97833 

22410 

97467 

24108 

97051 

25798 

96615 

3 

0 

27 

58 

19024 

98174 

20734 

97827 

22438 

97460 

24136 

97044 

25826 

96608 

2 

0 

28 

59 

19052 

98168 

20763 

97821 

22467 

97444 

24164 

97037 

26864 

96600 

1 

0 

28 

60 

19081 

98163 

20791 

97815 

22496 

97437 

24192 

97030 

26882 

96593 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

79° 

78° 

77° 

76° 

75° 

TABLE  41.                 [Page  749 
Natural  Sines  and  Cosines. 

Prop, 
parts 

27 

16° 

16° 

17° 

18° 

1V> 

Prop. 

parts 

9 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.coe. 

N.Bine. 

N.cos. 

0 
0 

1 

1 

2 
2 
3 
3 
4 
4 
5 
5 
5 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

25882 
25910 
25938 
25966 
25994 
26022 
26050 
26079 
26107 
26135 
26163 
26191 
26219 

96593 
96585 
96578 
96570 
96562 
96555 
96647 

27564 
27592 
27620 
27648 
27676 
27704 
27731 

96126 
96118 
96110 
96102 
96094 
96086 
96078 

29237 
29265 
29293 
29321 
29348 
29376 
29404 
29432 
29460 
29487 
29515 
29543 
29571 

95630 
95622 
95613 
95605 
95596 
95588 
95579 

30902 
30929 
30957 
30985 
31012 
31040 
31068 

95106 
95097 
95088 
95079 
95070 
95061 
95052 

32557 
32584 
32612 
32639 
32667 
32694 
32722 

94552 
94542 
94533 
94523 
94514 
94504 
94495 
94485 
94476 
94466 
94457 
94447 
94438 

60 
59 
58 

57 
56 
55 
54 

9 
9 
9 
9 
8 
8 
8 

96540 
96532 
96524 
96517 
96509 
96502 
96494 
96486 
96479 
96471 
96463 
96456 

27759 

27787 

27815 

27843 

27871 

27899 

27927' 

27955 

27983 

28011 

28039 

28067 

96070 
96062 
96054 
96046 
96037 
96029 

95571 
95562 
95554 
95545 
95536 
95528 

31095 
31123 
31151 
31178 
31206 
31233 

95043 
95033 
95024 
95015 
95006 
94997 
94988 
94979 
94970 
94961 
94952 
94943 
94933 
94924 
94915 
94906 
94897 
94888 

32749 
32777 
32804 
32832 
32859 
32887 
32914 
32942 
32969 
32997 
33024 
33051 
33079 
33106 
33134 
33161 
33189 
33216 
33244 
33271 
33298 
33326 
33353 
33381 
33408 
33436 
33463 
33490 
33518 
33545 
33573 
33600 
33627 
33655 
33682 
33710 

53 
52 
51 
50 
49 
48 

8 
8 
8 
8 

6 
6 
7 
7 
8 
8 
9 
9 
9 
10 
10 
11 
11 
12 
12 
13 
13 
14 
14 
14 
15 
15 
16 
16 
17 
17 
18 
18 
18 
19 
19 
20 
20 
21 
21 
22 
22 
23 
23 
23 
24 
24 
25 
25 
26 
26 
27 
27 

13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

26247 
26275 
26303 
26331 
26359 
26387 

96021 
96013 
96005 
95997 
95989 
95981 

29599 
29626 
29654 
29682 
29710 
29737 

95519 
95511 
95502 
95493 
95485 
95476 

31261 
31289 
31316 
31344 
31372 
31399 
31427 
31454 
31482 
31510 
31537 
31565 

94428 
94418 
94409 
94399 
94390 
94380 
94370 
94361 
94351 
94342 
94332 
94322 
94313 
94303 
94293 
94284 
94274 
94264 

47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 
36 

6 
6 

26415 
26443 
26471 
26500 
26528 
26556 

96448 
96440 
96433 
96425 
96417 
96410 

28095 
28123 
28150 
28178 
28206 
28234 

95972 
95964 
95956 
95948 
95940 
95931 
95923 
95915 
95907 
95898 
95890 
95882 

29765 
29793 
29821 
29849 
29876 
29904 
29932 
29960 
29987 
30015 
30043 
30071 

95467 
95459 
95450 
95441 
95433 
95424 

6 
6 
6 
6 
6 
5 

25 
26 
27 
28 
29 
30 

26584 
26612 
26640 
26668 
26696 
26724 

96402 
96394 
96386 
96379 
96371 
96363 

28262 
28290 
28318 
28346 
28374 
28402 

95415 
95407 
95398 
95389 
95380 
95372 

31593 
31620 
31648 
31675 
31703 
31730 

94878 
94869 
94860 
94851 
94842 
94832 

36 
34 
33 
32 
31 
30 

6 
5 
5 
5 
5 
5 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 

26752 
26780 
26808 
26836 
26864 
26892 

96355 
96347 
96340 
96332 
96324 
96316 

28429 
28457 
28485 
28513 
28541 
28569 

95874 
95865 
95857 
95849 
95841 
95832 
95824 
95816 
95807 
95799 
95791 
95782 
95774 
95766 
95757 
95749 
95740 
95732 
95724 
95715 
95707 
95698 
95690 
95681 

30098 
30126 
30154 
30182 
30209 
30237 

95363 
95354 
95345 
95337 
95328 
95319 

31758 
31786 
31813 
31841 
31868 
31896 

94823 
94814 
94805 
94795 
94786 
94777 

94254 
94245 
94235 
94225 
94215 
94206 

29 
28 
27 
26 
25 
24 

4 
4 
4 
4 
4 
4 

26920 
26948 
26976 
27004 
27032 
27060 

96308 
96301 
96293 
96285 
96277 
96269 

28597 
28625 
28652 
28680 
28708 
28736 

30265 
30292 
30320 
30348 
30376 
30403 
30431 
30459 
30486 
30514 
30542 
30570 

95310 
95301 
95293 
95284 
95275 
95266 
95257 
95248 
95240 
95231 
95222 
95213 

31923 
31951 
31979 
32006 
32034 
32061 

94768 
94758 
94749 
94740 
94730 
94721 

94196 
94186 
94176 
94167 
94157 
94147 

23 
22 
21 
20 
19 
18 

3 
3 
3 
3 
3 
3 
3 
2 
2 
2 
2 
2 

43 
44 
45 

46 
47 

48 

27088 
27116 
27144 
27172 
27200 
27228 

96261 
96253 
96246 
96238 
96230 
96222 

28764 
28792 
28820 

28847 
28875 
28903 

32089 
32116 
32144 
32171 
32199 
32227 

94712 
94702 
94693 
94684 
94674 
94665 

33737 
33764 
33792 
33819 
33846 
33874 

94137 
94127 
94118 
94108 
94098 
94088 

17 
16 
15 
14 
13 
12 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

27256 
27284 
27312 
27340 
27368 
27396 

96214 
96206 
96198 
96190 
96182 
96174 

28931 
28959 
28987 
29015 
29042 
29070 

30597 
30625 
30653 
30680 
30708 
30736 

95204 
95195 
95186 
95177 
95168 
95159 
95150 
95142 
95133 
95124 
95115 
95106 

32254 
32282 
32309 
32337 
32364 
32392 

94656 
94646 
94637 
94627 
94618 
94609 

33901 
33929 
33956 
33983 
34011 
34038 

94078 
94068 
94058 
94049 
94039 
94029 

11 
10 
9 
8 
7 
6 

2 

27424 
27452 
27480 
27508 
27536 
27564 

96166 
96158 
96150 
96142 
96134 
96126 

29098 
29126 
29154 
29182 
29209 
29237 

95673 
95664 
95656 
95647 
95639 
95630 

30763 
30791 
30819 
30846 
30874 
30902 

32419 
32447 
32474 
32502 
32529 
32557 

94599 
94590 
94580 
94571 
94561 
94552 

34065 
34093 
34120 
34147 
34175 
34202 

94019 
94009 
93999 
93989 
93979 
93969 

5 
4 
3 
2 

1 
0 

0 
0 
0 
0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

M. 

740 

J  3° 

72° 

71° 

70° 

Page  760]                 TABLE  41. 

Natural  Sines  and  Coeines, 

Prop. 

parts 

27 

M. 

20' 

21° 

22° 

23° 

24° 

Prop. 

parts 

11 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 
0 

1 

1 

2 

2 
3 

0 

1 

2 
3 
4 
5 
6 

34202 
34229 
34257 
34284 
34311 
34339 
34366 

93969 
93959 
93949 
93939 
93929 
93919 
93909 

35837 
35864 
35891 
35918 
36945 
35973 
36000 

93368 
93348 
93337 
93327 
93316 
93306 
93295 

37461 
37488 
37516 
37542 
37669 
37695 
37622 

92718 
92707 
92697 
92686 
92675 
92664 
92653 

39073 
39100 
39127 
39163 
39180 
39207 
39234 

92060 
92039 
92028 
92016 
92005 
91994 
91982 

40674 
40700 
40727 
40763 
40780 
40806 
40833 

91366 
91343 
91331 
91319 
91307 
91295 
91283 

60 
59 
58 
57 
56 
55 
54 

11 
11 
11 
10 
10 
10 
10 

3 
4 
4 
5 
5 
5 

7 
•  8 

9 
10 
11 
12 

34393 
34421 
34448 
34475 
34503 
34530 

93899 
93889 
93879 
93869 
93859 
93849 

36027 
36054 
36081 
36108 
36135 
36162 

93285 
93274 
93264 
93263 
93243 
93232 

37649 
37676 
37703 
37730 
37767 
37784 

92642 
92631 
92620 
92609 
92598 
92687 

39260 
39287 
39314 
39341 
39367 
39394 

91971 
91959 
91948 
91936 
91925 
91914 

40860 
40886 
40913 
40939 
40966 
40992 

91272 
91260 
91248 
91236 
91224 
91212 

53 
52 
51 
50 
49 
48 

10 
10 
9 
9 
9 
9 

6 
6 

7 
7 
8 
8 

13 
14 
15 
16 
17 
18 

34557 
34584 
34612 
34639 
34666 
34694 

93839 
93829 
93819 
93809 
93799 
93789 

36190 
36217 
36244 
36271 
36298 
36326 

93222 
93211 
93201 
93190 
93180 
93169 

37811 
37838 
37865 
37892 
37919 
37946 

92676 
92665 
92664 
92643 
92532 
92521 

39421 
39448 
39474 
39501 
39528 
39555 

91902 
91891 
91879 
91868 
91856 
91845 

41019 
41046 
41072 
41098 
41125 
41151 

91200 
91188 
91176 
91164 
91152 
91140 

47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 
36 

9 

8 
8 
8 
8 
8 

9 

9 

9 

10 

10 

11 

19 
20 
21 
22 
23 
24 

34721 
34748 
34775 
34803 
34830 
34867 

93779 
93769 
93759 
93748 
93738 
93728 

36362 
36379 
36106 
36434 
36461 
36488 

93169 
93148 
93137 
93127 
93116 
93106 

37973 
37999 
38026 
38063 
38080 
38107 

92610 
92499 
92488 
92477 
92466 
92455 

39681 
39608 
39636 
39661 
39688 
39715 

91833 
91822 
91810 
91799 
91787 
91775 
91764 
91752 
91741 
91729 
91718 
91706 

41178 
41204 
41231 
41257 
41284 
41310 

91128 
91116 
91104 
91092 
91080 
91068 

8 

7 
7 

7 
7 
7 

11 
12 
12 
13 
13 
14 
14 
14 
15 
15 
16 
16 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 

34884 
34912 
34939 
34966 
34993 
35021 

93718 
93708 
93698 
93688 
93677 
93667 

36515 
36542 
36569 
36596 
36623 
36660 

93096 
93084 
93074 
93063 
93062 
93042 

38134 
38161 
38188 
38215 
38241 
38268 

92444 
92432 
92421 
92410 
92399 
92388 

39741 
39768 
39796 
39822 
39848 
39875 

41337 
41363 
41390 
41416 
41443 
41469 

91056 
91044 
91032 
91020 
91008 
90996 

36 
34 
33 
32 
31 
30 

6 
6 
6 
6 
6 
6 

35048 
35075 
35102 
35130 
36157 
35184 

93657 
93647 
93637 
93626 
93616 
93606 

36677 
36704 
36731 
36768 
36785 
36812 

93031 
93020 
93010 
92999 
92988 
92978 

38295 
38322 
38349 
38376 
38403 
38430 

92377 
92366 
92356 
92343 
92332 
92321 

39902 
39928 
39956 
39982 
40008 
40035 

91694 
91683 
91671 
91660 
91648 
91636 

41496 
41522 
41649 
41575 
41602 
41628 

90984 
90972 
90960 
90948 
90936 
90924 

29 
28 
27 
26 
25 
24 

5 
5 
5 
5 
5 
4 

17 

17 

18 

18 

18 

19, 

19 

20 

20 

21 

21 

22 

22 

23 

23 

23 

24 

24 

25 

25 

26 

26 

27 

27 

37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

35211 
35239 
35266 
36293 
35320 
35347 

93696 
93585 
93676 
93665 
93655 
93544 

36839 
36867 
36894 
36921 
36948 
36976 

92967 
92956 
92946 
92935 
92924 
92913 
92902 
92892 
92881 
92870 
92859 
92849 

38456 
38483 
38610 
38537 
38564 
38691 

92310 
92299 
92287 
92276 
92265 
92254 

40062 
40088 
40116 
40141 
40168 
40196 

91625 
91613 
91601 
91590 
91578 
91666 

41655 
41681 
41707 
41734 
41760 
41787 

90911 
90899 
90887 
90876 
90863 
90851 

23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 

4 
4 
4 
4 
3 
3 

36376 
35402 
35429 
35456 
35484 
35511 

93634 
93524 
93614 
93503 
93493 
93483 

37002 
37029 
37066 
37083 
37110 
37137 

38617 
38644 
38671 
38698 
38725 
38752 

92243 
92231 
92220 
92209 
92198 
92186 

40221 
40248 
40276 
40301 
40328 
40365 

91666 
91543 
91531 
91619 
91508 
91496 

41813 
41840 
41866 
41892 
41919 
41945 

90839 
90826 
90814 
90802 
90790 
90778 

3 
3 
3 
3 

i 

35638 
35665 
35592 
35619 
35647 
36674 

93472 
93462 
93462 
93441 
93431 
93420 

37164 
37191 
37218 
37245 
37272 
37299 

92838 
92827 
92816 
92806 
92794 
92784 

38778 
38805 
38832 
38869 
38886 
38912 

92176 
92164 
92162 
92141 
92130 
92119 

40381 
40408 
40434 
40461 
40488 
40514 

91484 
91472 
91461 
91449 
91437 
91425 

41972 
41998 
42024 
42051 
42077 
42104 

90766 
90753 
90741 
90729 
90717 
90704 

11 

10 

9 

8 
7 
6 

2 

2 
2 

36701 
35728 
36755 
35782 
35810 
35837 

93410 
93400 
93389 
93379 
93368 
93368 

37326 
37353 
37380 
37407 
37434 
37461 

92773 
92762 
92761 
92740 
92729 
92718 

38939 
38966 
38993 
39020 
39046 
39073 

92107 
92096 
92085 
92073 
92062 
92050 

40541 
40567 
40594 
40621 
40647 
40674 

91414 
91402 
91390 
91378 
91366 
91355 

42130 
42156 
42183 
42209 
42235 
42262 

90692 
90680 
90668 
90655 
90643 
90631 

5 
4 
3 
2 
1 
0 

0 
0 
0 

N.  COS. 

N,  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.slne. 

M. 

i 

69° 

68"      1 

67°      1 

.66°      1 

6»°     1 

J 

TABLE  41.                 [Page  761 

Natural  Sines  and  Cosinee. 

Prop. 

part* 

26 

«6°      1 

2«o 

27°      1 

28° 

29°      1 

Prop. 

parts 

14 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.cos. 

N.  sine. 

N.cos. 

0 
0 

1 
1 

2 
2 
3 
3 
3 
4 
4 
5 
5 

0 

1 

2 
3 
4 
5 
6 

42262 
42288 
42315 
42341 
42367 
42394 
42420 

90631 
90618 
90606 
90594 
90582 
90569 
90557 

43837 
43863 
43889 
43916 
43942 
43968 
43994 

89879 
89867 
89864 
89841 
89828 
89816 
89803 

45399 
46425 
45461 
46477 
45603 
45529 
46554 

89101 

89087 
89074 
89061 
89048 
89036 
89021 

46947 
46973 
46999 
47024 
47050 
47076 
47101 

88295 
88281 
88267 
88254 
88240 
88226 
88213 

48481 

48606 

48532 

48567 

48683 

48608 

48634 

48659' 

48684 

48710 

48736 

48761 

48786 

87462 
87448 
87434 
87420 
87406 
87391 
87377 

60 
69 
58 
57 
56 
56 
54 

14 
14 
14 
13 
13 
13 
13 

7 

8 

9 

10 

11 

12 

42446 
42473 
42499 
42525 
42552 
42578 

90545 
90532 
90520 
90607 
90496 
90483 

44020 
44046 
44072 
44098 
44124 
44151 

89790 
89777 
89764 
89762 
89739 
89726 

46580 
45606 
46632 
46658 
45684 
45710 

89008 
88996 
88981 
88968 
88955 
88942 

47127 
47153 
47178 
47204 
47229 
47255 

88199 
88185 
88172 
88158 
88144 
88130 

87363 
87349 
87335 
87321 
87306 
87292 
87278 
87264 
87250 
87235 
87221 
87207 
87193 
87178 
87164 
87150 
87136 
87121 

53 
62 
51 
50 
49 
48 

12 

12 
12 
12 
11 
11 

6 
6 

7 
7 
7 
8 

13 

14 
15 
16 
17 
18 

42604 
42631 
42657 
42683 
42709 
42736 

90470 
90468 
90446 
90433 
90421 
90408 

44177 
44203 
44229 
44266 
44281 
44307 

89713 
89700 
89687 
89674 
89662 
89649 

46736 
45762 
45787 
45813 
45839 
46865 

88928 
88915 
88902 
88888 
88875 
88862 
88848 
88835 
88822 
88808 
88795 
88782 

47281 
47306 
47332 
47368 
47383 
47409 
47434 
47460 
47486 
47611 
47537 
47562 

88117 
88103 
88089 
88076 
88062 
88048 

48811 
48837 
48862 
48888 
48913 
48938 

47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 
36 

11 
11 
11 
10 
10 
10 

8 

9 

9 

10 

10 

10 

19 
20 
21 
22 
23 
24 

42762 
42788 
42815 
42841 
42867 
42894 

90396 
90383 
90371 
90368 
90346 
90334 

44333 
44369 
44385 
44411 
44437 
44464 

89636 
89623 
89610 
89597 
89584 
89671 

45891 
45917 
46942 
45968 
45994 
46020 

88034 
88020 
88006 
87993 
87979 
87965 

48964 
48989 
49014 
49040 
49065 
49090 

10 
9 

9 

9 
8 

11 
11 
12 
12 
13 
13 

25 
26 
27 
28 
29 
30 

42920 
42946 
42972 
42999 
43025 
43051 

90321 
90309 
90296 
90284 
90271 
90259 

44490 
44516 
44542 
44568 
44594 
44620 

89668 
89546 
89532 
89519 
89506 
89493 

46046 
46072 
46097 
46123 
46149 
46175 

88768 
88756 
88741 
88728 
88716 
88701 

47588 
47614 
47639 
47666 
47690 
47716 
47741 
47767 
47793 
47818 
47844 
47869 

87951 
87937 
87923 
87909 
87896 
87882 
87868 
87854 
87840 
87826 
87812 
87798 

49116 
49141 
49166 
49192 
49217 
49242 
49268 
49293 
49318 
49344 
49369 
49394 

87107 
87093 
87079 
87064 
87050 
87036 
87021 
87007 
86993 
86978 
86964 
86949 

35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 
24 

8 
8 
8 
7 
7 
7 

13 
14 
14 
15 
15 
16 

31 
32 
33 
34 
36 
36 

43077 
43104 
43130 
43156 
43182 
43209 

90246 
90233 
90221 
90208 
90196 
90183 

44646 
44672 
44698 
44724 
44750 
44776 

89480 
89467 
89454 
89441 
89428 
89415 

46201 
46226 
46252 
46278 
46.304 
46330 
46:^56 
46381 
46407 
46433 
46458 
46484 
46510 
46536 
46561 
46587 
46613 
46639 

88688 
88674 
88661 
88647 
88634 
88620 

7 
7 
6 
6 
6 
6 

16 
16 
17 
17 
18 
18 

37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

43235 
43261 
43287 
43313 
43340 
43366 

90171 
90158 
90146 
90133 
90120 
90108 

44802 
44828 
44854 
44880 
44906 
44932 

89402 
89389 
89376 
89363 
89350 
89337 
89324 
89311 
89298 
89286 
89272 
89259 

88607 
88693 
88580 
88566 
88553 
88539 
88526 
88512 
88499 
88485 
88472 
88468 

47895 
47920 
47946 
47971 
47997 
48022 
48048 
48073 
48099 
48124 
48150 
48176 

87784 
87770 
87766 
87743 
87729 
87715 

49419 
49445 
49470 
49495 
49621 
49546 
49571 
49596 
49622 
49647 
49672 
49697 

86935 
86921 
86906 
86892 
86878 
86863 

23 
22 
21 
20 
19 
18 

5 
5 
6 
5 
4 
4 

19 
19 
20 
20 
20 
21 
21 
22 
22 
23 
23 
23 

43392 
43418 
43445 
43471 
43497 
43523 

90095 
90082 
90070 
90067 
90045 
90032 

44958 
44984 
45010 
45036 
46062 
45088 

87701 
87687 
87673 
87659 
87645 
87631 

86849 
86834 
86820 
86806 
86791 
86777 

17 
16 
15 
14 
13 
12 

4 
4 
4 
3 
3 
3 

43549 
43575 
43602 
43628 
43664 
43680 

90019 
90007 
89994 
89981 
89968 
89966 

45114 
45140 
4516G 
46192 
45218 
45243 

89245 
89232 
89219 
89206 
89193 
89180 

46664 
46690 
46716 
46742 
46767 
46793 

88445 
88431 
88417 
88404 
8S390 
88377 

48201 
48226 
48252 
48277 
48303 
48328 

87617 
87603 
87689 
87575 
87561 
87.546 
87532 
87618 
87604 
87490 
87476 
87462 

49723 
49748 
49773 
49798 
49824 
49849 
49874 
49899 
49924 
49950 
49975 
60000 

86762 
86748 
86733 
86719 
86704 
86690 
86676 
86661 
86646 
86632 
86617 
86603 

11 

10 

9 

8 
7 
6 

3 

2 
2 

2 
2 

1 

24 
24 
25 
25 
26 
26 

43706 
43733 
43759 
43785 
43811 
43837 

89943 
89930 
89918 
89905 
89892 
89879 

45269 
45296 
45321 
45347 
45373 
45399 

89167 
89153 
89140 
89127 
89114 
89101 

46819 
46844 
46870 
46896 
46921 
46947 

88363 
88349 
88336 
88322 
88308 
88295 

48354 
48379 
48405 
48430 
48456 
48481 

5 
4 
3 
2 
1 
0 

1 

1 
1 
0 
0 
0 

N.  COB. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

., 

64° 

68° 

62° 

61° 

60°      1 

Page  752]                 TABLE  41. 

Natural  Sines  and  Cosines. 

Prop, 
parts. 

35 

80° 

81° 

32° 

S3° 

34° 

Prop. 

parts, 

16 

M. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  COS, 

N,  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N,  sine. 

N.  COS. 

0 
0 

1 
1 

2 
2 
3 

0 

1 

2 
3 
4 
6 
6 

50000 
50025 
50050 
50076 
50101 
50126 
50151 

86603 
86588 
86573 
86559 
86544 
86530 
86515 

51504 
51529 
51554 
51579 
51604 
51628 
51653 

85717 
85702 
85687 
85672 
85657 
85642 
85627 

52992 
53017 
63041 
53066 
63091 
63115 
53140 

84805 
84789 
84774 
84759 
84743 
84728 
84712 

54464 
64488 
64513 
54637 
54561 
54586 
54610 

83867 
83861 
83835 
83819 
83804 
83788 
83772 

65919 
55943 
66968 
65992 
56016 
56040 
56064 

82904 

82887 
82871 
82855 
82839 
82822 
82806 

60 
69 
58 
57 
56 
55 
54 

16 
16 
16 
15 
15 
15 
14 

3 
3 
4 

4 
5 
5 

7 

8 

9 

10 

11 

12 

50176 
50201 
50227 
50252 
50277 
50302 

86501 
86486 
86471 
86457 
86442 
86427 

51678 
51703 
51728 
51753 
51778 
51803 

85612 
85597 
85582 
85567 
85551 
85536 

53164 
53189 
53214 
53238 
53263 
53288 

84697 
84681 
84666 
84650 
84635 
84619 
84604 
84688 
84573 
84557 
84542 
84526 

64635 
54659 
54683 
54708 
54732 
54766 

83766 
83740 
83724 
83708 
83692 
83676 

66088 
56112 
56136 
56160 
56184 
66208 

82790 
82773 
82767 
82741 
82724 
82708 

53 
52 
51 
50 

49 
48 

14 
14 
14 
13 
13 
13 

5 

6 
6 

7 
7 
8 

13 

14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

50327 
50352 
50377 
50403 
50428 
50453 

86413 
86398 
86384 
86369 
86354 
86340 

51828 
51852 
51877 
51902 
51927 
51952 

85521 
85506 
85491 
85476 
85461 
85446 

53312 
63337 
53361 
53386 
53411 
53436 

54781 
64806 
54829 
64864 
54878 
64902 

83660 
83645 
83629 
83613 
83597 
83581 

66232 
56266 
56280 
56306 
56329 
66353 

82692 
82675 
82669 
82643 
82626 
82610 

47 
46 
46 
44 
43 
42 

13 
12 
12 
12 
11 
11 

8 
8 
9 
9 
10 
10 

50478 
50503 
50528 
50553 
60578 
50603 

86325 
86310 
86295 
86281 
86266 
86251 
86237 
86222 
86207 
86192 
86178 
86163 

51977 
52002 
52026 
52051 
52076 
52101 

85431 
85416 
85401 
85385 
85370 
85355 
85340 
85325 
85310 
85294 
85279 
85264 

63460 
53484 
63509 
63634 
53558 
63683 

84611 
84495 
84480 
84464 
84448 
84433 

64927 
64951 
54975 
64999 
56024 
55048 

83565 
83549 
83533 
83617 
83601 
83485 

66377 
56401 
66426 
66449 
56473 
56497 

82693 
82677 
82561 
82544 
82528 
82511 

41 
40 
39 
38 
37 
36 

11 
11 
10 
10 
10 
10 

10 
11 
11 
12 
12 
13 

25 

26 
27 
28 
29 
30 

50628 
50654 
50679 
50704 
50729 
50754 

52126 
52151 
52175 
52200 
52225 
52250 

63607 
53632 
63656 
53681 
63705 
53730 

84417 
84402 
84386 
84370 
84356 
84339 

55072 
66097 
55121 
55145 
66169 
55194 

83469 
83453 
83437 
83421 
83405 
83389 

66621 
56545 
66669 
56593 
56617 
56641 

82495 
82478 
82462 
82446 
82429 
82413 

35 
34 
33 
32 
31 
30 

9 
9 
9 
9 

8 
8 

13 
13 
14 
14 
15 
15 
15 
16 
16 
17 
17 
18 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 

50779 
50804 
50829 
50854 
50879 
50904 

86148 
86133 
86119 
86104 
86089 
86074 

52275 
52299 
52324 
52349 
52374 
52399 

85249 
85234 
85218 
85203 
85188 
85173 

53764 
53779 
63804 
63828 
63863 
53877 

84324 
84308 
84292 
84277 
84261 
84245 
84230 
84214 
84198 
84182 
84167 
84161 

65218 
65242 
55266 
66291 
55316 
56339 
65363 
55388 
55412 
55436 
56460 
65484 

83373 
83356 
83340 
83324 
83308 
83292 

56665 
66689 
66713 

66736 
56760 
56784 

82396 
82380 
82363 
82347 
82330 
82314 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
18 

8 
7 
7 
7 
7 
6 

50929 
50954 
50979 
51004 
51029 
51054 

86059 
86045 
86030 
86015 
86000 
85985 

52423 
52448 
52473 
52498 
52522 
52547 

85157 
85142 
85127 
85112 
85096 
85081 

53902 
63926 
63951 
63976 
54000 
64024 

83276 
83260 
83244 
83228 
83212 
83195 

56808 
56832 
56856 
66880 
56904 
56928 

82297 
82281 
82264 
82248 
82231 
82214 

6 
6 
6 
5 
5 
5 

18 
18 
19 
19 
20 
20 

43 
44 

45 
46 
47 
48 

51079 
51104 
51129 
51154 
51179 
51204 

85970 
85956 
85941 
85926 
85911 
85896 

52572 
52597 
52621 
52646 
52671 
52696 

85066 
85051 
85035 
85020 
85005 
84989 

64049 
54073 
54097 
54122 
64146 
54171 

84136 
84120 
84104 
84088 
84072 
84067 
84041 
84025 
84009 
83994 
83978 
83962 

56609 
55633 
66657 
55681 
55605 
55630 

83179 
83163 
83147 
83131 
83115 
83098 

56952 
66976 
67000 
57024 
67047 
57071 
57096 
67119 
57143 
57167 
57191 
57215 

82198 
82181 
82165 
82148 
82132 
82115 

17 
16 
15 
14 
13 
12 

5 
4 
4 
4 
3 
3 

20 
21 
21 
22 
22 
23 

49 
50 
51 
52 
53 
54 

51229 
51254 
51279 
51304 
51329 
51354 

85881 
85866 
85851 
85836 
85821 
85806 

52720 
52745 
52770 
52794 
52819 
52844 

84974 
84959 
84943 
84928 
84913 
84897 

54195 
54220 
64244 
54269 
54293 
54317 

56654 
56678 
55702 
55726 
56750 
66775 

83082 
83066 
83050 
83034 
83017 
83001 

82098 
82082 
82065 
82048 
82032 
82015 

11 
10 
9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

3 
3 
2 
2 
2 
2 

23 
23 
24 
24 
25 
25 

55 
56 
57 
58 
59 
60 

51379 
51404 
51429 
51454 
51479 
51504 

85792 
85777 
85762 
85747 
85732 
85717 

52869 
52893 
52918 
52943 
52967 
52992 

84882 
84866 
84851 
84836 
84820 
84805 

54342 
54366 
64391 
54415 
54440 
54464 

83946 
83930 
83915 
83899 
83883 
83867 

55799 
55823 
55847 
65871 
55895 
55919 

82985 
82969 
82953 
82936 
82920 
82904 

67238 
57262 
57286 
67310 
67334 
57358 

81999 
81982 
81965 
81949 
81932 
81915 

1 
1 
1 
1 
0 
0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  Bine. 

N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

M. 

69° 

68° 

57° 

66° 

66° 

•   TABLE  41.                  [Page  763 
Natural  Sines  and  Cosines. 

Prop, 
parts 

S3 

85°      1 

86°             37° 

38°      1 

89°      1 

Prop, 
parts 

18 

M. 

N.  sine. 

N.  COS. 

N.  sine.   N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 
0 

1 
1 

2 
2 
2 

0 
1 
2 

o 

4 
5 
6 

57358 
57381 
57405 
57429 
57453 
57477 
57501 

81915 
81899 
81882 
81865 
81848 
81832 
81815 

58779 
58802 
58826 
58849 
58873 
58896 
58920 

80902 
80885 
80867 
80850 
80833 
80816 
80799 

60182 
60205 
60228 
60251 
60274 
60298 
60321 

79864 
79846 
79829 
79811 
79793 
79776 
79758 

61566. 

61589 

61612 

61635 

61658 

61681 

61704 

78801 
78783 
78765 
78747 
78729 
78711 
78694 

62932 
62955 
62977 
63000 
63022 
63045 
63068 

77715 
77696 
77678 
77660 
77641 
77623 
77605 

60 
59 
58 
57 
56 
55 
54 

18 
18 
17 
17 
17 
17 
16 

3 
3 
3 
4 
4 
5 

7 

8 

9 

10 

11 

12 

57524 
57548 
57572 
57596 
57619 
57643 

81798 
81782 
81765 
81748 
81731 
81714 

58943 
58967 
58990 
59014 
59037 
59061 

80782 
80765 
80748 
80730 
80713 
80696 

60344 
60367 
60390 
60414 
60437 
60460 

79741 
79723 
79706 
79688 
79671 
79653 

61726 
61749 
61772 
61795 
61818 
61841 

78676 
78658 
78640 
78622 
78604 
78586 

63090 
63113 
63135 
63158 
63180 
63203 

77586 
77568 
77550 
77531 
77513 
77494 

53 
52 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42 

16 
16 
15 
15 
15 
14 

5 
5 
6 
6 

7 
7 

13 
14 
15 
16 
17 
18 

57667 
57691 
57715 
57738 
57762 
57786 

81698 
81681 
81664 
81647 
81631 
81614 

59084 
59108 
59131 
59154 
59178 
59201 

80679 
80662 
80644 
80627 
80610 
80593 

60483 
60506 
60529 
60553 
60576 
60599 

79635 
79618 
79600 
79583 
79565 
79547 

61864 
61887 
61909 
61932 
61955 
61978 

78568 
78550 
78632 
78514 
78496 
78478 

63225 
63248 
63271 
63293 
63316 
63338 

77476 
77458 
77439 
77421 
77402 
77384 

14 
14 
14 
13 
13 
13 

7 
•  8 
8 
8 
9 
9 

19 
20 
21 
22 
23 
24 

57810 
57833 
57857 
57881 
57904 
57928 

81597 
81580 
81563 
81546 
81530 
81513 

59225 
59248 
59272 
59295 
59318 
59342 
59365 
59389 
59412 
59436 
59459 
59482 

80576 
80558 
80541 
80524 
80507 
80489 
80472 
80455 
80438 
80420 
80403 
80386 

60622 
60645 
60668 
60691 
60714 
60738 

79530 
79512 
79494 
79477 
79459 
79441 

62001 
62024 
62046 
62069 
62092 
62115 
62138 
62160 
62183 
62206 
62229 
62251 
62274 
62297 
62320 
62342 
62365 
62388 

78460 
78442 
78424 
78405 
78387 
78369 
78351 
78333 
78315 
78297 
78279 
78261 
78243 
78225 
78206 
78188 
78170 
78152 

63361 
63383 
63406 
63428 
63451 
63473 

77366 
77347 
77329 
77310 
77292 
77273 

41 
40 
39 
38 
37 
36 

12 
12 
12 
11 
11 
11 

10 
10 
10 
11 
11 
12 

25 
26 
27 
28 
29 
30 

57952 
57976 
57999 
58023 
58047 
58070 

81496 
81479 
81462 
81445 
81428 
81412 

60761 
60784 
60807 
60830 
60853 
60876 
60899 
60922 
60945 
60968 
60991 
61015 

79424 
79406 
79388 
79371 
79353 
79335 
79318 
79300 
79282 
79264 
79247 
79229 

63496 
63518 
63540 
63563 
63585 
63608 
63630 
63653 
63675 
63698 
63720 
63742 

77255 
77236 
77218 
77199 
77181 
77162 

35 
34 
33 
32 
31 
30 

11 
10 
10 
10 
9 
9 

12 
12 
13 
13 
13 
14 

31 
32 
33 
34 
35 
36 

58094 
58118 
58141 
58165 
58189 
58212 

81395 
81378 
81361 
81344 
81327 
81310 

59506 
59529 
59552 
59576 
59599 
59622 

80368 
80351 
80334 
80316 
80299 
80282 

77144 
77125 
77107 
77088 
77070 
77051 

29 
28 
27 
26 
25 
24 

9 
8 
8 
8 

8 
7 

14 
15 
15 
15 
16 
16 

37 
38 
39 
40 
41 
42 

58236 
58260 
58283 
58307 
58330 
58354 

81293 
81276 
81259 
81242 
81225 
81208 

59646 
59669 
59693 
59716 
59739 
59763 

80264 
80247 
80230 
80212 
80195 
80178 

61038 
61061 
61084 
61107 
61130 
61153 

79211 
79193 
79176 
79158 
79140 
79122 
79105 
79087 
79069 
79051 
79033 
79016 

62411 
62433 
62456 
62479 
62502 
62524 
62547 
62570 
62592 
62615 
62638 
62660 

78134 
78116 
78098 
78079 
78061 
78043 
78025 
78007 
77988 
77970 
77952 
77934 

63765 
63787 
63810 
63832 
63854 
63877 
63899 
63922 
63944 
63966 
63989 
64011 

77033 
77014 
76996 
76977 
76959 
76940 
76921 
76903 
76884 
76866 
76847 
76828 

23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 

7 
7 
6 
6 
6 
5 

16 
17 
17 
18 
18 
18 

43 
44 
45 
46 
47 
48 

58378 
58401 
58425 
58449 
58472 
58496 

81191 
81174 
81157 
81140 
81123 
81106 

59786 
59809 
59832 
59856 
59879 
59902 

80160 
80143 
80125 
80108 
80091 
80073 

61176 
61199 
61222 
61245 
61268 
61291 

5 
5 

5 
4 
4 
4 

19 
19 
20 
20 
20 
21 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

58519 
58543 
58567 
58590 
58614 
58637 

81089 
81072 
81055 
81038 
81021 
81004 

59926 
59949 
59972 
59995 
60019 
60042 

80056 
80038 
80021 
80003 
79986 
79968 

61314 
61337 
61360 
61383 
61406 
61429 

78998 
78980 
78962 
78944 
78926 
78908 

62683 
62706 
62728 
62751 
62774 
62796 
62819 
62842 
62864 
62887 
62909 
62932 

77916 
77897 
77879 
77861 
77843 
77824 
77806 
77788 
77769 
77751 
77733 
77715 

64033 
64056 
64078 
64100 
64123 
64145 

76810 
76791 
76772 
76754 
76735 
76717 

11 

10 

9 

8 
7 
6 

3 
3 
3 
2 

2 
2 
2 

1 
1 
1 
0 
0 

21 
21 
22 
22 
23 
23 

58661 
58684 
58708 
58731 
58755 
58779 

80987 
80970 
80953 
80936 
80919 
80902 

60065 
60089 
60112 
60135 
60158 
60182 

79951 
79934 
79916 
79899 
79881 
79864 

61451 
61474 
61497 
61520 
61543 
61566 

78891 
78873 
78855 
78837 
78819 
78801 

64167 
64190 
64212 
64234 
64256 
64279 

76698 
76679 
76661 
76642 
76623 
76604 

5 
4 
3 
2 
1 
0 

N.C08. 

N.  sine. 

K.C08.  1  N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

64° 

68° 

58° 

'1 
61° 

50° 

Page  764j                TABLE  41.   • 

Natural  Sines  and  Cosines. 

Prop. 

parte 

82 

M. 

40° 

41° 

42° 

48° 

44° 

Prop. 

parte 

19 

N.Bine. 

N.  COS. 

N.  Bine. 

N.coa 

N.sine. 

N.  COS. 

N.sine. 

N.  COS. 

N.  sine. 

N.  cos. 

0 
0 

1 
1 
1 
2 
2 

0 

1 

2 
3 
4 
5 
6 

64279 
64301 
64323 
64346 
64368 
64390 
64412 

76604 
76586 
76567 
76548 
76530 
76511 
76492 

65606 
65628 
65650 
65672 
65694 
65716 
65738 

75471 
75452 
75433 
75414 
75395 
75375 
75356 

66913 
66936 
66956 
66978 
66999 
67021 
67043 

74314 
74296 
74276 
74266 
74237 
74217 
74198 

68200 
68221 
68242 
68264 
68285 
68306 
68327 

73135 
73116 
73096 
73076 
73056 
73036 
73016 

69466 
69487 
69608 
69629 
69649 
69570 
69591 

71934 
71914 
71894 
71873 
71853 
71833 
71813 
71792 
71772 
71762 
71732 
71711 
71691 

60 
59 
58 
57 
56 
55 
54 

19 
19 
18 
18 
18 
17 
17 

3 
3 
3 

4 
4 
4 

7 
8 
9 

10 
11 
12 

64435 
64457 
64479 
64501 
64524 
64546 

76473 
76455 
76436 
76417 
76398 
76380 

65759 
65781 
65803 
65825 
65847 
65869 

75337 
75318 
76299 
76280 
76261 
75241 

67064 
67086 
67107 
67129 
67151 
67172 

74178 
74159 
74139 
74120 
74100 
74080 

68349 
68370 
68391 
68412 
68434 
68455 

72996 
72976 

72957 
72937 
72917 
72897 

69612 
69633 
69654 
69676 
69696 
69717 

53 
52 
51 
50 
49 
48 

17 
16 
16 
16 
16 
15 

6 
5 
6 
6 
6 
7 

13 
14 
15 
16 
17 
18 

64568 
64590 
64612 
64635 
64657 
64679 

76361 
76342 
76323 
76304 
76286 
76267 

65891 
65913 
65935 
65956 
65978 
66000 

75222 
75203 
75184 
75165 
75146 
75126 

67194 
67215 
67237 
67258 
67280 
67301 

74061 
74041 
74022 
74002 
73983 
73963 

68476 
68497 
68618 
68639 
68561 
68582 

72877 
72867 
72837 
72817 
72797 
72777 

69737 
69758 
69779 
69800 
69821 
69842 

71671 
71650 
71630 
71610 
71590 
71669 

47 
46 
45 
44 
43 
42 

15 
16 
14 
14 
14 
13 
13 
13 
12 
12 
12 
11 

7 
7 
8 
8 
8 
9 

19 
20 
21 
22 
23 
24 

64701 
64723 
64746 
64768 
64790 
64812 

76248 
76229 
76210 
76192 
76173 
76154 

66022 
66044 
66066 
66088 
66109 
66131 

75107 
75088 
75069 
75050 
75030 
75011 

67323 
67344 
67366 
67387 
67409 
67430 

73944 
73924 
73904 
73885 
73866 
73846 

68603 
68624 
68645 
68666 
68688 
68709 

72757 
72737 
72717 
72697 
72677 
72657 

69862 
69883 
69904 
69926 
69946 
69966 

71649 
71629 
71608 
71488 
71468 
71447 

41 
40 
39 
38 
37 
36 

9 
10 
10 
10 
11 
11 

25 
26 
27 
28 
29 
30 

64834 
64856 
64878 
64901 
64923 
64945 

76135 
76116 
76097 
76078 
76059 
76041 

66153 
66175 
66197 
66218 
66240 
66262 

74992 
74973 
74953 
74934 
74915 
74896 

67452 
67473 
67495 
67616 
67538 
67659 

73826 
73806 

73787 
73767 
73747 
73728 

68730 
68751 
68772 
68793 
68814 
68835 

72637 
72617 
72697 
72577 
72557 
72537 
72517 
72497 
72477 
72457 
72437 
72417 

69987 
70008 
70029 
70049 
70070 
70091 

71427 
71407 
71386 
71366 
71.S45 
71325 

35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 
24 

11 
11 
10 
10 
10 
10 

11 
12 
12 
12 
13 
13 

31 
32 
33 
34 
35 
36 

64967 
64989 
65011 
65033 
65055 
65077 

76022 
76003 
75984 
75965 
75946 
75927 

66284 
66306 
66327 
66349 
66371 
66393 

74876 
74867 
74838 
74818 
74799 
74780 

67580 
67602 
67623 
67645 
67666 
67688 

73708 
73688 
73669 
73649 
73629 
73610 

68867 
68878 
68899 
68920 
68941 
68962 

70112 
70132 
70153 
70174 
70195 
70215 

71305 
71284 
71264 
71243 
71223 
71203 

9 
9 
9 

8 
8 
8 

14 
14 
14 
15 
15 
15 

37 
38 
39 
40 
41 
42 

65100 
65122 
65144 
65166 
65188 
65210 

75908 
75889 
75870 
75851 
75832 
75813 

66414 
66436 
66458 
66480 
66501 
66523 

74760 
74741 
74722 
74703 
74683 
74664 

67709 
67730 
67752 
67773 
67795 
67816 

73690 
73670 
73551 
73531 
73511 
73491 

68983 
69004 
69026 
69046 
69067 
69088 

72397 
72377 
72367 
72337 
72317 
72297 

70236 
70267 
70277 
70298 
70319 
70339 

71182 
71162 
71141 
71121 
71100 
71080 

23 
22 
21 
20 
19 
18 

7 
7 
7 
6 
6 
6 

16 
16 
17 
17 
17 
18 

43 
44 
45 
46 
47 
48 

65232 
65254 
65276 
65298 
66320 
65342 

75794 
75775 
75756 
75738 
75719 
75700 

66545 
66566 
66688 
66610 
66632 
66653 

74644 
74625 
74606 
74586 
74567 
74548 

67837 
67859 
67880 
67901 
67923 
67944 

73472 
73462 
73432 
73413 
73393 
73373 

69109 
69130 
69161 
69172 
69193 
69214 

72277 
72267 
72236 
72216 
72196 
72176 

70360 
70381 
70401 
70422 
70443 
70463 

71059 
71039 
71019 
70998 
70978 
70967 

17 
16 
15 
14 
13 
12 

6 
5 
5 
4 
4 
4 

18 
18 
19 
19 
19 
20 

49 
50 
51 
52 
53 
54 

65364 
65386 
65408 
65430 
65452 
65474 

75680 
75661 
75642 
75623 
75604 
75585 

66675 
66697 
66718 
66740 
66762 
66783 

74628 
74509 
74489 
74470 
74451 
74431 

67966 
67987 
68008 
68029 
68061 
68072 

73353 
73333 
73314 
73294 

73274 
73254 

69235 
69266 
69277 
69298 
69319 
69340 

72156 
72136 
72116 
72095 
72075 
72055 

70484 
70505 
70526 
70546 
70567 
70587 

70937 
70916 
70896 
70876 
70855 
70834 

11 

10 

9 

8 
7 
6 

3 
3 
3 
3 
2 
2 

20 
21 
21 
21 
22 
22 

55 
56 
57 
58 
59 
60 

65496 
65518 
65540 
65562 
65584 
65606 

75566 
75547 
75528 
75509 
75490 
75471 

66805 
66827 
66848 
66870 
66891 
66913 

74412 
74392 
74373 
74363 
74334 
74314 

68093 
68116 
68136 
68157 
68179 
68200 

73234 
73215 
73195 
73175 
73155 
73135 

69361 
69382 
69403 
69424 
69445 
69466 

72035 
72016 
71996 
71974 
71964 
71934 

70608 
70628 
70649 
70670 
70690 
70711 

70813 
70793 
70772 
70752 
70731 
70711 

5 
4 
3 
2 
1 
0 

2 
1 
1 
1 
0 
0 



N.C08. 

N.slne. 

N.cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

N.cos. 

N.  sine. 

M. 

49° 

48° 

47° 

46° 

46° 

TABLE  42. 

[Page  766 

Ix^arithms  of  Numbers. 

No. 

1 100. 

Log.  0.00000 ^2.00000.   | 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1 

0.00000 

21 

1.  32222 

41 

1. 61278 

61 

1.78533 

81 

1.90849 

2 

0. 30103 

22 

1.34242 

42 

1. 62325 

62 

1.  79239 

82 

1. 91381 

3 

0.47712 

23 

1. 36173 

43 

1. 63347 

63 

1.  79934 

83 

1. 91908 

4 

0.60206 

24 

1.38021 

44 

1.64345 

64 

1. 80618 

84 

1. 92428 

5 

0. 69897 

25 

1.39794 

45 

1. 65321 

65 

1. 81291 

86 

1.92942 

6 

0. 77815 

26 

1. 41497 

46 

1. 66276 

66 

1.  81954 

86 

1.93450 

7 

0. 84510 

27 

1. 43136 

47 

1. 67210 

67 

1.  82607 

87 

1. 93952 

8 

0. 90309 

28 

1. 44716 

48 

1.68124 

68 

1. 83251 

88 

1.94448 

9 

0. 95424 

29 

1.46240 

49 

1. 69020 

69 

1. 83885 

89 

1.94939 

10 

1.00000 

30 

1. 47712 

50 

1. 69897 

70 

1. 84510 

90 

1.95424 

11 

1.04139 

31 

1. 49136 

51 

1. 70757 

71 

1.  85126 

91 

1.95904 

12 

1. 07918 

32 

1. 50515 

52 

1.71600 

72 

1.86733 

92 

1. 96379 

13 

1. 11394 

33 

1.51851 

53 

1. 72428 

73 

1.86332 

98 

1.96848 

14 

1. 14613 

34 

1. 53148 

54 

1. 73239 

74 

1. 86923 

94 

1. 97313 

15 

1. 17609 

35 

1.54407 

65 

1.74036 

75 

1. 87606 

95 

1. 97772 

16 

1.  20412 

36 

1.  55630 

56 

1.  74819 

76 

1. 88081 

96 

1. 98227 

17 

1. 23045 

37 

1.56820 

57 

1.  75587 

77 

1. 88649 

97 

1. 98677 

18 

1. 25527 

38 

1. 57978 

58 

1.  76343 

78 

1. 89209 

98 

1. 99123 

19 

1. 27875 

39 

1.  59106 

59 

1. 77085 

79 

1. 89763 

99 

1.99664 

20 

1.  30103 

1 

40 

1.60206 

60 

1. 77815 

80 

1.90309 

100 

2.00000 

Page  766]                TABLE  42. 

Logarithms  of  Numbers. 

No.  100 1600.                                                            Log.  00000 20412. 

No. 

0   1   1 

8 

3 

4 

5 

6 

7 

8 

9 

100 
101 
102 
103 
104 

00000   00043 
00432  1  00475 
00860   00903 
01284   01326 
01703   01745 

00087 
00518 
00945 
01368 
01787 

00130 
00561 
00988 
01410 
01828 

00173 
00604 
01030 
01452 
01870 

00217 
00647 
01072 
01494 
01912 

00260 
00689 
01115 
01536 
01953 

00303 
00732 
01157 
01578 
01995 

00346 
00775 
01199 
01620 
02036 

00389 
00817 
01242 
01662 
02078 
02490 
02898 
03302 
03703 
04100 

43 

43 

1 

2 
3 
4 

5 
6 

7 
8 
9 

4 
9 

13 
17 
22 
26 
30 
34 
39 

4 
8 
13 
17 
21 
25 
29 
34 
38 

105 
106 
107 
108 
109 

02119 
02531 
02938 
03342 
03743 

02160 
02572 
02979 
03383 
03782 

02202 
02612 
03019 
03423 
03822 

02243 
02653 
03060 
03463 
03862 

02284 
02694 
03100 
03503 
03902 
04297 
04689 
05077 
05461 
05843 

02325 
02735 
03141 
03543 
03941 

02366 
02776 
03181 
03583 
03981 

02407 
02816 
03222 
03623 
04021 

02449 
02857 
03262 
03663 
04060 

110 
111 
112 
113 
114 

04139 
04532 
04922 
05308 
05690 

04179 
04571 
04961 
05346 
05729 

04218 
04610 
04999 
05385 
05767 

04258 
04650 
05038 
05423 
05805 

04336 
04727 
05115 
05500 
05881 
06258 
06633 
07004 
07372 
07737 
08099 
08458 
08814 
09167 
09517 

04376 
04766 
05154 
05538 
05918 

04415 
04805 
05192 
05576 
05956 

04454 
04844 
05231 
05614 
05994 

04493 
04883 
05269 
05652 
06032 

41 

40 

1 
2 
3 
4 
5 
6 
7 
8 
9 

4 
8 
12 
16 
21 
25 
29 
33 
37 

4 
8 
12 
16 
20 
24 
28 
32 
36 

115 
116 
117 
118 
119 

06070 
06446 
06819 
07188 
07555 

06108 
06483 
06856 
07225 
07591 
07954 
08314 
08672 
09026 
09377 

06145 
06521 
06893 
07262 
07628 

06183 
06558 
06930 
07298 
07664 

06221 
06595 
06967 
07335 
07700 

06296 
06670 
07041 
07408 
07773 

06333 
06707 
07078 
07445 
07809 

06371 
06744 
07115 
07482 
07846 

06408 
06781 
07151 
07518 
07882 

120 
121 
122 
123 
124 

07918 
08279 
08636 
08991 
09342 

07990 
08350 
08707 
09061 
09412 

08027 
08386 
08743 
09096 
09447 

08063 
08422 
08778 
09132 
09482 

08135 
08493 
08849 
09202 
09552 
09899 
10243 
10585 
10924 
11261 

08171 
08529 
08884 
09237 
09587 

08207 
08565 
08920 
09272 
09621 

08243 
08600 
08955 
09307 
09656 

39 

88 

1 

2 
3 
4 

5 
6 
7 
8 
9 

4 
8 
12 
16 
20 
23 
27 
31 
35 

4 
8 
11 
15 
19 
23 
27 
30 
34 

125 
126 
127 
128 
129 

09691 
10037 
10380 
10721 
11059 

09726 
10072 
10415 
10755 
11093 

09760 
10106 
10449 
10789 
11126 

09795 
10140 
10483 
10823 
11160 

09830 
10175 
10517 
10857 
11193 

09864 
10209 
10551 
10890 
11227 

09934 
10278 
10619 
10958 
11294 

09968 
10312 
10653 
10992 
11327 

10003 
10346 
10687 
11025 
11361 

130 
131 
132 
133 
134 

11394 
11727 
12057 
12385 
12710 

11428 
11760 
12090 
12418 
12743 

11461 
11793 
12123 
12450 
12775 

11494 
11826 
12156 
12483 
12808 

11528 
11860 
12189 
12516 
12840 

11561 
11893 
12222 
12548 
12872 

11594 
11926 
12254 
12581 
12905 

11628 
11959 
12287 
12613 
12937 

11661 
11992 
12320 
12646 
12969 

11694 
12024 
12352 
12678 
13001 

37 

36 

1 
2 
3 
4 
5 
6 
7 
8 
9 

4 
7 
11 
15 
19 
22 
26 
30 
33 

4 

7 
11 
14 
18 
22 
25 
29 
32 

135 
136 
137 
138 
139 

13033 
13354 
13672 
13988 
14301 

13066 
13386 
13704 
14019 
14333 

13098 
13418 
13735 
14051 
14364 

13130 
13450 
13767 
14082 
14395 

13162 
13481 
13799 
14114 
14426 

13194 
13513 
13830 
14145 
14457 

13226 
13545 
13862 
14176 
14489 

13258 
13577 
13893 
14208 
14520 

13290 
13609 
13925 
14239 
14551 

13322 
13640 
13956 
14270 
14582 

140 
141 
142 
143 
144 

14613 
14922 
15229 
15534 
15836 

14644 
14953 
15259 
15564 
15866 

14675 
14983 
15290 
15594 
15897 

14706 
15014 
15320 
15625 
15927 

14737 
15045 
15351 
15655 
15957 

14768 
15076 
15381 
15685 
15987 

14799 
15106 
15412 
15715 
16017 

14829 
15137 
15442 
15746 
16047 
16346 
16643 
16938 
17231 
17522 

14860 
15168 
15473 
15776 
16077 

14891 
15198 
15503 
15806 
16107 

35 

34 

1 
2 
3 

4 
5 

? 

8 
9 

4 
7 
11 
14 
18 
21 
25 
28 
32 

3 

7 
10 

14 
17 
20 
24 
27 
31 

145 
146 
147 
148 
149 

16137 
16435 
16732 
17026 
17319 

16167 
16465 
16761 
17056 
17348 

16197 
16495 
16791 
17085 
17377 

16227 
16524 
16820 
17114 
17406 

16256 
16554 
16850 
17143 
17435 

16286 
16584 
16879 
17173 
17464 

16316 
16613 
16909 
17202 
17493 

16376 
16673 
16967 
17260 
17551 

16406 
16702 
16997 
17289 
17580 

150 
151 
152 
153 
154 

17609 
17898 
18184 
18469 
18752 

17638 
17926 
18213 
18498 
18780 

17667 
17955 
18241 
18526 
18808 

17696 
17984 
18270 
18554 
18837 

17725 
18013 
18298 
18583 
18865 

17754 
18041 
18327 
18611 
18893 

17782 
18070 
18355 
18639 
18921 

17811 
18099 
18384 
18667 
18949 

17840 
18127 
18412 
18696 
18977 

17869 
18156 
18441 
18724 
19005 

33 

82 

1 
2 
3 
4 
5 
6 
7 
8 
9 

3 
7 

10 
13 
17 
20 
23 
26 
30 

3 
6 
10 
13 
16 
19 
22 
26 
29 

155 
156 
157 
158 
159 

19033 
19312 
19590 
19866 
20140 

19061 
19340 
19618 
19893 
20167 

19089 
19368 
19645 
19921 
20194 

19117 
19396 
19673 
19948 
20222 

19145 
19424 
19700 
19976 
20249 

19173 
19451 
19728 
20003 
20276 

19201 
19479 
19756 
20030 
20303 

19229 
19507 
19783 
20058 
20330 

19257 
19535 
19811 
20085 
20358 

19285 
19562 
19838 
20112 
20385 

No.     0 

1 

a 

8 

4 

6 

e 

7 

8 

9 

TABLE  42.                 [Page  767 
Logarithms  of  Numbers. 

No.  1600 2200.                                                      Log.  20412 34242. 

No. 

0 

1 

2 

8 

4 

6 

6 

7 

8 

9 

160 
161 
162 
163 
164 

20412 
20683 
20952 
21219 
21484 

20439 
20710 
20978 
21245 
21511 

20466 
20737 
21005 
21272 
21537 

20493 
20763 
21032 
21299 
21564 

20520 
20790 
21059 
21325 
21590 

20548 
20817 
21085 
21352 
21617 

20575 
20844 
21112 
21378 
21643 
21906 
22167 
22427 
22686 
22943 

20602 
20871 
21139 
21405 
21669 

20629 
20898 
21165 
21431 
21696 

20656 
20925 
21192 
21458 
21722 

31 

80 

1 
2 
3 
4 
5 
6 
7 
8 
<j 

3 
6 
9 
12 
16 
19 
22 
25 
28 

3 
6 
9 

12 
15 
18 
21 
24 
27 

165 
166 
167 
168 
169 

21748 
22011 
22272 
22531 
22789 

21775 
22037 
22298 
22557 
22814 

21801 
22063 
22324 
22583 
22840 

21827 
22089 
22350 
22608 
22866 

21854 
22115 
22376 
22634 
22891 

21880 
22141 
22401 
22660 
22917 

21932 
22194 
22453 
22712 
22968 
23223 
23477 
23729 
23980 
24229 

21958 
22220 
22479 
22737 
22994 

21985 
22246 
22505 
22763 
23019 

170 
171 
172 
173 
174 

23045 
23300 
23553 
23805 
24055 

23070 
23325 
23578 
23830 
24080 

23096 
23350 
23603 
23855 
24105 

23121 
23376 
23629 
23880 
24130 

23147 
23401 
23654 
23905 
24155 

23172 
23426 
23679 
23930 
24180 

23198 
23452 
23704 
23955 
24204 

23249 
23502 
23754 
24005 
24254 

23274 
23528 
23779 
24030 
24279 

1 
2 
3 
4 
5 
6 
7 
8 
9 

29 

3 
6 
9 
12 
15 
17 
20 
23 
26 

28 

3 
6 
8 
11 
14 
17 
20 
22 
25 

175 
176 
177 
178 
179 

24304 
24551 
24797 
25042 
25285 

24329 
24576 
24822 
25066 
25310 

24353 
24601 
24846 
25091 
25334 

24378 
24625 
24871 
25115 
25358 
25600 
25840 
26079 
26316 
26553 
26788 
27021 
27254 
27485 
27715 

24403 
24650 
24895 
25139 
25382 

24428 
24674 
24920 
25164 
25406 

24452 
24699 
24944 
25188 
25431 

24477 
24724 
24969 
25212 
25455 

24502 
24748 
24993 
25237 
25479 
25720 
25959 
26198 
26435 
26670 

24527 
24773 
25018 
25261 
25503 

180 
181 
182 
183 

184 

25527 
25768 
26007 
26245 
26482 

25551 
25792 
26031 
26269 
26505 

25575 
25816 
26055 
26293 
26529 

25624 
25864 
26102 
26340 
26576 

25648 
25888 
26126 
26364 
26600 

25672 
25912 
26150 
26387 
26623 

25696 
25935 
26174 
26411 
26647 
26881 
27114 
27346 
27577 
27807 

25744 
25983 
26221 
26458 
26694 

27 

26 

1 
2 
3 
4 
5 
6 
7 
8 
9 

3 
5 

8 
11 
14 
16 
19 
22 
24 

3 
5 

8 
10 
13 
16 
18 
21 
23 

185 
186 
187 
188 
189 

26717 
26951 
27184 
27416 
27646 

26741 
26975 
27207 
27439 
27669 

26764 
26998 
27231 
27462 
27692 

26811 
27045 
27277 
27508 
27738 

26834 
27068 
27300 
27531 
27761 

26858 
27091 
27323 
27554 
27784 

26905 
27138 
27370 
27600 
27830 

26928 
27161 
27393 
27623 
27852 

190 
191 
192 
193 
194 

27875 
28103 
28330 
28556 
28780 

27898 
28126 
28353 
28578 
28803 

27921 
28149 
28375 
28601 
28825 

27944 
28171 
28398 
28623 

28847 

27967 
28194 
28421 
28646 
28870 

27989 
28217 
28443 
28668 
28892 
29115 
29336 
29557 
29776 
29994 

28012 
28240 
28466 
28691 
28914 

28035 
28262 
28488 
28713 
28937 

28058 
28285 
28511 
28735 
28959 

28081 
28307 
28533 
28758 
28981 

26 

24 

1 
2 
3 
4 
5 
6 
7 
8 
9 

3 

5 
8 
10 
13 
15 
18 
20 
23 

2 

5 
7 

10 
12 
14 
17 
19 
22 

195 
196 
197 
198 
199 

29003 
29226 
29447 
29667 
29885 

29026 
29248 
29469 
29688 
29907 

29048 
29270 
29491 
29710 
29929 

29070 
29292 
29513 
29732 
29951 

29092 
29314 
29535 
29754 
29973 

29137 
29358 
29579 
29798 
30016 

29159 
29380 
29601 
29820 
30038 

29181 
29403 
29623 
29842 
30060 

29203 
29425 
29645 
29863 
30081 

200 
201 
202 
203 
204 

30103 
30320 
30535 
30750 
30963 

30125 
30341 
30557 
30771 
30984 

30146 
30363 
30578 
30792 
31006 

30168  1  30190 

30211 
30428 
30643 
30856 
31069 

30233 
30449 
30664 
30878 
31091 

30255 
30471 
30685 
30899 
31112 

30276  j  30298 
QfU.Q9   'incii  A 

30600 
30814 
31027 

30621 
30835 
31048 

30707 
30920 
31133 

30728 
30942 
31154 

28 

22 

1 
2 
3 
4 
6 
6 
7 
8 
9 

2 
5 

7 
9 
12 
14 
16 
18 
21 

2 

4 

7 

9 

11 

13 

15 

18 

20 

205 
206 
207 
208 
209 

31175 
31387 
31597 
31806 
32015 

31197 
31408 
31618 
31827 
32035 

31218 
31429 
31639 
31848 
32056 

31239 
31450 
31660 
31869 
32077 

31260 
31471 
31681 
31890 
32098 
32305 
32510 
32715 
32919 
33122 

31281 
31492 
31702 
31911 
32118 

31302 
31513 
31723 
31931 
32139 

31323 
31534 
31744 
31952 
32160 

31345 
31555 
31765 
31973 
32181 

31366 
31576 
31785 
31994 
32201 

210 
211 
212 
213 
214 

32222 
32428 
32634 
32838 
33041 

32243 
32449 
32654 
32858 
33062 

32263 
32469 
32675 
32879 
33082 

32284 
32490 
32695 
32899 
33102 

32325 
32531 
32736 
32940 
33143 

32346 
32552 
32756 
32960 
33163 

32366 
32572 
32777 
32980 
33183 

32387 
32593 
32797 
33001 
33203 

32408 
32613 
32818 
33021 
33224 

2 
3 
4 
5 
6 
7 
8 
9 

21 

2 

4 

20 

2 

4 

215 
216 
217 
218 
219 

33244 
33445 
33646 
33846 
34044 

33264 
33465 
33666 
33866 
34064 

33284 
33486 
33686 
33885 
34084 

33304 
33506 
33706 
33905 
34104 

33325 
33526 
33726 
33925 
34124 

33345 
33546 
33746 
33945 
34143 

33365 
33566 
33766 
33965 
34163 

33385 
33586 
33786 
33985 
34183 

33405 
33606 
33806 
34005 
34203 

33425 
33626 
33826 
34025 
34223 

6 
8 
11 
13 
15 
17 
19 

6 
8 
10 
12 
14 
16 
18 

No. 

0 

1 

2 

8 

4 

5 

6 

7 

8 

9 

Page  758]                 TABLE  42. 

Logarithms  of  Numbers. 

No.  2200 2800.                                                        Log.  34242 44716. 

No. 

0 

1 

2 

8 

4 

6 

6 

7 

8 

9 

220 
221 
222 
223 
224 

34242 
34439 
34635 
34830 
35025 

34262 
34459 
34655 
34850 
35044 

34282 
34479 
34674 
34869 
35064 

34301 
34498 
34694 
34889 
36083 

34321 
34518 
34713 
34908 
35102 

34341 
34537 
34733 
34928 
35122 

34361 
34557 
34763 
34947 
35141 

34380 
34577 
34772 
34967 
35160 

34400 
34596 
34792 
34986 
35180 

34420 
34616 
34811 
35005 
35199 

1 
2 
3 

4 
5 
6 

7 
8 
9 

20 

2 

4 

6 

8 

10 

12 

14 

16 

18 

225 
226 
227 
228 
229 

35218 
36411 
35603 
35793 
35984 

35238 
35430 
35622 
35813 
36003 

35257 
35449 
35641 
35832 
36021 

35276 
36468 
35660 
35851 
36040 

35295 
35488 
35679 
35870 
36059 

35315 
35507 
35698 
36889 
36078 

35334 
35526 
35717 
36908 
36097 

35363 
35545 
35736 
35927 
36116 

35372 
36664 
35755 
35946 
36135 

35392 
35583 
35774 
35965 
36154 

230 
231 
232 
233 
234 

36173 
36361 
36549 
36736 
36922 

36192 
36380 
36568 
36754 
36940 

36211 
36399 
36586 
36773 
36959 

36229 
36418 
36605 
36791 
36977 

36248 
36436 
36624 
36810 
36996 

36267 
36455 
36642 
36829 
37014 

36286 
36474 
36661 
36847 
37033 

36305 
36493 
36680 
36866 
37051 

36324 
36511 
36698 
36884 
37070 

36342 
36530 
36717 
36903 

37088 

19 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 

4 
6 
8 

10 
11 
13 
16 
17 

235 
236 
237 
238 
239 

37107 
37291 
37475 
37658 
37840 

37125 
37310 
37493 
37676 
37858 

37144 
37328 
37511 
37694 
37876 

37162 
37346 
37530 
37712 
37894 

37181 
37365 
37548 
37731 
37912 

37199 
37383 
37566 
37749 
37931 

37218 
37401 
37586 
37767 
37949 

37236 
37420 
37603 
37785 
37967 

37254 
37438 
37621 
37803 
37985 

37273 
37457 
37639 
37822 
38003 

240 
241 
242 
243 
244 

38021 
38202 
38382 
38561 
38739 

38039 
38220 
38399 
38578 
38757 

38057 
38238 
38417 
38596 
38775 

38075 
38266 
38435 
38614 
38792 

38093 
38274 
38463 
38632 
38810 

38112 
38292 
38471 
38650 
38828 

38130 
38310 
38489 
38668 
38846 

38148 
38328 
38507 
38686 
38863 

38166 
38346 
38625 
38703 
38881 

38184 
38364 
38543 
38721 
38899 

18 

1 
2 
3 

4 
5 
6 

7 
8 
9 

2 

4 

6 

7 

9 

11 

13 

14 

16 

245 
246 
247 
248 
249 

38917 
39094 
39270 
39445 
39620 

38934 
39111 
39287 
39463 
39637 

38952 
39129 
39305 
39480 
39655 

38970 
39146 
39322 
39498 
39672 

38987 
39164 
39340 
39515 
39690 

39005 
39182 
39358 
39533 
39707 

39023 
39199 
39376 
39550 
39724 

39041 
39217 
39393 
39568 
39742 
39915 
40088 
40261 
40432 
40603 

39058 
39235 
39410 
39585 
39759 

39076 
39252 
39428 
39602 
39777 

250 
251 
262 
253 
254 

39794 
39967 
40140 
40312 
40483 

39811 
39985 
40157 
40329 
40500 

39829 
40002 
40175 
40346 
40518 

39846 
40019 
40192 
40364 
40535 

39863 
40037 
40209 
40381 
40652 

39881 
40054 
40226 
40398 
40669 

39898 
40071 
40243 
40415 
40586 

39933 
40106 
40278 
40449 
40620 

39950 
40123 
40296 
40466 
40637 

1 
2 
3 
4 
5 
6 
7 
8 
9 

17 

2 

3 

5 

7 

9 

10 

12 

14 

15 

255 
256 
257 
258 
269 

40654 
40824 
40993 
41162 
41330 

40671 
40841 
41010 
41179 
41347 

40688 
40858 
41027 
41196 
41363 

40705 
40875 
41044 
41212 
41380 

40722 
40892 
41061 
41229 
41397 

40739 
40909 
41078 
41246 
41414 

40766 
40926 
41095 
41263 
41430 

40773 
40943 
41111 
41280 
41447 

40790 
40960 
41128 
41296 
41464 

40807 
40976 
41145 
41313 
41481 

260 
261 
262 
263 
264 

41497 
41664 
41830 
41996 
42160 

41514 
41681 
41847 
42012 
42177 

41531 
41697 
41863 
42029 
42193 

41547 
41714 
41880 
42045 
42210 

41664 
41731 
41896 
42062 
42226 

41581 
41747 
41913 
42078 
42243 

41597 
41764 
41929 
42096 
42259 

41614 
41780 
41946 
42111 
42275 

41631 
41797 
41963 
42127 
42292 

41647 
41814 
41979 
42144 
42308 

16 

1 
2 
3 

4 
5 
6 

7 
8 
9 

2 
3 
5 
6 
8 

10 
11 
13 
14 

265 
266 
267 
268 
269 

42325 
42488 
42651 
42813 
42975 

42341 
42504 
42667 
42830 
42991 

42357 
42521 
42684 
42846 
43008 

42374 
42537 
42700 
42862 
43024 

42390 
42553 
42716 
42878 
43040 

42406 
42570 
42732 
42894 
43056 

42423 
42586 
42749 
42911 
43072 

42439 
42602 
42765 
42927 
43088 

42456 
42619 
42781 
42943 
43104 

42472 
42635 
42797 
42959 
43120 

270 
271 
272 
273 
274 

43136 
43297 
43457 
43616 
43775 

43152 
43313 
43473 
43632 
43791 

43169 
43329 
43489 
43648 
43807 

43185 
43345 
43505 
43664 
43823 

43201 
43361 
43621 
43680 
43838 

43217 
43377 
43537 
43696 
43854 

43233 
43393 
43563 
43712 
43870 

43249 
43409 
43569 
43727 
43886 

43265 
43425 
43584 
43743 
43902 

43281 
43441 
43600 
43759 
43917 

15 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 
3 
5 
6 

8 

9 

11 

12 

14 

275 
276 
277 
278 
279 

43933 
44091 
44248 
44404 
44560 

43949 
44107 
44264 
44420 
44576 

43965 
44122 
44279 
44436 
44592 

43981 
44138 
44295 
44451 
44607 

43996 
44154 
44311 
44467 
44623 

44012 
44170 
44326 
44483 
44638 

44028 
44185 
44342 
44498 
44654 

44044 
44201 
44358 
44514 
44669 

44059 
44217 
44373 
44529 
44685 

44075 
44232 
44389 
44545 
44700 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

TABLE  42.                 [Page  769 
Logarithms  of  Numbers. 

No.  2800 3400.                                                         Log.  44716 53148. 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

» 

1 

280 
281 
282 
283 
284 

44716 
44871 
45025 
45179 
45332 

44731 
44886 
45040 
45194 
45347 

44747 
44902 
45056 
45209 
45362 

44762 
44917 
45071 
45225 
45378 

44778 
44932 
45086 
45240 
45393 

44793 

44948 
45102 
45255 
45408 

44809 
44963 
45117 
45271 
45423 

44824 
44979 
45133 
45286 
45439 

44840 
44994 
45148 
45301 
45454 

44855 
46010 
45163 
46317 
45469 

16 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 
3 
5 
6 
8 

10 
11 
13 
14 

285 
286 
287 
288 
289 

45484 
45637 
45788 
45939 
46090 

45500 
45652 
45803 
45954 
46105 

46515 
45667 
45818 
45969 
46120 

45530 
45682 
45834 
45984 
46135 

45545 
45697 
45849 
46000 
46150 

45561 
45712 
45864 
46015 
46165 

45576 
45728 
45879 
46030 
46180 

45591 
45743 
45894 
46045 
46195 

45606 
45758 
45909 
46060 
46210 

46621 
45773 
45924 
46075 
46225 

290 
291 
292 
293 
294 

46240 
46389 
46538 
46687 
46835 

46255 
46404 
46553 
46702 
46850 

46270 
46419 
46568 
46716 
46864 

46285 
46434 
46583 
46731 
46879 

46300 
46449 
46598 
46746 
46894 

46315 
46464 
46613 
46761 
46909 

46330 
46479 
46627 
46776 
46923 

46345 
46494 
46642 
46790 
46938 

46359 
46509 
46657 
46805 
46953 

46374 
46523 
46672 
46820 
46967 
47114 
47261 
47407 
47553 
47698 

1 

15 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 
3 
5 

I 

9 
11 
12 
14 

295 
296 
297 
298 
299 

46982 
47129 
47276 
47422 
47567 

46997 
47144 
47290 
47436 
47582 

47012 
47159 
47305 
47451 
47596 

47026 
47173 
47319 
47465 
47611 

47041 
47188 
47334 
47480 
47625 

47056 
47202 
47349 
47494 
47640 

47070 
47217 
47363 
47509 
47654 

47085 
47232 
47378 
47524 
47669 

47100 
47246 
47392 
47538 
47683 

300 
301 
302 
303 
304 

47712 
47857 
48001 
48144 
48287 

47727 
47871 
48015 
48159 
48302 

47741 
47885 
48029 
48173 
48316 

47756 
47900 
48044 
48187 
48330 

47770 
47914 
48058 
48202 
48344 

47784 
47929 
48073 
48216 
48359 

47799 
47943 
48087 
48230 
48373 

47813 
47958 
48101 
48244 
48387 

47828 
47972 
48116 
48259 
48401 

47842 
47986 
48130 
48273 
48416 

1 

305 
306 
307 
308 
309 

48430 
48572 
48714 
48855 
48996 

48444 
48586 
48728 
48869 
49010 

48458 
48601 
48742 
48883 
49024 

48473 
Aatn  K 

48487 

48501 
48643 
48785 
48926 
49066 

48515 
48657 
48799 
48940 
49080 

48530 
48671 
48813 
48954 
49094 
49234 
49374 
49513 
49651 
49790 

48544 
48686 
48827 
48968 
49108 

48558 
48700 
48841 
48982 
49122 
49262 
49402 
49541 
49679 
49817 

14 

48756   48770 
48897   48911 
49038   49052 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 

3 
4 
6 
7 
8 

10 
11 
13 

310 
311 
312 
313 
314 

49136 
49276 
49415 
49554 
49693 

49150 
49290 
49429 
49568 
49707 

49164 
49304 
49443 
49582 
49721 

49178 
49318 
49457 
49596 
49734 

49192 
49332 
49471 
49610 
49748 

49206 
49346 
49485 
49624 
49762 

49220 
49360 
49499 
49638 
49776 

49248 
49388 
49527 
49665 
49803 

315 
316 
317 
318 
319 

49831 
49969 
50106 
50243 
50379 

49845 
49982 
50120 
50256 
50393 

49859 
49996 
50133 
50270 
50406 

49872 
50010 
50147 
50284 
50420 

49886 
50024 
50161 
50297 
50433 
50569 
50705 
50840 
50974 
51108 

49900 
50037 

49914 

soa^ii 

49927 
50065 
50202 
50338 
50474 

49941 
50079 
50215 
50352 
50488 

49955 
50092 
50229 
50365 
50501 
50637 
50772 
50907 
51041 
61175 

50174  i  50188 
50311  i  50325 
50447  i  50461 

1 

IS 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
3 
4 
5 
7 
8 
9 
10 
12 

320 
321 
322 
323 
324 

50515 
50651 
50786 
50920 
51055 

50529 
50664 
50799 
50934 
51068 

50542 
50678 
50813 
50947 
51081 

50556 
50691 
50826 
50961 
51095 

50583  1  50596 
50718   50732 
50853   50866 
50987   51001 
51121   51135 

50610 
50745 
50880 
51014 
51148 

50623 
50759 
50893 
51028 
51162 

325 
326 
327 
328 
329 

51188 
51322 
51455 
51587 
51720 

51202 
51335 
51468 
51601 
51733 

51215 
51348 
51481 
51614 
51746 

51228 
51362 
51495 
51627 
51759 

51242 
51375 
51508 
51640 
51772 

51255 
51388 
51521 
51654 
51786 

51268 
51402 
51534 
51667 
51799 

51282 
51415 
51548 
51680 
51812 

51295 
51428 
51561 
51693 
51825 

51308 
51441 
61574 
51706 
51838 

1 

330 
331 
332 
333 
634 

51851 
51983 
52114 
52244 
52375 

51865 
51996 
52127 
52257 
52388 

51878 
52009 
52140 
52270 
52401 

51891 
52022 
52153 
52284 
52414 

51904 
52035 
52166 
52297 
52427 

51917 
52048 
52179 
52310 
52440 

51930 
52061 
52192 
52323 
52453 

51943 
52075 
52205 
52336 
52466 

51957 
52088 
52218 
52349 
52479 

51970 
52101 
52231 
52362 
52492 

12 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
4 
5 
6 
7 
8 
10 
11 

335 
336 
337 
338 
339 

52504 
52634 
52763 
52892 
53020 

52517 
52647 
52776 
52905 
53033 

52530 
52660 
52789 
52917 
53046 

52543 
52673 
52802 
52930 
53058 

52556 
52686 
52815 
52943 
53071 

52569 
52699 
52827 
52956 
53084 

52582 
52711 
52840 
52969 
53097 

52595 
52724 
52853 
52982 
53110 

52608 
52737 
52866 
52994 
53122 

52621 
52750 
52879 
53007 
53135 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Page  760]                 TABLE  42. 

Logarithms  of  Numbers. 

No.  3400 1000.                                                           Log.  53148 60206. 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

340 
341 
342 
343 
344 

53148 
53275 
53403 
53529 
53656 

53161 
53288 
53415 
53542 
53668 

53173 
53301 
53428 
53556 
53681 

53186 
53314 
53441 
53567 
53694 

63199 
63326 
63453 
53580 
53706 

53212 
53339 
63466 
63693 
63719 

53224 
53362 
63479 
63606 
63732 

63237 
63364 
53491 
53618 
53744 

63260 
63377 
53604 
63631 
53757 

63263 
53390 
53617 
53643 
63769 
53895 
54020 
54145 
54270 
54394 

13 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
3 
4 
5 
7 
8 
9 
10 
12 

345 
346 
347 
348 
349 

53782 
53908 
54033 
54158 
54283 

63794 
53920 
54045 
54170 
54295 

53807 
63933 
54058 
54183 
54307 

53820 
53945 
54070 
64195 
54320 

53832 
53958 
54083 
64208 
54332 

53845 
53970 
54095 
54220 
54346 

53867 
63983 
54108 
54233 
64357 

53870 
53996 
64120 
54245 
54370 

53882 
64008 
54133 
54258 
54382 

350 
351 
352 
353 
364 

54407 
54531 
54654 
54777 
54900 

54419 
54543 
54667 
54790 
54913 

64432 
64555 
64679 
64802 
64925 

64444 
54568 
54691 
64814 
54937 

54456 
54680 
54704 
54827 
64949 

64469 
64693 
64716 
54839 
54962 

54481 
64606 
54728 
54861 
54974 

54494 
54617 
54741 
54864 
64986 

54506 
54630 
64753 
54876 
54998 

54518 
54642 
54765 
54888 
55011 

355 
356 
357 
358 
359 

55023 
55145 
55267 
55388 
55509 

55035 
55157 
55279 
55400 
55522 

55047 
55169 
65291 
56413 
56634 

55060 
56182 
66303 
55425 
65646 

55072 
56194 
55315 
55437 
65558 

55084 
66206 
55328 
55449 
66570 

55096 
55218 
55340 
56461 
55582 

55108 
66230 
55352 
55473 
55594 

55121 
55242 
56364 
55486 
55606 

56133 
55255 
55376 
55497 
55618 

12 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
4 
5 
6 
7 
8 
10 
11 

360 
361 
362 
363 
364 

55630 
55751 
55871 
55991 
56110 

55642 
55763 
65883 
56003 
66122 

55664 
55776 
55895 
56016 
66134 

55666 
56787 
55907 
56027 
66146 

55678 
55799 
55919 
56038 
56158 

66691 
55811 
56931 
56050 
56170 

55703 
55823 
55943 
66062 
56182 

55715 
55835 
55955 
56074 
56194 

55727 

55847 
55967 
56086 
66205 

55739 
55859 
55979 
56098 
56217 

365 
366 
367 
368 
369 

56229 
56348 
56467 
56585 
56703 

56241 
56360 
56478 
56697 
66714 

56253 
56372 
56490 
56608 
56726 

66265 
56384 
56502 
56620 
56738 

56277 
56396 
56514 
56632 
66760 

66289 
66407 
56626 
66644 
56761 

56301 
56419 
56538 
56666 
66773 

66312 
56431 
66649 
66667 
56785 

56324 
56443 
56561 
56679 
56797 

56336 
56456 
56573 
56691 
56808 

370 
371 
372 
373 
374 

56820 
56937 
57054 
57171 
57287 

66832 
56949 
57066 
57183 
57299 

66844 
66961 
57078 
67194 
67310 

66856 
66972 
57089 
57206 
67322 

56867 
56984 
67101 
67217 
57334 

56879 
56996 
57113 
67229 
57346 

56891 
67008 
67124 
57241 
67357 

56902 
57019 
57136 
57262 
57368 

56914 
57031 
57148 
57264 
67380 

56926 
57043 
67159 
57276 
57392 

!  " 

1 

2 
3 

4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
6 
7 
8 
9 
10 

375 
376 
377 
378 
379 

57403 
57519 
57634 
57749 
57864 

57415 
57530 
57646 
57761 
57876 

67426 
57542 
67667 
67772 
57887 

67438 
67553 
57669 

57784 
57898 

57449 
57565 
67680 
57796 
57910 

57461 
67676 
67692 
57807 
57921 

67473 
57588 
57703 
57818 
57933 

57484 
57600 
57715 
57830 
57944 

67496 
57611 
57726 
57841 
57965 

57507 
57623 
67738 
67852 
57967 

380 
381 
382 
383 
384 

57978 
58092 
58206 
58320 
58433 

67990 
58104 
58218 
68331 
68444 

58001 
68116 
58229 
58343 
58466 

58013 
68127 
68240 
58354 
58467 

58024 
58138 
58262 
68365 
58478 

58036 
58149 
58263 
58377 
68490 

68047 
68161 

58274 
58388 
68501 

58058 
58172 
68286 
58399 
58512 

58070 
58184 
58297 
58410 
58524 

68081 
58195 
58309 
58422 
58535 

'  385 
386 
387 
388 
389 

58546 
58659 
58771 
58883 
58995 

58657 
68670 
58782 
58894 
59006 

58569 
68681 
58794 
68906 
69017 

58580 
58692 
58806 
58917 
69028 

68591 
58704 
58816 
68928 
69040 

68602 
58715 
68827 
58939 
69051 

58614 
58726 
58838 
58950 
69062 
69173 
69284 
59395 
59506 
59616 

58625 
58737 
58850 
68961 
59073 
59184 
59295 
69406 
59617 
59627 
59737 
59846 
69956 
60065 
60173 

58636 
68749 
68861 
58973 
59084 

58647 
68760 
58872 
58984 
59095 

10 

390 
391 
392 
393 
394 

59106 
59218 
59329 
59439 
69550 

59118 
59229 
69340 
69450 
59561 

69129 
69240 
69351 
59461 
59572 

59140 
59261 
69362 
59472 
69683 

59161 
59262 
69373 
69483 
69594 

69162 
69273 
59384 
59494 
59605 

59195 
59306 
59417 
59528 
59638 

69207 
69318 
69428 
59639 
59649 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 

2 

3 

4* 

6 

6 

7 

8 

9 

395 
396 
397 
398 
399 

59660 
59770 
59879 
59988 
60097 

59671 
59780 
59890 
59999 
60108 

59682 
59791 
69901 
60010 
60119 

59693 
59802 
59912 
60021 
60130 

59704 
59813 
69923 
60032 
60141 

59715 
69824 
69934 
60043 
60152 

59726 
59836 
59946 
60054 
60163 

69748 
59857 
69966 
60076 
60184 

59759 
59868 
69977 
60086 
60195 

No. 

0 

1 

2 

8 

4 

6 

6 

7 

8 

9 

1 

TABLE  42.                 [Page  761 
Logarithms  of  Numbers. 

No.  4000 4600.                                                         Log.  60206 66276. 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

400 
401 
402 
403 
404 

60206 
60314 
60423 
60531 
60638 

60217 
60325 
60433 
60541 
60649 

60228 
60336 
60444 
60552 
60660 

60239 
60347 
60455 
60563 
60670 

60249 
60358 
60466 
60574 
60681 

60260 
60369 
60477 
60584 
60692 

60271 
60379 
60487 
60596 
60703 

60282 
60390 
60498 
60606 
60713 

60293 
60401 
60509 
60617 
60724 

60304 
60412 
60520 
60627 
60736 
60842 
60949 
61055 
61162 
61268 

11 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
6 
7 
8 
9 
10 

405 
406 
407 
408 
409 
410 
411 
412 
413 
414 

60746 
60853 
60959 
61066 
61172 
61278 
61384 
61490 
61595 
61700 

60756 
60863 
60970 
61077 
61183 

60767 
60874 
60981 
61087 
61194 

60778 
60885 
60991 
61098 
61204 

60788 
60895 
61002 
61109 
61215 

60799 
60906 
61013 
61119 
61225 

60810 
60917 
61023 
61130 
61236 

60821 
60927 
61034 
61140 
61247 

60831 
60938 
61045 
61151 
61257 

61289 
61395 
61500 
61606 
61711 

61300 
61405 
61511 
61616 
61721 

61310 
61416 
61521 
61627 
61731 

61321 
61426 
61532 
61687 
61742 

61331 
61437 
61542 
61648 
61752 

61342 
61448 
61563 
61668 
61763 
61868 
61972 
62076 
62180 
62284 

61362 
61458 
61663 
61669 
61773 

61363 
61469 
61574 
61679 
61784 

61374 
61479 
61584 
61690 
61794 

415 
416 
417 
418 
419 

61805 
61909 
62014 
62118 
62221 

61815 
61920 
62024 
62128 
62232 

61826 
61930 
62034 
62138 
62242 

61836 
61941 
62045 
62149 
62252 

61847 
61951 
62065 
62159 
62263 

61857 
61962 
62066 
62170 
62273 

61878 
61982 
62086 
62190 
62294 

61888 
61993 
62097 
62201 
62304 

61899 
62003 
62107 
62211 
62315 

420 
421 
422 
423 
424 

62325 
62428 
62531 
62634 
62737 

62335 
62439 
62542 
62644 
62747 

62346 
62449 
62552 
62655 
62757 

62356 
62459 
62562 
62665 
62767 

62366 
62469 
62572 
62675 
62778 
62880 
62982 
63083 
63185 
63286 
63387 
63488 
63589 
63689 
63789 

62377 
62480 
62583 
62685 
62788 

62387 
62490 
62693 
62696 
62798 

62397 
62500 
62603 
62706 
62808 

62408 
62511 
62613 
62716 
62818 

62418 
62521 
62624 
62726 
62829 
62931 
63033 
63134 
63236 
63337 
63438 
63538 
63639 
63739 
63839 

10 

425 
426 
427 
428 
429 

62839 
62941 
63043 
63144 
63246 

62849 
62951 
63053 
63155 
63256 

62869 
62961 
63063 
63165 
63266 

62870 
62972 
63073 
63175 
63276 

62890 
62992 
63094 
63196 
63296 

62900 
63002 
63104 
63206 
63306 

62910 
63012 
63114 
63215 
63317 
63417 
63618 
63619 
63719 
63819 

62921 
63022 
63124 
63225 
63327 
63428 
63528 
63629 
63729 
63829 
63929 
64028 
64128 
64227 
64326 

1 
2 
3 
4 
6 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

430 
431 
432 
433 
434 

63347 
63448 
63548 
63649 
63749 

63357 
63458 
63558 
63659 
63759 

63367 
63468 
63568 
63669 
63769 

63377 
63478 
63579 
63679 
63779 

63397 
63498 
63599 
63699 
63799 

63407 
63508 
63609 
63709 
63809 

435 
436 
437 
438 
439 

63849 
63949 
64048 
64147 
64246 

63859 
63959 
64058 
64157 
64256 

63869 
63969 
64068 
64167 
64266 

63879  1  63889 

63899 
63998 
64098 
64197 
64296 

63909 
64008 
64108 
64207 
64306 

63919 
64018 
64118 
64217 
64316 

63939 
64038 
64137 
64237 
64336 

63979 
64078 
64177 
64276 

63988 
64088 
64187 
64286 

440 
441 
442 
443 
444 

64345 
64444 
64542 
64640 
64738 

64355 
64454 
64552 
64650 
64748 

64365 
64464 
64562 
64660 
64758 

64375 
64473 
64572 
64670 
64768 
64865 
64963 
65060 
65157 
65254 

64385 
64483 
64582 
64680 
64777 

64395 
64493 
64591 
64689 
64787 

64404 
64503 
64601 
64699 
64797 

64414 
64613 
64611 
64709 
64807 

64424 
64523 
64621 
64719 
64816 

64434 
64632 
64631 
64729 
64826 

445 
446 

447 
448 
449 

64836 
64933 
65031 
65128 
65225 

64846 
64943 
65040 
65137 
65234 

64856 
64953 
65050 
65147 
65244 

64875 
64972 
65070 
65167 
65263 

64885 
64982 
65079 
66176 
65273 

6*895 
64992 
65089 
65186 
66283 

6*904 
66002 
65099 
65196 
65292 

64914 
66011 
65108 
65206 
66302 
65398 
65495 
65591 
65686 
66782 

64924 
66021 
66118 
65216 
66312 

9 

450 
451 
452 
453 
454 

65321 
65418 
65514 
65610 
65706 

65331 
65427 
65523 
65619 
65715 

65341 
65437 
65533 
65629 
65725 

65350 
65447 
65543 
65639 
65734 

65360 
65456 
65552 
65648 
65744 

65369 
65466 
65562 
65658 
65763 

65379 
66475 
65571 
65667 
66763 

66389 
65485 
65681 
66677 
65772 

65408 
65604 
65600 
65696 
66792 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
6 
7 
8 

455 
456 
457 
458 
459 

65801 
65896 
65992 
66087 
66181 

65811 
65906 
66001 
66096 
66191 

65820 
65916 
66011 
66106 
66200 

65830 
65925 
66020 
66115 
66210 

66839 
66935 
66030 
66124 
66219 

65849 
65944 
66039 
66134 
66229 

65858 
66964 
66049 
66143 
66238 

66868 
65963 
66058 
66163 
66247 

65877 
65973 
66068 
66162 
66257 

66887 
65982 
66077 
66172 
66266 

No. 

0 

1 

i 

3 

4 

6 

« 

7 

8 

9 

1 

Page  762]                 TABLE  42. 

Logarithms  of  Numbers. 

No.  4600 6200.                                                            Log.  66276 ^71600. 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

460 
461 
462 
463 
464 

66276 
66370 
66464 
66558 
66652 

66285 
66380 
66474 
66567 
66661 

66295 
66389 
66483 
66577 
66671 

66304 
66398 
66492 
66586 
66680 

66314 
66408 
66502 
66596 
66689 

66323 
66417 
66511 
66605 
66699 

66332 
66427 
66521 
66614 
66708 

66342 
66436 
66530 
66624 
66717 

66361 
66445 
66539 
66633 
66727 

66361 
66465 
66549 
66642 
66736 

10 

1 
2 
3 
4 
6 
6 
7 
8 
9 

1 

2 
3 

4 
6 
6 

7 
8 
9 

465 
466 
467 
468 
469 

66745 
66839 
66932 
67025 
67117 

66755 
66848 
66941 
67034 
67127 

66764 
66857 
66950 
67043 
67136 

66773 
66867 
66960 
67052 
67145 

66783 
66876 
66969 
67062 
67154 

66792 
66885 
66978 
67071 
67164 

66801 
66894 
66987 
67080 
67173 

66811 
66904 
66997 
67089 
67182 

66820 
66913 
67006 
67099 
67191 

66829 
66922 
67015 
67108 
67201 

470 
471 
472 
473 
474 

67210 
67302 
67394 
67486 
67578 

67219 
67311 
67403 
67495 
67587 

67228 
67321 
67413 
67504 
67596 

67237 
67330 
67422 
67514 
67605 

67247 
67339 
67431 
67523 
67614 

67256 
67348 
67440 
67532 
67624 

67265 
67357 
67449 
67541 
67633 
67724 
67815 
67906 
67997 
68088 

67274 
67367 
67469 
67550 
67642 

67284 
67376 
67468 
67560 
67651 

67293 
67385 
67477 
67669 
67660 

475 
476 
477 
478 
479 

67669 
67761 
67852 
67943 
68034 

67679 
67770 
67861 
67952 
68043 

67688 
67779 
67870 
67961 
68052 

67697 
67788 
67879 
67970 
68061 

67706 
67797 
67888 
67979 
68070 

67715 
67806 
67897 
67988 
68079 

67733 
67826 
67916 
68006 
68097 

67742 
67834 
67925 
68015 
68106 

67762 
67843 
67934 
68024 
68115 

480 
481 
482 
483 
484 

68124 
68215 
68305 
68395 
68485 

68133 
68224 
68314 
68404 
68494 
68583 
68673 
68762 
68851 
68940 

68142 
68233 
68323 
68413 
68502 

68151 
68242 
68332 
68422 
68511 

68160 
68251 
68341 
68431 
68620 

68169 
68260 
68350 
68440 
68529 

68178 
68269 
68369 
68449 
68538 

68187 
68278 
68368 
68468 
68647 
68637 
68726 
68816 
68904 
68993 

68196 
68287 
68377 
68467 
68556 

68205 
68296 
68386 
68476 
68565 

9 

485 
486 
487 
488 
489 

68574 
68664 
68753 
68842 
68931 

68592 
68681 
68771 
68860 
68949 

68601 
68690 
68780 
68869 
68958 

68610 
68699 
68789 
68878 
68966 

68619 
68708 
68797 
68886 
68975 

68628 
68717 
68806 
68895 
68984 

68646 
68736 
68824 
68913 
69002 

68656 
68744 
68833 
68922 
69011 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
6 
5 
6 
7 
8 

490 
491 
492 
493 
494 

69020 
69108 
69197 
69285 
69373 

69028 
69117 
69205 
69294 
69381 

69037 
69126 
69214 
69302 
69390 

69046 
69135 
69223 
69311 
69399 

69055 
69144 
69232 
69320 
69408 

69064 
69152 
69241 
69329 
69417 

69073 
69161 
69249 
69338 
69425 

69082 
69170 
69268 
69346 
69434 

69090 
69179 
69267 
69366 
69443 

69099 
69188 
69276 
69364 
69452 

495 
496 
497 
498 
499 

69461 
69548 
69636 
69723 
69810 

69469 
69557 
69644 
69732 
69819 

69478 
69566 
69653 
69740 
69827 

69487 
69574 
69662 
69749 
69836 

69496 
69583 
69671 
69758 
69845 

69504 
69592 
69679 
69767 
69854 

69513 
69601 
69688 
69775 
69862 

69622 
69609 
69697 
69784 
69871 

69631 
69618 
69706 
69793 
69880 

69539 
69627 
69714 
69801 
69888 

500 
501 
502 
503 
504 

69897 
69984 
70070 
70157 
70243 

69906 
69992 
70079 
70165 
70252 

69914 
70001 
70088 
70174 
70260 

69923 
70010 
70096 
70183 
70269 

69932 
70018 
70105 
70191 
70278 

69940 
70027 
70114 
70200 
70286 

69949 
70036 
70122 
70209 
70296 

69958 
70044 
70131 
70217 
70303 

69966 
70053 
70140 
70226 
70312 

69976 
70062 
70148 
70234 
70321 

505 
506 
507 
508 
509 

70329 
70415 
70501 
70586 
70672 

70338 
70424 
70509 
70595 
70680 

70346 
70432 
70518 
70603 
70689 

70355 
70441 
70526 
70612 
70697 

70364 
70449 
70535 
70621 
70706 

70372 
70458 
70544 
70629 
70714 

70381 
70467 
70552 
70638 
70723 

70389 
70475 
70561 
70646 
70731 

70398 
70484 
70669 
70666 
70740 

70406 
70492 
70578 
70663 
70749 

8 

510 
511 
512 
513 
514 

70757 
70842 
70927 
71012 
71096 

70766 
70851 
70935 
71020 
71105 

70774 
70859 
70944 
71029 
71113 

70783 
70868 
70952 
71037 
71122 

70791 
70876 
70961 
71046 
71130 

70800 
70885 
70969 
71054 
71139 

70808 
70893 
70978 
71063 
71147 

70817 
70902 
70986 
71071 
71155 

70825 
70910 
70995 
71079 
71164 

70834 
70919 
71003 
71088 
71172 

1 
2 
3 

4 
6 
6 

7 
8 
9 

1 
2 
2 
3 
4 
5 
6 
6 
7 

515 
516 
517 
518 
519 

71181 
71265 
71349 
71433 
71517 

71189 
71273 
71357 
71441 
71525 

71198 
71282 
71366 
71450 
71533 

71206 
71290 
71374 
71458 
71542 

71214 
71299 
71383 
71466 
71550 

71223 
71307 
71391 
71475 
71559 

71231 
71315 
71399 
71483 
71567 

71240 
71324 
71408 
71492 
71575 

71248 
71332 
71416 
71500 
71684 

71267 
71341 
71426 
71608 
71592 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

TABLE  42. 

[Page  763  | 

Logarithms  of  Numbera. 

No 

5200 6800. 

Log.  71600 ^76343.    1 

No. 

0 

.  1 

2 

s 

4 

5 

6 

7 

8 

9 

1 

520 
521 

71600 
71684 

71609 
71692 

71617 
71700 

71625 
71709 

71634 

71717 

71642 
71725 

71650 

71734 

71659 
71742 

71667 
71750 

71675 
71759 

9 

522 

71767 

71775 

71784 

71792 

71800 

71809 

71817 

71825 

71834 

71842 

1 

1 

523 

71850 

71858 

71867 

71875 

71883 

71892 

71900 

71908 

71917 

71925 

2 

2 

524 

71933 

71941 

71950 

71958 

71966 

71975 

71983 

71991 

71999 

72008 

3 
4 
5 
6 

7 
8 
9 

3 

4 
5 
5 
6 
7 
8 

525 

72016 

72024 

72032 

72041 

72049 

72057 

72066 

72074 

72082 

72090 

526 

72099 

72107 

72115 

72123 

72132 

72140 

72148 

72156 

72165 

72173 

527 

72181 

72189 

72198 

72206 

72214 

72222 

72230 

72239 

72247 

72255 

528 

72263 

72272 

72280 

72288 

72296 

72304 

72313 

72321 

72329 

72337 

529 
530 

72346 

72354 

72362 

72370 

72378 

72387 

72395 

72403 

72411 
72493 

72419 

72428 

72436 

72444 

72452 

72460 

72469 

72477 

72485 

72501 

531 

72509 

72518 

72526 

72534 

72542 

72550 

72558 

72567 

72575 

72583 

532 

72591 

72599 

72607 

72616 

72624 

72632 

72640 

72648 

72656 

72665 

533 

72673 

72681 

72689 

72697 

72705 

72713 

72722 

72730 

72738 

72746 

534 

72754 
72835 

72762 

72770 

72779 

72787 

72795 

72803 

72811 

72819 
72900 

72827 
72908 

535 

72843 

72852 

72860 

72868 

72876 

72884 

72892 

536 

72916 

72925 

72933 

72941 

72949 

72957 

72965 

72973 

72981 

72989 

537 

72997 

73006 

73014 

73022 

73030 

73038 

73046 

73054 

73062 

73070 

538 

73078 

73086 

73094 

73102 

73111 

73119 

73127 

73135 

73143 

73151 

539 

73159 

73167 

73175 

73183 

73191 

73199 

73207 

73215 

73223 
73304 

73231 

540 

73239 

73247 

73255 

73263 

73272 

73280 

73288 

73296 

73312 

541 

73320 

73328 

73336 

73344 

73352 

73360 

73368 

73376 

73384 

73392 

542 

73400 

73408 

73416 

73424 

73432 

73440 

73448 

73456 

73464 

73472 

543 
544 

73480 
73560 

73488 
73568 

73496 
73576 

73504 
73584 

73512 
73592 

73520 
73600 

73528 
73608 

73636 
73616 

73644 
73624 

73652 
73632 

8 

545 
546 

73640 
73719 

73648 
73727 

73656 
73735 

73664 
73743 

73672 
73751 

73679 
73759 

73687 
73767 

73695 
73775 

73703 
73783 

73711 
73791 

1 
2 

1 

547 

73799 

73807 

73815 

73823 

73830 

73838 

73846 

73854 

73862 

73870 

2 

548 

73878 

73886 

73894 

73902 

73910 

73918 

73926 

73933 

73941 

73949 

3 
4 
5 

2 

549 

73957 

73965 

73973 

73981 

73989 

73997 

74005 

74013 

74020 

74028 

3 
4 

550 

74036 

74044 

74052 

74060 

74068 

74076 

74084 

74092 

74099 

74107 

551 

74115 

74123 

74131 

74139 

74147 

74155 

74162 

74170 

74178 

74186 

6 

5 

552 

74194 

74202 

74210 

74218 

74225 

74233 

74241 

74249 

74257 

74265 

7 

6 

553 

74273 

74280 

74288 

74296 

74304 

74312 

74320 

74327 

74335 

74343 

8 

6 

554 

74351 

74359 

74367 

74374 

74382 

74390 

74398 

74406 

74414 

74421 

9 

7 

555 
556 

74429 
74507 

74437 
74515 

74445 
74523 

74453 
74531 

74461 
74539 

74468 
74547 

74476 
74554 

74484 
74562 

74492 
74570 

74500 
74578 

557 

74586 

74593 

74601 

74609 

74617 

74624 

74632 

74640 

74648 

74666 

558 

74663 

74671 

74679 

74687 

74695 

74702 

74710 

74718 

74726 

74733 

559 

74741 

74749 

74757 

74764 

74772 

74780 

74788 

74796 

74803 

74811 
74889 

560 

74819 

74827 

74834 

74842 

74850 

74858 

74865 

74873 

74881 

561 

74896 

74904 

74912 

74920 

74927 

74935 

74943 

74950 

74958 

74966 

562 

74974 

74981 

74989 

74997 

75005 

75012 

75020 

75028 

75035 

75043 

563 

75051 

75059 

75066 

75074 

75082 

75089 

75097 

75105 

75113 

75120 

564 

75128 

75136 

75143 

75151 

75159 

75166 

75174 

75182 
75259 

75189 
75266 

75197 

565 

75205 

75213 

75220 

75228 

75236 

75243 

75251 

75274 

566 

75282 

75289 

75297 

75305 

75312 

75320 

75328 

75335 

75343 

75351 

567 

75358 

75366 

75374 

75381 

75389 

75397 

75404 

75412 

75420 

75427 

568 
569 
570 

75435 
75511 

75442 
75519 

75450 
75526 

75458 
75534 

75465 
75542 

75473 
75549 

75481 
75557 

75488 
75565 

75496 
75572 

75504 
75580 

7 

75587 

75595 

75603 

75610 

75618 

75626 

75633 

75641 

75648 

75656 

571 

75664 

75671 

75679 

75686 

75694 

75702 

75709 

75717 

75724 

75732 

1 

1 

572 

75740 

75747 

75755 

75762 

75770 

75778 

75785 

75793 

75800 

75808 

?, 

1 

573 

75815 

75823 

75831 

75838 

75846 

75853 

75861 

75868 

75876 

75884 

3 

2 

574 

75891 

75899 

75906 

75914 

75921 

75929 

75937 

75944 

75952 

75959 
76035 

4 
5 

3 

4 

575 

75967 

75974 

75982 

75989 

75997 

76005 

76012 

76020 

76027 

576 

76042 

76050 

76057 

76065 

76072 

76080 

76087 

76095 

76103 

76110 

6 

4 

577 

76118 

76125 

76133 

76140 

76148 

76155 

76163 

76170 

76178 

76185 

7 

5 

578 

76193 

76200 

76208 

76215 

76223 

76230 

76238 

76245 

76253 

76260 

8 

6 

579 

76268 

76275 

76283 

76290 

76298 

76305 

76313 

76320 

76328 

76335 

9 

6 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

21594°— 14 41 


Page  764] 

TABLE  42. 

Logarithms  of  Numbers. 

No. 

5800 6400. 

Log.  76343 60618.   j 

No. 

580 

581 
582 
583 
584 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

76343 

76418 
76492 
76567 
76641 

76350 
76425 
76500 
76574 
76649 

76358 
76433 
76507 
76582 
76656 

76365 
76440 
76515 
76589 
76664 

76373 

76448 
76522 
76597 
76671 

76380 
76455 
76530 
76604 
76678 

76388 
76462 
76537 
76612 
76686 

76395 
76470 
76545 
76619 
76693 

76403 
76477 
76552 
76626 
76701 
76775 
76849 
76923 
76997 
77070 

76410 
76485 
76559 
76634 
76708 

8 

1 
2 
3 
4 
6 
6 
7 
8 
9 

1 
2 
2 
3 
4 
5 
6 
6 
7 

585 
586 
587 
588 
589 

76716 
76790 
76864 
76938 
77012 

76723 
76797 
76871 
76945 
77019 

76730 
76805 
76879 
76953 
77026 

76738 
76812 
76886 
76960 
77034 

76745 
76819 
76893 
76967 
77041 

76753 
76827 
76901 
76975 
77048 

76760 
76834 
76908 
76982 
77056 

76768 
76842 
76916 
76989 
77063 

76782 
76856 
76930 
77004 
77078 

590 
591 
592 
593 
594 

77085 
77159 
77232 
77305 
77379 

77093 
77166 
77240 
77313 
77386 

77100 
77173 
77247 
77320 
77393 

77107 
77181 
77254 
77327 
77401 

77115 
77188 
77262 
77335 
77408 

77122 
77195 
77269 
77342 
77415 

77129 
77203 
77276 
77349 
77422 

77137 
77210 
77283 
77357 
77430 

77144 
77217 
77291 
77364 
77437 

77151 
77225 
77298 
77371 
77444 

595 
596 
597 
598 
599 

77452 
77525 
77597 
77670 
77743 

77459 
77532 
77605 
77677 
77750 

77466 
77539 
77612 
77685 

77757 

77474 
77546 
77619 
77692 
77764 

77481 
77554 
77627 
77699 

77772 

77488 
77561 
77634 
77706 
77779 

77495 
77568 
77641 
77714 
77786 

77503 
77576 
77648 
77721 
77793 

77510 
77583 
77656 
77728 
77801 

77517 
77590 
77663 
77735 
77808 
77880 
77952 
78025 
78097 
78168 

600 
601 
602 
603 
604 
605 
606 
607 
608 
609 

77815 
77887 
77960 
78032 
78104 

77822 
77895 
77967 
78039 
78111 

77830 
77902 
77974 
78046 
78118 

77837 
77909 
77981 
78053 
78125 

77844 
77916 
77988 
78061 
78132 

77851 
77924 
77996 
78068 
78140 

77859 
77931 
78003 
78075 
78147 

77866 
77938 
78010 
78082 
78154 

77873 
77945 
78017 
78089 
78161 

1 
2 
3 
4 
5 
6 
7 
8 
9 

7 

78176 
78247 
78319 
78390 
78462 

78183 
78254 
78326 
78398 
78469 

78190 
78262 
78333 
78405 
78476 
78547 
78618 
78689 
78760 
78831 

78197 
78269 
78340 
78412 
78483 

78204 
78276 
78347 
78419 
78490 

78211 
78283 
78355 
78426 
78497 

78219 
78290 
78362 
78433 
78504 

78226 
78297 
78369 
78440 
78612 

78233 
78305 
78376 
78447 
78519 

78240 
78312 
78383 
78455 
78526 

1 
1 
2 
3 
4 
4 
5 
6 
6 

610 
611 
612 
613 
614 

78533 
78604 
78675 
78746 
78817 

78540 
78611 
78682 
78753 
78824 

78554 
78625 
78696 
78767 
78838 

78561 
78633 
78704 
78774 
78845 

78569 
78640 
78711 
78781 
78852 

78676 
78647 
78718 
78789 
78859 

78583 
78654 
78725 
78796 
78866 

78590 
78661 
78732 
78803 
78873 

78597 
78668 
78739 
78810 
78880 
78951 
79021 
79092 
79162 
79232 

615 
616 
617 
618 
619 

78888 
78958 
79029 
79099 
79169 

78895 
78965 
79036 
79106 
79176 

78902 
78972 
.79043 
79113 
79183 

78909 
78979 
79050 
79120 
79190 

78916 
78986 
79057 
79127 
79197 

78923 
78993 
79064 
79134 
79204 

78930 
79000 
79071 
79141 
79211 

78937 
79007 
79078 
79148 
79218 

78944 
79014 
79085 
79155 
79225 

620 
621 
622 
623 
624 

79239 
79309 
79379 
79449 
79518 

79246 
79316 
79386 
79456 
79525 

79253 
79323 
79393 
79463 
79532 

79260 
79330 
79400 
79470 
79539 

79267 
79337 
79407 
79477 
79546 

79274 
79344 
79414 
79484 
79553 

79281 
79351- 
79421 
79491 
79560 

79288 
79358 
79428 
79498 
79567 

79295 
79365 
79435 
79505 
79574 

79302 
79372 
79442 
79511 
79581 

625 
626 
627 
628 
629 

79588 
79657 
79727 
79796 
79865 

79595 
79664 
79734 
79803 
79872 

79602 
79671 
79741 
79810 
79879 

79609 
79678 
79748 
79817 
79886 

79616 
79685 
79754 
79824 
79893 

79623 
79692 
79761 
79831 
79900 

79630 
79699 
79768 
79837 
79906 

79637 
79706 
79775 
79844 
79913 

79644 
79713 
79782 
79851 
79920 

79650 
79720 
79789 
79868 
79927 

6 

630 
631 
632 
633 
634 

79934 
80003 
80072 
80140 
80209 

79941 
80010 
80079 
80147 
80216 

79948 
80017 
80085 
80154 
80223 
80291 
80359 
80428 
80496 
80564 

79955 
80024 
80092 
80161 
80229 

79962 
80030 
80099 
80168 
80236 

79969 
80037 
80106 
80175 
80243 

79975 
80044 
80113 
80182 
80250 

79982 
80051 
80120 
80188 
80257 

79989 
80058 
80127 
80195 
80264 
80332' 
80400 
80468 
80536 
80604 

79996 
80065 
80134 
80202 
80271 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
6 
5 

635 
636 
637 
638 
639 

80277 
80346 
80414 
80482 
80550 

80284 
80353 
80421 
80489 
80557 

80298 
80366 
80434 
80502 
80570 

80305 
80373 
80441 
80509 
80577 

80312 
80380 
80448 
80516 
80584 

80318 
80387 
80455 
80523 
80591 

80325 
80393 
80462 
80530 
80598 

80339 
80407 
80475 
80543 
80611 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

TABLE  42.                 [Page  765 
Lo^rithms  of  Numbers. 

No.  6400 7000.                                                       Lojr.  80618 84510. 

No. 

0 

1 

2 

8 

4 

5 

6 

7 

8 

9 

1 

640 
641 
642 
643 
644 
645 
646 
647 
648 
649 

80618 
80686 
80754 
80821 
80889 

80625 
80693 
80760 
80828 
80895 

80632 
80699 
80767 
80835 
80902 

80638 
80706 
80774 
80841 
80909 

80645 
80713 
80781 
80848 
80916 

80652 
80720 
80787 
80855 
80922 

80659 
80726 
80794 
80862 
80929 

80665 
80733 
80801 
80868 
80936 
81003 
81070 
81137 
81204 
81271 

80672 
80740 
80808 
80875 
80943 

80679 
80747 
80814 
80882 
80949 
81017 
81084 
81151 
81218 
81285 

7 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
3 
4 
4 
5 
6 
6 

80956 
81023 
81090 
81158 
81224 

80963 
81030 
81097 
81164 
81231 

80969 
81037 
81104 
81171 
81238 

80976 
81043 
81111 
81178 
81245 

80983 
81050 
81117 
81184 
81251 

80990 
81057 
81124 
81191 
81258 

80996 
81064 
81131 
81198 
81265 

81010 
81077 
81144 
81211 
81278 

650 
661 
652 
653 
654 

81291 
81358 
81425 
81491 
81558 

81298 
81365 
81431 
81498 
81564 

81305 
81371 
81438 
81505 
81571 

81311 
81378 
81445 
81511 
81578 

81318 
81385 
81451 
81518 
81584 

81325 
81391 
81458 
81525 
81591 

81331 
81398 
81465 
81531 
81598 

81338 
81405 
81471 
81538 
81604 

81345 
81411 

81478 
81544 
81611 

81351 
81418 
81485 
81551 
81617 

655 
656 
657 
658 
659 

81624 
81690 
81757 
81823 
81889 

81631 
81697 
81763 
81829 
81895 

81637 
81704 
81770 
81836 
81902 

81644 
81710 
81776 
81842 
81908 

81651 
81717 
81783 
81849 
81915 

81657 
81723 
81790 
81856 
81921 

81664 
81730 
81796 
81862 
81928 

81671 
81737 
81803 
81869 
81935 

81677 
81743 
81809 
81875 
81941 
82007 
82073 
82138 
82204 
82269 

81684 
81750 
81816 
81882 
81948 
82014 
82079 
82145 
82210 
82276 

660 
661 
662 
663 
664 

81954 
82020 
82086 
82151 
82217 

81961 
82027 
82092 
82158 
82223 

81968 
82033 
82099 
82164 
82230 
82295 
82360 
82426 
82491 
82556 

81974 
82040 
82105 
82171 
82236 

81981 
82046 
82112 
82178 
82243 

81987  1  81994 
82053  i  82060 
82119   82125 
82184  i  82191 
82249  '  82256 

82000 
82066 
82132 
82197 
82263 

665 
666 
667 
668 
669 

82282 
82347 
82413 
82478 
82543 

82289 
82354 
82419 
82484 
82549 

82302 
82367 
82432 
82497 
82562 

82308 
82373 
82439 
82504 
82569 

82315  1  82321 
82380  1  82387 
82445  i  82452 
82510  ■  82517 
82575   82582 

82328 
82393 

82458 
82523 
82588 

82334 
82400 
82465 
82530 
82595 
82659 
82724 
82789 
82853 
82918 
82982 
83046 
83110 
83174 
83238 

82341 
82406 
82471 
82536 
82601 
82666 
82730 
82795 
82860 
82924 
82988 
83062 
83117 
83181 
83245 
'83308 
83372 
83436 
83499 
83563 

670 
671 
672 
673 
674 

82607 
82672 
82737 
82802 
82866 

82614 
82679 
82743 
82808 
82872 

82620 
82685 
82750 
82814 
82879 

82627 
82692 
82756 
82821 
82885 

82633 
82698 
82763 
82827 
82892 

82640 
82705 
82769 
82834 
82898 

82646 
82711 
82776 
82840 
82905 
82969 
83033 
83097 
83161 
83225 

82653 
82718 
82782 
82847 
82911 
82975 
83040 
83104 
83168 
83232 

675 
676 
677 
678 
679 

82930 
82995 
83059 
83123 
83187 

82937 
83001 
83065 
83129 
83193 

82943 
83008 
83072 
83136 
83200 

82950 
83014 
83078 
83142 
83206 

82956 
83020 
83085 
83149 
83213 

82963 
83027 
83091 
83155 
83219 

680 
681 
682 
683 
684 

83251 
83315 
83378 
83442 
83506 

83257 
83321 
83385 
83448 
83512 

83264 
83327 
83391 
83455 
83518 

83270 
83334 
83398 
83461 
83525 

83276 
83340 
83404 
83467 
83531 

83283   83289 
83347  :  83353 
83410  1  83417 
83474  1  83480 
83537  1  83544 

83296 
83359 
83423 
83487 
83550 
83613 
83677 
83740 
83803 
83866 

83302 
83366 
83429 
83493 
83556 
83620 
83683 
83746 
83809 
83872 
83935 
83998 
84061 
84123 
84186 
84248 
84311 
84373 
84435 
84497 

685 
686 
687 
688 
689 

83569 
83632 
83696 
83759 
83822 

83575 
83639 
83702 
83765 
83828 

83582 
83645 
83708 
83771 
83835 

83588 
83651 
83715 
83778 
83841 

83594 
83658 
83721 
83784 
83847 

83601  1  83607 
83664  1  83670 
83727  i  83734 
83790  i  83797 
83853  !  83860 

83626 
83689 
83753 
83816 
83879 

6 

690 
691 
692 
693 
694 

83885 
83948 
84011 
84073 
84136 

83891 
83954 
84017 
84080 
84142 

83897 
83960 
84023 
84086 
84148 

83904 
83967 
84029 
84092 
84155 

83910 
83973 
84036 
84098 
84161 

83916  i  83923 
83979  i  83985 
84042  1  84048 
84105  i  84111 
84167  1  84173 

83929 
83992 
84055 
84117 
84180 

83942 
84004 
84067 
84130 
84192 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
5 
5 

695 
696 
697 
698 
699 

84198 
84261 
84323 
84386 
84448 

84205 
84267 
84330 
84392 
84454 

84211 
84273 
84336 
84398 
84460 

84217 
84280 
84342 
84404 
84466 

84223 
84286 
84348 
84410 
84473 

84230 
84292 
84354 
84417 
84479 

84236 
84298 
84361 
84423 
84485 

84242 
84305 
84367 
84429 
84491 

84255 
84317 
84379 
84442 
84504 

Ko. 

0 

1 

2 

S 

4 

6 

6 

7 

8 

9 

\ 

Page  766]                 TABLE  42. 

Logarithms  of  Numbers. 

No.  7000 ^7600.                                                       Log.  84510 88081. 

No. 

0 

1 

2 

3 

4 

6 

6 

7      8 

9 

1 

700 
701 
702 
703 
704 

84510 
84572 
84634 
84696 
84757 

84516 
84578 
84640 
84702 
84763 

84522 
84584 
84646 
84708 
84770 

84528 
84590 
84652 
84714 
84776 

84535 

84597 
84658 
84720 

84782 

84541 
84603 
84665 
84726 
84788 

84547 
84609 
84671 
84733 
84794 

84563 
84615 
84677 
84739 
84800 
84862 
84924 
84986 
86046 
85107 

84569 
84621 
84683 
84745 
84807 
84868 
84930 
84991 
85062 
86114 

84566 
84628 
84689 
84751 
84813 

7 

1 
2 
3 
4 
6 
6 
7 
8 
9 

1 
1 
2 
3 
4 
4 
6 
6 
6 

705 
706 
707 
708 
709 

84819 
84880 
84942 
85003 
85065 

84825 
84887 
84948 
85009 
85071 

84831 
84893 
84954 
85016 
85077 

84837 
84899 
84960 
85022 
85083 

84844 
84905 
84967 
85028 
85089 

84850 
84911 
84973 
85034 
85095 

84866 
84917 
84979 
85040 
85101 

84874 
84936 
84997 
85058 
85120 

710 
711 
712 
713 
714 

85126 
85187 
85248 
85309 
85370 

85132 
85193 
85254 
85315 
85376 

85138 
85199 
85260 
85321 
85382 

85144 
85205 
85266 
85327 
85388 

85150 
85211 
85272 
85333 
85394 

85156 
85217 
86278 
86339 
85400 

85163 
85224 
85286 
85345 
85406 

85169 
86230 
85291 
85352 
85412 

85175 
85236 
85297 
85368 
86418 

85181 
85242 
85303 
86364 
85425 

715 
716 
717 
718 
719 

85431 
85491 
85552 
85612 
85673 

85437 
85497 
85558 
85618 
85679 

85443 
85503 
85564 
85625 
85685 
85745 
85806 
85866 
85926 
85986 

85449 
85609 
85570 
85631 
85691 

85455 
85516 
85576 
85637 
85697 

85461 
85522 
86682 
85643 
85703 

85467 
85628 
85688 
85649 
86709 

85473 
86534 
85694 
86655 
86715 

85479 
86540 
86600 
86661 
85721 
85781 
86842 
85902 
85962 
86022 
86082 
86141 
86201 
86261 
86320 
86380 
86439 
86499 
86558 
86617 

86486 
86546 
85606 
86667 
86727 

720 
721 
722 
723 
724 
725 
726 
727 
728 
729 

85733 
85794 
85854 
85914 
85974 

85739 
85800 
85860 
85920 
85980 

85751 
85812 
85872 
85932 
85992 

85757 
86818 
85878 
85938 
85998 

85763  i  85769 
85824  1  86830 
86884  \    85890 
85944   86950 
86004   86010 

85775 
85836 
86896 
86956 
86016 
86076 
86136 
86195 
86255 
86314 

86788 
86848 
85908 
85968 
86028 
86088 
86147 
86207 
86267 
86326 

6 

86034 
86094 
86153 
86213 
86273 

86040 
86100 
86159 
86219 
86279 

86046 
86106 
86165 
86225 
86285 

86052 
86112 
86171 
86231 
86291 

86058 
86118 
86177 
86237 
86297 

86064 
86124 
86183 
86243 
86303 

86070 
86130 
86189 
86249 
86308 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
5 
5 

730 
731 
732 
733 
734 

86332 
86392 
86451 
86510 
86570 

86338 
86398 
86457 
86516 
86576 

86344 
86404 
86463 
86522 
86581 

86350 
86410 
86469 
86528 
86587 

86356 
86416 
86475 
86534 
86593 

86362 
86421 
86481 
86540 
86599 

86368 
86427 
86487 
86546 
86605 

86374 
86433 
86493 
86652 
86611 

86386 
86446 
86504 
86564 
86623 

735 
736 
737 
738 
739 

86629 
86688 
86747 
86806 
86864 

86635 
86694 
86753 
86812 
86870 

86641 
86700 
86759 
86817 
86876 

86646 
86705 
86764 
86823 
86882 

86652 
86711 
86770 
86829 
86888 

86658 
86717 
86776 
86836 
86894 

86664 
86723 
86782 
86841 
86900 

86670 
86729 
86788 
86847 
86906 
86964 
87023 
87081 
87140 
87198 
87256 
87316 
87373 
87431 
87489 

86676 
86736 
86794 
86853 
86911 
86970 
87029 
87087 
87146 
87204 

86682 
86741 
86800 
86859 
86917 

740 
741 
742 
743 
744 

86923 
86982 
87040 
87099 

87157 

86929 
86988 
87046 
87105 
87163 

86935 
86994 
87052 
87111 
87169 

86941 
86999 
87058 
87116 
87175 

86947 
87005 
87064 
87122 
87181 

86963 
87011 
87070 
87128 
87186 

86968 
87017 
87075 
87134 
87192 

86976 
87035 
87093 
87161 
87210 

745 
746 

747 
748 
749 

87216 
87274 
87332 
87390 
87448 

87221 
87280 
87338 
87396 
87454 

87227 
87286 
87344 
87402 
87460 

87233 
87291 
87349 
87408 
87466 

87239 
87297 
87356 
87413 
87471 

87246 
87303 
87361 
87419 

87477 

87251 
87309 
87367 
87426 
87483 
87541 
87599 
87656 
87714 
87772 

87262 
87320 
87379 
87437 
87495 
87662 
87610 
87668 
87726 
87783 

87268 
87326 
87384 
87442 
87500 

5 

750 
751 
752 
753 
754 

87506 
87564 
87622 
87679 
87737 

87512 
87570 
87628 
87685 
87743 

87518 
87576 
87633 
87691 
87749 

87523 
87581 
87639 
87697 
87754 

87529 
87587 
87645 
87703 
87760 

87536 
87593 
87661 
87708 
87766 

87647 
87604 
87662 
87720 
87777 
87836 
87892 
87950 
88007 
88064 

87558 
87616 
87674 
87731 
87789 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
•2 
3 
3 
4 
4 
6 

755 
756 
757 
758 
759 

87795 
87852 
87910 
87967 
88024 

87800 
87858 
87915 
87973 
88030 

87806 
87864 
87921 
87978 
88036 

87812 
87869 
87927 
87984 
88041 

87818 
87875 
87933 
87990 
88047 

87823 
87881 
87938 
87996 
88053 

87829 
87887 
87944 
88001 
88058 

87841 
87898 
87966 
88013 
88070 

87846 
87904 
87961 
88018 
88076 

No. 

0 

1 

i 

3 

4 

6 

6 

7 

8 

9 

1 

TABLE  42.                  [Page  767 
Logarithms  of  Numbers. 

No.  7600 8200.                                                         Log.  88081 91381. 

No. 

0 

1 

2 

8 

4 

5 

6 

7 

8 

9 

1 

760 
761 
762 
763 
764 

88081 
88138 
88195 
88252 
88309 

88087 
88144 
88201 
88258 
88315 

88093 
88150 
88207 
88264 
88321 

88098 
88156 
88213 
88270 
88326 

88104 
88161 
88218 
88275 
88332 

88110 
88167 
88224 
88281 
88338 

88116 
88173 
88230 
88287 
88343 

88121 
88178 
88235 
88292 
88349 

88127 
88184 
88241 
88298 
88356 
88412 
88468 
88525 
88581 
88638 
88694 
88750 
88807 
88863 
88919 
88976 
89031 
89087 
89143 
89198 

88133 
88190 

88247 
88304 
88360 
88417 
88474 
88630 
88687 
88643 
88700 
88756 
88812 
88868 
88925 

6 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
5 
5 

765 
766 
767 
768 
769 

88366 
88423 
88480 
88536 
88593 

88372 
88429 
88485 
88542 
88598 

88377 
88434 
88491 
88547 
88604 

88383 
88440 
88497 
88553 
88610 

88389 
88446 
88502 
88559 
88615 

88395 
88451 
88508 
88564 
88621 

88400 
88457 
88613 
88570 
88627 

88406 
88463 
88519 
88676 
88632 

770 
771 
772 
773 
774 
775 
776 
777 
778 
779 

88649 
88705 
88762 
88818 
88874 

88655 
88711 
88767 
88824 
88880 

88660 
88717 
88773 
88829 
88885 

88666 
88722 
88779 
88835 
88891 

88672 
88728 
88784 
88840 
88897 

88677 
88734 
88790 
88846 
88902 

88683 
88739 
88796 
88852 
88908 

88689 
88745 
88801 
88857 
88913 

« 

88930 
88986 
89042 
89098 
89154 

88936 
88992 
89048 
89104 
89159 

88941 
88997 
89053 
89109 
89165 

88947 
89003 
89059 
89115 
89170 

88953 
89009 
89064 
89120 
89176 

88958 
89014 
89070 
89126 
89182 

88964 
89020 
89076 
89131 
89187 

88969 
89025 
89081 
89137 
89193 

88981 
89037 
89092 
89148 
89204 

780 
781 
782 
783 
784 

89209 
89265 
89321 
89376 
89432 

89215 
89271 
89326 
89382 
89437 

89221 
89276 
89332 
89387 
89443 

89226 
89282 
89337 
89393 
89448 

89232 
89287 
89343 
89398 
89454 

89237 
89293 
89348 
89404 
89459 
89515 
89570 
89625 
89680 
89736 

89243 
89298 
89354 
89409 
89465 
89520 
89575 
89631 
89686 
89741 

89248 
89304 
89360 
89415 
89470 
89526 
89581 
89636 
89691 
89746 

89254 
89310 
89365 
89421 
89476 
89531 
89586 
89642 
89697 
89752 

89260 
89315 
89371 
89426 
89481 
89537 
89592 
89647 
89702 
89757 

785 
786 
787 
788 
789 

89487 
89542 
89597 
89653 
89708 

89492 
89548 
89603 
89658 
89713 

89498 
89553 
89609 
89664 
89719 

89504 
89559 
89614 
89669 
89724 

89509 
89564 
89620 
89675 
89730 
89785 
89840 
89894 
89949 
90004 

790 
791 
792 
793 
794 

89763 
89818 
89873 
89927 
89982 

89768 
89823 
89878 
89933 
89988 

89774 
89829 
89883 
89938 
89993 

89779 
89834 
89889 
89944 
89998 

89790 
89846 
89900 
89955 
90009 

89796 
89851 
89906 
89960 
90015 

89801 
89856 
89911 
89966 
90020 

89807 
89862 
89916 
89971 
90026 

89812 
89867 
89922 
89977 
90031 

795 
796 
797 
798 
799 

90037 
90091 
90146 
90200 
90255 

90042 
90097 
90151 
90206 
90260 

90048 
90102 
90157 
90211 
90266 

90053 
90108 
90162 
90217 
90271 

90059 
90113 
90168 
90222 
90276 
90331 
90385 
90439 
90493 
90547 

90064 
90119 
90173 
90227 
90282 

90069 
90124 
90179 
90233 
90287 

90076 
90129 
90184 
90238 
90293 

90080 
90136 
90189 
90244 
90298 

90086 
90140 
90195 
90249 
90304 

800 
801 
802 
803 
804 

90309 
90363 
90417 
90472 
90526 

90314 
90369 
90423 
90477 
90531 

90320 
90374 
90428 
90482 
90536 

90326 
90380 
90434 
90488 
90542 

90336 
90390 
90445 
90499 
90553 

90342 
90396 
90450 
90604 
90558 

90347 
90401 
90465 
90609 
90663 
90617 
90671 
90725 
90779 
90832 

90352 
90407 
90461 
90515 
90669 
90623 
90677 
90730 
90784 
90838 

90358 
90412 
90466 
90520 
90574 

805 
806 
807 
808 
809 

90580 
90634 
90687 
90741 
90795 

90585 
90639 
90693 
90747 
90800 

90590 
90644 
90698 
90752 
90806 

90596 
90650 
90703 
90757 
90811 

90601 
90655 
90709 
90763 
90816 

90607 
90660 
90714 
90768 
90822 

90612 
90666 
90720 
90773 
90827 

90628 
90682 
90736 
90789 
90843 

6 

810 
811 
812 
813 
814 

90849 
90902 
90956 
91009 
91062 

90854 
90907 
90961 
91014 
91068 

90859 
90913 
90966 
91020 
91073 

90865 
90918 
90972 
91025 
91078 

90870 
90924 
90977 
91030 
91084 

90875 
90929 
90982 
91036 
91089 

90881 
90934 
90988 
91041 
91094 

90886 
90940 
90993 
91046 
91100 

90891 
90946 
90998 
91052 
91105 

90897 
90950 
91004 
91057 
91110 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
3 
4 
4 
5 

815 
816 
817 
818 
819 

91116 
91169 
91222 
91275 
91328 

91121 
91174 
91228 
91281 
91334 

91126 
91180 
91233 
91286 
91339 

91132 
91185 
91238 
91291 
91344 

91137 
91190 
91243 
91297 
91350 

91142 
91196 
91249 
91302 
91355 

91148 
91201 
91254 
91307 
91360 

91153 
91206 
91259 
91312 
91365 

91158 
91212 
91265 
91318 
91371 

91164 
91217 
91270 
91323 
91376 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

Page  768]                 TABLE  42. 

Logarithms  of  Numbers. 

No.  8200 880a                                                            Log.  91381 94448 

No. 

0 

1 

2 

s 

4 

5 

« 

7 

8 

91424 

91477 
91529 
91582 
91635 

» 

91429 
91482 
91535 
91587 
91640 

820 
821 
822 
823 
824 

91381 
91434 
91487 
91540 
91593 

91387 
91440 
91492 
91545 
91598 

91392 
91445 
91498 
91551 
91603 

91397 
91450 
91503 
91556 
91609 

91403 
91455 
91508 
91561 
91614 

91408 
91461 
91514 
91566 
91619 

91413 
91466 
91519 

91572 
91624 

91418 
91471 
91524 
91577 
91630 

1  6 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
5 
5 

825 
826 
827 
828 
829 

91645 
91698 
91751 
91803 
91855 

91651 
91703 
91756 
91808 
91861 

91656 
91709 
91761 
91814 
91866 

91661 
91714 
91766 
91819 
91871 

91666 
91719 
91772 
91824 
91876 

91672 
91724 
91777 
91829 
91882 

91677 
91730 
91782 
91834 

91887 

91682 
91735 
91787 
91840 
91892 

91687 
91740 
91793 

91845 
91897 

91693 
91745 
91798 
91850 
91903 

830 
831 
832 
833 
834 

91908 
91960 
92012 
92065 
92117 

91913 
91965 
92018 
92070 
92122 

91918 
91971 
92023 
92075 
92127 

91924 
91976 
92028 
92080 
92132 

91929 
91981 
92033 
92085 
92137 

91934 
91986 
92038 
92091 
92143 

91939 
91991 
92044 
92096 
92148 

91944 
91997 
92049 
92101 
92153 
92205 
92257 
92309 
92361 
92412 

91950 
92002 
92054 
92106 
92158 
92210 
92262 
92314 
92366 
92418 

91955 
92007 
92059 
92111 
92163 

835 
836 
837 
838 
839 

92169 
92221 
92273 
92324 
92376 

92174 
92226 
92278 
92330 
92381 

92179 
92231 
92283 
92335 
92387 

92184 
92236 
92288 
92340 
92392 

92189 
92241 
92293 
92345 
92397 

92195 
92247 
92298 
92350 
92402 
92454 
92505 
92557 
92609 
92660 
92711 
92763 
92814 
92865 
92916 

92200 
92252 
92304 
92355 
92407 

92215 
92267 
92319 
92371 
92423 

840 
841 
842 
843 
844 

92428 
92480 
92531 
92583 
92634 

92433 
92485 
92536 
92588 
92639 

92438 
92490 
92542 
92593 
92645 
92696 
92747 
92799 
92850 
92901 

92443 
92495 
92547 
92598 
92650 
92701 
92752 
92804 
92855 
92906 

92449 
92500 
92552 
92603 
92655 
92706 
92758 
92809 
92860 
92911 

92459 
92511 
92562 
92614 
92665 

92464 
92516 
92567 
92619 
92670 
92722 
92773 
92824 
92875 
92927 

92469 
92521 
92572 
92624 

92474 
92526 
92578 
92629 

92675  92681 
92727  Q^T^Q 

6 

845 
846 
847 
848 
849 

92686 
92737 
92788 
92840 
92891 

92691 
92742 
92793 
92845 
92896 

92716 
92768 
92819 
92870 
92921 

92778 
92829 
92881 
92932 

92783 
92834 
92886 
92937 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
3 
4 
4 
5 

850 
851 
852 
853 
854 

92942 
92993 
93044 
93095 
93146 

92947 
92998 
93049 
93100 
93151 

92952 
93003 
93054 
93105 
93156 

92957 
93008 
93059 
93110 
93161 

92962 
93013 
93064 
93115 
93166 

92967 
93018 
93069 
93120 
93171 

92973 
93024 
93075 
93125 
93176 

92978 
93029 
93080 
93131 
93181 

92983 
93034 
93085 
93136 
93186 

92988 
93039 
93090 
93141 
93192 

855 
856 
857 
858 
859 

•93197 
93247 
93298 
93349 
93399 

93202 
93252 
93303 
93354 
93404 

93207 
93258 
93308 
93359 
93409 

93212 
93263 
93313 
93364 
9^3414 

93217 
93268 
93318 
93369 
93420 

93222 
93273 
93323 
93374 
93425 

93227 
93278 
93328 
93379 
93430 

93232 
93283 
93334 
93384 
93435 
93485 
93536 
93586 
93636 
93687 

93237 
93288 
93339 
93389 
93440 

93242 
93293 
93344 
93394 
93445 

860 
861 
862 
863 
864 
865 
866 
867 
868 
869 

93450 
93500 
93551 
93601 
93651 

93455 
93505 
93556 
93606 
93656 

93460 
93510 
93561 
93611 
93661 

93465 
93515 
93566 
93616 
93666 

93470 
93520 
93571 
93621 
93671 

93475 
93526 
93576 
93626 
93676 

93480 
93531 
93581 
93631 
93682 

93490 
93541 
93591 
93641 
93692 

93495 
93546 
93596 
93646 
93697 

93702 
93752 
93802 
93852 
93902 

93707 
93757 
93807 
93857 
93907 

93712 
93762 
93812 
93862 
93912 

93717 
93767 
93817 
93867 
93917 

93722 
93772 
93822 
93872 
93922 

93727 
93777 
93827 
93877 
93927 

93732 
93782 
93832 
93882 
93932 

93737 
93787 
93837 
93887 
93937 
93987 
94037 
94086 
94136 
94186 

93742 
93792 
93842 
93892 
93942 
93992 
94042 
94091 
94141 
94191 

93747 
93797 
93847 
93897 
93947 

1 
2 
3 
4 
5 
6 
7 
8 
9 

4 

0 

1 
1 

2 
2 
2 
3 
3 
4 

870 
871 
872 
873 
874 

93952 
94002 
94052 
94101 
94151 

93957 
94007 
94057 
94106 
94156 

93962 
94012 
94062 
94111 
94161 

93967 
94017 
94067 
94116 
94166 

93972 
94022 
94072 
94121 
94171 

93977 
94027 
94077 
94126 
94176 

93982 
94032 
94082 
94131 
94181 

93997 
94047 
94096 
94146 
94196 

875 
876 
877 
878 
879 

94201 
94250 
94300 
94349 
94399 

94206 
94255 
94305 
94354 
94404 

94211 
94260 
94310 
94359 
94409 

94216 
94265 
94315 
94364 
94414 

94221 
94270 
94320 
94369 
94419 

94226 
94275 
94325 
94374 
94424 

94231 
94280 
94330 
94379 
94429 

94236 
94285 
94335 
94384 
94433 

94240 
94290 
94340 
94389 
94438 

94245 
94295 
94345 
94394 
94443 

9 

No. 

0       1 

i 

8 

4 

5 

6 

7 

8 

1 

TABLE  42.                 [Page  769 
Logarithms  of  Numbers. 

No.  8800 9400.                                                           Log.  94448 97313. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

880 
881 
882 
883 
884 

94448 
94498 
94547 
94596 
94645 

94453 
94503 
94552 
94601 
94650 

94458 
94507 
94557 
94606 
94655 

94463 
94512 
94562 
94611 
94660 

94468 
94517 
94567 
94616 
94665 

94473 
94522 
94571 
94621 
94670 

94478 
94527 
94576 
94626 
94675 

94483 
94532 
94581 
94630 
94680 

94488 
94537 
94586 
94635 
94685 

94493 
94542 
94591 
94640 
94689 

6 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
3 
4 
4 
5 

885 
886 
887 
888 
889 

94694 
94743 
94792 
94841 
94890 

94699 
94748 
94797 
94846 
94895 

94704 
94753 
94802 
94851 
94900 

94709 
94758 
94807 
94856 
94905 

94714 
94763 
94812 
94861 
94910 

94719 
94768 
94817 
94866 
94915 

94724 
94773 
94822 
94871 
94919 

94729 
94778 
94827 
94876 
94924 

94734 
94783 
94832 
94880 
94929 
94978 
95027 
95075 
95124 
95173 

94738 
94787 
94836 
94885 
94934 
94983 
95032 
95080 
95129 
95177 

890 
891 
892 
893 
894 

94939 
94988 
95036 
95085 
95134 

94944 
94993 
95041 
95090 
95139 

94949 
94998 
95046 
95095 
95143 

949.54 
95002 
95051 
95100 
95148 

94959 
95007 
95056 
95105 
95153 

94963 
95012 
95061 
95109 
95158 

94968 
95017 
95066 
95114 
95163 

94973 
95022 
95071 
95119 
95168 

895 
896 
897 
898 
899 

95182 
95231 
95279 
95328 
95376 

95187 
95236 
95284 
95332 
95381 

95192 
95240 
95289 
95337 
95386 

95197 
95245 
95294 
95342 
95390 

95202 
95250 
95299 
95347 
95395 

95207 
95255 
95303 
95352 
95400 

95211 
95260 
95308 
95357 
95405 

95216 
95265 
95313 
95361 
95410 

95221 
95270 
95318 
95366 
95415 

95226 
95274 
95323 
95371 
95419 

900 
901 
902 
903 
904 
905 
906 
907 
908 
909 

95424 
95472 
95521 
95569 
95617 

95429 
95477 
95525 
95574 
95622 

95434 
95482 
95530 
95578 
95626 

95439 
95487 
95535 
95583 
95631 

95444 
95492 
95540 
95588 
95636 

95448 
96497 
95545 
95593 
95641 

95453 
95501 
95550 
95598 
95646 

95458 
95506 
95554 
95602 
95650 

95463 
95511 
95559 
95607 
95655 

95468 
95516 
95564 
95612 
95660 

95665 
95713 
95761 
95809 
95856 

95670 
95718 
95766 
95813 
95861 

95674 
95722 
95770 
95818 
95866 

95679   95684 
95727   95732 
95775   95780 
95823   95828 
95871   95875 

95689 
95737 
95785 
95832 
95880 

95694 
95742 
95789 
95837 
95885 

95698 
95746 
95794 
95842 
95890 

95703 
95751 
95799 
95847 
95895 

95708 
95756 
95804 
95852 
95899 

910 
911 
912 
913 
914 

95904 
95952 
95999 
96047 
96095 

95909 
95957 
96004 
96052 
96099 

95914 
95961 
96009 
96057 
96104 

95918 
95966 
96014 
96061 
96109 

95923 
95971 
96019 
96066 
96114 

95928 
95976 
96023 
96071 
96118 

95933 
95980 
96028 
96076 
96123 

95938 
95985 
96033 
96080 
96128 

95942 
95990 
96038 
96085 
96133 

95947 
95995 
96042 
96090 
96137 

915 
916 
917 
918 
919 

96142 
96190 
96237 
96284 
96332 

96147 
96194 
96242 
96289 
96336 

96152 
96199 
96246 
96294 
96341 

96156 
96204 
96251 
96298 
96346 

96161 
96209 
96256 
96303 
96350 

96166 
96213 
96261 
96308 
96355 

96171 
96218 
96265 
96313 
96360 

96175 
96223 
96270 
96317 
96365 

96180 
96227 
96275 
96322 
96369 

96185 
96232 
96280 
96327 
96374 

920 
921 
922 
923 
924 

96379 
96426 
96473 
96520 
96567 

96384 
96431 
96478 
96525 
96572 

96388 
96435 
96483 
96530 
96577 

96393 
96440 
96487 
96534 
96581 

96398 
96445 
96492 
96539 
96586 

96402 
96450 
96497 
96544 
96591 

96407 
96454 
96501 
96548 
96595 

96412 
96459 
96506 
96553 
96600 

96417 
96464 
96511 
96558 
96605 

96421 
96468 
96515 
96562 
96609 

925 
926 

927 
928 
929 

96614 
96661 
96708 
96755 
96802 

96619 
96666 
96713 
96759 
96806 

96624 
96670 
96717 
96764 
96811 

96628 
96675 
96722 
96769 
96816 

96633 
96680 
96727 
96774 
96820 

96638 
96685 
96731 
96778 
96825 

96642 
96689 
96736 
96783 
96830 

96647 
96694 
96741 
96788 
96834 

96652 
96699 
96745 
96792 
96839 

96656 
96703 
96750 
96797 
96844 

4 

930 
931 
932 
933 
934 
935 
936 
937 
938 
939 

96848 
96895 
96942 
96988 
97035 

96853 
96900 
96946 
96993 
97039 

96858 
96904 
96951 
96997 
97044 

96862 
96909 
96956 
97002 
97049 

96867 
96914 
96960 
97007 
97053 

96872 
96918 
96965 
97011 
97058 

96876 
96923 
96970 
97016 
97063 

96881 
96928 
96974 
97021 
97067 

96886 
96932 
96979 
97025 
97072 

96890 
96937 
96984 
97030 
97077 
97123 
97169 
97216 
97262 
97308 

1 
2 
3 

4 
5 
6 

7 
8 
9 

0 

1 
1 

2 
2 
2 
3 
3 
4 

97081 
97128 
97174 
97220 
97267 

97086 
97132 
97179 
97225 
97271 

97090 
97137 
97183 
97230 
97276 

97095 
97142 
97188 
97234 
97280 

97100 
97146 
97192 
97239 
97285 

97104 
97151 
97197 
97243 
97290 

97109 
97155 
97202 
97248 
97294 

97114 
97160 
97206 
97253 
97299 

97118 
97165 
97211 
97257 
97304 

No. 

0         1 

2        3 

4 

5 

6 

7 

8 

9 

1 

Page  770]                TABLE  42. 

Logarithms  of  Numbers. 

No.  9400 ^10000.                                                        Log.  97313 09996. 

No. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

1 

940 
941 
942 
943 
944 

97313 
97359 
97405 
97451 
97497 

97317 
97364 
97410 
97456 
97502 

97322 
97368 
97414 
97460 
97506 

97327 
97373 
97419 
97465 
97511 

97331 
97377 
97424 
97470 
97516 

97336 
97382 
97428 
97474 
97520 

97340 
97387 
97433 
97479 
97525 

97345 
97391 
97437 
97483 
97529 

97350 
97396 
97442 

97488 
97534 

97354 
97400 
97447 
97493 
97539 

5 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
3 
4 
4 
5 

•  945 
946 
947 
948 
949 

97543 
97589 
97635 
97681 
97727 

97548 
97594 
97640 
97685 
97731 

97552 
97598 
97644 
97690 
97736 

97557 
97603 
97649 
97695 
97740 

97562 
97607 
97653 
97699 
97745 

97566 
97612 
97658 
97704 
97749 

97571 
97617 
97663 
97708 
97754 

97575 
97621 
97667 
97713 
97759 

97580 
97626 
97672 
97717 
97763 

97585 
97630 
97676 
97722 
97768 

950 
951 
952 
953 
954 

97772 
97818 
97864 
97909 
97955 

97777 
97823 
97868 
97914 
97959 

97782 
97827 
97873 
97918 
97964 

97786 
97832 
97877 
97923 
97968 

97791 
97836 
97882 
97928 
97973 

97795 
97841 
97886 
97932 
97978 

97800 
97845 
97891 
97937 

97982 

97804 
97850 
97896 
97941 
97987 

97809 
97855 
97900 
97946 
97991 

97813 
97859 
97905 
97950 
97996 

955 
956 
957 
958 
959 

98000 
98046 
98091 
98137 
98182 

98005 
98050 
98096 
98141 
98186 

98009 
98055 
98100 
98146 
98191 

98014 
98059 
98105 
98150 
98195 

98019 
98064 
98109 
98155 
98200 

98023 
98068 
98114 
98159 
98204 

98028 
98073 
98118 
98164 
98209 

98032 
98078 
98123 
98168 
98214 

98037 
98082 
98127 
98173 
98218 

98041 
98087 
98132 
98177 
98223 

960 
961 
962 
963 
964 

98227 
98272 
98318 
98363 
98408 

98232 
98277 
98322 
98367 
98412 

98236 
98281 
98327 
98372 
98417 

98241 
98286 
98331 
98376 
98421 

98245 
98290 
98336 
98381 
98426 

98250 
98295 
98340 
98385 
98430 

98254 
98299 
98345 
98390 
98435 

98259 
98304 
98349 
98394 
98439 

98263 
98308 
98354 
98399 
98444 

98268 
98313 
98358 
98403 
98448 
98493 
98538 
98583 
98628 
98673 

965 
966 
967 
968 
969 
970 
971 
972 
973 
974 

98453 
98498 
98543 
98588 
98632 

98457 
98502 
98547 
98592 
98637 

98462 
98507 
98552 
98597 
98641 

98466 
98511 
98556 
98601 
98646 

98471 
98516 
98561 
98605 
98650 

98475 
98520 
98565 
98610 
98655 

98480 
98525 
98570 
98614 
98659 

98484 
98529 
98574 
98619 
98664 

98489 
98534 
98579 
98623 
98668 

98677 
98722 
98767 
98811 
98856 

98682 
98726 
98771 
98816 
98860 

98686 
98731 
98776 
98820 
98865 

98691 
98735 
98780 
98825 
98869 

98695 
98740 
98784 
98829 
98874 

98700 
98744 
98789 
98834 
98878 

98704 
98749 
98793 
98838 
98883 

98709 
98753 
98798 
98843 
98887 

98713 
98758 
98802 
98847 
98892 

98717 
98762 
98807 
98851 
98896 

975 

976 
977 
978 
979 

98900 
98945 
98989 
99034 
99078 

98905 
98949 
98994 
99038 
99083 

98909 
98954 
98998 
99043 
99087 

98914 
98958 
99003 
99047 
99092 

98918 
98963 
99007 
99052 
99096 

98923 
98967 
99012 
99056 
99100 

98927 
98972 
99016 
99061 
99105 

98932 
98976 
99021 
99065 
99109 

98936 
98981 
99025 
99069 
99114 

98941 
98985 
99029 
99074 
99118 

980 
981 
982 
983 
984 

99123 
99167 
99211 
99256 
99300 

99127 
99171 
99216 
99260 
99304 

99131 
99176 
99220 
99264 
99308 

99136 
99180 
99224 
99269 
99313 

99140 
99185 
99229 
99273 
99317 

99145 
99189 
99233 
99277 
99322 

99149 
99193 
99238 
99282 
99326 

99154 
99198 
99242 
99286 
99330 

99158 
99202 
99247 
99291 
99335 

99162 
99207 
99251 
99295 
99339 

985 
986 
987 
988 
989 

99344 
99388 
99432 
99476 
99520 

99348 
99392 
99436 
99480 
99524 

99352 
99396 
99441 
99484 
99528 

99357 
99401 
99445 
99489 
99533 

99361 
99405 
99449 
99493 
99537 

99366 
99410 
99454 
99498 
99542 

99370 
99414 
99458 
99502 
99546 

99374 
99419 
99463 
99506 
99550 

99379 
99423 
99467 
99511 
99555 

99383 
99427 
99471 
99515 
99559 
99603 
99647 
99691 
99734 
99778 

4 

990 
991 
992 
993 
994 

99564 
99607 
99651 
99695 
99739 

99568 
99612 
99656 
99699 
99743 

99572 
99616 
99660 
99704 
99747 

99577 
99621 
99664 
99708 
99752 

99581 
99625 
99669 
99712 
99756 

99585 
99629 
99673 
99717 
99760 

99590 
99634 
99677 
99721 
99765 

99594 
99638 
99682 
99726 
99769 

99599 
99642 
99686 
99730 
99774 

1 
2 
3 
4 
5 
6 
7 
8 
9 

0 

1 
1 

2 
2 
2 
3 
3 
4 

995 
996 
997 
998 
999 

99782 
99826 
99870 
99913 
99957 

99787 
99830 
99874 
99917 
99961 

99791 
99835 
99878 
99922 
99965 

99795 
99839 
99883 
99926 
99970 

99800 
99843 
99887 
99930 
99974 

99804 
99848 
99891 
99935 
99978 

99808 
99852 
99896 
99939 
99983 

99813 
99856 
99900 
99944 
99987 

99817 
99861 
99904 
99948 
99991 

99822 
99865 
99909 
99952 
99996 

No. 

0 

1 

2 

8       4 

6 

6 

7 

8 

9 

1 

TABLE  43.                                          [Page  771 
Logarithmic  Sines,  Tangents,  and  Secants  to  every  Point  and  Quarter  Point  of  the  Compass. 

Points. 

Sine. 

Cosine. 

Tangent. 

Cotangent. 

Secant. 

Cosecant. 

0 
i 

Inf.  neg. 
8. 69080 
8. 99130 
9. 16652 

10.00000 
9. 99948 
9. 99790 
9. 99527 

Inf.  neg. 
8. 69132 
8. 99340 
9. 17125 

Infinite. 
11. 30868 
11.00660 
10.  82875 

10.00000 
10.  00052 
10. 00210 
10. 00473 

Infinite. 
11. 30920 
11. 00870 
10. 83348 

8 
7| 
7i 
7J 

1 

n 

If 

9. 29024 
9. 38557 
9. 46282 
9. 52749 

9. 99157 
9. 98679 
9. 98088 
9. 97384 

9.29866 
9. 39879 
9.48194 
9. 55365 

10.  70134 
10. 60121 
10. 51806 
10. 44635 

10. 00843 
10. 01321 
10. 01912 
10. 02616 

10.  70976 
10. 61443 
10. 53718 
10. 47251 

7 
61 

6t 

2 

2J 
2J 

9. 58284 
9. 63099 
9.  67339 
9. 71105 

9. 96562 
9. 95616 
9. 94543 
9. 93335 

9. 61722 
9. 67483 
9. 72796 
9. 77770 

10.  38278 
10.  32517 
10.  27204 
10.  22230 

10.03438 
10. 04384 
10. 05457 
10. 06665 

10. 41716 
10. 36901 
10. 32661 
10. 28895 

6 

51 

5i 

3 

3J 
3t 

9. 74474 
9. 77503 
9. 80236 
9.  82708 

9. 91985 
9. 90483 
9. 88819 
9. 86979 

9. 82489 
9. 87020 
9.91417 
9. 95729 

10. 17511 
10. 12980 
10. 08583 
10. 04271 

10. 08015 
10. 09517 
10. 11181 
10. 13021 

10. 25526 
10. 22497 
10. 19764 
10. 17292 

5 
4| 

^ 

4i 

4 

9.84949 

9.84949 

10.00000 

10.00000 

10. 15051 

10. 15051 

4 

Ckwine. 

Sine. 

Cotangent. 

Tangent. 

Cosecant. 

Secant. 

Points. 

Page  772j 

TABLE  44. 

0° 

Log.  Sines,  Tangents,  and  Secants. 

179° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Dlff.  1'. 

Cosecant. 

Tangent. 

Di£E.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

12  0  0 

0  0  0 

Inf.  neg. 

Infinite. 

Inf.  neg. 

Infinite. 

10. 00000 

10.  00000 

60 

1 

11  59  52 

0  8 

6. 46373 

30103 

13. 53627 

6. 46373 

30103 

13. 53627 

00000 

00000 

59 

2 

59  44 

0  16 

76476 

17609 

23524 

76476 

17609 

23524 

00000 

00000 

58 

3 

59  36 

0  24 

94085 

12494 

06915 

94085 

12494 

05915 

00000 

00000 

57 

4 

59  28 

0  32 

7. 06579 

9691 

12. 93421 

7. 06579 

9691 

12.  93421 

00000 

00000 

56 
65 

5 

11  59  20 

0  0  40 

7. 16270 

7918 

12.  83730 

7. 16270 

7918 

12.  83730 

10.  00000 

10. 00000 

6 

59  12 

0  48 

24188 

6694 

75812 

24188 

6694 

75812 

00000 

00000 

54 

7 

59  4 

0  56 

30882 

5800 

69118 

30882 

5800 

69118 

00000 

00000 

63 

8 

58  56 

1  4 

36682 

5115 

63318 

36682 

5115 

63318 

00000 

00000 

52 

9 

58  48 

1  12 

41797 

4676 

68203 

41797 

4576 

58203 

00000 

00000 

51 
50 

10 

11  58  40 

0  1  20 

7. 46373 

4139 

12. 63627 

7. 46373 

4139 

12. 53627 

10. 00000 

10. 00000 

11 

58  32 

1  28 

60512 

3779 

49488 

50612 

3779 

49488 

00000 

00000 

49 

12 

58  24 

1  36 

54291 

3476 

45709 

64291 

3476 

45709 

00000 

00000 

48 

13 

58  16 

1  44 

57767 

3218 

42233 

67767 

3219 

42233 

00000 

00000 

47 

14 

58  8 

1  52 

60985 

2997 

39015 

60986 

2996 
2803 

39014 

00000 

00000 

46 
45 

15 

11  58  0 

0  2  0 

7. 63982 

2802 

12. 36018 

7.  63982 

12.  36018 

10. 00000 

10. 00000 

16 

57  52 

2  8 

66784 

2633 

33216 

66785 

2633 

33215 

00000 

00000 

44 

17 

57  44 

2  16 

69417 

2483 

30583 

69418 

2482 

30582 

00001 

9. 99999 

43 

18 

57  36 

2  24 

71900 

2348 

28100 

71900 

2348 

28100 

00001 

99999 

42 

19 

57  28 

2  32 

74248 

2227 

26752 

74248 

2228 

26752 

00001 

99999 

41 

20 

11  57  20 

0  2  40 

7.  76475 

2119 

12. 23525 

7.  76476 

2119 

12.  23524 

10. 00001 

9. 99999 

40 

21 

57  12 

2  48 

78694 

2021 

21406 

78695 

2020 

21406 

00001 

99999 

39 

22 

57  4 

2  56 

80615 

1930 

19386 

80615 

1931 

19385 

00001 

99999 

38 

23 

56  56 

3  4 

82545 

1848 

17455 

82646 

1848 

17464 

00001 

99999 

37 

24 

56  48 

3  12 

84393 
7. 86166 

1773 

15607 

84394 

1773 

16606 

00001 

99999 

36 

25 

11  56  40 

0  3  20 

1704 

12. 13834 

7. 86167 

1704 

12.13833 

10.00001 

9. 99999 

35 

26 

56  32 

3  28 

87870 

1639 

12130 

87871 

1639 

12129 

00001 

99999 

34 

27 

56  24 

3  36 

89509 

1579 

10491 

89610 

1679 

10490 

00001 

99999 

33 

28 

56  16 

3  44 

91088 

1524 

08912 

91089 

1524 

08911 

00001 

99999 

32 

29 

56  8 

3  52 

92612 

1472 

07388 

92613 

1473 

07387 

00002 

99998 

31 

30 

11  56  0 

0  4  0 

7.  94084 

1424 

12. 05916 

7. 94086 

1424 

12. 05914 

10.  00002 

9. 99998 

30 

31 

55  52 

4  8 

95508 

1379 

04492 

95510 

1379 

04490 

00002 

99998 

29 

32 

55  44 

4  16 

96887 

1336 

03113 

96889 

1336 

03111 

00002 

99998 

28 

33 

55  36 

4  24 

98223 

1297 

01777 

98225 

1297 

01776 

00002 

99998 

27 

34 
35 

55  28 
11  55  20 

4  32 

0  4  40 

99520 

1259 

00480 

99522 

1259 

00478 

00002 

99998 

26 

8. 00779 

1223 

11. 99221 

8. 00781 

1223 

11. 99219 

10. 00002 

9. 99998 

25 

36 

55  12 

4  48 

02002 

1190 

97998 

02004 

1190 

97996 

00002 

99998 

24 

37 

55  4 

4  56 

03192 

1168 

96808 

03194 

1159 

96806 

00003 

99997 

23 

38 

54  56 

5  4 

04350 

1128 

95660 

04363 

1128 

95647 

00003 

99997 

22 

39 

54  48 

5  12 

06478 

1100 

94622 

05481 

1100 

94519 

00003 

99997 

21 

40 

11  54  40 

0  5  20 

8. 06678 

1072 

11. 93422 

8. 06581 

1072 

11. 93419 

10. 00003 

9. 99997 

20 

41 

54  32 

5  28 

07650 

1046 

92360 

07653 

1047 

92347 

00003 

99997 

19 

42 

54  24 

5  36 

08696 

1022 

91304 

08700 

1022 

91300 

00003 

99997 

18 

43 

54  16 

5  44 

09718 

999 

90282 

09722 

998 

90278 

00003 

99997 

17 

44 
45 

54  8 

6  52 

10717 

976 

89283 

10720 

976 

89280 

00004 

99996 
9. 99996 

16 
15 

11  54  0 

0  6  0 

8. 11693 

964 

11. 88307 

8. 11696 

965 

11. 88304 

10.  00004 

46 

53  52 

6  8 

12647 

934 

87353 

12651 

934 

87349 

00004 

99996 

14 

47 

53  44 

6  16 

13681 

914 

86419 

13586 

915 

86415 

00004 

99996 

13 

48 

53  36 

6  24 

14495 

896 

85506 

14600 

895 

86600 

00004 

99996 

12 

49 

53  28 

6  32 

15391 

877 

84609 

16395 

878 

84605 

00004 

99996 

11 

50 

11  53  20 

0  6  40 

8. 16268 

860 

11. 83732 

8. 16273 

860 

11. 83727 

10. 00006 

9. 99995 

10 

51 

53  12 

6  48 

17128 

843 

82872 

17133 

843 

82867 

00005 

99996 

9 

62 

53  4 

6  56 

17971 

827 

82029 

17976 

828 

82024 

00006 

99996 

8 

53 

52  56 

7  4 

18798 

812 

81202 

18804 

812 

81196 

00005 

99996 

7 

54 
65 

52  48 

7  12 

19610 
8. 20407 

797 

80390 

19616 

797 

80384 

00005 

99995 

6 

11  52  40 

0  7  20 

782 

11. 79693 

8. 20413 

782 

11. 79587 

10. 00006 

9. 99994 

5 

66 

52  32 

7  28 

21189 

769 

78811 

21195 

769 

78805 

00006 

99994 

4 

67 

52  24 

7  36 

21958 

765 

78042 

21964 

766 

78036 

00006 

99994 

3 

68 

52  16 

7  44 

22713 

743 

77287 

22720 

742 

77280 

00006 

99994 

2 

59 

52  8 

7  52 

23456 

730 

76544 

23462 

730 

76538 

00006 

99994 

1 

60 
M. 

52  0 

8  0 

.24186 

717 

75814 

24192 

718 

75808 

00007 

99993 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.l'. 

Secant. 

Cotangent. 

Diff.  1'. 

Tangent. 

Cosecant. 

Sine. 

M. 

WP 

89°  1 

TABLE  44. 

[Page  773 

1° 

LiOg.  Sines,  Tangents,  and  Secants 

178° 

M. 
0 

Hour  A,  M. 

Hour  p.  M. 

Sine. 

Diff.  1'. 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Coeine. 

M. 
60 

11  52  0 

0  8  0 

8. 24186 

717 

11. 75814 

8.  24192 

718 

11. 75808 

10.00007 

9.99993 

1 

51  52 

8  8 

24903 

706 

75097 

24910 

706 

75090 

00007 

99993 

59 

2 

51  44 

8  16 

25609 

695 

74391 

25616 

696 

74384 

00007 

99993 

58 

3 

51  36 

8  24 

26304 

684 

73696 

26312 

684 

73688 

00007 

99993 

57 

4 

51  28 

8  32 

26988 

673 

73012 

26996 

673 

73004 

00008 
10.00008 

99992 
"9. 99992 

56 
55 

5 

11  51  20 

0  8  40 

8. 27661 

663 

11. 72339 

8.  27669 

663 

11. 72331 

6 

51  12 

8  48 

28324 

653 

71676 

28332 

654 

71668 

00008 

99992 

54 

7 

51  4 

8  56 

28977 

644 

71023 

28986 

643 

71014 

00008 

99992 

53 

8 

50  56 

«  4 

29621 

634 

70379 

29629 

634 

70371 

00008 

99992 

52 

9 

50  48 

9  12 

30255 

624 

69745 

30263 

625 

69737 

00009 

99991 

51 

10 

11  50  40 

0  9  20 

8.  30879 

616 

11. 69121 

8. 30888 

617 

11.69112 

10.00009 

9. 99991 

50 

11 

50  32 

9  28 

31495 

608 

68505 

31505 

607 

68495 

00009 

99991 

49 

12 

50  24 

9  36 

32103 

599 

67897 

32112 

599 

67888 

00010 

99990 

48 

13 

50  16 

9  44 

32702 

590 

67298 

32711 

591 

67289 

00010 

99990 

47 

14 

50  8 

9  52 

33292 

583 

66708 

33302 

584 

66698 

00010 

99990 
9. 99990 

46 
45 

15 

11  50  0 

0  10  0 

8.  33875 

575 

11.  66125 

8.  33886 

575 

11.66114 

10. 00010 

16 

49  52 

10  8 

34450 

568 

65550 

34461 

568 

66539 

00011 

99989 

44 

17 

49  44 

10  16 

35018 

560 

64982 

35029 

561 

64971 

00011 

99989 

43 

18 

49  36 

10  24 

35578 

553 

64422 

35590 

553 

64410 

00011 

99989 

42 

19 
20 

49  28 
11  49  20 

10  32 

36131 

547 

63869 

36143 
8:36689 

546 

63857 

00011 

99989 

41 
40 

0  10  40 

8.36678 

539 

11. 63322 

540 

11.  63311 

10. 00012 

9. 99988 

21 

49  12 

10  48 

37217 

533 

62783 

37229 

533 

62771 

00012 

99988 

39 

22 

49  4 

10  56 

37750 

526 

62250 

37762 

527 

62238 

00012 

99988 

38 

23 

48  56 

11  4 

38276 

520 

61724 

38289 

520 

61711 

00013 

99987 

37 

24 

48  48 

11  12 

38796 

514 

61204 

38809 
8. 39323 

514 

61191 

00013 

99987 

36 

25 

11  48  40 

0  11  20 

8. 39310 

508 

11.60690 

509 

11.60677 

10. 00013 

9.99987 

36 

26 

48  32 

11  28 

39818 

502 

60182 

39832 

502 

60168 

00014 

99986 

34 

27 

48  24 

11  36 

40320 

496 

59680 

40334 

496 

59666 

00014 

99986 

33 

28 

48  16 

11  44 

40816 

491 

59184 

40830 

491 

59170 

00014 

99986 

32 

29 
30 

48  8 

11  52 

41307 

485 

58693 

41321 

486 

58679 

00015 

99985 
9. 99985 

31 
30 

11  48  0 

0  12  0 

8. 41792 

480 

11. 58208 

8. 41807 

480 

11.58193 

10. 00015 

31 

47  52 

12  8 

42272 

474 

57728 

42287 

475 

57713 

00015 

99985 

29 

32 

47  44 

12  16 

42746 

470 

57254 

42762 

470 

57238 

00016 

99984 

28 

33 

47  36 

12  24 

43216 

464 

56784 

43232 

464 

56768 

00016 

99984 

27 

34 
36 

47  28 

12  32 

43680 

459 

56320 

43696 

460 

56304 

00016 

99984 
9. 99983 

26 
'25" 

11  47  20 

0  12  40 

8. 44139 

455 

11. 55861 

8. 44156 

465 

11.55844 

10. 00017 

36 

47  12 

12  48 

44594 

450 

55406 

44611 

450 

55389 

00017 

99983 

24 

37 

47  4 

12  56 

45044 

445 

54956 

45061 

446 

54939 

00017 

99983 

23 

38 

46  56 

13  4 

45489 

441 

54511 

45507 

441 

54493 

00018 

99982 

22 

39 

46  48 

13  12 

45930 

436 

54070 

45948 

437 

54052 

00018 

99982 

21 
20 

40 

11  46  40 

0  13  20 

8. 46366 

433 

11. 53634 

8. 46385 

432 

11. 53615 

10. 00018 

9. 99982 

41 

46  32 

13  28 

46799 

427 

53201 

46817 

428 

53183 

00019 

99981 

19 

42 

46  24 

13  36 

47226 

424 

52774 

47245 

424 

52755 

00019 

99981 

18 

43 

46  16 

13  44 

47650 

419 

52350 

47669 

420 

52331 

00019 

99981 

17 

44 
45 

46  8 

13  52 

48069 

416 

51931 

48089 

416 

51911 

00020 

99980 
9. 99980 

16 
15 

11  46  0 

0  14  0 

8. 48485 

411 

11. 51515 

8.  48505 

412 

11. 51495 

10. 00020 

46 

45  52 

14  8 

48896 

408 

51104 

48917 

408 

51083 

00021 

99979 

14 

47 

45  44 

14  16 

49304 

404 

50696 

49325 

404 

50675 

00021 

99979 

13 

48 

45  36 

14  24 

49708 

400 

50292 

49729 

401 

50271 

00021 

99979 

12 

49 
50 

45  28 

14  32 

50108 

396 

49892 

50130 

397 

49870 

00022 

99978 

11 
10 

11  45  20 

0  14  40 

8. 50504 

393 

11. 49496 

8. 50527 

393 

11. 49473 

10. 00022 

9. 99978 

51 

45  12 

14  48 

50897 

390 

49103 

50920 

390 

49080 

00023 

99977 

9 

52 

45  4 

14  56 

51287 

386 

48713 

51310 

386 

48690 

00023 

99977 

8 

53 

44  56 

15  4 

51673 

382 

48327 

51696 

383 

48304 

00023 

99977 

7 

54 

44  48 

15  12 

52055 

379 

47945 

52079 

380 

47921 

00024 

99976 
9. 99976 

6 
5 

55 

11  44  40 

0  15  20 

8.52434 

376 

11. 47566 

8. 52459 

376 

11. 47541 

10. 00024 

56 

44  32 

15  28 

52810 

373 

47190 

52835 

373 

47165 

00025 

99975 

4 

57 

44  24 

15  36 

53183 

369 

46817 

53208 

370 

46792 

00025 

99975 

3 

58 

44  16 

15  44 

53552 

367 

46448 

53578 

367 

46422 

00026 

99974 

2 

59 

44  8 

15  52 

53919 

363 

46081 

53945 

363 

46055 

00026 

99974 

1 

60 

44  0 

16  0 

54282 

360 

45718 

54308 

361 

45692 

00026 

99974 

0 

M. 

91° 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.l'. 

Secant. 

Cotangent. 

Diflf.  1'. 

Tangent. 

Cosecant. 

Sine. 

M. 

88°  1 

Page  774] 

TABLE  44. 

go 

Log.  Sines,  Tangents,  and  Secanta 

177° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DifE.l'. 

Cosecant. 

Tangent. 

Difl.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

11  44  0 

0  16  0 

8. 54282 

360 

11.45718 

8. 54308 

361 

11.45692 

10. 00026 

9.  99974 

60 

1 

43  52 

16  8 

54642 

357 

45358 

54669 

358 

45331 

00027 

99973 

59 

2 

43  44 

16  16 

54999 

355 

45001 

55027 

355 

44973 

00027 

99973 

58 

3 

43  36 

16  24 

55354 

351 

44646 

55382 

352 

44618 

00028 

99972 

57 

4 
5 

43  28 

16  32 

55705 

349 

44295 

55734 

349 

44266 

00028 

99972 

56 

11  43  20 

0  16  40 

8. 56054 

346 

11. 43946 

8. 56083 

346 

11. 43917 

10.  00029 

9. 99971 

55 

6 

43  12 

16  48 

56400 

343 

43600 

56429 

344 

43571 

00029 

99971 

54 

7 

43  4 

16  56 

56743 

341 

43257 

56773 

341 

43227 

00030 

99970 

53 

8 

42  56 

17  4 

57084 

337 

42916 

57114 

338 

42886 

0«030 

99970 

52 

9 

42  48 

17  12 

57421 

336 

42579 

57452 

336 

42548 

00031 

99969 

51 

10 

11  42  40 

0  17  20 

8. 57757 

332 

11. 42243 

8. 57788 

333 

11. 42212 

10. 00031 

9. 99969 

50 

11 

42  32 

17  28 

58089 

330 

41911 

58121 

330 

41879 

00032 

99968 

49 

12 

42  24 

17  36 

58419 

328 

41581 

58451 

328 

41549 

00032 

99968 

48 

13 

42  16 

17  44 

58747 

325 

41253 

58779 

326 

41221 

00033 

99967 

47 

14 

42  8 

17  52 

59072 

323 

40928 

59105 

323 

40895 

00033 

99967 

46 
45 

15 

11  42  0 

0  18  0 

8. 59395 

320 

11.40605 

8. 59428 

321 

11. 40572 

10. 00033 

9. 99967 

16 

41  52 

18  8 

59715 

318 

40285 

59749 

319 

40251 

00034 

99966 

44 

17 

41  44 

18  16 

60033 

316 

39967 

60068 

316 

39932 

00034 

99966 

43 

18 

41  36 

18  24 

60349 

313 

39651 

60384 

314 

39616 

00035 

99965 

42 

19 

41  28 

18  32 

60662 

311 

39338 

60698 

311 

39302 

00036 

99964 

41 

20 

11  41  20 

0  18  40 

8. 60973 

309 

11. 39027 

8. 61009 

310 

11. 38991 

10. 00036 

9. 99964 

40 

21 

41  12 

18  48 

61282 

307 

38718 

61319 

307 

38681 

00037 

99963 

39 

22 

41  4 

18  56 

61589 

305 

38411 

61626 

305 

38374 

00037 

99963 

38 

23 

40  56 

19  4 

61894 

302 

38106 

61931 

303 

38069 

00038 

99962 

37 

24 

40  48 

19  12 

62196 

301 

37804 

62234 

301 

37766 

00038 

99962 

36 
35 

25 

11  40  40 

0  19  20 

8. 62497 

298 

11. 37503 

8. 62535 

299 

11.  .37465 

10. 00039 

9. 99961 

26 

40  32 

19  28 

62795 

296 

37205 

62834 

297 

37166 

00039 

99961 

34 

27 

40  24 

19  36 

63091 

294 

36909 

63131 

295 

36869 

00040 

99960 

33 

28 

40  16 

19  44 

63385 

293 

36615 

63426 

292 

36574 

00040 

99960 

32 

29 

40  8 

19  52 

63678 

290 

36322 

63718 

291 

36282 

00041 

99959 

31 
30 

30 

11  40  0 

0  20  0 

8. 63968 

288 

11. 36032 

8. 64009 

289 

11. 35991 

10.  00041 

9. 99959 

31 

39  52 

20  8 

64256 

287 

35744 

64298 

287 

35702 

00042 

99958 

29 

32 

39  44 

20  16 

64543 

284 

35457 

64585 

285 

35415 

00042 

99958 

28 

33 

39  36 

20  24 

64827 

283 

35173 

64870 

284 

35130 

00043 

99957 

27 

34 

39  28 

20  32 

65110 

281 

34890 

65154 

281 

34846 

00044 

99956 

26 

35 

11  39  20 

0  20  40 

8. 65391 

279 

11. 34609 

8. 65435 

280 

11. 34565 

10. 00044 

9. 99956 

25 

36 

39  12 

20  48 

65670 

277 

34330 

65715 

278 

34285 

00045 

99955 

24 

37 

39  4 

20  56 

65947 

276 

34053 

65993 

276 

34007 

00045 

99955 

23 

38 

38  56 

21  4 

66223 

274 

33777 

66269 

274 

33731 

00046 

99954 

22 

39 
40 

38  48 

21  12 

66497 

272 

33503 

66543 

273 

33457 

00046 

99954 

21 

11  38  40 

0  21  20 

8. 66769 

270 

11. 33231 

8. 66816 

271 

11. 33184 

10. 00047 

9. 99953 

20 

41 

38  32 

21  28 

67039 

269 

32961 

67087 

269 

32913 

00048 

99952 

19 

42 

38  24 

21  36 

67308 

267 

32692 

67356 

268 

32644 

00048 

99952 

18 

43 

38  16 

21  44 

67575 

266 

32425 

67624 

266 

32376 

00049 

99951 

17 

44 

38  8 

21  52 

67841 

263 

32159 

67890 

264 

32110 

00049 

99951 

16 

45 

11  38  0 

0  22  0 

8. 68104 

263 

11. 31896 

8.  68154 

263 

11. 31846 

10. 00050 

9. 99950 

15 

46 

37  52 

22  8 

68367 

260 

31633 

68417 

261 

31583 

00051 

99949 

14 

47 

37  44 

22  16 

68627 

259 

31373 

68678 

260 

31322 

00051 

99949 

13 

48 

37  36 

22  24 

68886 

258 

31114 

68938 

258 

31062 

00052 

99948 

12 

49 

37  28 

22  32 

69144 

256 

30856 

69196 

257 

30804 

00052 

99948 

11 
10 

50 

11  37  20 

0  22  40 

8. 69400 

254 

11. 30600 

8. 69453 

255 

11. 30547 

10. 00053 

9. 99947 

51 

37  12 

22  48 

69654 

253 

30346 

69708 

254 

30292 

00054 

99946 

9 

52 

37  4 

22  56 

69907 

252 

30093 

69962 

252 

30038 

00054 

99946 

8 

53 

36  56 

23  4 

70159 

250 

29841 

70214 

251 

29786 

00055 

99945 

7 

54 

36  48 

23  12 

70409 

249 

29591 

70465 

249 

29535 

00056 

99944 

6 

55 

11  36  40 

0  23  20 

8. 70658 

247 

11. 29342 

8.  70714 

248 

11.29286 

10. 00056 

9.  99944 

5 

56 

36  32 

23  28 

70905 

246 

29095 

70962 

246 

29038 

00057 

99943 

4 

57 

36  24 

23  36 

71151 

244 

28849 

71208 

245 

28792 

00058 

99942 

3 

58 

36  16 

23  44 

71395 

243 

28605 

71453 

244 

28547 

00058 

99942 

2 

59 

36  8 

23  52 

71638 

242 

28362 

71697 

243 

28303 

00059 

99941 

1 

60 

36  0 

24  0 

71880 

240 

28120 

71940 

241 

28060 

00060 

99940 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Dill.  1'. 

Secant. 

Cotangent. 

Diff.l'. 

Tangent. 

Cosecant. 

Sine. 

M. 

92° 

87° 

. 

TABLE  44. 

[Page  775 

8° 

[jog.  Sines,  Tangents,  and  Secants 

1760 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difif.  1'. 

Ck)8ecaiit. 

Tangent. 

Difl.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

11  36  0 

0  24  0 

8. 71880 

240 

11. 28120 

8. 71940 

241 

11.  28060 

10.00060 

9.99940 

60 

1 

35  52 

24  8 

72120 

239 

27880 

72181 

239 

27819 

00060 

99940 

59 

2 

35  44 

24  16 

72359 

238 

27641 

72420 

239 

27580 

00061 

99939 

58 

3 

35  36 

24  24 

72597 

237 

27403 

72659 

237 

27341 

00062 

99938 

57 

4 
5 

35  28 

24  32 

72834 

235 

27166 

72896 

236 

27104 

00062 

99938 

56 
55 

11  35  20 

0  24  40 

8. 73069 

234 

11. 26931 

8. 73132 

234 

11. 26868 

10. 00063 

9. 99937 

6 

35  12 

24  48 

73303 

232 

26697 

73366 

234 

26634 

00064 

99936 

54 

7 

35  4 

24  56 

73535 

232 

26465 

73600 

232 

26400 

00064 

99936 

53 

8 

:i4  56 

25  4 

73767 

230 

26233 

73832 

231 

26168 

00065 

99935 

52 

9 

34  48 

25  12 

73997 

229 

26003 

74063 

229 

25937 

00066 

99934 

51 

10 

11  34  40 

0  25  20 

8. 74226 

228 

11. 25774 

8.  74292 

229 

11. 25708 

10.00066 

9. 99934 

50 

11 

34  32 

25  28 

74454 

226 

25546 

74521 

227 

25479 

00067 

99933 

49 

12 

34  24 

25  36 

74680 

226 

25320 

74748 

226 

25252 

00068 

99932 

48 

13 

34  16 

25  44 

74906 

224 

25094 

74974 

225 

25026 

00068 

99932 

47 

14 

34  8 

25  52 

75130 

223 

24870 

75199 

224 

24801 

00069 

99931 

46 

15 

11  34  0 

0  26  0 

8. 75353 

222 

11. 24647 

8. 75423 

222 

11. 24577 

10. 00070 

9.99930 

45 

16 

33  52 

26  8 

75575 

220 

24425 

75645 

222 

24355 

00071 

99929 

44 

17 

33  44 

26  16 

75795 

220 

24205 

75867 

220 

24133 

00071 

99929 

43 

18 

33  36 

26  24 

76015 

219 

23985 

76087 

219 

23913 

00072 

99928 

42 

19 

33  28 

26  32 

76234 

217 

23766 

76306 

219 

23694 

00073 

99927 

41 

20 

11  33  20 

0  26  40 

8.76451 

216 

11. 23549 

8. 76525 

217 

11.  23475 

10. 00074 

9. 99926 

40 

21 

33  12 

26  48 

76667 

216 

23333 

76742 

216 

23258 

00074 

99926 

39 

22 

33  4 

26  56 

76883 

214 

23117 

76958 

215 

23042 

00075 

99925 

38 

23 

32  56 

27  4 

77097 

213 

22903 

77173 

214 

22827 

00076 

99924 

37 

24 

32  48 

27  12 

77310 

212 

22690 

77387 

213 

22613 

00077 

99923 

36 

25 

11  32  40 

0  27  20 

8. 77522 

211 

11. 22478 

8.77600 

211 

11. 22400 

10. 00077 

9.99923 

35 

26 

32  32 

27  28 

77733 

210 

22267 

77811 

211 

22189 

00078 

99922 

34 

27 

32  24 

27  36 

77943 

209 

22057 

78022 

210 

21978 

00079 

99921 

33 

28 

32  16 

27  44 

78152 

208 

21848 

78232 

209 

21768 

00080 

99920 

32 

29 

32  8 

27  52 

78360 

208 

21640 

78441 

208 

21559 

00080 

99920 

31 
30 

30 

11  32  0 

0  28  0 

8.  78568 

206 

11. 21432 

8. 78649 

206 

11. 21351 

10. 00081 

9. 99919 

31 

31  52 

28  8 

78774 

205 

21226 

78855 

206 

21145 

00082 

99918 

29 

32 

31  44 

28  16 

78979 

204 

21021 

79061 

205 

20939 

00083 

99917 

28 

33 

31  36 

28  24 

79183 

203 

20817 

79266 

204 

207.34 

00083 

99917 

27 

34 
35 

31  28 

28  32 

79386 

202 

20614 

79470 

203 

2^530 

00084 

99916 

26 

11  31  20 

0  28  40 

8. 79588 

201 

11.20412 

8. 79673 

202 

11. 20327 

10.00085 

9.99915 

25 

36 

31  12 

28  48 

79789 

201 

20211 

79875 

201 

20125 

00086 

99914 

24 

37 

31  4 

28  56 

79990 

199 

20010 

80076 

201 

19924 

00087 

99913 

23 

38 

30  56 

29  4 

80189 

199 

19811 

80277 

199 

19723 

00087 

99913 

22 
21 

39 

30  48 

29  12 

80388 

197 

19612 

80476 

198 

19524 

00088 

99912 

40 

11  30  40 

0  29  20 

8. 80585 

197 

11. 19415 

8. 80674 

198 

11. 19326 

10. 00089 

9. 99911 

20 

41 

30  32 

29  28 

80782 

196 

19218 

80872 

196 

19128 

00090 

99910 

19 

42 

30  24 

29  36 

80978 

195 

19022 

81068 

196 

18932 

00091 

99909 

18 

43 

30  16 

29  44 

81173 

194 

18827 

81264 

195 

18736 

00091 

99909 

17 

44 

30  8 

29  52 

81367 

193 

18633 

81459 

194 

18541 

00092 

99908 

16 

45 

11  30  0 

0  30  0 

8. 81560 

192 

11. 18440 

8. 81653 

193 

11. 18347 

10.00093 

9. 99907 

15 

46 

29  52 

30  8 

81752 

192 

18248 

81846 

192 

18154 

00094 

99906 

14 

47 

29  44 

30  16 

81944 

190 

18056 

82038 

192 

17962 

00095 

99905 

13 

48 

29  36 

30  24 

82134 

190 

17866 

82230 

190 

17770 

00096 

99904 

12 

49 
50 

29  28 

30  32 
0  30  40 

82324 

189 

17676 

82420 

190 

17580 

00096 

99904 

11 
10 

11  29  20 

8. 82513 

188 

11. 17487 

8. 82610 

189 

11. 17390 

10.00097 

9.99903 

51 

29  12 

30  48 

82701 

187 

17299 

82799 

188 

17201 

00098 

99902 

9 

52 

29  4 

30  56 

82888 

187 

17112 

82987 

188 

17013 

00099 

99901 

8 

53 

28  56 

31  4 

83075 

186 

16925 

83175 

186 

16825 

00100 

99900 

7 

54 
55^ 

28  48 

31  12 

83261 

185 

16739 

83361 

186 

16639 

00101 

99899 

6 
5 

11  28  40 

0  31  20 

8. 83446 

184 

11. 16554 

8. 83547 

185 

11. 16453 

10. 00102 

9. 99898 

56 

28  32 

31  28 

83630 

183 

16370 

83732 

184 

16268 

00102 

99898 

4 

57 

28  24 

31  36 

83813 

183 

16187 

83916 

184 

16084 

00103 

99897 

3 

58 

28  16 

31  44 

83996 

181 

16004 

84100 

182 

15900 

00104 

99896 

2 

59 

28  8 

31  52 

84177 

181 

15823 

84282 

182 

15718 

00105 

99895 

1 

60 

28  0 

32  0 

84358 

181 

15642 

84464 

182 

15536 

00106 

99894 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosiiie. 

Difl.l'. 

Secant. 

Cotangent. 

Difif.  I'. 

Tangent. 

Cosecant. 

Sine 

M. 

98° 

86°  1 

Page  776] 

TABLE  44. 

4° 

Log.  Sines,  Tangents,  and  Secants 

175° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.r. 

Cosecant. 

Tangent. 

Diff.l'. 

'Cotangent. 

Secant. 

Cosine.  1  M. 

0 

11  28  0 

0  32  0 

8.  84358 

181 

11. 15642 

8.84464 

182 

11. 15536 

10.  00106 

9. 99894 

60 

1 

27  52 

32  8 

84539 

179 

15461 

84646 

180 

15354 

00107 

99893 

59 

2 

27  44 

32  16 

84718 

179 

15282 

84826 

180 

15174 

00108 

99892 

58 

3 

27  36 

32  24 

84897 

178 

15103 

85006 

179 

14994 

00109 

99891 

57 

4 

27  28 

32  32 

85075 

177 

14925 

85185 

178 

14815 

00109 

99891 

56 
55 

5 

11  27  20 

0  32  40 

8. 85252 

177 

11. 14748 

8.  86363 

177 

11. 14637 

10.  001 10 

9. 99890 

6 

27  12 

32  48 

85429 

176 

14571 

85540 

177 

14460 

00111 

99889 

54 

7 

27  4 

32  56 

85605 

175 

14395 

85717 

176 

14283 

00112 

99888 

58 

8 

26  56 

33  4 

85780 

175 

14220 

85893 

176 

14107 

00113 

99887 

52 

9 

26  48 

33  12 

85955 

173 

14045 

86069 

174 

13931 

00114 

99886 

51 

10 

11  26  40 

0  33  20 

8. 86128 

173 

11. 13872 

8. 86243 

174 

11.13757 

10.  00115 

9. 99885 

50 

11 

26  32 

33  28 

86301 

173 

13699 

86417 

174 

13583 

00116 

99884 

49 

12 

26  24 

33  36 

86474 

171 

13526 

86591 

172 

13409 

00117 

99883 

48 

13 

26  16 

33  44 

86645 

171 

13355 

86763 

172 

13237 

00118 

99882 

47 

14 

15 

26  8 

33  52 

86816 

171 

13184 

86935 

171 

13065 

00119 

99881 

46 
45 

11  26  0 

0  34  0 

8. 86987 

169 

11. 13013 

8.  87106 

171 

11. 12894 

10. 00120 

9. 99880 

16 

25  52 

34  8 

87156 

169 

12844 

87277 

170 

12723 

00121 

99879 

44 

17 

25  44 

34  16 

87325 

169 

12675 

87447 

169 

12553 

00121 

99879 

43 

18 

25  36 

34  24 

87494 

167 

12506 

87616 

169 

12384 

00122 

99878 

42 

19 

25  28 

34  32 

87661 

168 

12339 

87785 

168 

12215 

00123 

99877 

41 

20 

11  25  20 

0  34  40 

8. 87829 

166 

11.12171 

8. 87953 

167 

11. 12047 

10. 00124 

9. 99876 

40 

21 

25  12 

34  48 

87995 

166 

12005 

88120 

167 

11880 

00125 

99875 

39 

22 

25  4 

34  56 

88161 

165 

11839 

88287 

166 

11713 

00126 

99874 

38 

23 

24  56 

35  4 

88326 

164 

11674 

88453 

165 

11547 

00127 

99873 

37 

24 

24  48 

35  12 

88490 

164 

11510 

88618 

165 

11382 

00128 

99872 

36 
35 

25 

11  24  40 

0  35  20 

8. 88654 

163 

11. 11346 

8. 887)53 

165 

11. 11217 

10. 00129 

9. 99871 

26 

24  32 

35  28 

88817 

163 

11183 

88948 

163 

11052 

00130 

99870 

34 

27 

24  24 

35  36 

88980 

162 

11020 

89111 

163 

10889 

00131 

99869 

33 

28 

24  16 

35  44 

89142 

162 

10a58 

89274 

163 

10726 

00132 

99868 

32 

29 
30 

24  8 

35  52 

89304 

160 

10696 

89437 

161 

10563 

00133 

99867 

31 

11  24  0 

0  36  0 

8.  89464 

161 

11. 10536 

8. 89598 

162 

11. 10402 

10.  00134 

9. 99866 

30 

31 

23  52 

36  8 

89625 

169 

10375 

89760 

160 

10240 

00135 

99865 

29 

32 

23  44 

36  16 

89784 

159 

10216 

89920 

160 

10080 

00136 

99864 

28 

33 

23  36 

36  24 

89943 

159 

10057 

90080 

160 

09920 

00137 

99863 

27 

34 

23  28 

36  32 

90102 

158 

09898 

90240 

159 

09760 

00138 

99862 

26 

35 

11  23  20 

0  36  40 

8. 90260 

157 

11. 09740 

8. 90399 

158 

11. 09601 

10. 00139 

9. 99861 

26 

36 

23  12 

36  48 

90417 

157 

09583 

90557 

158 

09443 

00140 

99860 

24 

37 

23  4 

36  56 

90574 

156 

09426 

90715 

157 

09285 

00141 

99859 

23 

38 

22  56 

37  4 

90730 

155 

09270 

90872 

157 

09128 

00142 

99858 

22 

39 

22  48 

37  12 

90885 

155 

09115 

91029 

156 

08971 

00143 

99857 

21 

40 

11  22  40 

0  37  20 

8. 91040 

155 

11. 08960 

8. 91185 

155 

11. 08815 

10. 00144 

9. 99856 

20 

41 

22  32 

37  28 

91195 

154 

08805 

91340 

155 

08660 

00145 

99855 

19 

42 

22  24 

37  36 

91349 

153 

08651 

91495 

155 

08505 

00146 

99854 

18 

43 

22  16 

37  44 

91502 

153 

08498 

91650 

153 

08350 

00147 

99853 

17 

44 

22  8 

37  52 

91655 

152 

08345 

91803 

154 

08197 

00148 

99852 

16 

45 

11  22  0 

0  38  0 

8. 91807 

152 

11. 08193 

8. 91957 

153 

11. 08043 

10. 00149 

9. 99851 

16 

46 

21  52 

38  8 

91959 

151 

08041 

92110 

152 

07890 

00150 

99850 

14 

47 

21  44 

38  16 

92110 

151 

07890 

92262 

152 

07738 

00152 

99848 

13 

48 

21  36 

38  24 

92261 

150 

07739 

92414 

151 

07586 

00153 

99847 

12 

49 

21  28 

38  32 

92411 

150 

07589 

92565 

151 

07435 

00154 

99846 

11 

50 

11  21  20 

0  38  40 

8. 92561 

149 

11. 07439 

8.  92716 

150 

11. 07284 

10.  00155 

9.  99845 

10 

51 

21  12 

38  48 

92710 

149 

07290 

92866 

150 

07134 

00156 

99844 

9 

52 

21  4 

38  56 

92859 

148 

07141 

93016 

149 

06984 

00157 

99843 

8 

53 

20  56 

39  4 

93007 

147 

06993 

93165 

148 

06835 

00158 

99842 

7 

54 

20  48 

39  12 

93154 

147 

06846 

93313 

149 

06687 

00159 

99841 

6 

55 

11  20  40 

0  39  20 

8. 93301 

147 

11. 06699 

8. 93462 

147 

11. 06538 

10. 00160 

9. 99840 

6 

56 

20  32 

39  28 

93448 

146 

06552 

93609 

147 

06391 

00161 

99839 

4 

57 

20  24 

39  36 

93594 

146 

06406 

93756 

147 

06244 

00162 

99838 

3 

58 

20  16 

39  44 

93740 

145 

06260 

93903 

146 

06097 

00163 

99837 

2 

69 

20  8 

39  52 

93885 

145 

06115 

94049 

146 

05951 

00164 

99836 

1 

60 

20  0 

40  0 

94030 

144 

05970 

94195 

145 

05806 

00166 

99834 

0 

M. 

Hour  p.  M. 

Hour  A.  M . 

Cosine. 

Diff.r. 

Secant. 

Cotangent. 

Diff.l'. 

Tangent. 

Cosecant 

Sine. 

M. 

»4o 

85°  1 

TABLE  44. 

[Page  777 

Log. 

Sines,  Tangents,  and  Secants. 

e° 

A 

A         B 

B 

C 

C    174° 

M. 
0 

Hour  A.  K. 

Hour  p.  H. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

11  20  00 

0  40  00 

8.  94030 

0 

11.  05970 

8.  94195 

0 

11. 05805 

10. 00166 

0 

9. 99834 

60 

1 

19  52 

40  08 

94174 

2 

05826 

94340 

2 

05660 

00167 

0 

99833 

59 

2 

19  44 

40  16 

94317 

4 

05683 

94485 

4 

05515 

00168 

0 

99832 

58 

3 

19  36 

40  24 

94461 

7 

05539 

94630 

7 

05370 

00169 

0 

99831 

57 

4 

19  28 

40  32 

94603 

9 

05397 

94773 

9 

05227 

00170 

0 

99830 

56 

5 

11  19  20 

0  40  40 

8. 94746 

11 

11. 05254 

8. 94917 

11 

11.05083 

10.00171 

0 

9. 99829 

55 

6 

19  12 

40  48 

94887 

13 

05113 

95060 

13 

04940 

00172 

0 

99828 

54 

7 

19  04 

40  56 

95029 

15 

04971 

95202 

15 

04798 

00173 

0 

99827 

53 

8 

18  56 

41  04 

95170 

18 

04830 

95344 

18 

04656 

00175 

0 

99825 

52 

9 

18  48 

41  12 

95310 

20 

04690 

95486 

20 
22 

04514 

00176 

0 

99824 

51 
50 

10 

11  18  40 

0  41  20 

8. 95450 

22 

11. 04550 

8. 95627 

11.04373 

10.00177 

0 

9. 99823 

n 

18  32 

41  28 

95589 

24 

04411 

95767 

24 

04233 

00178 

0 

99822 

49 

12 

18  24 

41  36 

95728 

26 

04272 

95908 

27 

04092 

00179 

0 

99821 

48 

13 

18  16 

41  44 

95867 

29 

04133 

96047 

29 

03953 

00180 

0 

99820 

47 

14 
15 

18  08 

41  52 

96005 

31 

03995 

96187 

31 

03813 

00181 

0 

99819 
9. 99817 

46 
45 

11  18  00 

0  42  00 

8. 96143 

33 

11.03857 

8. 96325 

33 

11.03675 

10. 00183 

0 

16 

17  52 

42  08 

96280 

35 

03720 

96464 

35 

03536 

00184 

0 

99816 

44 

17 

17  44 

42  16 

96417 

37 

03583 

96602 

38 

03398 

00185 

0 

99815 

43 

18 

17  36 

42  24 

96553 

39 

03447 

96739 

40 

03261 

00186 

0 

99814 

42 

19 

17  28 

42  32 

96689 

42 

03311 

96877 

42 

03123 

00187 

0 

99813 

41 

20 

11  17  20 

0  42  40 

8. 96825 

44 

11. 03175 

8. 97013 

44 

11. 02987 

10. 00188 

0 

9. 99812 

40 

21 

17  12 

42  48 

96960 

46 

03040 

97150 

46 

02850 

00190 

0 

99810 

39 

22 

17  04 

42  56 

97095 

48 

02905 

97285 

49 

02715 

00191 

0 

99809 

38 

23 

16  56 

43  04 

97229 

50 

02771 

97421 

51 

02579 

00192 

0 

99808 

37 

24 

16  48 

43  12 

97363 

53 

02637 

97556 

53 
55 

02444 

00193 

0 

99807 

36 
35 

25 

11  16  40 

0  43  20 

8. 97496 

55 

11. 02504 

8. 97691 

11.02309 

10. 00194 

9.99806 

26 

16  32 

43  28 

97629 

57 

02371 

97825 

58 

02175 

00196 

99804 

34 

27 

16  24 

43  36 

97762 

59 

02238 

97959 

60 

02041 

00197 

99803 

33 

28 

16  16 

43  44 

97894 

61 

02106 

98092 

62 

01908 

00198 

99802 

32 

29 

16  08 

43  52 

98026 

64 

01974 

98225 

64 

01775 
11.01642 

00199 

99801 

31 

30 

11  16  00 

0  44  00 

8. 98157 

66 

11.01843 

8.  98358 

66 

10.00200 

9.99800 

30 

31 

15  62 

44  08 

98288 

68 

01712 

98490 

69 

01510 

00202 

1 

99798 

29 

32 

15  44 

44  16 

98419 

70 

01581 

98622 

71 

01378 

00203 

99797 

28 

33 

15  36 

44  24 

98549 

72 

01451 

98753 

73 

01247 

00204 

99796 

27 

34 
35" 

15  28 

44  32 

98679 

75 

01321 

98884 

75 

01116 

00205 

99795 

26 
25 

11  15  20 

0  44  40 

8. 98808 

77 

11. 01192 

8.99015 

77 

11.00985 

10. 00207 

9. 99793 

36 

15  12 

44  48 

98937 

79 

01063 

99145 

80 

00855 

00208 

99792 

24 

37 

15  04 

44  56 

99066 

81 

00934 

99275 

82 

00725 

00209 

1 

99791 

23 

38 

14  56 

45  04 

99194 

83 

00806 

99405 

84 

00595 

00210 

1 

99790 

22 

39 
40 

14  48 

45  12 

99322 

86 

00678 

99534 
8.99662 

86 
89 

00466 

00212 

99788 

21 

11  14  40 

0  45  20 

8.  99450 

88 

11. 00550 

11. 00338 

10. 00213 

9. 99787 

20 

41 

14  32 

45  28 

99577 

90 

00423 

99791 

91 

00209 

00214 

1 

99786 

19 

42 

14  24 

45  36 

99704 

92 

00296 

99919 

93 

00081 

00215 

1 

99785 

18 

43 

14  16 

45  44 

99830 

94 

00170 

9.00046 

95 

10.  99954 

00217 

99783 

17 

44 
45 

14  08 

45  52 

99956 

96 

00044 

00174 

97 

99826 

00218 

99782 

16 

15 

11  14  00 

0  46  00 

9. 00082 

99 

10. 99918 

9. 00301 

100 

10. 99699 

10. 00219 

9. 99781 

46 

13  52 

46  08 

00207 

101 

99793 

00427 

102 

99573 

00220 

99780 

14 

47 

13  44 

46  16 

00332 

103 

99668 

00553 

104 

99447 

00222 

1 

99778 

13 

48 

13  36 

46  24 

00456 

105 

99544 

00679 

106 

99321 

00223 

1 

99777 

12 

49 

13  28 

46  32 

00581 

107 

99419 

00805 

108 

99195 

00224 

1 

99776 

11 

50 

11  13  20 

0  46  40 

9.00704 

110 

10.  99296 

9.00930 

111 

10. 99070 

10. 00225 

9. 99775 

10 

51 

13  12 

46  48 

00828 

112 

99172 

01055 

113 

98945 

00227 

99773 

9 

52 

13  04 

46  56 

00951 

114 

99049 

01179 

115 

98821 

00228 

99772 

8 

53 

12  56 

47  04 

01074 

116 

98926 

01303 

117 

98697 

00229 

99771 

7 

54 

12  48 

47  12 

01196 

118 

98804 

01427 

120 

98573 

00231 

99769 

6 

55 

11  12  40 

0  47  20 

9.  01318 

121 

10. 98682 

9. 01550 

122 

10. 98450 

10. 00232 

99768 

5 

56 

12  32 

47  28 

01440 

123 

98560 

01673 

124 

98327 

00233 

99767 

4 

57 

12  24 

47  36 

01561 

125 

98439 

01796 

126 

98204 

00235 

99765 

3 

58 

12  16 

47  44 

01682 

127 

98318 

01918 

128 

98082 

00236 

99764 

2 

59 

12  08 

47  52 

01803 

129 

98197 

02040 

131 

97960 

00237 

99763 

1 

60 

12  00 

48  00 

01923 

132 

98077 

02162 

133 

97838 

00239 

99761 

0 

M. 

Hour  p.  K. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

96° 

A 

A        B 

B 

C 

C    84°  1 

Seconds  of  time 


Prop,  parts 


of  cols.  ■<  B 

Ic 


115 

116 

1 


Page  778] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

«° 

A            A 

B            B 

C 

C   178° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

11  12  00 

0  48  00 

9. 01923 

0 

10.  98077 

9. 02162 

0 

10. 97838 

10.  00239 

0 

9. 99761 

60 

1 

11  52 

48  08 

02043 

2 

97957 

02283 

2 

97717 

00240 

0 

99760 

59 

2 

11  44 

48  16 

02163 

4 

97837 

02404 

4 

97596 

00241 

0 

99759 

58 

3 

11  36 

48  24 

02283 

6 

97717 

02525 

6 

97475 

00243 

0 

99757 

57 

4 

11  28 

48  32 

02402 

7 
9 

97598 

02645 

8 

97355 
10.  97234 

00244 
10. 00245 

0 
0 

99756 
9. 99755 

56 
55 

fi 

11  11  20 

0  48  40 

9. 02520 

10. 97480 

9. 02766 

9 

6 

11  12 

48  48 

02639 

11 

97361 

02885 

11 

97115 

00247 

0 

99753 

54 

7 

11  04 

48  56 

02757 

13 

97243 

03005 

13 

96995 

00248 

0 

99752 

53 

8 

10  56 

49  04 

02874 

15 

97126 

03124 

15 

96876 

00249 

0 

99751 

52 

9 
10 

10  48 

49  12 
0  49  20" 

02992 

17 

97008 

03242 

17 

96758 

00251 

0 

99749 

51 

11  10  40 

9. 03109 

19 

10.  96891 

9. 03361 

19 

10.  96639 

10. 00252 

0 

9. 99748 

50 

n 

10  32 

49  28 

03226 

20 

96774 

03479 

21 

96521 

00253 

0 

99747 

49 

12 

10  24 

49  36 

03342 

22 

96658 

03597 

23 

96403 

00255 

0 

99745 

48 

13 

10  16 

49  44 

03458 

24 

96542 

03714 

24 

96286 

00256 

0 

99744 

47 

14 

10  08 

49  52 

03574 

26 

96426 

03832 

26 

96168 

00258 

0 

99742 

46 
45 

15 

11  10  00 

0  50  00 

9. 03690 

28 

10. 96310 

9. 03948 

28 

10. 96052 

10. 00259 

0 

9. 99741 

16 

9  52 

50  08 

03805 

30 

96195 

04065 

30 

95935 

00260 

0 

99740 

44 

17 

9  44 

50  16 

03920 

31 

96080 

04181 

32 

95819 

00262 

0 

99738 

43 

18 

9  36 

50  24 

04034 

33 

95966 

04297 

34 

95703 

00263 

0 

99737 

42 

19 

9  28 

50  32 

04149 

35 

95851 

04413 

36 

95587 

00264 

0 

99736 

41 

40 

20 

11  9  20 

0  50  40 

9. 04262 

37 

10. 95738 

9.  04528 

38 

10.  95472 

10.  00266 

0 

9. 99734 

21 

9  12 

50  48 

04376 

39 

95624 

04643 

39 

95357 

00267 

99733 

39 

22 

9  04 

50  56 

04490 

41 

95510 

04758 

41 

95242 

00269 

99731 

38 

23 

8  56 

51  04 

04603 

43 

95397 

04873 

43 

95127 

00270 

99730 

37 

24 

8  48 

51  12 

04715 

44 

95285 

04987 

45 

95013 

00272 

1 

99728 

36 
35 

25 

11  8  40 

0  51  20 

9. 04828 

46 

10. 95172 

9. 05101 

47 

10. 94899 

10.  00273 

9. 99727 

26 

8  32 

51  28 

04940 

48 

95060 

05214 

49 

94786 

00274 

99726 

34 

27 

8  24 

51  36 

05052 

50 

94948 

05328 

51 

94672 

00276 

99724 

33 

28 

8  16 

51  44 

05164 

52 

94836 

05441 

53 

94559 

00277 

1 

99723 

32 

29 

8  08 

51  52 

05275 

54 

94725 

05553 

54 

94447 

00279 

1 

99721 

31 

30 

11  8  00 

0  52  00 

9. 05386 

56 

10.  94614 

9. 05666 

56 

10.  94334 

10. 00280 

9. 99720 

30 

31 

7  52 

52  08 

05497 

57 

94503 

05778 

58 

94222 

00282 

99718 

29 

32 

7  44 

52  16 

05607 

59 

94393 

05890 

60 

94110 

00283 

99717 

28 

33 

7  36 

52  24 

05717 

61 

94283 

06002 

62 

93998 

00284 

99716 

27 

34 

7  28 

52  32 

05827 

63 

94173 

06113 

64 

93887 

00286 

99714 

26 

35 

11  7  20 

0  52  40 

9. 05937 

65 

10.  94063 

9. 06224 

66 

10. 93776 

10. 00287 

9. 99713 

25 

36 

7  12 

52  48 

06046 

67 

93954 

06335 

68 

93665 

00289 

99711 

24 

37 

7  04 

52  56 

06155 

69 

93845 

06445 

69 

93555 

00290 

99710 

23 

38 

6  56 

53  04 

06264 

70 

93736 

06556 

71 

93444 

00292 

99708 

22 

39 

6  48 

53  12 

06372 

72 

93628 

06666 

73 

93334 

00293 

99707 
9. 99705 

21 
20 

40 

11  6  40 

0  53  20 

9. 06481 

74 

10.  93519 

9. 06775 

75 

10.  93225 

10. 00295 

41 

6  32 

53  28 

06589 

76 

93411 

06885 

77 

93115 

00296 

99704 

19 

42 

6  24 

53  36 

06696 

78 

93304 

06994 

79 

93006 

00298 

99702 

18 

43 

6  16 

53  44 

06804 

80 

93196 

07103 

81 

92897 

00299 

99701 

17 

44 

6  08 

53  52 

06911 

81 

93089 

07211 

83 

84 

92789 

00301 

99699 

16 
15 

45 

11  6  00 

0  54  00 

9. 07018 

83 

10. 92982 

9. 07320 

10. 92680 

10.  00302 

9. 99698 

46 

5  52 

54  08 

07124 

85 

92876 

07428 

86 

92572 

00304 

99696 

14 

47 

5  44 

54  16 

07231 

87 

92769 

07536 

88 

92464 

00305 

99695 

13 

48 

5  36 

54  24 

07337 

89 

92663 

07643 

90 

92357 

00307 

99693 

12 

49 

5  28 

54  32 

07442 

91 
93 

92558 

07751 

92 

92249 
10. 92142 

00308 

1 

99692 
9.99690 

11 
10 

50 

11  5  20 

0  54  40 

9. 07548 

10. 92452 

9.  07858 

94 

10.  00310 

51 

5  12 

54  48 

07653 

94 

92347 

07964 

96 

92036 

00311 

99689 

9 

52 

5  04 

54  56 

07758 

96 

92242 

08071 

98 

91929 

00313 

99687 

8 

53 

4  56 

55  04 

07863 

98 

92137 

08177 

99 

91823 

00314 

99686 

7 

54 

4  48 

55  12 

07968 

100 

92032 

08283 

101 

91717 

00316 

99684 

6 
5 

55 

11  4  40 

0  55  20 

9. 08072 

102 

10. 91928 

9.  08389 

103 

10. 91611 

10. 00317 

9. 99683 

56 

4  32 

55  28 

08176 

104 

91824 

08495 

105 

91505 

00319 

99681 

4 

57 

4  24 

55  36 

08280 

106 

91720 

08600 

107 

91400 

00320 

99680 

3 

58 

4  16 

55  44 

08383 

107 

91617 

08705 

109 

91295 

00322 

99678 

2 

59 

4  08 

55  52 

08486 

109 

91514 

08810 

111 

91190 

00323 

99677 

1 

60 

4  00 

56  00 

08589 

111 

91411 

08914 

113 

91086 

00325 

99675 

0 
M. 

M. 

Hour  p.  K. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent 

Diff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

96° 

A           A 

B           B 

C 

C    88°  1 

Seconds  of  time 


Prop,  parts 


of  cols.  < 


2> 

28 
28 
0 


8< 

42 

42 

1 


4' 

56 

56 

1 


6' 

69 

70 

1 


6i 

83 

84 

1 


TABLE  44. 

[Page  779 

Log.  Sines,  Tangents,  and  Secants. 

7" 

A 

A 

B           B 

C 

C    178° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

11  4  0 

0  56  0 

9.  08589 

0 

10.91411 

9.  08914 

0 

10.  91086 

10.  00325 

0 

9. 99675 

1 

3  52 

56  8 

08692 

2 

91308 

09019 

2 

90981 

00326 

0  1   99674 

59 

2 

3  44 

56  16 

08795 

3 

91205 

09123 

3 

90877 

00328 

0  !  99672 

58 

3 

3  36 

56  24 

08897 

5 

91103 

09227 

5 

90773 

00330 

0  1  99670 

57 

4 

3  28 

56  32 

08999 

6 

91001 

09330 
9.09434 

1 
8 

90670 
10. 90566 

00331 

0 

99669 
9. 99667 

56 
55 

5 

11  3  20 

0  56  40 

9. 09101 

8 

10. 90899 

10. 00333 

0 

6 

3  12 

56  48 

09202 

10 

90798 

09537 

10 

90463 

00334 

0 

99666 

54 

7 

3  4 

56  56 

09304 

11 

90696 

09640 

11 

90360 

00336 

0 

99664 

53 

8 

2  56 

57  4 

09405 

13 

90595 

09742 

13 

90258 

00337 

0 

99663 

52 

9 

2  48 

57  12 

09506 

14 
16 

90494 
10. 90394 

09845 
9. 09947 

15 
16 

90155 
10. 90053 

00339 

0 

99661 

51 

10 

11  2  40 

0  57  20 

9. 09606 

10. 00341 

0 

9. 99659 

50 

11 

2  32 

57  28 

09707 

18 

90293 

10049 

18 

89951 

00342 

0 

99658 

49 

12 

2  24 

57  36 

09807 

19 

90193 

10150 

20 

89850 

00344 

0 

99656 

48 

13 

2  16 

57  44 

09907 

21  1   90093 

10252 

21 

89748 

00346 

0 

99655 

47 

14 

2  8 

57  52 

10006 

22 

89994 

10353 
9. 10454 

23 

89647 

00347 

0 

99653 

46 
45 

15 

11  2  0 

0  58  0 

9. 10106 

24 

10. 89894 

24 

10. 89546 

10. 00349 

0 

9. 99651 

16 

1  52 

58  8 

10205 

26 

89795 

10555 

26 

89445 

00350 

0  1   99650 

44 

17 

1  44 

58  16 

10304 

27 

89696 

10656 

28 

89344 

00352 

0 

99648 

43 

18 

1  36 

58  24 

10402 

29 

89598 

10756 

29 

89244 

00353 

99647 

42 

19 

1  28 

58  32 

10501 
9. 10599 

30 

89499 

10856 

31 

89144 

00355 

99645 

41 

20 

11  1  20 

0  58  40 

32 

10. 89401 

9.10956 

33 

10.89044 

10. 00357 

9. 99643 

40 

21 

1  12 

58  48 

10697 

34 

89303 

11056 

34 

88944 

00358 

99642 

39 

22 

1  4 

58  56 

10795 

35  i   89205 

11155 

36 

88845 

00360 

1  1  99640 

38 

23 

0  56 

59  4 

10893 

37  !   89107 

11254 

37 

88746 

00362 

1  ,  99638 

37 

24 

0  48 

59  12 

10990 

38 

89010 

11353 

39 

88647 

00363 
10.00365 

1  1  99637 

36 
35 

25 

11  0  40 

0  59  20 

9. 11087 

40 

10. 88913 

9. 11452 

41 

10. 88548 

9. 99635 

26 

0  32 

59  28 

11184 

42 

88816 

11551 

42 

88449 

00367 

99633 

34 

27 

0  24 

59  36 

11281 

43  i   88719 

11649 

44 

88351 

00368 

99632 

33 

28 

0  16 

59  44 

11377 

45  :   88623 

11747 

46 

88253 

00370 

99630 

32 

29 

0  8 

59  52 

11474 

46    88526 

11845 

47 

88155 

00371 

J- 

99629 
9. 99627 

31 
30 

30 

11  0  0 

10  0 

9. 11570 

48  10,88430 

9. 11943 

49 

10.  88057 

10. 00373 

31 

10  59  52 

0  8 

11666 

50    88334 

12040 

51 

87960 

00375 

1  :  99625 

29 

32 

59  44 

0  16 

11761 

51    88239 

12138 

52 

87862 

00376 

99624 

28 

33 

59  36 

0  24 

11857 

53    88143 

12235 

54 

877a5 

00378 

99622 

27 

34 

59  28 

0  32 

11952 

54 

88048 

12332 

55 
57 

87668 
10.  87572 

00380 
10.00382 

99620 

26 

35 

10  59  20 

1  0  40 

9. 12047 

56 

10. 87953 

9. 12428 

9.  99618 

25 

36 

59  12 

0  48 

12142 

58 

87858 

12525 

59 

87475 

00383 

99617 

24 

37 

59  4 

0  56 

12236 

59 

87764 

12621 

60  !   87379 

00385 

99615 

23 

38 

58  56 

1  4 

12331 

61 

87669 

12717 

62  1   87283 

00387 

99613 

22 

39 

58  48 

1  12 

12425 

62 

87575 

12813 

64 

87187 

00388 

—Y 

99612 
9.99610 

21 
20 

40 

10  58  40 

1  1  20 

9. 12519 

64 

10.  87481 

9.12909 

65 

10.  87091 

10. 00390 

41 

58  32 

1  28 

12612 

66 

87388 

13004 

67 

86996 

00392 

1 

99608 

19 

42 

58  24 

1  36 

12706 

67 

87294 

13099 

68 

86901 

00393 

99607 

18 

43 

58  16 

1  44 

12799 

69 

87201 

13194 

70 

86806 

00395 

99605 

17 

44 

58  8 

1  52 

12892 

70 

87108 

13289 

72 

86711 

00397 

■'■ 

99603 

16 

45 

10  58  0 

12  0 

9. 12985 

72 

10.  87015 

9. 13384 

73 

10. 86616 

10. 00399 

1 

9. 99601 

15 

46 

57  52 

2  8 

13078 

74 

86922 

13478 

75 

86522 

00400 

99600 

14 

47 

57  44 

2  16 

13171 

75 

86829 

13573 

77 

86427 

00402 

99598 

13 

48 

57  36 

2  24 

13263 

77 

86737 

13667 

78 

86333 

00404 

99596 

12 

49 

57  28 

2  32 

13355 

78 

86645 

13761 

80 

86239 

00405 

99595 

11 

50 

10  57  20 

1  2  40 

9.13447 

80 

10.  86553 

9.13854 

81 

10. 86146 

10.00407 

9. 99593 

10 

51 

57  12 

2  48 

13539 

82 

86461 

13948 

83 

86052 

00409 

99591 

9 

52 

57  4 

2  56 

13630 

83 

86370 

14041 

85 

85959 

00411 

99589 

8 

53 

56  56 

3  4 

13722 

85 

86278 

14134 

86 

85866 

00412 

99588 

7 

54 

56  48 

3  12 

13813 

87 

86187 

14227 

88 
90 

85773 

00414 

2 

99586 
9. 99584 

6 
5 

55 

10  56  40 

1  3  20 

9.13904 

88 

10.  86096 

9. 14320 

10. 85680 

10. 00416 

2 

56 

56  32 

3  28 

13994 

90 

86006 

14412 

91 

85588 

00418 

2 

99582 

4 

57 

56  24 

3  36 

14085 

91 

85915 

14504 

93 

85496 

00419 

2 

99581 

3 

58 

56  16 

3  44 

14175 

93 

85825 

14597 

95 

85403 

00421 

2 

99579 

2 

59 

56  8 

3  52 

14266 

95 

85734 

14688 

96 

85312 

00423 

2 

99577 

1 

60 

56  0 

4  0 

14356 

96 

85644 

14780 

98 

85220 

00425 

2 

99575 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

97J 

A 

A 

B           B 

C 

C     82°  1 

Seconds  of  time 

!■ 

2' 

8" 

4" 

6-  1  6-    7«  1 

Prop,  parts  of  cols.  ■{  B 

12 
12 
0 

24 

24 

0 

36  48 

37  49 
1     1 

60 
61 

1 

72  84 

73  1  86 

1  I   1 

21594°— 14- 


-42 


Page  780] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secante. 

8° 

A 

A 

B 

B 

C 

C    171= 

M. 

Hour  A,  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

DiflE. 

Cosine. 

M. 

0 

10  56  0 

14  0 

9. 14356 

0 

10. 85644 

9. 14780 

0 

10.  85220 

10. 00425 

0 

9.  99575 

60 

1 

55  52 

4  8 

14445 

1 

85555 

14872 

1 

85128 

00426 

0 

99574 

59 

2 

55  44 

4  16 

14535 

3 

85465 

14963 

3 

85037 

00428 

0 

99572 

58 

3 

55  36 

4  24 

14624 

4 

85376 

15054 

4 

84946 

00430 

0 

99570 

57 

4 

55  28 

4  32 

14714 

6 

85286 

15145 

6 

84855 

00432 

0 

99568 

56 

5 

10  55  20 

1  4  40 

9. 14803 

7 

10.  85197 

9. 15236 

7 

10.  84764 

10. 00434 

0 

9. 99566 

55 

6 

55  12 

4  48 

14891 

8 

85109 

15327 

9 

84673 

00435 

0 

99565 

54 

7 

55  4 

4  56 

14980 

10 

85020 

15417 

10 

84583 

00437 

0 

99563 

53 

8 

54  56 

5  4 

15069 

11 

84931 

15508 

12 

84492 

00439 

0 

99561 

52 

9 

54  48 

5  12 

15157 

13 

84843 

15598 

13 

84402 

00441 

0 

99559 

51 

10 

10  54  40 

1  5  20 

9. 15245 

14 

10. 84755 

9. 15688 

14 

10. 84312 

10. 00443 

0 

9. 99557 

50 

11 

54  32 

5  28 

15333 

16 

84667 

15777 

16 

84223 

00444 

0 

99556 

49 

12 

54  24 

5  36 

15421 

17 

84579 

15867 

17 

84133 

00446 

0 

99554 

48 

13 

54  16 

5  44 

15508 

18 

84492 

15956 

19 

84044 

00448 

0 

99552 

47 

14 

54  8 

5  52 

15596 

20 

84404 

16046 

20 

83954 

00450 

0 

99550 

46 

15 

10  54  0 

1  6  0 

9. 15683 

21 

10. 84317 

9. 16135 

22 

10. 83865 

10. 00452 

0 

9. 99548 

45 

16 

53  52 

6  8 

15770 

23 

84230 

16224 

23 

83776 

00454 

99546 

44 

17 

53  44 

6  16 

15857 

24 

84143 

16312 

25 

83688 

00455 

99545 

43 

18 

53  36 

6  24 

15944 

25 

84056 

16401 

26 

83599 

00457 

99543 

42 

19 

53  28 

6  32 

16030 

27 

83970 

16489 

27 

83511 

00459 

99541 

41 
40 

20 

10  53  20 

1  6  40 

9. 16116 

28 

10.  83884 

9. 16577 

29 

10.  83423 

10.  00461 

9. 99539 

21 

53  12 

6  48 

16203 

30 

83797 

16665 

30 

83335 

00463 

99537 

39 

22 

53  4 

6  56 

16289 

31 

83711 

16753 

32 

83247 

00465 

99535 

38 

23 

52  56 

7  4 

16374 

32 

83626 

16841 

33 

83159 

00467 

99533 

37 

24 

52  48 

7  12 

16460 

34 

83540 

16928 

35 

83072 

00468 

99532 

36 

25 

10  52  40 

1  7  20 

9. 16545 

35 

10.  83455 

9. 17016 

36 

10.  82984 

10. 00470 

9. 99530 

35 

26 

52  32 

7  28 

16631 

37 

83369 

17103 

37 

82897 

00472 

99528 

34 

27 

52  24 

7  36 

16716 

38 

83284 

17190 

39 

82810 

00474 

99526 

33 

28 

52  16 

7  44 

16801 

39 

83199 

17277 

40 

82723 

00476 

99524 

32 

29 
30 

52  8 

7  52 

16886 

41 

83114 

17363 

42 

82637 

00478 

99522 

31 

10  52  0 

1  8  0 

9. 16970 

42 

10. 83030 

9. 17450 

43 

10. 82550 

10. 00480 

9. 99520 

30 

31 

51  52 

8  8 

17055 

44 

82945 

17536 

45 

82464 

00482 

99518 

29 

32 

51  44 

8  16 

17139 

45 

82861 

17622 

46 

82378 

00483 

99517 

28 

33 

51  36 

8  24 

17223 

47 

82777 

17708 

48 

82292 

00485 

99515 

27 

34 

51  28 

8  32 

17307 

48 

82693 

17794 

49 

82206 

00487 

99513 

26 

35 

10  51  20 

1  8  40 

9. 17391 

49 

10. 82G09 

9. 17880 

50 

10.  82120 

10. 00489 

9. 99511 

25 

36 

51  12 

8  48 

17474 

51 

82526 

17965 

52 

82035 

00491 

99509 

24 

37 

51  4 

8  56 

17558 

52 

82442 

18051 

53 

81949 

00493 

99507 

23 

38 

50  56 

9  4 

17641 

54 

82359 

18136 

55 

81864 

00495 

99505 

22 

39 

50  48 

9  12 

17724 
9. 17807 

55 

82276 

18221 

56 

81779 

00497 

99503 

21 

40 

10  50  40 

1  9  20 

56 

10. 82193 

9. 18306 

58 

10. 81694 

10. 00499 

9. 99501 

20 

41 

50  32 

9  28 

17890 

58 

82110 

18391 

59 

81609 

00501 

99499 

19 

42 

50  24 

9  36 

17973 

59 

82027 

18475 

61 

81525 

00503 

99497 

18 

43 

50  16 

9  44 

18055 

61 

81945 

18560 

62 

81440 

00505 

99495 

17 

44 

50  8 

9  52 

18137 

62 

81863 

18644 

63 

81356 

00506 

99494 

16 

45 

10  50  0 

1  10  0 

9. 18220 

63 

10.  81780 

9. 18728 

65 

10. 81272 

10. 00508 

9. 99492 

15 

46 

49  52 

10  8 

18302 

65 

81698 

18812 

66 

81188 

00510 

99490 

14 

47 

49  44 

10  16 

18383 

66 

81617 

18896 

68 

81104 

00512 

99488 

13 

48 

49  36 

10  24 

18465 

68 

81535 

18979 

69 

81021 

00514 

2 

99486 

12 

49 

49  28 

10  32 

18547 

69 

81453 

19063 

71 

80937 
10. 80854 

00516 

2 

99484 
9. 99482 

11 
10 

50 

10  49  20 

1  10  40 

9. 18628 

71 

10.  81372 

9. 19146 

72 

10. 00518 

2 

51 

49  12 

10  48 

18709 

72 

81291 

19229 

74 

80771 

00520 

2 

99480 

9 

52 

49  4 

10  56 

18790 

73 

81210 

19312 

75 

80688 

00522 

2 

99478 

8 

53 

48  56 

11  4 

18871 

75 

81129 

19395 

76 

80605 

00524 

2 

99476 

7 

54 
55 

48  48 
10  48  40 

11  12 
1  11  20 

18952 

76 

81048 

19478 

78 
79 

80522 

00526 

2 

2 

99474 

6 

5 

9. 19033 

78 

10. 80967 

9. 19561 

10. 80439 

10.  00528 

9.  99472 

56 

48  32 

11  28 

19113 

79 

80887 

19643 

81 

80357 

00530 

2 

99470 

4 

57 

48  24 

11  36 

19193 

80 

80807 

19725 

82 

80275 

00532 

2 

99468 

3 

58 

48  16 

11  44 

19273 

82 

80727 

19807 

84 

80193 

00534 

2 

99466 

2 

59 

48  8 

11  52 

19353 

83 

80647 

19889 

85 

80111 

00536 

2 

99464 

1 

60 

48  0 

12  0 

19433 

85 

80567 

19971 

87 

80029 

00538 

2 

99462 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

u. 

98° 

A 

A 

B 

B 

C 

C    81°  1 

Seconds  of  time !  !■ 

1 

2- 

3- 

4' 

5< 

6< 

7- 

Prop,  parts  of  cols.  iB 

11 
11 
0 

21 
22 
0 

32 
32 

42 

43 

1 

53 

54 

1 

63 

65 

1 

74 

76 

2 

Log. 

TABLE  44. 

Sines,  Tangents,  and  Secants. 

[Page  781 

9° 

A 

A 

B            B        C 

C    170° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Dift. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  48  0 

1  12  0 

9. 19433 

0 

10.  80567 

9. 19971 

0 

10.  80029 

10.  00538 

0 

9. 99462 

60 

1 

47  52 

12  8 

19513 

1 

80487 

20053   1 

79947 

00540 

0 

99460 

59 

2 

47  44 

12  16 

19592 

3 

80408 

20134   3 

79865 

00542 

0 

99458 

58 

3 

47  36 

12  24 

19672 

4 

80328 

20216   4 

79784 

00544 

0 

99456 

57 

4 

47  28 

12  32 

19751 

5 

80249 

20297 

5 
6 

79703 
10.  79622' 

00546 
10.  00548 

0 
0 

99454 
9. 99452 

56 
55 

5 

10  47  20 

1  12  40 

9. 19830 

6 

10.  80170 

9.  20378 

6 

47  12 

12  48 

19909 

8 

80091 

20459 

8 

79541 

00550 

0 

99450 

54 

7 

47  4 

12  56 

19988 

9 

80012 

20540 

9 

79460 

00552 

0 

99448 

53 

8 

46  56 

13  4 

20067 

10 

79933 

20621 

10 

79379 

00554 

0 

99446 

52 

9 
10 

46  48 

13  12 

20145 
9. 20223 

11 
13 

79855 
10. 79777 

20701 
9. 20782 

12 

79299 

00556 

0 

99444 

51 

10  46  40 

1  13  20 

13 

10.  79218 

10. 00558 

0 

9. 99442 

50 

11 

46  32 

13  28 

20302 

14 

79698 

20862 

14 

79138 

00560 

0 

99440 

49 

12 

46  24 

13  36 

20380 

15 

79620 

20942 

16 

79058 

00562 

0 

99438 

48 

13 

46  16 

13  44 

20458 

16 

79542 

21022 

17 

78978 

00564 

0 

99436 

47 

14 

46  8 

13  52 

20535 

18 

79465 

21102 

18 
19 

78898 
10.78818 

00566 

0 

99434 

46 
45 

15 

10  46  0 

1  14  0 

9. 20613 

19 

10.  79387 

9.  21182 

10.  00568 

1 

9. 99432 

16 

45  52 

14  8 

20691 

20 

79309 

21261 

21 

78739 

00571 

99429 

44 

17 

45  44 

14  16 

20768 

21 

79232 

21341 

22 

78659 

00573 

99427 

43 

18 

45  36 

14  24 

20845 

23 

79155 

21420 

23 

78580 

00575 

99425 

42 

19 
20 

45  28 

14  32 

20922 

24 

79078 

21499 

25 

78501 

00577 

99423 

41 

10  45  20 

1  14  40 

9.20999 

25 

10.  79001 

9.  21578 

26 

10.  78422 

10. 00579 

9. 99421 

40 

21 

45  12 

14  48 

21076 

26 

78924 

21657 

27 

78343 

00581 

99419 

39 

22 

45  4 

14  56 

21153 

28 

78847 

21736 

28 

78264 

00583 

99417 

38 

23 

44  56 

15  4 

21229 

29 

78771 

21814 

30 

78186 

00585 

99415 

37 

24 

44  48 

16  12 

21306 
9. 21382 

30 
31 

78694 
10.  78618 

21893 
9. 21971 

31 
32 

78107 

00587 

io:o6589 

99413 

36 

25 

10  44  40 

1  15  20 

10.  78029 

9. 99411 

35 

26 

44  32 

15  28 

21458 

33 

78542 

22049 

34 

77951 

00591 

99409 

34 

27 

44  24 

15  36 

21534 

34 

78466 

22127 

35 

77873 

00593 

99407 

33 

28 

44  16 

15  44 

21610 

35 

78390 

22205 

36 

77795 

00596 

99404 

32 

29 

44  8 

15  52 

21685 

37 

78315 

22283 

38 
39 

77717 

00598 

99402 

31 

30 

10  44  0 

1  16  0 

9.21761 

38 

10.  78239 

9. 22361 

10.  77639 

10.00600 

9.99400 

30 

31 

43  52 

16  8 

21836 

39 

78164 

22438 

40 

77562 

00602 

99398 

29 

32 

43  44 

16  16 

21912 

40 

78088 

22516 

41 

77484 

00604 

99396 

28 

33 

43  36 

16  24 

21987 

42 

78013 

22593 

43 

77407 

00606 

99394 

27 

34 

43  28 

16  32 

22062 

43 
44 

77938 
10.  77863 

22670 

44 

77330 

00608 

99392 

26 

35 

10  43  20 

1  16  40 

9. 22137 

9.  22747 

45 

10.  77253 

10. 00610 

9. 99390 

25 

36 

43  12 

16  48 

22211 

45 

77789 

22824 

47 

77176 

00612 

99388 

24 

37 

43  4 

16  56 

22286 

47 

77714 

22901 

48 

77099 

00615 

99385 

23 

38 

42  56 

17  4 

22361 

48 

77639 

22977 

49 

77023 

00617 

99383 

22 

39 
40 

42  48 

17  12 
1  17  20 

22435 

49 

77565 

23054 

50 

76946 

00619 

99381 

21 

10  42  40 

9. 22509 

50 

10.  77491 

9. 23130 

52 

10.  76870 

10. 00621 

9. 99379 

20 

41 

42  32 

17  28 

22583 

52 

77417 

23206 

53 

76794 

00623 

99377 

19 

42 

42  24 

17  36 

22657 

53 

77343 

23283 

54 

76717 

00625 

99375 

18 

43 

42  16 

17  44 

22731 

54 

77269 

23359 

56 

76641 

00628 

2 

99372 

17 

44 

42  8 

17  52 
1  18  0 

22805 

55 

77195 

23435 

57 

76565 

00630 

2 

99370 

16 

45 

10  42  0 

9. 22878 

57 

10.  77122 

9.  23510 

58 

10.  76490 

10. 00632 

2 

9. 99368 

15 

46 

41  52 

18  8 

22952 

58 

77048 

23586 

60 

76414 

00634 

2 

99366 

14 

47 

41  44 

18  16 

23025 

59 

76975 

23661 

61 

76339 

00636 

2 

99364 

13 

48 

41  36 

18  24 

23098 

60 

76902 

23737 

62 

76263 

00638 

2 

99362 

12 

49 

41  28 

18  32 

23171 

62 

76829 

23812 

63 

76188 

00641 

2 

99359 

11 

50 

10  41  20 

1  18  40 

9.  23244 

63 

10.  76756 

9. 23887 

65 

10.  76113 

10. 00643 

2 

9. 99357 

10 

51 

41  12 

18  48 

23317 

64 

76683 

23962 

66 

76038 

00645 

2 

99355 

9 

52 

41  4 

18  56 

23390 

65 

76610 

24037 

67 

75963 

00647 

2 

99353 

8 

53 

40  56 

19  4 

23462 

67 

76538 

24112 

69 

75888 

00649 

2 

99351 

7 

54 
55 

40  48 

19  12 

23535 

68 

76465 

24186 

70 

75814 

00652 

2 

99348 

6 

10  40  40 

1  19  20 

9. 23607 

69 

10.  76393 

9.  24261 

71 

10.  75739 

10.00654 

2 

9. 99346 

5 

56 

40  32 

19  28 

23679 

71 

76321 

24335 

73 

75665 

00656 

2 

99344 

4 

57 

40  24 

19  36 

23752 

72 

76248 

24410 

74 

75590 

00658 

2 

99342 

3 

58 

40  16 

19  44 

23823 

73 

76177 

24484 

75 

75516 

00660 

2 

99340 

2 

59 

40  8 

19  52 

23895 

74 

76105 

24558 

76 

75442 

00663 

2 

99337 

1 

60 

40  0 

20  0 

23967 

76 

76033 

24632 

78 

75368 

00665 

2 

99335 

0 

M. 

Hour  P.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

99° 

A 

A 

B           B        C 

C    80°  1 

Seconds  of  time 

!• 

2- 

3' 

4> 

6" 

6- 

7.i 

A 

Prop,  parts  of  eols.^B 

Ic 

9 
10 
0 

19 
19 
1 

28 

29 

1 

38 
39 

1 

47 

49 

1 

57 
58 
2 

66 
68 
2 

Page  782 

TABLE  44. 

Log.  Sines.  Tangents,  and  Secants. 

10° 

A 

A 

B 

B 

C 

C 

169° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DifiE. 

Cosecant. 

Tangent. 

Diff. ;  Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  40  0 

1  20  0 

9. 23967 

0 

10.  76033 

9. 24632 

0 

10.  75368 

10. 00665 

0 

9. 99335 

60 

1 

39  62 

20  8 

24039 

1 

75961 

24706 

1 

75294 

00667 

0 

99333 

59 

2 

39  44 

20  16 

24110 

2 

75890 

24779 

2 

75221 

00669 

0 

99331 

58 

3 

39  36 

20  24 

24181 

3 

75819 

24853 

4 

75147 

00672 

0 

99328 

57 

4 

39  28 

20  32 

24253 

5 

75747 

24926 

5 

75074 

00674 

0 

99326 

56 
55 

5 

10  39  20 

1  20  40 

9. 24324 

6 

10.  75676 

9.  25000 

6 

10. 75000 

10. 00676 

0 

9. 99324 

6 

39  12 

20  48 

24395 

7 

75605 

25073 

7 

74927 

00678 

0 

99322 

54 

7 

39  4 

20  56 

24466 

8 

75534 

25146 

8 

74854 

00681 

0 

99319 

53 

8 

38  56 

21  4 

24536 

9 

75464 

25219 

9 

74781 

00683 

0 

99317 

52 

9 

38  48 

21  12 

24607 

10 

75393 

25292 

11 
12 

74708 

00685 

0 

99315 

51 

10 

10  38  40 

1  21  20 

9. 24677 

11 

10.  75323 

9. 25365 

10. 74635 

10. 00687 

0 

9. 99313 

50 

11 

38  32 

21  28 

24748 

13 

75252 

25437 

13 

74563 

00690 

0 

99310 

49 

12 

38  24 

21  36 

24818 

14 

75182 

25510 

14 

74490 

00692 

0 

99308 

48 

13 

38  16 

21  44 

24888 

15 

75112 

25582 

15 

74418 

00694 

99306 

47 

14 
15 

38  8 

21  52 

24958 

16 

75042 

25655 

16 
18 

74345 

00696 

99304 

46 
45 

10  38  0 

1  22  0 

9. 25028 

17 

10.  74972 

9. 25727 

10. 74273 

10.  00699 

9.  99301 

16 

37  52 

22  8 

25098 

18 

74902 

25799 

19 

74201 

00701 

99299 

44 

17 

37  44 

22  16 

25168 

19 

74832 

25871 

20 

74129 

00703 

99297 

43 

18 

37  36 

22  24 

25237 

20 

74763 

25943 

21 

74057 

00706 

99294 

42 

19 
20 

37  28 

22  32 

25307 
9.  25376 

22 
23 

74693 
10.  74624 

26015 

22 

73985 

00708 

99292 

41 

10  37  20 

1  22  40 

9. 26086 

24 

10. 73914 

10. 00710 

9. 99290 

40 

21 

37  12 

22  48 

25445 

24 

74555 

26158 

25 

73842 

00712 

99288 

39 

22 

37  4 

22  56 

25514 

25 

74486 

26229 

26 

73771 

00715 

99285 

38 

23 

36  56 

23  4 

25583 

26 

74417 

26301 

27 

73699 

00717 

99283 

37 

24 

36  48 

23  12 

25652 

27 
28 

74348 
10.  74279 

26372 

28 
29 

73628 

00719 

99281 

36 
35 

25 

10  36  40 

1  23  20 

9.  25721 

9. 26443 

10.  73557 

10. 00722 

9. 99278 

26 

36  32 

23  28 

25790 

30 

74210 

26514 

31 

73486 

00724 

99276 

34 

27 

36  24 

23  36 

25858 

31 

74142 

26585 

32 

73415 

00726 

99274 

33 

28 

36  16 

23  44 

25927 

32 

74073 

26655 

33 

73345 

00729 

99271 

32 

29 
30 

36  8 

23  52 

25995 

33 

74005 

26726 

34 
35 

73274 

00731 

99269 

31 
30 

10  36  0 

1  24  0 

9.  26063 

34 

10.  73937 

9. 26797 

10.  73203 

10. 00733 

9. 99267 

31 

35  52 

24  8 

26131 

35 

73869 

26867 

36 

73133 

00736 

99264 

29 

32 

35  44 

24  16 

26199 

36 

73801 

26937 

38 

73063 

00738 

99262 

28 

33 

35  36 

24  24 

26267 

38 

73733 

27008 

39 

72992 

00740 

99260 

27 

34 

35  28 

24  32 

26335 

39 
40 

73665 

27078 

40 
41 

72922 

00743 

99257 
9. 99255 

26 

35 

10  35  20 

1  24  40 

9.  26403 

10. 73597 

9. 27148 

10.  72852 

10. 00745 

36 

35  12 

24  48 

26470 

41 

73530 

27218 

42 

72782 

00748 

99252 

24 

37 

35  4 

24  56 

26538 

42 

73462 

27288 

44 

72712 

00750 

99250 

23 

38 

34  56 

25  4 

26605 

43 

73395 

27357 

45 

72643 

00752 

99248 

22 

39 
40 

34  48 

25  12 

26672 

44 

73328 

27427 

46 
47 

72573 

00755 
10.00757' 

2 
2 

99245 
9. 99243 

21 
20 

10  34  40 

1  25  20 

9. 26739 

45 

10.  73261 

9.  27496 

10.  72504 

41 

34  32 

25  28 

26806 

47 

73194 

27566 

48 

72434 

00759 

2 

99241 

19 

42 

34  24 

25  36 

26873 

48 

73127 

27635 

49 

72365 

00762 

2 

99238 

18 

43 

34  16 

25  44 

26940 

49 

73060 

27704 

51 

72296 

00764 

2 

99236 

17 

44 

34  8 

25  52 

27007 

50 

72993 

27773 

52 

72227 

00767 

2 

99233 

16 
15 

45 

10  34  0 

1  26  0 

9.  27073 

51 

10.  72927 

9. 27842 

53 

10. 72158 

10. 00769 

2 

9. 99231 

46 

33  52 

26  8 

27140 

52 

72860 

27911 

54 

72089 

00771 

2 

99229 

14 

47 

33  44 

26  16 

27206 

53 

72794 

27980 

55 

72020 

00774 

2 

99226 

13 

48 

33  36 

26  24 

27273 

55 

72727 

28049 

56 

71951 

00776 

2 

99224 

12 

49 

33  28 

26  32 

27339 

56 

72661 

28117 

58 

71883 

00779 

2 

99221 

11 
10 

50 

10  33  20 

1  26  40 

9.  27405 

57 

10.  72595 

9. 28186 

59 

10. 71814 

10. 00781 

2 

9. 99219 

51 

33  12 

26  48 

27471 

58 

72529 

28254 

60 

71746 

00783 

2 

99217 

9 

52 

33  4 

26  56 

27537 

59 

72463 

28323 

61 

71677 

00786 

2 

99214 

8 

53 

32  56 

27  4 

27602 

60 

72396 

28391 

62 

71609 

00788 

2 

99212 

7 

54 
55 

32  48 

27  12 

27668 

61 

72332 

28459 
9. 28527 

63 
65 

71541 

00791 

2 

99209 
9. 99207 

6 
5 

10  32  40 

1  27  20 

9.  27734 

63 

10. 72266 

10. 71473 

10. 00793 

2 

56 

32  32 

27  28 

27799 

64 

72201 

28595 

66 

71405 

00796 

2 

99204 

4 

57 

32  24 

27  36 

27864 

65 

72136 

28662 

67 

71338 

00798 

2 

99202 

3 

58 

32  16 

27  44 

27930 

66 

72070 

28730 

68 

71270 

00800 

2 

99200 

2 

59 

32  8 

27  52 

27995 

67 

72005 

28798 

69 

71202 

00803 

2 

99197 

1 

60 

32  0 

28  0 

28060 

68 

71940 

28865 

71 

71135 

00805 

2 

99195 

0 

M. 

Hour  P.M. 

Hour  A.  H. 

Cosine. 

Dili. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

100° 

A 

A 

B 

B 

C 

C 

79° 

Seconds  of  time 

1> 

2-    S« 

4* 

5« 

G" 

7» 

Prop,  parts  of  cols,  i  B 

Ic 

9 
9 
0 

17  26 

18  26 

34 
36 

1 

43 

44 

1 

51 

53 

2 

60 
62 

TABLE  44. 

[Page  783 

Log.  Sines,  Tangents,  and  Secants. 

11° 

A            A 

B 

B       C 

C    168° 

M. 

0 

Hour  A.  M. 

Hotir  p.  M. 

Sine. 

Difl. 

Cosecant. 

TanKent. 

Diff.  Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

10  32  0 

1  28  0 

9.28060 

0 

10.  71940 

9.  28865 

'  0  10.  71135 

10.  00805 

0 

9.  99195 

60 

1 

31  52 

28  8 

28125 

1 

71875 

28933 

1 

71067 

00808 

0 

99192 

59 

2 

31  44 

28  16 

28190 

2 

71810 

29000 

2 

71000 

00810 

0 

99190 

58 

3 

31  36 

28  24 

28254 

3 

71746 

29067 

3 

70933 

00813 

0 

99187 

57 

4 

31  28 

28  32 

28319 

4 

71681 

29134 

4 

70866 

00816 

0 

99185 

56 
55 

5 

10  31  20 

1  28  40 

9. 28384 

5 

10.  71616 

9. 29201 

5 

10.  70799 

10. 00818 

0 

9. 99182 

6 

31  12 

28  48 

28448 

6 

71552 

29268 

6 

70732 

00820 

0 

99180 

64 

7 

31  4 

28  56 

28512 

7 

71488 

29335 

8  !   70665 

00823 

0 

99177 

53 

8 

30  56 

29  4 

28577 

8 

71423 

29402 

9 

70598 

00826 

0 

99175 

52 

9 

30  48 

29  12 

28641 

9 

71359 

29468 

10 

70532 

00828 

0 

99172 

51 

10 

10  30  40 

1  29  20 

9. 28705 

10 

10.  71295 

9.29535 

11 

10.  70466 

10. 00830 

0 

9. 99170 

60 

n 

30  32 

29  28 

28769 

11 

71231 

29601 

12 

70399 

008.33 

0 

99167 

49 

12 

30  24 

29  36 

28833 

12 

71167 

29668 

13 

70332 

00835 

99165 

48 

13 

30  16 

29  44 

28896 

13  ,   71104 

29734 

14 

70266 

00838 

99162 

47 

14 

30  8 

29  52 

28960 

14  !   71040 

29800 

15 

70200 

00840 

99160 

46 
45 

15 

10  30  0 

1  30  0 

9.  29024 

16  jlO.  70976 

9.29866 

16 

10.  70134 

10.  00843 

9. 99157 

16 

29  52 

30  8 

29087 

17  1   70913 

29932  1  17 

70068 

00846 

99156 

44 

17 

29  44 

30  16 

29150 

18    70850 

29998 

18 

70002 

00848 

99162 

43 

18 

29  36 

30  24 

29214 

19    70786 

30064 

19 

69936 

00850 

99150 

42 

19 

29  28 

30  32 

29277 

20  !   70723 

30130 

20 

69870 

00853 

99147 

41 
40 

20 

10  29  20 

1  30  40 

9.  29340 

21  10.70660 

9.  30195 

22 

10. 69806 

10.00866 

9. 99145 

21 

29  12 

30  48 

29403 

22  1   70597 

30261 

23 

69739 

00868 

99142 

39 

22 

29  4 

30  56 

29466 

23  1   70534 

30326 

24 

69674 

00860 

99140 

38 

23 

28  56 

31  4 

29529 

24    70471 

30391 

25 

69609 

00863 

99137 

37 

24 

28  48 

31  12 

29591 

25  '   70409 

30457 

26 

69543 

00865 

99135 

36 

35 

25 

10  28  40 

1  31  20 

9. 29654 

26  10.70346 

9.  30522 

27  10.69478 

10. 00868 

9. 99132 

26 

28  32 

31  28 

29716 

27  i   70284 

.30587 

28 

69413 

00870 

99130 

34 

27 

28  24 

31  36 

29779 

28  1   70221 

30652 

29 

69348 

00873 

99127 

33 

28 

28  16 

31  44 

29841 

29  j   70159 

30717 

30 

69283 

00876 

99124 

32 

29 

28  8 

31  52 

29903 

30 

70097 

30782 

31 

69218 

00878 

99122 

31 

30 

10  28  0 

1  32  0 

9.  29966 

31 

10.  70034 

9.30846 

32 

10. 69164 

10. 00881 

9.99119 

30 

31 

27  52 

32  8 

30028 

32 

69972 

30911 

33 

69089 

00883 

99117 

29 

32 

27  44 

32  16 

30090 

33 

69910 

30975 

35 

69026 

00886 

99114 

28 

33 

27  36 

32  24 

.30151 

34 

69849 

31040 

36 

68960 

00888 

99112 

27 

34 
35 

27  28 

32  32 

30213 

35 

69787 

31104 

37 

68896 

00891 

2 

99109 

26 

10  27  20 

1  32  40 

9.  30275 

36 

10. 69725 

9.  .31168 

38 

10.  68882 

10. 00894 

9. 99106 

25 

36 

27  12 

32  48 

30336 

37 

69664 

31233 

39 

68767 

00896 

2 

99104 

24 

37 

27  4 

32  56 

30398 

38    69602 

31297 

40 

68703 

00899 

2 

99101 

23 

38 

26  56 

33  4 

30459 

39  1   69.^^41 

31361 

41 

68639 

00901 

2 

99099 

22 

39 

26  48 

33  12 

30521 

40  1   69479 

31425 

42 

68575 

00904 

2 

99096 

21 
20 

40 

10  26  40 

1  33  20 

9. 30582 

41  10.69418 

9.  31489 

43 

10.  68511 

10. 00907 

2 

9. 99093 

41 

26  32 

33  28 

30643 

42    69357 

31562 

44 

68448 

00909 

2 

99091 

19 

42 

26  24 

33  36 

30704 

43  1   69296 

31616 

45 

68384 

00912 

2 

99088 

18 

43 

26  16 

33  44 

30765 

45  :   69236 

31679 

46 

68321 

00914 

2 

99086 

17 

44 

26  8 

33  52 

30826 

46  1   69174 

31743 

47 

68257 

00917 

2 

99083 

16 

45 

10  26  0 

1  34  0 

9. 30887 

47  10.69113 

9. 31806 

49 

10. 68194 

10.  00920 

2 

9. 99080 

15 

46 

25  52 

34  8 

30947 

48    69053 

31870 

50 

68130 

00922 

2 

99078 

14 

47 

25  44 

34  16 

31008 

49  !   68992 

31933 

51 

68067 

00925 

2 

99075 

13 

48 

25  36 

34  24 

31068 

50  1   68932 

31996 

52 

68004 

00928 

2 

99072 

12 

49 
50 

25  28 

34  32 

31129 

51 

68871 

32059 

53 

67941 

00930 

2 

99070 

11 

10  25  20 

1  34  40 

9. 31189 

52 

10. 68811 

9. 32122 

54 

10.  67878 

10. 00933 

2 

9. 99067 

10 

51 

25  12 

34  48 

31250 

53 

68750 

32185 

56 

67815 

00936 

2 

99064 

9 

52 

25  4 

34  56 

31310 

54 

68690 

32248 

56 

67752 

00938 

2 

99062 

8 

53 

24  56 

35  4 

31370 

55 

68630 

32311 

57 

67689 

00941 

2 

99059 

7 

54 

24  48 

35  12 

31430 

56 

68570 

32373 

58 

67627 

00944 

2 

99056 

6 

55 

10  24  40 

1  35  20 

9. 31490 

57 

10. 68510 

9. 32436 

59 

10. 67564 

10. 00946 

2 

9. 99054 

5 

56 

24  32 

35  28 

31549 

58 

68451 

32498 

60 

67502 

00949 

2 

99051 

4 

57 

24  24 

35  36 

31609 

59 

68391 

32661 

61 

67439 

00962 

2 

99048 

3 

58 

24  16 

35  44 

31669 

60 

68331 

32623 

63 

67377 

00954 

2 

99046 

2 

59 

24  8 

35  52 

31728 

61 

68272 

32685 

64 

67315 

00957 

3 

99043 

1 

60 

24  0 

36  0 

31788 

62 

68212 

32747 

65 

67253 

00960 

3 

99040 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

101° 

A           A 

B 

B        C 

C     78°  1 

Seconds  of  time 

1" 

2- 

8» 

4' 

o> 

6. 

7" 

Prop,  parts  of  cols.  {B 

ic 

8 
8 
0 

16 
16 

1 

23 

24 

1 

31 
32 

1 

39 
40 
2 

47 
49 
2 

54 

67 

2 

Page  784] 

TABLE  44. 

I/^.  Sines,  Tangents,  and  Secants. 

l«o 

A 

A 

B 

B        C 

C    167° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

DiS. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  24  0 

1  36  0 

9. 31788 

0 

10. 68212 

9. 32747 

0 

10. 67253 

10.  00960 

0 

9.99040 

60 

1 

23  52 

36  8 

31847 

1 

68153 

32810 

1 

67190 

00962 

0 

99038 

59 

2 

23  44 

36  16 

31907 

2 

68093 

32872 

2 

67128 

00965 

0 

99035 

58 

3 

23  36 

36  24 

31966 

3 

68034 

32933 

3 

67067 

00968 

0 

99032 

57 

4 

23  28 

36  32 

32025 

4 

67975 

32995 

4 

67005 

00970 

0 

99030 

56 
55 

5 

10  23  20 

1  36  40 

9.  32084 

5 

10. 67916 

9. 33057 

5 

10. 66943 

10.  00973 

0 

9. 99027 

6 

23  12 

36  48 

32143 

6 

67857 

33119 

6 

66881 

00976 

0 

99024 

54 

7 

23  4 

36  56 

32202 

7 

67798 

33180 

7 

66820 

00978 

0 

99022 

53 

8 

22  56 

37  4 

32261 

8 

67739 

33242 

8 

66758 

00981 

0 

99019 

52 

9 

22  48 

37  12 

32319 

9 

67681 

33303 

9 

66697 

00984 

0 
0 

99016 

51 

10 

10  22  40 

1  37  20 

9. 32378 

10 

10. 67622 

9.  33365 

10 

10. 66635 

10. 00987 

9.  99013 

50 

11 

22  32 

37  28 

32437 

10 

67563 

33426 

11 

66574 

00989 

99011 

49 

12 

22  24 

37  36 

32495 

11 

67505 

33487 

12 

66513 

00992 

99008 

48 

13 

22  16 

37  44 

32553 

12 

67447 

33548 

13 

66452 

00995 

99005 

47 

14 

22  8 

37  52 

32612 

13 

67388 

33609 

14 

66391 
10.  66330 

00998 

99002 

46 
45 

15 

10  22  0 

1  38  0 

9. 32670 

14 

10. 67330 

9. 33670 

15 

10. 01000 

9. 99000 

16 

21  52 

38  8 

32728 

15 

67272 

33731 

16 

66269 

01003 

98997 

44 

17 

21  44 

38  16 

32786 

16 

67214 

33792 

17 

66208 

01006 

98994 

43 

18 

21  36 

38  24 

32844 

17 

67156 

33853 

18 

66147 

01009 

1 

98991 

42 

19 
20 

21  28 

38  32 

32902 

18 

67098 

33913 

19    66087 

01011 

98989 

41 

10  21  20 

1  38  40 

9. 32960 

19 

10. 67040 

9. 33974 

20 

10. 66026 

10. 01014 

9. 98986 

40 

21 

21  12 

38  48 

33018 

20 

66982 

34034 

21 

65966 

01017 

98983 

39 

22 

21  4 

38  56 

33075 

21 

66925 

34095 

22 

65905 

01020 

98980 

38 

23 

20  56 

39  4 

33133 

22 

66867 

34155 

23 

65845 

01022 

98978 

37 

24 

20  48 

39  12 

33190 

23 

66810 

34215 

24 

65785 

01025 

98975 

36 

26 

10  20  40 

1  39  20 

9. 33248 

24 

10. 66752 

9.  34276 

25 

10. 65724 

10. 01028 

9. 98972 

35 

26 

20  32 

39  28 

33305 

25 

66695 

34336 

26 

65664 

01031 

98969 

34 

27 

20  24 

39  36 

33362 

26 

66638 

34396 

27 

65604 

01033 

98967 

33 

28 

20  16 

39  44 

33420 

27 

66580 

:M456 

28 

65544 

01036 

98964 

32 

29 

20  8 

39  52 

33477 

28 

66523 

34516 

29 

65484 

01039 

98961 

31 

30 

10  20  0 

1  40  0 

9.33534 

29 

10. 66466 

9. 34576 

30 

10. 65424 

10. 01042 

9. 98958 

30 

31 

19  52 

40  8 

33591 

29 

66409 

34635 

31 

65365 

01045 

98955 

29 

32 

19  44 

40  16 

33647 

30 

66353 

34695 

32 

65305 

01047 

98953 

28 

33 

19  36 

40  24 

33704 

31 

66296 

34755 

33 

65245 

01050 

2 

98950 

27 

34 

19  28 

40  32 

33761 

32 

66239 

34814 

34 

65186 

01053 

2 

98947 

26 

35 

10  19  20 

1  40  40 

9. 33818 

33 

10. 66182 

9. 34874 

35 

10.  65126 

10. 01056 

2 

9. 98944 

25 

36 

19  12 

40  48 

33874 

34 

66126 

34933 

36 

65067 

01059 

2 

98941 

24 

37 

19  4 

40  56 

33931 

35 

66069 

34992 

37 

65008 

01062 

2   98938 

23 

38 

18  56 

41  4 

33987 

36 

66013 

35051 

38 

64949 

01064 

2   98936 

22 

39 

18  48 

41  12 

34043 

37 

65957 

35111 

39 

64889 

01067 

2  !  98933 

21 

40 

10  18  40 

1  41  20 

9.34100 

38 

10. 65900 

9.  .35170 

40 

10. 64830 

10. 01070 

2  19.98930 

20 

41 

18  32 

41  28 

34156 

39 

65844 

35229 

41 

64771 

01073 

2  1  98927 

19 

42 

18  24 

41  36 

34212 

40 

65788 

35288 

42 

64712 

01076 

2  1  98924 

18 

43 

18  16 

41  44 

34268 

41 

65732 

35347 

43 

64653 

01079 

2   98921 

17 

44 

18  8 

41  52 

34324 

42 

65676 

35405 

44 

64595 

01081 

2 

98919 

16 

45 

10  18  0 

1  42  0 

9. 34380 

43 

10. 65620 

9.35464 

45 

10. 64536 

10. 01084 

2 

9. 98916 

15 

46 

17  52 

42  8 

34436 

44 

65564 

35523 

46 

64477 

01087 

2   98913 

14 

47 

17  44 

42  16 

34491 

45 

65509 

35581 

47 

64419 

01090 

2   98910 

13 

48 

17  36 

42  24 

34547 

46 

65453 

35640 

48 

64360 

01093 

2 

98907 

12 

49 

17  28 

42  32 

34602 

47 

65398 

35698 

49 

64302 

01096 

2 

98904 

11 

50 

10  17  20 

1  42  40 

9. 34658 

48 

10. 65342 

9. 35757 

50 

10. 64243 

10. 01099 

2 

9. 98901 

10 

51 

17  12 

42  48 

34713 

48 

65287 

35815 

51 

64185 

01102 

2 

98898 

9 

52 

17  4 

42  56 

34769 

49 

65231 

35873 

52 

64127 

01104 

2 

98896 

8 

53 

16  56 

43  4 

34824 

50 

65176 

35931 

53 

64069 

01107 

2 

98893 

7 

54 

16  48 

43  12 

34879 

51 

65121 

35989 

54 

64011 

OHIO 

3 

98890 

6 
5 

55 

10  16  40 

1  43  20 

9.34934 

52 

10. 65066 

9. 36047 

55 

10. 63953 

10.  01113 

3 

9. 98887 

56 

16  32 

43  28 

34989 

53 

65011 

36105 

56 

63895 

01116 

3 

98884 

4 

57 

16  24 

43  36 

35044 

54 

64956 

36163 

57 

63837 

01119 

3 

98881 

3 

58 

16  16 

43  44 

35099 

55 

64901 

36221 

58 

63779 

01122 

3 

98878 

2 

59 

16  8 

43  52 

35154 

56 

64846 

36279 

59 

63721 

01125 

3 

98875 

1 

60 

16  0 

44  0 

35209 

57 

64791 

36336 

60 

63664 

01128 

3 

98872 

0 

M. 

Hour  p.  u. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

102° 

A 

A 

B 

B         C 

C    77°  1 

Seconds  of  time 

!• 

2" 

8- 

4« 

6' 

6- 

7" 

fA 
Prop,  parts  of  cols.  B 

7 
7 
0 

14 
15 

1 

21 

22 

1 

29 
30 

1 

36 
37 
2 

43 
45 
2 

50 
62 
2 

TABLE  44. 

[Page  785 

liOg.  Sines,  Tangents,  and  Secants. 

18° 

A           A 

B            B        C 

C    166° 

M. 

Hour  A,  M. 

Hour  p.  M. 

Sine. 

Dlfl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant 

Difl. 

Cosine. 

M. 

0 

10  16  0 

1  44  0 

9. 36209 

0 

10. 64791 

9. 36336 

0 

10, 63664 

10. 01128 

0 

9. 98872 

60 

1 

15  52 

44  8 

35263 

1 

64737 

36394 

1 

63606 

01131 

0 

98869 

59 

2 

15  44 

44  16 

35318 

2 

64682 

36452 

2 

63648 

01133 

0 

98867 

58 

3 

15  36 

44  24 

35373 

3 

64627 

36509 

3 

63491 

01136 

0 

98864 

67 

4 

15  28 

44  32 

35427 

4 

64573 

36566 

4 

63434 

01139 

0 

98861 

56 
55 

5 

10  15  20 

1  44  40 

9. 36481 

4 

10. 64519 

9.36624 

5 

10. 63376 

10. 01142 

0 

9. 98858 

6 

15  12 

44  48 

36636 

5 

64464 

36681 

6 

63319 

01145 

0 

98856 

54 

7 

15  4 

44  56 

35690 

6 

64410 

36738 

6 

63262 

01148 

0 

98852 

53 

8 

14  56 

45  4 

35644 

7 

64356 

36795 

7 

63205 

01151 

0 

98849 

52 

9 

14  48 

45  12 

35698 
9.  36762 

8 
9 

64302 

36852 

8 

63148 

01154 

0 

98846 
9.98843 

51 
60 

10 

10  14  40 

1  45  20 

10.  64248 

9.  36909 

9 

10. 63091 

10. 01157 

n 

14  32 

45  28 

36806 

10 

64194 

36966 

10 

63034 

01160 

98840 

49 

12 

14  24 

45  36 

36860 

11 

64140 

37023 

11 

62977 

01163 

98837 

48 

13 

14  16 

45  44 

36914 

11 

64086 

37080 

12 

62920 

01166 

98834 

47 

14 

14  8 

45  52 

36968 

12 

64032 

37137 

13 

62863 

01169 

98831 

46 

15 

10  14  0 

1  46  0 

9. 36022 

13 

10. 63978 

9. 37193 

14 

10. 62807 

10.01172 

9. 98828 

45 

16 

13  52 

46  8 

36075 

14 

63925 

37260 

15 

62750 

01175 

98825 

44 

17 

13  44 

46  16 

36129 

15 

63871 

37306 

16 

62694 

01178 

98822 

43 

18 

13  36 

46  24 

36182 

16 

63818 

37363 

17 

62637 

01181 

98819 

42 

19 

13  28 

46  32 

36236 

17 

63764 

37419 

18 

62581 

01184 

98816 

41 
40 

20 

10  13  20 

1  46  40 

9. 36289 

18 

10. 63711 

9. 37476 

19 

10. 62524 

10.01187 

9. 98813 

21 

13  12 

46  48 

36342 

18 

63658 

37532 

19 

62468 

01190 

98810 

39 

22 

13  4 

46  56 

36395 

19 

63605 

37688 

20 

62412 

01193 

98807 

38 

23 

12  56 

47  4 

36449 

20 

63551 

37644 

21 

62356 

01196 

98804 

37 

24 
25 

12  48 

47  12 

36502 

21 

63498 

37700 

22 

62300 

01199 

98801 

36 
35 

10  12  40 

1  47  20 

9.  36566 

22 

10. 63445 

9. 37756 

23 

10. 62244 

10. 01202 

9. 98798 

26 

12  32 

47  28 

36608 

23 

63392 

37812 

24 

62188 

01205 

98795 

34 

27 

12  24 

47  36 

36660 

24 

63340 

37868 

25 

62132 

01208 

98792 

33 

28 

12  16 

47  44 

36713 

25 

63287 

37924 

26 

62076 

01211 

98789 

32 

29 

12  8 

47  52 

36766 

25 

63234 

37980 

27 

62020 

01214 

98786 

31 

30 

10  12  0 

1  48  0 

9. 36819 

26 

10. 63181 

9. 38035 

28 

10. 61965 

10.01217 

2 

9. 98783 

30 

31 

11  52 

48  8 

36871 

27 

63129 

38091 

29 

61909 

01220 

2 

98780 

29 

32 

11  44 

48  16 

36924 

28 

63076 

38147 

30 

61853 

01223 

2 

98777 

28 

33 

11  36 

48  24 

36976 

29 

63024 

38202 

31 

61798 

01226 

2 

98774 

27 

34 

11  28 

48  32 

37028 

30 

62972 

38257 

32 

61743 

01229 

2 

98771 

26 
25 

35 

10  11  20 

1  48  40 

9. 37081 

31 

10. 62919 

9. 38313 

32 

10. 61687 

10.01232 

2 

9. 98768 

36 

11  12 

48  48 

37133 

32 

62867 

38368 

33 

61632 

01235 

2 

98765 

24 

37 

11  4 

48  56 

37185 

32 

62815 

38423 

34 

61577 

01238 

2 

98762 

23 

38 

10  56 

49  4 

37237 

33 

62763 

38479 

35 

61521 

01241 

2 

98759 

22 

39 

10  48 

49  12 

37289 

34 

62711 

38534 

36 

61466 

01244 

2 

98756 

21 

40 

10  10  40 

1  49  20 

9. 37341 

35 

10. 62659 

9. 38589 

37 

10.61411 

10.01247 

2 

9. 98753 

20 

41 

10  32 

49  28 

37393 

36 

62607 

38644 

38 

61356 

01250 

2 

98760 

19 

42 

10  24 

49  36 

37445 

37 

62555 

38699 

39 

61301 

01254 

2 

98746 

18 

43 

10  16 

49  44 

37497 

38 

62503 

38754 

40 

61246 

01267 

2 

98743 

17 

44 
45 

10  8 

49  52 

37549 

39 

62451 

38808 

41 

61192 

01260 

2 

98740 

16 

10  10  0 

1  50  0 

9.3760vy 

39 

10. 62400 

9. 38863 

42 

10. 61137 

10.01263 

2 

9. 98737 

15 

46 

9  52 

50  8 

37652 

40 

62348 

38918 

43 

61082 

01266 

2 

98734 

14 

47 

9  44 

50  16 

37703 

41 

62297 

38972 

44 

61028 

01269 

2 

98731 

13 

48 

9  36 

50  24 

37765 

42 

62245 

39027 

45 

60973 

01272 

2 

98728 

12 

49 
50 

9  28 

50  32 

37806 

43 

62194 

39082 

45 

60918 

01275 

2 

98725 

11 

10  9  20 

1  50  40 

9.  37868 

44 

10. 62142 

9. 39136 

46 

10.  G0864 

10. 01278 

3 

9. 98722 

10 

51 

9  12 

50  48 

37909 

45 

62091 

39190 

47 

60810 

01281 

3 

98719 

9 

52 

9  4 

50  56 

37960 

46 

62040 

39245 

48 

60755 

01285 

3 

98715 

8 

53 

8  56 

51  4 

38011 

47 

61989 

39299 

49 

60701 

01288 

3 

98712 

7 

54 
55 

8  48 

51  12 

38062 

47 

61938 

39353 

50 

60647 

01291 

3 

98709 

6 

10  8  40 

1  51  20 

9.38113 

48 

10. 61887 

9. 39407 

51 

10. 60593 

10. 01294 

\    3 

9. 98706 

5 

56 

8  32 

51  28 

38164 

49 

61836 

39461 

62 

60539 

01297 

/  3 

98703 

4 

57 

8  24 

51  36 

38215 

50 

61785 

39615 

63 

60485 

01300 

3 

98700 

3 

58 

8  16 

51  44 

38266 

61 

61734 

39669 

54 

60431 

01303 

3 

98697 

2 

59 

8  8 

51  52 

38317 

52 

61683 

39623 

55 

60377 

01306 

3 

98694 

1 

60 

8  0 

52  0 

38368 

53 

61632 

39677 

56 

60323 

01310 

3 

98690 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

103° 

A           A 

B           B        C 

C     76°  1 

Seconds  of  time 

1« 

2» 

8> 

*• 

5" 

6* 

?• 

fA 
Prop,  parts  of  cols.  B 

7 
7 
0 

13 
14 

1 

20 
21 

1 

26 

28 

2 

33 

35 

2 

39 

42 

2 

46 

49 

3 

Page  786] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

14° 

A            A 

B           B        C 

C    1«6° 

M. 

Hour  A.  H. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant 

Diff. 

Cosine. 

M. 

0 

10  8  0 

1  52  0 

9. 38368 

0 

10.  61632 

9. 39677 

0 

10.  60323 

10. 01310 

0 

9. 98690 

60 

1 

7  52 

52  8 

38418 

1 

61582 

39731 

1 

60269 

01313 

0 

98687 

59 

2 

7  44 

52  16 

38469 

2 

61531 

39785 

2 

60215 

01316 

0 

98684 

58 

3 

7  36 

52  24 

38519 

2 

61481 

39838 

3 

60162 

01319 

0 

98681 

57 

4 

7  28 

52  32 

38570 

3 

61430 

39892 

3 

60108 

01322 

0 

98678 

56 
55 

5 

10  7  20 

1  52  40 

9.  38620 

4 

10. 61380 

9. 39945 

4 

10. 60055 

10.  01325 

0 

9. 98675 

6 

7  12 

52  48 

38670 

5 

61330 

39999 

5 

60001 

01329 

0 

98671 

54 

7 

7  4 

52  56 

38721 

6 

61279 

40052 

6 

599-»8 

01332 

0 

98668 

53 

8 

6  56 

53  4 

38771 

7 

61229 

40106 

7 

59894 

01335 

0 

98665 

52 

9 

6  48 

53  12 

38821 

7 

61179 

40159 

8 

59841 

01338 

0 

98662 

51 
50 

10 

10  6  40 

1  53  20 

9. 38871 

8 

10.  61129 

9. 40212 

9 

10. 69788 

10. 01341 

9. 98659 

11 

6  32 

53  28 

38921 

9 

61079 

40266 

10 

59734 

01344 

98656 

49 

12 

6  24 

53  36 

38971 

10 

61029 

40319 

10 

59681 

01348 

98652 

48 

13 

6  16 

53  44 

39021 

11 

60979 

40372 

11 

59628 

01351 

98649 

47 

14 

6  8 

53  52 

39071 

11 

60929 

40425 

12 

59575 

01354 

98646 

46 
45 

15 

10  6  0 

1  54  0 

9. 39121 

12 

10. 60879 

9. 40478 

13 

10. 59522 

10. 01357 

9. 98643 

16 

5  62 

54  8 

39170 

13 

60830 

40531 

14 

59469 

01360 

98640 

44 

17 

5  44 

54  16 

39220 

14 

60780 

40584 

15 

59416 

01364 

98636 

43 

18 

5  36 

54  24 

39270 

15 

60730 

40636 

16 

59364 

01367 

98633 

42 

19 

5  28 

54  32 

39319 

15 

60681 

40689 

17 

59311 

01370 

98630 

41 
40^ 

20 

10  5  20 

1  54  40 

9. 39369 

16 

10.60631. 

9. 40742 

17 

10. 59258 

10. 01373 

9. 98627 

21 

5  12 

54  48 

39418 

17 

60582 

40795 

18 

59205 

01377 

98623 

39 

22 

5  4 

54  56 

39467 

18 

60533 

40847 

19 

59153 

01380 

98620 

38 

23 

4  56 

55  4 

39517 

19 

60483 

40900 

20 

59100 

01383 

98617 

37 

24 

4  48 

55  12 

39566 

20 

60434 

40952 

21 

59048 

01386 

98614 

36 

25 

10  4  40 

1  55  20 

9. 39615 

20 

10. 60385 

9. 41005 

22 

10. 58995 

10. 01390 

9. 98610 

35 

26 

4  32 

55  28 

39664 

21 

60336 

41057 

23 

58943 

01393 

98607 

34 

27 

4  24 

55  36 

39713 

22 

60287 

41109 

23 

58891 

01396 

98604 

33 

28 

4  16 

55  44 

39762 

23 

60238 

41161 

24 

58839 

01399 

2 

98601 

32 

29 
30 

4  8 

55  52 

39811 
9. 39860 

24 

60189 

41214 

25 

58786 

01403 

2 

98597 

31 
30 

10  4  0 

1  56  0 

24 

10. 60140 

9. 41266 

26 

10. 58734 

10. 01406 

2 

9. 98594 

31 

3  52 

56  8 

39909 

25 

60091 

41318 

27 

58682 

01409 

2 

98591 

29 

32 

3  44 

56  16 

39958 

26 

60042 

41370 

28 

58630 

01412 

2 

98588 

28 

33 

3  36 

56  24 

40006 

27 

59994 

41422 

29 

58578 

01416 

2 

98584 

27 

34 

3  28 

56  32 

40055 

28 

59945 

41474 

30 

58526 

01419 

2 

98581 

26 

36 

10  3  20 

1  56  40 

9. 40103 

29 

10.  59897 

9. 41526 

30 

10. 58474 

01422 

2 

9. 98578 

25 

36 

3  12 

56  48 

40152 

29 

59848 

41578 

31 

58422 

01426 

2 

98574 

24 

37 

3  4 

56  56 

40200 

30 

59800 

41629 

32 

58371 

01429 

2 

98571 

23 

38 

2  56 

57  4 

40249 

31 

59751 

41681 

33 

58319 

01432 

2 

98568 

22 

39 

2  48 

57  12 

40297 

32 

59703 

41733 

34 

58267 

01435 

2 

98565 

21 

40 

10  2  40 

1  57  20 

9. 40346 

33 

10.  59654 

9. 41784 

35 

10.  58216 

10. 01439 

2 

9. 98561 

20 

41 

2  32 

57  28 

40394 

33 

59606 

41S36 

36 

58164 

01442 

2 

98558 

19 

42 

2  24 

57  36 

40442 

34 

59558 

41887 

36 

58113 

01445 

2 

98556 

18 

43 

2  16 

57  44 

40490 

35 

59510 

41939 

37 

58061 

01449 

2 

98551 

17 

44 

2  8 

57  52 

40538 

36 

59462 

41990 

38 

58010 

01452 

2 

985*8 

16 

45 

10  2  0 

1  58  0 

9. 40586 

37 

10. 59414 

9.  42041 

39 

10. 57959 

10. 01455 

2 

9. 98545 

16 

46 

1  52 

58  8 

40634 

37 

59366 

42093 

40 

57907 

01459 

3 

98541 

14 

47 

1  44 

58  16 

40682 

38 

59318 

42144 

41 

57856 

01462 

3 

98538 

13 

48 

1  36 

58  24 

40730 

39 

59270 

42195 

42 

57805 

01465 

3 

98535 

12 

49 

1  28 

58  32 

40778 

40 

59222 

42246 

43 

57754 

01469 

3 

98531 

11 

50 

10  1  20 

1  58  40 

9. 40825 

41 

10.  59175 

9. 42297 

43 

10. 57703 

10. 01472 

3 

9. 98528 

10 

51 

1  12 

58  48 

40873 

42 

59127 

42348 

44 

57652 

01475 

3 

98525 

9 

62 

1  4 

58  56 

40921 

42 

59079 

42399 

45 

57601 

01479 

3 

98521 

8 

53 

0  56 

59  4 

40968 

43 

59032 

42450 

46 

57550 

01482 

3 

98518 

7 

54 

0  48 

59  12 

41016 

44 

58984 

42501 

47 

67499 

01485 

3 

98515 

6 

55 

10  0  40 

1  59  20 

9.41063 

45 

10. 58937 

9. 42552 

48 

10. 57448 

10. 01489 

3 

9. 98511 

6 

56 

0  32 

59  28 

41111 

46 

58889 

42603 

49 

57397 

01492 

3 

98508 

4 

57 

0  24 

59  36 

41158 

46 

58842 

42653 

50 

57347 

01495 

3 

98505 

3 

58 

0  16 

59  44 

41205 

47 

58795 

42704 

50 

57296 

01499 

3 

98501 

2 

59 

0  8 

59  52 

41252 

48 

58748 

42755 

51 

67246 

01602 

3 

98498 

1 

60 

0  0 

2  0  0 

41300 

49 

58700 

42805 

52 

57196 

01506 

3 

98494 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difif. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

104'= 

A           A 

B           B        C 

C     76°  j 

Seconds  of  time 

1' 

» 

S* 

4* 

6- 

6» 

7" 

Prop,  parts  of  cols.'tB 

Ic 

6 
7 
0 

12 

13 

1 

18 
20 

1 

24 

26 

2 

31 

38 

2 

87 

S9 

2 

43 
46 
3 

TABLE  44. 
Log.  Sines,  Tangents,  and  Secants. 

[Page  787 

16° 

A            A 

B           B 

C 

C    164° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  0  0 

2  0  0 

9. 41300 

0 

10. 58700 

9. 42805 

0 

10. 57195 

10.  01606 

0 

9. 98494 

60 

1 

9  59  52 

0  8 

41347 

1 

58653 

42856 

1 

57144 

01609 

0 

98491 

69 

2 

59  44 

0  16 

41394 

2 

58606 

42906 

2 

67094 

01512 

0 

98488 

58 

3 

59  36 

0  24 

41441 

2 

58559 

42957 

2 

57043 

01616 

0 

98484 

67 

4 

59  28 

0  32 

41488 

3 

58512 

43007 

3 

56993 

01619 

0 

98481 

56 

ft 

9  59  20 

2  0  40 

9. 41535 

4 

10. 58465 

9. 43057 

4 

10. 66943 

10. 01623 

0 

9. 98477 

55 

6 

59  12 

0  48 

41582 

5 

58418 

43108 

6 

56892 

01626 

0 

98474 

54 

7 

59  4 

0  56 

41628 

5 

58372 

43158 

6 

56842 

01529 

0 

98471 

58 

8 

58  56 

1  4 

41675 

6 

58325 

43208 

7 

56792 

01633 

0 

98467 

52 

9 

58  48 

1  12 

41722 

7 

58278 

43258 

7 

66742 

01536 

98464 

61 

10 

9  58  40 

2  1  20 

9.41768 

8 

10. 58232 

9. 43308 

8 

10. 66692 

10. 01540 

9.98460 

50 

11 

58  32 

1  28 

41815 

8 

58185 

43358 

9 

56642 

01543 

98467 

49 

12 

58  24 

1  36 

41861 

9 

58139 

43408 

10 

56592 

01647 

98453 

48 

13 

58  16 

1  44 

41908 

10 

58092 

43458 

11 

56542 

01550 

98450 

47 

14 
1ft 

58  8 

1  52 

41954 

11 

58046 

43508 

11 

56492 

01553 

1   98447 

46 

9  58  0 

2  2  0 

9. 42001 

11 

10. 57999 

9. 43558 

12 

10. 56442 

10. 01557 

1  [9.98443 

45 

16 

57  52 

2  8 

42047 

12 

57953 

43607 

13 

56393 

01560 

1 

98440 

44 

17 

57  44 

2  16 

42093 

13 

57907 

43657 

14 

56343 

01664 

1 

98436 

43 

18 

57  36 

2  24 

42140 

14 

57860 

43707 

15 

66293 

01567 

1 

98433 

42 

19 
20 

57  28 

2  32 

42186 

14 

57814 

43756 

16 
16 

66244 

01571 

98429 

41 
40 

9  57  20 

2  2  40 

9. 42232 

15 

10. 57768 

9. 43806 

10. 66194 

10. 01574 

9. 98426 

21 

57  12 

2  48 

42278 

16 

57722 

43855 

17 

66145 

01578 

98422 

39 

22 

57  4 

2  56 

42324 

17 

57676 

43905 

18    56095 

01581 

1 

98419 

38 

23 

56  56 

3  4 

42370 

17 

57630 

43954 

19    56046 

01585 

1   98415 

37 

24 

56  48 

3  12 

42416 

18 

57584 

44004 

20    65996 

01588 

1  1  98412 

36 

2ft 

9  56  40 

2  3  20 

9. 42461 

19 

10. 57539 

9. 44053 

20  10.55947 

10. 01591 

1 

•*• 

9.98409 

35 

26 

56  32 

3  28 

42507 

20 

57493 

44102 

21 

66898 

01596 

2 

98405 

34 

27 

56  24 

3  36 

42553 

21 

57447 

44151 

22 

56849 

01598 

2 

98402 

33 

28 

56  16 

3  44 

42599 

21 

57401 

44201 

23 

55799 

01602 

2 

98398 

32 

29 
30 

56  8 

3  52 

42644 

22 
23 

57356 

44250 

24 

65750 

01605 

2 

98395 

31 

9  56  0 

2  4  0 

9. 42690 

10. 57310 

9.44299 

25 

10. 55701 

10. 01609 

2 

9. 98391 

30 

31 

55  52 

4  8 

42735 

24 

57265 

44348 

25 

55652 

01612 

2 

98388 

29 

32 

55  44 

4  16 

42781 

24 

57219 

44397 

26 

56603 

01616 

2 

98384 

28 

33 

55  36 

4  24 

42826 

25 

57174 

44446 

27 

65554 

01619 

2 

98381 

27 

34 

55  28 

4  32 

42872 

26 

57128 

44495 

28 

66605 

01623 

2  ;  98377 

26 
25 

3ft 

9  55  20 

2  4  40 

9. 42917 

27 

10. 57083 

9.44644 

29 

10. 66456 

10. 01627 

2  i  9. 98373 

36 

55  12 

4  48 

42962 

27 

57038 

44692 

29 

66408 

01630 

2  1  98370 

24 

37 

55  4 

4  56 

43008 

28 

56992 

44641 

30 

55359 

01634 

2 

98366 

23 

38 

54  56 

5  4 

43053 

29 

56947 

44690 

.31 

66310 

01637 

2 

98363 

22 

39 
40 

54  48 

5  12 

43098 

30 

56902 

44738 

32 

55262 

01641 

2 

98369 

21 
20 

9  54  40 

2  5  20 

9. 43143 

30 

10. 56867 

9. 44787 

33 

10.55213 

10. 01644 

2 

9.98366 

41 

54  32 

5  28 

43188 

31 

56812 

44836 

34 

65164 

01648 

2 

98362 

19 

42 

54  24 

5  36 

43233 

32 

56767 

44884 

34 

66116 

01651 

2 

98349 

18 

43 

54  16 

5  44 

43278 

33 

56722 

44933 

36 

55067 

01655 

3 

98345 

17 

44 

4ft 

54  8 

5  52 

43323 

33 

56677 

44981 

36 
37 

55019 

01658 

3 

98342 

16 

9  54  0 

2  6  0 

9. 43367 

34 

10. 56633 

9. 45029 

10. 54971 

10. 01662 

3 

9. 98338 

15 

46 

53  52 

6  8 

43412 

35 

56588 

45078 

38 

54922 

01666 

3 

98334 

14 

47 

53  44 

6  16 

43457 

36 

56543 

45126 

38 

54874 

01669 

3 

98331 

13 

48 

53  36 

6  24 

43502 

36 

56498 

46174 

39 

64826 

01673 

3 

98327 

12 

49 
ftO 

53  28 

6  32 

43546 

37 

56454 

46222 

40 

64778 

01676 

3 

98324 

11 
10 

9  53  20 

2  6  40 

9. 43591 

38 

10.  56409 

9. 45271 

41 

10. 54729 

10. 01680 

3 

9. 98320 

ft! 

53  12 

6  48 

43635 

39 

56365 

46319 

42 

54681 

01683 

3 

98317 

9 

ft2 

53  4 

6  56 

43680 

39 

56320 

45367 

43 

54633 

01687 

3 

98313 

8 

ft3 

52  56 

7  4 

43724 

40 

56276 

45415 

43 

54585 

01691 

3 

98309 

7 

54 

ft5 

52  48 

7  12 
2  7  20 

43769 

41 

56231 

46463 
9.45511 

44 
45 

54537 

01694 

3 
3 

98306 

6 

9  52  40 

9. 43813 

42 

10. 56187 

10. 54489 

10. 01698 

9. 98302 

6 

56 

52  32 

7  28 

43857 

43 

56143 

46559 

46 

54441 

01701 

3 

98299 

4 

57 

52  24 

7  36 

43901 

43 

56099 

45606 

•47 

54394 

01705 

3 

98295 

3 

58 

52  16 

7  44 

43946 

44 

56054 

45654 

47 

54346 

01709 

3 

98291 

2 

59 

52  8 

7  52 

43990 

45 

56010 

45702 

48 

54298 

01712 

3 

98288 

1 

60 

52  0 

8  0 

44034 

46 

55966 

46750 

49 

54250 

01716 

4 

98284 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Di£f. 

Sine. 

M. 

106 

3 

A             A 

B           B 

C 

C    74°  1 

Seconds  of  time  , 


Prop,  parts 


of  cols,  i 


Page  788 

] 

^     TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

16° 

A            A 

B            B 

C 

C    168° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

DiS. 

Cosine. 

M. 

0 

9  52  0 

2  8  0 

9. 44034 

0 

10.  55966 

9. 45750 

0 

10. 54250 

10.01716 

0 

9.  98284 

60 

1 

51  52 

8  8 

44078 

1 

55922 

45797 

1 

54203 

01719 

0 

98281 

59 

2 

51  44 

8  16 

44122 

1 

55878 

45845 

2 

54155 

01723 

0 

98277 

58 

3 

51  36 

8  24 

44166 

2 

55834 

45892 

2 

54108 

01727 

0 

98273 

57 

4 

51  28 

8  32 

44210 

3 

55790 

45940 

3 

54060 

01730 

0 

98270 
9. 98266 

56 
55 

5 

9  51  20 

2  8  40 

9. 44253 

4 

10. 55747 

9. 45987 

4 

10. 54013 

10. 01734 

0 

6 

51  12 

8  48 

44297 

4 

55703 

46035 

5 

53965 

01738 

0 

98262 

54 

7 

51  4 

8  56 

44341 

5 

55659 

46082 

5 

53918 

01741 

0 

98259 

53 

8 

50  56 

9  4 

44385 

6 

55615 

46130 

6 

53870 

01745 

0 

98255 

52 

9 
10 

50  48 

9  12 

44428 

6 

55572 

46177 

7 
8 

53823 

01749 

-Y 

98251 

51 
50 

9  50  40 

2  9  20 

9.  44472 

7 

10. 55528 

9. 46224 

10.  53776 

10.  01752 

9. 98248 

11 

50  32 

9  28 

44516 

8 

55484 

46271 

9 

53729 

01756 

98244 

49 

12 

50  24 

9  36 

44559 

9 

55441 

46319 

9 

53681 

01760 

98240 

48 

13 

50  16 

9  44 

44602 

9 

55398 

46366 

10 

53634 

01763 

98237 

47 

14 

50  8 

9  52 

44646 

10 

55354 

46413 

11 

53587 

01767 

98233 

46 

15 

9  50  0 

2  10  0 

9.44689 

11 

10. 55311 

9. 46460 

12 

10. 53540 

10. 01771 

9. 98229 

45 

16 

49  52 

10  8 

44733 

11 

55267 

46507 

12 

53493 

01774 

98226 

44 

17 

49  44 

10  16 

44776 

12 

55224 

46554 

13 

53446 

01778 

98222 

43 

18 

49  36 

10  24 

44819 

13 

55181 

46601 

14 

53399 

01782 

98218 

42 

19 
20 

49  28 

10  32 

44862 

14 

55138 

46648 
9. 46694 

15 
15 

53352 

01785 

1 

98215 

41 
40 

9  49  20 

2  10  40 

9. 44905 

14 

10.  55095 

10. 53306 

10. 01789 

9. 98211 

21 

49  12 

10  48 

44948 

15 

55052 

46741 

16 

53259 

01793 

98207 

39 

22 

49  4 

10  56 

44992 

16 

55008 

46788 

17 

53212 

01796 

98204 

38 

23 

48  56 

11  4 

45035 

16 

54965 

46835 

18 

53165 

01800 

98200 

37 

24 

48  48 

11  12 

45077 

17 
18 

54923 
10.54880 

46881 

19 

53119 

01804 

98196 
9. 98192 

36 
35 

25 

9  48  40 

2  11  20 

9. 45120 

9.  46928 

19 

10. 53072 

10.  01808 

2 

26 

48  32 

11  28 

45163 

18 

54837 

46975 

20 

53025 

01811 

2 

98189 

34 

27 

48  24 

11  36 

45206 

19 

54794 

47021 

21 

52979 

01815 

2 

98185 

33 

28 

48  16 

11  44 

45249 

20 

54751 

47068 

22 

52932 

01819 

2 

98181 

32 

29 

48  8 

11  52 

45292 

21 
21 

54708 

47114 

22 

52886 

01823 

2 

98177 

31 
30 

30 

9  48  0 

2  12  0 

9. 45334 

10. 54666 

9. 47160 

23 

10. 52840 

10. 01826 

2 

9. 98174 

31 

47  52 

12  8 

45377 

22 

54623 

47207 

24 

52793 

01830 

2 

98170 

29 

32 

47  44 

12  16 

45419 

23 

54581 

47253 

25 

52747 

01834 

2 

98166 

28 

33 

47  36 

12  24 

45462 

23 

54538 

47299 

26 

52701 

01838 

2 

98162 

27 

34 

47  28 

12  32 

45504 

24 

54496 

47346 

26 

52654 

01841 

2 

98159 
9. 98155 

26 
25 

35 

9  47  20 

2  12  40 

9.45547 

25 

10. 54453 

9. 47392 

27 

10. 52608 

10. 01845 

2 

36 

47  12 

12  48 

45589 

26 

54411 

47438 

28 

52562 

01849 

2 

98151 

24 

37 

47  4 

12  56 

45632 

26 

54368 

47484 

29 

52516 

01853 

2 

98147 

23 

38 

46  56 

13  4 

45674 

27 

54326 

47530 

29 

52470 

01856 

2 

98144 

22 

39 

46  48 

13  12 

45716 

28 

54284 

47576 

30 

52424 

01860 

2 

98140 

21 

40 

9  46  40 

2  13  20 

9. 45758 

28 

10. 54242 

9. 47622 

31 

10. 52378 

10. 01864 

2 

9. 98136 

20 

41 

46  32 

13  28 

45801 

29 

54199 

47668 

32 

52332 

01868 

3 

98132 

19 

42 

46  24 

13  36 

45843 

30 

54157 

47714 

32 

52286 

01871 

3 

98129 

18 

43 

46  16 

13  44 

45885 

31 

54115 

47760 

33 

52240 

01875 

3 

98125 

17 

44 

46  8 

13  52 

45927 

31 

54073 

47806 

34 

52194 

01879 

3 

98121 

16 
15 

45 

9  46  0 

2  14  0 

9. 45969 

32 

10. 54031 

9. 47852 

35 

10. 52148 

10. 01883 

3 

9. 98117 

46 

45  52 

14  8 

46011 

33 

53989 

47897 

36 

52103 

01887 

3 

98113 

14 

47 

45  44 

14  16 

46053 

33 

53947 

47943 

36 

52057 

01890 

3 

98110 

13 

48 

45  36 

14  24 

46095 

34 

53905 

47989 

37 

52011 

01894 

3 

98106 

12 

49 
60 

45  28 

14  32 

46136 

35 

53864 

48035 

38 

51965 

01898 

3 

98102 

11 
10 

9  45  20 

2  14  40 

9. 46178 

36 

10. 53822 

9.48080 

39 

10. 51920 

10. 01902 

3 

9.98098 

51 

45  12 

14  48 

46220 

36 

53780 

48126 

39 

51874 

01906 

3 

98094 

9 

52 

45  4 

14  56 

46262 

37 

53738 

48171 

40 

51829 

01910 

3 

98090 

8 

53 

44  56 

15  4 

46303 

38 

53697 

48217 

41 

51783 

01913 

3 

98087 

7 

54 
55 

44  48 

15  12 

46345 

38 

53655 

48262 

42 

51738 

01917 

3 

98083 

6 

5 

9  44  40 

2  15  20 

9. 46386 

39 

10. 53614 

9. 48307 

43 

10. 51693 

10. 01921 

3 

9. 98079 

56 

44  32 

15  28 

46428 

40 

53572 

48353 

43 

51647 

01925 

3 

98075 

4 

57 

44  24 

15  36 

46469 

41 

,53531 

48398 

44 

51602 

01929 

4 

98071 

3 

58 

44  16 

15  44 

46511 

41 

53489 

48443 

45 

51557 

01933 

4 

98067 

2 

59 

44  8 

15  52 

46552 

42 

53448 

48489 

46 

51511 

01937 

4 

98063 

1 

60 

44  0 

16  0 

46594 

43 

53406 

48534 

46 

51466 

01940 

4 

98060 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

106° 

A        '   A 

B           B 

C 

C    78°  1 

Seconds  of  time 

1« 

2' 

3« 

4* 

6* 

6« 

7« 

Prop,  parts  of  cols,  -i  B 

5 
6 
0 

11 
12 
1 

16 
17 
I 

21 

23 

2 

27 
29 
2 

32 
S5 
3 

37 
41 
3 

. 

TABLE  44. 

[Page  789 

Log.  Sines,  Tangents,  and  Secants. 

JJO 

A            A 

B 

B 

C 

C    168° 

M. 

Hour  A.  M. 

Hour  P.  u. 

Sine. 

DIff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

9  44  0 

2  16  0 

9. 46594 

0 

10.  53406 

9.48534 

0 

10.  51466 

10.  01940 

0 

9. 98060 

60 

1 

43  62 

16  8 

46635 

1 

53365 

48679 

1 

51421 

01944 

0 

98066 

69 

2 

43  44  \   16  16 

i6676 

1 

53324 

48624 

1 

51376 

01948 

0 

98062 

58 

3 

43  36 

16  24 

46717 

2 

53283 

48669 

2 

51331 

01962 

0 

98048 

57 

4 

43  28 

16  32 

46758 

3 

53242 

48714 

3 

51286 

01966 

0 
■  0 

98044 

56 
55 

5 

9  43  20 

2  16  40 

9. 46800 

3 

10. 53200 

9. 48759 

4 

10. 51241 

10. 01960 

9. 98040 

6 

43  12 

16  48 

46841 

4 

53159 

48804 

4 

51196 

01964 

0 

98036 

54 

7 

43  4 

16  56 

46882 

5 

53118 

48849 

5 

51161 

01968 

0 

98032 

63 

8 

42  56 

17  4 

46923 

5 

53077 

48894 

6 

61106 

01971 

98029 

62 

9 
10 

42  48 

17  12 

46904 

6 

7' 

53036 

48939 

7 

51061 

01975 

98025 

51 
50 

9  42  40 

2  17  20 

9. 47005 

10. 52995 

9. 48984 

7 

10. 51016 

10. 01979 

9. 98021 

11 

42  32 

17  28 

47045 

7 

52955 

49029 

8 

60971 

01983 

98017 

49 

12 

42  24 

17  36 

47086 

8 

52914 

49073 

9 

60927 

01987 

98013 

48 

13 

42  16 

17  44 

47127 

9 

52873 

49118 

10 

50882 

01991 

98009 

47 

14 

42  8 

17  52 

47168 

9 
10 

52832 

49163 

10 
11 

50837 

01995 

98005 
9.98001 

46 

45 

15 

9  42  0 

2  18  0 

9. 47209 

10. 52791 

9. 49207 

10. 50793 

10. 01999 

16 

41  52 

18  8 

47249 

11 

52751 

49262 

12 

60748 

02003 

97997 

44 

17 

41  44 

18  16 

47290 

11 

52710 

49296 

12 

60704 

02007 

97993 

43 

18 

41  36 

18  24 

47330 

12 

52670 

49341 

13 

50659 

02011 

97989 

42 

19 

41  28 

18  32 

47371 

13 

52629 

49386 

14 

50616 

02014 

97986 

41 
40 

20 

9  41  20 

2  18  40 

9. 47411 

13 

10. 52589 

9. 49430 

16 

10. 60570 

10. 02018 

9. 97982 

21 

41  12 

18  48 

47452 

14 

52548 

49474 

16 

50526 

02022 

97978 

39 

22 

41  4 

18  56 

47492 

15 

52608 

49619 

16 

60481 

02026 

97974 

38 

23 

40  56 

19  4 

47533 

15 

52467 

49563 

17 

50437 

02030 

2 

97970 

37 

24 

40  48 

19  12 

47573 

16 

52427 

49607 

18 

50393 

02034 

2 

97966 

36 
35 

25 

9  40  40 

2  19  20 

9. 47613 

17 

10. 52387 

9.49652 

18 

10. 50348 

10. 02038 

2 

9. 97962 

26 

40  32 

19  28 

47654 

17 

52346 

49696 

19 

50304 

02042 

2 

97968 

34 

27 

40  24 

19  36 

47694 

18 

52306 

49740 

20 

50260 

02046 

2 

97964 

33 

28 

40  16 

19  44 

47734 

19 

52266 

49784 

21 

50216 

02060 

2 

97950 

32 

29 

40  8 

19  52 

47774 

19 

52226 

49828 

21 

50172 

02054 

2 

97946 

31 
30 

30 

9  40  0 

2  20  0 

9. 47814 

20 

10. 52186 

9. 49872 

22 

10. 50128 

10.  02068 

2 

9. 97942 

31 

39  52 

20  8 

47854 

21 

52146 

49916 

23 

50084 

02062 

2 

97938 

29 

32 

39  44 

20  16 

47894 

21 

52106 

49960 

24 

60040 

02066 

2 

97934 

28 

33 

39  36 

20  24 

47934 

22 

52066 

50004 

24 

49996 

02070 

2 

97930 

27 

34 

39  28 

20  32 

47974 

23 

52026 

50048 

25 

49952 

02074 

2 

97926 

26 
26 

35 

9  39  20 

2  20  40 

9. 48014 

23 

10. 51986 

9.50092 

26 

10. 49908 

10. 02078 

2 

9. 97922 

36 

39  12 

20  48 

48054 

24 

51946 

50136 

26 

49864 

02082 

2 

97918 

24 

37 

39  4 

20  56 

48094 

25 

61906 

60180 

27 

49820 

02086 

2 

97914 

23 

38 

38  56 

21  4 

48133 

25 

51867 

60223 

28 

49777 

02090 

3 

97910 

22 

39 

38  48 

21  12 

48173 

26 

51827 

50267 

29 

49733 

02094 

3 

97906 

21 

40 

9  38  40 

2  21  20 

9.48213 

27 

10. 51787 

9. 50311 

29 

10.49689 

10.  02098 

3 

9. 97902 

20 

41 

38  32 

21  28 

48252 

27 

51748 

50366 

30 

49645 

02102 

3 

97898 

19 

42 

,  38  24 

21  36 

48292 

28 

51708 

60398 

31 

49602 

02106 

3 

97894 

18 

43 

38  16 

21  44 

48332 

29 

51668 

50442 

32 

49568 

02110 

3 

97890 

17 

44 

38  8 

21  52 

48371 

29 
30 

51629 
10. 51589 

60486 
9. 50529 

32 
33 

49515 

02114 

3 

97886 

16 
15 

45 

9  38  0 

2  22  0 

9. 48411 

10.  49471 

10.02118 

3 

9. 97882 

46 

37  52 

22  8 

48450 

31 

51550 

50572 

34 

49428 

02122 

3 

97878 

14 

47 

37  44 

22  16 

48490 

31 

61510 

50616 

35 

49384 

02126 

3 

97874 

13 

48 

37  36 

22  24 

48529 

32 

51471 

60659 

35 

49341. 

02130 

3 

97870 

12 

49 

37  28 

22  32 

48568 

33 
33 

51432 
10. 51393 

60703 

36 

49297 

02134 

3 

97866 

11 
10 

60 

9  37  20 

2  22  40 

9.48607 

9. 50746 

37 

10. 49264 

10. 02139 

3 

9. 97861 

51 

37  12 

22  48 

48647 

34 

51363 

50789 

37 

49211 

02143 

3 

97867 

9 

52 

37  4 

22  56 

48686 

35 

51314 

50833 

38 

49167 

02147 

3 

97863 

8 

53 

36  56 

23  4 

48725 

35 

51276 

60876 

39 

49124 

02151 

4 

97849 

7 

54 

36  48 

23  12 

48764 

36 

51236 

60919 

40 

49081 

02166 

4 
4 

97846 

6 
5 

55 

9  36  40 

2  23  20 

9. 48803 

37 

10. 51197 

9. 60962 

40 

10. 49038 

10. 02159 

9. 97841 

56 

36  32 

23  28 

48842 

37 

51158 

51005 

41 

48995 

02163 

4 

97837 

4 

67 

36  24 

23  36 

48881 

38 

51119 

51048 

42 

48952 

02167 

4 

97833 

3 

58 

36  16 

23  44 

48920 

39 

51080 

51092 

43 

48908 

02171 

4 

97829 

2 

59 

36  8 

23  52 

48959 

39 

51041 

61135 

43 

48865 

02176 

4 

97826 

1 

60 

36  0 

24  0 

48998 

40 

51002 

51178 

44 

48822 

02179 

4 

97821 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

103° 

A            A 

B 

B 

C 

C     78»I 

Seconds  of  time 

1" 

2" 

3" 

4* 

6. 

6» 

7- 

Prop,  parts  of  cols.  ^B 

ic 

6 
6 
0 

10 
11 

1 

15 
17 
1 

20 

22 

2 

25 

9.8 

2 

30 
33 
,3 

35 

39 

3 

Page  790] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secanta. 

18° 

A 

A 

B 

B 

C 

C    1610 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DiGE. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

DiS. 

Cosine. 

M. 

9  36  0 

2  24  0 

9.  48998 

0 

10.  51002 

9.51178 

0 

10. 48822 

10.  02179 

0 

9.  97821 

60 

I 

35  52 

24  8 

49037 

1 

50963 

51221 

1 

48779 

02183 

0 

97817 

59 

2 

35  44 

24  16 

49076 

1 

50924 

51264 

1 

48736 

02188 

0 

97812 

58 

3 

35  36 

24  24 

49115 

2 

50885 

51306 

2 

48694 

02192 

0 

97808 

57 

4 

35  28 

24  32 

49153 

3 

50847 

51349 

3 

48651 

02196 

0 

97804 

56 
55 

5 

9  35  20 

2  24  40 

9. 49192 

3 

10. 50808 

9. 51392 

3 

10. 48608 

10.  02200 

0 

9. 97800 

6 

35  12 

24  48 

49231 

4 

50769 

51435 

4 

48565 

02204 

0 

97796 

54 

7 

35  4 

24  56 

49269 

4 

50731 

51478 

5 

48522 

02208 

0 

97792 

53 

8 

34  56 

25  4 

49308 

5 

50692 

51520 

6 

48480 

02212 

97788 

52 

9 
10 

34  48 

25  12 

49347 

6 

50653 

51563 

6 

7 

48437 

02216 

97784 

51 
50 

9  34  40 

2  25  20 

9. 49385 

6 

10. 50615 

9.  51606 

10. 48394 

10. 02221 

9. 97779 

11 

34  32 

25  28 

49424 

7 

50576 

51648 

8 

48352 

02225 

97775 

49 

12 

34  24 

25  36 

49462 

8 

50538 

51691 

8 

48309 

02229 

97771 

48 

13 

34  16 

25  44 

49500 

8 

50500 

51734 

9 

48266 

02233 

97767 

47 

14 

34  8 

25  52 

49539 

9 

50461 

51776 

10 

48224 

02237 

97763 

46 

15 

9  34  0 

2  26  0 

9. 49577 

9 

10. 50423 

9. 51819 

10 

10. 48181 

10.  02241 

9. 97759 

45 

16 

33  52 

26  8 

49615 

10 

50385 

51861 

11 

48139 

02246 

97754 

44 

17 

33  44 

26  16 

49654 

11 

50346 

51903 

12 

48097 

02250 

97750 

43 

18 

33  36 

26  24 

49692 

11 

50308 

51946 

13 

48054 

02254 

97746 

42 

19 
20 

33  28 

26  32 

49730 

12 

50270 

51988 

13 

48012 

02258 

97742 

41 
40 

9  33  20 

2  26  40 

9. 49768 

13 

10. 50232 

9. 52031 

14 

10. 47969 

10.  02262 

9. 97738 

21 

33  12 

26  48 

49806 

13 

50194 

52073 

15 

47927 

02266 

97734 

39 

22 

33  4 

26  56 

49844 

14 

50156 

52115 

15 

47885 

02271 

2 

97729 

38 

23 

32  56 

27  4 

49882 

14 

50118 

52157 

16 

47843 

02275 

2 

97725 

37 

24 

32  48 

27  12 

49920 

15 

50080 

52200 

17 
17 

47800 

02279 

2 

97721 

36 
35 

25 

9  32  40 

2  27  20 

9.  49958 

16 

10. 50042 

9. 52242 

10. 47758 

10.  02283 

2 

9. 97717 

26 

32  32 

27  28 

49996 

16 

50004 

52284 

18 

47716 

02287 

2 

97713 

34 

27 

32  24 

27  36 

50034 

17 

49966 

52326 

19 

47674 

02292 

2 

97708 

33 

28 

32  16 

27  44 

50072 

18 

49928 

52368 

20 

47632 

02296 

2 

97704 

32 

29 

32  8 

27  52 

50110 

18 

49890 

52410 

20 

47590 

02300 

2 

97700 

31 

30 

9  32  0 

2  28  0 

9. 50148 

19 

10. 49852 

9. 52452 

21 

10. 47548 

10. 02304 

2 

9.  97696 

30 

31 

31  52 

28  8 

50185 

20 

49815 

52494 

22 

47506 

02309 

2 

97691 

29 

32 

31  44 

28  16 

50223 

20 

49777 

52536 

22 

47464 

02313 

2 

97687 

28 

33 

31  36 

28  24 

50261 

21 

49739 

52578 

23 

47422 

02317 

2 

97683 

27 

34 

31  28 

28  32 

50298 

21 

49702 

52620 

24 

47380 

02321 

2 

97679 

26 
25 

35 

9  31  20 

2  28  40 

9. 50336 

22 

10. 49664 

9. 52661 

24 

10. 47339 

10. 02326 

2 

9.  97674 

36 

31  12 

28  48 

50374 

23 

49626 

52703 

25 

47297 

02330 

3 

97670 

24 

37 

31  4 

28  56 

50411 

23 

49589 

52745 

26 

47255 

02334 

3 

97666 

23 

38 

30  56 

29  4 

50449 

24 

49551 

52787 

27 

47213 

02338 

3 

97662 

22 

39 

30  48 

29  12 

50486 

25 

49514 

52829 

27 

47171 

02343 

3 

97657 

21 
20 

40 

9  30  40 

2  29  20 

9. 50523 

25 

10. 49477 

9. 52870 

28 

10. 47130 

10. 02347 

3 

9. 97653 

41 

30  32 

29  28 

50561 

26 

49439 

52912 

29 

47088 

02351 

3 

97649 

19 

42 

30  24 

29  36 

50598 

26 

49402 

52953 

29 

47047 

02355 

3 

976^ 

18 

43 

30  16 

29  44 

50635 

27 

49365 

52995 

30 

47005 

02360 

3 

97640 

17 

44 
45 

30  8 

29  52 

50673 

28 

49327 

53037 

31 

46963 

02364 

3 

97636 
9. 97632 

16 
15 

9  30  0 

2  30  0 

9. 50710 

28 

10.49290 

9. 53078 

31 

10. 46922 

10. 02368 

3 

46 

29  52 

30  8 

50747 

29 

49253 

53120 

32 

46880 

02372 

3 

97628 

14 

47 

29  44 

30  16 

50784 

30 

49216 

53161 

33 

46839 

02377 

3 

97623 

13 

48 

29  36 

30  24 

50821 

30 

49179 

53202 

34 

46798 

02381 

3 

97619 

12 

49 
50 

29  28 

30  32 

50858 

31 

49142 

53244 

34 

46756 

02385 

3 

97615 

11 
10 

9  29  20 

2  30  40 

9. 50896 

31 

10. 49104 

9. 53285 

35 

10.46715 

10. 02390 

4 

9. 97610 

51 

29  12 

30  48 

50933 

32 

49067 

53327 

36 

46673 

02394 

4 

97606 

9 

52 

29  4 

30  56 

50970 

33 

49030 

53368 

36 

46632 

02398 

4 

97602 

8 

53 

28  56 

31  4 

ri007 

33 

48993 

53409 

37 

46591 

02403 

4 

97597 

7 

54 

28  48 

31  12 

51043 

34 

48957 

53450 

38 

46550 

02407 

4 

97593 

6 

55 

9  28  40 

2  31  20 

9. 51080 

35 

10. 48920 

9. 53492 

38 

10. 46508 

10.02411 

4 

9. 97589 

5 

56 

28  32 

31  28 

51117 

35 

48883 

53533 

39 

46467 

02416 

4 

97584 

4 

57 

28  24 

31  36 

51154 

36 

48846 

53574 

40 

46426 

02420 

4 

97580 

3 

58 

28  16 

31  44 

51191 

37 

48809 

53615 

41 

46385 

02424 

4 

97576 

2 

59 

28  8 

31  52 

51227 

37 

48773 

53656 

41 

46344 

02429 

4 

97571 

1 

60 

28  0 

32  0 

51264 

38 

48736 

53697 

42 

46303 

02433 

4 

97567 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

108' 

A 

A 

B 

B 

C 

C    71«>l 

Seconds  of  time 

!• 

2* 

8- 

4« 

6> 

6- 

7' 

IK 
Prop,  parts  of  cols.  •  B 

5 
5 
1 

9 
10 

1 

14 
16 
2 

19 
21 
2 

24 

26 
3 

28 
31 
3 

33 
37 

4 

TABLE  44. 

[Page  791 

Log.  Sines,  Tangents,  and  Secants. 

19° 

A            A 

B           B 

C 

c 

160O 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotanger.t. 

Secant. 

Dlfl. 

Cosine. 

M. 

0 

9  28  0 

2  32  0 

9. 51264 

0 

10. 48736 

9. 53697 

0 

10. 46303 

10.  02433 

0 

9.97567 

60 

1 

27  52 

32  8 

51301 

1 

48699 

53738 

1 

46262 

02437 

0 

97563 

59 

2 

27  44 

32  16 

51338 

1 

48662 

53779 

1 

46221 

02442 

0 

97558 

58 

3 

27  36 

32  24 

51374 

2 

48626 

53820 

2 

46180 

02446 

0 

97554 

57 

4 

27  28 

32  32 

51411 

2 

48589 

53861 

3 

46139 

02450 

0 
0 

97550 

56 

5 

9  27  20 

2  32  40 

9. 51447 

3 

10. 48553 

9. 53902 

3 

10. 46098 

10. 02455 

9. 97545 

55 

6 

27  12 

32  48 

51484 

4 

48516 

53943 

4 

46057 

02459 

0 

97541 

54 

7 

27  4 

32  56 

51520 

4 

48480 

53984 

5 

46016 

02464 

97536 

53 

8 

26  56 

33  4 

51557 

5 

48443 

54025 

5  ]      45975 

02468 

97532 

52 

9 
10 

26  48 

33  12 
2  33  20 

51593 

5 

48407 

54065 

6 

45935 

02472 

97528 

51 
50 

9  26  40 

9. 51629 

6 

10. 48371 

9. 54106 

7 

10. 45894 

10. 02477 

9. 97523 

11 

26  32 

33  28 

51666 

7 

48334 

54147 

7 

45853 

02481 

1 

97519 

49 

12 

26  24 

33  36 

51702 

7 

48298 

54187 

8 

45813 

02485 

1 

97515 

48 

18 

26  16 

33  44 

51738 

8 

48262 

54228 

9 

45772 

02490 

97510 

47 

14 

26  8 

33  52 

51774 

8 

48226 

54269 

9 

45731 

02494 

97506 

46 
45 

15 

9  26  0 

2  34  0 

9. 51811 

9 

10. 48189 

9. 54309 

10 

10. 45691 

10. 02499 

9. 97501 

16 

25  52 

34  8 

51847 

10 

48153 

54350 

11 

45650 

02503 

97497 

44 

17 

25  44 

34  16 

51883 

10 

48117 

54390 

11 

45610 

02508 

97492 

43 

18 

25  36 

34  24 

51919 

11 

48081 

54431 

12 

45569 

02512 

97488 

42 

19 

25  28 

34  32 

51955 

11 

48045 

54471 

13 

45529 

02516 

97484 
9. 97479 

41 
40 

20 

9  25  20 

2  34  40 

9. 51991 

12 

10. 48009 

9. 54512 

13 

10. 45488 

10. 02521 

21 

25  12 

34  48 

52027 

12 

47973 

54552 

14 

45448 

02525 

2 

97475 

39 

22 

25  4 

34  56 

52063 

13 

47937 

54593 

15 

45407 

02530 

2 

97470 

38 

23 

24  56 

35  4 

52099 

14    47901 

54633 

15 

45367 

02534 

2 

97466 

37 

24 
25 

24  48 
9  24  40 

35  12 

52135 

14 

47865 

54673 

16 

45327 

02539 

2 

97461 

36 
35 

2  35  20 

9. 52171 

15 

10. 47829 

9. 54714 

17 

10. 45286 

10. 02543 

2 

9. 97457 

26 

24  32 

35  28 

52207 

15 

47793 

54754 

17 

45246 

02547 

2 

97453 

34 

27 

24  24 

36  36 

52242 

16 

47758 

54794 

18 

45206 

02.552 

2 

97448 

33 

28 

24  16 

35  44 

52278 

17 

47722 

54835 

19 

45165 

02556 

2 

97444 

32 

29 

24  8 

35  52 

52314 

17 

47686 

54875 

19 

45125 

02561 

2 

97439 
9. 97435 

31 
30 

30 

9  24  0 

2  36  0 

9. 52350 

18 

10. 47650 

9. 54915 

20 

10. 45085 

10. 02565 

2 

31 

23  52 

36  8 

52385 

18 

47615 

54955 

21 

45045 

02570 

2 

97430 

29 

32 

23  44 

36  16 

52421 

19 

47579 

54995 

21 

45005 

02574 

2 

97426 

28 

33 

23  36 

36  24 

52456 

20 

47544 

55035 

22 

44965 

02579 

2 

97421 

27 

34 

23  28 

36  32 

52492 

20 

47508 

55075 

23 

44925 

02583 

3 
3 

97417 

26 

35 

9  23  20 

2  36  40 

9.  52527 

21 

10. 47473 

9.55115 

23 

10. 44885 

10. 02588 

9.  97412 

25 

36 

23  12 

36  48 

52563 

21 

47437 

55155 

24 

44845 

02592 

3 

97408 

24 

37 

23  4 

36  56 

52598 

22 

47402 

55195 

25 

44805 

02597 

3 

97403 

23 

38 

22  56 

37  4 

52634 

23 

47366 

55235 

25 

44765 

02601 

3 

97399 

22 

39 

22  48 

37  12 

52669 

23 

47331 

55275 

26 

44725 

02606 

3 
3 

97394 

21 

40 

9  22  40 

2  37  20 

9. 52705 

24 

10. 47295 

9.55315  i  27 

10. 44685 

10.02610 

9. 97390 

20 

41 

22  32 

37  28 

52740 

24 

47260 

55355 

27 

44645 

02615 

3 

97385 

19 

42 

•  22  24 

37  36 

52775 

25 

47225 

55395 

28 

44605 

02619 

3 

97381 

18 

43 

22  16 

37  44 

52811 

26 

47189 

55434 

29 

44566 

02624 

3 

97376 

17 

44 
45 

22  8 
9  22  0 

37  52 
2  38  0 

52846 

26 

47154 

55474 

29 

44526 

02628 

3 

97372 

16 
15 

9. 52881 

27 

10. 47119 

9. 55514 

30 

10. 44486 

10. 026^3 

3 

9. 97367 

46 

21  52 

38  8 

52916 

27 

47084 

55554 

31 

44446 

02637 

3 

97363 

14 

47 

21  44 

38  16 

52951 

28 

47049 

55593 

31 

44407 

02642 

3 

97358 

13 

48 

21  36 

38  24 

52986 

29 

47014 

55633 

32 

44367 

02647 

4 

97353 

12 

49 
50 

21  28 
9  21  20 

38  32 
2  38  40 

53021 
9. 53056 

29 

46979 

55673 

33 

44327 

02651 

4 

97349 

11 

30 

10. 46944 

9. 55712 

33 

10. 44288 

10. 02656 

4 

9. 97344 

10 

51 

21  12 

38  48 

53092 

30 

46908 

55752 

34 

44248 

02660 

4 

97340 

9 

52 

21  4 

38  56 

53126 

31 

46874 

55791 

35 

44209 

02665 

4 

97335 

8 

53 

20  56 

39  4 

53161 

32 

46839 

55831 

35 

44169 

02669 

4 

97331 

7 

54 
55 

20  48 

39  12 
2  39  20 

53196 

32 

46804 

55870 

36 

44130 

02674 

4 

97326 

6 
5 

9  20  40 

9. 53231 

33 

10.  46769 

9.  55910 

37 

10. 44090 

10.  02678 

4 

9.97322 

56 

20  32 

39  28 

53266 

33 

46734 

55949 

37 

44051 

02683 

4 

97317 

4 

57 

20  24 

39  36 

53301 

34 

46699 

55989 

38 

44011 

02688 

4 

97312 

3 

58 

20  16 

39  44 

53336 

34 

46664 

56028 

39 

4.3972 

02692 

4 

97308 

2 

59 

20  8 

39  52 

53370 

35 

46630 

56067 

39 

43933 

02697 

4 

97303 

1 

60 

20  0 

40  0 

53405 

36 

46595 

56107 

40 

43893 

02701 

4 

97299 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

109'= 

A           A 

B           B 

c 

C     70°  1 

Seconds  of  time 

1' 

2' 

3» 

4> 

o' 

6' 

7. 

Prop,  parts  of  cols.<B 

Ic 

4 
5 

1 

9 
10 

1 

13 

15 

2 

18 
20 

22  !  27 

25  '  30 

3    3 

31 

35 

4 

Page  792J 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

20° 

A            A 

B 

B       C 

C    159° 

M. 

Hour  A.  u. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Difif. 

Cotangent. 

Secant. 

Diflf. 

Cosine. 

M. 

0 

9  20  0 

2  40  0 

9. 53405 

0 

10. 46595 

9.  56107 

0 

10. 43893 

10.  02701 

0 

9. 97299 

60 

1 

19  52 

40  8 

53440 

1 

46560 

56146 

1 

43854 

02706 

0 

97294 

59 

2 

19  44 

40  16 

53475 

1 

46525 

56185 

1 

43815 

02711 

0 

97289 

58 

3 

19  36 

40  24 

53509 

2 

46491 

56224 

2 

43776 

02715 

0 

97285 

57 

4 

19  28 

40  32 

53544 

2 

46456 

56264 

3 

43736 

02720 

0 

97280 

56 
55 

5 

9  19  20 

2  40  40 

9. 53578 

3 

10. 46422 

9. 56303 

3 

10. 43697 

10.  02724 

0 

9. 97276 

6 

19  12 

40  48 

53613 

3 

46387 

56342 

4 

43658 

02729 

0 

97271 

54 

7 

19  4 

40  56 

53647 

4 

46353 

56381 

4 

43619 

02734 

97266 

53 

8 

18  56 

41  4 

53682 

5 

46318 

56420 

5 

43580 

02738 

97262 

52 

9 
10 

18  48 

41  12 

63716 

5 

46284 

56459 

6 

43541 
10. 43502 

02743 

97257 

51 
50 

9  18  40 

2  41  20 

9. 53751 

6 

10. 46249 

9. 56498 

6 

10. 02748 

9. 97252 

11 

18  32 

41  28 

53785 

6 

46215 

56537 

7 

43463 

02752 

97248 

49 

12 

18  24 

41  36 

53819 

7 

46181 

56576 

8 

43424 

02757 

97243 

48 

13 

18  16 

41  44 

53854 

7 

46146 

56615 

8 

43385 

02762 

97238 

47 

14 

18  8 

41  52 

53888 

8 

46112 

56654 

9 

43346 

02766 

1 

97234 

46 

15 

9  18  0 

2  42  0 

9. 53922 

8 

10. 46078 

9. 56693 

10 

10. 43307 

10. 02771 

9. 97229 

45 

16 

17  52 

42  8 

53957 

9 

46043 

56732 

10 

43268 

02776 

97224 

44 

17 

17  44 

42  16 

53991 

10 

46009 

56771 

11 

43229 

02780 

97220 

43 

18 

17  36 

42  24 

54025 

10 

45975 

56810 

12 

43190 

02785 

97215 

42 

19 

17  28 

42  32 

54059 

11 

45941 

56849 

12 

43151 

02790 

97210 

41 

20 

9  17  20 

2  42  40 

9. 54093 

11 

10. 45907 

9. 56887 

13 

10. 43113 

10. 02794 

2 

9. 97206 

40 

21 

17  12 

42  48 

54127 

12 

45873 

56926 

13 

43074 

02799 

2 

97201 

39 

22 

17  4 

42  56 

54161 

12 

45839 

56965 

14 

43035 

02804 

2 

97196 

38 

23 

16  56 

43  4 

54195 

13 

45805 

57004 

15 

42996 

02808 

2 

97192 

37 

24 

16  48 

43  12 

54229 

14 

45771 

57042 

15 

42958 

02813 

2 

97187 

36 

35 

25 

9  16  40 

2  43  20 

9. 54263 

14 

10. 45737 

9. 57081 

16  10.42919 

10. 02818 

2 

9. 97182 

26 

16  32 

43  28 

54297 

15 

45703 

57120 

17 

42880 

02822 

2 

97178 

34 

27 

16  24 

43  36 

54331 

15 

45669 

57158 

17 

42842 

02827 

2 

97173 

33 

28 

16  16 

43  44 

54365 

16 

45635 

57197 

18 

42803 

02832 

2 

97168 

32 

29 

16  8 

43  52 

54399 

16 

45601 

57235 

19 

42765 

02837 

2 

97163 

31 

30 

9  16  0 

2  44  0 

9. 54433 

17 

10. 45567 

9. 57274 

19  110.42726 

10. 02841 

2 

9. 97159 

30 

31 

15  52 

44  8 

54466 

17 

45534 

57312 

20 

42688 

02846 

2 

97154 

29 

32 

15  44 

44  16 

54500 

18 

45500 

57351 

21 

42649 

02851 

3 

97149 

28 

33 

15  36 

44  24 

54534 

19 

45466 

57389 

21 

42611 

02855 

3 

97145 

27 

34 

15  28 

44  32 

54567 

19 

45433 

57428 

22 

42572 

02860 

3 
3 

97140 

26 

35 

9  15  20 

2  44  40 

9. 54601 

20 

10. 45399 

9. 57466 

22 

10. 42534 

10.  02865 

9. 97135 

25 

36 

15  12 

44  48 

54635 

20 

45365 

57504 

23 

42496 

02870 

3 

97130 

24 

87 

15  4 

44  56 

54668 

21 

45332 

57543 

24 

42457 

02874 

3 

97126 

23 

88 

14  56 

45  4 

54702 

21 

45298 

57581 

24 

42419 

02879 

3 

97121 

22 

39 

14  48 

45  12 

54735 

22 

45265 

57619 

25 

42381 

02884 

3 

97116 

21 

40 

9  14  40 

2  45  20 

9. 54769 

23 

10. 45231 

9. 57658 

26 

10. 42342 

10.  02889 

3 

9. 97111 

20 

41 

14  32 

45  28 

54802 

23 

45198 

57696 

26 

42304 

02893 

3 

97107 

19 

42 

14  24 

45  36 

54836 

24 

45164 

57734 

27  1   42266 

02898 

3 

97102 

18 

43 

14  16 

45  44 

54869 

24 

4513] 

57772 

28  i   42228 

02903 

3 

97097 

17 

44 

14  8 

45  52 

54903 

25 

45097 

57810 

28  1   42190 

02908 
10. 02913 

3 

97092 

16 
15 

45 

9  14  0 

2  46  0 

9. 54936 

25 

10. 45064 

9. 57849 

29  ilO.  42151 

4 

9. 97087 

46 

13  52 

46  8 

54969 

26 

45031 

57887 

30  ;   42113 

02917 

4 

97083 

14 

47 

13  44 

46  16 

55003 

26 

44997 

57925 

30  :   42075 

02922 

4 

97078 

13 

48 

13  36 

46  24 

55036 

27 

44964 

57963 

31 

42037 

02927 

4 

97073 

12 

49 

13  28 

46  32 

55069 

28 

44931 

58001 
9. 58039 

31 

41999 

02932 

4 

97068 

11 
10 

50 

9  13  20 

2  46  40 

9. 55102 

28' 

10.  44898 

32 

10. 41961 

10. 02937 

4 

9. 97063 

51 

13  12 

46  48 

55136 

29 

44864 

58077 

33 

41923 

02941 

4 

97059 

9 

52 

13  4 

46  56 

55169 

29 

44831 

58115 

33 

41885 

02946 

4 

97054 

8 

63 

12  56 

47  4 

55202 

30 

44798 

58153 

34 

41847 

02951 

4 

97049 

7 

54 

12  48 

47  12 

55235 

30 

44765 

58191 

35 

41809 

02956 

4 

97044 

6 
5 

55 

9  12  40 

2  47  20 

9. 55268 

31 

10. 44732 

9. 58229 

35 

10. 41771 

10. 02961 

4 

9. 97039 

56 

12  32 

47  28 

55301 

32 

44699 

58267 

36 

41733 

02965 

4 

97035 

4 

57 

12  24 

47  36 

55334 

32 

44666 

58304 

37 

41696 

02970 

4 

97030 

3 

58 

12  16 

47  44 

55367 

33 

44633 

58342 

37 

41658 

02975 

5 

97025 

2 

59 

12  8 

47  52 

55400 

33 

44600 

58380 

38 

41620 

02980 

5 

97020 

1 

60 

12  0 

48  0 

55433 

34 

44567 

58418 

39 

41582 

02985 

5 

97015 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

DlfE. 

Tangent. 

Cosecant. 

Dfff. 

Sine. 

M. 

110° 

A           A 

B 

B        C 

C     69°  1 

Seconds  of  time 

1"    2- 

»• 

4« 

6' 

6< 

"!' 

Prop,  parta  of  cols.  <  B 

Ic 

4    8 
6    10 

1  1   1 

13 
14 

2 

17 

19 

2 

21 

24 

3 

26 
29 

4 

30 
34 
4 

TABLE  44. 

[Page  793 

Log.  Sines,  Tangents,  and  Secants. 

21° 

A 

A 

B           B        C 

C    158° 

M. 
0 

Hour  A.  H. 

Hour  P.M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

9  12  0 

2  48  0 

9. 55433 

0 

10.  44567 

9.  68418 

0 

10.  41582 

10.  02985 

0 

9.  97015 

60 

1 

11  52 

48  8 

55466 

1 

44634 

68466 

1 

41545 

02990 

0 

97010 

59 

2 

11  44 

48  16 

56499 

1 

44601 

58493 

1 

41507 

02995 

0 

97005 

58 

3 

11  36 

48  24 

55632 

2 

44468 

58531 

2 

41469 

02999 

0 

97001 

57 

4 

11  28 

48  32 

66664 

2 

44436 

68669 

2 

41431 

03004 

0 

96996 

56 
56 

5 

9  11  20 

2  48  40 

9. 55597 

3 

10. 44403 

9. 68606 

3 

10. 41394 

10. 03009 

0 

9. 96991 

6 

11  12 

48  48 

55630 

3 

44370 

68644 

4 

41366 

03014 

0 

96986 

54 

7 

11  4 

48  56 

65663 

4 

44337 

58681 

4 

41319 

03019 

96981 

53 

8 

10  56 

49  4 

66695 

4 

44306 

68719 

5 

41281 

03024 

96976 

52 

9 

10  48 

49  12 

56728 

6 

44272 

58757 

6 

41243 

03029 

96971 

51 
50 

10 

9  10  40 

2  49  20 

9.  55761 

6 

10. 44239 

9. 58794 

6 

10. 41206 

10. 03034 

9. 96966 

11 

10  32 

49  28 

56793 

6 

44207 

58832 

7 

41168 

03038 

96962 

49 

12 

10  24 

49  36 

55826 

6 

44174 

58869 

7 

41131 

03043 

96967 

48 

13 

10  16 

49  44 

55858 

7 

44142 

58907 

8 

41093 

03048 

96962 

47 

14 

10  8 

49  52 

66891 

7 

44109 

68944 

9 

41066 

03063 

96947 

46 

16 

9  10  0 

2  60  0 

9. 55923 

8 

10. 44077 

9. 58981 

9 

10. 41019 

10. 03058 

9. 96942 

46 

16 

9  52 

50  8 

55966 

9 

44044 

69019 

10 

40981 

03063 

96937 

44 

17 

9  44 

50  16 

65988 

9 

44012 

69066 

10  ,   40944 

03068 

96932 

43 

18 

9  36 

50  24 

56021 

10 

43979 

69094 

11  1   40906 

03073 

96927 

42 

19 

9  28 

60  32 

56063 

10 

43947 

59131 

12 

40869 
10. 40832 

03078 
10. 03083 

2 

2 

96922 

41 

20 

9  9  20 

2  50  40 

9.56085 

11 

10. 43915 

9. 59168 

12 

9. 96917 

40 

21 

9  12 

60  48 

56118 

11 

43882 

59205 

13  i   40795 

03088 

2 

96912 

39 

22 

9  4 

60  56 

66160 

12 

43850 

59243 

14  1   40757 

03093 

2 

96907 

38 

23 

8  56 

51  4 

56182 

12 

43818 

59280 

14  1   40720 

03097 

2 

96903 

37 

24 

8  48 

51  12 

56216 
9. 56247 

13 
13 

43785 

59317 
9.59354 

15 
15 

40683 

03102 
10. 03107 

2 
2 

96898 
9.96893 

36 
35 

25 

9  8  40 

2  61  20 

10. 43753 

10. 40646 

26 

8  32 

61  28 

56279 

14 

43721 

59391 

16 

40609 

03112 

2 

96888 

34 

27 

8  24 

51  36 

56311 

14 

43689 

59429 

17  i   40571 

03117 

2 

96883 

33 

28 

8  16 

61  44 

66343 

15 

43657 

59466 

17  I   40634 

03122 

2 

96878 

32 

29 

8  8 

61  62 

66375 

16 

43625 

59603 

18    40497 

03127 

2 

96873 

31 
30 

30 

9  8  0 

2  62  0 

9. 56408 

16 

10. 43592 

9. 59540 

19  10.40460 

10. 03132 

2 

9. 96868 

31 

7  62 

62  8 

56440 

17 

4^560 

59677 

19  '   40423 

03137 

3 

96863 

29 

32 

7  44 

52  16 

56472 

17 

43628 

59614 

20    40386 

03142 

3 

96868 

28 

33 

7  36 

52  24 

56604 

18 

43496 

59651 

20    40349 

03147 

3 

96863 

27 

34 

7  28 

52  32 

56536 

18 

434G4 

69688 

21  1   40312 

03152 

3 

96848 

26 
25 

36 

9  7  20 

2  52  40 

9. 56568 

19 

10. 43432 

9. 69725 

22  10.40275 

10. 03157 

3 

9. 96843 

36 

7  12 

62  48 

56599 

19 

43401 

69762 

22    40238 

03162 

3 

96838 

24 

37 

7  4 

62  66 

56631 

20 

43369 

59799 

23    40201 

03167 

3 

96833 

23 

38 

6  56 

63  4 

66663 

20 

43337 

59836 

23  I   40165 

03172 

3 

96828 

22 

39 

6  48 

53  12 

56695 

21 

43306 

59872 

24 

40128 

03177 

3 
3 

96823 
9. 96818 

21 
20 

40 

9  6  40 

2  53  20 

9. 56727 

21 

10. 43273 

9.59909 

25 

10. 40091 

10. 03182 

41 

6  32 

53  28 

56759 

22 

43241 

59946 

25 

40064 

03187 

3 

96813 

19 

42 

6  24 

53  36 

56790 

22 

43210 

59983 

26  1   40017 

03192 

3 

96808 

18 

43 

6  16 

53  44 

66822 

23 

43178 

60019 

27    39981 

03197 

4 

96803 

17 

44 

6  8 

63  52 
2  54  0 

56854 

24 

43146 

60056 

27 
28 

39944 

03202 

4 

96798 

16 

46 

9  6  0 

9. 56886 

24 

10. 43114 

9.60093 

10.  39907 

10. 03207 

4 

9. 96793 

16 

46 

5  62 

54  8 

56917 

25 

43083 

60130 

28    39870 

03212 

4 

96788 

14 

47 

6  44 

54  16 

66949 

26 

43061 

60166 

29    39834 

03217 

4 

96783 

13 

48 

6  36 

54  24 

66980 

26 

43020 

60203 

30    39797 

03222 

4 

96778 

12 

49 

5  28 

54  32 

67012 

26 

42988 

60240 

30    39760 

03228 

4 

96772 

11 
10 

50 

9  5  20 

2  54  40 

9.57044 

27 

10. 42956 

9. 60276 

31  10.39724 

10. 03233 

4 

9. 96767 

51 

5  12 

54  48 

67075 

27 

42925 

60313 

31    39687 

03238 

4 

96762 

9 

52 

5  4 

54  66 

67107 

28 

42893 

60349 

32  1   39651 

03243 

4 

96757 

8 

53 

4  56 

66  4 

67138 

28 

42862 

60386 

33    39614 

03248 

4 

96752 

7 

64 

4  48 

56  12 

67169 

29 

42831 

60422 

33 

39578 
10. 39541 

03253 

4 

96747 

6 

55 

9  4  40 

2  65  20 

9. 57201 

29 

10. 42799 

9. 60459 

34 

10. 03258 

6 

9. 96742 

5 

56 

4  32 

^56  28 

57232 

30 

42768 

60495 

35 

39606 

03263 

6 

96737 

4 

57 

4  24 

66  36 

67264 

30 

42736 

60532 

35 

39468 

03268 

6 

96732 

3 

58 

4  16 

65  44 

67295 

31 

42705 

60568 

36 

39432 

03273 

5 

96727 

2 

59 

4  8 

65  52 

57326 

32 

42674 

60606 

36 

39396 

03278 

6 

96722 

1 

60 

4  0 

56  0 

57358 

32 

42642 

60641 

37 

39359 

03283 

5 

96717   0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Dlfl. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine.    M. 

111° 

A 

A 

B           B       C 

C     68°  1 

Second  of  time  , 


Prop,  parts 


of  cols.'{B 

Ic 


1    Page  794] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

220 

A          A 

B            B 

C 

C 

157° 

•M. 

Hour  A..  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

DifE. 

Cotangent. 

Secant. 

Dift. 

Cosine. 

M. 

0 

9  4  0 

2  56  0 

9.  57358 

0 

10. 42642 

9.60641 

0 

10.  39359 

10. 03283 

0 

9.96717 

60 

1 

3  52 

56  8 

57389 

1 

42611 

60677 

1 

39323 

03289 

0 

96711 

59 

2 

3  44 

56  16 

57420 

1 

42580 

60714 

1 

39286 

03294 

0 

96706 

58 

3 

3  36 

56  24 

57451 

2 

42549 

60750 

2 

39250 

03299 

0 

96701 

57 

4 

3  28 

56  32 

57482 

2 

42518 

60786 

2 
3 

39214 

03304 

0 

96696 

56 
55 

5 

9  3  20 

2  56  40 

9. 57514 

3 

10. 42486 

9. 60823 

10. 39177 

10. 03309 

0 

9. 96691 

6 

3  12 

,  56  48 

57545 

3 

42455 

60859 

4 

39141- 

03314 

96686 

54 

7 

3  4 

56  56 

57576 

4 

42424 

60895 

4 

39105 

03319 

96681 

53 

8 

2  56 

57  4 

57607 

4 

42393 

60931 

5 

39069 

03324 

96676 

52 

9 

2  48 

57  12 

57638 

5 

42362 

60967 

5 

39033 

03330 
10. 03335 

96670 

51 
50 

10 

9  2  40 

2  57  20 

9. 57669 

5 

10. 42331 

9.  61004 

6 

10. 38996 

9. 96665 

11 

2  32 

57  28 

57700 

6 

42300 

61040 

7 

38960 

03340 

96660 

49 

12 

2  24 

57  36 

57731 

6 

42269 

61076 

7 

38924 

03345 

96655 

48 

13 

2  16 

57  44 

57762 

7 

42238 

61112 

8 

38888 

03350 

96650 

47 

14 
15 

2  8 

57  52 

57793 

7 

42207 

61148 

8 

38852 

03355 

96645 
9. 96640 

46 

45 

9  2  0 

2  58  0 

9. 57824 

8 

10. 42176 

9. 61184 

9 

10. 38816 

10. 03360 

16 

1  52 

58  8 

57855 

8 

42145 

61220 

10 

38780 

03366 

96634 

44 

17 

1  44 

58  16 

57885 

9 

42115 

61256 

10 

38744 

03371 

96629 

43 

18 

1  36 

58  24 

57916 

9 

42084 

61292 

11 

38708 

03376 

2 

96624 

42 

19 
20 

1  28 

58  32 

57947 

10 

42053 

61328 

11 

38672 

03381 

2 

96619 
9. 96614 

41 
40 

9  1  20 

2  58  40 

9. 57978 

10 

10. 42022 

9.  61364 

12 

10. 38636 

10. 03386 

2 

21 

1  12 

58  48 

58008 

11 

41992 

61400 

13 

38600 

03392 

2 

96608 

39 

22 

1  4 

58  56 

58039 

11 

41961 

61436 

13 

38564 

03397 

2 

96603 

38 

23 

0  56 

59  4 

58070 

12 

41930 

61472 

14 

38528 

03402 

2 

96598 

37 

24 
25 

0  48 

59  12 

58101 

12 

41899 

61508 
9.  61544 

14 

38492 

03407 

2 

96593 
9.  96588 

36 
35 

9  0  40 

2  59  20 

9. 58131 

13 

10. 41869 

15 

10. 38456 

10.  03412 

2 

26 

0  32 

59  28 

58162 

13 

41838 

61579 

15 

38421 

03418 

2 

96582 

34 

27 

0  24 

59  36 

58192 

14 

41808 

61615 

16 

38385 

03423 

2 

96577 

33 

28 

0  16 

59  44 

58223 

14 

41777 

61651 

17 

38349 

03428 

2 

96572 

32 

29 

0  8 

59  52 

58253 

15 

41747 

61687 

17 

38313 
10. 38278 

03433 

3 
3 

96567 
9. 96562 

31 
30" 

30 

9  0  0 

3  0  0 

9. 58284 

15 

10. 41716 

9. 61722 

18 

10. 03438 

31 

8  59  52 

0  8 

58314 

16 

41686 

61758 

18 

38242 

03444 

3 

96556 

29 

32 

59  44 

0  16 

58345 

16 

41655 

61794 

19 

38206 

03449 

3 

96551 

28 

33 

59  36 

0  24 

58375 

17 

41625 

61830 

20 

38170 

03454 

3 

96546 

27 

34 

59  28 

0  32 

58406 

17 

41594 

61865 

20 

38135 

03459 

3 
3 

96541 
9. 96535 

26 
25 

35 

8  59  20 

3  0  40 

9. 58436 

18 

10. 41564 

9. 61901 

21 

10. 38099 

10. 03465 

36 

59  12 

0  48 

58467 

18 

41533 

61936 

21 

38064 

03470 

3 

96530 

24 

37 

59  4 

0  56 

58497 

19 

41503 

61972 

22 

38028 

03475 

3 

96525 

23 

38 

58  56 

1  4 

58527 

19 

41473 

62008 

23 

37992 

03480 

3 

96520 

22 

39 
40 

58  48 
8  58  40 

1  12 

58557 

20 

41443 

62043 

23 

37957 

03486 

3 

96514 

21 
20 

3  1  20 

9. 58588 

20 

10.  41412 

9. 62079 

24 

10. 37921 

10. 03491 

3 

9.  96509 

41 

58  32 

1  28 

58618 

21 

41382 

62114 

24 

37886 

03496 

4 

.  96504 

19 

42 

58  24 

1  36 

58648 

21 

41352 

62150 

25 

37850 

03502 

4 

96498 

18 

43 

58  16 

1  44 

58678 

22 

41322 

62185 

26 

37815 

03507 

4 

96493 

17 

44 

58  8 

1  52 

58709 

22 
23 

41291 
10. 41261 

62221 

26 

27 

37779 

03512 

4 

96488 

16 

45 

8  58  0 

3  2  0 

9. 58739 

9.  62256 

10. 37744 

10. 03517 

4 

9. 96483 

15 

46 

57  52 

2  8 

58769 

23 

41231 

62292 

27 

37708 

03523 

4 

96477 

14 

47 

57  44 

2  16 

58799 

24 

41201 

62327 

28 

37673 

03528 

4 

96472 

13 

48 

57  36 

2  24 

58829 

24 

41171 

62362 

29 

37638 

03533 

4 

96467 

12 

49 

57  28 

2  32 

58859 

25 

41141 

62398 

29 

37602 

03539 

4 

96461 

11 

50 

8  57  20 

3  2  40 

9. 58889 

25 

10.41111 

9. 62433 

30 

10. 37567 

10. 03544 

4 

9.  96456 

10 

51 

57  12 

2  48 

58919 

26 

41081 

62468 

30 

37532 

03549 

4 

96451 

9 

52 

57  4 

2  56 

58949 

26 

41051 

62504 

31 

37496 

03555 

5 

96445 

8 

53 

56  56 

3  4 

58979 

27 

41021 

62539 

32 

37461 

03560 

5 

96440 

7 

54 

56  48 

3  12 

59009 

27 

40991 

62574 

32 

37426 

03565 

5 

96435 

6 
5 

55 

8  56  40 

3  3  20 

9. 59039 

28 

10. 40961 

9. 62609 

33 

10. 37391 

10. 03571 

5 

9. 96429 

66 

56  32 

3  28 

59069 

28 

40931 

62645 

33 

37355 

03576 

5 

96424 

4 

57 

56  24 

3  36 

59098 

29 

40902 

62680 

34 

37320 

03581 

5 

96419 

3 

58 

56  16 

3  44 

59128 

29 

40872 

62715 

35 

37285 

03587 

5 

96413 

2 

59 

56  8 

3  52 

59158 

30 

40842 

62750 

35 

37250 

03592 

5 

96408 

1 

60 
M. 

56  0 

4  0 

59188 

31 

40812 

62785 

36 

37215 

03597 

5 

96403 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

1129 

A            A 

B           B 

C 

C 

67° 

Seconds  of  time 

1« 

2> 

8" 

4" 

6> 

e- 

7' 

(A 
Prop,  parts  of  cols.^B 

Ic 

4 

4 
1 

8 
9 

1 

11 
13 

2 

16 
18 
3 

19 

22 

3 

23 

27 

4 

27 
31 

5 

TABLE  44. 
Log.  Sines,  Tangents,  and  Secants. 

[Page  795 

«3° 

A             A 

B            B 

C 

C    166° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

8  56  0 

3  4  0 

9. 59188 

0 

10. 40812 

9. 62785 

0 

10. 37215 

10. 03597 

0 

9.96403 

60 

1 

55  52 

4  8 

59218 

0 

40782 

62820 

1 

37180 

03603 

0 

96397 

59 

? 

55  44 

4  16 

59247 

1 

40753 

62855 

1 

37145 

03608 

0 

96392 

58 

3 

55  36 

4  24 

59277 

1 

40Z23 

62890 

2 

37110 

03613 

0 

96387 

57 

4 

55  28 

4  32 

59307 

2 

40693 

62926 

2 

37074 

03619 

0 

96381 
9.96376 

56 
55 

5 

8  55  20 

3  4  40 

9. 59336 

2 

10. 40664 

9. 62961 

3 

10. 37039 

10. 03624 

0 

fi 

55  12 

4  48 

59366 

3 

40634 

62996 

3 

37004 

03630 

96370 

54 

7 

55  4 

4  56 

59396 

3 

40604 

63031 

4 

36969 

03635 

96365 

53 

8 

54  56 

5  4 

59425 

4 

40575 

63066 

5 

36934 

03640 

96360 

52 

9 

54  48 

5  12 

59455 

4 

40545 

63101 

5 

36899 

03646 

96354 

51 
50 

10 

8  54  40 

3  5  20 

9. 59484 

5 

10. 40516 

9.  63135 

6 

10. 36865 

10. 03651 

9.96349 

11 

54  32 

5  28 

59514 

5 

40486 

63170 

6 

36830 

03667 

96343 

49 

12 

54  24 

5  36 

59543 

6 

40457 

63205 

7 

36795 

03662 

96338 

48 

13 

54  16 

5  44 

59573 

6 

40427 

63240 

7 

36760 

03667 

96333 

47 

14 
15 

54  8 

5  52 

59602 

7 

40398 

63275 

8 

36725 

03673 

96327 

46 

8  54  0 

3  6  0 

9. 59632 

7 

10. 40368 

9. 63310 

9 

10. 36690 

10. 03678 

9. 96322 

45 

16 

53  52 

6  8 

59661 

8 

40339 

63345 

9 

36655 

03684 

96316 

44 

17 

53  44 

6  16 

59690 

8 

40310 

63379 

10 

36621 

03689 

2 

96311 

43 

18 

53  36 

6  24 

59720 

9 

40280 

63414 

10 

36586 

03695 

2 

96305 

42 

19 

53  28 

6  32 

59749 

9 

40251 

63449 

11 

36551 

03700 

2 

96300 

41 

20 

8  53  20 

3  6  40 

9. 59778 

10 

10. 40222 

9.63484 

12 

10.  36516 

10. 03706 

2 

9. 96294 

40 

21 

53  12 

6  48 

59808 

10 

40192 

63519 

12 

36481 

03711 

2 

96289 

39 

22 

53  4 

6  56 

59837 

11 

40163 

63553 

13 

36447 

03716 

2 

96284 

38 

2r, 

52  56 

7  4 

59866 

11 

40134 

63588 

13 

36412 

03722 

2 

96278 

37 

24 

25 

52  48 
8  52  40 

7  12 

59895 

12 

40105 

63623 

14 

36377 

03727 

2 

96273 

36 
36 

3  7  20 

9. 59924 

12 

10. 40076 

9. 63657 

14 

10. 36343 

10. 03733 

2 

9. 96267 

26 

52  32 

7  28 

59954 

13 

40046 

63692 

15 

36308 

03738 

2 

96262 

34 

27 

52  24 

7  36 

59983 

13 

40017 

63726 

16 

36274 

03744 

2 

96256 

33 

28 

52  16 

7  44 

60012 

14 

39988 

63761 

16 

36239 

03749 

3 

96251 

32 

29 

52  8 

7  52 

60041 

14 

39959 

63796 

17 

36204 

03755 

3 

96245 

31 
30 

30 

8  52  0 

3  8  0 

9. 60070 

15 

10. 39930 

9. 63830 

17 

10. 36170 

10. 03760 

3 

9. 96240 

31 

51  52 

8  8 

60099 

15 

39901 

63865 

18 

36135 

03766 

3 

96234 

29 

32 

51  44 

8  16 

60128 

15 

39872 

63899 

18 

36101 

03771 

3 

96229 

28 

33 

51  36 

8  24 

60157 

16 

39843 

63934 

19 

36066 

03777 

3 

96223 

27 

34 

51  28 

8  32 

60186 

16 

39814 

63968 

20 

36032 

03782 

3 

96218 

26 

35 

8  51  20 

3  8  40 

9. 60215 

17 

10. 39785 

9.64003 

20 

10. 35997 

10. 03788 

3 

9. 96212 

25 

36 

51  12 

8  48 

60244 

17 

39756 

64037 

21 

35963 

03793 

3 

96207 

24 

37 

51  4 

8  56 

60273 

18 

39727 

64072 

21 

35928 

03799 

3 

96201 

23 

38 

50  56 

9  4 

60302 

18 

39698 

64106 

22 

35894 

03804 

3 

96196 

22 

39 

50  48 

9  12 

60331 

19 

39669 

64140 

22 

35860 

03810 

4 

96190 

21 

40 

8  50  40 

3  9  20 

9. 60359 

19 

10.  39641 

9. 64175 

23 

10.  35825 

10. 03815 

4 

9. 96185 

20 

41 

50  32 

9  28 

60388 

20 

39612 

64209 

24 

35791 

03821 

4 

96179 

19 

42 

50  24 

9  36 

G0417 

20 

39583 

64243 

24 

35757 

03826 

4 

96174 

18 

43 

50  16 

9  44 

60446 

21 

39554 

64278 

25 

35722 

03832 

4 

96168 

17 

44 

50  8 

9  52 

60474 

21 

39526 

64312 

25 

35688 

03838 

4 

96162 

16 

45 

8  50  0 

3  10  0 

9. 60503 

22 

10. 39497 

9.64346 

26 

10. 35654 

10. 03843 

4 

9. 96157 

15 

46 

49  52 

10  8 

60532 

22 

39468 

64381 

26 

35619 

03849 

4 

96151 

14 

47 

49  44 

10  16 

60561 

23 

39439 

64415 

27 

35585 

03854 

4 

96146 

13 

48 

49  36 

10  24 

60589 

23 

39411 

64449 

28 

35551 

03860 

4 

96140 

12 

49 

49  28 

10  32 

60618 

24 

39382 

64483 

28 

35517 

03865 

4 

96135 

11 
10 

50 

8  49  20 

3  10  40 

9. 60646 

24 

10.  39354 

9. 64517 

29 

10.  35483 

10. 03871 

5 

9. 96129 

51 

49  12 

10  48 

60675 

25 

39325 

64552 

29 

35448 

03877 

5 

96123 

9 

52 

49  4 

10  56 

60704 

25 

39296 

64586 

30 

35414 

03882 

5 

96118 

8 

53 

48  56 

11  4 

60732 

26 

39268 

64620 

31 

35380 

03888 

5 

96112 

7 

54 

48  48 

11  12 

60761 

26 

27 

39239 

64654 

31 

35346 

03893 

5 

96107 

6 

55 

8  48  40 

3  11  20 

9. 60789 

10.  39211 

9. 64688 

32 

10.  35312 

10. 03899 

5 

9. 96101 

5 

56 

48  32 

11  28 

60818 

27 

39182 

64722 

32 

35278 

03905 

5 

96095 

4 

57 

48  24 

11  36 

60846 

28 

39154 

64756 

33 

35244 

03910 

5 

96090 

3 

58 

48  16 

11  44 

60875 

28 

39125 

64790 

33 

35210 

03916 

5 

96084 

2 

59 

48  8 

11  52 

60903 

29 

39097 

64824 

34 

35176 

03921 

5 

96079 

1 

60 

48  0 

12  0 

60931 

29 

39069 

64858 

35 

35142 

03927 

6 

96073 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

ICosecant. 

DIfl. 

Sine. 

M. 

118° 

A            A 

B           B 

C 

C    66° 

Seconds  of  time 

1> 

2» 

8- 

4* 

6" 

6» 

7» 

Prop,  parts  of  cols.  -<  B 

4 

4 

1 

7 
9 
1 

11 

13 
2 

15 

17 

3 

18 

22 

3 

22 

26 

4 

25 
31 
5 

21594°— 14 43 


Page  796] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

24° 

A 

•       A 

B            B 

C 

C    155° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

8  48  0 

3  12  0 

9. 60931 

0 

10. 39069 

9.  64858 

0 

10. 35142 

10.  03927 

0 

9. 96073 

1 

47  52 

12  8 

60960 

0 

39040 

64892 

1 

35108 

03933 

0 

96067 

59 

2 

47  44 

12  16 

60988 

1 

39012 

64926 

1 

35074 

03938 

0 

96062 

58 

3 

47  36 

12  24 

61016 

1 

38984 

64960 

2 

35040 

03944 

0 

96056 

57 

4 

47  28 

12  32 

61045 

2 

38955 

64994 

2 

35006 

03950 

0 

96050 
9. 96045 

56 
55 

5 

8  47  20 

3  12  40 

9. 61073 

2 

10. 38927 

9.  65028 

3 

10. 34972 

10. 03955 

0 

6 

47  12 

12  48 

61101 

3 

38899 

65062 

3 

34938 

03961 

96039 

54 

7 

47  4 

12  56 

61129 

3 

38871 

65096 

4 

34904 

03966 

96034 

53 

8 

46  56 

13  4 

61158 

4 

38842 

65130 

4 

34870 

03972 

96028 

52 

9 

46  48 

13  12 

61186 

4 

38814 

65164 

5 

34836 

03978 

96022 

51 

10 

8  46  40 

3  13  20 

9. 61214 

5 

10. 38786 

9. 65197 

6 

10. 34803 

10. 03983 

9. 96017 

50 

11 

46  32 

13  28 

61242 

5 

38758 

65231 

6 

34769 

03989 

96011 

49 

12 

46  24 

13  36 

61270 

6 

38730 

65265 

7 

34735 

03995 

96005 

48 

13 

46  16 

13  44 

61298 

6 

38702 

65299 

7 

34701 

04000 

96000 

47 

14 

46  8 

13  52 

61326 

6 

38674 

65333 

8 

34667 

04006 

95994 

46 
45 

15 

8  46  0 

3  14  0 

9.  61354 

7 

10. 38646 

9. 65366 

8 

10. 34634 

10. 04012 

9. 95988 

16 

45  52 

14  8 

61382 

7 

38618 

65400 

9 

34600 

04018 

2 

95982 

44 

17 

45  44 

14  16 

61411 

8 

38589 

65434 

9 

34566 

04023 

2 

95977 

43 

18 

45  36 

14  24 

61438 

8 

38562 

65467 

10 

34533 

04029 

2 

95971 

42 

19 

45  28 

14  32 

61466 

9 

38534 

65501 

11 

34499 

04035 

2 

95965 

41 

20 

8  45  20 

3  14  40 

9. 61494 

9 

10.  38506 

9. 65535 

11 

10.  34465 

10. 04040 

2 

9. 95960 

40 

21 

45  12 

14  48 

61522 

10 

38478 

65568 

12 

34432 

04046 

2 

95954 

39 

22 

45  4 

14  56 

61550 

10 

38450 

65602 

12 

34398 

04052 

2 

95948 

38 

23 

44  56 

15  4 

61578 

11 

38422 

65636 

13 

34364 

04058 

2 

95942 

37 

24 

44  48 

15  12 

61606 

11 

38394 

65669 

13 

34331 

04063 

2 

95937 

36 

26 

8  44  40 

3  15  20 

9. 61634 

12 

10. 38366 

9. 65703 

14 

10. 34297 

10. 04069 

2 

9. 95931 

35 

26 

44  32 

15  28 

61662 

12 

38338 

65736 

15 

34264 

04075 

2 

95925 

34 

27 

44  24 

15  36 

61689 

12 

38311 

65770 

15 

34230 

04080 

3 

95920 

33 

28 

44  16 

15  44 

61717 

13 

38283 

65803 

16 

34197 

04086 

3 

95914 

32 

29 

44  8 

15  52 

61745 

13 

38255 

65837 

16 

34163 

04092 

3 

95908 

31 

30 

8  44  0 

3  16  0 

9.61773 

14 

10.  38227 

9.  65870 

17 

10.  34130 

10. 04098 

3 

9. 95902 

30 

31 

43  52 

16  8 

61800 

14 

38200 

65904 

17 

34096 

04103 

3 

95897 

29 

32 

43  44 

16  16 

61828 

15 

38172 

65937 

18 

34063 

04109 

3 

95891 

28 

33 

43  36 

16  24 

61856 

15 

38144 

65971 

18 

34029 

04115 

3 

95885 

27 

34 

43  28 

16  32 

61883 

16 

38117 

66004 

19 

33996 

04121 

3 

95879 

26 

35 

8  43  20 

3  16  40 

9.61911 

16 

10.  38089 

9.  66038 

20 

10.  33962 

10.  04127 

3 

9. 95873 

25 

36 

43  12 

16  48 

61939 

17 

38061 

66071 

20 

33929 

04132 

3 

95868 

24 

37 

43  4 

16  56 

61966 

17 

38034 

66104 

21 

33896 

04138 

4 

95862 

23 

38 

42  56 

17  4 

61994 

18 

38006 

66138 

21 

33862 

04144 

4 

95856 

22 

39 

42  48 

17  12 

62021 

18 

37979 

66171 

22 

33829 

04150 

4 

95850 

21 

40 

8  42  40 

3  17  20 

9. 62049 

18 

10.  37951 

9.  66204 

22 

10. 33796 

10. 04156 

4 

9. 95844 

20 

41 

42  32 

17  28 

62076 

19 

37924 

66238 

23 

33762 

04161 

4 

95839 

19 

42 

42  24 

17  36 

62104 

19 

37896 

66271 

23 

33729 

04167 

4 

95833 

18 

43 

42  16 

17  44 

62131 

20 

37869 

66304 

24 

33696 

04173 

4 

95827 

17 

44 

42  8 

17  52 

62159 

20 

37841 

66337 

25 

33663 

04179 

4 

95821 

16 
15 

45 

8  42  0 

3  18  0 

9. 62186 

21 

10.  37814 

9. 66371 

25 

10.  33629 

10. 04185 

4 

9. 95815 

46 

41  52 

18  8 

62214 

21 

37786 

66404 

26 

33596 

04190 

4 

95810 

14 

47 

41  44 

18  16 

62241 

22 

37759 

66437 

26 

33563 

04196 

5 

95804 

13 

48 

41  36 

18  24 

62268 

22 

37732 

66470 

27 

33530 

04202 

5 

95798 

12 

49 

41  28 

18  32 

62296 

23 

37704 

66503 

27 

33497 

04208 

5 

95792 

11 

bO 

8  41  20 

3  18  40 

9. 62323 

23 

10.  37677 

9. 66537 

28 

10.  33463 

10.  04214 

5 

9. 95786 

10 

51 

41  12 

18  48 

62350 

24 

37650 

66570 

28 

33430 

04220 

5 

95780 

9 

52 

41  4 

18  56 

62377 

24 

37623 

66603 

29 

33397 

04225 

5 

95775 

8 

53 

40  56 

19  4 

62405 

24 

37595 

66636 

30 

33364 

04231 

5 

95769 

7 

54 

40  48 

19  12 

62432 

25 

37568 

66669 

30 

33331 

04237 

5 

95763 

6 
5 

55 

8  40  40 

3  19  20 

9. 62459 

25 

10. 37541 

9. 66702 

31 

10.  33298 

10. 04243 

5 

9. 95757 

56 

40  32 

19  28 

62486 

26 

37514 

66735 

31 

33265 

04249 

5 

95751 

4 

67 

40  24 

19  36 

62513 

26 

37487 

66768 

32 

33232 

04255 

5 

95745 

3 

68 

40  16 

19  44 

62541 

27 

37459 

66801 

32 

33199 

04261 

6 

95739 

2 

59 

40  8 

19  52 

62568 

27 

37432 

66834 

33 

33166 

04267 

6 

95733 

1 

60 

40  0 

20  0 

62595 

28 

37405 

66867 

33 

33133 

04272 

6 

95728 

0 

M. 

M. 

Hour  p.  H. 

Hour  A.  M 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

114° 

A 

A 

B           B 

C 

C     65°  1 

Seconds  of  time 

1» 

2" 

8* 

*• 

6* 

6< 

7" 

Prop,  parts  of  col8.'(B 

Ic 

3 
4 
1 

7 
8 
1 

10 
13 
2 

14 
17 

3 

17 
21 

4 

21 
26 
4 

24 

29 

6 

TABLE  44. 

[Page  797 

Log.  Sines,  Tangents,  and  Secanta. 

26° 

A            A 

B           B        C 

C    16*0 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difif. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Dilf. 

Cosine. 

M. 

60 

0 

8  40  0 

3  20  0 

9. 62595 

0 

10.  37405 

9. 66867 

0 

10.  33133 

10.  04372 

0 

9. 95728 

1 

39  52 

20  8 

62622 

0 

37378 

66900 

1 

3310© 

04278 

0 

95722 

59 

2 

39  44 

20  16 

62649 

1 

37351 

66933 

1 

33067 

04284 

0 

95716 

58 

3 

39  36 

20  24 

62676 

1 

37324 

66966 

2 

33034 

04290 

0 

95710 

57 

4 

39  28 

20  32 

62703 

2 

37297 

66999 

2 

33001 

04296 

0 

95704 

56 
55 

5 

8  39  20 

3  20  40 

9. 62730 

2 

10. 37270 

9. 67032 

3 

10. 32968 

10.04302 

9. 95698 

6 

39  12 

20  48 

62757 

3 

37243 

67065 

3 

32935 

04308 

95692 

54 

7 

39  4 

20  56 

62784 

3 

37216 

67098 

4 

32902 

04314 

95686 

53 

8 

38  56 

21  4 

62811 

4 

37189 

67131 

4 

32869 

04320 

95680 

52 

9 
10 

38  48 

21  12 

62838 

4 

37162 

67163 

5 

32837 

04326 

95674 

51 

8  38  40 

3  21  20 

9. 62865 

4 

10.  37135 

9. 67196 

5 

10. 32804 

10. 04332 

9. 95668 

50 

11 

38  32 

21  28 

62892 

5 

37108 

67229 

6 

32771 

04337 

95663 

49 

12 

38  24 

21  36 

62918 

5 

37082 

67262 

7 

32738 

04343 

95657 

48 

13 

38  16 

21  44 

62945 

6 

37055 

67295 

7 

32705 

04349 

95651 

47 

14 

38  8 

21  52 

62972 

6 

37028 

67327 

8 

32673 

04355 

95645 

46 

15 

8  38  0 

3  22  0 

9. 62999 

7 

10.  37001 

9. 67360 

8 

10. 32640 

10.04361 

2 

9. 95639 

45 

16 

37  52 

22  8 

63026 

7 

36974 

67393 

9 

32607 

04367 

2 

95633 

44 

17 

37  44 

22  16 

63052 

8 

36948 

67426 

9 

32574 

04373 

2 

95627 

43 

18 

37  36 

22  24 

63079 

8 

36921 

67458 

10 

32542 

04379 

2 

95621 

42 

19 
20 

37  28 

22  32 

63106 

8 

36894 

67491 

10 

32509 

04385 

2 

95615 

41 
40 

8  37  20 

3  22  40 

9.63133 

9 

10. 36867 

9. 67524 

11 

10. 32476 

10. 04391 

2 

9.95609 

21 

37  12 

22  48 

63159 

9 

36841 

67556 

11 

32444 

04397 

2 

95603 

39 

22 

37  4 

22  56 

63186 

10 

36814 

67589 

12 

32411 

04403 

2 

95597 

38 

23 

36  56 

23  4 

63213 

10 

36787 

67622 

12 

32378 

04409 

2 

95591 

37 

24 
25 

36  48 

23  12 

63239 

11 

36761 

67654 

13 

32346 

04415 

2 
3 

95585 

36 
35 

8  36  40 

3  23  20 

9. 63266 

11 

10. 36734 

9. 67687 

14 

10. 32313 

10. 04421 

9.95579 

26 

36  32 

23  28 

63292 

11 

36708 

67719 

14 

32281 

04427 

3 

95573 

34 

27 

36  24 

23  36 

63319 

12 

36681 

67752 

15 

32248 

04433 

3 

95567 

33 

28 

36  16 

23  44 

63345 

12 

36655 

67785 

15 

32215 

04439 

3 

95561 

32 

29 

36  8 

23  52 

63372 

13 

36628 

67817 

16 

32183 

04445 

3 

95555 

31 

m 

30 

8  36  0 

3  24  0 

9. 63398 

13 

10.  36602 

9.67850 

16 

10. 32150 

10. 04451 

3 

9. 95549 

31 

35  52 

24  8 

63425 

14 

36575 

67882 

17 

32118 

04457 

3 

95543 

29 

32 

35  44 

24  16 

63451 

14 

36549 

67915 

17 

32085 

04463 

3 

95537 

28 

33 

35  36 

24  24 

63478 

15 

36522 

67947 

18 

32053 

04469 

3 

95531 

27 

34 

35  28 

24  32 

63504 

15 

36496 

67980 

18 

32020 

04475 

3 

95525 

26 
25 

35 

8  35  20 

3  24  40 

9. 63531 

15 

10. 36469 

9. 68012 

19 

10. 31988 

10. 04481 

4 

9. 95519 

36 

35  12 

24  48 

63557 

16 

36443 

68044 

20 

31956 

04487 

4 

95513 

24 

37 

35  4 

24  56 

63583 

16 

36417 

68077 

20 

31923 

04493 

4 

95507 

23 

38 

34  56 

25  4 

63610 

17 

36390 

68109 

21 

31891 

04500 

4 

95500 

22 

39 
40 

34  48 

25  12 

63636 

17 

36364 

68142 

21 

31858 

04506 

4 

95494 

21 

8  34  40 

3  25  20 

9. 63662 

18 

10. 36338 

9. 68174 

22 

10. 31826 

10. 04512 

4 

9. 95488 

20 

41 

34  32 

25  28 

63689 

18 

36311 

68206 

22 

31794 

04518 

4 

95482 

19 

42 

34  24 

25  36 

63715 

19 

36285 

68239 

23 

31761 

04524 

4 

95476 

18 

43 

34  16 

25  44 

63741 

19 

36259 

68271 

23 

31729 

04530 

4 

95470 

17 

44 

34  8 

25  52 

63767 

19 

36233 

68303 

24 

31697 

04536 

4 

95464 

16 

45 

8  34  0 

3  26  0 

9. 63794 

20 

10. 36206 

9. 68336 

24 

10. 31664 

10. 04542 

5 

9. 95458 

15 

46 

33  52 

26  8 

63820 

20 

36180 

68368 

25 

31632 

04548 

5 

95452 

14 

47 

33  44 

26  16 

63846 

21 

36154 

68400 

25 

31600 

04554 

5 

95446 

13 

48 

33  36 

26  24 

63872 

21 

36128 

68432 

26 

31568 

04560 

5 

95440 

12 

49 

33  28 

26  32 

63898 

22 

36102 

68465 

27 

31535 

04566 

5 

95434 

11 
10 

50 

8  33  20 

3  26  40 

9. 63924 

22 

10. 36076 

9. 68497 

27 

10. 31503 

10. 04573 

5 

9. 95427 

51 

33  12 

26  48 

63950 

23 

36050 

68529 

28 

31471 

04579 

5 

95421 

9 

52 

33  4 

26  56 

63976 

23 

36024 

68561 

28 

31439 

04585 

5 

95415 

8 

53 

32  56 

27  4 

64002 

23 

35998 

68593 

29 

31407 

04591 

5 

95409 

7 

54 
55 

32  48 

27  12 

64028 

24 

35972 

68626 

29 

31374 

04597 

5 

95403 

6 

5 

8  32  40 

3  27  20 

9. 64054 

24 

10.  35946 

9. 68658 

30 

10. 31342 

10. 04603 

6 

9. 95397 

56 

32  32 

27  28 

64080 

25 

35920 

68690 

30 

31310 

04609 

6 

95391 

4 

57 

32  24 

27  36 

64106 

25 

35894 

68722 

31 

31278 

04616 

6 

95384 

3 

58 

32  16 

27  44 

64132 

26 

35868 

68754 

31 

31246 

04622 

6 

95378 

2 

59 

32  8 

27  52 

64158 

26 

35842 

68786 

32 

31214 

04628 

6 

95372 

1 

60 

32  0 

28  0 

64184 

26 

35816 

68818 

33 

31182 

04634 

6 

95366 

0 

M. 

Hour  p.  u. 

Hour  A.  K. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diflf. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

116° 

A             A 

B           B        C 

C     64°  j 

Seconds  of  time . 


Prop,  parts 


of  cols.  •< 


1» 


10 
12 
2 


Page  798] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

26° 

A            A 

B           B       C 

C    1680 

M. 

Hoar  A.  H. 

riour  p.  M. 

Sine. 

Dift. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

8  32  0 

3  28  0 

9.64184 

0 

10.  35816 

9. 68818 

0 

10.  31182 

10. 04634 

0 

9.  96366 

60 

1 

31  52 

28  8 

64210 

0 

35790 

68860 

1 

31150 

04640 

0 

96360 

59 

2 

31  44 

28  16 

64236 

1 

35764 

68882 

1 

31118 

04646 

0 

96354 

58 

3 

31  36 

28  24 

64262 

1 

35738 

68914 

2 

31086 

04652 

0 

96348 

57 

4 

31  28 

28  32 

64288 

2 

35712 

68946 

2 

31064 

04659 

0 

96341 

56 
55 

5 

8  31  20 

3  28  40 

9.  64313 

2 

10.  35687 

9. 68978 

3 

10.  31022 

10. 04665 

9. 96335 

6 

31  12 

28  48 

64339 

3 

35661 

69010 

3 

30990 

04671 

95329 

64 

7 

31  4 

28  56 

64365 

3 

35635 

69042 

4 

30968 

04677 

95323 

63 

8 

30  56 

29  4 

64391 

3 

35609 

69074 

4 

30926 

04683 

95317 

52 

9 

30  48 

29  12 

64417 

4 

35583 

69106 

5 

30894 

04690 

95310 

51 
60 

10 

8  30  40 

3  29  20 

9. 64442 

4 

10.  35558 

9. 69138 

5 

10.  30862 

10. 04696 

9. 95304 

11 

30  32 

29  28 

64468 

5 

35532 

69170 

6 

30830 

04702 

96298 

49 

12 

30  24 

29  36 

64494 

5 

35506 

69202 

6 

30798 

04708 

96292 

48 

13 

30  16 

29  44 

64519 

5 

35481 

69234 

7 

30766 

04714 

96286 

47 

14 

30  8 

29  52 

64545 

6 

35455 

69266 

7 

30734 

04721 

95279 

46 

45 

15 

8  30  0 

3  30  0 

9. 64571 

6 

10. 35429 

9. 69298 

8 

10. 30702 

10.  04727 

2 

9. 96273 

16 

29  52 

30  8 

64596 

7 

35404 

69329 

8 

30671 

04733 

2 

95267 

44 

17 

29  44 

30  16 

64622 

7 

35378 

69361 

9 

30639 

04739 

2 

95261 

43 

18 

29  36 

30  24 

64647 

8 

35353 

69393 

9 

30607 

04746 

2 

95264 

42 

19 

29  28 

30  32 

64673 

8 

35327 

69425 

10 

30575 

04752 

2 

95248 

41 

20 

8  29  20 

3  30  40 

9. 64698 

8 

10. 35302 

9. 69457 

11 

10. 30543 

10. 04758 

2 

9. 96242 

40 

21 

29  12 

30  48 

64724 

9 

35276 

69488 

11 

30512 

04764 

2 

96236 

39 

22 

29  4 

30  56 

64749 

9 

35251 

69520 

12 

30480 

04771 

2 

95229 

38 

23 

28  56 

31  4 

64775 

10 

35225 

69562 

12 

30448 

04777 

2 

95223 

37 

24 

28  48 

31  12 

64800 

10 

35200 

69584 

13 

30416 

04783 

3 

96217 

36 
35 

25 

8  28  40 

3  31  20 

9. 64826 

11 

10.  35174 

9. 69616 

13 

10.  30386 

10. 04789 

3 

9.95211 

26 

28  32 

31  28 

64851 

11 

35149 

69647 

14 

30353 

04796 

3 

95204 

34 

27 

28  24 

31  36 

64877 

11 

35123 

69679 

14 

30321 

04802 

3 

96198 

33 

28 

28  16 

31  44 

64902 

12 

35098 

69710 

16 

30290 

04808 

3 

95192 

32 

29 

28  8 

31  52 

64927 

12 

35073 

69742 

16 

30268 

04815 

3 

96186 

31 
30 

30 

8  28  0 

3  32  0 

9. 64953 

13 

10. 35047 

9.  69774 

16 

10.  30226 

10. 04821 

3 

9. 95179 

31 

27  52 

32  8 

64978 

13 

35022 

69805 

16 

30195 

04827 

3 

95173 

29 

32 

27  44 

32  16 

65003 

14 

34997 

69837 

17 

30163 

04833 

3 

95167 

28 

33 

27  36 

32  24 

65029 

14 

34971 

69868 

17 

30132 

04840 

3 

95160 

27 

34 
35 

27  28 

32  32 

65054 

14 

34946 

69900 

18 

30100 

04846 

4 

96154 

26 
25 

8  27  20 

3  32  40 

9. 65079 

15 

10. 34921 

9. 69932 

18 

10. 30068 

10.  04862 

4 

9. 96148 

36 

27  12 

32  48 

65104 

15 

34896 

69963 

19 

30037 

04859 

4 

95141 

24 

37 

27  4 

32  56 

65130 

16 

34870 

69996 

20 

30006 

04866 

4 

95136 

23 

38 

26  56 

33  4 

65155 

16 

34845 

70026 

20 

29974 

04871 

4 

96129 

22 

39 

26  48 

33  12 

65180 

16 

34820 

70068 

21 

29942 

04878 

4 

95122 

21 

40 

8  26  40 

3  33  20 

9. 65205 

17 

10. 34795 

9.  70089 

21 

10.29911 

10. 04884 

4 

9.  96116 

20 

41 

26  32 

33  28 

65230 

17 

34770 

70121 

22 

29879 

04890 

4 

95110 

19 

42 

26  24 

33  36 

65255 

18 

34745 

70162 

22 

29848 

04897 

4 

95103 

18 

43 

26  16 

33  44 

65281 

18 

34719 

70184 

23 

29816 

04903 

5 

95097 

17 

44 

26  8 

33  52 

65306 

19 

34694 

70215 

23 

29785 

04910 

5 

95090 

16 

45 

8  26  0 

3  34  0 

9. 65331 

19 

10.  34669 

9. 70247 

24 

10.  29763 

10. 04916 

5 

9. 95084 

15 

46 

25  52 

34  8 

65356 

19 

34644 

70278 

24 

29722 

04922 

5 

95078 

14 

47 

25  44 

34  16 

65381 

20 

34619 

70309 

26 

29691 

04929 

5 

96071 

13 

48 

25  36 

34  24 

65406 

20 

34594 

70341 

25 

29669 

04936 

6 

96066 

12 

49 

25  28 

34  32 

65431 

21 

34569 

70372 

26 

29628 

04941 

5 

96069 

11 
10 

60 

8  25  20 

3  34  40 

9. 65456 

21 

10. 34544 

9.70404 

26 

10.  29596 

10. 04948 

5 

9. 95052 

51 

25  12 

34  48 

65481 

22 

34519 

70435 

27 

29566 

04954 

5 

95046 

9 

52 

25  4 

34  56 

65506 

22 

34494 

70466 

27 

29634 

04961 

6 

96039 

8 

53 

24  56 

35  4 

65531 

22 

34469 

70498 

28 

29602 

04967 

6 

96033 

7 

54 

24  48 

35  12 

65556 

23 

34444 

70529 

28 

29471 

04973 

6 

96027 

6 

55 

8  24  40 

3  35  20 

9. 65580 

23 

10.  34420 

9. 70560 

29 

10. 29440 

10. 04980 

6 

9. 95020 

5 

•56 

24  32 

35  21 

65605 

24 

34395 

70592 

30 

29408 

04986 

6 

95014 

4 

57 

24  24 

35  36 

65630 

24 

34370 

70623 

30 

29377 

04993 

6 

95007 

3 

58 

24  16 

35  44 

65655 

25 

34345 

70654 

31 

29346 

04999 

6 

95001 

2 

59 

24  8 

35  52 

65680 

25 

34320 

70685 

31 

29315 

05006 

6 

94995 

1 

60 

24  0 

36  0 

65705 

25 

34295 

70717 

32 

29283 

05012 

6 

94988 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Di£f. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

116° 

A            A 

B           B        C 

C    63°  1 

Seconds  of  time 

1« 

2" 

8» 

4« 

6»  I  C» 

7> 

Prop,  parts  of  cols.  <  B 

3 
4 

1 

6 
8 
2 

10 
12 
2 

13 
16 
3 

16 

20 

4 

19 

24 

5 

22 
28 
6 

TABLE  44. 

[Page  799 

Log.  Sines,  Tangents,  and  Secants. 

27° 

A 

A 

B            B 

C 

C    162° 

M. 

Hour  A.  M. 

Hour  p.  M, 

Sine. 

DIff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 
60 

n 

8  24  0 

3  36  0 

9. 65705 

0 

10.  34295 

9.  70717 

0 

10. 29283 

10. 05012 

0 

9. 94988 

1 

23  52 

36  8 

65729 

0 

34271 

70748 

1 

29252 

05018 

0 

94982 

59 

9 

23  44 

36  16 

65754 

1 

34246 

70779 

1 

29221 

05025 

0 

94975 

58 

3 

23  36 

36  24 

65779 

1 

34221 

70810 

2 

29190 

05031 

0 

94969 

57 

4 
5 

23  28 

36  32 

65804 

2 

34196 

70841 

2 

29159 

05038 

0 

94962 

56 

8  23  20 

3  36  40 

9. 65828 

2 

10.  34172 

9. 70873 

3 

10.  29127 

10.05044 

9. 94956 

55 

6 

23  12 

36  48 

65853 

2 

34147 

70904 

3 

29096 

05051 

1 

94949 

54 

7 

23  4 

36  56 

65878 

3 

34122 

70935 

4 

29065 

05057 

94943 

53 

S 

22  56 

37  4 

65902 

3 

34098 

70966 

4 

29034 

05064 

94936 

52 

9 

22  48 

37  12 

65927 

4 

34073 

70997 

5 

29003 

05070 

94930 

51 
50 

10 

8  22  40 

3  37  20 

9. 65952 

4 

10. 34048 

9. 71028 

5 

10. 28972 

10. 05077 

9. 94923 

11 

22  32 

37  28 

65976 

4 

34024 

71059 

6 

28941 

05083 

94917 

49 

1? 

22  24 

37  36 

66001 

5 

33999 

71090 

6 

28910 

05089 

94911 

48 

18 

22  16 

37  44 

66025 

5 

33975 

71121 

7 

28879 

05096 

94904 

47 

14 
15 

22  8 

37  52 

66050 

6 

33950 

71153 

7 

28847 

05102 

2 

94898 

46 

8  22  0 

3  38  0 

9. 66075 

6 

10.  33925 

9.  71184 

8 

10.  28816 

10. 05109 

2 

9. 94891 

45 

16 

21  52 

38  8 

66099 

6 

33901 

71215 

8 

28785 

05115 

2 

94885 

44 

17 

21  44 

38  16 

66124 

7 

33876 

71246 

9 

28754 

05122 

2 

94878 

43 

18 

21  36 

38  24 

66148 

7 

33852 

71277 

9 

28723 

05129 

2 

94871 

42 

19 

21  28 

38  32 

66173 

8 

33827 

71308 

10 

28692 

05135 

2 
2 

94865 

41 
40 

^0 

8  21  20 

3  38  40 

9. 66197 

8 

10.  33803 

9.  71339 

10 

10.28661 

10. 05142 

9. 94858 

?1 

21  12 

38  48 

66221 

8 

33779 

71370 

11 

-  286.30 

05148 

2 

94852 

39 

?? 

21  4 

38  56 

66246 

9 

83754 

71401 

11 

28599 

05155 

2 

94845 

38 

?8 

20  56 

39  4 

66270 

9 

33730 

71431 

12 

28569 

05161 

3 

94839 

37 

24 

20  48 

39  12 

66295 

10 

33705 

71462 

12 

28538 

05168 

3 

94832 

36 

?5 

8  20  40 

3  39  20 

9. 66319 

10 

10.  33681 

9. 71493 

13 

10.  28507 

10. 05174 

3 

9. 94826 

35 

^6 

20  32 

39  28 

66343 

11 

33657 

71524 

13 

28476 

05181 

3 

94819 

34 

?7 

20  24 

39  36 

66368 

11 

33632 

71555 

14. 

28445 

05187 

3 

94813 

33 

7.f>, 

20  16 

39  44 

66392 

11 

33608 

71586 

14 

28414 

05194 

3 

94806 

32 

29 

20  8 

39  52 

66416 

12 

33584 

71617 

15 

28383 

05201 

3 

94799 

31 

80 

8  20  0 

3  40  0 

9.66441 

12 

10. 33559 

9.  71648 

15 

10.  28352 

10. 05207 

3 

9. 94793 

30 

81 

19  52 

40  8 

66465 

13 

33635 

71679 

16 

28321 

05214 

3 

94786 

29 

8? 

19  44 

40  16 

66489 

13 

33511 

71709 

16 

28291 

05220 

4 

94780 

28 

88 

19  36 

40  24 

66513 

13 

33487 

71740 

17 

28260 

05227 

4 

94773 

27 

34 

19  28 

40  32 

66537 

14 

33463 

71771 

17 

28229 

05233 
10. 05240 

4 

94767 

26 
25 

85 

8  19  20 

3  40  40 

9. 66562 

14 

10. 33438 

9.  71802 

18 

10.  28198 

4 

9. 94760 

86 

19  12 

40  48 

66586 

15 

33414 

71833 

19 

28167 

05247 

4 

94753 

24 

87 

19  4 

40  56 

66610 

15 

33390 

71863 

19 

28137 

05253 

4 

94747 

23 

88 

18  56 

41  4 

66634 

15 

33366 

71894 

20 

28106 

05260 

4 

94740 

22 

39 

18  48 

41  12 

66658 

16 

33342 

71925 

20 

28075 

05266 

4 
4 

94734 

21 

40 

8  18  40 

3  41  20 

9. 66682 

16 

10.  33318 

9.  71955 

21 

10. 28045 

10. 05273 

9. 94727 

20 

41 

18  32 

41  28 

66706 

17 

33294 

71986 

21 

28014 

05280 

4 

94720 

19 

42 

18  24 

41  36 

66731 

17 

33269 

72017 

22 

27983 

05286 

5 

94714 

18 

48 

18  16 

41  44 

66755 

17 

33245 

72048 

22 

27952 

05293 

5 

94707 

17 

44 
45 

18  8 

41  52 

66779 

18 

33221 

72078 

23 

27922 

05300 

5 

94700 
9. 94694 

16 
15 

8  18  0 

3  42  0 

9. 66803 

18 

10.  33197 

9.  72109 

23 

10. 27891 

10. 05306 

5 

46 

17  52 

42  8 

66827 

19 

33173 

72140 

24 

27860 

05313 

5 

94687 

14 

47 

17  44 

42  16 

66851 

19 

33149 

72170 

24 

27830 

05320 

5 

94680 

13 

48 

17  36 

42  24 

66875 

19 

33125 

72201 

25 

27799 

05326 

5 

94674 

12 

49 
50 

17  28 
8  17  20 

42  32 

66899 

20 

33101 

72231 

25 

27769 

05333 

5 

94667 

11 

3  42  40 

9. 66922 

20 

10. 33078 

9. 72262 

26 

10. 27738 

10. 05340 

5 

9. 94660 

10 

51 

17  12 

42  48 

66946 

21 

33054 

72293 

26 

27707 

05346 

6 

94654 

9 

52 

17  4 

42  56 

66970 

21 

33030 

72323 

27 

27677 

05353 

6 

94647 

8 

53 

16  56 

43  4 

66994 

21 

33006 

72354 

27 

27646 

05360 

6 

94640 

7 

54 

16  48 

43  12 

67018 

22 

32982 

72384 

28 

27616 

05366 

6 

94634 

6 

55 

8  16  40 

3  43  20 

9. 67042 

22 

10.  32958 

9.  72415 

28 

10. 27585 

10. 05373 

6 

9. 94627 

5 

56 

16  32 

43  28 

67066 

23 

32934 

72445 

29 

27555 

05380 

6 

94620 

4 

57 

16  24 

43  36 

67090 

23 

32910 

72476 

29 

27524 

05386 

6 

94614 

3 

58 

16  16 

43  44 

67113 

23 

32887 

72506 

30 

27494 

05393 

6 

94607 

2 

59 

16  8 

43  52 

67137 

24 

32863 

72537 

30 

27463 

05400 

6 

94600 

1 

60 

16  0 

44  0 

67161 

24 

32839 

72567 

31 

27433 

05407 

7 

94593 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Dlff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

117° 

A 

A 

B           B 

C 

C     62°  j 

Seconds  of  time 

1« 

«• 

8« 

4> 

&> 

6« 

7« 

fA 
Prop,  parts  of  cols.  {B 

Ic 

3 

4 
1 

6 

8 
2 

9 
12 
2 

12 

16 

3 

15 
19 
4 

18 

23 

6 

21 

27 

6 

Page  800] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

88° 

A 

A 

B 

B 

C 

C    161° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

8  16  0 

3  44  0 

9.  67161 

0 

10.  32839 

9. 72567 

0 

10. 27433 

10.  05407 

0 

9. 94593 

60 

1 

15  52 

44  8 

67185 

0 

32815 

72598 

1 

27402 

05413 

0 

94587 

59 

2 

15  44 

44  16 

67208 

1 

32792 

72628 

1 

27372 

05420 

0 

94580 

58 

3 

15  36 

44  24 

67232 

1 

32768 

72659 

2 

27341 

05427 

0 

94573 

57 

4 

15  28 

44  32 

67256 

2 

32744 

72689 

2 

27311 

05433 

0 

94567 

56 
55 

5 

8  15  20 

3  44  40 

9. 67280 

2 

10. 32720 

9. 72720 

3 

10. 27280 

10. 05440 

9. 94560 

6 

15  12 

44  48 

67303 

2 

32697 

72750 

3 

27250 

05447 

94553 

54 

7 

15  4 

44  56 

67327 

3 

32673 

72780 

4 

27220 

05454 

94546 

53 

8 

14  56 

45  4 

67350 

3 

32650 

72811 

4 

27189 

05460 

94540 

52 

9 
10 

14  48 

45  12 

67374 

3 

32626 

72841 

5 

27159 

05467 

94533 

51 

8  14  40 

3  45  20 

9. 67398 

4 

10.  32602 

9. 72872 

5 

10. 27128 

10. 05474 

9. 94526 

50 

11 

14  32 

45  28 

67421 

4 

32579 

72902 

6 

27098 

05481 

94519 

49 

12 

14  24 

45  36 

67445 

5 

32555 

72932 

6 

27068 

05487 

94513 

48 

13 

14  16 

45  44 

67468 

5 

32532 

72963 

7 

27037 

05494 

94506 

47 

14 

14  8 

45  52 

67492 
9. 67515 

5 

32508 

72993 

7 

27007 

05501 

2 

94499 

46 
45 

15 

8  14  0 

3  46  0 

6 

10. 32485 

9. 73023 

8 

10. 26977 

10. 05508 

2 

9. 94492 

16 

13  52 

46  8 

67539 

6 

32461 

73054 

8 

26946 

05515 

2 

94485 

44 

17 

13  44 

46  16 

67562 

7 

32438 

73084 

9 

26916 

05521 

2 

94479 

43 

18 

13  36 

46  24 

67586 

7 

32414 

73114 

9 

26886 

05528 

2 

94472 

42 

19 

13  28 

46  32 

67609 

7 

32391 

73144 

10 

26856 

05535 

2 

94465 

41 
40 

20 

8  13  20 

3  46  40 

9. 67633 

8 

10. 32367 

9. 73175 

10 

10. 26825 

10. 05542 

2 

9. 94458 

21 

13  12 

46  48 

67656 

8 

32344 

73205 

11 

26795 

05549 

2 

94451 

39 

22 

13  4 

46  56 

67680 

9 

32320 

73235 

11 

26765 

05555 

3 

94445 

38 

23 

12  56 

47  4 

67703 

9 

32297 

73265 

12 

26735 

05562 

3 

94438 

37 

24 

12  48 

47  12 

67726 

9 

32274 

73295 

12 

26705 

05569 

3 
3 

94431 
9. 94424 

36 
35 

25 

8  12  40 

3  47  20 

9. 67750 

10 

10. 32250 

9.  73326 

13 

10.  26674 

10. 05576 

26 

12  32 

47  28 

67773 

10 

32227 

73356 

13 

26644 

05583 

3 

94417 

34 

27 

12  24 

47  36 

67796 

10 

32204 

73386 

14 

26614 

05590 

3 

94410 

33 

28 

12  16 

47  44 

67820 

11 

32180 

73416 

14 

26584 

05596 

3 

94404 

32 

29 

12  8 

47  52 

67843 

11 

32157 

73446 

15 

26554 

05603 

3 

94397 

31 

30 

8  12  0 

3  48  0 

9.  67866 

12 

10.  32134 

9. 73476 

15 

10. 26524 

10. 05610 

3 

9. 94390 

30 

31 

11  52 

48  8 

67890 

12 

32110 

73507 

16 

26493 

05617 

4 

94383 

29 

32 

11  44 

48  16 

67913 

12 

32087 

73537 

16 

26463 

05624 

4 

94376 

28 

33 

11  36 

48  24 

67936 

13 

32064 

73567 

17 

26433 

05631 

4 

94369 

27 

34 

11  28 

48  32 

67959 

13 
14 

32041 

73597 

17 

26403 

05638 
10. 05645 

4 
4 

94362 
9. 94355 

26 
25 

35 

8  11  20 

3  48  40 

9. 67982 

10.  32018 

9. 73627 

18 

10. 26373 

36 

11  12 

48  48 

68006 

14 

31994 

73657 

18 

26343 

05651 

4 

94349 

24 

37 

11  4 

48  56 

68029 

14 

31971 

73687 

19 

26313 

05658 

4 

94342 

23 

38 

10  56 

49  4 

68052 

15 

31948 

73717 

19 

26283 

05665 

4 

94335 

22 

39 
40 

10  48 
8  10  40 

49  12 

68075 
9. 68098 

15 

31925 

73747 

20 

26253 

05672 

4 

94328 

21 
20 

3  49  20 

16 

10.  31902 

9. 73777 

20 

10. 26223 

10. 05679 

5 

9. 94321 

41 

10  32 

49  28 

68121 

16 

31879 

73807 

21 

26193 

05686 

5 

94314 

19 

42 

10  24 

49  36 

68144 

16 

31856 

73837 

21 

26163 

05693 

5 

94307 

18 

43 

10  16 

49  44 

68167 

17 

31833 

73867 

22 

26133 

05700 

5 

94300 

17 

44 
45 

10  8 

49  52 

68190 

17 

31810 

73897 

22 

26103 
10.  26073 

05707 

5 

5 

94293 

16 
15 

8  10  0 

3  50  0 

9. 68213 

17 

10.  31787 

9. 73927 

23 

10. 05714 

9. 94286 

46 

9  52 

50  8 

68237 

18 

31763 

73957 

23 

26043 

05721 

5 

94279 

14 

47 

9  44 

50  16 

68260 

18 

31740 

73987 

24 

26013 

05727 

5 

94273 

13 

48 

9  36 

50  24 

68283 

19 

31717 

74017 

24 

25983 

05734 

5 

94266 

12 

49 
50 

9  28 

50  32 

68305 

19 

31695 

74047 

25 

25953 

05741 

6 
6 

94259 
9. 94252 

11 
10 

8  9  20 

3  50  40 

9. 68328 

19 

10.31672 

9. 74077 

25 

10. 25923 

10.  05748 

51 

9  12 

50  48 

68351 

20 

31649 

74107 

26 

25893 

05755 

6 

94245 

9 

52 

9  4 

50  56 

68374 

20 

31626 

74137 

26 

25863 

05762 

6 

94238 

8 

53 

8  56 

51  4 

68397 

21 

31603 

74166 

27 

25834 

05769 

6 

94231 

7 

54 

8  48 

51  12 

68420 

21 

31580 

74196 

27 

25804 

05776 

6 

94224 

6 

55 

8  8  40 

3  51  20 

9. 68443 

21 

10. 31557 

9. 74226 

28 

10.  25774 

10. 05783 

6 

9. 94217 

5 

56 

8  32 

51  28 

68466 

22 

31534 

74256 

28 

25744 

05790 

6 

94210 

4 

57 

8  24 

51  36 

68489 

22 

31511 

74286 

29 

25714 

05797 

7 

94203 

3 

58 

8  16 

51  44 

68512 

22 

31486 

74316 

29 

25684 

05804 

7 

94196 

2 

59 

8  8 

51  52 

68534 

23 

31466 

74345 

30 

25655 

05811 

7 

94189 

1 

60 

8  0 

52  0 

68557 

23 

31443 

74375 

30 

25625 

05818 

7 

94182 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M 

118° 

A 

A 

B 

B 

C 

C     61°  1 

Seconds  of  time 

1« 

2" 

8- 

4* 

6* 

6* 

7« 

Prop,  parts  of  cols.  <  B 

3 
4 
1 

6 
8 
2 

9 
11 
3 

3 

15 
19 
4 

17 

23 

6 

20 
26 
6 

TABLE  44. 

[Page  801 

Log.  Sines,  Tangents,  and  Secants. 

w> 

A           A 

B           B       G 

C    160° 

M. 

Hoar  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diff. 

Cotangent 

Secant. 

Diff. 

Cosine. 

M. 

0 

8  8  0 

3  52  0 

9.68557 

0 

10.  31443 

9.  74375 

0 

10. 25625 

10. 05818 

0 

9.  94182 

60 

1 

7  52 

52  8 

68580 

0 

31420 

74405 

0 

25595 

05825 

0 

94175 

59 

2 

7  44 

52  16 

68603 

1 

31397 

74435 

1 

25565 

05832 

0 

94168 

58 

3 

7  36 

52  24 

68625 

1 

31375 

74465 

1 

25535 

05839 

0 

94161 

57 

4 

7  28 

52  32 

68648 

1 

31352 

74494 

2 

25506 

05846 

0 

94154 

56 
55 

5 

8  7  20 

3  52  40 

9. 68671 

2 

10.  31329 

9. 74524 

2 

10. 25476 

10. 05853 

9. 94147 

6 

7  12 

52  48 

68694 

2 

31306 

74554 

3 

25446 

05860 

94140 

54 

T 

7  4 

52  56 

68716 

3 

31284 

74583 

3 

25417 

05867 

94133 

53 

8 

6  56 

53  4 

68739 

3 

31261 

74613 

4 

25387 

05874 

94126 

52 

9 

6  48 

53  12 

68762 

3 

31238 

74643 

4 

25357 

05881 

94119 

51 
50 

10 

8  6  40 

3  53  20 

9. 68784 

4 

10. 31216 

9.  74673 

5 

10. 25327 

10. 05888 

9.94112 

11 

6  32 

53  28 

68807 

4 

31193 

74702 

5 

25298 

05895 

94105 

49 

12 

6  24 

53  36 

68829 

4 

31171 

74732 

6 

25268 

05902 

94098 

48 

13 

6  16 

53  44 

68852 

5 

31148 

74762 

6 

25238 

05910 

2 

94090 

47 

14 

15 

6  8 

53  52 

68875 

5 

31125 

74791 

7 

25209 

05917 

2 

94083 

46 

8  6  0 

3  54  0 

9.  68897 

6 

10.31103 

9.  74821 

7 

10. 25179 

10. 05924 

2 

9. 94076 

45 

16 

5  52 

54  8 

68920 

6 

31080 

74^51 

8 

25149 

05931 

2 

94069 

44 

17 

5  44 

54  16 

68942 

6 

31058 

74880 

8 

25120 

05938 

2 

94062 

43 

18 

5  36 

54  24 

68965 

7 

31035 

74910 

9 

25090 

05945 

2 

94055 

42 

19 
20 

5  28 

54  32 

68987 

7 

31013 

74939 

9 

25061 

05952 

2 

94048 

41 

8  5  20 

3  54  40 

9. 69010 

7 

10.30990 

9. 74969 

10 

10.  25031 

10. 05959 

2 

9. 94041 

40 

21 

5  12 

54  48 

69032 

8 

30968 

74998 

10 

25002 

05966 

3 

94034 

39 

22 

5  4 

54  56 

69055 

8 

30945 

75028 

11 

24972 

05973 

3 

94027 

38 

23 

4  56 

55  4 

69077 

9 

30923 

75058 

11 

24942 

05980 

3 

94020 

37 

24 
25 

4  48 

55  12 

69100 

9 

30900 

75087 

12 

24913 
10.  24883 

05988 

3 

94012 

36 
36 

8  4  40 

3  55  20 

9. 69122 

9 

10. 30878 

9.  75117 

12 

10. 05995 

3 

9.94005 

26 

4  32 

55  28 

69144 

10 

30856 

75146 

13 

24854 

06002 

3 

93998 

34 

27 

4  24 

55  36 

69167 

10 

30833 

75176 

13 

24824 

06009 

3 

93991 

33 

28 

4  16 

55  44 

69189 

10 

30811 

75205 

14 

24795 

06016 

3 

93984 

32 

29 

4  8 

55  52 

69212 

11 

30788 

75235 

14 

24765 

06023 

3 

93977 

31 

30 

8  4  0 

3  56  0 

9. 69234 

11 

10.  30766 

9. 75264 

15 

10.  24736 

10. 06030 

4 

9. 93970 

30 

31 

3  52 

56  8 

69256 

12 

30744 

75294 

15 

24706 

06037 

4 

93963 

29 

32 

3  44 

56  16 

69279 

12 

30721 

75323 

16 

24677 

06045 

4 

93955 

28 

33 

3  36 

56  24 

69301 

12 

30699 

75353 

16 

24647 

06052 

4 

93948 

27 

34 

3  28 

56  32 

69323 

13 

30677 

75382 

17 

24618 

06059 

4 

93941 

26 

35 

8  3  20 

3  56  40 

9. 69345 

13 

10. 30655 

9.75411 

17 

10. 24589 

10.06066 

4 

9. 93934 

25 

36 

3  12 

56  48 

69368 

13 

30632 

75441 

18 

24559 

06073 

4 

93927 

24 

37 

3  4 

56  56 

69390 

14 

30610 

75470 

18 

24530 

06080 

4 

93920 

23 

38 

2  56 

57  4 

69412 

14 

30588 

75500 

19 

24500 

06088 

5 

93912 

22 

39 

2  48 

57  12 

69434 

15 

30566 

75529 

19 

24471 

06095 

5 

93905 

21 

20 

40 

8  2  40 

3  57  20 

9. 69456 

15 

10. 30544 

9. 75558 

20 

10.24442 

10. 06102 

5 

9. 93898 

41 

2  32 

57  28 

69479 

15 

30521 

75588 

20 

24412 

06109 

5 

93891 

19 

42 

2  24 

57  36 

69501 

16 

30499 

75617 

21 

24383 

06116 

5 

93884 

18 

43 

2  16 

57  44 

69523 

16 

30477 

75647 

21 

24353 

06124 

5 

93876 

17 

44 
45 

2  8 

57  52 

69545 

16 
17 

30455 

75676 

22 

24324 

06131 

5 

93869 

16 

8  2  0 

3  58  0 

9. 69567 

10.  30433 

9.  75705 

22 

10. 24295 

10. 06138 

5 

9. 93862 

15 

46 

1  52 

58  8 

69589 

17 

30411 

75735 

23 

24265 

06145 

5 

93855 

14 

47 

1  44 

58  16 

69611 

17 

30389 

75764 

23 

24236 

06153 

6 

93847 

13 

48 

1  36 

58  24 

69633 

18 

30367 

75793 

24 

24207 

06160 

6 

93840 

12 

49 
50 

1  28 

58  32 

69655 

18 

30345 

75822 

24 

24178 

06167 

6 

93833 

11 
10 

8  1  20 

3  58  40 

9. 69677 

19 

10. 30323 

9. 75852 

25 

10. 24148 

10. 06174 

6 

9. 93826 

51 

1  12 

58  48 

69699 

19 

30301 

75881 

25 

24119 

06181 

6 

93819 

9 

52 

1  4 

58  56 

69721 

19 

30279 

75910 

26 

24090 

06189 

6 

93811 

8 

53 

0  56 

59  4 

69743 

20 

30257 

75939 

26 

24061 

06196 

6 

93804 

7 

54 

0  48 

59  12 

69765 

20 

30235 

75969 

27 

24031 

06203 

6 

93797 

6 
5 

55 

8  0  40 

3  59  20 

9. 69787 

20 

10.  30213 

9. 75998 

27 

10. 24002 

10. 06211 

7 

9. 93789 

56 

0  32 

59  28 

69809 

21 

30191 

76027 

28 

23973 

06218 

7 

93782 

4 

57 

0  24 

59  36 

69831 

21 

30169 

76056 

28 

23944 

06225 

7 

93775 

3 

58 

0  16 

59  44 

69853 

22 

30147 

76086 

29 

23914 

06232 

7 

93768 

2 

59 

0  8 

59  52 

69875 

22 

30125 

76115 

29 

23885 

06240 

7 

93760 

1 

60 

0  0 

4  0  0 

69897 

22 

30103 

76144 

29 

23856 

06247 

7 

93753   0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine.    M. 

11»° 

A            A 

B           B        C 

C    60°  1 

Seconds  of  time 


Prop,  parts 


of  cols.^B 


6* 

17 
22 
5 


Page  802] 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

800 

▲           A 

B           B 

C 

C    149° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

8  0  0 

4  0  0 

9. 69897 

0 

10. 30103 

9. 76144 

0 

10.  23856 

10. 06247 

0 

9. 93753 

60 

1 

7  59  52 

0  8 

69919 

0 

30081 

76173 

0 

23827 

06254 

0 

93746 

59 

2 

59  44 

0  16 

69941 

1 

30059 

76202 

1 

23798 

06262 

0 

93738 

58 

3 

59  36 

0  24 

69963 

1 

30037 

76231 

1 

23769 

06269 

0 

93731 

57 

4 

59  28 

0  32 

69984 

1 

30016 

76261 

2 

23739 

06276 

0 

93724 

56 

fi 

7  59  20 

4  0  40 

9. 70006 

2 

10. 29994 

9. 76290 

2 

10. 23710 

10. 06283 

9.  93717 

55 

6 

59  12 

0  48 

70028 

2 

29972 

76319 

3 

23681 

06291 

93709 

54 

7 

59  4 

0  56 

70050 

3 

29950 

76348 

3 

23652 

06298 

93702 

53 

8 

58  56 

1  4 

70072 

3 

29928 

76377 

4 

23623 

06305 

93695 

52 

9 

58  48 

1  12 

70093 

3 

29907 

76406 

4 

23594 

06313 

93687 

51 

10 

7  58  40 

4  1  20 

9. 70115 

4 

10. 29885 

9. 76435 

5 

10. 23565 

10. 06320 

9. 93680 

50 

n 

58  32 

1  28 

70137 

4 

29863 

76464 

5 

23536 

06327 

93673 

49 

12 

58  24 

1  36 

70159 

4 

29841 

76493 

6 

23507 

06335 

93665 

48 

13 

58  16 

1  44 

70180 

5 

29820 

76522 

6 

23478 

06342 

2 

93658 

47 

14 

58  8 

1  52 

70202 

5 

29798 

76551 

7 

23449 

06350 

2 

93650 

46 
45 

15 

7  58  0 

4  2  0 

9.  70224 

5 

10. 29776 

9. 76580 

7 

10.  23420 

10. 06357 

2 

9. 93643 

16 

57  52 

2  8 

70245 

6 

29755 

76609 

8 

23391 

06364 

2 

93636 

44 

17 

57  44 

2  16 

70267 

6 

29733 

76639 

8 

23361 

06372 

2 

93628 

43 

18 

57  36 

2  24 

70288 

6 

29712 

76668 

9 

23332 

06379 

2 

93621 

42 

19 

57  28 

2  32 

70310 

7 

29690 

76697 

9 

23303 

06386 

2 
2 

93614 

41 
40 

20 

7  57  20 

4  2  40 

9. 70332 

7 

10. 29668 

9. 76725 

10 

10. 23275 

10.  06394 

9. 93606 

21 

57  12 

2  48 

70353 

8 

29647 

76754 

10 

23246 

06401 

3 

93599 

39 

22 

57  4 

2  56 

70375 

8 

29625 

76783 

11 

23217 

06409 

3 

93591 

38 

23 

56  56 

3  4 

70396 

8 

29604 

76812 

11 

23188 

06416 

3 

93584 

37 

24 

56  48 

3  12 

70418 

9 

29582 

76841 

12 

23159 

06423 

3 

93577 

36 

25 

7  56  40 

4  3  20 

9. 70439 

9 

10. 29561 

9.  76870 

12 

10. 23130 

10. 06431 

3 

9. 93569 

35 

26 

56  32 

3  28 

70461 

9 

29539 

76899 

13 

23101 

06438 

3 

93562 

34 

27 

56  24 

3  36 

70482 

10 

29518 

76928 

13 

23072 

06446 

3 

93554 

33 

28 

56  16 

3  44 

70504 

10 

29496 

76957 

13 

23043 

06453 

3 

93547 

32 

29 

56  8 

3  52 

70525 

10 

29475 

76986 

14 

23014 

06461 

4 
4 

93539 

31 

30 

7  56  0 

4  4  0 

9. 70547 

11 

10. 29453 

9.  77015 

14 

10. 22985 

10. 06468 

9. 93532 

30 

31 

55  52 

4  8 

70568 

11 

29432 

77044 

15 

22956 

06475 

4 

93525 

29 

32 

55  44 

4  16 

70590 

11 

29410 

77073 

15 

22927 

06483 

4 

93517 

28 

33 

55  36 

4  24 

70611 

12 

29389 

77101 

16 

22899 

06490 

4 

93510 

27 

34 

55  28 

4  32 

70633 

12 

29367 

77130 

16 

22870 

06498 

4 

93502 

26 

35 

7  55  20 

4  4  40 

9.  70654 

13 

10. 29346 

9. 77159 

17 

10. 22841 

10. 06505 

4 

9. 93495 

25 

36 

55  12 

4  48 

70675 

13 

29325 

77188 

17 

22812 

06513 

4 

93487 

24 

37 

55  4 

4  56 

70697 

13 

29303 

77217 

18 

22783 

06520 

5 

93480 

23 

38 

54  56 

5  4 

70718 

14 

29282 

77246 

18 

22754 

06528 

5 

93472 

22 

39 
40 

54  48 

5  12 

•  70739 

14 

29261 

77274 

19 

22726 

06535 

5 

93465 

21 

7  54  40 

4  5  20 

9.  70761 

14 

10. 29239 

9.  77303 

19 

10.  22697 

10.  06543 

5 

9. 93457 

20 

41 

54  32 

5  28 

70782 

15 

29218 

77332 

20 

22668 

06550 

5 

93450 

19 

42 

54  24 

5  36 

70803 

15 

29197 

77361 

20 

22639 

06558 

5 

93442 

18 

43 

54  16 

5  44 

70824 

15 

29176 

77390 

21 

22610 

06565 

5 

93435 

17 

44 

54  8 

5  52 

70846 

16 

29154 

77418 

21 
22 

22582 
10.  22553 

06573 

5 

93427 

16 
15 

45 

7  54  0 

4  6  0 

9. 70867 

16 

10. 29133 

9. 77447 

10.  06580 

6 

9. 93420 

46 

53  52 

6  8 

70888 

16 

29112 

77476 

22 

22524 

06588 

6 

93412 

14 

47 

53  44 

6  16 

70909 

17 

29091 

77505 

23 

22495 

06595 

6 

93405 

13 

48 

53  36 

6  24 

70931 

17 

29069 

77533 

23 

22467 

06603 

6 

93397 

12 

49 

53  28 

6  32 

70952 

18 

29048 

77562 

24 

22438 

06610 

6 

93390 

11 
10 

50 

7  53  20 

4  6  40 

9. 70973 

18 

10.  29027 

9. 77591 

24 

10.  22409 

10.  06618 

6 

9. 93382 

51 

53  12 

6  48 

70994 

18 

29006 

77619 

25 

22381 

06625 

6 

93375 

9 

52 

53  4 

6  56 

71015 

19 

28985 

77648 

25 

22352 

06633 

6 

93367 

8 

53 

52  56 

7  4 

71036 

19 

28964 

77677 

26 

22323 

06640 

7 

93360 

7 

54 

52  48 

7  12 

71058 

19 

28942 

77706 

26 

22294 

06648 

7 

93352 

6 
5 

55 

7  52  40 

4  7  20 

9.  71079 

20 

10. 28921 

9.  77734 

26 

10. 22266 

10. 06656 

7 

9. 93344 

56 

52  32 

7  28 

71100 

20 

28900 

77763 

27 

22237 

06663 

7 

93337 

4 

57 

52  24 

7  36 

71121 

20 

28879 

77791 

27 

22209 

06671 

7 

93329 

3 

58 

52  16 

7  44 

71142 

21 

28858 

77820 

28 

22180 

06678 

7 

93322 

2 

59 

52  8 

7  52 

71163 

21 

28837 

77849 

28 

22151 

06686 

7 

93314 

1 

60 

52  0 

8  0 

71184 

21 

28816 

77877 

29 

22123 

06693 

7 

93307 

0 

M. 

Hour  p.  M. 

Hour  A.  H. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

120^ 

> 

A           A 

B           B 

C 

C    69°l 

Seconds  of  time 

!■ 

2« 

8« 

4- 

&> 

6- 

?• 

A 
Prop,  parts  of  cols.  B 

Ic 

3 

4 
1 

5 
7 
2 

8 
U 
8 

11 
14 

4 

13 
18 
5 

16 
22 
6 

19 

25 

7 

TABLE  44. 

[Page  803 

Log.  Sines,  Tangents,  and  Secants. 

81° 

A 

A 

B 

B        C 

C   148° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difif. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

7  52  0 

4  8  0 

9.  71184 

0 

10.  28816 

9. 77877 

0 

10.  22123 

10. 06693 

0 

9. 93307 

60 

1 

51  52 

8  8 

71205 

0 

28795 

77906 

0 

22094 

06701 

0 

93299 

59 

'?, 

51  44 

8  16 

71226 

1 

28774 

77935 

1 

22065 

06709 

0 

93291 

58 

3 

51  36 

8  24 

71247 

1 

28753 

77963 

1 

22037 

06716 

0 

93284 

57 

4 
5 

51  28 

8  32 

71268 

1 
2 

28732 
10. 28711 

77992 

2 

22008 

06724 

93276 

56 
55 

7  51  20 

4  8  40 

9.  71289 

9. 78020 

2 

10. 21980 

10. 06731 

9. 93269 

6 

51  12 

8  48 

71310 

2 

28690 

78049 

3 

21951 

06739 

93261 

54 

7 

51  4 

8  56 

71331 

2 

28669 

78077 

3 

21923 

06747 

93253 

53 

« 

50  56 

9  4 

71352 

3 

28648 

78106 

4 

21894 

06754 

93246 

52 

9 

50  48 

9  12 

71373 

3 

28627 

78135 

4 

21865 

06762 

93238 

51 

10 

7  50  40 

4  9  20 

9. 71393 

3 

10. 28607 

9.  78163 

5 

10. 21837 

10. 06770 

9. 93230 

50 

11 

50  32 

9  28 

71414 

4 

28586 

78192 

5 

21808 

06777 

93223 

49 

12 

50  24 

9  36 

71435 

4 

28565 

78220 

6 

21780 

06785 

2 

93215 

48 

13 

50  16 

9  44 

71456 

4 

28544 

78249 

6 

21751 

06793 

2 

93207 

47 

14 

50  8 

9  52 

71477 

5 

28523 

78277 

7 

21723 

06800 

2 

93200 
9. 93192 

46 

45 

1ft 

7  50  0 

4  10  0 

9. 71498 

5 

10. 28502 

9. 78306 

7 

10.  21694 

10. 06808 

2 

16 

49  52 

10  8 

71519 

5 

28481 

78334 

8 

21666 

06816 

2 

93184 

44 

17 

49  44 

10  16 

71539 

6 

28461 

78363 

8 

21637 

06823 

2 

93177 

43 

18 

49  36 

10  24 

71560 

6 

28440 

78391 

9 

21609 

06831 

2 

93169 

42 

19 
20 

49  28 

10  32 

71581 

7 

28419 

78419 

9 

21581 

06839 

2 

93161 

41 
40 

7  49  20 

4  10  40 

9. 71602 

7 

10. 28398 

9.78448 

9 

10. 21552 

10. 06846 

3 

9. 93154 

21 

49  12 

10  48 

71622 

7 

28378 

78476 

10 

21524 

06854 

3 

93146 

39 

22 

49  4 

10  56 

71643 

8 

28357 

78505 

10 

21495 

06862 

3 

93138 

38 

23 

48  56 

11  4 

71664 

8 

28336 

78533 

11 

21467 

06869 

3 

93131 

37 

24 

48  48 

11  12 

71685 

8 

28315 

78562 

11 

21438 

06877 

3 

93123 

36 
3ft 

2ft 

7  48  40 

4  11  20 

9. 71705 

9 

10. 28295 

9. 78590 

12 

10.  21410 

10. 06885 

3 

9.93115 

26 

48  32 

11  28 

71726 

9 

28274 

78618 

12 

21382 

06892 

3 

93108 

34 

27 

48  24 

11  36 

71747 

9 

28253 

78647 

13 

21353 

06900 

3 

93100 

33 

28 

48  16 

11  44 

71767 

10 

28233 

78675 

13 

21325 

06908 

4 

93092 

32 

29 

48  8 

11  52 

71788 

10 

28212 

78704 

14 

21296 

06916 

4 

93084 

31 
30 

30 

7  48  0 

4  12  0 

9.  71809 

10 

10. 28191 

9.  78732 

14 

10. 21268 

10. 06923 

4 

9. 93077 

31 

47  52 

12  8 

71829 

11 

28171 

78760 

15 

21240 

06931 

4 

93069 

29 

32 

47  44 

12  16 

71850 

11 

28150 

78789 

15 

21211 

06939 

4 

93061 

28 

33 

47  36 

12  24 

71870 

11 

28130 

78817 

16 

21183 

06947 

4 

93053 

27 

34 

47  28 

12  32 

71891 

12 

28109 

78845 

16 

21155 

06954 

4 

93046 

26 

3ft 

7  47  20 

4  12  40 

9.  71911 

12 

10. 28089 

9. 78874 

17 

10.  21126 

10. 06962 

5 

9. 93038 

•25 

36 

47  12 

12  48 

71932 

12 

28068 

78902 

17 

21098 

06970 

5 

93030 

24 

37 

47  4 

12  56 

71952 

13 

28048 

78930 

17 

21070 

06978 

5 

93022 

23 

38 

46  56 

13  4 

71973 

13 

28027 

78959 

18 

21041 

06986 

5 

93014 

22 

39 

46  48 

13  12 

71994 

13 
14 

28006 

78987 

18 

21013 

06993 

5 

93007 

21 

40 

7  46  40 

4  13  20 

9.  72014 

10.  27986 

9.  79015 

19 

10. 20985 

10. 07001 

5  19.92999 

20 

41 

46  32 

13  28 

72034 

14 

27966 

79043 

19 

20957 

07009 

5 

92991 

19 

42 

46  24 

13  36 

72055 

14 

27945 

79072 

20 

20928 

07017 

5 

92983 

18 

43 

46  16 

13  44 

72075 

15 

27925 

79100 

20 

20900 

07024 

6 

92976 

17 

44 

46  8 

13  52 

72096 

15 

27904 

79128 

21 

20872 

07032 

6 

92968 

16 

4ft 

7  46  0 

4  14  0 

9.  72116 

15 

10. 27884 

9. 79156 

21 

10. 20844 

10. 07040 

6 

9. 92960 

15 

46 

45  52 

14  8 

72137 

16 

27863 

79185 

22 

20815 

07048 

6 

92952 

14 

47 

45  44 

14  16 

72157 

16 

27843 

79213 

22 

20787 

07056 

6 

92944 

13 

48 

45  36 

14  24 

72177 

16 

27823 

79241 

23 

20759 

07064 

6 

92936 

12 

49 

45  28 

14  32 

72198 

17 

27802 

79269 

23 

20731 

07071 

6 

92929 

11 

ftO 

7  45  20 

4  14  40 

9. 72218 

17 

10.  27782 

9. 79297 

24 

10.  20703 

10. 07079 

6 

9. 92921 

10 

ftl 

45  12 

14  48 

72238 

18 

27762 

79326 

24 

20674 

07087 

7 

92913 

9 

ft2 

45  4 

14  56 

72259 

18 

27741 

79354 

25 

20646 

07095 

7 

92905 

8 

ft3 

44  56 

15  4 

72279 

18 

27721 

79382 

25 

20618 

07103 

7 

92897 

7 

54 

44  48 

15  12 

72299 

19 

27701 

79410 

26 

20590 

07111 

7 

92889 

6 

ftft 

7  44  40 

4  15  20 

9. 72320 

19 

10.  27680 

9.  79438 

26 

10. 20562 

10. 07119 

7 

9. 92881 

5 

ft6 

44  32 

15  28 

72340 

19 

27660 

79466 

26 

20534 

07126 

7 

92874 

4 

ft7 

44  24 

15  36 

72360 

20 

27640 

79495 

27 

20505 

07134 

7 

92866 

3 

ft8 

44  16 

15  44 

72381 

20 

27619 

79523 

27 

20477 

07142 

7 

92858 

2 

ft9 

44  8 

15  52 

72401 

20 

27599 

79551 

28 

20449 

07150 

8 

92850 

1 

60 

44  0 

16  0 

72421 

21 

27579 

79579 

28 

20421 

07158 

8 

92842 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Di«f. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

121° 

A 

A 

B 

B        C 

C     68°  1 

Seconds  of  time 

!■ 

2« 

8> 

4« 

6> 

6« 

7« 

Prop,  parts  of  cols.^  B 

|c 

3 

4 
1 

5 

7 
2 

8 
11 
3 

10 

14 

4 

13 
18 
5 

15 

21 

6 

18 

26 

7 

Page  804] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

82° 

A 

A 

B 

B 

C 

C    147° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  44  0 

4  16  0 

9. 72421 

0 

10.  27579 

9.  79579 

0 

10.  20421 

10.  07158 

0 

9. 92842 

60 

1 

43  52 

16  8 

72441 

0 

27559 

79607 

0 

20393 

07166 

0 

92834 

59 

2 

43  44 

16  16 

72461 

1 

27539 

79635 

1 

20365 

07174 

0 

92826 

58 

3 

43  36 

16  24 

72482 

1 

27518 

79663 

1 

20337 

07182 

0 

92818 

57 

4 

43  28 

16  32 

72502 

1 

27498 

79691 

2 

20309 

07190 

92810 

56 

5 

7  43  20 

4  16  40 

9.  72522 

2 

10. 27478 

9. 79719 

2 

10. 20281 

10. 07197 

9. 92803 

55 

6 

43  12 

16  48 

72542 

2 

27458 

79747 

3 

20253 

07205 

92795 

54 

7 

43  4 

16  56 

72562 

2 

27438 

79776 

3 

20224 

07213 

92787 

53 

8 

42  56 

17  4 

72582 

3 

27418 

79804 

4 

20196 

07221 

92779 

52 

9 

42  48 

17  12 

72602 

3 

27398 

79832 

4 

20168 

07229 

92771 

51 

50 

10 

7  42  40 

4  17  20 

9. 72622 

3 

10. 27378 

9. 79860 

5 

10. 20140 

10. 07237 

9. 92763 

11 

42  32 

17  28 

72643 

4 

27357 

79888 

5 

20112 

07245 

92755 

49 

12 

42  24 

17  36 

72663 

4 

27337 

79916 

6 

20084 

07253 

2 

92747 

48 

13 

42  16 

17  44 

72683 

4 

27317 

79944 

6 

20056 

07261 

2 

92739 

47 

14 
15 

42  8 

17  52 

72703 

5 

27297 

79972 

7 

20028 

07269 

2 

92731 

46 
45 

7  42  0 

4  18  0 

9. 72723 

5 

10.  27277 

9.  80000 

7 

10.  20000 

10.  07277 

2 

9. 92723 

16 

41  52 

18  8 

72743 

5 

27257 

80028 

7 

19972 

07285 

2 

92715 

44 

17 

41  44 

18  16 

72763 

6 

27237 

80056 

8 

19944 

07293 

2 

92707 

43 

18 

41  36 

18  24 

72783 

6 

27217 

80084 

8 

19916 

07301 

2 

92699 

42 

19 
20 

41  28 

18  32 

72803 

6 

27197 

80112 

9 

19888 

07309 

3 

92691 

41 
40 

7  41  20 

4  18  40 

9.  72823 

7 

10.  27177 

9. 80140 

9 

10. 19860 

10. 07317 

3 

9. 92683 

21 

41  12 

18  48 

72843 

7 

27157 

80168 

10 

19832 

07325 

3 

92675 

39 

22 

41  4 

18  56 

72863 

7 

27137 

80195 

10 

19805 

07333 

3 

92667 

38 

23 

40  56 

19  4 

72883 

8 

27117 

80223 

11 

19777 

07341 

3 

92659 

37 

24 

40  48 

19  12 

72902 

8 

27098 

80251 

11 

19749 

07349 

3 

92651 

36 

25 

7  40  40 

4  19  20 

9. 72922 

8 

10.  27078 

9.  80279 

12 

10. 19721 

10. 07357 

3 

9. 92643 

35 

26 

40  32 

19  28 

72942 

9 

27058 

80307 

12 

19693 

07365 

3 

92635 

34 

27 

40  24 

19  36 

72962 

9 

27038 

80335 

13 

19665 

07373 

4 

92627 

33 

28 

40  16 

19  44 

72982 

9 

27018 

80363 

13 

19637 

07381 

4 

92619 

32 

29 

40  8 

19  52 

73002 

10 

26998 

80391 

13 

19609 

07389 

4 

92611 

31 

30 

7  40  0 

4  20  0 

9.  73022 

10 

10. 26978 

9. 80419 

14 

10. 19581 

10. 07397 

4 

9. 92603 

30 

31 

39  52 

20  8 

73041 

10 

26959 

80447 

14 

19553 

07405 

4 

92595 

29 

32 

39  44 

20  16 

73061 

11 

26939 

80474 

15 

19526 

07413 

4 

92587 

28 

33 

39  36 

20  24 

73081 

11 

26919 

80502 

15 

19498 

07421 

4 

92579 

27 

34 
35 

39  28 

20  32 

73101 

11 

26899 

80530 

16 

19470 

07429 

5 

92571 

26 

7  39  20 

4  20  40 

9.  73121 

12 

10. 26879 

9. 80558 

16 

10. 19442 

10. 07437 

5 

9. 92563 

25 

36 

39  12 

20  48 

73140 

12 

26860 

80586 

17 

19414 

07445 

5 

92555 

24 

37 

39  4 

20  56 

73160 

12 

26840 

80614 

17 

19386 

07454 

5 

92546 

23 

38 

38  56 

21  4 

73180 

13 

26820 

80642 

18 

19358 

07462 

5 

92538 

22 

39 

38  48 

21  12 

73200 

13 

26800 

80669 

18 

19331 

07470 

5 

92530 

21 
20 

40 

7  38  40 

4  21  20 

9.  73219 

13 

10. 26781 

9. 80697 

19 

10. 19303 

10. 07478 

5 

9. 92522 

41 

38  32 

21  28 

73239 

14 

26761 

80725 

19 

19275 

07486 

6 

92514 

19 

42 

38  24 

21  36 

73259 

14 

26741 

80753 

20 

19247 

07494 

6 

92506 

18 

43 

38  16 

21  44 

73278 

14 

26722 

80781 

20 

19219 

07502 

6 

92498 

17 

44 

38  8 

21  52 

73298 

15 

26702 

80808 

20 

19192 

07510 

6 

92490 

16 
15 

45 

7  38  0 

4  22  0 

9. 73318 

15 

10. 26682 

9. 80836 

21 

10. 19164 

10. 07518 

6 

9.  92482 

46 

37  52 

22  8 

73337 

15 

26663 

80864 

21 

19136 

07527 

6 

92473 

14 

47 

37  44 

22  16 

73357 

16 

26643 

80892 

22 

19108 

07535 

6 

92465 

13 

48 

37  36 

22  24 

73377 

16 

26623 

80919 

22 

19081 

07543 

6 

92457 

12 

49 

37  28 

22  32 

73396 

16 

26604 

80947 

23 

19053 

07551 

7 

92449 

11 
10 

50 

7  37  20 

4  22  40 

9. 73416 

17 

10.  26584 

9. 80975 

23 

10. 19025 

10. 07559 

7 

9. 92441 

51 

37  12 

22  48 

73435 

17 

26565 

81003 

24 

18997 

07567 

7 

92433 

9 

52 

37  4 

22  56 

73455 

17 

26545 

81030 

24 

18970 

07575 

7 

92425 

8 

53 

36  56 

23  4 

73474 

18 

26526 

81058 

25 

18942 

07584 

7 

92416 

7 

54 

36  48 

23  12 

73494 

18 

26506 

81086 

25 

18914 

07592 

7 

92408 

6 

55 

7  36  40 

4  23  20 

9. 73513 

18 

10.  26487 

9.81113 

26 

10. 18887 

10. 07600 

7 

9. 92400 

5 

56 

36  32 

23  28 

73533 

19 

26467 

81141 

26 

18859 

07608 

8 

92392 

4 

57 

36  24 

23  36 

73552 

19 

26448 

81169 

26 

18831 

07616 

8 

92384 

3 

58 

36  16 

23  44 

73572 

19 

26428 

81196 

27 

18804 

07624 

8 

92376 

2 

59 

36  8 

23  52 

73591 

20 

26409 

81224 

27 

18776 

07633 

8 

92367 

1 

60 

M. 

36  0 

24  0 

73611 

20 

26389 

81252 

28 

18748 

07641 

8 

92359 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

122° 

A 

A 

B 

B 

C 

C     67°  1 

Seconds  of  time 

1" 

2' 

8« 

4' 

5> 

6- 

T 

Prop,  parts  of  cols.  ■{B 

Ic 

2 
3 
1 

6 
7 
2 

7 
10 
3 

10 
14 
4 

12 
17 
6 

15 
21 
6 

17 
24 

7 

TABLE  44. 

[Page  806 

Log.  Sines,  Tangents,  and  Secants. 

88« 
M. 

0 

A 

A 

B 

B 

C 

C    1460 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

DiflE. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

7  36  0 

4  24  0 

9. 73611 

0 

10.  26389 

9. 81252 

0 

10. 18748 

10. 07641 

0 

9. 92359 

60 

1 

35  52 

24  8 

73630 

0 

26370 

81279 

0 

18721 

07649 

0 

92351 

59 

2 

35  44 

24  16 

73660 

1 

26350 

81307 

1 

18693 

07657 

0 

92343 

58 

3 

35  36 

24  24 

73669 

1 

26331 

81335 

1 

18665 

07665 

0 

92335 

57 

4 

35  28 

24  32 

73689 

1 

26311 

81362 

2 

18638 

07674 

92326 

56 
55 

5 

7  35  20 

4  24  40 

9. 73708 

2 

10. 26292 

9.  81390 

2 

10. 18610 

10. 07682 

9. 92318 

6 

35  12 

24  48 

73727 

2 

26273 

81418 

3 

18682 

07690 

92310 

54 

7 

35  4 

24  56 

73747 

2 

26253 

81445 

3 

18656 

07698 

92302 

53 

8 

34  56 

25  4 

73766 

3 

26234 

81473 

4 

18627 

07707 

92293 

52 

9 

34  48 

25  12 

73785 

3 

26215 

81500 

4 

18600 

07715 

92285 

51 

10 

7  34  40 

4  25  20 

9. 73805 

3 

10. 26195 

9. 81628 

5 

10. 18472 

10. 07723 

9. 92277 

50 

11 

34  32 

25  28 

73824 

3 

26176 

81556 

5 

18444 

07731 

2 

92269 

49 

12 

34  24 

26  36 

73843 

4 

26157 

81583 

5 

18417 

07740 

2 

92260 

48 

13 

34  16 

25  44 

73863 

4 

26137 

81611 

6 

18389 

07748 

2 

92262 

47 

14 
15 

34  8 

25  52 

73882 

4 

26118 

81638 

6 

18362 

07756 

2 

92244 

46 
46 

7  34  0 

4  26  0 

9.  73901 

5 

10.  26099 

9. 81666 

7 

10. 18334 

10. 07765 

2 

9. 92236 

16 

33  52 

26  8 

73921 

6 

26079 

81693 

7 

18307 

07773 

2 

92227 

44 

17 

33  44 

26  16 

73940 

6 

26060 

81721 

8 

18279 

07781 

2 

92219 

43 

18 

33  36 

26  24 

73959 

6 

26041 

81748 

8 

18252 

07789 

3 

92211 

42 

19 

33  28 

26  32 

73978 

6 

26022 

81776 

9 
9 

18224 
10. 18197 

07798 

3 

92202 

41 

20 

7  33  20 

4  26  40 

9. 73997 

6 

10. 26003 

9. 81803 

10. 07806 

3 

9.92194 

40 

21 

33  12 

26  48 

74017 

7 

25983 

81831 

10 

18169 

07814 

3 

92186 

39 

22 

33  4 

26  56 

74036 

7 

25964 

81858 

10 

18142 

07823 

3 

92177 

38 

23 

32  56 

27  4 

74055 

7 

25946 

81886 

11 

18114 

07831 

3 

92169 

37 

24 

32  48 

27  12 

74074 

8 

25926 

81913 

11 

18087 

07839 

3 

92161 

36 

25 

7  32  40 

4  27  20 

9.74093 

8 

10. 25907 

9. 81941 

11 

10. 18069 

10. 07848 

3 

9. 92162 

35 

26 

32  32 

27  28 

74113 

8 

26887 

81968 

12 

18032 

07856 

4 

92144 

34 

27 

32  24 

27  36 

74132 

9 

25868 

81996 

12 

18004 

07864 

4 

92136 

33 

28 

32  16 

27  44 

74151 

9 

25849 

82023 

13 

17977 

07873 

4 

92127 

32 

29 

32  8 

27  52 

74170 

9 

25830 

82051 

13 

17949 

07881 

4 

92119 

31 

30 

7  32  0 

4  28  0 

9.  74189 

10 

10.25811 

9. 82078 

14 

10. 17922 

10. 07889 

4 

9. 92111 

30 

31 

31  52 

28  8 

74208 

10 

25792 

82106 

14 

17894 

07898 

4 

92102 

29 

32 

31  44 

28  16 

74227 

10 

25773 

82133 

15 

17867 

07906 

4 

92094 

28 

33 

31  36 

28  24 

74246 

10 

25764 

82161 

15 

17839 

07914 

5 

92086 

27 

34 

31  28 

28  32 

74265 

11 

25735 

82188 

16 

17812 

07923 

5 

92077 

26 

35 

7  31  20 

4  28  40 

9.  74284 

11 

10.  25716 

9. 82215 

16 

10. 17786 

10. 07931 

5 

9. 92069 

26 

36 

31  12 

28  48 

74303 

11 

25697 

82243 

16 

17757 

07940 

6 

92060 

24 

37 

31  4 

28  56 

74322 

12 

25678 

82270 

17. 

17730 

07948 

5 

92062 

23 

38 

30  56 

29  4 

74341 

12 

25659 

82298 

17 

17702 

07966 

5 

92044 

22 

39 

30  48 

29  12 

74360 

12 

25640 

82325 

18 

17675 

07965 

5 

92035 

21 
20 

40 

7  30  40 

4  29  20 

9. 74379 

13 

10. 25621 

9. 82362 

18 

10. 17648 

10. 07973 

6 

9. 92027 

41 

30  32 

29  28 

74398 

13 

25602 

82380 

19 

17620 

07982 

6 

92018 

19 

42 

30  24 

29  36 

74417 

13 

25583 

82407 

19 

17593 

07990 

6 

92010 

18 

43 

30  16 

29  44 

74436 

14 

25564 

82436 

20 

17565 

07998 

6 

92002 

17 

44 

30  8 

29  52 

74455 

14 

25546 

82462 

20 

17538 

08007 

6 

91993 

16 

45 

7  30  0 

4  30  0 

9.  74474 

14 

10.  26526 

9. 82489 

21 

10.17511 

10. 08016 

6 

9.91986 

16 

46 

29  52 

30  8 

74493 

15 

26507 

82617 

21 

17483 

08024 

6 

91976 

14 

47 

29  44 

30  16 

74512 

15 

25488 

82644 

22 

17466 

08032 

7 

91968 

13 

48 

29  36 

30  24 

74531 

15 

25469 

82671 

22 

17429 

08041 

7 

91969 

12 

49 

29  28 

30  32 

74549 

16 

25461 

82599 

22 

17401 

08049 

7 

91951 

11 

50 

7  29  20 

4  30  40 

9. 74568 

16 

10. 25432 

9. 82626 

23 

10. 17374 

10. 08058 

7 

9. 91942 

10 

61 

29  12 

30  48 

74587 

16 

25413 

82653 

23 

17347 

08066 

7 

91934 

9 

52 

29  4 

30  56 

74606 

17 

26394 

82681 

24 

17319 

08075 

7 

91925 

8 

53 

28  56 

31  4 

74625 

17 

25375 

82708 

24 

17292 

08083 

7 

91917 

7 

54 

28  48 

31  12 

74644 

17 

25356 

82735 

25 

17266 

08092 

8 

91908 

6 

55 

7  28  40 

4  31  20 

9.  74662 

17 

10. 25338 

9. 82762 

25 

10.17238 

10. 08100 

8 

9. 91900 

5 

56 

28  32 

31  28 

74681 

18 

25319 

82790 

26 

17210 

08109 

8 

91891 

4 

57 

28  24 

31  36 

74700 

18 

25300 

82817 

26 

17183 

08117 

8 

91883 

3 

58 

28  16 

31  44 

74719 

18 

25281 

82844 

27 

17166 

08126 

8 

91874 

2 

59 

28  8 

31  52 

74737 

19 

25263 

82871 

27 

17129 

08134 

8 

91866 

1 

60 

28  0 

32  0 

74756 

19 

25244 

82899 

27 

17101 

08143 

8 

91867 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difif. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

128= 

A 

A 

B 

B 

C 

C    66°  1 

Seconds  of  time 

1» 

2» 

S< 

4» 

S* 

6' 

7- 

Prop,  parte  of  cols.  ^B 

2 
3 

1 

5 

7 
2 

7 
10 
3 

10 

14 
4 

12 

17 

6 

14 
21 
6 

17 
24 

7 

Page  806] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

840 

A 

A 

B           B 

C 

C    145° 

M. 

Hour  A.M. 

Hoiir  p.  M. 

Sine. 

Difl. 

Cosecant 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  28  0 

4  32  0 

9. 74766 

0 

10. 25244 

9. 82899 

0 

10. 17101 

10. 08143 

0 

9. 91857 

60 

1 

27  62 

32  8 

74775 

0 

25226 

82926 

0 

17074 

08161 

0 

91849 

59 

2 

27  44 

32  16 

74794 

1 

26206 

82953 

1 

17047 

08160 

0 

91840 

58 

3 

27  36 

32  24 

74812 

1 

26188 

82980 

1 

17020 

08168 

0 

91832 

67 

4 

27  28 

32  32 

74831 

1 

26169 

83008 

2 

16992 

08177 

91823 

56 

5 

7  27  20 

4  32  40 

9. 74850 

2 

10.  26150 

9.  83036 

2 

10. 16965 

10.  08186 

9. 91816 

65 

6 

27  12 

32  48 

74868 

2 

25132 

83062 

3 

16938 

08194 

91806 

64 

7 

27  4 

32  56 

74887 

2 

26113 

83089 

3 

16911 

08202 

91798 

53 

8 

26  56 

33  4 

74906 

2 

26094 

83117 

4 

16883 

08211 

91789 

52 

9 

26  48 

33  12 

74924 

3 

25076 

83144 

4 

16856 

08219 

91781 

51 
50 

10 

7  26  40 

4  33  20 

9. 74943 

3 

10. 25067 

9. 83171 

6 

10. 16829 

10. 08228 

9. 91772 

11 

26  32 

33  28 

74961 

3 

25039 

83198 

6 

16802 

08237 

2 

91763 

49 

12 

26  24 

33  36 

74980 

4 

25020 

83225 

5 

16775 

08246 

2 

91755 

48 

13 

26  16 

33  44 

74999 

4 

25001 

83262 

6 

16748 

08264 

2 

91746 

47 

14 

26  8 

33  62 

76017 

4 

24983 

83280 

6 

16720 

08262 

2 

91738 

46 

15 

7  26  0 

4  34  0 

9. 75036 

5 

10. 24964 

9. 83307 

7 

10. 16693 

10.  08271 

2 

9. 91729 

45 

16 

25  52 

34  8 

75054 

5 

24946 

83334 

7 

16666 

08280 

2 

91720 

44 

17 

25  44 

34  16 

76073 

6 

24927 

83361 

8 

16639 

08288 

2 

91712 

43 

18 

25  36 

34  24 

76091 

6 

24909 

83388 

8 

16612 

08297 

3 

91703 

42 

19 

25  28 

34  32 

75110 

6 

24890 

83416 

9 

16585 

08306 

3 

91695 

41 

20 

7  25  20 

4  34  40 

9. 75128 

6 

10. 24872 

9.  83442 

9 

10. 16668 

10. 08314 

3 

9. 91686 

40 

21 

25  12 

34  48 

76147 

6 

24853 

83470 

9 

16530 

08323 

3 

91677 

39 

22 

25  4 

34  66 

75166 

7 

24835 

83497 

10 

16503 

08331 

3 

91669 

38 

23 

24  66 

35  4 

75184 

7 

24816 

83524 

10 

16476 

08340 

3 

91660 

37 

24 

24  48 

35  12 

75202 

7 

24798 

83661 

11 

16449 

08349 

3 

91651 

36 

25 

7  24  40 

4  35  20 

9. 75221 

8 

10.  24779 

9. 83678 

11 

10. 16422 

10. 08367 

4 

9. 91643 

36 

26 

24  32 

35  28 

75239 

8 

24761 

83606 

12 

16395 

08366 

4 

91634 

34 

27 

24  24 

35  36 

76268 

8 

24742 

83632 

12 

16368 

08376 

4 

91626 

33 

28 

24  16 

35  44 

75276 

9 

24724 

83659 

13 

16341 

08383 

4 

91617 

32 

29 

24  8 

35  52 

75294 

9 

24706 

83686 

13 

16314 

08392 

4 

91608 

31 

30 

7  24  0 

4  36  0 

9.  76313 

9 

10. 24687 

9. 83713 

14 

10. 16287 

10.  08401 

4 

9. 91599 

30 

31 

23  52 

36  8 

76331 

9 

24669 

83740 

14 

16260 

08409 

4 

91591 

29 

32 

23  44 

36  16 

76350 

10 

24650 

83768 

14 

16232 

08418 

5 

91582 

28 

33 

23  36 

36  24 

75368 

10 

24632 

83795 

15 

16205 

08427 

6 

91673 

27 

34 

23  28 

36  32 

75386 

10 

24614 

83822 

15 

16178 

08436 

5 

91565 

26 
26 

35 

7  23  20 

4  36  40 

9. 75405 

11 

10. 24596 

9. 83849 

16 

10. 16151 

10. 08444 

5 

9. 91566 

36 

23  12 

36  48 

76423 

11 

24577 

83876 

16 

16124 

08453 

6 

91647 

24 

37 

23  4 

36  56 

76441 

11 

24559 

83903 

17 

16097 

08462 

5 

91538 

23 

38 

22  66 

37  4 

76459 

12 

24541 

83930 

17 

16070 

08470 

5 

91630 

22 

39 

22  48 

37  12 

76478 

12 

24622 

83967 

18 

16043 

08479 

6 

91621 

21 
20 

40 

7  22  40 

4  37  20 

9. 76496 

12 

10.  24504 

9. 83984 

18 

10. 16016 

10. 08488 

6 

9. 91612 

41 

22  32 

37  28 

75514 

13 

24486 

84011 

18 

15989 

08496 

6 

91504 

19 

42 

22  24 

37  36 

75533 

13 

24467 

84038 

19 

16962 

08505 

6 

91495 

18 

43 

22  16 

37  44 

76661 

13 

24449 

84065 

19 

15936 

08514 

6 

91486 

17 

44 

22  8 

37  52 

76669 

13 

24431 

84092 

20 

15908 

08523 

6 

91477 

16 

45 

7  22  0 

4  38  0 

9. 75587 

14 

10. 24413 

9.  84119 

20 

10. 15881 

10. 08531 

7 

9. 91469 

15 

46 

21  62 

38  8 

75605 

14 

24395 

84146 

21 

15854 

08540 

7 

91460 

14 

47 

21  44 

38  16 

75624 

14 

24376 

84173 

21 

15827 

08549 

7 

91451 

13 

48 

21  36 

38  24 

75642 

15 

24358 

84200 

22 

16800 

08558 

7 

91442 

12 

49 
50 

21  28 

38  32 

75660 

15 
16 

24340 

84227 

22 

16773 

08567 

7 

91433 

11 
10 

7  21  20 

4  38  40 

9. 75678 

10.  24322 

9.  84254 

23 

10. 16746 

10.  08575 

7 

9. 91425 

51 

21  12 

38  48 

75696 

16 

24304 

84280 

23 

15720 

08584 

7 

91416 

9 

52 

21  4 

38  56 

75714 

16 

24286 

84307 

23 

15693 

08693 

8 

91407 

8 

53 

20  56 

39  4 

75733 

16 

24267 

84334 

24 

15666 

08602 

8 

91398 

7 

54 

20  48 

39  12 

76751 

17 

24249 

84361 

24 

16639 

08611 

8 

91389 

6 

65 

7  20  40 

4  39  20 

9.  76769 

17 

10. 24231 

9. 84388 

25 

10. 16612 

10. 08619 

8 

9. 91381 

5 

56 

20  32 

39  28 

75787 

17 

24213 

84415 

25 

16686 

08628 

8 

91372 

4 

57 

20  24 

39  36 

75806 

17 

24195 

84442 

26 

15668 

08637 

8 

91363 

3 

58 

20  16 

39  44 

75823 

18 

24177 

84469 

26 

15531 

08646 

8 

91354 

2 

59 

20  8 

39  52 

76841 

18 

24159 

84496 

27 

15504 

08655 

9 

91345 

1 

60 

20  0 

40  0 

75859 

18 

24141 

84523 

27 

15477 

08664 

9 

91336 

0 
M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl.  Tangent. 

Cosecant. 

Difl. 

Sine. 

ia4< 

t 

A 

A 

B           B 

C 

C    66  1 

Seconds  of  time 

!• 

«• 

S> 

4^ 

6' 

e* 

T 

fA 
Prop,  parts  of  cols.  B 

Ic 

2 
3 
1 

5 
7 
2 

7 
10 
3 

9 
14 
4 

11 

17 

6 

14 
20 
7 

16 

24 

8 

TABLE  4A. 

[Page  807 

Log.  Sines,  Tangents,  and  Secants. 

86<» 

▲ 

A 

B 

B 

C 

C    144° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Dlfif. 

Cosine. 

M. 

0 

7  20  0 

4  40  0 

9.  75859 

0 

10. 24141 

9. 84623 

0 

10. 15477 

10. 08664 

0 

9. 91336 

60 

1 

19  52 

40  8 

75877 

0 

24123 

84660 

0 

15450 

08672 

0 

91328 

69 

2 

19  44 

40  16 

75895 

1 

24105 

84576 

1 

15424 

08681 

0 

91319 

68 

3 

19  36 

40  24 

75913 

1 

24087 

84603 

1 

16397 

08690 

0 

91310 

57 

4 

19  28 

40  32 

75931 

1 

24069 

84630 

2 

16370 

08699 

91301 

56 

5 

7  19  20 

4  40  40 

9. 75949 

1 

10. 24051 

9.84657 

2 

10. 16343 

10. 08708 

9. 91292 

55 

6 

19  12 

40  48 

75967 

2 

24033 

84684 

3 

16316 

08717 

91283 

54 

7 

19  4 

40  56 

75985 

2 

24015 

84711 

3 

15289 

08726 

91274 

53 

8 

18  56 

41  4 

76003 

2 

23997 

84738 

4 

16262 

08734 

91266 

52 

9 

18  48 

41  12 

76021 

3 

23979 

84764 

4 

15236 

08743 

91257 

51 

10 

7  18  40 

4  41  20 

9. 76039 

3 

10.  23961 

9. 84791 

4 

10. 15209 

10. 08752 

2 

9.91248 

60 

11 

18  32 

41  28 

76067 

3 

23943 

84818 

5 

15182 

08761 

2 

91239 

49 

12 

18  24 

41  36 

76075 

4 

23925 

84845 

5 

15165 

08770 

2 

91230 

48 

13 

18  16 

41  44 

76093 

4 

23907 

84872 

6 

15128 

08779 

2 

91221 

47 

14 

18  8 

41  52 

76111 

4 

23889 

84899 

6 

15101 

08788 

2 
2 

91212 

46 

45 

15 

7  18  0 

4  42  0 

9. 76129 

4 

10. 23871 

9.84925 

7 

10. 15075 

10. 08797 

9. 91203 

16 

17  52 

42  8 

76146 

5 

23854 

84952 

7 

15048 

08806 

2 

91194 

44 

17 

17  44 

42  16 

76164 

5 

23836 

84979 

8 

16021 

08815 

3 

91186 

43 

18 

17  36 

42  24 

76182 

5 

23818 

85006 

8 

14994 

08824 

3 

91176 

42 

19 
20 

17  28 

42  32 

76200 

6 

23800 

85033 

8 

14967 
10. 14941 

08833 

3 

91167 
9.91158 

41 
40 

7  17  20 

4  42  40 

9. 76218 

6 

10. 23782 

9. 85059 

9 

10.08842 

3 

21 

17  12 

42  48 

76236 

6 

23764 

86086 

9 

14914 

08851 

3 

91149 

39 

22 

17  4 

42  56 

76253 

6 

23747 

86113 

10 

14887 

08869 

3 

91141 

38 

23 

16  56 

43  4 

76271 

7 

23729 

85140 

10 

14860 

08868 

3 

91132 

37 

24 

25 

16  48 

43  12 

76289 

7 

23711 

85166 

11 

14834 

08877 

4 

91123 

36 

7  16  40 

4  43  20 

9. 76307 

7 

10.  23693 

9. 86193 

11 

10. 14807 

10. 08886 

4 

9.91114 

35 

26 

16  32 

43  28 

76324 

8 

23676 

85220 

12 

14780 

08896 

4 

91105 

34 

27 

16  24 

43  36 

76342 

8 

23658 

85247 

12 

14753 

08904 

4 

91096 

33 

28 

16  16 

43  44 

76360 

8 

23640 

85273 

12 

14727 

08913 

4 

91087 

32 

29 
30 

16  8 

43  62 

76378 

9 

23622 

85300 

13 

14700 

08922 

4 

91078 

31 

7  16  0 

4  44  0 

9. 76395 

9 

10. 23605 

9. 85327 

13 

10. 14673 

10. 08931 

5 

9. 91069 

30 

31 

15  52 

44  8 

76413 

9 

23587 

86364 

14 

14646 

08940 

5 

91060 

29 

32 

15  44 

44  16 

76431 

9 

23569 

86380 

14 

14620 

08949 

5 

91061 

28 

33 

15  36 

44  24 

76448 

10 

23552 

85407 

16 

14693 

08968 

5 

91042 

27 

34 
35 

15  28 

44  32 

76466 

10 

23534 

85434 

15 

14666 

08967 

5 

91033 

26 

7  15  20 

4  44  40 

9.  76484 

10 

10.  23516 

9.85460 

16 

10. 14640 

10. 08977 

5 

9. 91023 

25 

36 

15  12 

44  48 

76501 

11 

23499 

85487 

16 

14513 

08986 

6 

91014 

24 

37 

15  4 

44  56 

76519 

11 

23481 

85614 

16 

14486 

08996 

6 

91006 

23 

38 

14  66 

45  4 

76537 

11 

23463 

86640 

17 

14460 

09004 

6 

90996 

22 

39 

14  48 

45  12 

76554 

12 

23446 

85567 

17 

14433 

09013 

6 

90987 
9. 90978 

21 
20 

40 

7  14  40 

4  45  20 

9.  76572 

12 

10.  23428 

9.85594 

18 

10. 14406 

10. 09022 

6 

41 

14  32 

.  45  28 

76590 

12 

23410 

85620 

18 

14380 

09031 

6 

90969 

19 

42 

14  24 

45  36 

76607 

12 

23393 

85647 

19 

14353 

09040 

6 

90960 

18 

43 

14  16 

45  44 

76625 

13 

23375 

85674 

19 

14326 

09049 

6 

90951 

17 

44 

14  8 

45  52 

76642 

13 

23358 

85700 

20 

14300 

09058 

7 

90942 

16 

45 

7  14  0 

4  46  0 

9.76660 

13 

10. 23340 

9. 86727 

20 

10. 14273 

10. 09067 

7 

9. 90933 

15 

46 

13  52 

46  8 

76677 

14 

23323 

86764 

20 

14246 

09076 

7 

90924 

14 

47 

13  44 

46  16 

76695 

14 

23305 

85780 

21 

14220 

09086 

7 

90915 

13 

48 

13  36 

46  24 

76712 

14 

23288 

85807 

21 

14193 

09094 

7 

90906 

12 

49 

13  28 

46  32 

76730 

14 

23270 

85834 

22 

14166 

09104 

7 

90896 

11 

50 

7  13  20 

4  46  40 

9. 76747 

15 

10.  23253 

9. 85860 

22 

10. 14140 

10.09113 

8 

9. 90887 

10 

51 

13  12 

46  48 

76765 

15 

23235 

86887 

23 

14113 

09122 

8 

90878 

9 

52 

13  4 

46  56 

76782 

15 

23218 

85913 

23 

14087 

09131 

8 

90869 

8 

53 

12  56 

47  4 

76800 

16 

23200 

85940 

24 

14060 

09140 

8 

90860 

7 

54 

12  48 

47  12 

76817 

16 

23183 

85967 

24 

14033 

09149 

8 
8 

90861 

6 

55 

7  12  40 

4  47  20 

9. 76835 

16 

10.  23165 

9. 85993 

24 

10. 14007 

10. 09168 

9. 90842 

5 

56 

12  32 

47  28 

76852 

17 

23148 

86020 

25 

13980 

09168 

8 

90832 

4 

57 

12  24 

47  36 

76870 

17 

23130 

86046 

26 

13954 

09177 

9 

90823 

3 

58 

12  16 

47  44 

76887 

17 

23113 

86073 

26 

13927 

09186 

9 

90814 

2 

59 

12  8 

47  52 

76904 

17 

23096 

86100 

26 

13900 

09195 

9 

90805 

1 

60 

12  0 

48  0 

76922 

18 

23078 

86126 

27 

13874 

09204 

9 

90796 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

125° 

A 

A 

B 

B 

C 

C     64°  1 

Seconds  of  time 

1" 

2» 

S* 

4« 

5- 

6» 

7» 

fA 
Prop,  parts  of  cols.^JB 

2 
3 
1 

4 

7 
2 

7 

10 

3 

9 
13 

5 

11 
17 
6 

13 
20 

7 

16 
23 

8 

Page  808] 

TABLE  44. 

Log.  Sines,  Tan 

gents,  and  Secants. 

86° 

A 

A 

B 

B 

C 

C   14S° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

DifiE. 

Cosine. 

M. 

0 

7  12  0 

4  48  0 

9.  76922 

0 

10.  23078 

9. 86126 

0 

10. 13874 

10. 09204 

0 

9. 90796 

60 

1 

11  52 

48  8 

76939 

0 

23061 

86153 

0 

13847 

09213 

0 

90787 

59 

2 

11  44 

48  16 

76957 

1 

23043 

86179 

1 

13821 

09223 

0 

90777 

58 

3 

11  36 

48  24 

76974 

1 

23026 

86206 

1 

13794 

09232 

0 

90768 

57 

4 

11  28 

48  32 

76991 

1 

23009 

86232 

2 

13768 

09241 

90759 

56 
55 

5 

7  11  20 

4  48  40 

9. 77009 

1 

10.  22991 

9. 86259 

2 

10. 13741 

10. 09250 

9.  90750 

6 

11  12 

48  48 

77026 

2 

22974 

86285 

3 

13715 

09259 

90741 

54 

7 

11  4 

48  56 

77043 

2 

22957 

86312 

3 

13688 

09269 

90731 

53 

8 

10  56 

49  4 

77061 

2 

22939 

86338 

4 

13662 

09278 

90722 

52 

9 
10 

10  48 

49  12 

77078 

3 

22922 
10.22905 

86365 

4 

13635 

09287 

90713 

51 
50 

7  10  40 

4  49  20 

9.  77095 

3 

9. 66392 

4 

10. 13608 

10.  09296 

2 

9. 90704 

11 

10  32 

49  28 

77112 

3 

22888 

86418 

5 

13582 

09306 

2 

90694 

49 

12 

10  24 

49  36 

77130 

3 

22870 

86445 

5 

13555 

09316 

2 

90686 

48 

13 

10  16 

49  44 

77147 

4 

22853 

86471 

6 

13529 

09324 

2 

90676 

47 

14 
15 

10  8 

49  52 

77164 

4 

22836 

86498 

6 

13502 

09333 

2 

90667 

46 

45 

7  10  0 

4  50  0 

9.  77181 

4 

10. 22819 

9. 86524 

7 

10. 13476 

10. 09343 

2 

9. 90657 

16 

9  52 

50  8 

77199 

5 

22801 

86551 

7 

13449 

09352 

2 

90648 

44 

17 

9  44 

50  16 

77216 

5 

22784 

86577 

7 

13423 

09361 

3 

90639 

43 

18 

9  36 

50  24 

77233 

5 

22767 

86603 

8 

13397 

09370 

3 

90630 

42 

19 

9  28 

50  32 

77250 

5 

22750 

86630 

8 

13370 

09380 

3 

90620 

41 

20 

7  9  20 

4  50  40 

9. 77268 

6 

10. 22732 

9. 86656 

9 

10. 13344 

10. 09389 

3 

9. 90611 

40 

21 

9  12 

50  48 

77285 

6 

22715 

86683 

9 

13317 

09398 

3 

90602 

39 

22 

9  4 

50  56 

77302 

6 

22698 

86709 

10 

13291 

09408 

3 

90592 

38 

23 

8  56 

51  4 

77319 

7 

22681 

86736 

10 

13264 

09417 

4 

90583 

37 

24 
25 

8  48 

51  12 

77336 

7 

22664 

86762 

11 

13238 

09426 

4 

90574 

36 
36 

7  8  40 

4  61  20 

9. 77353 

7 

10. 22647 

9. 86789 

11 

10. 13211 

10. 09435 

4 

9. 90665 

26 

8  32 

51  28 

77370 

7 

22630 

86815 

11 

13185 

09446 

4 

90566 

34 

27 

8  24 

51  36 

77387 

8 

22613 

86842 

12 

13158 

09454 

4 

90546 

33 

28 

8  16 

51  44 

77405 

8 

22595 

86868 

12 

13132 

09463 

4 

90537 

32 

29 

8  8 

51  52 

77422 

8 
9 

22578 

86894 

13 

13106 

09473 

6 

90527 

31 
30 

30 

7  8  0 

4  52  0 

9.  77439 

10. 22561 

9. 86921 

13 

10. 13079 

10. 09482 

5 

9. 90518 

31 

7  52 

52  8 

77456 

9 

22544 

86947 

14 

13053 

09491 

6 

90509 

29 

32 

7  44 

52  16 

77473 

9 

22527 

86974 

14 

13026 

09601 

6 

90499 

28 

33 

7  36 

52  24 

77490 

9 

22510 

87000 

16 

13000 

09510 

5 

90490 

27 

34 

7  28 

52  32 

77507 

10 

22493 

87027 

16 

12973 

09520 

5 

90480 

26 

35 

7  7  20 

4  52  40 

9. 77524 

10 

10. 22476 

9. 87053 

16 

10. 12947 

10. 09529 

5 

9. 90471 

26 

36 

7  12 

52  48 

77541 

10 

22459 

87079 

16 

12921 

09538 

6 

90462 

24 

37 

7  4 

52  56 

77558 

11 

22442 

87106 

16 

12894 

09548 

6 

90452 

23 

38 

6  56 

53  4 

77575 

11 

22425 

87132 

17 

12868 

09567 

6 

90443 

22 

39 

6  48 

53  12 

77592 

11 

22408 

87158 

17 

12842 

09566 

6 

90434 

21 

20 

40 

7  6  40 

4  53  20 

9. 77609 

11 

10. 22391 

9. 87185 

18 

10. 12815 

10. 09576 

6 

9. 90424 

41 

6  32 

53  28 

77626 

12 

22374 

87211 

18 

12789 

09685 

6. 

90416 

19 

42 

6  24 

53  36 

77643 

12 

22357 

87238 

18 

12762 

09595 

7 

90405 

18 

43 

6  16 

53  44 

77660 

12 

22340 

87264 

19 

12736 

09604 

7 

90396 

17 

44 

6  8 

63  52 

77677 

13 

22323 

87290 

19 

12710 

09614 

7 

90386 

16 

45 

7  6  0 

4  54  0 

9. 77694 

13 

10. 22306 

9. 87317 

20 

10. 12683 

10. 09623 

7 

9. 90377 

15 

46 

5  52 

54  8 

77711 

13 

22289 

87343 

20 

12667 

09632 

7 

90368 

14 

47 

5  44 

54  16 

77728 

13 

22272 

87369 

21 

12631 

09642 

7 

90358 

13 

48 

5  36 

54  24 

77744 

14 

22256 

87396 

21 

12604 

09651 

7 

90349 

12 

49 

5  28 

54  32 

77761 

14 

22239 

87422 

22 

12678 

09661 

8 

90339 

11 
10 

50 

7  5  20 

4  54  40 

9. 77778 

14 

10.  22222 

9. 87448 

22 

10. 12552 

10. 09670 

8 

9. 90330 

51 

5  12 

54  48 

77796 

15 

22205 

87476 

22 

12625 

09680 

8 

90320 

9 

52 

5  4 

54  56 

77812 

16 

22188 

87501 

23 

12499 

09689 

8 

90311 

8 

53 

4  56 

55  4 

77829 

16 

22171 

87527 

23 

12473 

09699 

8 

90301 

7 

54 

4  48 

55  12 

77846 

16 

22154 

87554 

24 

12446 

09708 

8 

90292 
9. 90282 

6 
5 

55 

7  440 

4  55  20 

9. 77862 

16 

10.  22138 

9. 87580 

24 

10. 12420 

10. 09718 

9 

56 

4  32 

55  28 

77879 

16 

22121 

87606 

25 

12394 

09727 

9 

90273 

4 

57 

4  24 

55  36 

77896 

16 

22104 

87633 

25 

12367 

09737 

9 

90263 

3 

58 

4  16 

55  44 

77913 

16 

22087 

87659 

26 

12341 

09746 

9 

90264 

2 

59 

4  8 

55  52 

77930 

17 

22070 

87686 

26 

12316 

09766 

9 

90244 

1 

60 

4  0 

56  0 

77946 

17 

22054 

87711 

26 

12289 

09766 

9 

90235 

0 

M. 

Hour  p.  K. 

Hour  A.  M. 

Cosine. 

Difif. 

Secant. 

Cotangent. 

DiflF. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

126« 

A 

A 

B 

B 

C 

C     58°  1 

Seconds  of  time 

1» 

2« 

8' 

4" 

&• 

6> 

7« 

Prop,  parts  of  cols.  ■{B 

Ic 

2 
3 
1 

4 

7 
2 

6 

10 
4 

9 

13 

6 

11 
17 
6 

13 
20 

7 

16 

28 

8 

-" 

TABLE  44. 

[Page  809 

Log.  Sines,  Tangents,  and  Secants. 

87° 

A 

A 

B 

B 

C 

C    142° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  4  0 

4  56  0 

9. 77946 

0 

10.  22054 

9.  87711 

0 

10. 12289 

10.  09765 

0 

9. 90235 

60 

1 

3  52 

56  8 

77963 

0 

22037 

87738 

0 

12262 

09775 

0 

90225 

59 

2 

3  44 

56  16 

77980 

1 

22020 

87764 

1 

12236 

09784 

0 

90216 

58 

3 

3  36 

56  24 

77997 

1 

22003 

87790 

1 

12210 

09794 

0 

90206 

57 

4 

3  28 

56  32 

78013 

1 

21987 

87817 

2 

12183 

09803 

90197 

56 

6 

7  3  20 

4  56  40 

9. 78030 

1 

10. 21970 

9. 87843 

2 

10. 12157 

10. 09813 

9. 90187 

55 

6 

3  12 

56  48 

78047 

2 

21953 

87869 

3 

12131 

09822 

90178 

54 

7 

3  4 

56  56 

78063 

2 

21937 

87895 

3 

12105 

09832 

90168 

53 

8 

2  56 

57  4 

78080 

2 

21920 

87922 

3 

12078 

09841 

90159 

52 

9 

2  48 

67  12 

78097 

2 

21903 

87948 

4 

12052 

09851 

90149 

51 
50 

10 

7  2  40 

4  57  20 

9.  78113 

3 

10. 21887 

9. 87974 

4 

10. 12026 

10. 09861 

2 

9. 90139 

11 

2  32 

57  28 

78130 

3 

21870 

88000 

5 

12000 

09870 

2 

90130 

49 

12 

2  24 

57  36 

78147 

3 

21853 

88027 

5 

11973 

09880 

2 

90120 

48 

13 

2  16 

57  44 

78163 

4 

21837 

88053 

6 

11947 

09889 

2 

90111 

47 

14 

2  8 

57  52 

78180 

4 

21820 

88079 
9. 88105 

6 

7 

11921 

09899 

2 

90101 

46 

15 

7  2  0 

4  58  0 

9. 78197 

4 

10.  21803 

10. 11895 

10. 09909 

2 

9.90091 

45 

16 

1  52 

58  8 

78213 

4 

21787 

88131 

7 

11869 

09918 

3 

90082 

44 

17 

1  44 

58  16 

78230 

5 

21770 

88158 

7 

11842 

09928 

3 

90072 

43 

18 

1  36 

58  24 

78246 

5 

21754 

88184 

8 

11816 

09937 

3 

90063 

42 

19 

1  28 

58  32 

78263 

5 

21737 

88210 

8 

11790 

09947 

3 

90053 

41 
40 

20 

7  1  20 

4  58  40 

9.  78280 

5 

10.  21720 

9.  88236 

9 

10. 11764 

10. 09957 

3 

9.90043 

21 

1  12 

58  48 

78296 

6 

21704 

88262 

9 

11738 

09966 

3 

90034 

39 

22 

1  4 

58  56 

78313 

6 

21687 

88289 

10 

11711 

09976 

4 

90024 

38 

23 

0  56 

59  4 

78329 

6 

21671 

88315 

10 

11685 

09986 

4 

90014 

37 

24 

0  48 

59  12 

78346 

7 

21654 

88341 

10 

11659 

09995 

4 

90005 

36 

35 

25 

7  0  40 

4  59  20 

9.  78362 

7 

10. 21638 

9. 88367 

11 

10. 11633 

10. 10005 

4 

9. 89995 

26 

0  32 

59  28 

78379 

7 

21621 

88393 

11 

11607 

10015 

4 

89985 

34 

27 

0  24 

59  36 

78395 

7 

21605 

88420 

12 

11580 

10024 

4 

89976 

33 

28 

0  16 

59  44 

78412 

8 

21588 

88446 

12 

11554 

10034 

5 

89966 

32 

29 

0  8 

59  52 

78428 

8 

21572 

88472 

13 

11528 

10044 

5 

89956 

31 
30 

80 

7  0  0 

5  0  0 

9.78445 

8 

10.  21555 

9.  88498 

13 

10. 11502 

10. 10053 

5 

9.  89947 

31 

6  59  52 

0  8 

78461 

^ 

21539 

88524 

14 

11476 

10063 

5 

89937 

29 

32 

59  44 

0  16 

78478 

9 

21522 

88550 

14 

11450 

10073 

5 

89927 

28 

33 

59  36 

0  24 

78494 

9 

21506 

88577 

14 

11423 

10082 

5 

89918 

27 

34 

59  28 

0  32 

78510 

9 

21490 

88603 

15 

11397 

10092 

5 

89908 

26 
25 

35 

6  59  20 

5  0  40 

9. 78527 

10 

10.  21473 

9. 88629 

15 

10. 11371 

10. 10102 

6 

9. 89898 

36 

59  12 

0  48 

78543 

10 

21457 

88655 

16 

11345 

10112 

6 

89888 

24 

37 

59  4 

0  56 

78560 

10 

21440 

88681 

16 

11319 

10121 

6 

89879 

23 

38 

58  56 

1  4 

78576 

10 

21424 

88707 

17 

11293 

10131 

6 

89869 

22 

39 
40 

58  48 

1  12 

78592 

11 

21408 

88733 

17 

11267 

10141 

6 

89859 

21 

6  58  40 

5  1  20 

9. 78609 

11 

10.  21391 

9. 88759 

17 

10. 11241 

10. 10151 

6 

9. 89849 

20 

41 

58  32 

1  28 

78625 

11 

21375 

88786 

18 

11214 

10160 

7 

89840 

19 

42 

58  24 

1  36 

78642 

12 

21358 

88812 

18 

11188 

10170 

7 

89830 

18 

43 

58  16 

1  44 

78658 

12 

21342 

88838 

19 

11162 

10180 

7 

89820 

17 

44 

45 

58  8 

1  52 

78674 

12 

21326 

88864 

19 

11136 

10190 

7 

89810 
9. 89801 

16 
15 

6  58  0 

5  2  0 

9.  78691 

12 

10.  21309 

9. 88890 

20 

10. 11110 

10. 101y9 

7 

46 

57  52 

2  8 

78707 

13 

21293 

88916 

20 

11084 

10209 

7 

89791 

14 

47 

57  44 

2  16 

78723 

13 

21277 

88942 

20 

11058 

10219 

8 

89781 

13 

48 

57  36 

2  24 

78739 

13 

21261 

88968 

21 

11032 

10229 

8 

89771 

12 

49 

57  28 

2  32 

78756 

13 

21244 

88994 

21 

11006 

10239 

8 

89761 

11 

50 

6  57  20 

5  2  40 

9.  78772 

14 

10. 21228 

9. 89020 

22 

10. 10980 

10. 10248 

8 

9. 89752 

10 

51 

57  12 

2  48 

78788 

14 

21212 

89046 

22 

10954 

10258 

8 

89742 

9 

52 

57  4 

2  56 

78805 

14 

21195 

89073 

23 

10927 

10268 

8 

89732 

8 

53 

56  56 

3  4 

78821 

15 

21179 

89099 

23 

10901 

10278 

9 

89722 

7 

54 

56  48 

3  12 

78837 

15 

21163 

89125 

24 

10875 

10288 

9 

89712 

6 
5 

55 

6  56  40 

5  3  20 

9.  78853 

15 

10. 21147 

9. 89151 

24 

10. 10849 

10. 10298 

9 

9. 89702 

56 

56  32 

3  28 

78869 

15 

21131 

89177 

24 

10823 

10307 

9 

89693 

4 

57 

56  24 

3  36 

78886 

16 

21114 

89203 

25 

10797 

10317 

9 

89683 

3 

58 

56  16 

3  44 

78902 

16 

21098 

89229 

25 

10771 

10327 

9 

89673 

2 

59 

56  8 

3  52 

78918 

16 

21082 

89255 

26 

10745 

10337 

10 

89663 

1 

60 
M. 

56  0 

4  0 

78934 

16 

21066 

89281 

26 

10719 

10347 

10 

89653 

0 
M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

127° 

A 

A 

B 

B 

C 

C     52°  1 

Seconds  of  time 

!• 

2- 

S- 

4" 

6' 

6" 

7» 

(A 
Prop,  parts  of  cols.^B 

Ic 

2 
3 

1 

4 
7 

t 

6 
10 
4 

8 
13 
6 

10 
16 
6 

12 

20 

7 

14 

23 

8 

Page  810] 

TABLE  44. 

Log,  Sines,  Tangents,  and  Secants. 

88° 

A 

A 

B 

B 

C 

C    141° 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

DifE. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

6  66  0 

5  4  0 

9. 78934 

0 

10.  21066 

9. 89281 

0 

10. 10719 

10. 10347 

0 

9. 89653 

60 

1 

55  52 

4  8 

78950 

0 

21050 

89307 

0 

10693 

10357 

0 

89643 

59 

2 

55  44 

4  16 

78967 

1 

21033 

89333 

1 

10667 

10367 

0 

89633 

58 

3 

55  36 

4  24 

78983 

1 

21017 

89359 

1 

10641 

10376 

89624 

57 

4 

55  28 

4  32 

78999 

1 
1 

21001 

89385 

2 

10615 

10386 

89614 

56 
55 

5 

6  55  20 

5  4  40 

9.  79015 

10.  20985 

9. 89411 

2 

10. 10589 

10. 10396 

9. 89604 

6 

55  12 

4  48 

79031 

2 

20969 

89437 

3 

10563 

10406 

89594 

54 

7 

55  4 

4  56 

79047 

2 

20953 

89463 

3 

10537 

10416 

89584 

53 

8 

54  56 

5  4 

79063 

2 

20937 

89489 

3 

10511 

10426 

89574 

52 

9 

54  48 

5  12 

79079 

2 

20921 

89515 

4 

10485 

10436 

2 

89564 

51 
50 

10 

6  54  40 

5  5  20 

9. 79095 

3 

10. 20905 

9. 89541 

4 

10. 10459 

10. 10446 

2 

9. 89554 

11 

54  32 

5  28 

79111 

3 

20889 

89567 

5 

10433 

10456 

2 

89544 

49 

12 

54  24 

5  36 

79128 

3 

20872 

89593 

5 

10407 

10466 

2 

89534 

48 

13 

54  16 

5  44 

79144 

3 

20856 

89619 

6 

10381 

10476 

2 

89524 

47 

14 

54  8 

5  52 

79160 

4 

20840 

89645 

6 

10355 

10486 

2 

89514 

46 
45 

15 

6  54  0 

5  6  0 

9. 79176 

4 

10. 20824 

9.  89671 

6 

10. 10329 

10. 10496 

3 

9.  89504 

16 

53  52 

6  8 

79192 

4 

20808 

89697 

7 

10303 

10505 

3 

89495 

44 

17 

53  44 

6  16 

79208 

5 

20792 

89723 

7 

10277 

10515 

3 

89485 

43 

18 

53  36 

6  24 

79224 

5 

20776 

89749 

8 

10251 

10525 

3 

89475 

42 

19 

53  28 

6  32 

79240 

5 

20760 

89775 

8 

10225 

10535 

3 

89465 

41 

20 

6  53  20 

5  6  40 

9. 79256 

5 

10.  20744 

9.  89801 

9 

10. 10199 

10. 10545 

3 

9. 89455 

40 

21 

53  12 

6  48 

79272 

6 

20728 

89827 

9 

10173 

10555 

4 

89445 

39 

22 

53  4 

6  56 

79288 

6 

20712 

89853 

10 

10147 

10565 

4 

89435 

38 

23 

52  56 

7  4 

79304 

6 

20696 

89879 

10 

10121 

10575 

4 

89425 

37 

24 

52  48 

7  12 

79319 

6 

7 

20681 
10. 20665 

89905 

10 

10095 

10585 

4 

89415 

36 

25 

6  52  40 

5  7  20 

9.  79335 

9. 89931 

11 

10. 10069 

10. 10595 

4 

9. 89405 

35 

26 

52  32 

7  28 

79351 

7 

20649 

89957 

11 

10043 

10605 

4 

89395 

34 

27 

52  24 

7  36 

79367 

7 

20633 

89983 

12 

10017 

10615 

5 

89385 

33 

28 

52  16 

7  44 

79383 

7 

20617 

90009 

12 

09991 

10625 

5 

89375 

32 

29 

52  8 

7  52 

79399 

8 

20601 

90035 

13 

09965 

10636 

5 

89364 

31 

30 

6  52  0 

5  8  0 

9.  79415 

8 

10. 20585 

9. 90061 

13 

10. 09939 

10. 10646 

5 

9. 89354 

30 

31 

51  52 

8  8 

79431 

8 

20569 

90086 

13 

.  09914 

10656 

5 

89344 

29 

32 

51  44 

8  16 

79447 

8 

20553 

90112 

14 

09888 

10666 

5 

89334 

28 

33 

51  36 

8  24 

79463 

9 

20537 

90138 

14 

09862 

10676 

6 

89324 

27 

34 

51  28 

8  32 

79478 

9 

20522 

90164 

15 

09836 

10686 

6 

89314 

26 

35 

6  51  20 

5  8  40 

9. 79494 

9 

10. 20506 

9. 90190 

15 

10.  09810 

10. 10696 

6 

9. 89304 

25 

36 

51  12 

8  48 

79510 

10 

.  20490 

90216 

16 

09784 

10706 

6 

89294 

24 

37 

51  4 

8  56 

79526 

10 

20474 

90242 

16 

09758 

10716 

6 

89284 

23 

38 

50  56 

9  4 

79542 

10 

20458 

90268 

16 

09732 

10726 

6 

89274 

22 

39 

50  48 

9  12 

79558 

10 

20442 

90294 

17 

09706 

10736 

7 

89264 

21 

40 

6  50  40 

5  9  20 

9. 79573 

11 

10. 20427 

9. 90320 

17 

10. 09680 

10. 10746 

7 

9. 89254 

20 

41 

50  32 

9  28 

79589 

11 

20411 

90346 

18 

09654 

10756 

7 

89244 

19 

42 

50  24 

9  36 

79605 

11 

20395 

90371 

18 

09629 

10767 

7 

89233 

18 

43 

50  16 

9  44 

79621 

11 

20379 

90397 

19 

09603 

10777 

7 

89223 

17 

44 

50  8 

9  52 

79636 

12 

20364 

90423 

.19 

09577 

10787 

7 

89213 

16 
15 

45 

6  50  0 

6  10  0 

9. 79652 

12 

10.  20348 

9. 90449 

19 

10. 09551 

10. 10797 

8 

9. 89203 

46 

49  52 

10  8 

79668 

12 

20332 

90475 

20 

09525 

10807 

8 

89193 

14 

47 

49  44 

10  16 

79684 

12 

20316 

90501 

20 

09499 

10817 

8 

89183 

13 

48 

49  36 

10  24 

79699 

13 

20301 

90527 

21 

09473 

10827 

8 

89173 

12 

49 

49  28 

10  32 

79715 

13 

20285 

90553 

21 

09447 

10838 

8 

89162 

11 

50 

6  49  20 

5  10  40 

9. 79731 

13 

10.  20269 

9. 90578 

22 

10. 09422 

10. 10848 

8 

9. 89152 

10 

51 

49  12 

10  48 

79746 

14 

20254 

90604 

22 

09396 

10858 

9 

89142 

9 

52 

49  4 

10  56 

79762 

14 

20238 

90630 

22 

09370 

10868 

9 

89132 

8 

53 

48  56 

11  4 

79778 

14 

20222 

90656 

23 

09344 

10878 

9 

89122 

7 

54 

48  48 

11  12 

79793 

14 

20207 

90682 

23 

09318 

10888 

9 

89112 

6 
5 

55 

6  48  40 

5  11  20 

9. 79809 

15 

10.  20191 

9. 90708 

24 

10.  09292 

10. 10899 

9 

9. 89101 

56 

48  32. 

11  28 

79825 

15 

20175 

90734 

24 

09266 

10909 

9 

89091 

4 

57 

48  24 

11  36 

79840 

15 

20160 

90759 

25 

09241 

10919 

10 

89081 

3 

58 

48  16 

11  44 

79856 

15 

20144 

90785 

25 

09215 

10929 

10 

89071 

2 

59 

48  8 

11  52 

79872 

16 

20128 

90811 

26 

09189 

10940 

10 

89060 

1 

60 

48  0 

12  0 

79887 

16 

20113 

90837 

26 

09163 

10950 

10 

89050 

0 

M.  1  Hour  P.M. 

Hour  A.  M. 

Cosine. 

Biff. 

Secant. 

Cotangent. 

Die. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

128° 

A 

A 

B 

B 

C 

C    61°  1 

Seconds  of  time 

!■ 

2* 

8> 

4- 

6* 

6* 

7« 

A 
Prop,  parts  of  cols.'jB 

2 
3 
1 

4 
6 
3 

6 
10 
4 

8 

13 

6 

10 
16 
6 

12 

19 

8 

14 

23 

9 

r 

TABLE  44. 

[Page  811 

Log. 

Sines,  Tangents,  and  Secants. 

80° 

JL 

A 

B           B 

C 

C    140° 

M. 

Hour  X.  H. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  48  0 

5  12  0 

9.  79887 

0 

10.  20113 

9. 90837 

0 

10. 09163 

10. 10950 

0 

9.89050 

60 

1 

47  52 

12  8 

79903 

0 

20097 

90863 

0 

09137 

10960 

0 

89040 

59 

2 

47  44 

12  16 

79918 

1 

20082 

90889 

1 

09111 

10970 

0 

89030 

58 

3 

47  36 

12  24 

79934 

1 

20066 

90914 

1 

09086 

10980 

89020 

57 

4 
5 

47  28 
6  47  20 

12  32 
5  12  40 

79950 

1 

20050 
10. 20035 

90940 
"9. 90966 

2 

09060 

10991 

89009 

56 

9. 79965 

1 

2 

10. 09034 

10. 11001 

9. 88999 

55 

6 

47  12 

12  48 

79981 

2 

20019 

90992 

3 

09008 

11011 

88989 

54 

7 

47  4 

12  56 

79996 

2 

20004 

91018 

3 

08982 

11022 

88978 

53 

8 

46  56 

13  4 

80012 

2 

19988 

91043 

3 

08957 

11032 

88968 

52 

9 

46  48 

13  12 

80027 

2 

19973 

91069 

4 

08931 

11042 

2 

88958 

51 
50 

10 

6  46  40 

5  13  20 

9. 80043 

3 

10. 19957 

9. 91095 

4 

10. 08905 

10. 11052 

2 

9. 88948 

11 

46  32 

13  28 

80058 

3 

19942 

91121 

5 

08879 

11063 

2 

88937 

49 

12 

46  24 

13  36 

80074 

3 

19926 

91147 

5 

08853 

11073 

2 

88927 

48 

13 

46  16 

13  44 

80089 

3 

19911 

91172 

6 

08828 

11083 

2 

88917 

47 

14 

46  8 

13  52 
5  14  0 

80105 

4 

19895 

91198 

6 

08802 

11094 

2 

88906 

46 
45 

15 

6  46  0 

9. 80120 

4 

10. 19880 

9. 91224 

6 

10. 08776 

10. 11104 

3 

9. 88896 

16 

45  52 

14  8 

80136 

4 

19864 

91250 

7 

08750 

11114 

3 

88886 

44 

17 

45  44 

14  16 

80151 

4 

19849 

91276 

7 

08724 

11125 

3 

88875 

43 

18 

45  36 

14  24 

80166 

5 

19834 

91301 

8 

08699 

11135 

3 

88865 

42 

19 

45  28 

14  32 

80182 
9. 80197 

5 

19818 

91327 

8 

08673 

11145 

3 

88855 

41 

20 

6  45  20 

5  14  40 

5 

10. 19803 

9. 91353 

9 

10. 08647 

10. 11156 

3 

9.88844 

40 

21 

45  12 

14  48 

80213 

5 

19787 

91379 

9 

08621 

11166 

4 

88834 

39 

22 

45  4 

14  56 

80228 

6 

19772 

91404 

9 

08596 

11176 

4 

88824 

38 

23 

44  56 

15  4 

80244 

6 

19756 

91430 

10 

08570 

11187 

4 

88813 

37 

24 
25 

44  48 

15  12 

80259 

6 

19741 

91456 

10 

08544 

11197 

4 
4 

88803 
9. 88793 

36 
35 

6  44  40 

5  15  20 

9.  80274 

6 

10. 19726 

9. 91482 

11 

10. 08518 

10. 11207 

26 

44  32 

15  28 

80290 

7 

19710 

91507 

11 

08493 

11218 

5 

88782 

34 

27 

44  24 

15  36 

80305 

7 

19695 

91533 

12 

08467 

11228 

5 

88772 

33 

28 

44  16 

15  44 

80320 

7 

19680 

91559 

12 

08441 

11239 

6 

88761 

32 

29 

44  8 

15  52 

80336 

7 

19664 

91585 

12 
13 

08415 

11249 

5 

88751 

31 

30 

6  44  0 

5  16  0 

9. 80351 

8 

10. 19649 

9.  91610 

10. 08390 

10. 11259 

5 

9. 88741 

30 

31 

43  52 

16  8 

80366 

8 

19634 

91636 

13 

08364 

11270 

6 

88730 

29 

32 

43  44 

16  16 

80382 

8 

19618 

91662 

14 

08338 

11280 

6 

88720 

28 

33 

43  36 

16  24 

80397 

8 

19603 

91688 

14 

08312 

11291 

6 

88709 

27 

34 

43  28 

16  32 

80412 
9.80428 

9 

19588 

91713 

15 

08287 

11301 

6 

88699 

26 
25 

35 

6  43  20 

5  16  40 

9 

10. 19572 

9. 91739 

15 

10. 08261 

10. 11312 

6 

9. 88688 

36 

43  12 

16  48 

80443 

9 

19557 

91765 

15 

08235 

11322 

6 

88678 

24 

37 

43  4 

16  56 

80458 

9 

19542 

91791 

16 

08209 

11332 

6 

88668 

23 

38 

42  56 

17  4 

80473 

10 

19527 

91816 

16 

08184 

11343 

7 

88657 

22 

39 
40 

42  48 

17  12 

80489 

10 
10 

19511 

91842 
9. 91868 

17 

08158 

11353 

7 

88647 

21 

6  42  40 

5  17  20 

9. 80504 

10. 19496 

17 

10. 08132 

10. 11364 

7 

9. 88636 

20 

41 

42  32 

17  28 

80519 

10 

19481 

91893 

18 

08107 

11374 

7 

88626 

19 

42 

42  24 

17  36 

80534 

11 

. 19466 

91919 

18 

08081 

11385 

7 

88615 

18 

43 

42  16 

17  44 

80550 

11 

19450 

91945 

18 

08055 

11395 

7 

88605 

17 

44 
45 

42  8 

17  52 

80565 
9.80580 

11 
12 

19435 

91971 

19 

08029 

11406 

8 

88594 

16 
15 

6  42  0 

5  18  0 

10. 19420 

9. 91996 

19 

10. 08004 

10. 11416 

8 

9. 88584 

46 

41  52 

18  8 

80595 

12 

19405 

92022 

20 

07978 

11427 

8 

88573 

14 

47 

41  44 

18  16 

80610 

12 

19390 

92048 

20 

07952 

11437 

8 

88563 

13 

48 

41  36 

18  24 

80625 

12 

19375 

92073 

21 

07927 

11448 

8 

88552 

12 

49 
50 

41  28 

18  32 
5  18  40 

80641 

13 

19359 

92099 

21 

07901 

11458 

9 

88542 

11 
10 

6  41  20 

9. 80656 

13 

10. 19344 

9. 92125 

21 

10. 07875 

10. 11469 

9 

9. 88531 

51 

41  12 

18  48 

80671 

13 

19329 

92150 

22 

07850 

11479 

9 

88521 

9 

52 

41  4 

18  56 

80686 

13 

19314 

92176 

22 

07824 

11490 

9 

88510 

8 

53 

40  56 

19  4 

80701 

14 

19299 

92202 

23 

07798 

11501 

9 

88499 

7 

54 

40  48 

19  12 

80716 

14 

19284 

92227 

23 

07773 

11511 

9 

88489 

6 
5 

55 

6  40  40 

5  19  20 

9. 80731 

14 

10. 19269 

9. 92253 

24 

10. 07747 

10. 11522 

10 

9. 88478 

56 

40  32 

19  28 

80746 

14 

19254 

92279 

24 

07721 

11532 

10 

88468 

4 

57 

40  24 

19  36 

80762 

15 

19238 

92304 

24 

07696 

11543 

10 

88457 

3 

58 

40  16 

19  44 

80777 

15 

19223 

92330 

25 

07670 

11553 

10 

88447 

2 

59 

40  8 

19  52 

80792 

15 

19208 

92356 

25 

07644 

11564 

10 

88436 

1 

60 

40  0 

20  0 

80807 

15 

19193 

92381 

26 

07619 

11675 

10 

88425 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

129° 

A 

A 

B           B 

C 

C    50°  1 

Seconds  of  time 

1» 

2" 

&' 

4> 

6> 

6- 

7- 

fA 

Prop,  parts  of  cols.'jB 

Ic 

2 
3 

1 

4 
6 
3 

6 
10 
4 

8 
13 
6 

10 
16 

7 

12 
19 

8 

13 

23 

9 

21594°— 14- 


-44 


Page  812] 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

40° 

A 

. 

A 

B 

B 

C 

C    189° 

M. 

Honr  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

DiflE. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  40  0 

6  20  0 

9. 80807 

0 

10. 19193 

9. 92381 

0 

10. 07619 

10. 11575 

0 

9.  88425 

60 

1 

39  52 

20  8 

80822 

0 

19178 

92407 

0 

07593 

11585 

0 

88415 

59 

2 

39  44 

20  16 

80837 

0 

19163 

92433 

1 

07567 

11596 

0 

88404 

58 

3 

39  36 

20  24 

80852 

1 

19148 

92458 

1 

07542 

11606 

88394 

57 

4 

39  28 

20  32 

80867 

1 

19133 

92484 

2 

07516 

11617 

88383 

56 

5 

6  39  20 

5  20  40 

9. 80882 

1 

10. 19118 

9. 92510 

2 

10. 07490 

10. 11628 

9. 88372 

55 

6 

39  12 

20  48 

80897 

1 

19103 

92535 

3 

07465 

11638 

88362 

54 

7 

39  4 

20  56 

80912 

2 

19088 

92561 

3 

07439 

11649 

88351 

53 

8 

38  56 

21  4 

80927 

2 

19073 

92587 

3 

07413 

11660 

88340 

52 

9 

38  48 

21  12 

80942 

2 

19058 

92612 

4 

07388 

11670 

2 

88330 

51 

10 

6  38  40 

5  21  20 

9. 80957 

2 

10. 19043 

9. 92638 

4 

10. 07362 

10. 11681 

2 

9. 88319 

50 

11 

38  32 

21  28 

80972 

3 

19028 

92663 

5 

07337 

11692 

2 

88308 

49 

12 

38  24 

21  36 

80987 

3 

19013 

92689 

5 

07311 

11702 

2 

88298 

48 

13 

38  16 

21  44 

81002 

3 

18998 

92715 

6 

07285 

11713 

2 

88287 

47 

14 

38  8 

21  62 

81017 

3 

18983 

92740 

6 

07260 

11724 

3 

88276 

46 

15 

6  38  0 

5  22  0 

9. 81032 

4 

10. 18968 

9. 92766 

6 

10. 07234 

10. 11734 

3 

9.  88266 

45 

16 

37  52 

22  8 

81047 

4 

18953 

92792 

7 

07208 

11745 

3 

88255 

44 

17 

37  44 

22  16 

81061 

4 

18939 

92817 

7 

07183 

11756 

3 

88244 

43 

18 

37  36 

22  24 

81076 

4 

18924 

92843 

8 

07157 

11766 

3 

88234 

42 

19 

37  28 

22  32 

81091 

5 

18909 

92868 

8 

07132 

11777 

3 

88223 

41 

20 

6  37  20 

5  22  40 

9.  81106 

5 

10. 18894 

9. 92894 

9 

10. 07106 

10. 11788 

4 

9. 88212 

40 

21 

37  12 

22  48 

81121 

5 

18879 

92920 

9 

07080 

11799 

4 

88201 

39 

22 

37  4 

22  56 

81136 

6 

18864 

92945 

9 

07055 

11809 

4 

88191 

38 

23 

36  56 

23  4 

81151 

6 

18849 

92971 

10 

07029 

11820 

4 

88180 

37 

24 

36  48 

23  12 

81166 

6 

18834 

92996 

10 

07004 

11831 

4 

88169 

36 

25 

6  36  40 

5  23  20 

9. 81180 

6 

10. 18820 

9. 93022 

11 

10. 06978 

10. 11842 

4 

9. 88158 

35 

26 

36  32 

23  28 

81195 

6 

18805 

93048 

11 

06952 

11852 

5 

88148 

34 

27 

36  24 

23  36 

81210 

7 

18790 

93073 

12 

06927 

11863 

5 

88137 

33 

28 

36  16 

23  44 

81225 

7 

18775 

93099 

12 

06901 

11874 

5 

88126 

32 

29 

36  8 

23  52 

81240 

7 

18760 

93124 

12 

06876 

11885 

5 

88115 

31 

30 

6  36  0 

5  24  0 

9. 81254 

7 

10. 18746 

9. 93150 

13 

10. 06850 

10. 11895 

5 

9. 88105 

30 

31 

35  52 

24  8 

81269 

8 

18731 

93175 

13 

06825 

11906 

6 

88094 

29 

32 

35  44 

24  16 

81284 

8 

18716 

93201 

14 

06799 

11917 

6 

88083 

28 

33 

35  36 

24  24 

81299 

8 

18701 

93227 

14 

06773 

11928 

6 

88072 

27 

34 

35  28 

24  32 

81314 

8 

18686 

93252 

14 

06748 

11939 

6 

88061 

26 
25 

35 

6  35  20 

5  24  40 

9. 81328 

9 

10. 18672 

9. 93278 

15 

10. 06722 

10. 11949 

6 

9.88051 

36 

35  12 

24  48 

81343 

9 

18657 

93303 

15 

06697 

11960 

6 

88040 

24 

37 

35  4 

24  56 

81358 

9 

18642 

93329 

16 

06671 

11971 

7 

88029 

23 

38 

34  56 

25  4 

81372 

9 

18628 

93354 

16 

06646 

11982 

7 

88018 

22 

39 
40 

34  48 

25  12 

81387 

10 

18613 

93380 

17 

06620 

11993 

7 

88007 

21 

6  34  40 

5  25  20 

9. 81402 

10 

10. 18598 

9. 93406 

17 

10. 06594 

10. 12004 

7 

9. 87996 

20 

41 

34  32 

25  28 

81417 

10 

18583 

93431 

17 

06569 

12015 

7 

87985 

19 

42 

34  24 

25  36 

81431 

10 

18569 

93457 

18 

06543 

12025 

8 

87975 

18 

43 

34  16 

25  44 

81446 

11 

18554 

93482 

18 

06518 

12036 

8 

87964 

17 

44 

34  8 

25  52 

81461 

11 

18539 

93508 

19 

06492 

12047 

8 

87953 

16 

45 

6  34  0 

5  26  0 

9. 81475 

11 

10. 18525 

9. 93533 

19 

10. 06467 

10. 12058 

8 

9. 87942 

15 

46 

33  52 

26  8 

81490 

11 

18510 

93559 

20 

06441 

12069 

8 

87931 

14 

47 

33  44 

26  16 

81505 

12 

18495 

93584 

20 

06416 

12080 

8 

87920 

13 

48 

33  36 

26  24 

81519 

12 

18481 

93610 

20 

06390 

12091 

9 

87909 

12 

49 

33  28 

26  32 

81534 

12 

18466 

93636 

21 

06364 

12102 

9 

87898 
9. 87887 

11 
10 

50 

6  33  20 

5  26  40 

9. 81549 

12 

10. 18451 

9. 93661 

21 

10.  06339 

10. 12113 

9 

51 

33  12 

26  48 

81563 

13 

18437 

93687 

22 

06313 

12123 

9 

87877 

9 

52 

33  4 

26  56 

81578 

13 

18422 

93712 

22 

06288 

12134 

9 

87866 

8 

53 

32  56 

27  4 

81592 

13 

18408 

93738 

23 

06262 

12145 

10 

87855 

7 

54 

32  48 

27  12 

81607 

13 

18393 

93763 

23 

06237 

12156 

10 

87844 

6 

55 

6  32  40 

5  27  20 

9. 81622 

14 

10. 18378 

9. 93789 

23 

10. 06211 

10. 12167 

10 

9. 87833 

5 

56 

32  32 

27  28 

81636 

14 

18364 

93814 

24 

06186 

12178 

10 

87822 

4 

57 

32  24 

27  36 

81651 

14 

18349 

93840 

24 

06160 

12189 

10 

87811 

3 

58 

32  16 

27  44 

81665 

14 

18335 

93865 

25 

06135 

12200 

10 

87800 

2 

59 

32  8 

27  52 

81680 

15 

18320 

93891 

25 

06109 

12211 

11 

87789 

1 

60 

32  0 

28  0 

81694 

15 

18306 

93916 

26 

06084 

12222 

11 

87778 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

DiflE. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

DiS. 

Sine. 

M. 

180^ 

A 

A 

B 

B 

C 

C    49°  1 

Seconds  of  time 

1« 

2« 

8*    4< 

6*  1  6> 

1 

1 ' 

A 

Prop,  parts  of  cols.  B 

C 

2 
8 

1 

4 
6 
3 

6    7 
10    13 
4    6 

9 

16 

7 

11 
19 
8 

13 

22 

9 

TABLE  44. 

[Page  813 

Log. 

Sines,  Tangents,  and  Secants. 

il° 

A 

A 

B 

B 

C 

C    1880 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

6  32  0 

5  28  0 

9.  81694 

0 

10. 18306 

9.  93916 

0 

10.06084 

10. 12222 

0 

9.  87778 

,60 

1 

31  52 

28  8 

81709 

0 

18291 

93942 

0 

06058 

12233 

0 

87767 

69 

2 

31  44 

28  16 

81723 

0 

18277 

93967 

1 

06033 

12244 

0 

87756 

58 

3 

31  36 

28  24 

81738 

1 

18262 

93993 

1 

06007 

12256 

87746 

57 

4 

31  28 

28  32 

81752 

1 

18248 

94018 

2 

05982 

12266 

87734 

56 
55 

5 

6  31  20 

5  28  40 

9. 81767 

1 

10. 18233 

9.94044 

2 

10. 05956 

10. 12277 

9. 87723 

6 

31  12 

28  48 

81781 

1 

18219 

94069 

3 

05931 

12288 

87712 

54 

7 

31  4 

28  56 

81796 

2 

18204 

94095 

3 

05905 

12299 

87701 

53 

8 

30  56 

29  4 

81810 

2 

18190 

94120 

3 

05880 

12310 

87690 

52 

9 
10 

30  48 

29  12 

81825 

2 

18175 

94146 

4 

05854 

12321 

2 

87679 

51 

6  30  40 

5  29  20 

9. 81839 

2 

lO:  18161 

9.94171 

4 

10. 05829 

10. 12332 

2 

9.  87668 

50 

11 

30  32 

29  28 

81854 

3 

18146 

94197 

5 

05803 

12343 

2 

87657 

49 

12 

30  24 

29  36 

81868 

3 

18132 

94222 

5 

06778 

12364 

2 

87646 

48 

13 

30  16 

29  44 

81882 

3 

18118 

94248 

6 

05762 

12366 

2 

87636 

47 

14 
15 

30  8 

29  52 

81897 

3 

18103 

94273 

6 

05727 

12376 

3 

87624 

46 
45 

6  30  0 

5  30  0 

9. 81911 

4 

10. 18089 

9. 94299 

6 

10. 05701 

10. 12387 

3 

9. 87613 

16 

29  52 

30  8 

81926 

4 

18074 

94324 

7 

05676 

12399 

3 

87601 

44 

17 

29  44 

30  16 

81940 

4 

18060 

94350 

7 

05650 

12410 

3 

87590 

43 

18 
19 
20 

29  36 

30  24 

81955 

4 

18045 

94375 

8 

05625 

12421 

3 

87679 

42 

29  28 

30  32 

81969 

5 

18031 

94401 

8 

06599 

12432 

87568 

41 
40 

6  29  20 

5  30  40 

9. 81983 

5 

10. 18017 

9.94426 

8 

10. 05574 

10. 12443 

9. 87557 

21 

29  12 

30  48 

81998 

5 

18002 

94452 

9 

06548 

12464 

87546 

39 

22 

29  4 

30  56 

82012 

5 

17988 

94477 

9 

05523 

12466 

87536 

38 

23 

28  56 

31  4 

82026 

6 

17974 

94503 

10 

06497 

12476 

87524 

37 

24 

28  48 

31  12 

82041 

6 

17959 

94528 

10 

05472 

12487 

87613 

36 
35 

25 

6  28  40 

6  31  20 

9. 82055 

6 

10. 17945 

9.94554 

11 

10.06446 

10. 12499 

5 

9.  87501 

26 

28  32 

31  28 

82069 

6 

17931 

94679 

11 

06421 

12510 

5 

87490 

34 

27 

28  24 

31  36 

82084 

6 

17916 

94604 

11 

05396 

12521 

5 

87479 

33 

28 

28  16 

31  44 

82098 

7 

17902 

94630 

12 

05370 

12532 

5 

87468 

32 

29 

28  8 

31  52 

82112 

7 

17888 

94655 

12 

05346 

12543 

5 

87457 

31 
30 

30 

6  28  0 

5  32  0 

9. 82126 

7 

10. 17874 

9. 94681 

13 

10. 05319 

10. 12554 

6 

9. 87446 

31 

27  52 

32  8 

82141 

7 

17859 

94706 

13 

05294 

12566 

6 

87434 

29 

32 

27  44 

32  16 

82155 

8 

17845 

94732 

14 

05268 

12577 

6 

87423 

28 

33 

27  36 

32  24 

82169 

8 

17831 

94757 

14 

05243 

12588 

6 

87412 

27 

34 
35 

27  28 

32  32 

82184 

8 

17816 

94783 

14 

05217 

12699 

6 

87401 

26 

6  27  20 

5  32  40 

9. 82198 

8 

10. 17802 

9. 94808 

15 

10. 05192 

10. 12610 

7 

9. 87390 

25 

36 

27  12 

32  48 

82212 

9 

17788 

94834 

15 

06166 

12622 

7 

87378 

24 

37 

27  4 

32  56 

82226 

9 

17774 

94859 

16 

05141 

12633 

7 

87367 

23 

38 

26  56 

33  4 

82240 

9 

17760 

94884 

16 

05116 

12644 

7 

87356 

22 

39 
40 

26  48 

33  12 

82255 

9 

17745 

94910 

17 

05090 

12655 

7 

87345 

21 
20 

6  26  40 

6  33  20 

9. 82269 

10 

10. 17731 

9. 94936 

17 

10. 05066 

10. 12666 

7 

9.  87334 

41 

26  32 

33  28 

82283 

10 

17717 

94961 

17 

05039 

12678 

8 

87322 

19 

42 

26  24 

33  36 

82297 

10 

17703 

94986 

18 

05014 

12689 

8 

87311 

18 

43 

26  16 

33  44 

82312 

10 

17689 

95012 

18 

04988 

12700 

8 

87300 

17 

44 
45 

26  8 

33  52 

82326 

10 

17674 

95037 

19 

04963 

12712 

8 

87288 

16 
15 

6  26  0 

5  34  0 

9. 82340 

11 

10. 17660 

9. 95062 

19 

10. 04938 

10. 12723 

8 

9. 87277 

46 

25  52 

34  8 

82354 

11 

17646 

95088 

20 

04912 

12734 

9 

87266 

14 

47 

25  44 

34  16 

82368 

11 

17632 

95113 

20 

04887 

12745 

9 

87255 

13 

48 

25  36 

34  24 

82382 

11 

17618 

95139 

20 

04861 

12757 

9 

87243 

12 

49 

25  28 

34  32 

82396 

12 

17604 

95164 

21 

04836 

12768 

9 

87232 

11 
10 

50 

6  25  20 

5  34  40 

9. 82410 

12 

10. 17590 

9. 95190 

21 

10. 04810 

10. 12779 

9 

9. 87221 

51 

25  12 

34  48 

82424 

12 

17576 

95215 

22 

04785 

12791 

10 

87209 

9 

52 

25  4 

34  56 

82439 

12 

17561 

95240 

22 

04760 

12802 

10 

87198 

8 

53 

24  56 

35  4 

82453 

13 

17547 

95266 

22 

04734 

12813 

10 

87187 

7 

54 

24  48 

35  12 

82467 

13 

17533 

95291 

23 

04709 

12825 

10 

87175 

6 

55 

6  24  40 

5  35  20 

9. 82481 

13 

10. 17519 

9. 95317 

23 

10. 04683 

10. 12836 

10 

9.  87164 

5 

56 

24  32 

35  28 

82495 

13 

17505 

95342 

24 

04658 

12847 

10 

87153 

4 

57 

24  24 

35  36 

82509 

14 

17491 

95368 

24 

04632 

12859 

11 

87141 

3 

58 

24  16 

35  44 

82523 

14 

17477 

95393 

25 

04607 

12870 

11 

87130 

2 

59 

24  8 

35  52 

82537 

14 

17463 

95418 

25 

04582 

12881 

11 

87119 

1 

60 
M. 

24  0 

36  0 

82551 

14 

17449 

95444 

25 

04556 

12893 

11 

87107 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

181° 

A 

A 

B 

B 

C 

C    48*1 

Seconds  of  time 

1" 

2" 

3- 

4' 

&• 

6> 

7« 

A 

Prop,  parts  of  cols.  B 

2 
3 

2 

4 

6 
8 

6 
10 

4 

7 

13 

6 

9 
16 
7 

11 
19 
8 

12 
22 
10 

Page  814] 

TABLE  44. 

Log. 

Bines,  Tangents,  and  Secants.                       j 

42° 

A 

A 

B 

B        C           C    187°  1 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

DifE. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  24  0 

5  36  0 

9. 82551 

0 

10. 17449 

9.  95444 

0 

10. 04566 

10. 12893 

0 

9.  87107 

60 

1 

23  52 

36  8 

82566 

0 

17435 

95469 

0 

04531 

12904 

0 

87096 

59 

2 

23  44 

36  16 

82579 

0 

17421 

95496 

1 

04505 

12915 

0 

87085 

58 

3 

23  36 

36  24 

82593 

1 

17407 

95520 

1 

04480 

12927 

87073 

57 

4 
5 

23  28 

36  32 

82607 

1 

17393 

95545 

2 

04455 

12938 

87062 
9. 87050 

56 
55 

6  23  20 

5  36  40 

9. 82621 

1 

10. 17379 

9. 95671 

2 

10. 04429 

10. 12960 

6 

23  12 

36  48 

82635 

1 

17366 

95696 

3 

04404 

12961 

87039 

54 

7 

23  4 

36  56 

82649 

2 

17351 

96622 

3 

04378 

12972 

87028 

53 

8 

22  56 

37  4 

82663 

2 

17337 

96647 

3 

04353 

12984 

2 

87016 

52 

9 

22  48 

37  12 

82677 

2 

17323 

96672 

4 

04328 

12995 

2 

87005 

51 
60 

10 

6  22  40 

5  37  20 

9. 82691 

2 

10. 17309 

9. 95698 

4 

10. 04302 

10. 13007 

2 

9. 86993 

11 

22  32 

37  28 

82705 

3 

17295 

95723 

5 

04277 

13018 

2 

86982 

49 

12 

22  24 

37  36 

82719 

3 

17281 

95748 

6 

04252 

13030 

2 

86970 

48 

13 

22  16 

37  44 

82733 

3 

17267 

96774 

5 

04226 

13041 

3 

86959 

47 

14 

22  8 

37  52 

82747 

3 

17263 

95799 

6 

04201 

13053 

3 
3 

86947 

46 

45 

15 

6  22  0 

5  38  0 

9. 82761 

3 

10. 17239 

9.  95825 

6 

10.  04175 

10. 13064 

9.  86936 

16 

21  52 

38  8 

82775 

4 

17226 

95850 

7 

04160 

13076 

3 

86924 

44 

17 

21  44 

38  16 

82788 

4 

17212 

95876 

7 

04125 

13087 

3 

86913 

43 

18 

21  36 

38  24 

82802 

4 

17198 

95901 

8 

04099 

13098 

3 

86902 

42 

19 
20 

21  28 

38  32 

82816 

4 

17184 

95926 

8 

04074 

13110 

4 

86890 

41 

6  21  20 

6  38  40 

9. 82830 

5 

10. 17170 

9. 95952 

8 

10. 04048 

10. 13121 

4 

9. 86879 

40 

21 

21  12 

38  48 

82844 

5 

17166 

95977 

9 

04023 

13133 

4 

86867 

39 

22 

21  4 

38  56 

82858 

5 

17142 

96002 

9 

03998 

13145 

4 

86855 

38 

23 

20  56 

39  4 

82872 

5 

17128 

96028 

10 

03972 

13156 

4 

86844 

37 

24 

20  48 

39  12 

82885 

6 

17115 

96063 

10 

03947 

13168 

6 

86832 

36 
35 

25 

6  20  40 

5  39  20 

9.  82899 

6 

10. 17101 

9. 96078 

11 

10. 03922 

10. 13179 

6 

9. 86821 

26 

20  32 

39  28 

82913 

6 

17087 

96104 

11 

03896 

13191 

5 

86809 

34 

27 

20  24 

39  36 

82927 

6 

17073 

96129 

11 

03871 

13202 

6 

86798 

33 

28 

20  16 

39  44 

82941 

6 

17069 

96155 

12 

03845 

13214 

6 

86786 

32 

29 
30 

20  8 

39  52 

82955 

7 

17046 
10. 17032 

96180 

12 

03820 

13225 

6 

86776 

31 
30 

6  20  0 

5  40  0 

9. 82968 

7 

9. 96205 

13 

10. 03795 

10. 13237 

6 

9. 86763 

31 

19  52 

40  8 

82982 

7 

17018 

96231 

13 

03769 

13248 

6 

86762 

29 

32 

19  44 

40  16 

82996 

7 

17004 

96266 

14 

03744 

13260 

6 

86740 

28 

33 

19  36 

40  24 

83010 

8 

16990 

96281 

14 

03719 

13272 

6 

86728 

27 

34 

19  28 

40  32 

83023 

8 

16977 

96307 

14 

03693 

13283 

7 

86717 

26 

36 

6  19  20 

5  40  40 

9. 83037 

8 

10. 16963 

9. 96332 

15 

10. 03668 

10. 13296 

7 

9. 86706 

25 

36 

19  12 

40  48 

83051 

8 

16949 

96357 

15 

03643 

13306 

7 

86694* 

24 

37 

19  4 

40  56 

83065 

8 

16936 

96383 

16 

03617 

13318 

7 

86682 

23 

38 

18  56 

41  4 

83078 

9 

16922 

96408 

16 

03592 

13330 

7 

86670 

22 

39 

18  48 

41  12 

83092 

9 

16908 

96433 

16 

03567 

13341 

8 

86659 

21 

40 

6  18  40 

6  41  20 

9. 83106 

9 

10. 16894 

9.96459 

17 

10. 03541 

10. 13353 

8 

9. 86647 

20 

41 

18  32 

41  28 

83120 

9 

16880 

96484 

17 

03616 

13366 

8 

86635 

19 

42 

18  24 

41  36 

83133 

10 

16867 

96610 

18 

03490 

13376 

8 

86624 

18 

43 

18  16 

41  44 

83147 

10 

16853 

96635 

18 

03466 

13388 

8 

86612 

17 

44 
45 

18  8 

41  52 

83161 

10 

16839 

96560 

19 

03440 

13400 

8 

86600 

16 
15 

6  18  0 

5  42  0 

9.83174 

10 

10. 16826 

9. 96686 

19 

10. 03414 

10. 13411 

9 

9.  86589 

46 

17  52 

42  8 

83188 

11 

16812 

96611 

19 

03389 

13423 

9 

86677 

14 

47 

17  44 

42  16 

83202 

11 

16798 

96636 

20 

03364 

13436 

9 

86665 

13 

48 

17  36 

42  24 

83215 

11 

16786 

96662 

20 

03338 

13446 

9 

86654 

12 

49 

17  28 

42  32 

83229 

11 

16771 

96687 

21 
21 

03313 

13458 

9 
10 

86542 

11 
10 

50 

6  17  20 

5  42  40 

9. 83242 

11 

10. 16758 

9.  96712 

10. 03288 

10. 13470 

9. 86530 

51 

17  12 

42  48 

83266 

12 

16744 

96738 

22 

03262 

13482 

10 

86618 

9 

52 

17  4 

42  56 

83270 

12 

16730 

96763 

22 

03237 

13493 

10 

86507 

8 

53 

16  56 

43  4 

83283 

12 

16717 

96788 

22 

03212 

13606 

10 

86495 

7 

54 

16  48 

43  12 

83297 

12 

16703 

96814 

23 

03186 

13617 

10 

86483 

6 

55 

6  16  40 

5  43  20 

9. 83310 

13 

10. 16690 

9. 96839 

23 

10.03161 

10. 13528 

11 

9. 86472 

5 

66 

16  32 

43  28 

83324 

13 

16676 

96864 

24 

03136 

13540 

11 

86460 

4 

57 

16  24 

43  36 

83338 

13 

16662 

96890 

24 

03110 

13552 

11 

86448 

3 

58 

16  16 

43  44 

83361 

13 

16649 

96915 

26 

03086 

13564 

11 

86436 

2 

59 

16  8 

43  52 

83365 

14 

16636 

96940 

25 

03060 

13575 

11 

86425 

1 

60 

16  0 

44  0 

83378 

14 

16622 

96966 

25 

03034 

13587 

12 

86413 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

DifE. 

Secant. 

Cotangent. 

Did. 

Tangent. 

Cosecant. 

Diff. 

Sine.    M.  | 

132 

0 

A 

A 

B 

B        C           C     4701 

Seconds  of  time 

1' 

2« 

3« 

4« 

6' 

9 
16 

7 

6" 

7» 

Prop,  parts  of  cols.  <  B 

ic 

2 
3 
1 

3 
6 
3 

6 
10 
4 

7 
13 
6 

10 
19 
9 

12 
22 
10 

TABLE  44. 

[Page  816 

Log. 

Sines,  Tangents,  and  Secants. 

4«o 

A 

A 

B 

B 

C 

C    186° 

M. 

Hour  A.  M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  16  0 

5  44  0 

9.  83378 

0 

10. 16622 

9. 96966 

0 

10.  03034 

10. 13587 

0 

9.  86413 

60 

1 

15  52 

44  8 

83392 

0 

16608 

96991 

0 

03009 

13599 

0 

86401 

59 

2 

15  44 

44  16 

83405 

0 

16595 

97016 

1 

02984 

13611 

0 

86389 

58 

3 

15  36 

44  24 

83419 

1 

16581 

97042 

1 

02958 

13623 

86377 

57 

4 

15  28 

44  32 

83432 

1 

16568 

97067 

2 

02933 

13634 

86366 
9.  86.354 

56 
55 

5 

6  15  20 

5  44  40 

9. 83446 

1 

10. 16554 

9. 97092 

2 

10. 02908 

10. 13646 

6 

15  12 

44  48 

83459 

1 

16541 

97118 

3 

02882 

13658 

86342 

54 

7 

15  4 

44  56 

83473 

2 

16527 

97143 

3 

02857 

13670 

86330 

53 

8 

14  56 

45  4 

83486 

2 

16514 

97168 

3 

02832 

13682 

2 

86318 

52 

9 

14  48 

45  12 

83500 

2 

16500 

97193 

4 

02807 

13694 

2 

86306 

51 
50 

10 

6  14  40 

5  45  20 

9. 83513 

2 

10. 16487 

9. 97219 

4 

10. 02781 

10. 13705 

2 

9. 86295 

11 

14  32 

45  28 

83527 

2 

16473 

97244 

5 

02756 

13717 

2 

86283 

49 

12 

14  24 

45  36 

83540 

3 

16460 

97269 

5 

02731 

13729 

2 

86271 

48 

13 

14  16 

45  44 

83554 

3 

16446 

97295 

o 

02705 

13741 

3 

86259 

47 

14 

14  8 

45  52 

83567 

3 

16433 

97320 

6 

02680 

13753 

3 

86247 

46 

15 

6  14  0 

6  46  0 

9. 83581 

3 

10. 16419 

9. 97345 

6 

10. 02655 

10. 13765 

3 

9.86235 

45 

16 

13  52 

46  8 

83594 

4 

16406 

97371 

7 

02629 

13777 

3 

86223 

44 

17 

13  44 

46  16 

83608 

4 

16392 

97396 

7 

02604 

13789 

3 

86211 

43 

18 

13  36 

46  24 

83621 

4 

16379 

97421 

8 

02579 

13800 

4 

86200 

42 

19 

13  28 

46  32 

83634 

4 

16366 

97447 

8 

02553 

13812 

4 

86188 

41 
40 

20 

6  13  20 

5  46  40 

9, 83648 

4 

10. 16352 

9. 97472 

8 

10. 02528 

10. 13824 

4 

9. 86176 

21 

13  12 

46  48 

83661 

5 

16339 

97497 

9 

02503 

13836 

4 

86164 

39 

22 

13  4 

46  56 

83674 

5 

16.326 

97523 

9 

02477 

.  13848 

4 

86152 

38 

23 

12  56 

47  4 

83688 

5 

16312 

97548 

10 

02452 

13860 

5 

86140 

37 

24 

12  48 

47  12 

83701 

5 

16299 

97573 

10 

02427 

13872 

5 

86128 

36 

25 

6  12  40 

5  47  20 

9. 83715 

6 

10. 16285 

9. 97598 

11 

10.  02402 

10. 13884 

5 

9.  86116 

35 

26 

12  32 

47  28 

83728 

6 

16272 

97624 

11 

02376 

13896 

5 

86104 

34 

27 

12  24 

47  36 

83741 

6 

16259 

97649 

11 

02351 

13908 

5 

86092 

33 

28 

12  16 

47  44 

83755 

6 

16245 

97674 

12 

02326 

13920 

6 

86080 

32 

29 

12  8 

47  52 

83768 

6 

16232 

97700 

12 

02300 

13932 

6 

86068 

31 
30 

30 

6  12  0 

5  48  0 

9. 83781 

7 

10. 16219 

9. 97725 

13 

10. 02275 

10. 13944 

6 

9. 86056 

31 

11  52 

48  8 

83795 

7 

16205 

97750 

13 

02250 

13956 

6 

86044 

29 

32 

11  44 

48  16 

83808 

7 

16192 

97776 

13 

02224 

13968 

6 

86032 

28 

33 

11  36 

48  24 

83821 

7 

16179 

97801 

14 

02199 

13980 

7 

86020 

27 

34 

11  28 

48  32 

83834 

8 

16166 

97826 

14 

02174 

13992 

7 

86008 

26 

35 

6  11  20 

5  48  40 

9. 83848 

8 

10. 16152 

9. 97851 

15 

10. 02149 

10.14004 

7 

9. 85996 

25 

36 

11  12 

48  48 

83861 

8 

16139 

97877 

15 

02123 

14016 

7 

85984 

24 

37 

11  4 

48  56 

83874 

8 

16126 

97902 

16 

02098 

14028 

7 

85972 

23 

38 

10  56 

49  4 

83887 

8 

16113 

97927 

16 

02073 

14040 

8 

85960 

22 

39 

10  48 

49  12 

83901 

9 

16099 

97953 

16 

02047 

14052 

8 

85948 

21 

40 

6  10  40 

5  49  20 

9. 83914 

9 

10. 16086 

9. 97978 

17 

10. 02022 

10. 14064 

8 

9. 85936 

20 

41 

10  32 

49  28 

83927 

9 

16073 

98003 

17 

01997 

14076 

8 

85924 

19 

42 

10  24 

49  36 

83940 

9 

16060 

98029 

18 

01971 

14088 

8 

8.5912 

18 

43 

10  16 

49  44 

83954 

10 

.  16046 

98054 

18 

01946 

14100 

9 

85900 

17 

44 

45 

10  8 

49  52 

83967 

10 

16033 

98079 

19 

01921 

14112 

9 

85888 

16 

6  10  0 

5  50  0 

9. 83980 

10 

10. 16020 

9. 98104 

19 

10. 01896 

10. 14124 

9 

9. 85876 

15 

46 

9  52 

50  8 

83993 

10 

16007 

98130 

19 

01870 

14136 

9 

85864 

14 

47 

9  44 

50  16 

84006 

10 

15994 

98155 

20 

01845 

14149 

9 

85851 

13 

48 

9  36 

50  24 

84020 

11 

15980 

98180 

20 

01820 

14161 

10 

85839 

12 

49 

9  28 

50  32 

84033 

11 

15967 

98206 

21 

01794 

14173 

10 

85827 

11 
10 

50 

6  9  20 

5  50  40 

9. 84046 

11 

10. 15954 

9. 98231 

21 

10. 01769 

10. 14185 

10 

9. 85815 

51 

9  12 

50  48 

84059 

11 

15941 

98256 

22 

01744 

14197 

10 

85803 

9 

52 

9  4 

50  56 

84072 

12 

15928 

98281 

22 

01719 

14209 

10 

85791 

8 

53 

8  56 

51  4 

84085 

12 

15915 

98307 

22 

01693 

14221 

11 

85779 

7 

54 

8  48 

51  12 

84098 

12 

15902 

98332 

23 

01668 

14234 

11 

85766 

6 

55 

6  8  40 

5  51  20 

9.84112 

12 

10. 15888 

9. 98357 

23 

10. 01643 

10. 14246 

11 

9.  85754 

5 

56 

8  32 

51  28 

84125 

12 

15875 

98383 

24 

01617 

14258 

11 

85742 

4 

57 

8  24 

51  36 

84138 

13 

15862 

98408 

24 

01592 

14270 

11 

85730 

3 

58 

8  16 

51  44 

84151 

13 

15849 

98433 

24 

01567 

14282 

12 

85718 

2 

59 

8  8 

51  52 

84164 

13 

15836 

98458 

25 

01542 

14294 

12 

85706 

1 

60 

8  0 

52  0 

84177 

13 

15823 

98484 

25 

01516 

14307 

12 

85693 

0 

M. 

Hour  p.  M. 

Hgur  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

188° 

A 

A 

B 

B 

C 

C     46°  1 

Seconds  of  time 

1> 

2"    3' 

4' 

fj» 

6» 

7' 

A 

Prop,  parts  of  cols.  B 

[0 

2 
3 
2 

3    5    7 
6    9    13 
3  i   6    6 

8 
16 

8 

10 
19 
9 

12 
22 
11 

Page  816] 

Log. 

TABLE  44. 

Sines,  Tangents,  and  Secanta 

440 

A 

A 

B           B 

C 

C    185° 

M. 

0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 
60 

6  8  0 

5  52  0 

9.  84177 

0 

10. 15823 

9. 98484 

0 

10. 01516 

10. 14307 

0 

9. 85693 

1 

7  52 

52  8 

84190 

0 

15810 

98509 

0 

01491 

14319 

0 

85681 

59 

2 

7  44 

52  16 

84203 

0 

15797 

98534 

1 

01466 

14331 

0 

85669 

58 

3 

7  36 

52  24 

84216 

1 

15784 

98560 

1 

01440 

14343 

85657 

57 

4 

7  28 

52  32 

84229 
9.  84242 

1 

15771 

98585 

2 

01415 

14355 

85645 

56 

5 

6  7  20 

5  52  40 

1 

10. 15758 

9. 98610 

2 

10. 01390 

10. 14368 

9. 85632 

55 

6 

7  12 

52  48 

84255 

1 

15745 

98635 

3 

01365 

14380 

85620 

54 

7 

7  4 

52  56 

84269 

2 

15731 

98661 

3 

01339 

14392 

85608 

53 

8 

6  56 

53  4 

84282 

2 

15718 

98686 

3 

01314 

14404 

2 

85596 

52 

9 

6  48 

53  12 

84295 

2 

15705 

98711 

4 

01289 

14417 

2 

85583 

51 

10 

6  6  40 

5  53  20 

9. 84308 

2 

10. 15692 

9. 98737 

4 

10. 01263 

10. 14429 

2 

9.  85571 

50 

11 

6  32 

53  28 

84321 

2 

15679 

98762 

5 

01238 

14441 

2 

85559 

49 

12 

6  24 

53  36 

84334 

3 

15666 

98787 

5 

01213 

14453 

2 

85547 

48 

13 

6  16 

53  44 

84347 

3 

15653 

98812 

5 

01188 

14466 

3 

85534 

47 

14 

6  8 

53  52 

84360 

3 

15640 

98838 

6 

01162 

14478 

3 

85522 

46 

15 

6  6  0 

5  54  0 

9.  84373 

3 

10. 15627 

9. 98863 

6 

10. 01137 

10. 14490 

3 

9. 85510 

45 

16 

5  52 

54  8 

84385 

3 

15615 

98888 

7 

01112 

14503 

3 

85497 

44 

17 

5  44 

54  16 

84398 

4 

15602 

98913 

7 

01087 

14515 

4 

85485 

43 

18 

5  36 

54  24 

84411 

4 

15589 

98939 

8 

01061 

14527 

4 

85473 

42 

19 

5  28 

54  32 

84424 

4 

15576 

98964 

8 

01036 

14540 

4 

85460 

41 
40 

20 

6  5  20 

5  54  40 

9.84437 

4 

10. 15563 

9. 98989 

8 

10. 01011 

10. 14552 

4 

9.  85448 

21 

5  12 

54  48 

84450 

5 

15550 

99015 

9 

00985 

14564 

4 

85436 

39 

22 

5  4 

54  56 

84463 

5 

15537 

99040 

9 

00960 

14577 

5 

85423 

38 

23 

4  56 

55  4 

84476 

5 

15524 

99065 

10 

00935 

14589 

5 

85411 

37 

24 

4  48 

55  12 

84489 

5 

15511 

99090 

10 

00910 

14601 

5 

85399 

36 

25 

6  4  40 

5  55  20 

9. 84502 

5 

10. 15498 

9.99116 

11 

10. 00884 

10. 14614 

5 

9. 85386 

35 

26 

4  32 

55  28 

84515 

6 

15485 

99141 

11 

00859 

14626 

5 

85374 

34 

27 

4  24 

55  36 

84528 

6 

15472 

99166 

11 

00834 

14639 

6 

85361 

33 

28 

4  16 

55  44 

84540 

6 

15460 

99191 

12 

00809 

14651 

6 

85349 

32 

29 

4  8 

55  52 

84553 

6 

15447 

99217 

12 

00783 

14663 

6 

85337 

31 
30 

30 

6  4  0 

5  56  0 

9. 84566 

6 

10. 15434 

9. 99242 

13 

10. 00758 

10. 14676 

6 

9. 85324 

31 

3  52 

56  8 

84579 

7 

15421 

99267 

13 

00733 

14688 

6 

85312 

29 

32 

3  44 

56  16 

84592 

7 

15408 

99293 

13 

00707 

14701 

7 

85299 

28 

33 

3  36 

56  24 

84605 

7 

15395 

99318 

14 

00682 

14713 

7 

85287 

27 

34 

3  28 

56  32 

84618 

7 

15382 

99343 

14 

00657 

14726 

7 

85274 

26 
25 

35 

6  3  20 

5  56  40 

9. 84630 

8 

10. 15370 

9. 99368 

15 

10.  00632 

10. 14738 

7 

9. 85262 

36 

3  12 

56  48 

84643 

8 

15357 

99394 

15 

00606 

14750 

7 

85250 

24 

37 

3  4 

56  56 

84656 

8 

15344 

99419 

16 

00581 

14763 

8 

85237 

23 

38 

2  56 

57  4 

84669 

8 

15331 

99444 

16 

00556 

14775 

8 

85225 

22 

39 

2  48 

57  12 

84682 

8 

15318 

99469 

16 

00531 

14788 

8 

85212 

21 
20 

40 

6  2  40 

5  57  20 

9. 84694 

9 

10. 15306 

9. 99495 

17 

10. 00505 

10. 14800 

8 

9.  85200 

41 

2  32 

57  28 

84707 

9 

15293 

99520 

17 

00480 

14813 

8 

85187 

19 

42 

2  24 

57  36 

84720 

9 

15280 

99545 

18 

00455 

14825 

9 

85175 

18 

43 

2  16 

57  44 

84733 

9 

15267 

99570 

18 

00430 

14838 

9 

85162 

17 

44 

2  8 

57  52 

84745 

9 

15255 

99596 

19 

00404 

14850 

9 

85150 

16 
15 

45 

6  2  0 

5  58  0 

9. 84758 

10 

10. 15242 

9. 99621 

19 

10. 00379 

10. 14863 

9 

9. 85137 

46 

1  52 

58  8 

84771 

10 

15229 

99646 

19 

00354 

14875 

10 

85125 

14 

47 

1  44 

58  16 

84784 

10 

15216 

99672 

20 

00328 

14888 

10 

85112 

13 

48 

1  36 

58  24 

84796 

10 

15204 

99697 

20 

00303 

14900 

10 

85100 

12 

49 

1  28 

58  32 

84809 

11 

15191 

99722 

21 
21 

00278 
10.  00253 

14913 

10 

85087 

11 
10 

50 

6  1  20 

5  58  40 

9. 84822 

11 

10. 15178 

9. 99747 

10. 14926 

10 

9. 85074 

51 

1  12 

58  48 

84835 

11 

15165 

99773 

21 

00227 

14938 

11 

85062 

9 

52 

1  4 

58  56 

84847 

11 

15153 

99798 

22 

00202 

14951 

11 

85049 

8 

53 

0  56 

59  4 

84860 

11 

15140 

99823 

22 

00177 

14963 

11 

85037 

7 

54 

0  48 

59  12 

84873 

12 

15127 

99848 

23 

00152 

14976 

11 

85024 

6 
5 

55 

6  0  40 

5  59  20 

9. 84885 

12 

10. 15115 

9. 99874 

23 

10. 00126 

10. 14988 

11 

9. 85012 

56 

0  32 

59  28 

84898 

12 

15102 

99899 

24 

00101 

15001 

12 

84999 

4 

57 

0  24 

59  36 

84911 

12 

15089 

99924 

24 

00076 

15014 

12 

84986 

3 

58 

0  16 

59  44 

84923 

12 

15077 

99949 

24 

00051 

15026 

12 

84974 

2 

59 

0  8 

69  52 

84936 

13 

15064 

99975 

25 

00025 

15039 

12 

84961 

1 

60 

0  0 

6  0  0 

84949 

13 

15051 

10.00000 

25 

00000 

15051 

12 

84949 

0 

M. 

Hour  p.  M. 

Hour  A.  H. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine. 

M. 

184° 

A 

A 

B           B 

C 

C     46°  1 

Seconds  of  time 

1" 

2' 

8< 

4- 

5" 

6" 

7» 

fA 
Prop,  parts  of  coIs.^B 

2 
3 
2 

3 
6 
3 

5 
0 
5 

6 
13 
6 

8 
16 
8 

10 
19 
9 

11 
22 
11 

TABLE  45.                  [Page  817 

Haversines. 

8  ' 

Oh  0»»  0°  O' 

Oh  2m  0°  3(K 

Oh  4m  1°  (K 

Oh  em  1°  30^ 

0h8m2°9^ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat  Hav. 

0      0 

-00 

0.00000 

5.27963 

0.00002 

5.88168 

0.00008 

6.23385 

0.00017 

6.48371 

0.00030 

60 

2 

1.72333 

.00000 

.29399 

.00002 

.88889 

.00008 

.23866 

.00017 

.48732 

.00031 

58 

4-\-  1 

2.32539 

.00000 

.30811 

.00002 

.89604 

.00008 

.24345 

.00018 

.49092 

.00031 

56 

6 

2.67757 

.00000 

.32201 

.00002 

.90313 

.00008 

.24821 

.00018 

.49450 

.00031 

54 

8+   2 

2.92745 

0.00000 

5.33569 

0.00002 

5.91016 

0.00008 

6.25294 

0.00018 

6.49807 

0.00031 

52 

10 

3.12127 

.00000 

.34916 

.00002 

.91714 

.00008 

.25765 

.00018 

.50162 

.00032 

50 

12+   3 

3.27963 

.00000 

.36242 

.00002 

.92406 

.00008 

.26233 

.00018 

.50516 

.00032 

48 

U 

3.41353 

.00000 

.37548 

.00002 

.93093 

.00009 

.26699 

.00018 

.50868 

.00032 

46 

16+   4 

3.52951 

0.00000 

5.38835 

0.00002 

5.93774 

0.00009 

6.27162 

0.00019 

6.51219 

0.00033 

44 

18 

3.63182 

.00000 

.40103 

.00003 

.94450 

.00009 

.27623 

.00019 

.51568 

.00033 

42 

20+   5 

3.72333 

.00000 

.41352 

.00003 

.95121 

.00009 

.28081 

.00019 

.51916 

.00033 

40 

22 

3.80612 

.00000 

.42585 

.00003 

.95786 

.00009 

.28537 

.00019 
0.00019 

.52263 

.00033 

38 

24+   6 

3.88169 

0.00000 

5.43799 

0.00003 

5.96447 

0.00009 

6.28991 

6.52608 

0.00034 

S6 

26 

3.95122 

.00000 

.44997 

.00003 

.97102 

.00009 

29442 

.00020 

.52952 

.00034 

S4 

28+   7 

4.01559 

.00000 

.46179 

.00003 

.97753 

.00010 

.29891 

.00020 

.53295 

.00034 

32 

SO 

4.07551 

.00000 

.47345 

.00003 

.98399 

.00010 

.30337 

.00020 

.53636 

.00034 

SO 

32+   8 

4.13157 

0.00000 

5.48496 

0.00003 

5.99040 

0.00010 

6.30781 

0.00020 

6.53976 

0.00035 

28 

54 

.18423 

.00000 

.49631 

.00003 

5.99676 

.00010 

.31223 

.00021 

.54315 

.00035 

26 

56+  9 

.23388 

.00000 

.50752 

.00003 

6.00308 

.00010 

.31663 

.00021 

.54652 

.00035 

24 

S8 

.28084 

.00000 

.51858 

.00003 

.00935 

.00010 

.32101 

.00021 
0.00021 

.54988 

.00035 
0.00036 

22 
20 

40+10 

4.32539 

0.00000 

5.52951 

0.00003 

6.01557 

0.00010 

6.32536 

6.55323 

42 

.36777 

.00000 

.54030 

.00003 

.02176 

.00011 

.32969 

.00021 

.55656 

.00036 

18 

44+n 

.40818 

.00000 

.55095 

.00004 

.02789 

.00011 

.33400 

.00022 

.55988 

.00036 

16 

46 

.44679 

.00000 

.56148 

.00004 

.03399 

.00011 

.33829 

.00022 

.56319 

.00037 

14 

48+n 

4.48375 

0.00000 

5.57189 

0.00004 

6.04004 

0.00011 

6.34256 

0.00022 

6.56649 

0.00037 

12 

50 

.51921 

.00000 

.58216 

.00004 

.04605 

.00011 

.34681 

.00022 

.56977 

.00037 

10 

52+13 

.55328 

.00000 

.59232 

.00004 

.05202 

.00011 

.35103 

.00022 

.57304 

.00037 

8 

54 

.58606 

.00000 

.60236 

.00004 
0.00004 

.05795 

.00011 
0.00012 

.35524 
6.35943" 

.00023 

.57630 
'6.57955 

.00038 

6 

66+U 

4.61765 

0.00000 

5.61229 

6.06384 

0.00023 

0.00038 

4 

58 

4.64813 

0.00000 

5.62211 

0.00004 

6.06969 

0.00012 

6.36359 

0.00023 

6.58278 

0.00038 

2 

2Sh  59m 

2Sh  57m 

2Sh  65m 

23h  53m 

2Sh  5im 

8   ' 
0+15 

Oh  im  0°  (/ 

Oh  Sm  0°  30^ 

Oh  5m  1°  r 

Oh  7m  1°  30/ 

Oh  gm  2°  O' 

s 
60 

4.67757 

0.00000 

5.63181 

0.00004 

6.07550 

0.00012 

6.36774 

0.00023 

6.58600 

0.00039 

2 

.70605 

.00000 

.64141 

.00004 

.08127 

.00012 

.37186 

.00024 

.58921 

.00039 

58 

4+16 

.73363 

.00001 

.65090 

.00004 

.08700 

.00012 

.37597 

.00024 

.59241 

.00039 

56 

6 

.76036 

.00001 

.66029 

.00005 

.09270 

.00012 

.38006 

.00024 

.59560 

.00039 

54 
52 

8+n 

4.78629 

0.00001 

5.66958 

0.00005 

6.09836 

0.00013 

6.38412 

0.00024 

6.59878 

0.00040 

10 

.81147 

.00001 

.67877 

.00005 

.10398 

.00013 

.38817 

.00024 

.60194 

.00040 

50 

12+l'i 

.83594 

.00001 

.68787 

.00005 

.10956 

.00013 

.39220 

.00025 

.60509 

.00040 

48 

14 

.85973 

.00001 

.69687 

.00005 

.11511 

.00013 

.39622 

.00025 

.60823 

.00041 

46 

16+19 

4.88290 

0.00001 

5.70578 

0.00005 

6.12063 

0.00013 

6.40021 

0.00025 

6.61136 

0.00041 

U 

18 

.90546 

.00001 

.71460 

.00005 

.12611 

.00013 

.40418 

.00025 

.61448 

.00041 

42 

20+%^ 

.92745 

.00001 

.72332 

.00005 

.13155 

.00014 

.40814 

.00026 

.61759 

.00041 

40 

22 

.94890 

.00001 

.73197 

.00005 

.13696 

.OOOUj 

.41208 

.00026 

.62068 

.00042 

S8 
36 

24+21 

4.96983 

0.00001 

5.74052 

0.00006 

6.14234 

0.00014 

6.41600 

0.00026 

6.62377 

0.00042 

26 

4.99027 

.00001 

.74900 

.00006 

.14769 

.00014 

.41990 

.00026 

.62684 

.00042 

S4 

28+22 

5.01024 

.00001 

.75739 

.00006 

.15300 

.00014 

.42379 

.00027 

.62991 

.00043 

32 

SO 

.02976 

.00001 

.76570 

.00006 

.15828 

.00014 

.42766 

.00027 

.63296 

.00043 

30 

S2+23 

5.04885 

0.00001 

5.77394 

0.00006 

6.16353 

0.00015 

6.43151 

0.00027 

6.63600 

0.00043 

28 

S4 

.06753 

.00001 

.78209 

.00006 

.16874 

.00015 

.43534 

.00027 

.63903 

.00044 

26 

56+24 

.08581 

.00001 

.79017 

.00006 

.17393 

.00015 

.43916 

.00027 

.64205 

.00044 

24 

S8 

.10372 

.00001 

.79818 

.00006 

.17908 

.00015 

.44296 

.00028 

.64504 

.00044 

22 

40+25 

5.12127 

0.00001 

5.80611 

0.00006 

6.18421 

0.00015 

6.44675 

0.00028 

6.64806 

0.00044 

20 

42 

.13847 

.00001 

.81397 

.00007 

.18930 

.00015 

.45052 

.00028 

.65105 

.00045 

18 

44+26 

.15534 

.00001 

.82176 

.00007 

.19437 

.00016 

.45427 

.00028 

.65403 

.00045 

16 

46 

.17188 

.00001 

.82948 

.00007 

.19940 

.00016 

.45800 

.00029 

.65700 

.00045 

14 

48+21 

5.18812 

0.00002 

5.83713 

0.00007 

6.20441 

0.00016 

6.46172 

0.00029 

6.65996 

0.00046 

12 

50 

.20406 

.00002 

.84472 

.00007 

.20938 

.00016 

.46543 

.00029 

.66291 

.00046 

10 

62+2S 

.21971 

.00002 

.85224 

.00007 

.21433 

.00016 

.46911 

.00029 

.66585 

.00046 

8 

54 

.23508 

.00002 

.85969 

.00007 

.21925 

.00017 

.47279 
6.47644 

.00030 
0.00030 

.66878 

.00047 

6 

4 

66+29 

5.25019 

0.00002 

5.86709 

0.00007 

6.22415 

0.00017 

6.67170 

0.00047 

68 

.26503 

.00002 

.87442 

.00008 

.22901 

.00017 

.48008 

.00030 

.67461 

.00047 

2 

60+30 

5.27963 

0.00002 

5.88168 

0.00008 

6.23385 

0.00017 

6.48371 

0.00030 

6.67751 

0.00048 

0 

2Sh  58m 

23h  56m 

2Sh  5pn 

23h  52m 

2Sh  50m 

Page  818]                 TABLE  45. 

Haversines. 

s 

OA  lOm  2°  30' 

Oh  12m.  30  (y 

Oh  14m  3°  30^ 

Oh  16m  4°  0' 

Oh  18m  4°  30' 

s 

Log.  Hav.  Xat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

6.67751 

0.00048 

6.83584 

0.00069 

6.96970 

0.00093 

7.08564 

0.00122 

7.18790 

0.00154 

60 

2 

.68040 

.00048 

.83825 

.00069 

.97176 

.00094 

.08745 

.00122 

.18950 

.00155 

58 

4+  1 

.68328 

.00048 

.84065 

.00069 

.97382 

.00094 

.08925 

.00123 

.19111 

.00155 

56 

6 

.68615 

.00049 

.84304 

.00070 

.97588 

.00095 

.09105 

.00123 

.19271 

.00156 

54 

8+  % 

6.68901 

0.00049 

6.84543 

0.00070 

6.97793 

0.00095 

7.09284 

0.00124 

7.19430 

0.00156 

52 

10 

.69186 

.00049 

.84782 

.00070 

.97997 

.00095 

.09464 

.00124 

.19590 

.00157 

50 

12+   3 

.69470 

.00050 

.85019 

.00071 

.98201 

.00096 

.09642 

.00125 

.19749 

.00158 

48 

14 

.69754 

.00050 

.85256 

.00071 

.98405 

.00096 

.09821 

.00125 

.19908 

.00158 

46 

16+  i 

6.70036 

0.00050 

6.85492 

0.00072 

6.98608 

0.00097 

7.09999 

0.00126 

7.20060 

0.00159 

44 

18 

.70318 

.00050 

.85728 

.00072 

.98811 

.00097 

.10177 

.00126 

.20225 

.00159 

42 

20+  5 

.70598 

.00051 

.85963 

.00072 

.99013 

.00098 

.10354 

.00127 

.20383 

.00160 

40 

22 

.70878 

.00051 

.86197 

.00073 

.99214 

.00098 

.10531 

.00127 

.20540 

.00160 

38 

24+  6 

6.71157 

0.00051 

6.86431 

0.00073 

6.99416 

0.00099 

7.10708 

0.00128 

7.20098 

0.00161 

36 

26 

.71435 

.00052 

.86664 

.00074 

6.99616 

.00099 

.10884 

.00128 

.20855 

.00162 

34 

28+   7 

.71712 

.00052 

.86897 

.00074 

6.99817 

.00100 

.11060 

.00129 

.21012 

.00163 

32 

SO 

.71988 

.00052 

.87129 

.00074 

7.00017 

.00100 

.11236 

.00130 

.21168 

.00163 

30 

S2+   8 

6.72263 

0.00053 

6.87360 

0.00075 

7.00216 

0.00101 

7.11411 

0.00130 

7.21325 

0.00163 

28 

S4 

.72537 

.00053 

.87591 

.00075 

.00415 

.00101 

.11586 

.00131 

.21481 

.00164 

26 

S6+  9 

.72811 

.00053 

.87821 

.00076 

.00613 

.00101 

.11760 

.00131 

.21636 

.00165 

24 

S8 

.73084 

.00054 

.88050 

.00076 

.00811 
7.01009 

.00102 

.11934 

.00132 

.21792 

.00165 

22 
20 

40+10 

6.73355 

0.00054 

6.88279 

0.00076 

0.00102 

7.12108 

0.00132 

7.21947 

0.00166 

42 

.73626 

.00054 

.88507 

.00077 

.01206 

.00103 

.12282 

.00133 

.22102 

.00166 

18 

u+ti 

.73896 

.00055 

.88735 

.00077 

.01403 

.00103 

.12455 

.00133 

.22256 

.00167 

16 

46 

.74166 

.00055 

.88962 

.00078 

.01599 

.00104 

.12627 

.00134 

.22411 

.00168 

14 

48+12 

6.74434 

0.00056 

6.89188 

0.00078 

7.01795 

0.00104 

7.12800 

0.00134 

7.22565 

0.00168 

12 

50 

.74702 

.00056 

.89414 

.00078 

.01990 

.00105 

.12972 

.00135 

.22718 

.00169 

10 

62+lS 

.74969 

.00056 

.89639 

.00079 

.02185 

.00105 

.13144 

.00135 

.22872 

.00169 

8 

54 

.75235 

.00057 

.89864 

.00079 
0.00080 

.02379 

.00106 

.13315 

.00136 

.23025 
7.23178 

.00170 

6 

4 

56 +U 

6.75500 

0.00057 

6.90088 

7.02573 

0.00106 

7.13486 

0.00136 

0.00171 

58 

6.75764 

0.00057 

6.90312 

0.00080 

7.02767 

0.00107 

7.13657 

0.00137 

7.23331 

0.00171 

2 

23  k  59m 

23  h  47m 

23h  45m 

23h  43m 

23h  41m 

a       ' 
0+15 

Oh  11m  3°  30^ 

Oh  ism  3°  0' 

Oft  15m  3°  30' 

Oh  17m  4°  0' 

Oh  19m  4°  30' 

s 
60 

6.76028 

0.00058 

6.90535 

0.00080 

7.02960 

0.00107 

7.13827 

0.00137 

7.23483 

0.00172 

2 

.76290 

.00058 

.90757 

.00081 

.03153 

.00108 

.13997 

.00138 

.23035 

.00173 

58 

•4+16 

.76552 

.00058 

.90979 

.00081 

.03345 

.00108 

.14167 

.00139 

.23787 

.00173 

56 

6 

.76814 

.00059 

.91200 

.00082 

.03537 

00108 

.14337 
7.14500 

.00139 

.23939 

.00174 

54 

8+Vi 

6.77074 

0.00059 

6.91421 

0.00082 

7.03729 

0.00109 

0.00140 

7.24090 

0.00174 

52 

10 

.77334 

.00059 

.91641 

.00082 

.03920 

.00109 

.14674 

.00140 

.24241 

.00175 

50 

12+\& 

.77592 

.00060 

.91860 

.00083 

.04110 

.00110 

.14843 

.00141 

.24392 

.00175 

48 

14 

.77851 

.00060 

.92079 

.00083 

.04300 

.00110 

.15011 

.00141 

.24543 

.00176 

46 

16+n 

6.78108 

0.00060 

6.92298 

0.00084 

7.04490 

0.00111 

7.15179 

0.00142 

7.24093 

0.00177 

44 

18 

.78364 

.00061 

.92516 

.00084 

.04680 

.00111 

.15346 

.00142 

.24843 

.00177 

42 

fO+20 

.78620 

.00061 

.92733 

.00085 

.04809 

.00112 

.15513 

.00143 

.24993 

.00178 

40 

22 

.78875 

.00061 

.92950 
6.93166 

.00085 

.05057 

.00112 
0.00113 

.15680 

.00143 

.25143 

.00178 

38 

24+21 

6.79129 

0.00062 

0.00085 

7.05245 

7.15846 

0.00144 

7.25292 

0.00179 

36 

26 

.79383 

.00062 

.93382 

.00086 

.05433 

.00113 

.16013 

.00145 

.25441 

.00180 

34 

28+22 

.79630 

.00063 

.93597 

.00086 

.05620 

.00114 

.16178 

.00145 

.25590 

.00180 

32 

30 

.79888 

.00063 

.93812 

.00087 

.05807 

.00114 

.16344 

.00146 

.25738 

.00181 

30 

32+2S 

6.80139 

0.00063 

6.94026 

0.00087 

7.05994 

0.00115 

7.16509 

0.00146 

7.25886 

0.00181 

28 

S4 

.80390 

.00064 

.94239 

.00088 

.06180 

.00115 

.16674 

.00147 

.26034 

.00182 

26 

S6+U 

.80640 

.00064 

.94453 

.00088 

.06366 

.00116 

.16839 

.00147 

.26182 

.00183 

24 

38 

.80889 

.00064 

.94665 

.00088 

.06551 

.00116 

.17003 

.00148 

.26330 

.00183 

22 
20 

40+25 

6.81137 

0.00065 

6.94877 

0.00089 

7.06736 

0.00117 

7.17167 

0.00148 

7.26477 

0.00184 

42 

.81385 

.00065 

.95089 

.00089 

.06920 

.00117 

.17331 

.00149 

.26624 

.00185 

18 

44+26 

.81632 

.00066 

.95300 

.00090 

.07105 

.00118 

.17494 

.00150 

.26771 

.00185 

16 

46 

.81879 

.00060 

.95510 

.00090 

.07288 

.00118 

.17657 

.00150 

.20917 

.00186 

14 

48+21 

6.82124 

0.00066 

6.95720 

0.00091 

7.07472 

0.00119 

7.17820 

0.00151 

7.27004 

0.00186 

12 

50 

.82369 

.00067 

.95930 

.00091 

.07655 

.00119 

.17982 

.00151 

.27210 

.00187 

10 

52+2S 

.82614 

.00067 

.96139 

.00091 

.07837 

.00120 

.18144 

.00152 

.27355 

.00188 

8 

54 

.82857 

.00067 

.90347 

.00092 
0.00092 

.08019 
7.08201 

.00120 

.18306 

.00152 
0.00153 

.27501 

.00188 

6 

56+29 

6.83100 

0.00068 

6.90555 

0.00121 

7.18468 

7.27046 

0.00189 

4 

58 

.83342 

.00068 

.60763 

.00093 

.08383 

.00121 

.18029 

.00154 

.27791 

.00190 

2 

60+30 

6.83584 

0.00069 

6.96970 

0.00093 

7.08504 

0.00122 

7.18790 

0.00154 

7.27936 

0.00190 

0 

23^48^ 

23)^  46 '« 

23h  44m 

2Sh 42m 

23h40m 

TABLE  45.                  [Page  819 

Haversines. 

s     ' 

OA  :20'»  5°  0' 

Oh  22^n  5°  30^ 

Oh  24"'  6°  0' 

Oh  26m  6°  30' 

Oh  28m  7°  (K 

s 

Log.  Ilav. 

Nat.  Hav. 

Log.  Ilav. 

Nat.  Ilav. 

Log.  Ilav. 

Nat.  Ilav. 

Log.  Ilav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0   0 

2 

4+   1 
6 

7.27936 
.28080 
.28225 
.28369 

0.00190 
.00191 
.00192 
.00192 

0.00193 
.00193 
.00194 
.00195 

0.00195 
.00196 
.00197 
.00197 

0.00198 
.00199 
.00199 
.00200 

0.00201 
.00201 
.00202 
.00203 

7.36209 
.36340 
.36471 
.36602 

7.36733 
.36864 
.36994 
.37124 

7.37254 
.37384 
.37514 
.37643 

7.37773 
.37902 
.38030 
.38159 

7.38288 
.38416 
.38544 
.38672 

7.38800 
.38927 
.39054 
.39182 

7.39309 
.39435 
.39562 
.39688 

0.00230 
.00231 
.00233 
.00333 

0.00233 
.00334 
.00334 
.00335 

0.00336 
.00237 
.00337 
.00338 

0.00339 
.00239 
.00240 
.00341 

0.00341 
.00343 
.00343 
.00244 

0.00244 
.00245 
.00246 
.00247 

0.00247 
.00248 
.00249 
.00249 

0.00250 

0.00251 

7.43760 
.43880 
.44001 
.44121 

0.00274 
.00275 
.00275 
.00276 

7.50706 
.50817 
.50928 
.51039 

0.00321 
.00322 
.00323 
.00324 

7.57135 
.57238 
.57341 
.57444 

0.00373 
.00374 
.00374 
.00375 

60 
58 
56 
54 
52 
50 
48 
46 
U 
42 
40 
38 

8+   2 
10 

12+   3 
14 

16+   4 
18 

20+   5 
22 

7.28513 
.28656 
.28800 
.28943 

7.29086 
.29228 
.29371 
.29513 

7.44241 
.44361 
.44480 
.44600 

7.44719 
.44838 
.44957 
.45076 

0.00277 
.00278 
.00278 
.00279 

0.00280 
.00281 
.00282 
.00282 

0.00283 
.00284 
.00385 
.00385 

0.00386 
.00287 
.00288 
.00289 

0.00289 
.00290 
.00291 
.00292 

0.00392 
.00293 
.00294 
.00295 

7.51149 
.51260 
.51370 
.51481 

7.51591 
.51701 
.51811 
.51921 

7.52030 
.52140 
.52249 
.52358 

7.52467 
.52576 
.52685 
.52794 

7.52902 
.53011 
.35119 
.53227 

7.53335 
.53443 
.53550 
.53658 

0.00325 
.00326 
.00326 
.00327 

0.00328 
.00329 
.00330 
.00331 

0.00331 
.00332 
.00333 
.00334 

0.00335 
.00336 
.00336 
.00337 

0.00338 
.00339 
.00340 
.00341 

0.00341 
.00342 
.00343 
.00344 

0.00345 

0.00346 

7.57547 
.75650 
.57752 
.57855 

7.57957 
.58060 
.58162 
.58264 

7.58366 
.58467 
.58569 
.58670 

7.58772 
.58873 
.58974 
.59075 

0.00376 
.00377 
.00378 
.00379 

0.00380 
.00381 
.00383 
.00383 

24+   6 
26 

28+   7 
30 

32+   8 
34 

36+  9 
38 

7.29655 
.29797 
.29938 
.30079 

7.30220 
.30361 
.30502 
.30642 

7.45194 
.45313 
.45431 
.45549 

7.45667 
.45785 
.45903 
.46020 

7.46138 
.46255 
.46372 
.46489 

7.46605 
.46722 
.46838 
.46955 

0.00383 
.00384 
.00385 
.00386 

0.00387 
.00388 
.00389 
.00390 

36 
34 
32 
30 
28 
26 
24 
22 
20 
18 
16 
14 
12 
10 
8 
6 

40+10 

42 

44+11 

46 

4S+12 

50 

52+lZ 

54 

7.30782 
.30922 
.31062 
.31201 

7.31340 
.31479 
.31618 
.31757 

0.00203 
.00204 
.00204 
.00205 

0.00206 
.00206 
.00207 
.00208 

7.59176 
.59277 
.59378 
.59478 

7.59579 
.59679 
.59779 
.59879 

0.00391 
.00392 
.00392 
.00393 

0.00394 
.00395 
.00396 
.00397 

56+14 
58 

7.31895 
7.32033 

0.00208 
0.00209 

7.39815 
7.39941 

7.47071 
7.47187 

0.00396 
0.00296 

7.53766 
7.53873 

7.59979 
7.60079 

0.00398 
0.00399 

4 
2 

23^  39"* 

23 1^  37  ri 

23  h  .?5"' 

23  h  33  m 

23h31m 

8          ' 

0+15 
2 

4+16 
6 

^+17 

io 

12+lS 

14 

16+19 

18 

20+20 

22 

0Afi'»5°0" 

Oh  23^  5°  W 

Oh  25m  6°  0' 

Oh  27m  6°  30^ 

Oh  29m  7°  0" 

s 

60 
58 
56 
54 

7.32171 
.32309 
.32446 
,32583 

0.00210 
.00210 
.00211 
.00212 

7.40067 
.40192 
.40318 
.40443 

0.00252 
.00252 
.00353 
.00254 

0.00255 
.00255 
.00256 
.00257 

0.00257 
.00258 
.00259 
.00260 

7.47302 
.47418 
.47533 
.47649 

0.00297 
.00298 
.00299 
.00300 

7.53980 
.54087 
.54194 
.54301 

7.54407 
.54514 
.54620 
.54727 

7.54833 
.54939 
.55045 
.55150 

7.55256" 
.55361 
.55467 
.55572 

7.55677 
.55782 
.55887 
.55992 

0.00347 
.00347 
.00348 
.00349 

0.00350 
.00351 
.00352 
.00353 

0.00353 
.00354 
.00355 
.00356 

0.00357 
.00358 
.00359 
.00360 

0.00360 
.00361 
.00362 
.00363 

0.00364 
.00385 
.00366 
.00367 

0.00367 
.00368 
.00369 
.00370 

7.60179 
.60279 
.60378 
.60478 

0.00400 
.00401 
.00403 
.00403 

0.00403 
.00404 
.00405 
.00406 

0.00407 
.00408 
.00409 
.00410 

7.32720 
.32857 
.32994 
.33130 

7.332G6 
.33402 
.33538 
.33673 

7.33809 
.33944 
.34079 
.34213 

7.34348 
.34482 
.34616 
.34750 

7.34884 
.35017 
.35150 
.35283 

7.35416 
.35549 
.35681 
.35813 

0.00212 
.00213 
.00214 
.00214 

0.00215 
.00216 
.00216 
.00217 

7.40568 
.40693 
.40818 
.40943 

7.41067 
.41191 
.41315 
.41439 

7.47764 
.47879 
.47994 
.48109 

7.48223 
.48337 
.48452 
.48566 

0.00300 
.00301 
.00302 
.00303 

0.00304 
.00304 
.00305 
.00306 

0.00307 
.00308 
.00308 
.00309 

0.00310 
.00311 
.00312 
.00312 

7.60577 
.60676 
.60775 
.60874 

7.60973 
.61072 
.61170 
.61269 

52 
50 
48 
46 
44 
42 
40 
38 
36 
34 
32 
30 
28 
26 
24 
22 

24+21 

26 

28+22 

30 

32+2Z 

34 

.S6+24 

38 

40+25 

42 

44+26 

46 

48+21 

50 

52+2S 

54 

0.00218 
.00218 
.00219 
.00220 

0.00221 
.00231 
.00222 
.00223 

7.41563 
.41686 
.41810 
.41933 

7.42056 
.42179 
.42301 
.42424 

0.00260 
.00261 
.00362 
.00263 

0.00263 
.00264 
.00265 
.00266 

7.48680 
.48794 
.48907 
.49021 

7.49134 
.49247 
.49360 
.49473 

7.49586 
.49699 
.49811 
.49923 

7.50036 
.50148 
.50259 
.50371 

7.61367 
.61466 
.61564 
.61662 

7.61760 
.61858 
.61955 
.62053 

0.00411 
.00413 
.00413 
.00414 

0.00415 
.00416 
.00416 
.00417 

0.00223 
.00224 
.00225 
.00225 

0.00226 
.00227 
.00227 
.00228 

7.42546 
.42668 
.42790 
.42912 

7.43034 
.43155 
.43277 
.43398 

0.00266 
.00267 
.00268 
.00269 

0.00369 
.00370 
.00371 
.00272 

0.00313 
.00314 
.00315 
.00316 

0.00316 
.00317 
.00318 
.00319 

7.56096 
.56201 
.56305 
.56409 

7.56513 
.56617 
.56721 
.56825 

7.62151 
.62248 
.62345 
.62442 

7.62540 
.62636 
.62733 
.62830 

0.00418 
.00419 
.00430 
.00431 

0.00433 
.00423 
.00424 
.00435 

20 
18 
16 
14 
12 
10 
8 
6 

56+29 

58 

60+30 

7.35945 

.36077 

7.36209 

0.00229 

.00229 

0.00230 

7.43519 

.43639 

7.43760 

0.00272 

.00273 

0.00274 

7.50483 

.50594 

7.50706 

0.00330 

.00331 

0.00331 

7.56928 

.57032 

7.57135 

0.00371 

.00372 

0.00373 

7.62927 

.63023 

7,63120 

0.00426 

.00427 

0.00428 

4 
2 
0 

23h  38^ 

23h  36m 

23 h  34m 

23h  32m 

23h  30m 

Page  820]                 TABLE  45.                        | 

Haversines.                              1 

s 

OMO^T'^SO'  1 

0»  5;?™  8°  C 

Oh  34^  8°  30^  1 

Oh  36m  9°  (K  1 

01^  38m  9°  W    1 

3 

Log.  Hav. 

Nat.  Hav. 

Ivog.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

7.63120 

0.0042S 

7.68717 

0.00487 

7.73974 

0.00549 

7.78929 

0.00616 

7.83615 

0.00686 

60 

2 

.63216 

.00429 

.68807 

.00488 

.74059 

.00550 

.79009 

.00617 

.83691 

.00687 

58 

4+  1 

.63312 

.00430 

.68897 

.00489 

.74143 

.00551 

.79089 

.00618 

.83767 

.00688 

56 

6 

.63408 

.00431 
0.00432 

.68987 

.00490 

.74228 

.00552 

.79169 

.00619 

.83842 

.00689 

54 

8-\-   3 

7.63504 

7.69077 

0.00491 

7.74313 

0.00554 

7.79249 

0.00620 

7.83918 

0.00691 

52 

10 

.63600 

.00433 

.69167 

.00492 

.74398 

.00555 

.79329 

.00621 

.83994 

.00692 

50 

12+   3 

.63696 

.00433 

.69257 

.00493 

.74482 

.00556 

.79409 

.00622 

.84070 

.00693 

48 

U 

.63792 

.00434 

.69347 

.00494 

.74567 

.00557 

.79489 

.00624 

.84145 

.00694 

46 

16+  4 

7.63887 

0.00435 

7.69437 

0.00495 

7.74651 

0.00558 

7.79568 

0.00625 

7.84221 

0.00695 

U 

18 

.63983 

.00436 

.69526 

.00496 

74735 

.00559 

.79648 

.00626 

.84296 

.00697 

42 

20+  5 

.64078 

.00437 

.69616 

.00497 

.74819 

.00560 

.79728 

.00627 

.84372 

.00698 

40 

22 

.64173 

.00438 

.69705 

.00498 

.74904 

.00561 

.79807 

.00628 

.84447 

.00699 

38 

24+   6 

7.64269 

0.00439 

7.69794 

0.00499 

7.74988 

0.00562 

7.79886 

0.00629 

7.84522 

0.00700 

36 

26 

.64364 

.00440 

.69883 

.00500 

.75072 

.00563 

.79966 

.00630 

.84597 

.00701 

34 

28+  7 

.64458 

.00441 

.69972 

.00501 

.75155 

.00564 

.80045 

.00632 

.84672 

.00703 

32 

50 

.64553 

.00442 

.70061 

.00502 

.75239 

.00565 

.80124 

.00633 

.84747 

.00704 

SO 

32+   8 

7.64648 

0.00443 

7.70150 

0.00503 

7.75323 

0.00567 

7.80203 

0.00634 

7.84822 

0.00705 

28 

54 

.64743 

.00444 

.70239 

.00504 

.75407 

.00568 

.80282 

.00635 

.84897 

.00706 

26 

56+  9 

.64837 

.00445 

.70328 

.00505 

.75490 

.00569 

.80361 

.00636 

.84972 

.00707 

24 

S8 

.64932 

.00446 

.70416 

.00506 

.75574 

.00570 

.80440 

.00637 
0.00639 

.85047 

.00709 

22 

40+10 

7.65026 

0.00447 

7.70505 

0.00507 

7.75657 

0.00571 

7.80519 

7.85122 

0.00710 

20 

42 

.65120 

.00448 

.70593 

.00508 

.75740 

.00572 

.80598 

.00640 

.85196 

.00711 

18 

44+11 

.65214 

.00449 

.70682 

.00509 

.75824 

.00573 

.80677 

.00641 

.85271 

.00712 

16 

46 

.65308 

.00450 

.70770 

.00510 

.75907 

.00574 

.80755 

.00642 

.85346 

.00714 

14 

48+n 

7.65402 

0.00451 

7.70858 

0.00511 

7.75990 

0.00575 

7.80834 

0.00643 

7.85420 

0.00715 

12 

50 

.65496 

.00452 

.70946 

.00512 

.76073 

.00576 

.80912 

.00644 

.85494 

.00716 

10 

52+lZ 

.65590 

.00453 

.71034 

.00513 

.76156 

.00578 

.80991 

.00646 

.85569 

.00717 

8 

54 

.65683 

.00454 

.71122 

.00514 

.76239 

.00579 

.81069 
7.81147 

.00647 

.85643 

.00719 

6 

56+14 

7.65777 

0.00455 

7.71210 

0.00515 

7.76321 

0.00580 

0.00648 

7.85717 

0.00720 

4 

58 

7.65870 

0.00456 

7.71298 

0.00516 

7.76404 

0.00581 

7.81225 

0.00649 

7.85791 

0.00721 

2 

23h 29^ 

2Sh  27'^ 

23  h  25m 

2Sh  23m 

23h  21m 

8   ' 
0+15 

Oh  Sim  7°  30' 

Oh  ssm  8°  O' 

OA  S5m  8°  30" 

Oh  37m  9°  0' 

Oh  39m  9°  30' 

s 
60 

7.65964 

0.00457 

7.71385 

0.00517 

7.76487 

0.00582 

7.81303 

0.00650 

7.85866 

0.00722 

f 

.66057 

.00458 

.71473 

.00518 

.76669 

.00583 

.81382 

.00651 

.85940 

.00723 

58 

4+16 

.66150 

.00459 

.71560 

.00520 

.76652 

.00584 

.81459 

.00653 

.86014 

.00725 

56 

6 

.66243 

.00460 

.71648 

.00521 

.76734 

.00585 

.81537 
7.81615 

.00654 

.86087 

.00726 
0.00727 

54 
52 

5+17 

7.66336 

0.00461 

7.71735 

0.00522 

7.76816 

0.00586 

0.00655 

7.86161 

io 

.66429 

.00462 

.71822 

.00523 

.76898 

.00587 

.81693 

.00656 

.86235 

.00728 

50 

1^+18 

.66521 

.00463 

.71909 

.00524 

.76981 

.00589 

.81771 

.00657 

.86309 

.00730 

48 

14 

.66614 

.00464 

.71996 

.00525 

.77063 

.00590 

.81848 

.00658 

.86382 

.00731 

46 

16+19 

7.66706 

0.00465 

7.72083 

0.00526 

7.77145 

0.00591 

7.81926 

0.00860 

7.86456 

0.00732 

44 

18 

.66799 

.00466 

.72170 

.00527 

.77227 

.00592 

.82003 

.00661 

.86530 

.00733 

42 

20+20 

.66891 

.00467 

.72257 

.00528 

.77308 

.00593 

.82081 

.00662 

.86603 

.00735 

40 

22 

.66983 

.00468 

.72343 

.00529 

.77390 

.00594 
0.00595 

.82158 
7.82235 

.00663 

.86676 

.00736 
0.00737 

38 
36 

24+n 

7.67075 

0.00469 

7.72430 

0.00530 

7.77472 

0.00664 

7.86750 

26 

.67167 

.00470 

.72516 

.00531 

.77553 

.00596 

.82313 

.00665 

.86823 

.00738 

34 

28+22 

.67259 

.00471 

.72603 

.00532 

.77635 

.00598 

.82390 

.00667 

.86896 

.00740 

32 

SO 

.67351 

.00472 

.72689 

.00533 

.77716 

.00599 

.82467 

.00668 

.86969 

.00741 

SO 

S2+23 

7.67443 

0.00473 

7.72775 

0.00534 

7.77798 

0.00600 

7.82544 

0.00669 

7.87042 

0.00742 

28 

84 

.67535 

.00474 

.72861 

.00535 

.77879 

.00601 

.82621 

.00670 

.87115 

.00743 

26 

56+34 

.67626 

.00475 

.72948 

.00536 

.77960 

.00602 

.82698 

.00671 

.87188 

.00745 

24 

88 

.67718 

.00476 

.73034 

.00537 

.78041 

.00603 

.82774 

.00673 

.87261 

.00746 

22 

40+26 

7.67809 

0.00477 

7.73119 

0.00539 

7.78122 

0.00604 

7.82851 

0.00674 

7.87334 

0.00747 

20 

42 

.67900 

.00478 

.73205 

.00540 

.78203 

.00605 

.82928 

.00675 

.87407 

.00748 

18 

44+20 

.67991 

.00479 

.73291 

.00541 

.78284 

.00607 

.83004 

.00676 

.87480 

.00750 

16 

46 

.68082 

.00480 

.73377 

.00542 

.78365 

.00608 

.83081 

.00677 

.87552 

.00751 

14 

48+21 

7.68173 

0.00481 

7.73462 

0.00543 

7.78446 

0.00609 

7.83157 

0.00679 

7.87625 

0.00752 

12 

50 

.68264 

.00482 

.73548 

.00544 

.78526 

.00610 

.83234 

.00680 

.87697 

.00753 

10 

52+29, 

.68355 

.00483 

.73633 

.00545 

.78607 

.00611 

.83310 

.00681 

.87770 

.00755 

8 

54 

.68445 

.00484 

.73718 

.00546 

.78688 

.00612 

.83386 

.00682 

.87842 

.00756 

6 

56+29 

7.68536 

0.00485 

7.73803 

0.00547 

7.78768 

0.00613 

7.83463 

0.00683 

7.87915 

0.00757 

4 

58 

.68627 

.00486 

.73889 

.00548 

.78848 

.00614 

.83539 

.00685 

.87987 

.00758 

2 

60+30 

7.68717 

0.00487 

7.73974 

0.00549 

7.78929 

0.00616 

7.83615 

0.00686 

7.88059 

0.00760 

0 

23h  28r^ 

2Sh  26m 

23  h  24^ 

23h  22m 

23  h  20m 

TABLE  45.                 [Page  821 

Haversines. 

s    ' 

Qh  40in  10°  0" 

Oh  42m  10°  30^ 

Oh  44m  u°  0" 

Ok  .^e™  11°  SO'  1 

Oh  4smia°o'  1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

2 

4+  1 
6 

7.88059 
.88131 
.88203 
.88276 

0.00760 
.00761 
.00762 
.00763 

7.92286 
.92354 
.92423 
.92492 

0.00837 
.00839 
.00840 
.00841 

0.00843 
.00844 
.00845 
.00847 

0.00848 
.00849 
.00851 
.00852 

7.96315 
.96380 
.96446 
.96511 

0.00919 
.00920 
.00921 
.00923 

0.00924 
.00926 
.00927 
.00928 

0.00930 
.00931 
.00933 
.00934 

0.00935 
.00937 
.00938 
.00940 

0.00941 
.00942 
.00944 
.00945 

8.00163 
.00226 
.00289 
.00351 

0.01004 
.01005 
.01007 
.01008 

0.01010 
.01011 
.01012 
.01014 

0.01015 
.01017 
.01018 
.01020 

0.01021 
.01023 
.01024 
.01026 

0.01027 
.01029 
.01030 
.01032 

8.03847 
.03907 
.03967 
.04027 

8.04087 
.04147 
.04207 
.04267 

8.04326 
.04386 
.04446 
.04506 

0.01093 
.01094 
.01096 
.01097 

0.01099 
.01100 
.01102 
.01103 

0.01105 
.01106 
.01108 
.01109 

60 
58 
56 

54 
52 
50 
48 
46 
44 
42 
40 
38 

8+  2 
10 

12+   3 
14 

16+   4 
18 

20+   6 
22 

7.88348 
.88419 
.88491 
.88563 

7.88635 
.88707 
88778 
.88850 

0.00765 
.00766 
.00767 
.0076S 

0.00770 
.00771 
.00772 
.00774 

0.00775 
.00776 
.00777 
.00779 

0.00780 
.00781 
.00783 
.00784 

0.00785 
.00786 
.00788 
.00789 

0.00790 
.00792 
.00793 
.00794 

7.92560 
.92629 
.92697 
.92766 

7.92834 
.92902 
.92970 
.93039 

7.93107 
.93175 
.93243 
.93311 

7.93379 
.93447 
.93514 
.93582 

7.96577 
.96642 
.96707 
.96773 

7.96838 
.96903 
.96968 
.97033 

8.00414 
.00476 
.00539 
.00601 

8.00664 
.00726 
.00788 
.00851 

8.00913" 
.00975 
.01037 
.01099 

8.01161 
.01223 
.01285 
.01347 

8:01469 
.01471 
.01532 
.01594 

8.01656 
.01717 
.01779 
.01840 

8.01902 

8.01963 

24+   6 
26 

28+   7 
SO 

32+   8 
34 

36+   9 
38 

7.88921 
.88993 
.89064 
.89135 

7.89207 
.89278 
.89349 
.89420 

0.00853 
.00855 
.00856 
.60857 

0.00859 
.00860 
.00861 
.00863 

7.97098 
.97163 
.97228 
.97293 

7.97358 
.97423 
.97478 
.97552 

8.04565 
.04625 
.04684 
.04744 

8.04803 
.04863 
.04922 
.04981 

0.01111 
.01112 
.01114 
.01115 

0.01117 
.01118 
.01120 
.01122 

0.01123 
.01125 
.01126 
.01128 

0.01129 
.01131 
.01132 
.01134 

36 
34 
32 
30 
28 
26 
24 
22 
20 
18 
16 
14 
12 
10 
8 
6 

40+19 

42 

U+11 

46 

48+12 

50 

52+lZ 

54 

7.89491 
.89562 
.89633 
.89704 

7.89775 
.89846 
.89916 
.89987 

7.93650 
.93717 
.93785 
.93852 

7.93920 
.93987 
.94055 
.94122 

0.00864 
.00865 
.00867 
.00888 

0.00869 
.00871 
.00872 
.00873 

0.00875 

0.00876 

7.97617 
.97681 
.97746 
.97810 

7.97875 
.97939 
.98003 
.98068 

0.00947 
.00948 
.00949 
.00951 

0.00952 
.00954 
.00955 
.00956 

0.01033 
.01034 
.01036 
.01037 

0.01039 
.01040 
.01042 
.01043 

0.01045 

0.01046 

8.05041 
.05100 
.05159 
.05218 

8.05277 
.05336 
.05395 
.05454 

56+U 
58 

7.90057 
7.90128 

0.00795 
0.00797 

7.94189 
7.94257 

7.98132 
7.98196 

0.00958 
0.00959 

8.05513 
8.05572 

0.01135 
0.01137 

4 

2 

231^  19m 

23h  nm 

23h  15m 

2Sh ISm 

2Sh  11m 

6     ' 

0+15 
2 

4+10 
6 

Oft  4-?™  10°  O' 

OA  43^  10°  30' 

Oh  45m  11°  0' 

Oh  47m  11°  30' 

Oh  49m  12°  O' 

s 

60 
58 
56 
54 
52 
50 
48 
46 
44 
42 
40 
38 

7.90198 
.90269 
.90339 
.90409 

0.00798 
.00799 
.00801 
.00802 

7.94324 
.94391 
.94458 
.94525 

0.00877 
.00879 
.00880 
.00882 

7.98260 
.98325 
.98389 
.98453 

0.00961 
.00962 
.00964 
.00965 

8.02025 
.02086 
.02148 
.02209 

8.02270 
.02331 
.02392 
.02453 

8.02515 
.02576 
.02637 
.02697 

0.01048 
.01049 
.01051 
.01052 

8.05631 
.05690 
.05749 
.05808 

0.01138 
.01140 
.01142 
.01143 

0.01145 
.01146 
.01148 
.01149 

0.01151 
.01152 
.01154 
.01155 

8+n 

10 

12+18 

14 

16+19 

18 

20+20 

22 

7.90480 
.90550 
.90620 
.90690 

7.90760 
.90830 
.90900 
.90970 

0.00803 
.00804 
.00806 
.00807 

0.00808 
.00810 
.00811 
.00812 

7.94592 
.94659 
.94726 
.94792 

7.94859 
.94926 
.94992 
.95059 

0.00883 
.00884 
.00886 
.00887 

0.00888 
.00890 
.00891 
.00892 

7.98517 
.98581 
.98644 
.98708 

7.98772 
.98836 
.98899 
.98963 

0.00966 
.00968 
.00969 
.00971 

0.00972 
.00974 
.00975 
.00976 

0.01054 
.01055 
.01057 
.01058 

0.01060 
.01061 
.01063 
.01664 

8.05866 
.05925 
.05984 
.06042 

8.06101 
.06159 
.06218 
.06276 

24+21 

26 

28+22 

SO 

S2+2Z 

34 

36+24 

38 

7.91039 
.91109 
.91179 
.91248 

7.91318 
.91387 
.91457 
.91526 

0.00814 
.00815 
.00816 
.00817 

0.00819 
.00820 
.00821 
.00823 

7.95126 
.95192 
.95259 
.95325 

7.95391 
.95458 
.95524 
.95590 

0.00894 
.00895 
.00897 
.00898 

0.00899 
.00901 
.00902 
.00903 

7.99027 
99090 
.99154 
.99217 

7.99281 
.99344 
.99407 
.99470 

0.00978 
.00979 
.00981 
.00982 

0.00984 
.06985 
.00886 
.00888 

8.02758 
.02819 
.02880 
.02941 

8.03001 
.03062 
.03123 
.03183 

0.01066 
.01087 
.01089 
.01070 

0.01072 
.01073 
.01075 
.01076 

8.06335 
.06393 
.06451 
.06510 

8.06568 
.06626 
.06684 
.06742 

0.01157 
.01159 
.01160 
.01162 

0.01163 
.01165 
.01166 
.01168 

36 
34 
32 
30 
28 
26 
24 
22 
20 
18 
16 
14 
12 
10 
8 
6 

40+25 

42 

44+20 

46 

48+21 

50 

52+28 

54 

7.91596 
.91665 
.91734 
.91803 

7.91872 
.91941 
.92010 
.92079 

0.00824 
.00825 
.00827 
.00828 

0.00829 
.00831 
.00832 
.00833 

7.95656 
.95722 
.95788 
.95854 

7.95920 
.95986 
.96052 
.96118 

0.00905 
.00906 
.00908 
.00909 

0.00910 
.00912 
.00913 
.00914 

7.99534 
.99597 
.99660 
.99723 

7.99786 
.99849 
.99912 

7.99975 

0.00989 
.00991 
.00992 
.00994 

0.00995 
.00997 
.00898 
.00999 

8.03244 
.03304 
.03365 
.03425 

8.03486 
.03546 
.03606 
.03666 

0.01078 
.01079 
.01081 
.01082 

0.01084 
.01085 
.01087 
.01088 

8.06800 
.06859 
.06917 
.06975 

8.07032 
.07090 
.07148 
.07206 

0.01170 
.01171 
.01173 
.01174 

0.01176 
.01177 
.01179 
.01180 

0.01182 
.01184 

0.01185 

56+219 

58 

60+30 

7.92148 

.92217 

7.92286 

0.00835 

.00836 

0.00837 

7.96183 

.96249 

7.96315 

0.00916 

.00917 

0.00919 

8.00038 

.00100 

8.00163 

0.01001 

.01002 

0.01004 

8.03727 

.03787 

8.03847 

0.01090 

.01091 

0.01093 

8.07264 

.07322 

8.07379 

4 
2 
0 

2Sh  18'n 

23h  16^ 

23h 14m 

2S>^  12m 

2St^  lOrn 

Page  822]                 TABLE  45.                        | 

Haversines.                                1 

s 

Oft  60r»  12°  3(K 

Oh  52m  13°  0' 

Oh  54^  13°  30^ 

Oh  56m  14°  0' 

Oh  68r<^  14°  30^ 

s 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

8.07379 

0.01185 

8.10772 

0.01282 

8.14035 

0.01382 

8.17179 

0.01485 

8.20211 

0.01593 

60 

2 

.07437 

.01187 

.10827 

.01283 

.14089 

.01383 

.17230 

.01487 

.20261 

.01594 

58 

4+   1 

.07494 

.01188 

.10883 

.01285 

.14142 

.01385 

.17282 

.01489 

.20310 

.01596 

56 

6 

.07552 

.01190 

.10938 

.01286 
0.01288 

.14195 

.01387 

.17333 
8.17384 

.01491 

.20360 
8.20410 

.01598 
0.01600 

54 

52 

8+   2 

8.07610 

0.01193 

8.10993 

8.14248 

0.01388 

0.01492 

10 

.07667 

.01193 

.11049 

.01290 

.14302 

.01390 

.17436 

.01494 

.20459 

.01603 

50 

12+   3 

.07725 

.01195 

.11104 

.01291 

.14355 

.01392 

.17487 

.01496 

.20509 

.01604 

4S 

14 

.07782 

.01196 

.11159 

.01393 

.14408 

.01393 

.17538 

.01498 

.20558 

.01605 

46 

16+   4 

8.07839 

0.01198 

8.11214 

0.01395 

8.14461 

0.01395 

8.17590 

0.01499 

8.20608 

0.01607 

44 

18 

.07897 

.01199 

.11269 

.01396 

.14514 

.01397 

.17641 

.01501 

.20657 

.01609 

42 

20+   5 

.07954 

.01301 

.11324 

.01398 

.14567 

.01399 

.17692 

.01503 

.20706 

.01011 

40 

22 

.08011 

.01303 

.11379 

.01300 

.14620 

.01400 

.17743 

.01505 

.20756 

.01613 

38 

24+   6 

8.08069 

0.01304 

8.11435 

0.01301 

8.14673 

0.01402 

8.17794 

0.01506 

8.20805 

0.01615 

36 

26 

.08126 

.01306 

.11490 

.01303 

.14726 

.01404 

.17845 

.01508 

.20854 

.01616 

34 

28+   7 

.08183 

.01307 

.11544 

.01305 

.14779 

.01405 

.17896 

.01510 

.20904 

.01618 

32 

^0 

.08240 

.01309 

.11599 

.01306 

.14832 

.01407 

.17947 

.01512 

.20953 

.01630 

30 

32+   8 

8.08297 

0.01311 

8.11654 

0.01308 

8.14885 

0.01409 

8.17998 

0.01513 

8.21002 

0.01633 

28 

^4 

.08354 

.01312 

.11709 

.01309 

.14938 

.01411 

.18049 

.01515 

.21051 

.01624 

26 

56+  9 

.08411 

.01214 

.11764 

.01311 

.14991 

.01413 

.18100 

.01517 

.21100 

.01626 

24 

S8 

.08468 

.01315 

.11819 
8.11873 

.01313 

.15043 

.01414 

.18151 

.01519 
0.01521 

.21149 

.01637 

22 
20 

40+10 

8.08525 

0.01317 

0.01314 

8.15096 

0.01416 

8.18202 

8.21199 

0.01629 

42 

.08582 

.01318 

.11928 

.01316 

..15149 

.01417 

.18253 

.01522 

.21248 

.01631 

18 

44+n 

.08639 

.01330 

.11983 

.01317 

.15201 

.01419 

.18303 

.01524 

.21297 

.01633 

16 

46 

.08696 

.01232 

.12038 

.01319 

.15254 

.01431 

.18354 

.01526 

.21346 

.01635 

14 

48+12 

8.08752 

0.01233 

8.12092 

0.01331 

8.15307 

0.01433 

8.18405 

0.01528 

8.21395 

0.01637 

12 

SO 

.08809 

.01335 

.12147 

.01323 

.15359 

.01434 

.18455 

.01530 

.21444 

.01638 

10 

62+13 

.08866 

.01226 

.12201 

.01334 

.15412 

.01436 

.18506 

.01531 

.21493 

.01640 

8 

54 

.08922 

.01228 

.12256 

.01326 

.15464 
8.15517 

.01438 
0.01429 

.18557 

.01533 

.21541 

.01643 
0.01644 

6 

4 

56 +U 

8.08979 

0.01330 

8.12310 

0.01328 

8.18607  0.01535 

8.21590 

58 

8.09036 

0.01331 

8.12365 

0.01329 

8.15569 

0.01431 

8.18658  0.01537 

8.21639 

0.01646 

2 

23h9rn 

23h  7'« 

23h  5™ 

23  h  3  "I 

2Sh  Im 

B       ' 
0+15 

Oh  51^  13°  W 

Oh  53m  13°  0' 

Oh  55r<i  13°  30' 

Oh  51rn.   14°  0' 

Oh  59m  14°  30'' 

s 
60 

8.09092 

0.01333 

8.12419 

0.01331 

8.15622 

0.01433 

8.18709 

0.01538 

8.21688 

0.01648 

2 

.09149 

.01234 

.12473 

.01333 

.15674 

.01435 

.18759 

.01540 

.21737 

.01650 

58 

4+16 

.09205 

.01336 

.12528 

.01334 

.15726 

.01436 

.18810 

.01542 

.21785 

.01651 

56 

6 

.09262 

.01338 

.12582 

.01336 

.15779 
8.15831 

.01438 
0.01440 

.18860 

.01544 

.21834 

.01653 

54 

52 

8+n 

8.09318 

0.01339 

8.12636 

0.01338 

8.18910 

0.01546 

8.21883 

0.01655 

10 

.09374 

.01341 

.12691 

.01339 

.15883 

.01442 

.18961 

.01547 

.21932 

.01657 

50 

12+18 

.09431 

.01343 

.12745 

.01341 

.15935 

.01443 

.19011 

.01549 

.21980 

.01659 

48 

14 

.09487 

.01344 

.12799 

.01343 

.15987 

.01445 

.19062 

.01551 

.22029 

.01661 

46 

16+19 

8.09543 

0.01346 

8.12853 

0.01344 

8.16040 

0.01447 

8.19112 

0.01553 

8.22077 

0.01663 

44 

18 

.09600 

.01347 

.12907 

.01346 

.16092 

.01448 

.19162 

.01555 

.22126 

.01664 

42 

20+20 

.09656 

.01349 

.12961 

.01348 

.16144 

.01450 

.19212 

.01556 

.22175 

.01666 

40 

22 

.09712 

.01351 

.13015 

.01349 

.16196 

.01452 
0.01454 

.19263 
8.19313 

.01558 
0.01560 

.22223 

.01668 

38 
36 

24+21 

8.09768 

0.01353 

8.13069 

0.01351 

8.16248 

8.22272 

0.01670 

26 

.09824 

.01354 

.13123 

.01353 

.16300 

.01455 

.19363 

.01562 

.22320  !  .01672 

34 

28+22 

.09880 

.01355 

.13177 

.01354 

.16352 

.01457 

.19413 

.01564 

.22368  :  .01674 

32 

SO 

.09936 

.01357 

.13231 

.01356 

.16404 

.01459 

.19463 

.01565 

.22417 

.01676 

30 

32+23 

8.09992 

0.01359 

8.13285 

0.01358 

8.16456 

0.01461 

8.19513 

0.01567 

8.22465 

0.01677 

28 

34 

.10048 

.01360 

.13339 

.01360 

.16508 

.01463 

.19563 

.01569 

.22514 

.01679 

26 

36 +U 

.10104 

.01362 

.13392 

.01361 

.16559 

.01464 

.19613 

.01571 

.22562 

.01681 

24 

38 

.10160 

.01364 

.13446 

.01363 

.16611 

.01466 

.19663 

.01573 

.22610 

.01683 

22 

40+25 

8.10216 

0.01365 

8.13500 

0.01365 

8.16663 

0.01468 

8.19713 

0.01574 

8.22658 

0.01685 

20 

42 

.10271 

.01367 

.13554 

.01366 

.16715 

.01469 

.19763 

.01576 

.22707 

.01687 

18 

44+26 

.10327 

.01268 

.13607 

.01368 

.16766 

.01471 

.19813 

.01578 

.22755 

.01689 

16 

46 

.10383 

.01270 

.13661 

.01370 

.16818 

.01473 

.19863 

.01580 

.22803 

.01691 

14 

48+2^ 

8.10439 

0.01272 

8.13714 

0.01371 

8.16870 

0.01475 

8.19913 

0.01583 

8.22851 

0.01693 

12 

50 

.10494 

.01273 

.13768 

.01373 

.16921 

.01476 

.19963 

.01584 

.22899 

.01694 

10 

52+28 

.10550 

.01275 

.13822 

.01375 

.16973 

.01478 

.20012 

.01585 

.22947 

.01696 

8 

54 
56+29 

.10605 
8.10661 

.01277 

.13875 

.01376 

.17024 
8.17076 

.01480 
0.01482 

.20062 

.01587 

.22996 

.01698 

6 

0.01278 

8.13928 

0.01378 

8.20112 

0.01589 

8.23044 

0.01700 

4 

68 

.10716 

.01280 

.13982 

.01380 

.17127 

.01483 

.20162 

.01591 

.23092 

.01703 

2 

60+30 

8.10772 

0.01283 

8.14035 

0.01382 

8.17179 

0.01485 

8.20211 

0.01593 

8.23140 

0.01704 

0 

23^8^ 

2Sh6m 

23h4m 

23h  2r^ 

23h0'>^ 

TABLE  45.                  [Page  823 

Haversines. 

s 

nomi5°(^    1 

iW»15°15'  1 

JA:^''15°30'  1 

iA5™15°45'  1 

iA4'»16°0'  1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

8.23140 
.23164 
.23188 
.23212 

.01704 
.01705 
.01706 
.01707 

8.24567 
.24591 
.24614 
.24638 

.01761 
.01762 
.01763 
.01764 

8.25971 
.25994 
.26017 
.26040 

.01818 
.01819 
.01820 
.01821 

8.27352 
.27375 
.27398 
.27420 

.01877 
.01878 
.01879 
.01880 

8.28711 
.28734 
.28756 
.28779 

.01937 
.01938 
.01939 
.01940 

60 
59 
58 
67 

+     r 

5 
6 

7 

8.23235 
.23259 
.23283 
.23307 

.01707 
.01708 
.01709 
.01710 

8.24661 
.24685 
.24708 
.24732 

.01764 
.01765 
.01766 
.01767 

8.26064 
.26087 
.26110 
.26133 

.01822 
.01823 
.01824 
.01835 

8.27443 
.27466 
.27489 
.27512 

.01881 
.01883 
.01883 
.01884 
.01885 
.01886 
.01887 
.01888 

8.28801 
.28823 
.28846 
.28868 

.01941 
.01943 
.01943 
.01944 
.01945 
.01946 
.01947 
.01948 

56 
55 
54 
53 
52 
51 
50 
49 

+   2' 

9 

10 

11 

8.23331 
.23355 
.23379 
.23403 

.01711 
.01713 
.01713 
.01714 

8.24755 
.24779 
.24803 
.24826 

.01768 
.01769 
.01770 
.01771 

8.26156 
.26179 
.26203 
.26226 

.01836 
.01827 
.01828 
.01829 

8.27534 
.27557 
.27580 
.27603 

8.28891 
.28913 
.28936 
.28958 

8.28980 
.29003 
.29025 
.29048 

+       3' 

13 
14 
15 

8.23427 
.23451 
.23475 
.23499 

.01715 
.01716 
.01717 
.01718 

8.24850 
.24873 
.24897 
.24920 

.01773 
.01773 
.01774 
.01775 

8.26249 
.26272 
.26295 
.26318 

.01830 
.01831 
.01832 
.01833 

8.27626 
.27648 
.27671 
.27694 

.01889 
.01890 
.01891 
.01893 

.01949 
.01950 
.01951 
.01952 

48 
47 
46 
45 

+       4^ 
17 
18 
19 

8.23523 
.23546 
.23570 
.23594 

.01719 
.01730 
.01731 
.01733 

8.24944 
.24967 
.24991 
.25014 

.01776 
.01777 
.01778 
.01779 

8.26341 
.26364 
.26388 
.26411 

.01834 
.01835 
.01836 
.01837 

8.27717 
.27739 
.27762 

.27785 

.01893 
.01894 
.01895 
.01896 

8.29070 
.29092 
.29115 
.29137 

.01953 
.01954 
.01955 
.01956 

44 
43 
42 
41 

+       5' 
21 
22 
23 

8.23618 
.23642 
.23666 
.23690 

.01723 
.01734 
.01734 
.01735 

8.25037 
.25061 
.25084 
.25108 

.01780 
.01781 
.01783 
.01783 

8.26434 
.26457 
.26480 
.26503 

.01838 
.01839 
.01840 
.01841 

8.27807 
.27830 
.27853 
.27876 

.01897 
.01898 
.01899 
.01900 

8.29159 
.29182 
.29204 
.29226 

.01957 
.01958 
.01959 
.01960 

40 
39 
38 
37 

+       6' 

25 
26 

27 

8.23713 
.23737 
.23761 
.23785 

.01736 
.01727 
.01738 
.01729 

8.25131 
.25155 
.25178 
.25202 

8.25225 
.25248 
.25272 
.25295 

.01784 
.01785 
.01786 
.01787 
.01788 
.01789 
.01789 
.01790 

8.26526 
.26549 
.26572 
.26595 

8.26618 
.26641 
.26664 
.26687 

.01843 
.01843 
.01844 
.01845 

8.27898 
.27921 
.27944 
.27966 

.01901 
.01903 
.01903 
.01904 

8.29249 
.29271 
.29293 
.29316 

.01961 
.01962 
.01963 
.01964 

36 
35 
34 
33 
32 
31 
30 
29 

+    r 

29 
30 
31 

8.23809 
.23832 
.23856 
.23880 

.01730 
.01731 
.01732 
.01733 

.01846 
.01847 
.01848 
.01849 

8.27989 
.28012 
.28034 
.28057 

.01905 
.01906 
.01907 
.01908 

8.29338 
.29360 
.29383 
.29405 

.01965 
.01966 
.01967 
.01968 

+       8' 
33 
34 
35 

8.23904 
.23928 
.23951 
.23975 

.01734 
.01735 
.01736 
.01737 

8.25319 
.25342 
.25365 
.25389 

.01791 
.01793 
.01793 
.01794 

8.26710 
.26733 
.26756 
.26779 

.01850 
.01851 
.01852 
.01853 

8.28080 
.28102 
.28125 
.28147 

.01909 
.01910 
.01911 
.01913 

8.29427 
.29449 
.29472 
.29494 

.01969 
.01970 
.01971 
.01973 

28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
IS 

+  9^ 

37 
38 
39 

8.23999 
.24022 
.24046 
.24070 

.01738 
.01739 
.01740 
.01741 

8.25412 
.25435 
.25459 
.25482 

.01795 
.01796 
.01797 
.01798 

8.26802 
.26825 
.26848 
.26871 

.01854 
.01855 
.01856 
.01857 

8.28170 
.28193 
.28215 
.28238 

.01913 
.01914 
.01915 
.01916 

8.29516 
.29539 
.29561 
.29583 

.01973 
.01974 
.01975 
.01976 
.01977 
.01978 
.01979 
.01980 

41 
42 
43 

8.24094 
.24118 
.24141 
.24165 

.01742 
.01743 
.01743 
.01744 

8.25505 
.25529 
.25552 
.25575 

.01799 
.01800 
.01801 
.01803 

8.26894 
.26917 
.26940 
.26963 

.01858 
.01859 
.01860 
.01861 

8.28260 
.28283 
.28306 
.28328 

.01917 
.01918 
.01919 
.01930 

8.29605 
.29628 
.29650 
.29672 

+   ir 

45 
46 
47 

8.24189 
.24212 
.24236 
.24260 

.01745 
.01746 
.01747 
.01748 

8.25599 
.25622 
.25645 
.25669 

.01803 
.01804 
.01805 
.01806 

8.26986 
.27009 
.27032 
.27055 

.01861 
.01862 
.01863 
.01864 

8.28351 
.28373 
.28396 
.28418 

.01931 
.01933 
.01933 
.01924 

8.29694 
.29716 
.29739 
.29761 

.01981 
.01982 
.01983 
.01984 

+     13' 

49 
60 
51 

8.24283 
.24307 
.24331 
.24354 

.01749 
.01750 
.01751 
.01753 

8.25692 
.25715 
.25738 
.25762 

.01807 
.01808 
.01809 
.01810 
.01811 
.01813 
.01813 
.01814 

8.27078 
.27100 
.27123 
.27146 

.01865 
.01866 
.01867 
.01868 

8.28441 
.28464 
.28486 
.28509 

.01935 
.01936 
.01937 
.01938 
.01939 
.01930 
.01931 
.01933 

8.29783 
.29805 
.29827 
.29850 

8.29872 
.29894 
.29916 
.29938 

.01985 
.01986 
.01987 
.01988 

12 

11 

10 

9 

+  13' 

53 
64 
65 

8.24378 
.24402 
.24425 
.24449 

.01753 
.01754 
.01755 
.01756 

8.25785 
.25808 
.25831 
.25855 

8.27169 
.27192 
.27215 
.27238 

.01869 
.01870 
.01871 
.01873 

8.28531 
.28554 
.28576 
.28599 

.01989 
.01990 
.01991 
.01992 

8 
7 
6 
5 

+  U' 

67 
68 
69 

8.24473 
.24496 
.24520 
.24543 

.01757 
.01758 
.01759 
.01760 

8.25878 
.25901 
.25924 
.25948 

.01815 
.01816 
.01817 
.01818 

8.27261 
.27283 
.27306 
.27329 

.01873 
.01874 
.01875 
.01876 

8.28621 
.28644 
.28666 
.28689 

.01933 
.01934 
.01935 
.01936 

8.29960 
.29982 
.30005 
.30027 

.01993 
.01994 
.01995 
.01997 

4 

s 

2 
1 

+  15' 

8.24567 

.01761 

8.25971 

.01818 

8.27352 

.01877 

8.28711  1  .01937 

8.30049 

.01998 

0 

22 h  59m 

22"  58^         1    22k  57m 

f^ft  5(5 "» 

22  h  55m 

Page  824]                 TABLE  45. 

Haversines. 

s 

J*  5m  16°  15' 

ift  6m  16°  30' 

lA  7m  16°  45' 

lA5ml7°0' 

Ih  9m  17°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

8.30049 
.30071 
.30093 
.30115 

.01998 
.01999 
.03000 
.03001 

8.31366 
.3138. 
.31410 
.31431 

.02059 
.02060 
.02061 
.02062 

8.32663 
.32684 
.32706 
.32727 

.02121 
.02122 
.02124 
.02125 

8.33940 
.33962 
.33983 
.34004 

.02185 
.02186 
.02187 
.02188 

8.35199 
.35220 
.35241 
.35261 

.02249 
.02250 
.02251 
.02252 

60 
59 
58 

67 

+   1' 

6 
6 

7 

8.30137 
.30159 
.30182 
.30204 

.03002 
.02003 
.02004 
.02005 

8.31453 
.31475 
.31497 
.31518 

.02063 
.02064 
.02065 
.02066 

8.32749 
.32770 
.32792 
.32813 

.02126 
.02127 
.02128 
.02129 

8.34025 
.34046 
.34067 
.34088 

.02189 
.02190 
.02191 
.02192 

8.35282 
.35303 
.35324 
.35345 

.02253 
.02254 
.02255 
.02257 

56 
55 
54 
53 

+   2' 

9 

10 

11 

8.30226 
.30248 
.30270 
.30292 

.02006 
.02007 
.02008 
.02009 

8.31540 
.31562 
.31584 
.31605 

.02067 
.02068 
.02069 
.02070 

8.32834 
.32856 
.32877 
.32899 

.02130 
.02131 
.02132 
.02133 

8.34109 
.34130 
.34152 
.34173 

.02193 
.02194 
.02195 
.02196 

8.35365 
.35386 
.35407 
.35428 

.02258 
.02259 
.02260 
.02261 

52 
51 
50 
49 
48' 
47 
46 
45 

+      3' 

13 
14 
15 

8.30314 
.30336 
.30358 
.30380 

.02010 
.02011 
.02012 
.02013 

8.31627 
.31649 
.31670 
.31692 

.02071 
.02072 
.02074 
.02075 

8.32920 
.32941 
.32963 
.32984 

.02134 
.02135 
.02136 
.02137 

8.34194 
.34215 
.34236 
.34257 

.02198 
.02199 
.02200 
.02201 

8.35449 
.35469 
.35490 
.35511 

.02262 
.02263 
.02264 
.02265 

+   4' 
17 

19 

8.30402 
.30424 
.30446 
.30468 

.02014 
.02015 
.02016 
.02017 

8.31714 
.31735 
.31757 
.31779 

.02076 
.02077 
.02078 
.02079 

8.33006 
.33027 
.33048 
.33070 

.02138 
.02139 
.02140 
.02141 

8.34278 
.34299 
.34320 
.34341 

.02202 
.02203 
.02204 
.02205 

8.35532 
.35552 
.35573 
.35594 

.02266 
.02267 
.02268 
.02270 

44 
43 
42 
41 

+   6' 

;?1 

«5 

8.30490 
.30512 
.30534 
.30556 

.02018 
.02019 
.02020 
.02021 

8.31800 
.31822 
.31844 
.31865 

.02080 
.02081 
.02082 
.02083 

8.33091 
.33112 
.33134 
.33155 

.02142 
.02143 
.02145 
.02146 

8.34362 
.34383 
.34404 
.34425 

.02206 
.02207 
.02208 
.02209 

8.35614 
.35635 
.35656 
.35677 

.02271 
.02272 
.02273 
.02274 

40 
S9 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 

^7 

8.30578 
.30600 
.30622 
.30644 

.02022 
.02023 
.02024 
.02025 

8.31887 
.31909 
.31930 
.31952 

.02084 
.02085 
.02086 
.02087 

8.33176 
.33198 
.33219 
.33240 

.02147 
.02148 
.02149 
.02150 

8.34446 
.34467 
.34488 
.34509 

.02210 
.02211 
.02212 
.02214 

8.35697 
.35718 
.35739 
.35759 

.02275 
.02276 
.02277 
.02278 

+     r 

29 
30 
31 

8.30666 
.30688 
.30710 
.30732 

.02026 
.02027 
.02028 
.02029 

8.31974 
.31995 
.32017 
.32039 

.02088 
.02089 
.02090 
.02091 

8.33262 
.33283 
.33304 
.33325 

.02151 
.02152 
.02153 
.02154 

8.34530 
.34551 
.34572 
.34593 

.02215 
.02216 
.02217 
.02218 

8.35780 
.35801 
.35821 
.35842 

.02279 
.02280 
.02281 
.02283 

+   8' 
33 
34 
35 

8.30754 
.30776 
.30798 
.30820 

.02030 
.02031 
.02032 
.02033 

8.32060 
.32082 
.32103 
.32125 

.02092 
.02093 
.02094 
.02095 

8.33347 
.33368 
.33389 
.33411 

.02155 
.02156 
.02157 
.02158 

8.34614 
.34635 
.34656 
.34677 

.02219 
.02220 
.02221 
.02222 

8.35863 
.35883 
.35904 
.35925 

.02284 
.02285 
.02286 
.02287 

28 

27 
26 
25 

24 
23 

22 
21 

+   9^ 

37 
38 
39 

8.30842 
.30863 
.30885 
.30907 

.02034 
.02035 
.02036 
.02037 

8.32147 
.32168 
.32190 
.32211 

.02096 
.02097 
.02098 
.02099 

8.33432 
.33453 
.33474 
.33496 

.02159 
.02160 
.02161 
.02162 

8.34698 
.34719 
.34740 
.34761 

.02223 
.02224 
.02225 
.02226 

8.35945 
.35966 
.35987 
.36007 

.02288 
.02289 
.02290 
.02291 

+  W 

41 
42 
43 

8.30929 
.30951 
.30973 
.30995 

.02038 
.02039 
.02040 
.02042 

8.32233 
.32254 
.32276 
.32297 

.02101 
.02102 
.02103 
.02104 

8.33517 
.33538 
.33559 
.33580 

.02164 
.02165 
.02166 
.02167 

8.34782 
.34803 
.34823 
.34844 

.02227 
.02229 
.02230 
.02231 

8.36028 
.36048 
.36069 
.36090 

.02292 
.02293 
.02295 
.02296 

20 
19 
18 
17 
16 
15 
14 
13 

+  11' 

45 
46 
47 

8.31017 
.31039 
.31060' 
.31082 

.02043 
.02044 
.02045 
.02046 

8.32319 
.32341 
.32362 
.32384 

.02105 
.02106 
.02107 
.02108 

8.33602 
.33623 
.33644 
.33665 

.02168 
.02169 
.02170 
.02171 

8.34865 
.34886 
.34907 
.34928 

.02232 
.02233 
.02234 
.02235 

8.36110 
.36131 
.36151 
.36172 

.02297 
.02298 
.02299 
.02300 

+     12' 

49 
50 
51 

8.31104 
.31126 
.31148 
.31170 

.02047 
.02048 
.02049 
.02050 

8.32405 
.32427 
.32448 
.32470 

.02109 
.02110 
.02111 
.02112 

8.33686 
.33708 
.33729 
.33750 

.02172 
.02173 
.02174 
.02175 

8.34949 
.34970 
.34991 
.35011 

.02236 
.02237 
.02238 
.02239 

8.36193 
.36213 
.36234 
.36254 

.02301 
.02302 
.02303 
.02304 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

8.31192 
.31213 
.31235 
.31257 

.02051 
.02052 
.02053 
.02054 

8.32491 
.32513 
.32534 
.32556 

.02113 
.02114 
.02115 
.02116 

8.33771 
.33792 
.33814 
.33835 

.02176 
.02177 
.02178 
.02179 

8.35032 
.35053 
.35074 
.35095 

.02240 
.02241 
.02243 
.02244 

8.36275 
.36295 
.36316 
.36337 

.02305 
.02307 
.02308 
.02309 

+  14' 

57 
55 
59 

8.31279 
.31301 
.31322 
.31344 

.02055 
.02056 
.02057 
.02058 

8.32577 
.32599 
.32620 
.32642 

.02117 
.02118 
.02119 
.02120 

8.33856 
.33877 
.33898 
.33919 

.02181 
.02182 
.02183 
.02184 

8.35116 
.35137 
.35157 
.35178 

.02245 
.02246 
.02247 
.02248 
.02249 

8.36357 
.36378 
.36398 
.36419 

.02310 
.02311 
.02312 
.03313 

4 
3 
2 
1 

+  15' 

8.31366 

.02059 

8.32663 

.02121 

8.33940 

.02185 

8.35199 

8.36439 

.02314 

0 

22^  54^ 

22h  5Sm 

22h  52m 

22h  51r^ 

22h  50m 

TABLE  45.                 [Page  825 
Haversines. 

s 

nior^nw 

niimn°  i5' 

Ih  12ml%°(i' 

nis^WW 

1*^4"  18°  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

8.36439 
.36460 
.36480 
.36501 

.02314 
.02315 
.02316 
.02317 

8.37662 
.37682 
.37702 
.37722 

.02380 
.02381 
.02382 
.02384 

8.38867 
.38886 
.38906 
.38926 

.02447 
.02448 
.02449 
.02451 

8.40055 
.40074 
.40094 
.40114 

.02515 
.02516 
.02517 
.02518 

8.41226 
.41246 
.41265 
.41284 

.02584 
.02585 
.02586 
.02587 

60 
59 
58 
57 

+   r 

6 
6 

7 

8.36521 
.36542 
.36562 
.36583 

.02319 
.02320 
.02321 
.02322 

8.37742 
.37763 
.37783 
.37803 

.02385 
.02386 
.02387 
.02388 

8.38946 
.38966 
.38986 
.39006 

.02452 
.02453 
.02454 
.02455 

8.40133 
.40153 
.40172 
.40192 

.02520 
.02521 
.02522 
.02523 

8.41304 
.41323 
.41343 
.41362 

.02588 
.02590 
.02591 
.02592 

56 
55 
54 
53 

+   2^ 

9 

10 

11 

8.36603 
.36624 
.36644 
.36665 

.02323 
.02324 
.02325 
.02326 

8.37823 
.37843 
.37864 
.37884 

.02389 
.02390 
.02391 
.02392 

8.39026 
.39046 
.39066 
.39086 

8.39105 
.39125 
.39145 
.39165 

.02456 
.02457 
.02458 
.02460 

8.40212 
.40231 
.40251 
.40271 

.02524 
.02525 
.02526 
.02528 

8.41381 
.41401 
.41420 
.41439 

.02593 
.02594 
.02595 
.02597 

52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 

+   3' 

13 
14 
16 

8.36685 
.36706 
.36726 
.36746 

.02327 
.02328 
.02329 
.02331 

8.37904 
.37924 
.37944 
.37964 

.02394 
.02395 
.02396 
.02397 

.02461 
.02462 
.02463 
.02464 

8.40290 
.40310 
.40329 
.40349 

.02529 
.02530 
.02531 
.02532 

8.41459 
.41478 
.41497 
.41517 

.02598 
.02599 
.02600 
.02601 

+       4' 
17 
18 
19 

8.36767 
.36787 
.36808 
.36828 

.02332 
.02333 
.02334 
.02335 

8.37985 
.38005 
.38025 
.38045 

.02398 
.02399 
.02400 
.02401 
.02402 
.02404 
.02405 
.02406 

8.39185 
.39205 
.39225 
.39245 

.02465 
.02466 
.02467 
.02469 

8.40369 
.40388 
.40408 
.40427 

.02533 
.02534 
.02536 
.02537 

8.41536 
.41555 
.41575 
.41594 

8.41613 
.41632 
.41652 
.41671 

.02602 
.02603 
.02605 
.02606 
.02607 
.02608 
.02609 
.02610 

+       y 
21 
22 
23 

8.36849 
.36869 
.36889 
.36910 

.02336 
.02337 
.02338 
.02339 

8.38065 
.38085 
.38105 
.38126 

8.39264 
.39284 
.39304 
.39324 

.02470 
.02471 
.02472 
.02473 

8.40447 
.40467 
.40486 
.40506 

.02538 
.02539 
.02540 
.02541 

+      6' 

25 
26 
27 

8.36930 
.36951 
.36971 
.36991 

.02340 
.02342 
.02343 
.02344 

8.38146 
.38166 
.38186 
.38206 

.02407 
.02408 
.02409 
.02410 

8.39344 
.39364 
.39384 
.39403 

.02474 
.02475 
.02476 
.02478 

8.40525 
.40545 
.40564 
.40584 

.02542 
.02544 
.02545 
.02546 

8.41690 
.41710 
.41729 
.41748 

.02612 
.02613 
.02614 
.02615 

36 
85 
34 
33 

+    r 

29 
SO 
31 

8.37012 
.37032 
.37053 
.37073 

.02345 
.02346 
.02347 
.02348 

8.38226 
.38246 
.38266 
.38286 

.02411 
.02412 
.02414 
.02415 

8.39423 
.39443 
.39463 
.39482 

.02479 
.02480 
.02481 
.02482 

8.40603 
.40623 
.40642 
.40662 

.02547 
.02548 
.02549 
.02550 

8.41767 
.41787 
.41806 
.41825 

.02616 
.02617 
.02619 
.02620 

32 
31 
30 
29 
28 
27 
26 
25 

+      8' 
33 
34 
35 

8.37093 
.37114 
.37134 
.37154 

.02349 
.02350 
.02351 
.02353 

8.38306 
.38326 
.38346 
.38367 

.02416 
.02417 
.02418 
.02419 

8.39502 
.39522 
.39542 
.39562 

.02483 
.02484 
.02486 
.02487 

8.40681 
.40701 
.40721 
.40740 

.02552 
.02553 
.02554 
.02555 

8.41845 
.41864 
.41883 
.41902 

.02621 
.02622 
.02623 
.02624 

+   9^ 

37 
38 
39 

8.37175 
.37195 
.37215 
.37236 

.02354 
.02355 
.02356 
.02357 

8.38387 
.38407 
.38427 
.38447 

.02420 
.02421 
.02423 
.02424 

8.39581 
.39601 
.39621 
.39641 

.02488 
.02489 
.02490 
.02491 

8.40760 
.40779 
.40799 
.40818 

.02556 
.02557 
.02559 
.02560 

8.41921 
.41941 
.41960 
.41979 

.02626 
.02627 
.02628 
.02629 

24 

23 
22 
21 

+  W 

41 
42 
43 

8.37256 
.37276 
.37297 
.37317 

.02358 
.02359 
.02360 
.02361 

8.38467 
.38487 
.38507 
.38527 

.02425 
.02426 
.02427 
.02428 

8.39660 
.39680 
.39700 
.39720 

.02492 
.02493 
.02495 
.02496 

8.40837 
.40857 
.40876 
.40896 

.02561 
.02562 
.02563 
.02564 

8.41998 
.42018 
.42037 
.42056 

.02630 
.02631 
.02633 
.02634 

20 
19 
18 
17 
16 
15 
14 
13 

+  11' 

45 

46 
47 

8.37337 
.37358 
.37378 
.37398 

.02363 
.02364 
.02365 
.02366 

8.38547 
.38567 
.38587 
.38607 

.02429 
.02430 
.02431 
.02433 

8.39739 
.39759 
.39779 
.39799 

.02497 
.02498 
.02499 
.02500 

8.40915 
.40935 
.40954 
.40974 

.02565 
.02567 
.02568 
.02569 

8.42075 
.42095 
.42114 
.42133 

.026351 
.02636 
.02637 
.02638 

+  lit' 

49 
50 
61 

8.37419 
.37439 
.37459 
.37479 

.02367 
.02368 
.02369 
.02370 

8.38627 
.38647 
.38667 
.38687 

.02434 
.02435 
.02436 
.02437 

8.39818 
.39838 
.39858 
.39877 

.02501 
.02503 
.02504 
.02505 

8.40993 
.41013 
.41032 
.41052 

.02570 
.02571 
.02572 
.02573 

8.42152 
.42171 
.42190 
,42210 

.02639 
.02641 
.02642 
.02643 

12 

11 

10 

9 

+  13^ 

53 
54 
55 

8.37500 
.37520 
.37540 
.37560 

.02371 
.02372 
.02374 
.02375 

8.38707 

.38727 
.38747 
.38767 

.02438 
.02439 
.02440 
.02442 

8.39897 
.39917 
.39937 
.39956 

.02506 
.02507 
.02508 
.02509 

8.41071 
.41090 
.41110 
.41129 

.02575 
.02576 
.02577 
.02578 

8.42229 
.42248 
.42267 
.42286 

.02644 
.02645 
.02646 
.02648 

8 
7 
6 
6 

+  W 

67 
68 
59 

8.37581 
.37601 
.37621 
.37641 

.02376 
.02377 
.02378 
.02379 
.02380 

8.38787 
.38807 
.38827 
.38847 

.02443 
.02444 
.02445 
.02446 

8.39976 
.39996 
.40015 
.40035 

.02510 
.02512 
.02513 
.02514 

8.41149 
.41168 
.41187 
.41207 

.02579 
.02580 
.02582 
.02583 

8.42305 
.42324 
.42344 
.42363 

.02649 
.02650 
.02651 
.02652 

4 
3 

2 
1 
0 

+  15' 

8.37662 

8.38867 

.02447 

8.40055 

.02515 

8.41226 

.02584 

8.42382 

.02653 

221^  49"" 

22^48^'* 

22^  47 ■^ 

22^46-«^ 

22^46^ 

Page  826] 

TABLE  45. 

Haversines. 

s 

Ih  15m  18°  45' 

Ih  16m  19°  0' 

Ih  17m  19°  15/ 

lM8m  19°  30' 

Ih  19m  19°  45' 

s 

60 
59 
58 

57 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

8.42382 
.42401 
.42420 
.42439 

.03053 
.03655 
.03656 
.02657 

8.43522 
.43541 
.43560 

.43578 

.03734 
.03735 
.03736 
.03738 

8.44647 
.44665 
.44684 
.44703 

.03796 
.03797 
.03798 
.03799 

8.45757 
.45775 
.45794 
.45812 

.03868 
.03869 
.03870 
.03871 

8.46852 
.46871 
.46889 
.46907 

.03941 
.03943 
.03944 
.03945 

+     r 

5 
6 

7 

8.42458 
.42477 
.42497 
.42516 

.0365S 
.02659 
.03661 
.03663 

8.43597 
.43616 
.43635 
.43654 

.03739 
.03730 
.03731 
.03733 

8.44721 
.44740 
.44758 
.44777 

8:44796 
.44814 
.44833 
.44851 

.03800 
.02803 
.03803 
.03804 
.03805 
.03806 
.03808 
.03809 

8.45830 
.45849 
.45867 
.45885 

8.45904 
.45922 
.45940 
.45959 

.03873 
.03874 
.03875 
.03376 

8.46925 
.46943 
.46961 
.46979 

.03946 
.03947 
.03949 
.03950 

56 

55 
54 
53 

+       2^ 

9 

10 

11 

8.42535 
.42554 
.42573 
.42592 

.03663 
.02664 
.03665 
.03666 

8.43673 
.43692 
.43710 
.43729 

.03734 
.03735 
.03736 
.03737 

.03878 
.03879 
.03880 

.03881 

8.46998 
.47016 
.47034 
.47052 

.03951 
.03953 
.03954 
.03955 
.03956 
.03957 
.03958 
.03960 

52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 

+   3' 

13 
14 
15 

8.42611 
.42630 
.42649 
.42668 

.03668 
.03669 
.03670 
.03671 

8.43748 
.43767 
.43786 
.43805 

.03738 
.03739 
.03741 
.03743 

8.44870 
.44889 
.44907 
.44926 

.03810 
.03811 
.03813 
.03814 

8.45977 
.45995 
.46014 
.46032 

.03883 
.03884 

.03885 
.03886 

8.47070 
.47088 
.47106 
.47124 

+   4' 
17 
18 
19 

8.42687 
.42706 
.42725 
.42745 

.03673 
.03673 
.02675 
.03676 

8.43823 
.43842 
.43861 
.43880 

.03743 
.03744 
.03745 
.03747 

8.44944 
.44963 
.44981 
.45000 

.03815 
.03816 
.03817 

.03818 

8.46050 
.46069 
.46087 
.46105 

.03887 
.03889 
.03890 
.03891 

8.47142 
.47160 
.47178 
.47197 

.03961 
.03963 
.03963 
.03965 

+       5^ 
21 
22 
23 

8.42764 
.42783 
.42802 
.42821 

.03677 
.02678 
.03679 
.036S0 

8.43899 
.43917 
.43936 
.43955 

8.43974 
.43992 
.44011 
.44030 

.03748 
.03749 
.03750 
.03751 

8.45018 
.45037 
.45055 
.45074 

.03830 
.03831 
.03833 
.03833 

8.46124 
.46142 
.46160 
.46179 

.03893 
.03893 
.03895 
.03896 

8.47215 
.47233 
.47251 
.47269 

.03966 
.03967 
.03968 
.03970 

40 
39 
38 
37 

+       6^ 

25 
26 
27 

8.42840 
.42859 
.42878 
.42897 

.03683 
.03683 
.03684 
.03685 

.03753 
.03754 
.03755 
.03756 

8.45093 
.45111 
.45130 
.45148 

.03834 
.03836 
.03837 

.03838 

8.46197 
.46215 
.46233 
.46252 

.03897 
.03898 
.03900 
.03901 

8.47287 
.47305 
.47323 
.47341 

.03971 
.03973 
.03973 
.02974 

36 
35 
34 
33 

+     r 

29 
30 
31 

8.42916 
.42935 
.42954 
.42973 

.03686 
.03688 
.03689 
.03890 

8.44049 
.44067 
.44086 
.44105 

.03757 
.03759 
.03760 
.03761 

8.45167 
.45185 
.45204 
.45222 

.03839 
.03830 
.03832 
.03833 
.03834 
.03835 
.03836 
.03838 
.03839 
.03840 
.03841 
.03843 

8.46270 
.46288 
.46306 
.46325 

.03903 
.03903 
.03904 
.03906 

8.47359 
.47377 
.47395 
.47413 

.03976 
.03977 
.03978 
.03979 

32 
31 
30 

29 

+      8' 
33 
34 
35 

8.42992 
.43011 
.43030 
.43049 

.03691 
.03693 
.03693 
.03695 

8.44124 
.44142 
.44161 
.44180 

.03763 
.03763 
.02764 
.03766 

8.45241 
.45259 
.45278 
.45296 

8.46343 
.46361 
46379 
.46398 

.03907 
.03908 
.03909 
.03911 

8.47431 
.47449 
.47467 
.47485 

.03981 
.03983 
.03983 
.02984 

28 
27 
26 
25 

+     r 

37 
38 
39 

8.43068 
.43087 
.43106 
.43125 

.03696 
.03697 
.03698 
.03699 

8.44199 
.44217 
.44236 
.44255 

.03767 
.03768 
.03769 
.03771 

8.45315 
.45333 
.45352 
.45370 

8.46416 
.46434 
.46452 
.46471 

.03913 
.03913 
.03914 
V03915 

8.47503 
.47521 
.47539 
.47557 

.03986 
.03987 
.03988 
.03989 

24 
23 
22 
21 

+  10' 

41 

42 

43 

8.43144 
.43163 
.43181 
.43200 

.03700 
.03703 
.03703 
.03704 

8.44273 
.44292 
.44311 
.44330 

.03773 
.03773 
.03774 
.03775 

8.45388 
.45407 
.45425 
.45444 

.02844 
.03845 
.03846 
.03847 

8.46489 
.46507 
.46525 
.46544 

.03917 
.03918 
.03919 
.03930 

8.47575 
.47593 
.47611 
.47629 

.03991 
.03993 
.03993 
.03994 

20 
19 
18 
17 

+     11' 

45 
46 

47 

8.43219 
.43238 
.43257 
.43276 

.03705 
.03706 
.03708 
.03709 

8.44348 
.44367 
.44386 
.44404 

.03776 
.03778 
.03779 
.03780 

8.45462 
.45481 
.45499 
.45518 

.03849 
.03850 
.03851 
.03853 

8.46562 
.46580 
.46598 
.46616 

.03933 
.03933 
.03934 
.03935 

8.47647 
.47665 
.47683 
.47701 

.03996 
.03997 
.03998 
.03999 

16 
15 
14 
IS 

+    n' 

49 
50 
51 

8.43295 
.43314 
.43333 
.43352 

.03710 
.03711 
.03713 
.03713 

8.44423 
.44442 
.44460 
.44479 

.03781 
.03783 
.03784 
.03785 

8.45536 
.45554 
.45573 
.45591 

.03853 
.03855 
.03856 
.03857 

8.46634 
.46653 
.46671 
.46689 

.03936 
.03938 
.03939 
.03930 

8.47719 

.47737 
.47755 
.47773 

.03000 
.03003 
.03003 
.03004 

12 

11 

10 

9 

+  13' 

53 
54 
55 

8.43371 
.43390 
.43409 
.43427 

.03715 
.03716 
.03717 
.03718 

8.44498 
.44516 
.44535 
.44554 

.03786 
.03787 

.03788 
.03790 

8.45610 
.45628 
.45646 
.45665 

.03858 
.02859 
.02861 
.02863 

8.46707 
.46725 
.46744 
.46762 

.03931 
.03933 
.03934 
.03935 

8.47791 
.47809 
.47827 
.47844 

.03005 
.03007 
.03008 
.03009 

8 
7 
6 
5 

4 
S 
2 
1 

+     W 

57 
58 
59 

8.43446 
.43465 
.43484 
.43503 

8.43522 

.03719 
.03731 
.03733 
.02733 

8.44572 
.44591 
.44610 
.44628 

.03791 
.03793 
.03793 
.03794 

8.45683 
.45702 
.45720 
.45738 

.03863 
.02864 
.02868 
.02867 

8.46780 
.46798 
.46816 
.46834 

.03936 
.03938 
.03939 
.03940 

8.47862 
.47880 
.47898 
.47916 

.03010 
.03013 
.03013 
.03014 

+  15' 

.03734 

8.44647 

.03796 

8.45757 

.03868 

8.46852 

.03941 

8.47934 

.03015 

0 

22  h 

44m 

22  "■ 

43^ 

22  >^ 

42  m 

22!^ 

4im 

22h 

40n 

TABLE  45.                  [Page  827 
Haversines. 

s 

lh20mW°fy 

Ih  2irn.  20°  15' 

lh22:rn,  20°  30' 

Ih  23m  20°  ^5' 

Ih  24m  21°  0' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
8 

8.47934 
.47952 
.47970 

.47988 

.03015 
.03017 
.03018 
.03019 

8.49002 
.49020 
.49037 
.49055 

.03090 
.03092 
.03093 
.03094 

8.50056 
.50074 
.50091 
.50109 

.03166 
.03168 
.03169 
.03170 

8.51098 
.51115 
.51132 
.51150 

.03243 
.03245 
.03246 
.03247 

8.52127 
.52144 
.52161 
.52178 

.03321 
.03322 
.03324 
.03325 

60 
59 
58 
57 
66 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+   1^ 

5 

6 

7 

8.48006 
.48024 
.48041 
.48059 

.03020 
.03022 
.03023 
.03024 

8.49073 
.49090 
.49108 
.49126 

.03095 
.03097 
.03098 
.03099 

8.50126 
.50144 
.50161 
.50179 

.03171 
.03173 
.03174 
.03175 

8.51167 
.51184 
.51201 
.51219 

.03248 
.03250 
.03251 
.03252 

8.52195 
.52212 
.52229 
.52246 

.03326 
.03328 
.03329 
.03330 

+       V 

9 

10 

11 

8.48077 
.48095 
.48113 
.48131 

.03025 
.03027 
.03028 
.03029 

8.49143 
.49161 
.49179 
.49196 

.03101 
.03102 
.03103 
.03104 

8.50196 
.50214 
.50231 
.50248 

.03177 
.03178 
.03179 
.03180 

8.51236 
.51253 
.51270 
.51287 

.03254 
.03255 
.03256 
.03257 

8.52263 
.52280 
.52297 
.52314 

.03331 
.03333 
.03334 
.03335 

+       3' 

IS 
14 
15 

8.48149 
.48167 
.48184 
.48202 

.03030 
.03032 
.03033 
.03034 

8.49214 
.49232 
.49249 
.49267 

.03106 
.03107 
.03108 
.03109 

8.50266 
.50283 
.50301 
.50318 

.03182 
.03183 
.03184 
.03186 

8.51305 
.51322 
.51339 
.51356 

.03259 
.03260 
.03261 
.03263 

8.52331 
.52348 
.52365 
.52382 

.03337 
.03338 
.03339 
.03341 

+   4^ 
17 
18 
19 

8.48220 
.48238 
.48256 
.48274 

.03035 
.03037 
.03038 
.03039 

8.49284 
.49302 
.49320 
.49337 

.03111 
.03112 
.03113 
.03114 

8.50335 
.50353 
.50370 
.50388 

8.50405 
.50422 
.50440 
.50457 

.03187 
.03188 
.03189 
.03191 

8.51374 
.51391 
.51408 
.51425 

.03264 
.03265 
.03266 
.03268 

8.52399 
.52416 
.52433 
.52450 

.03342 
.03343 
.03344 
.03346 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

21 

22 
2S 

8.48292 
.48309 
.48327 
.48345 

.03040 
.03042 
.03043 
.03044 

8.49355 
.49373 
.49390 
.49408 

.03116 
.03117 
.03118 
.03119 

.03192 
.03193 
.03194 
.03196 

8.51442 
.51459 
.51477 
.51494 

.03269 
.03270 
.03272 
.03273 

8.52467 
.52484 
.52501 
.52518 

.03347 
.03348 
.03350 
.03351 

•+   6' 

25 
26 
27 

8.48363 
.48381 
.48399 
.48416 

.03045 
.03047 
.03048 
.03049 

8.49425 
.49443 
.49461 
.49478 

.03121 
.03122 
.03123 
.03125 

8.50475 
.50492 
.50509 
.50527 

.03197 
.03198 
.03200 
.03201 

8.51511 
.51528 
.51545 
.51562 

.03274 
.03275 
.03277 
.03278 

8.52535 
.52552 
.52569 
.52585 

.03352 
.03354 
.03355 
.03356 

+     r 

29 
SO 
SI 

8.48434 
.48452 
.48470 
.48488 

.03050 
.03052 
.03053 
.03054 

8.49496 
.49513 
.49531 
.49548 

.03126 
.03127 
.03128 
.03130 

8.50544 
.50561 
.50579 
.50596 

.03202 
.03204 
.03205 
.03206 

8.51580 
.51597 
.51614 
.51631 

.03279 
.03281 
.03282 
.03283 

8.52602 
.52619 
.52636 
.52653 

.03358 
.03359 
.03360 
.03361 

32 
31 

SO 
29 
28 
27 
26 
25 

+   8' 

ss 
S4 
S5 

8.48505 
.48523 
.48541 
.48559 

.03055 
.03057 
.03058 
.03059 

8.49566 
.49584 
.49601 
.49619 

.03131 
.03132 
.03133 
.03135 

8.50614 
.50631 
.50648 
.50666 

.03207 
.03209 
.03210 
.03211 

8.51648 
.51665 
.51682 
.51700 

.03285 
.03286 
.03287 
.03288 

8.52670 
.52687 
.52704 
.52721 

.03363 
.03364 
.03365 
.03367 

+   9^ 

S7 
S8 
S9 

8.48576 
.48594 
.48612 
.48630 

.03060 
.03062 
.03063 
.03064 

8.49636 
.49654 
.49671 
.49689 

.03136 
.03137 
.03138 
.03140 

8.50683 
.50700 
.50718 
.50735 

.03212 
.03214 
.03215 
.03216 

8.51717 
.51734 
.51751 
.51768 

.03290 
.03291 
.03292 
.03294 

8.52738 
.52755 
.52772 
.52789 

.03368 
.03369 
.03371 
.03372 

24 
23 
22 
21 

+     10' 

41 
42 
4S 

8.48648 
.48665 
.48683 
.48701 

.03065 
.03067 
.03068 
.03069 

8.49706 
.49724 
.49742 
.49759 

.03141 
.03142 
.03144 
.03145 

8.50752 
.50770 
.50787 
.50804 

.03218 
.03219 
.03220 
.03221 

8.51785 
.51802 
.51819 
.51836 

.03295 
.03296 
.03298 
.03299 

8.52806 
.52822 
.52839 
.52856 

.03373 
.03375 
.03376 
.03377 

20 
19 
18 
17 

+     11^ 

45 
46 
47 

8.48719 
.48736 
.48754 
.48772 

.03070 
.03073 
.03073 
.03074 

8.49777 
.49794 
.49812 
.49829 

.03146 
.03147 
.03149 
.03150 

8.50821 
.50839 
.50856 
.50873 

.03223 
.03224 
.03225 
.03227 

8.51854 
.51871 
.51888 
.51905 

.03300 
.03301 
.03303 
.03304 

8.52873 
.52890 
.52907 
.52924 

.03379 
.03380 
.03381 
.03382 

16 
15 
14 
13 

+  12' 

49 
50 
51 

8.48789 
.48807 
.48825 
.48843 

.03075 
.03077 
.03078 
.03079 

8.49847 
.49864 
.49882 
.49899 

.03151 
.03152 
.03154 
.03155 

8.50891 
.50908 
.50925 
.50943 

.03228 
.03229 
.03230 
.03232 

8.51922 
.51939 
.51956 
.51973 

.03305 
.03307 
.03308 
.03309 

8.52941 
.52958 
.52974 
.52991 

.03384 
.03385 
.03386 
.03388 

12 

11 

10 

9 

4-  13' 

53 
54 
55 

8.48860 
.48878 
.48896 
.48914 

.03080 
.03082 
.03083 
.03084 

8.49917 
.49934 
.49952 
.49969 

.03156 
.03157 
.03159 
.03160 

8.50960 
.50977 
.50994 
.51012 

.03233 
.03234 
.03236 
.03237 

8.51990 
.52007 
.52024 
.52041 

.03311 
.03312 
.03313 
.03314 

8.53008 
.53025 
.53042 
.53059 

.03389 
.03390 
.03392 
.03393 

8 

7 
6 

5 

4-  U' 

57 
58 
59 

8.48931 
.48949 
.48967 
.48984 

.03085 
.03087 
.03088 
.03089 

8.49987 
.50004 
.50022 
.50039 

.03161 
.03163 
.03164 
.03165 

8.51029 
.51046 
.51063 
.51081 

.03238 
.03239 
.03241 
.03242 

8.52058 
.52076 
.52093 
.52110 

.03316 
.03317 
.03318 
.03320 

8.53076 
.53092 
.53109 
.53126 

.03394 
.03396 
.03397 
.03398 

4 
3 
2 
1 

f  15' 

8.49002 

.03090 

8.50056 

.03166 

8.51098 

.03243 

8.52127 

.03321 

8.53143 

.03400 

0 

22^  39'"^ 

22^  SS^ 

22^  37^ 

22h  36m 

22^  35m 

21594°— 14- 


-45 


Page  828]                 TABLE  45. 

Haversines. 

s 

Ih  25m  21°  15^ 

ift  26m  21°  30^ 

Ih  27m  21°  45' 

jh  28m  23°  0' 

J  ft  29m  22°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

8.53143 
.53160 
.53177 
.53193 

.03400 
.03401 
.03403 
.03404 

8.54147 
.54164 
.54180 
.54197 

.03479 
.03480 
.03483 
.03483 

8.55139 
.55156 
55172 
.55189 

.03560 
.03561 
.03563 
.03564 

8.56120 
.56136 
.56152 
.56169 

.03641 
.03643 
.03644 
.03645 

8.57089 
.57105 
.57121 
.57137 

.03733 
.03734 
.03736 
.03737 

60 
59 
58 
57 

+  1' 

5 
6 

7 

8.53210 
.53227 
.53244 
.53261 

.03405 
.03406 
.03408 
.03409 

8.54214 
.54230 
.54247 
.54263 

.03484 
.03486 
.03487 
.03488 

8.55205 
.55221 
55238 
.55254 

.03565 
.03566 
.03568 
.03569 

8.56185 
.56201 
.56217 
.56233 

.03646 
.03648 
.03649 
.03650 

8.57153 
.57169 

.57185 
.57201 

.03738 
.03730 
.03731 
.03733 

56 
55 

54 
53 

+   2' 

9 

10 

11 

8.53277 
.53294 
.53311 
.53328 

.03410 
.03411 
.03413 
.03414 

8.54280 
.54297 
.54313 
.54330 

.03490 
.03491 
.03493 
.03494 

8.55271 
.55287 
.55303 
.55320 

.03570 
.03573 
.03573 
.03574 

8.56250 
.56266 
.56282 
.56298 

.03653 
.03053 
.03654 
.03656 

8.57217 
.57233 
.57230 
.57266 

.03734 
.03735 
.03737 
.03738 

52 
51 
50 
49 

+   3' 

13 
14 
15 

8.53345 
.53361 
.53378 
.53395 

.03415 
.03417 
.03418 
.03419 

8.54346 
.54363 
.54380 
.54396 

.03495 
.03496 
.03498 
.03499 

8.55336 
.55353 
.55369 
.55385 

.03576 
.03577 
.03578 
.03580 

8.56315 
.56331 
.56347 
.56363 

.03657 
.03659 
.03660 
.03661 

8.57282 
.57298 
.57314 
.57330 

.03740 
.03741 
.03743 
.03744 

48 
47 
46 
45 

+   4' 
17 
18 
19 

8.53412 
.53429 
.53445 
.53462 

.03431 
.03433 
.03433 
.03435 

8.54413 
.54429 
.54446 
.54462 

.03500 
.03503 
.03503 
.03504 

8.55402 
.55418 
.55435 
.55451 

.03581 
.03583 
.03584 
.03585 

8.56379 
.56396 
.56412 
.56428 

.03663 
.03664 
.03665 
.03667 

8.57346 
.57362 
.57378 
.57394 

.03745 
.03746 
.03748 
.03749 

44 
43 
42 
41 

+   5^ 
21 
22 
23 

8.53479 
.53496 
.53512 
.53529 

.03436 
.03437 
.03439 
.03430 

8.54479 
.54496 
.54512 
.54529 

.03506 
.03507 
.03509 
.03510 

8.55467 
.55484 
.55500 
.55516 

.03587 
.03588 
.03589 
.03591 

8.56444 
.56460 
.56477 
.56493 

.03668 
.03669 
.03671 
.03673 

8.57410 
.57426 
.57442 
.57458 

.03751 
.03753 
.03753 
.03755 

40 
39 
38 
37 

+   6^ 

25 
26 
27 

8.53546 
.53563 
.53580 
.53596 

.03431 
.03433 
.03434 
.03435 

8.54545 
.54562 
.54578 
.54595 

.03511 
.03513 
.03514 
.03515 

8.55533 
.55549 
.55566 
.55582 

.03593 
.03593 
.03595 
.03596 

8.56509 
.56525 
.56541 
.56557 

.03674 
.03675 
.03676 
.03678 

8.57474 
.57490 
.57506 

.57522 

.03756 
.03757 
.03759 
.03760 

36 
35 

34 
33 

+    r 

29 
30 
31 

8.53613 
.53630 
.53646 
.53663 

.03437 
.03438 
.03439 
.03441 

8.54612 
.54628 
.54645 
.54661 

.03517 
.03518 
.03519 
.03531 

8.55598 
.55615 
.55631 
.55647 

.03597 
.03599 
.03600 
.03601 

8.56574 
.56590 
.56606 
.56622 

.03679 
.03680 
.03683 
.03683 

8.57538 
.57554 
.57570 
.57585 

.03763 
.03763 
.03764 
.03766 

32 
31 
30 
29 

+   8' 
33 
34 
35 

8.53680 
.53697 
.53713 
.53730 

.03443 
.03443 
.03445 
.03446 

8.54678 
.54694 
.54711 

.54727 

.03533 
.03533 
.03535 
.03536 

8.55664 
.55680 
.55696 
.55713 

.03603 
.03604 
.03605 
.03607 

8.56638 
.56654 
.56670 
.56687 

.03685 
.03686 
.03687 
.03689 

8.57601 
.57617 
.57633 
.57649 

.03767 
.03769 
.03770 
.03771 

28 
27 
26 

25 

+      9" 

37 
38 
39 

8.53747 
.53764 
.53780 
.53797 

.03447 
.03449 
.03450 
.03451 

8.54744 
.54760 
.54777 
.54793 

.03537 
.03539 
.03530 
.03531 

8.55729 
.55745 
.55762 
.55778 

.03608 
.03610 
.03611 
.03613 

8.56703 
.56719 
.56735 
.56751 

.03690 
.03691 
.03693 
.03694 

8.57665 
.57681 
.57697 
.57713 

.03773 
.03774 
.03775 
.03777 

24 
23 
22 
21 

+     W 

41 
42 
43 

8.53814 
.53830 
.53847 
.53864 

.03453 
.03454 
.03455 
.03457 

8.54810 
.54826 
.54843 
.54859 

.03533 
.03534 
.03535 
.03537 

8.55794 
.55811 
.55827 
.55843 

.03614 
.03615 
.03616 
.03618 

8.56767 
.56783 
.56799 
.56816 

.03695 
.03697 
.03698 
.03700 

8.57729 
.57745 
.W761 

.57777 

.03778 
.03780 
.03781 
.03783 

20 
19 
18 
17 
16 
15 
14 
13 

+   ir 

45 
46 
47 

8.53880 
.53897 
.53914 
.53930 

.03448 
.03459 
.03460 
.03463 

8.54876 
.54892 
.54909 
.54925 

.03538 
.03539 
.03541 
.03543 

8.55859 
.55876 
.55892 
.55908 

.03619 
.03630 
.03633 
.03633 

8.56832 
.56848 
.56864 
.56880 

.03701 
.03703 
.03704 
.03705 

8.57793 
.57809 
.57825 
.57841 

.03784 
.03785 
.03787 

.03788 

+     ir 

49 
50 
51 

8.53947 
.53964 
.53980 
.53997 

.03463 
.03464 
.03466 
.03467 

8.54942 
.54958 
.54975 
.54991 

.03543 
.03545 
.03546 
.03547 

8.55925 
55941 
.55957 
.55973 

.03634 
.03636 
.03637 
.03639 

8.56896 
.56912 
56928 
.56944 

.03706 
.03708 
.03709 
.03711 

8.57856 
.57872 
.57888 
.57904 

.03789 
.03791 
.03793 
.03794 

12 

11 

10 

9 

+     13^ 

53 
54 
55 

8.54014 
.54030 
.54047 
.45064 

.03468 
.03470 
.03471 
.03473 

8.55008 
.55024 
.55041 
.55057 

.03549 
.03550 
.03551 
.03553 

8.55990 
56006 
.56022 
.56039 

.03630 
.03631 
.03633 
.03634 

8.56960 
56977 
.56993 
.57009 

.03713 
.03713 
.03715 
.03716 

8.57920 
.57936 
57952 
.57968 

.03795 
.03796 
.03798 
.03799 

8 
7 
6 
5 

+  W 

57 
58 
59 

8.54080 
.54097 
.54114 
.54130 

.03474 
.03475 
.03476 
.03478 

8.55073 
.55090 
.55106 
.55123 

.03554 
.03555 
.03557 
.03558 

8.56055 
.56071 
.56087 
.56104 

.03635 
.03637 
.03638 
.03639 

8.57025 
.57041 
.57057 
.57073 

.03717 
.03719 
.03730 
.03733 

8.57984 
.58000 
.58015 
.58031 

.03800 
.03803 
.03803 
.03805 

4 
3 
2 
1 
0 

+     16' 

8.54147 

.03479 

8.55139 

.03560 

8.56120 

.03641 

8.57089 

.03733 

8.58047 

.03806 

22^  34"^ 

ff  ft  33m 

22^  32m         1 

22^  3lm 

22^  30m 

TABLE  45.                 [Page  829 

Havereines. 

s 

insOrn  22°  30' 

lhSim^°i5' 

lhS2mZ3°0' 

in  ssm  23°  15' 

1A54"»23°30' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

s 
s 

8.58047 
.58063 
.58079 
.58095 

.03806 
.03807 
.03809 
.03810 

8.58994 
.59010 
.59026 
.59042 

.03890 
.03891 
.03893 
.03894 

8.59931 
.59947 
.59962 
.59978 

.03975 
.03976 
.03978 
.03979 

8.60857 
.60873 
.60888 
.60903 

.04060 
.04062 
.04063 
.04065 

8.61773 
61789 
.61804 
.61819 

.04147 
.04148 
.04150 
.04151 

60 
59 
58 

57 

+     r 

5 
6 
7 

8.58111 
.58127 
.58142 
.58158 

.03812 
.03813 
.03814 
.03816 

8.59057 
.59073 
.59089 
.59104 

.03896 
.03897 
.03898 
.03900 

8.59993 
.60009 
.60024 
.60040 

.03980 
.03982 
.03983 
.03985 

8.60919 
.60934 
.60949 
.60965 

.04066 
.04068 
.04069 
.04070 

8.61834 
.61849 
.61864 
.61880 

.04153 
.04154 
.04156 
.04157 

56 
55 
54 
53 
52 
51 
50 
49 
4S 
47 
46 
45 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

+       r 

9 

10 

11 

8.58174 
.58190 
.58206 
.58222 

.03817 
.03819 
.03820 
.03821 

8.59120 
.59136 
.59151 
.59167 

.03901 
.03903 
.03904 
.03905 

8.60055 
.60071 
,60086 
.60102 

.03986 
.03988 
.03989 
.03990 

8.60980 
.60995 
.61011 
.61026 

8.61041 
.61057 
.61072 
.61087 

.04072 
.04073 
.04075 
.04076 

8.61895 
.61910 
.61925 
.61940 

.04159 
.04160 
.04162 
.04163 

+      3' 

IS 
14 
15 

8.58238 
.58253 
.58269 
.58285 

.03823 
.03824 
.03826 
.03827 

8.59183 
.59198 
.59214 
.59230 

.03907 
.03908 
.03910 
.03911 

8.60117 
.60133 
.60148 
.60164 

.03992 
.03993 
.03995 
.03996 

.04078 
.04079 
.04081 
.04082 

8.61955 
.61971 
.61986 
.62001 

.04164 
.04166 
.04167 
.04169 

17 
18 
19 

8.58301 
.58317 
.58333 
.58348 

.03828 
.03830 
.03831 
.03833 

8.59245 
.59261 
.59277 
.59292 

.03912 
.03914 
.03915 
.03917 

8.60179 
.60195 
.60210 
.60226 

.03998 
.03999 
.04000 
.04002 

8.61103 
.61118 
.61133 
.61149 

.04083 
.04085 
.04086 
.04088 

8.62016 
.62031 
.62046 
.62061 

.04170 
.04172 
04173 
.04175 

+   5' 
21 
22 
2S 

8.58364 
.58380 
.58396 
.58412 

.03834 
.03835 
.03837 
.03838 

8.59308 
.59323 
.59339 
.59355 

8.59370 
.59386 
.59402 
.59417 

.03918 
.03920 
.03921 
.03922 

8.60241 
.60256 
.60272 
.60287 

.04003 
.04005 
.04006 
.04007 

8.61164 
.61179 
.61194 
.61210 

.04089 
.04091 
.04092 
.04094 

8.62077 
.62092 
.62107 
.62122 

.04176 
.04177 
.04179 
.04180 

+   6' 

25 
26 
27 

8.58427 
.58443 
.58459 
.58475 

.03839 
.03841 
.03842 
.03844 

.03924 
.03925 
.03927 
.03928 

8.60303 
.60318 
.60334 
.60349 

.04009 
.04010 
.04012 
.04013 

8.61225 
.61240 
.61256 
.61271 

.04095 
.04096 
.04098 
.04099 

8.62137 
.62152 
.62167 
.62182 

.04182 
.04183 
.04185 
.04186 

+    r 

29 
SO 
SI 

8.58491 
.58506 

.58522 
.58538 

.03845 
.03846 
.03848 
.03849 

8.59433 
.59448 
.59464 
.59480 

.03929 
.03931 
.03932 
.03934 

8.60365 
.60380 
.60396 
.60411 

.04015 
.04016 
.04017 
.04019 

8.61286 
.61301 
.61317 
.61332 

.04101 
.04102 
.04104 
.04105 

8.62197 
.62213 
.62228 
.62243 

.04188 
.04189 
.04191 
.04192 

32 
31 
30 
29 

+   8' 
SS 
34 
S5 

8.58554 
.58570 
.58585 
.58601 

.03851 
.03852 
.03853 
.03855 

8.59495 
.59511 
.59527 
.59542 

.03935 
.03936 
.03938 
.03939 

8.60426 
.60442 
.60457 
.60473 

.04020 
.04022 
.04023 
.04025 

8.61347 
.61362 
.61378 
.61393 

.04106 
.04108 
.04109 
.04111 

8.62258 
.62273 
.62288 
.62303 

.04194 
.04195 
.04196 
.04198 

28 

27 
26 

25 

+       9' 

S7 
S8 
S9 

8.58617 
.58633 
.58648 
.58664 

.03856 
.03858 
.03859 
.03860 

8.59558 
.59573 
.59589 
.59604 

.03941 
.03942 
.03944 
.03945 

8.60488 
.60504 
.60519 
.60534 

.04026 
.04027 
.04029 
.04030 

8.61408 
.61423 
.61439 
.61454 

.04112 
.04114 
.04115 
.04117 

8.62318 
.62333 
.62348 
.62363 

.04199 
.04201 
.04202 
.04204 

24 
23 
22 
21 

+  W 

41 

42 
4S 

8.58680 
.58696 
.58711 

.58727 

.03862 
.03863 
.03865 
.03866 

8.59620 
.59636 
.59651 
.59667 

.03946 
.03948 
.03949 
.03951 

8.60550 
.60565 
.60581 
.60596 

.04032 
.04033 
.04035 
.04036 

8.61469 
.61484 
.61500 
.61515 

.04118 
.04119 
.04121 
.04122 

8.62379 
.62394 
.62409 
.62424 

.04205 
.04207 
.04208 
.04210 

20 
19 
18 
17 

+  11' 

45 
46 

47 

8.58743 
.58759 
.58774 
.58790 

.03867 
.03869 
.03870 
.03872 

8.59682 
.59698 
.59714 
.59729 

.03952 
.03953 
.03955 
.03956 

8.60611 
.60627 
.60642 
.60658 

.04038 
.04039 
.04040 
.04042 

8.61530 
.61545 
.61561 
.61576 

.04124 
.04125 
.04127 
.04128 

8.62439 
.62454 
.62469 
.62484 

.04211 
.04212 
.04214 
.04215 

16 
15 
14 
13 

+  13' 

49 
50 
51 

8.58806 
.58822 
.58837 
.58853 

.03873 
.03875 
.03876 
.03877 

8.59745 
.59760 
.59776 
.59791 

.03958 
.03959 
.03961 
.03962 

8.60673 
.60688 
.60704 
.60719 

.04043 
.04045 
.04046 
.04048 

8.61591 
.61606 
.61621 
.61637 

.04130 
.04131 
.04133 
.04134 

8.62499 
.62514 
.62529 
.62544 

.04217 
.04218 
.04220 
.04221 

12 

11 

10 

9 

+  13' 

5S 
54 
55 

8.58869 
.58885 
.58900 
.58916 

.03879 
.03880 
.03882 
.03883 

8.59807 
.59822 
.59838 
.59853 

.03963 
.03965 
.03966 
.03968 

8.60734 
.60750 
.60765 
.60781 

.04049 
.04050 
.04052 
.04053 

8.61652 
.61667 
.61682 
.61697 

.04135 
.04137 
.04138 
.04140 

8.62559 
.62574 
.62589 
.62604 

.04223 
.04224 
.04226 
.04227 

8 
7 
6 
5 

+  14' 

57 
55 
59 

8.58932 
.58947 
.58963 
.58979 

.03884 
.03886 
.03887 
.03889 

5.59869 
.59885 
.59900 
.59916 

.03969 
.03971 
.03972 
.03973 

8.60796 
.60811 
.60827 
.60842 

.04055 
.04056 
.04058 
.04059 

8.61713 
.61728 
.61743 
.61758 

.04141 
.04143 
.04144 
.04146 

8.62619 
.62634 
.62649 
.62664 

.04229 
.04230 
.04232 
.04233 

4 
3 
2 
1 

+  .  16' 

8.58994 

.03890 

8.59931 

.03975 

8.60857 

.04060 

8.61773 

.04147 

8.62680 

.04234 

0 

_ 

22'h'  29in 

22^ 28^ 

22h 2Tm 

22^26^ 

22^  25m          1 

Page  830] 

TABLE  45. 

Haversines. 

3 

Ih35m^3°i5' 

lhS6m24k°0' 

Ih37m2i°15' 

lhS8m2i°W 

lh§9mzi°^5' 

s 

60 
69 
58 
57 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 

2 
3 

8.62680 
.62695 
.62710 
.62725 

.04234 
.04236 
.04237 
.04239 

8.63576 
.63591 
.63606 
.63620 

.04333 
.04334 
.04336 
.04337 

8.64463 
.64477 
.64492 
.64507 

.04413 
.04413 
.04415 
.04416 

8.65340 
.65355 
.65369 
.65384 

.04503 
.04503 
.04505 
.04506 

8.66208 
.66223 
.66237 
.66251 

.04593 
.04594 
.04596 
.04597 

+     r 

6 
6 

7 

8.62740 
.62755 
.62770 
.62785 

.04340 
.04242 
o04243 
.04345 

8.63635 
.63650 
.63665 
.63680 

.04329 
.04330 
.04333 
.04333 

8.64521 
.64536 
.64551 
.64565 

.04418 
.04419 
.04431 
.04433 

8.65398 
.65413 
.65427 
.65442 

.04508 
.04509 
.04511 
.04513 

8.66266 
.66280 
.66295 
.66309 

.04599 
.04600 
.04602 
.04604 

66 
65 
64 
63 

+      3' 

9 

10 

11 

8.62800 
.62815 
.62830 
.62845 

.04246 
.04248 
.04249 
.04351 

8.63695 
.63709 
.63724 
.63739 

.04335 
.04336 
.04338 
.04339 

8.64580 
.64595 
.64609 
.64624 

.04434 
.04435 
.04437 
.04428 

8.65456 
.65471 
.65485 
.65500 

.04514 
.04516 
.04517 
.04519 

8.66323 
.66338 
.66352 
.66366 

.04605 
.04607 
.04608 
.04610 

62 
61 
60 
49 

+       3' 

IS 
14 
15 

8.62860 
.62875 
.62890 
.62904 

8.62919 
.62934 
.62949 
.62964 

.04352 
.04353 
.04355 
.04256 

8.63754 
.63769 
.63784 
.63798 

.04340 
.04343 
.04343 
.04345 

8.64639 
.64653 
.64668 
.64683 

.04430 
.04431 
.04433 
.04434 

8.65514 
.65529 
.65543 
.65558 

.04530 
.04533 
.04533 
.04525 

8.66381 
.66395 
.66409 
.66424 

.04611 
.04613 
.04614 
.04616 

48 
47 
46 
46 

+      i' 
17 
18 
19 

.04258 
.04259 
.04361 
.04363 

8.63813 
.63828 
.63843 
.63858 

.04346 
.04348 
.04349 
.04351 

8.64697 
.64712 
.64727 
.64741 

.04436 
.04437 
.04439 
.04440 

8.65572 
.65587 
.65601 
.65616 

.04526 
.04538 
.04539 
.04531 

8.66438 
.66453 
.66467 
.66481 

.04617 
.04619 
.04620 
.04622 

44 
43 
42 
41 

+   5' 

21 
22 
23 

8.62979 
.62994 
.63009 
.63024 

8.63039 
.63054 
.63069 
.63084 

.04364 
.04365 
.04367 

.04268 

8.63872 
.63887 
.63902 
.63917 

.04353 
.04354 
.04355 
.04357 

8.64756 
.64771 
.64785 
.64800 

.04442 
.04443 
.04445 
.04446 

8.65630 
.65645 
.65659 
.65674 

.04532 
.04534 
.04535 
.04537 

8.66496 
.66510 
.66524 
.66539 

.04623 
.04625 
.04636 
.04638 

40 
39 
38 
37 
36 
36 
34 
33 

+       6' 

25 
26 
27 

.04270 
.04271 
.04373 
.04374 

8.63932 
.63946 
.63961 
.63976 

.04358 
.04360 
.04361 
.04363 

8.64815 
.64829 
.64844 
.64859 

.04448 
.04449 
.04451 
.04452 

8.65688 
.65703 
.65717 
.65732 

.04538 
.04540 
.04541 
.04543 

8.66553 
.66567 
.66582 
.66596 

.04639 
.04631 
.04633 
.04634 

+     r 

29 
SO 
31 

8.63099 
.63114 
.63129 
.63144 

.04376 
.04377 
.04378 
.04280 

8.63991 
.64006 
.64020 
.64035 

.04364 
.04366 
.04367 
.04369 

8.64873 
.64888 
.64902 
.64917 

.04454 
.04455 
.04457 
.04458 

8.65746 
.65761 
.65775 
.65790 

.04544 
.04546 
.04547 
.04549 

8.66610 
.66625 
.66639 
.66653 

.04636 
.04637 
.04639 
.04640 

32 
31 
30 
29 

{ 

+       S' 
S3 
34 
35 

8.63159 
.63174 
.63189 
.63204 

.04281 
.04283 
.04284 
.04286 

8.64050 
.64065 
.64079 
.64094 

.04370 
.04372 
.04373 
.04375 

8.64932 
.64946 
.64961 
.64976 

.04460 
.04461 
.04463 
.04464 

8.65804 
.65819 
.65833 
.65848 

.04550 
.04553 
.04553 
.04555 

8.66668 
.66682 
.66696 
.66710 

.04643 
.04643 
.04645 
.04646 

28 
27 
26 

25 

+       9^ 

37 
38 
39 

8.63218 
.63233 
.63248 
.63263 

.04287 
.04289 
.04290 
.04292 

8.64109 
.64124 
.64139 
.64153 

.04376 
.04378 
.04379 
.04381 

8.64990 
.65005 
.65019 
.65034 

.04466 
.04467 
.04469 
.04470 

8.65862 
.65876 
.65891 
.65905 

.04556 
.04558 
.04559 
.04561 

8.66725 
.66739 
.66753 
.66768 

.04648 
.04649 
.04651 
.04653 

24 
23 
22 
21 

+  10' 

41 
42 
43 

8.63278 
.63293 
.63308 
.63323 

.04293 
.04295 
.04396 
.04398 

8.64168 
.64183 
.64198 
.64212 

.04383 
.04384 
.04385 
.04387 

8.65049 
.65063 
.65078 
.65092 

.04472 
.04473 
.04475 
.04476 

8.65920 
.65934 
.65949 
.65963 

.04563 
.04564 
.04565 
.04567 

8.66782 
.66796 
.66811 
.66825 

.04654 
.04655 
.04657 
.04659 

20 
19 
18 
17 

+  11' 

45 
46 
47 

8.63338 
.63353 
.63368 
.63382 

.04399 
.04301 
.04303 
.04304 

8.64227 
.64242 
.64257 
.64271 

.04388 
.04390 
.04391 
.04393 

8.65107 
.65122 
.65136 
.65151 

.04478 
.04479 
.04481 
.04482 

8.65978 
.65992 
.66006 
.66021 

.04569 
.04570 
.04573 
.04573 

8.66839 
.66853 
.66868 
.66882 

.04660 
.04663 
.04663 
.04665 

16 
15 

14 
13 

+  13' 

49 
50 
51 

8.63397 
.63412 
.63427 
.63442 

.04305 
.04306 
.04308 
.04309 

8.64286 
.64301 
.64315 
.64330 

.04394 
.04395 
.04397 
.04398 

8.65165 
.65180 
.65194 
.65209 

.04484 
.04485 
.04487 
.04488 

8.66035 
.66050 
.66064 
.66079 

.04575 
.04576 
.04578 
.04579 

8.66896 
.66911 
.66925 
.66939 

.04666 
.04668 
.04669 
.04671 

12 

11 

10 

9 

1 

+  13' 

53 
54 
55 

8.63457 
.63472 
.63487 
.63502 

.04311 
.04313 
.04314 
.04315 

8.64345 
.64360 
.64374 
.64389 

.04400 
.04401 
.04403 
.04404 

8.65224 
.65238 
.65253 
.65267 

.04490 
.04491 
.04493 
.04494 

8.66093 
.66107 
.66122 
.66136 

.04581 
.04582 
.04584 
.04585 
.04587 
.04588 
.04590 
.04591 

8.66953 
.66968 
.66982 
.66996 

.04673 
.04674 
.04675 
.04677 

8 
7 
6 
5 

+     14' 

57 
58 
59 

8.63516 
.63531 
.63546 
.63561 

.04317 
.04318 
.04330 
.04331 

8.64404 
.64418 
.64433 
.64448 

.04405 
.04407 
.04409 
.04410 

8.65282 
.65296 
.65311 
.65325 

.04496 
.04497 
.04499 
.04500 

8.66151 
.66165 
.66179 
.66194 

8.67010 
.67025 
.67039 
.67053 

.04678 
.04680 
.04682 
.04683 

4 
3 
2 
1 

+  15' 

8.63576 

.04333 

8.64463 

.04413 

8.65340 

.04502 

8.66208 

.04593 

8.67067 

.04685 

0 

22fi' 

24'"'' 

^:gft  23->n 

22^  22^ 

22  Jt  21'"* 

22Ji20m 

1 

1 

TABLE  45.                 [Page  831 

Havereines. 

s 

Ih  40m  25°  (K  | 

Ih  4im  25°  15^ 

in  42m  25°  W    1 

lh43mU°i5'    1 

lhum2&°0'     1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

8.67067 
.67082 
.67096 
.67110 

.04685 
.04686 
.04688 
.04689 

8.67918 
.67932 
.67946 
.67960 

.04777 
.04779 
.04780 
.04782 

8.68760 
.68773 
.68787 
.68801 

.04871 
.04872 
.04874 
.04875 

8.69593 
.69607 
.69620 
.69634 

.04965 
.04967 
.04968 
.04970 

8.70418 
.70431 
.70445 
.70459 

.05060 
.05062 
.05063 
.05085 

60 
59 
58 
57 

+   1^ 

5 
6 

7 

8.67124 
.67139 
.67153 
.67167 

.04691 
.04692 
.04694 
.04695 

8.67974 
.67988 
.68002 
.68016 

.04783 
.04785 
.04787 
.04788 

8.68815 
.68829 
.68843 
.68857 

.04877 
.04879 
.04880 
.04882 

8.69648 
.69662 
.69676 
.69690 

.04971 
.04973 
.04975 
.04976 

8.70472 
.70486 
.70500 
.70513 

.05067 
.05068 
.05070 
.05071 

56 
55 
54 
53 

+   2^ 

9 

10 

11 

8.67181 
.67196 
.67210 
.67224 

.04697 
.04698 
.04700 
.04702 

8.68030 
.68045 
.68059 
.68073 

.04790 
.04791 
.04793 
.04794 

8.68871 
.68885 
.68899 
.68913 

.04883 
.04885 
.04886 

.04888 

8.69703 
.69717 
.69731 
.69745 

.04978 
.04979 
.04981 
.04982 

8.70527 
.70541 
.70554 
.70568 

.05073 
.05075 
.05076 
.05078 

52 
51 
50 
49 
48 
47 
46 
45 

44 
4S 
42 
41 
40 
39 
38 
37 

+   3^ 

IS 

14 
15 

8.67238 
.67252 
.67267 
.67281 

.04703 
.04705 
.04706 
.04708 

8.68087 
.68101 
.68115 
.68129 

.04796 
.04797 
.04799 
.04801 

8.68927 
.68941 
.68955 
.68969 

.04890 
.04891 
.04893 
.04894 

8.69758 
.69772 
.69786 
.69800 

.04984 
.04986 
.04987 
.04989 

8.70582 
.70595 
.70609 
.70623 

.05079 
.05081 
.05083 
.05084 

+   4^ 
17 
18 
19 

8.67295 
.67309 
.67323 
.67338 

.04709 
.04711 
.04712 
.04714 

8.68143 
.68157 
.68171 
.68185 

.04802 
.04804 
.04805 
.04807 

8.68983 
.68996 
.69010 
.69024 

.04896 
.04897 
.04899 
.04901 

8.69814 
.69827 
.69841 
.69855 

.04990 
.04992 
.04994 
.04995 

8.70636 
.70650 
.70664 
.70677 

.05086 
.05087 
.05089 
.05091 

+  ^ 
21 
22 
23 

8.67352 
.67366 
.67380 
.67394 

.04715 
.04717 
.04718 
.04720 

8.68199 
.68213 
.68227 
.68241 

.04808 
.04810 
.04811 
.04813 

8.69038 
.69052 
.69066 
.69080 

.04902 
.04904 
.04905 
.04907 

8.69869 
.69882 
.69896 
.69910 

.04997 
.04998 
.05000 
.05001 

8.70691 
.70704 
.70718 
.70732 

.05092 
.05094 
.05095 
.05097 

+   6^ 

25 
26 

27 

8.67409 
.67423 
.67437 
.67451 

.04722 
.04723 
.04725 
.04726 

8.68256 
.68270 
.68284 
.68298 

.04815 
.04816 
.04818 
.04819 

8.69094 
.69108 
.69122 
.69136 

.04908 
.04910 
.04912 
.04913 

8.69924 
.69937 
.69951 
.69965 

.05003 
.05005 
.05006 
.05008 

8.70745 
.70759 
.70773 

.70786 

.05099 
.05100 
.05102 
.05104 

36 
35 
34 
33 

+    r 

29 
SO 
SI 

8.67465 
.67480 
.67494 
.67508 

.04728 
.04729 
.04731 
.04732 

8.68312 
.68326 
.68340 
.68354 

.04821 
.04822 
.04824 
.04825 

8.69149 
.69163 
.69177 
.69191 

.04915 
.04916 
.04918 
.04919 

8.69979 
.69992 
.70006 
.70020 

.05009 
.05011 
.05013 
.05014 

8.70800 
.70813 
.70827 
.70841 

.05105 
.05107 
.05108 
.05110 

32 
31 
30 
29 
28 
27 
26 
25 

24 
23 
22 
21 

+       8^ 
SS 
S4 
35 

8.67522 
.67536 
.67550 
.67565 

.04734 
.04735 
.04737 
.04739 

8.68368 
.68382 
.68396 
.68410 

.04827 
.04829 
.04830 
.04832 

8.69205 
.69219 
.69233 
.69247 

.04921 
.04923 
.04924 
.04926 

8.70034 
.70047 
.70061 
.70075 

.05016 
.05017 
.05019 
.05021 

8.70854 
.70868 
.70881 
.70895 

.05111 
.05113 
.05115 
.05116 

+   9^ 

S7 
38 
39 

8.67579 
.67593 
.67607 
.67621 

.04740 
.04742 
.04743 
.04745 

8.68424 
.68438 
.68452 
.68466 

.04833 
.04835 
.04836 
.04838 

8.69260 
.69274 
.69288 
.69302 

.04927 
.04929 
.04930 
.04932 

8.70089 
.70102 
.70116 
.70130 

.05022 
.05024 
.05025 
.05027 

8.70909 
.70922 
.70936 
.70949 

.05118 
.05119 
.05121 
.05123 

+  W 

41 
42 
AS 

8.67635 
.67649 
.67664 
.67678 

.04746 
.04748 
.04749 
.04751 

8.68480 
.68494 
.68508 
.68522 

.04839 
.04841 
.04843 
.04844 

8.69316 
.69330 
.69344 
.69358 

.04934 
.04935 
.04937 
.04938 

8.70144 
.70157 
.70171 
.70185 

.05028 
.05030 
.05032 
.05033 

8.70963 
.70977 
.70990 
.71004 

.05124 

.05126 

1 .05127 

.05129 

20 
19 
18 
17 

+  11^ 

45 
46 
47 

8.67692 
.67706 
.67720 
.67734 

.04752 
.04754 
.04756 
.04757 

8.68536 
.68550 
.68564 
.68578 

.04846 
.04847 
.04849 
.04850 

8.69371 
.69385 
.69399 
.69413 

.04940 
.04941 
.04943 
.04945 

8.70198 
.70212 
.70226 
.70240 

.05035 
.05036 
.05038 
.05040 

8.71017 
.71031 
.71045 
.71058 

.05131 
.05132 
.05134 
.05135 

16 
15 
U 
IS 
12 
11 
10 
9 

+  ir 

5i 

8.67748 
.67763 
.67777 
.67791 

.04759 
.04760 
.04762 
.04763 

8.68592 
.68606 
.68620 
.68634 

.04852 
.04854 
.04855 
.04857 

8.69427 
.69441 
.69454 
.69468 

.04946 
.04948 
.04949 
.04951 

8.70253 
.70267 
.70281 
.70294 

.05041 
.05043 
.05044 
.05046 

8.71072 
.71085 
.71099 
.71112 

.05137 
.05139 
.05140 
.05142 

+  13^ 

53 

54 
55 

8.67805 
.67819 
.67833 

.67847 

.04765 
.04766 
.04768 
.04769 

8.68648 
.68662 
.68676 
.68690 

.04858 
.04860 
.04861 
.04863 

8.69482 
.69496 
.69510 
.69524 

.04952 
.04954 
.04956 
.04957 

8.70308 
.70322 
.70336 
.70349 

.05048 
.05049 
.05051 
.05052 

8.71126 
.71140 
.71153 
.71167 

.05144 
.05145 
.05147 
.05148 

8 
7 
6 
5 

+   14^ 

57 
55 
59 

8.67861 
.67875 
.67890 
.67904 

.04771 
.M773 
.•4V74 
.04776 

8.68704 
.68718 
.68732 
.68746 

.04864 
.04866 
.04868 
.04869 

8.69537 
.69551 
.69565 
.69579 

.04959 
.04960 
.04962 
.04964 

8.70363 
.70377 
.70390 
.70404 

.05054 
.05055 
.05057 
.05059 

8.71180 
.71194 
.71207 
.71221 

.05150 
.05152 
.05153 
.05155 

4 
3 

2 

1 

+  W 

8.67918 

.•1777 

8.68760 

.04871 

8.69593 

.04965 

8.70418 

.05060 

8.71234 

.05156 

0 

22^  19^ 

22n  igm 

22h  nm 

22^  16m 

22h  15m 

Page  832]                 TABLE  45. 

Haversines. 

s 

ift  ^"«  26°  15' 

Ih  46m  36°  30' 

Ih  47m  26°  45' 

Ih  48m  27°  0' 

Ih  49m  27°  15' 

s 

Log.  Hav 

Nat.  Hav 

Log.  Hav 

Nat.  Hav 

Log.  Hav 

Nat.  Hav 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
S 

8.71234 
.71248 
.71261 
.71275 

.05156 
.05158 
.05160 
.05161 

8.72043 
.72057 
.72070 
.72083 

.05253 
.05255 
.05257 
.05258 

8.72844 
.72857 
.72871 
.72884 

.05351 
.05353 
.05354 
.05356 

8.73637 
.73650 
.73663 
.73677 

.05450 
.05451 
.05453 
.05455 

8.74423 
.74436 
.74449 
.74462 

.05549 
.05551 
.05552 
.05554 

60 
59 

58 
57 
66 
65 
54 
53 

+     r 

5 

6 
7 

8.71289 
.71302 
.71316 
.71329 

.05163 
.05164 
.05166 
.05168 

8.72097 
.72110 
.72124 
.72137 

.05260 
.05261 
.05263 
.05265 

8.72897 
.72910 
.72924 
.72937 

.05358 
.05359 
.05361 
.05363 

8.73690 
.73703 
.73716 
.73729 

.05456 
.05458 
.05460 
.05461 

8.74475 
.74488 
.74501 
.74514 

.05556 
.05557 
.05559 
.05561 

+   2' 

9 

10 

11 

8.71343 
.71356 
.71370 
.71383 

.05169 
.05171 
.05172 
.05174 

8.72150 
.72164 
.72177 
.72191 

.05266 
.05268 
.05270 
.05271 

8.72950 
.72963 
.72977 
.72990 

.05364 
.05366 
.05367 
.05369 

8.73742 
.73755 
.73769 
.73782 

.05463 
.05464 
.05466 
.05468 

8.74527 
.74540 
.74553 
.74566 

.05562 
.05564 
.05566 
.05567 

52 
51 
60 
49 

+   3' 

IS 
14 
15 

8.71397 
.71410 
.71424 
.71437 

.05176 
.05177 
.05179 
.05181 

8.72204 
.72217 
.72231 
.72244 

.05273 
.05274 
.05276 
.05278 

8.73003 
.73016 
.73030 
.73043 

.05371 
.05372 
.05374 
.05376 

8.73795 
.73808 
.73821 
.73834 

.05470 
.05471 
.05473 
.05474 

8.74579 
.74592 
.74605 
.74618 

.05569 
.05571 
.05572 
.05574 

48 
47 
46 
46 

+   4' 
17 
18 
19 

8.71451 
.71464 
.71478 
.71491 

.05182 
.05184 
.05185 
.05187 

8.72257 
.72271 
.72284 
.72298 

.05279 
.05281 
.05283 
.05284 

8.73056 
.73069 
.73083 
.73096 

.05377 
.05379 
.05381 
.05382 

8.73847 
.73860 
.73874 
.73887 

.05476 
.05478 
.05479 
.05481 

8.74631 
.74644 
.74657 
.74670 

.05576 
.05577 
.05579 
.05581 

44 
43 
42 
41 

+  ^ 

21 
22 
23 

8.71505 
.71518 
.71532 
.71545 

.05189 
.05190 
.05192 
.05193 

8.72311 
.72324 
.72338 
.72351 

.05286 
.05287 
.05289 
.05291 

8.73109 
.73122 
.73136 
.73149 

.05384 
.05385 
.05387 
.05389 

8.73900 
.73913 
.73926 
.73939 

.05483 
.05484 
.05486 
.05488 

8.74683 
.74696 
.74709 

.74722 

.05582 
.05584 
.05586 
.05587 

40 
39 
38 
37 
36 
36 
34 
33 

+   6' 

25 
26 

27 

8.71559 
.71572 
.71586 
.71599 

.05195 
.05197 
.05198 
.05200 

8.72364 
.72378 
.72391 
.72404 

.05292 
.05294 
.05296 
.05297 

8.73162 
.73175 
.73189 
.73202 

.05390 
.05392 
.05394 
.05395 

8.73952 
.73965 
.73978 
.73992 

.05489 
.05491 
.05493 
.05994 

8.74735 
.74748 
.74761 
.74774 

.05589 
.05591 
.05593 
.05594 

+    r 

29 
SO 
SI 

8.71613 
.71626 
.71640 
.71653 

.05201 
.05203 
.05205 
.05206 

8.72418 
.72431 
.72445 
.72458 

.05299 
.05300 
.05302 
.05304 

8.73215 
.73228 
.73241 
.73255 

.05397 
.05399 
.05400 
.05402 

8.74005 
.74018 
.74031 
.74044 

.05496 
.05498 
.05499 
.05501 

8.74787 
.74800 
.74813 
.74826 

.05596 
.05597 
.05599 
.05601 

32 
31 
30 
29 

+   8' 
33 
34 
35 

8.71667 
.71680 
.71694 
.71707 

.05208 
.05210 
.05211 
.05213 

8.72471 
.72485 
.72498 
.72511 

.05305 
.05307 
.05309 
.05310 

8.73268 
.73281 
.73294 
.73308 

.05404 
.05405 
.05407 
.05408 

8.74057 
.74070 
.74083 
.74096 

.05503 
.05504 
.05506 
.05508 

8.74839 
.74852 
.74864 
.74877 

.05603 
.05604 
.05606 
.05607 

28 
27 
26 

25 

37 
38 
39 

8.71721 
.71734 
.71748 
.71761 

.05214 
.05216 
.05218 
.05219 

8.72525 
.72538 
.72551 
.72565 

.05312 
.05314 
.05315 
.05317 

8.73321 
.73334 
.73347 
.73360 

.05410 
.05412 
.05413 
.05415 

8.74109 
.74122 
.74135 
.74149 

.05509 
.05511 
.05513 
.05514 

8.74890 
.74903 
.74916 
.74929 

.05609 
.05611 
.05613 
.05614 

24 
23 

22 
21 

+  lO' 

41 
42 
43 

8.71774 
.71788 
.71801 
.71815 

.05221 
.05222 
.05224 
.05226 

8.72578 
.72591 
.72605 
.72618 

.05318 
.05320 
.05322 
.05323 

8.73374 
.73387 
.73400 
.73413 

.05417 
.05418 
.05420 
.05422 

8.74162 
.74175 
.74188 
.74201 

.05516 
.05518 
.05519 
.05521 

8.74942 
.74955 
.74968 
.74981 

.05616 
.05618 
.05619 
.05621 

20 
19 
18 
17 

+  11' 

45 
46 

47 

8.71828 
.71842 
.71855 
.71869 

.05227 
.05229 
.05231 
.05232 

8.72631 
.72644 
.72658 
.72671 

.05325 
.05326 
.05328 
.05330 

8.73426 
.73440 
.73453 
.73466 

.05423 
.05425 
.05427 
.05428 

8.74214 
.74227 
.74240 
.74253 

.05523 
.05524 
.05526 
.05528 

8.74994 
.75007 
.75020 
.75033 

.05623 
.05624 
.05626 
.05628 

16 
16 
14 
13 

+  12' 

50 
5/ 

8.71882 
.71895 
.71909 
.71922 

.05234 
.05235 
.05237 
.05239 

8.72684 
.72698 
.72711 
.72724 

.05331 
.05333 
.05335 
.05336 

8.73479 
.73492 
.73505 
.73519 

.05430 
.05431 
.05433 
.05435 

8.74266 
.74279 
.74292 
.74305 

.05529 
.05531 
.05533 
.05534 

8.75046 
.75059 
.75072 
.75084 

.05629 
.05631 
.05633 
.05634 

12 

11 

10 

9 

+  13' 

53 
54 
55 

8.71936 
.71949 
.71963 
.71976 

.05240 
.05242 
.05244 
.05245 

8.72738 
.72751 
.72764 
.72778 

.05338 
.05340 
.05341 
.05343 

8.73532 
.73545 
.73558 
.73571 

.05436 
.05438 
.05440 
.05441 

8.74318 
.74331 

.74344 
.74357 

.05536 
.05537 
.05539 
.05541 

8.75097 
.75110 
.75123 
.75136 

.05636 
.05638 
.05639 
.05641 

8 
7 
6 
5 

+  14' 

55 
59 

8.71989 
.72003 
.72016 
.72030 

.05247 
.05248 
.05250 
.05252 

8.72791 
.72804 
.72817 
.72831 

.05345 
.05346 
.05348 
.05349 

8.73584 
.73598 
.73611 
.73624 

.05443 
.05445 
.05446 
.05448 

8.74371 
.74384 
.74397 
.74410 

.05542 
.05544 
.05546 
.05547 

8.75149 
.75162 
.75175 
.75188 

.05643 
.05644 
.05646 
.05648 

4 
3 
2 
1 

+  15' 

8.72043 

.05253 

8.72844 

.05351 

8.73637 

.05450 

8.74423 

.05549 

8.75201 

.05649 

: 

22^  14™-         1 

SSfi  13m         1 

■  22h  12m 

22^  llm 

22^  IQm 

TABLE  45.                 [Page  833 

Haversines. 

s 

iA5om27o30'  1 

lh5iTO27°45'  1 

Ih  52m  28°  O' 

Ih  53m  28°  15' 

Ih  54-^  28°  3^ 

1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

8.75201 
.75214 
.75227 
.75239 

.05649 
.05651 
.05653 
.05655 

8.75972 
.75984 
.75997 
.76010 

.05751 
.05752 
.05754 
.05756 

8.76735 
.76748 
.76760 
.76773 

.05853 
.05854 
.05856 
.05858 

8.77492 
.77504 
.77517 
.77529 

.05955 
.05957 
.05959 
.05961 

8.78241 
.78254 
.78266 

.78278 

.06059 
.06061 
.06063 
.06064 

60 
59 

58 
57 

+       r 

5 
6 

7 

8.75252 
.75265 
.75278 
.75291 

.05656 
.05658 
.05660 
.05661 

8.76023 
.76035 
.76048 
.76061 

.05757 
.05759 
.05761 
.05762 

8.76786 
.76798 
76811 
.76824 

.05859 
.05861 
.05863 
.05865 

8.77542 
.77554 
.77567 
.77579 

.05962 
.05964 
.05966 
.05968 

8.78291 
.78303 
.78316 
.78328 

.06066 
.06068 
.06070 
.06071 

66 
55 
54 
53 

+      2' 

9 

10 

11 

8.75304 
.75317 
.75330 
.75343 

.05663 
.05665 
.05666 
.05668 
.05670 
.05671 
.05673 
.05675 

8.76074 
.76086 
.76099 
.76112 

.05764 
.05766 
.05768 
.05769 

8.76836 
.76849 
.76862 
.76874 

.05866 
.05868 
.05870 
.05871 

8.77592 
.77604 
.77617 
.77630 

.05969 
.05971 
.05973 
.05974 

8.78341 
.78353 
.78365 
.78378 

.06073 
.06075 
.06077 
.06078 

62 
51 
50 
49 

+     3' 

IS 
14 
15 

8.75355 
.75368 
.75381 
.75394 

8.76125 
.76138 
.76150 
.76163 

.05771 
.05773 
.05774 
.05776 

8.76887 
.76900 
.76912 
.76925 

.05873 
.05875 
.05877 

.05878 

8.7.7642 
.77655 
.77667 
.77680 

.05976 
.05978 
.05980 
.05981 
.05983 
.05985 
.05986 
.05988 

8.78390 
.78403 
.78415 

.78428 
8.78440 
.78452 
.78465 
.78477 

.06080 
.06082 
.06083 
.06085 

48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
S3 

+     4' 
17 
18 
19 

8.75407 
.75420 
.75433 
.75446 

.05676 
.05678 
.05680 
.05681 
.05683 
.05685 
.05686 
.05688 

8.76176 
.76189 
.76201 
.76214 

.05778 
.05779 
.05781 
.05783 
.05785 
.05786 
.05788 
.05790 

8.76938 
.76950 
.76963 
.76975 

8.76988 
.77001 
.77013 
.77026 

8.77039 
.77051 
.77064 
.77076 

.05880 

.05882 
.05883 
.05885 

.05887 
.05888 
.05890 
.05892 

8.77692 
.77705 
.77717 
.77730 

.06087 
.06089 
.06090 
.96092 

+  5' 
21 
22 
23 

8.75458 
.75471 
.75484 
.75497 

8.76227 
.76240 
.76252 
.76265 

8.77742 
.77755 
.77767 
.77780 

.05990 
.05992 
.05993 
.05995 
.05997 
.05999 
.06000 
.06002 

8.78490 
.78502 
.78514 
.78527 

.06094 
.06096 
.06097 
.06099 

+   6' 

25 
26 

27 

8.75510 
.75523 
.75536 
.75548 

.05690 
.05691 
.05693 
.05695 
.05697 
.05698 
.05700 
.05702 

8.76278 
.76291 
.76303 
.76316 

.05791 
.05793 
.05795 
.05796 

.05894 
.05895 
.05897 
.05899 

8.77792 
.77805 
.77817 
.77830 

8.78539 
.78551 
.78564 
.78576 

.06101 
.06103 
.06104 
.06106 

+    r 

29 
SO 
31 

8.75561 
.75574 
.75587 
.75600 

8.76329 
.76341 
.76354 
.76367 

.05798 
.05800 
.05802 
.05803 

8.77089 
.77102 
.77114 
.77127 

.05901 
.05902 
.05904 
.05906 

8.77842 
.77855 
.77867 
.77880 

.06004 
.06005 
.06007 
.06009 

8.78589 
.78601 
.78613 
.78626 

.06108 
.06110 
.06111 
.06113 

32 
31 
SO 
29 

+     S' 
33 
34 
35 

8.75613 
.75626 
.75638 
.75651 

.05703 
.05705 
.05707 
.05708 

8.76380 
.76392 
.76405 
.76418 

.05805 
.05807 
.05808 
.05810 

8.77139 
.77152 
.77165 
.77177 

.05907 
.05909 
.05911 
.05913 

8.77892 
.77905 
.77917 
.77930 

.06011 
.06012 
.06014 
.06016 

8.78638 
.78651 
.78663 
.78675 

.06115 
.06117 
.06118 
.06120 

28 
27 
26 
25 

+    r 

37 
38 
39 

8.75664 
.75677 
.75690 
.75703 

.05710 
.05712 
.05713 
.05715 

8.76431 
.76443 
.76456 
.76469 

.05812 
.05813 
.05815 
.05817 

8.77190 
.77202 
.77215 

.77228 

.05914 
.05916 
.05918 
.05919 

8.77942 
.77955 
.77967 
.77980 

.06018 
.06019 
.06021 
.06023 

8.78688 
.78700 
.78712 
.78725 

.06122 
.06124 
.06125 
.06127 

24 
23 
22 
21 

+    W 
41 
42 
43 

8.75715 
.75728 
.75741 
.75754 

.05717 
.05718 
.05720 
.05722 

8.76481 
.76494 
.76507 
.76519 

.05819 
.05820 
.05822 
.05824 

8.77240 
.77253 
.77265 

.77278 

.05921 
.05923 
.05925 
.05926 

8.77992 
.78005 
.78017 
.78029 

.06024 
.06026 
.06028 
.06030 

8.78737 
.78749 
.78762 
.78774 

.06129 
.06130 
.06132 
.06134 

20 
19 
18 
17 

+  11' 

45 
46 
47 

8.75767 
.75779 
.75792 
.75805 

.05724 
.05725 
.05727 
.05729 

8.76532 
.76545 
.76558 
.76570 

.05825 
.05827 
.05829 
.05830 

8.77291 
.77303 
.77316 
.77328 

.05928 
.05930 
.05931 
.05933 

8.78042 
.78054 
.78067 
.78079 

.06031 
.06033 
.06035 
.06037 

8.78787 
.78799 
.78811 
.78824 

.06136 
.06137 
.06139 
.06141 

16 
15 
14 
13 

+    ir 

49 
50 
51 

8.75818 
.75831 
.75844 
.75856 

.05730 
.05732 
.05734 
.05735 

8.76583 
.76596 
.76608 
.76621 

.05832 
.05834 
.05836 
.05837 

8.77341 
.77353 
.77366 
.77379 

.05935 
.05936 
.05938 
.05940 

8.78092 
.78104 
.78117 
.78129 

.06038 
.06040 
.06042 
.06044 

8.78836 
.78848 
.78861 
.78873 

.06143 
.06144 
.06146 
.06148 

12 

11 

10 

9 

+  13' 

53 
54 
55 

8.75869 
.75882 
.75895 
.75908 

.05737 
.05739 
.05740 
.05742 

8.76634 
.76646 
.76659 
.76672 

.05839 
.05841 
.05842 
.05844 

8.77391 
.77404 
.77416 
.77429 

.05942 
.05943 
.05945 
.05947 

8.78142 
.78154 
.78167 
.78179 

.06045 
.06047 
.06049 
.06050 
.06052 
.06054 
.06056 
.06057 

8.78885 
.78898 
.78910 
.78922 

.06150 
.06151 
.06153 
.06155 

8 
7 
6 
5 

+  ir 

57 
58 
59 

8.75920 
.75933 
.75946 
.75959 

.05744 
.05745 
.05747 
.05749 

8.76684 
.76697 
.76710 
.76722 

8.76735 

.05846 
.05847 
.05849 
.05851 
.05853 

8.77441 
.77454 
.77466 
.77479 

.05949 
.05950 
.05952 
.05954 

8.78191 
.78204 
.78216 
.78229 

8.78935 
.78947 
.78959 
.78972 

.06157 
.06158 
.06160 
.06162 

4 
S 
2 
1 

+    15' 

8.75972 

.05751 

8.77492  1  .05955 

8.78241 

.06059 

8.78984 

.06164 

0 

22h9m, 

22^  Sm 

22^  7m 

22^  6m 

22^  5m 

Page  834]                 TABLE  45. 

Haversines. 

s 

J  A  55"»  38°  45' 

^'t  56"*  29°  0' 

Ih  57m  29°  15' 

1^  58mZ9°  30' 

Ifi59m29°  W 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

8.78984 
.78996 
.79009 
.79021 

.06164 
.06165 
.06167 
.06169 

8.79720 
.79732 
.79744 
.79757 

.06369 
.06371 
.06373 
.06374 

8.80449 
.80462 
.80474 
.80486 

.06375 
.06377 
.06379 
.06381 

8.81172 
.81184 
.81196 
.81208 

.06482 
.08484 
.06486 
.06488 

8.81889 
.81901 
.81913 
.81925 

.06590 
.06593 
.06594 
.06595 

60 
59 
58 
57 

+     r 

5 
6 

7 

8.79033 
.79046 
.79058 
.79070 

.06171 
.06172 
.06174 
.06176 

8.79769 
.79781 
.79793 
.79805 

.06376 
.06378 
.06380 
.06281 

8.80498 
.80510 
.80522 
.80534 

.06382 
.06384 
.06386 
.06388 

8.81220 
.81232 
.81244 
.81256 

.06489 
.06491 
.06493 
.06495 

8.81937 
.81948 
.81960 
.81972 

.06597 
.06599 
.06601 
.06603 

56 
55 
54 
53 

+   2^ 

9 

10 

11 

8.79082 
.79095 
.79107 
.79119 

.06178 
.06179 
.06181 
.06183 

8.79818 
.79830 
.79842 
.79854 

.06383 
.06385 
.06387 
.06388 

8.80546 
.80558. 
.80570 
.80582 

.06389 
.06391 
.06393 
.06395 

8.81268 
.81280 
.81292 
.81304 

.06497 
.06498 
.06500 
.06502 

8.81984 
.81996 
.82008 
.82020 

.06605 
.06606 
.06608 
.06610 

52 
51 
50 
49 

+       3' 

13 
14 
15 

8.79132 
.79144 
.79156 
.79169 

.06185 
.06186 
.06188 
.06190 

8.79866 
.79879 
.79891 
.79903 

.06390 
.06392 
.06294 
.06295 

8.80595 
.80607 
.80619 
.80631 

.06397 
.06398 
'.06400 
.06402 

8.81316 
.81328 
.81340 
.81352 

.06504 
.06505 
.06507 
.06509 

8.82032 
.82043 
.82055 
.82067 

.08613 
.06614 
.06615 
.06617 

48 
47 
46 
45 

44 
43 
42 
41 

+       4^ 

17 
18 
19 

8.79181 
.79193 
.79205 
.79218 

.06192 
.06193 
.06195 
.06197 

8.79915 
.79927 
.79940 
.79952 

.06397 
.06399 
.06301 
.06303 

8.80643 
.80655 
.80667 
.80679 

/^. 06404 
.06405 
.06407 
.06409 

8.81364 
-♦.81376 
.81388 
.81400 

.06511 
.06513 
.06514 
.06516 

8.82079 
.82091 
.82103 
.82115 

.06619 
.06621 
.06633 
.08634 

+     r 

21 
22 
23 

8.79230 
.79242 
.79255 
.79267 

.06199 
.06300 
.06202 
.06204 

8.79964 
.79976 
.79988 
.80000 

.06304 
.06306 
.06308 
.06310 

8.80691 
.80703 
.80715 
.80727 

.06411 
.06413 
.06414 
.06416 

8.81412 
.81424 
.81436 
.81448 

.06518 
.06520 
.06522 
.06523 

8.82126 
.82138 
.82150 
.82162 

.06836 
.06638 
.06630 
.06633 

40 
39 
38' 
37 

+   6^ 

25 
26 

27 

8.79279 
.79291 
.79304 
.79316 

.06206 
.06207 
.06209 
.06211 

8.80013 
.80025 
.80037 
.80049 

.06311 
.06313 
.06315 
.06317 

8.80739 
.80751 
.80764 
.80776 

.06418 
.06420 
.06431 
.06433 

8.81460 
.81472 
.81484 
.81496 

.06525 
.06527 
.06529 
.06531 

8.82174 
.82186 
.82198 
.82209 

.06633 
.06635 
.06637 
.06639 

36 
35 
34 
33 

+     r 

29 
SO 
31 

8.79328 
.79341 
.79353 
.79365 

.06213 
.06214 
.06216 
.06218 

8.80061 
.80073 
.80086 
.80098 

.06318 
.06330 
.06323 
.06324 

8.80788 
.80800 
.80812 
.80824 

.06435 
.06437 
.06439 
.06430 

8.81508 
.81520 
.81531 
.81543 

.06533 
.06534 
.06536 
.06538 

8.82221 
.82233 
.82245 
.82257 

.06641 
.06643 
.06644 
.06646 

32 
SI 
SO 
29 
28 
27 
26 
25 

+   8' 
33 
34 
35 

8.79377 
.79390 
.79402 
.79414 

.06220 
.06221 
.06233 
.06325 

8.80110 
.80122 
.80134 
.80146 

.06326 
.06327 
.06329 
.06331. 

8.80836 
.80848 
.80860 

.80872 

.06433 
.06434 
.06436 
.06438 

8.81555 
.81567 
.81579 
.81591 

.06540 
.06541 
.06543 
.06545 

8.82269 
.82280 
.82292 
.82304 

.06648 
.06650 
.06652 
.06853 

+   9' 
59 

8.79426 
.79439 
.79451 
.79463 

.06237 
.06229 
.06230 
.06233 

8.80158 
.80171 
.80183 
.80195 

.06333 
.06334 
.06336 
.06338 

8.808;54 
.80896 
.80908 
.80920 

.06439 
.06441 
.06443 
.06445 

8.81603 
.81615 
.81627 
.81639 

.06547 
.06549 
.06550 
.06552 

8.82316 
.82328 
.82340 
.82351 

.06855 
.06657 
.06659 
.06661 

24 
23 
22 
21 

+  10' 

41 
42 
43 

8.79475 
.79488 
.79500 
.79512 

.06234 
.06236 
.06337 
.06339 

8.80207 
.80219 
.80231 
.80243 

.06340 
.06341 
.06343 
.06345 

8.80932 
.80944 
.80956 
.80968 

.06446 
.06448 
.06450 
.06452 

8.81651 
.81663 
.81675 
.81687 

.06554 
.06556 
.06558 
.06559 

8.82363 
.82375 
.82387 
.82399 

.08882 
.06684 
.06868 
.06668 

20 
19 
18 
17 

+    ir 

•^7 

8.79524 
.79537 
.79549 
.79561 

.06241 
.06343 
.06344 
.06346 

8.80256 
.80268 
.80280 
.80292 

.06347 
.06349 
.06350 
.06352 

8.80980 
.80992 
.81004 
.81016 

.06454 
.06455 
.06457 
.06459 

8.81699 
.81710 
.81722 
.81734 

.06561 
.06563 
.06565 
.06567 

8.82410 
.82422 
.82434 
.82446 

.06670 
.06871 
.06673 
.06675 

16 
15 
14 
IS 

+  ir 

49 
50 
51 

8.79573 
.79586 
.79598 
.79610 

.06348 
,06350 
.06351 
.06353 

8.80304 
.80316 
.80328 
.80340 

.06354 

.06356 

,.06357 

.06359 

8.81028 
.81040 
.81052 
.81064 

.06461 
.06463 
.06464 
.06466 

8.81746 
.81758 
.81770 
.81782 

.06568 
•.06570 
.06572 
.06574 

8.82458 
.82470 
.82481 
.82493 

,  .06877 

\  .06679 

\08881 

.06683 

12 
11 
10 
9 
8 
7 
6 
5 

+     13' 

53 
54 
55 

8.79622 
.79634 
.79647 
.79659 

.06355 
.06357 
.06358 
.06360 

8.80353 
.80365 
.80377 
.80389 

.06361 
.06363 
.06365 
.66366 

8.81076 
.81088 
.81100 
.81112 

.06468 
.06470 
.06471 
.06473 

8.81794 
.81806 
.81818 
.81830 

.06576 
.06577 
.06579 
.06581 

8.82505 
.82517 
.82529 
.82540 

.06684 
.06886 
.06688 
.08690 

+  14' 

57 
55 
59 

8.79671 
.79683 
.79696 
.79708 

.06363 
.06264 
.06265 
.06367 

8.80401 
.80413 
.80425 
.80437 

.06368 
.06370 
.06373 
.06373 

8.81124 
.81136 
.81148 
.81160 

.06475 
.06477 
.06479 
.06480 

8.81841 
.81853 
.81865 
.81877 

.06583 
.06585 
.06586 
.06588 

8.82552 
.82564 
.82576 

.82588 

.06691 
.08693 
.08695 
.08697 

4 
3 

2 
1 

+  15' 

8.79720 

.06369 

8.80449 

.06375 

8.81172 

.06482 

8.81889 

.06590 

8.82599 

.08899 

0 

22h4m 

22h3'm 

22h  2m 

22^  im 

o^h  Qm 

TABLE  45.                  [Page  836 

Havereines. 

s 

2h  Om  30°  (K   1 

2h  im  30°  15'  | 

2h  2m  30°  30' 

2h  3m  30°  45'  5   .gft  4^  31°  C 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.'  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav.  Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

8.82599 
.82611 
.82623 
.82635 

.06699 
.06701 
.06702 
.06704 

8.83303 
.83315 
.83327 
.83338 

.06808 
.06810 
.06812 
.06814 

8.84002 
.84013 
.84025 
.84036 

.06919 
.06920 
.06923 
.06924 

8.84694 
.84705 
.84717 
.84728 

.07030 1 
.07032 
.07033 
.07035 

8.85380 
.85391 
.85403 
.85414 

.07142 
.07144 
.07145 
.07147 

60 
59 
58 
57 

+    r 

5 
6 

7 

8.82646 
.82658 
.82670 
.82682 

.06706 
.06708 
.06710 
.06711 

8.83350 
.83362 
.83374 
.83385 

.06816 
.06817 
.06819 
.06821 

8.84048 
.84059 
.84071 
.84083 

8.84094 
.84106 
.84117 
.84129 

.06926 
.06928 
.06930 
.06931 

8.84740 
.84751 
.84762 
.84774 

.07037 
.07039 
.07041 
.07043 

8.85425 
.85437 
.85448 
.85459 

8^85471 
.85482 
.85494 
.85505 

.07149 
.07151 
.07153 
.07155 

56 
55 
54 
53 

+  3^ 

9 

10 

11 

8.82694 
.82705 
.82717 
.82729 

.06713 
.06715 
.06717 
.06719 

8.83397 
.83409 
.83420 
.83432 

.06823 
.06825 
.06826 
.06828 

.06933 
.06935 
.06937 
.06939 

8.84785 
.84797 
.84808 
.84820 

.07045 
.07046 
.07048 
.07050 

.07157 
.07158 
.07160 
.07162 

52 
51 
50 
49 

+  3' 

13 
14 
15 

8.82741 
.82752 
.82764 
.82776 

.06721 
.07722 
.06724 
.06726 

8.834^ 
.83455 
.83467 
.83479 

.06830 
.06832 
.06834 
.06836 

8.84140 
.84152 
.84164 
.84175 

.06941 
.06943 
.06944 
.06946 

8.84831 
.84843 
.84854 
.84866 

.07052 
.07054 
.07056 
.07058 

8.85516 
.85528 
.85539 
.85550 

.07164 
.07166 
.07168 
.07170 

48 
47 
46 
45 

+   *' 
17 
18 
19 

8.82788 
.82799 
.82811 
.82823 

.06728 
.06730 
.06731 
.06733 

8.83490 
.83502 
.83513 
.83525 

.06838 
.06839 
.06841 
.06843 

8.84187 
.84198 
.84210 
.84221 

.06948 
.06950 
.06952 
.06954 

8.84877 
.84889 
.84900 
.84912 

.07059 
.07061 
.07063 
.07065 

8.85562 
.85573 
.85585 
.85596 

8.85607 
.85619 
.85630 
.85641 

8.85653 
.85664 
.85675 
.85687 

.07172 
.07173 
.07175 
.07177 

44 
43 
42 
41 

+     5' 
21 

22 
23 

8.82835 
.82846 
.82858 
.82870 

8.82882 
.82893 
.82905 
.82917 

.06735 
.06737 
.06730 
.06741 
.06742 
.06744 
.06746 
.06748 

8.83537 
.83548 
.83560 
.83572 

8.83583 
.83595 
.83607 
.83618 

.06845 
.06847 
.06849 
.06850 

8.84233 
.84244 
.84356 
.84268 

8:84279 
.84291 
.84302 
.84314 

.06956 
.06957 
.06959 
.06961 
.06963 
.06965 
.06967 
.06968 

8.84923 
.84934 
.84946 
.84957 

8.84969 
.84980 
.84992 
.85003 

.07067 
.07069 
.07071 
.07073 

.07179 
.07181 
.07183 
.07185 

40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 

+   6' 

25 
26 

27 

.06852 
.06854 
.06856 
.06858 

.07074 
.07076 
.07078 
.07080 

.07187 
.07189 
.07190 
.07192 

+    r 

29 
30 
31 

8.82929 
.82940 
.82952 
.82964 

.06750 
.06752 
.06753 
.06755 

8.83630 
.83642 
.83653 
.83665 

.06860 
.06861 
.06863 
.06865 

8.84325 
.84337 
.84348 
.84360 

8.84371 
.84383 
.84394 
.84406 

8.84417 
.84429 
.84441 
.84452 

.06970 
.06972 
.06974 
.06976 
.06978 
.06980 
.06981 
.06983 
.06985 
.06987 
.06989 
.06991 

8.85015 
.85026 
.85037 
.85049 

.07082 
.07084 
.07086 
.07087 
.07089 
.07091 
.07093 
.07095 
.07097 
.07099 
.07100 
.07102 
.07104 
.07106 
.07108 
.07110 

8.85698 
.85709 
.85721 
.85732 

.07194 
.07196 
.07198 
.07200 

+     8' 
33 
24 
35 

8.82976 
.82987 
.82999 
.83011 

.06757 
.06759 
.06761 
.06763 

8.83676 
.83688 
.83700 
.83711 

.06867 
.06869 
.06871 
.06872 

8.85060 
.85072 
.85083 
.85095 

8.85106 
.85117 
.85129 
.85140 

8.85152 
.85163 
.85175 
.85186 

8.85743 
.85755 
.85766 
.85777 

8.85789 
.85800 
.85811 
.85823 

8.85834 
.85845 
.85857 
.85868 

.07203 
.07304 
.07205 
.07207 
.07209 
.07311 
.07213 
.07215 
.07217 
.07219 
.07330 
.07333 

+     9" 

37 
38 
39 

8.83023 
.83034 
.83046 
.83058 

.06764 
.06766 
.06788 
.06770 

8.83723 
.83735 
.83746 
.83758 

.06874 
.06876 
.06878 
.06880 

+    1(K 

41 

42 
43 

8.83069 
.83081 
.83093 
.83105 

.06772 
.06773 
.06775 
.06777 

8.83769 
.83781 
.83793 
.83804 

.06882 
.06884 
.06885 
.06887 

8.84464 
.84475 
.84487 
.84498 

.06993 
.06994 
.06996 
.06998 

+  ir 

45 
46 
47 

8.83116 
.83128 
.83140 
.83151 

.06779 
.06781 
.06783 
.06784 

8.83816 
.83828 
.83839 
.83851 

.06889 
.06891 
.06893 
.06895 

8.84510 
.84521 
.84533 
.84544 

8.84556 
.84567 
.84579 
.84590 

.07000 
.07003 
.07004 
.07006 

8.85197 
.85209 
.85220 
.85232 

.07112 
.07114 
.07115 
.07117 

8.85879 
.85891 
.85902 
.85913 

.07324 
.07236 
.07238 
.07330 

+  12' 

49 
50 
51 

8.83163 
.83175 
.83187 
.83198 

.06786 
.06788 
.06790 
.06792 

8.83862 
.83874 
.83886 
.83897 

.06896 
.06898 
.06900 
.06902 

.07007 
.07009 
.07011 
.07013 

8.85243 
.85254 
.85266 
.85277 

.07119 
.07121 
.07123 
.07125 

8.85925 
.85936 
.85947 
.85959 

.07333 
.07334 
.07236 
.07337 

12 

11 

10 

9 

+  13' 
53 
54 
55 

8.83210 
.83222 
.83233 
.83245 

.06794 
.06795 
.06797 
.06799 

8.83909 
.83920 
.83932 
.83944 

.06904 
.06906 
.06907 
.06909 

8.84602 
.84613 
.84625 
.84636 

.07015 
.07017 
.07019 
.07030 

8.85289 
.85300 
.85311 
.85323 

.07127 
.07129 
.07130 
.07132 

8.85970 
.85981 
.85992 
.86004 

.07339 
.07341 
.07343 
.07345 
.07347 
.07249 
.07251 
.07253 
.07254 

8 
7 
6 
5 

4 
3 
2 
1 
0 

+  14' 

57 
58 
59 

8.83257 
.83268 
.83280 
.83292 

.06801 
.06803 
.06805 
.06806 

8.83955 
.83967 
.83978 
.83990 

.06911 
.06913 
.06915 
.06917 

8.84648 
.84659 
.84671 
.84682 

.07022 
.07024 
.07026 
.07028 

8.85334 
.85346 
.85357 
.85368 

.07134 
.07136 
.07138 
.07140 

8.86015 
.86026 
.86038 
.86049 

+    15' 

8.83303 

.06808 

8.84002  !  .06919 

8.84694 

.07030 

8.85380 

.07142 

8.86060 

21^59^ 

21^  58^ 

21h  57m 

21'''  56m 

21h  55m 

Page  836]                 TABLE  45. 

Haversineg. 

s 

2h  5m  31°  15' 

2h  6m  31°  30' 

2h  Tm  31°  45/ 

2li  8m  33°  C 

2h  gm  33°  15/ 

s 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

8.86060 
.86072 
.86085 
.86094 

.07354 
.07256 
.07258 
.07260 

8.86735 
.86746 
.86757 
.86769 

.07368 
.07370 
.07373 
.07374 

8.87404 
.87415 
.87426 
.87437 

.07483 
.07484 
.07486 
.07488 

8.88068 
.88079 
.88090 
.88101 

.07598 
.07600 
.07601 
.07603 

8.88726 
.88737 
.88748 
.88759 

.07714 
.07716 
.07717 
.07719 

60 
59 
58 
57 

+      r 

5 
6 
7 

8.86105 
.86117 
.86128 
.86139 

.07263 
.07264 
.07266 
.07268 

8.86780 
.86791 
.86802 
.86813 

.07376 
.07377 
.07379 
.07381 

8.87448 
.87460 
.87471 

.87482 

.07490 
.07493 
.07494 
.07496 

8.88112 
.88123 
.88134 
.88145 

.07605 
.07607 
.07609 
.07611 

8.88769 
.88780 
.88791 
.88802 

.07721 
.07723 
.07725 
.07727 

56 
55 
54 
53 

+   2^ 

9 

10 

11 

8.86151 
.86162 
.86173 
.86184 

.07270 
.07271 
.07273 
.07275 

8.86825 
.86836 
.86847 
.86858 

.07383 
.07385 
.07387 
.07389 

8.87493 
.87504 
.87515 
.87526 

.07498 
.07500 
.07503 
.07503 

8.88156 
.88167 
.88178 
.88189 

.07613 
.07615 
.07617 
.07619 

8.88813 
.88824 
.88835 
.88846 

.07729 
.07731 
.07733 
.07735 

52 
51 
50 
49 

+   3' 

13 
14 
15 

8.86196 
.86207 
.86218 
.86229 

.07277 
.07279 
.07281 
.07283 

8.86869 
.86880 
.86892 
.86903 

.07391 
.07393 
.07395 
.07397 

8.87537 
.87548 
.87559 
.87570 

.07505 
.07507 
.07509 
.07511 

8.88200 
.88211 
.88222 
.88233 

.07631 
.07633 
.07635 
.07637 

8.88857 
.88868 
.88879 
.88890 

.07737 
.07739 
.07741 
.07743 

48 
47 
46 
45 

+   *^ 
17 
18 
19 

8.86241 
.86252 
.86263 
.86275 

.07285 
.07287 

.07288 
.07290 

8.86914 
.86925 
.86936 
.86947 

.07398 
.07400 
.07403 
.07404 

8.87582 
.87593 
.87604 
.87615 

.07513 
.07515 
.07517 
.07519 

8.88244 
.88255 
.88266 
.88277 

.07638 
.07630 
.07633 
.07634 

8.88900 
.88911 
.88922 
.88933 

.07745 
.07747 
.07749 
.07751 

44 
43 
42 
41 

+     5^ 

21 
22 
23 

8.86286 
.86297 
.86308 
.86320 

.07292 
.07294 
.07296 
.07298 

8.86959 
.86970 
.86981 
.86992 

.07406 
.07408 
.07410 
.07413 

8.87626 
.87637 
.87648 
.87659 

.07531 
.07533 
.07535 
.07527 

8.88288 
.88299 
.88310 
.88321 

.07636 
.07638 
.07640 
.07643 

8.88944 
.88955 
.88966 
.88977 

.07753 
.07754 
.07756 
.07758 

40 
39 
38 
37 

+   6' 

25 
26 
27 

8.86331 
.86342 
.86353 
.86365 

.07300 
.07302 
.07304 
.07305 

8.87003 
.87014 
.87026 
.87037 

.07414 
.07416 
.07417 
.07419 

8.87670 
.87681 
.87692 
.87703 

.07528 
.07530 
.07533 
.07534 

8.88332 
.88343 
.88354 
.88364 

.07644 
.07646 
.07648 
.07650 

8.88988 
.88998 
.89009 
.89020 

.07760 
.07762 
.07764 
.07766 

36 
35 
34 
33 

+    r 

29 
30 
31 

8.86376 
.86387 
.86398 
.86410 

.07307 
.07309 
.07311 
.07323 

8.87048 
.87059 
.87070 
.87081 

.07431 
.07433 
.07435 
.07437 

8.87714 
.87725 
.87737 
.87748 

.07536 
.07538 
.07540 
.07543 

8.88375 
.88386 
.88397 
.88408 

8.88419 
.88430 
.88441 
.88452 

.07652 
.07654 
.07656 
.07657 

8.89031 
.89042 
.89053 
.89064 

.07768 
.07770 
.07772 
.07774 

32 
31 
SO 
29 

+  8' 
33 
34 
35 

8.86421 
.86432 
.86443 
.86455 

.07315 
.07317 
.07319 
.07321 

8.87093 
.87104 
.87115 
.87126 

.07439 
.07431 
.07433 
.07435 

8.87759 
.87770 
.87781 
.87792 

.07544 
.07546 
.07548 
.07549 

.07659 
.07661 
.07663 
.07665 

8.89075 
.89086 
.89096 
.89107 

.07776 
.07778 
.07780 
.07782 

28 
27 
26 

25 

+      9^ 

37 
38 
39 

8.86466 
.86477 
.86488 
.86499 

.07323 
.07324 
.07326 
.07328 

8.87137 
.87148 
.87159 
.87171 

.07437 
.07438 
.07440 
.07443 

8.87803 
.87814 
.87825 
.87836 

.07551 
.07553 
.07555 
.07557 

8.88463 
.88474 
.88485 
.88496 

.07667 
.07669 
.07671 
.07673 

8.89118 
.89129 
.89140 
.89151 

.07784 
.07786 

.07788 
.07789 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
IS 

+    W 

41 
42 
43 

8.86511 
.86522 
.86533 
.86544 

.07330 
.07332 
.07334 
.07336 

8.87182 
.87193 
.87204 
.87215 

.07444 
.07446 
.07448 
.07450 

8.87847 
.87858 
.87869 
.87880 

.07559 
.07561 
.07563 
.07565 

8.88507 
.88518 
.88529 
.88540 

.07675 
.07677 
.07679 
.07681 

8.89162 
.89172 
.89183 
.89194 

.07791 
.07793 
.07795 
.07797 

+  n' 

45 
46 

47 

8.86556 
.86667 
.86578 
.86589 

.07338 
.07340 
.07341 
.07343 

8.87226 
.87237 
.87248 
.87260 

.07453 
.07454 
.07456 
.07458 

8.87891 
.87902 
.87913 
.87924 

.07567 
.07569 
.07571 
.07573 

8.88551 
.88562 
.88573 
.88584 

.07683 
.07685 
.07686 
.07688 

8.89205 
.89216 
.89227 
.89238 

.07799 
.07801 
.07803 
.07805 

+    ir 

49 
50 
51 

8.86600 
.86611 
.86623 
.86634 

.07345 
.07347 
.07349 
.07351 

8.87271 
.87282 
.87293 
.87304 

.07459 
.07461 
.07463 
.07465 

8.87935 
.87946 
.87957 
.87968 

.07574 
.07576 
.07578 
.07580 

8.88595 
.88606 
.88616 
.88627 

.07690 
.07692 
.07694 
.07696 

8.89248 
.89259 
.89270 
.89281 

.07807 
.07809 
.07811 
.07813 

12 

11 

10 

9 

+    13' 

5S 
54 

55 

8.86645 
.86657 
.86668 
.86679 

.07353 
.07355 
.07357 
.07359 

8.87315 
.87326 
.87337 
.87349 

.07467 
.07469 
.07471 
.07473 

8.87980 
.87991 
.88002 
.88013 

.07582 
.07584 
.07586 
.07588 

8.88638 
.88649 
.88660 
.88671 

.07698 
.07700 
.07702 
.07704 

8.89292 
.89303 
.89314 
.89324 

.07815 
.07817 
.07819 
.07821 

8 
7 
6 
5 

+    14' 

57 
58 
59 

8.86690 
.86701 
.86713 
.86724 

.07360 
.07362 
.07364 
.07366 

8.87360 
.87371 
.87382 

■  .87393 

.07475 
.07477 
.07479 
.07480 

8.88024 
.88035 
.88046 
.88057 

.07590 
.07592 
.07694 
.07590 

8.88682 
.88693 
.88704 
.88715 

.07706 
.07708 
.07710 
.07712 

8.89335 
.89346 
.89357 
.89368 

.07823 
.07825 
.07827 
.07829 

4 
3 
2 
1 

+    15' 

8.86735 

.07368 

8.87404 

.07483 

8.88068 

.07598 

8.88726 

.07714 

8.89379 

.07830 

0 

21^  54^ 

21  h  53m 

21h  52m          1 

21h  Sim 

21h50m         1 

TABLE  45.                 [Page  837 

Havereinea. 

s 

2^iam^°w  1 

2hlim^°^^    1 

2h  ipn  33°  o'  1 

2^  13m  33/  U' 

2hl4m^°S(/    1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

8.89379 
.89389 
.89400 
.89411 

.07830 
.07832 
.07834 
.07836 

8.90026 
.90037 
.90048 
.90058 

.07948 
.07950 
.07952 
.07954 

8.90668 
.90679 
.90690 
.90700 

8.90711 
.90722 
.90732 
.90743 

.08066 
.08068 
.08070 
.08072 

8.91306 
.91316 
.91327 
.91337 

.08186 
.08188 
.08190 
.08192 

8.91938 
.91948 
.91959 
.91969 

.08306 
.08308 
.08310 
.08312 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

+    r 

5 
6 

7 

8.89422 
.89433 
.89444 
.89454 

.07838 
.07840 
.07843 
.07844 

8.90069 
.90080 
.90091 
.90101 

8.90112 
.90123 
.90134 
.90144 

.07956 
.07958 
.07960 
.07962 
.07964 
.07966 
.07968 
.07970 

.08074 
.08076 
.08078 
.08080 

8.91348 
.91358 
.91369 
.91380 

.08194 
.08196 
.08198 
.08200 

8.91980 
.91990 
.92001 
.92011 

.08314 
.08316 
.08318 
.08320 

+   2' 

9 

10 

11 

8.89465 
.89476 
.89487 
.89498 

.07846 
.07848 
.07850 
.07853 

8.90754 
.90764 
.90775 
.90786 

.08082 
.08084 
.08086 

.08088 

8.91390 
.91401 
.91411 
.91422 

.08202 
.08204 
.08206 
.08208 

8.92022 
.92032 
.92043 
.92053 

.08322 
.08324 
.08326 
.08328 

+  3' 
13 
14 
15 

8.89509 
.89519 
.89530 
.89541 

.07854 
.07856 

.07858 
.07860 

8.90155 
.90166 
.90176 
.90187 

.07972 
.07974 
.07976 
.07978 

8.90796 
.90807 
.90818 
.90828 

8.90839 
.90849 
.90860 
.90871 

.08090 
.08092 
.08094 
.08096 
.08098 
.08100 
.08102 
.08104 

8.91432 
.91443 
.91454 
.91464 

.08210 
.08212 
.08214 
.08216 

8.92064 
.92074 
.92084 
.92095 

.08330 
.08332 
.08334 
.08336 

+      *' 
17 
18 
19 

8.89552 
.89563 
.89573 
.89584 

.07862 
.07864 
.07866 
.07868 

8.90198 
.90209 
.90219 
.90230 

8.90241 
.90252 
.90262 
.90273 

.07980 
.07982 
.07983 
.07985 
.07987 
.07989 
.07991 
.07993 

8.91475 
.91485 
.91496 
.91506 

.08218 
.08220 
.08222 
.08224 

8.92105 
.92116 
.92126 
.92137 

8.92147 
.92158 
.92168 
.92179 

8.92189 
.92200 
.92210 
.92221 

.08338 
.08340 
.08342 
.08344 
.08346 
.08348 
.08350 
.08352 

+     5^ 
21 
22 
23 

8.89595 
.89606 
.89617 
.89627 

.07870 
.07872 
.07873 
.07875 
.07877 
.07879 
.07881 
.07883 

8.90881 
.90892 
.90903 
.90913 

8.90924 
.90935 
.90945 
.90956 

.08106 
.08108 
.08110 
.08112 

8.91517 
.91527 
.91538 
.91549 

.08226 
.08228 
.08230 
.08232 
.08234 
.08236 
.08238 
.08240 

+   6' 

25 
26 

27 

8.89638 
.89649 
.89660 
.89671 

8.90284 
.90294 
.90305 
.90316 

.07995 
.07997 
.07999 
.08001 

.08114 
.08116 
.08118 
.08120 

8.91559 
.91570 
.91580 
.91591 

.08354 
.08356 
.08358 
.08360 

+    r 

29 
30 
31 

8.89681 
.89692 
.89703 
.89714 

.07885 
.07887 
.07889 
.07891 

8.90326 
.90337 
.90348 
.90359 

.08003 
.08005 
.08007 
.08009 

8.90966 
.90977 
.90988 
.90998 

.08122 
.08124 
.08126 
.08128 

8.91601 
.91612 
.91622 
.91633 

.08242 
.08244 
.08246 
.08248 

8.92231 
.92241 
.92252 
.92262 

8.92273 
.92283 
.92294 
.92304 

.08362 
.08364 
.08366 
.08368 
.08370 
.08372 
.08374 
.08376 

32 
31 
30 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 

+     S" 
33 
34 
35 

8.89725 
.89735 
.89746 
.89757 

.07893 
.07895 
.07897 
.07899 

8.90369 
.90380 
.90391 
.90401 

.08011 
.08013 
.08015 
.08017 

8.91009 
.91019 
.91030 
.91041 

.08130 
.08132 
.08134 
.08136 

8.91643 
.91654 
.91664 
.91675 

.08250 
.08252 
.08254 
.08256 

+   IK 

37 
38 
39 

8.89768 
.89779 
.89789 
.89800 

.07901 
.07903 
.07905 
.07907 

8.90412 
.90423 
.90433 
.90444 

.08019 
.08021 
.08023 
.08025 

8.91051 
.91062 
.91073 
.91083 

.08138 
.08140 
.08142 
.08144 

8.91685 
.91696 
.91707 
.91717 

.08258 
.08260 
.08262 
.08264 

8.92315 
.92325 
.92335 
.92346 

.08378 
.08380 
.08382 
.08384 

+  W 

41 

42 
43 

8.89811 
.89822 
.89832 

.89343 

.07909 
.07911 
.07913 
.07915 

8.90455 
.90466 
.90476 
.90487 

.08027 
.08029 
.08031 
.08033 

8.91094 
.91104 
.91115 
.91126 

.08146 
.08148 
.08150 
.08152 

8.91728 
.91738 
.91749 
.91759 

.08266 
.08268 
.08270 
.08272 

8.92356 
.92367 
.92377 
.92388 

.08386 

.08388 
.08390 
.08392 

+  11' 

45 
46 
47 

8.89854 
.89865 
.89875 
.89886 

.07917 
.07919 
.07921 
.07923 

8.90498 
.90508 
.90519 
.90530 

.08035 
.08037 
.08039 
.08041 

8.91136 
.91147 
.91157 
.91168 

.08154 
.08156 
.08158 
.08160 

8.91770 
.91780 
.91791 
.91801 

.08274 
.08276 

.08278 
.08280 

8.92398 
.92409 
.92419 
.92429 

.08394 
.08396 
.08398 
.08400 

16 
15 
14 
13 
12 
11 
10 
9 

+   IV 

49 
50 
51 

8.89897 
.89908 
.89919 
.89929 

.07924 
.07926 
.07928 
.07930 

8.90540 
.90551 
.90562 
.90572 

.08043 
.08045 
.08047 
.08049 

8.91179 
.91189 
.91200 
.91210 

.08162 
.08164 
.08166 
.08168 

8.91812 
.91822 
.91833 
.91843 

.08282 
.08284 
.08286 

.08288 

8.92440 
.92450 
.92461 
.92471 

.08402 
.08404 
.08406 
.08408 

+    13^ 

53 
54 
55 

8.89940 
.89951 
.89962 
.89972 

.07932 
.07934 
.07936 
.07938 

8.90583 
.90594 
.90604 
.90615 

.08051 
.08053 
.08055 
.08057 

8.91221 
.91232 
.91242 
.91253 

.08170 
.08172 
.08174 
.08176 

8.91854 
.91864 
.91875 
.91885 

.08290 
.08292 
.08294 
.08296 

8.92482 
.92492 
.92502 
.92513 

.08410 
.08412 
.08414 
.08416 

8 
7 
6 
5 

+    W 

57 
58 
59 

8.89983 
.89994 
.90005 
.90015 

.07940 
.07942 
.07944 
.07946 

8.90626 
.90636 
.90647 
.90658 

.08059 
.08061 
.08063 
.08065 

8.91263 
.91274 
.91284 
.91295 

.08178 
.08180 
.08182 
.08184 

8.91896 
.91906 
.91917 
.91927 

.08298 
.08300 
.08302 
.08304 
.08306 

8.92523 
.92534 
.92544 
.92554 

.08418 
.08420 
.08422 
.08425 

4 
3 

2 
1 
0 

+  15' 

8.90026 

.07948 

8.90668 

.08066 

8.91306 

.08186 

8.91938 

8.92566 

.08427 

2lTi49m 

21h48m          1    21^47'm 

21^46^ 

21h45m 

k 


Page  838]                  TABLE  45. 

Haversines. 

s 

2Ji  15m  33°  45^ 

2li  l&n  340  (K 

2h  17m  34°  15' 

2h  igm  34°  3r 

2h  19m  34°  45' 

s 

Log.  Hav 

Nat.  Hav 

Log.  Hav 

Nat.  Hav 

Log.  Hav 

Nat.  Hav 

Log.  Hav.  Nat.  Hav 

Log.  Hav 

Nat.  Hav 

0 
1 

2 
3 

8.92565 
.92575 
.92586 
.92596 

.08437 
.08439 
.08431 
.08433 

8.93187 
.93197 
.93208 
.93218 

.08548 
.08550 
.08553 
.08554 

8.93805 
.93815 
.93825 
.93835 

.08671 
.08673 
.08675 
.08677 

8.94417 
.94427 
.94438 
.94448 

.08794 
.08796 

.08798 
.08800 

8.95025 
.95035 
.95045 
.95055 

.08918 
.08930 
.08933 
.08934 

60 
59 

58 
57 

+    r 

5 

6 

7 

8.92607 
.92617 
.92627 
.92638 

.08435 
.08437 
.08439 
.08441 

8.93228 
.93239 
.93249 
.93259 

.08556 

.08558 
.08560 
.08563 

8.93846 
.93856 
.93866 
.93876 

.08679 

.08681 
.08683 
.08685 

8.94458 
.94468 
.94478 
.94488 

.08803 
.08804 
.08806 

.08808 

8.95065 
.95076 
.95086 
.95096 

.08936 
.08938 
.08930 
.08933 

56 
55 
54 
53 

+  r 

9 

10 

11 

8.92648 
.32659 
.92669 
.92679 

.08443 
.08445 
.08447 
.08449 

8.93270 
.93280 
.93290 
.93301 

.08564 
.08566 
.08568 
.08571 

8.93886 
.93897 
.93907 
.93917 

.08687 
.08689 
.08691 
.08693 

8.94498 
.94509 
.94519 
.94529 

.08810 
.08813 
.08814 
.08816 

8.95106 
.95116 
.95126 
.95136 

.08934 
.08936 
.08938 
.08940 

52 
51 
50 
49 
48 
47 
46 
45 

+  y 

IS 

u 

15 

8.92690 
.92700 
.92710 
.92721 

.08451 
.08453 
.08455 
.08457 

8.93311 
.93321 
.93332 
.93342 

.08573 
.08575 
.08577 
.08579 

8.93927 
.93938 
.93948 
.93958 

.08695 
.08697 
.08699 
.08701 

8.94539 
.94549 
.94559 
.94570 

.08818 
.08830 
.08833 

.08835 

8.95146 
.95156 
.95166 
.95176 

.08943 
.08945 
.08947 
.08949 

+     i' 
17 
18 
19 

8.92731 
.92742 
.92752 
.92762 

.08459 
.08461 
.08463 
.08465 

8.93352 
.93363 
.93373 
.93383 

.08581 
.08583 

.08585 
.08587 

8.93968 
.93979 
.93989 
.93999 

.08703 
.08705 
.08707 
.08709 

8.94580 
.94590 
.94600 
.94610 

.08837 
.08839 
.08831 
.08833 

8.95186 
.95197 
.95207 
.95217 

.08951 
.08953 
.08955 
.08957 

44 
43 
42 
41 

+      5^ 

21 
22 
23 

8.92773 
.92783 
.92794 
.92804 

.08467 
.08469 
.08471 
.08473 

8.93393 
.93404 
.93414 
.93424 

.08589 
.08591 
.08593 
.08595 

8.94009 
.94019 
.94030 
.94040 

.08711 
.08714 
.08716 

.08718 

8.94620 
.94630 
.94641 
.94651 

.08835 
.08837 

.08839 
.08841 

8.95227 
.95237 
.95247 
.95257 

.08959 
.08961 
.08963 
.08965 

40 
39 
38 
37 

+   6' 

25 
26 

27 

8.92814 
.92825 
.92835 
.92845 

.08475 
.08477 
.08479 
.08481 

8.93435 
.93445 
.93455 
.93466 

.08597 
.08599 
.08601 
.08603 

8.94050 
.94060 
.94071 
.94081 

.08730 
.08733 
.08734 
.08736 

8.94661 
.94671 
.94681 
.94691 

.08843 
.08845 

.08847 
.08849 

8.95267 
.95277 
.95287 
.95297 

.08967 
.08970 
.08973 
.08974 

36 

35 
34 
S3 

+    r 

29 
SO 
31 

8.92856 
.92866 
.92877 
.92887 

.08483 
.08485 

.08487 
.08489 

8.93476 
.93486 
.93496 
.93507 

.08605 
.08607 
.08609 
.08611 

8.94091 
.94101 
.94111 
.94122 

.08738 
.08730 
.08733 
.08734 

8.94701 
.94712 
.94722 
.94732 

.08851 

.08853 
.08856 

.08858 

8.95307 
.95317 
.95327 
.95337 

.08976 
.08978 
.08980 
.08983 

32 
SI 
SO 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
IS 

+   8^ 

33 
34 
35 

8.92897 
.92908 
.92918 
.92928 

.08491 
.08493 
.08495 
.08497 

8.93517 
.93527 
.93538 
.93548 

.08613 
.08615 
.08617 
.08619 
.08631 
.08634 
.08636 
.08638 

8.94132 
.94142 
.94152 
.94162 

.08736 
.08738 
.08740 
.08743 

8.94742 
.94752 
.94762 
.94772 

.08860 
.08863 
.08864 
.08866 

8.95347 
.95357 
.95368 
.95378 

.08984 

.08986 
.08988 
.08990 

+    r 

37 
38 
39 

8.92939 
.92949 
.92960 
.92970 

.08499 
.08501 
.08503 
.08505 

8.93558 
.93568 
.93579 
.93589 

8.94173 
.94183 
.94193 
.94203 

.08744 
.08746 

.08748 
.08750 

8.94782 
.94793 
.94803 
.94813 

.08868 
.08870 

.08873 
.08874 

8.95388 
.95398 
.95408 
.95418 

.08993 
.08994 
.08997 
.08999 

+  10^ 

41 
42 
43 

8.92980 
.92991 
.93001 
.93011 

.08508 
.08510 
.08513 
.08514 

8.93599 
.93610 
.93620 
.93630 

.08630 
.08633 
.08634 
.08636 

8.94213 
.94224 
.94234 
.94244 

.08753 
.08755 
.08757 
.08759 

8.94823 
.94833 
.94843 
.94853 

.08876 

.08878 
.08880 

.08883 

8.95428 
.95438 
.95448 
.95458 

.09001 
.09003 
.09005 
.09007 

+  11' 

45 
46 
47 

8.93022 
.93032 
.93042 
.93053 

.08516 
.08518 
.08530 
.08533 

8.93640 
.93651 
.93661 
.93671 

.08638 
.08640 
.08643 
.08644 

8.94254 
.94264 
.94275 
.94285 

.08761 
.08763 
.08765 
.08767 

8.94863 
.94874 
.94884 
.94894 

.08885 
.08887 
.08889 
.08891 

8.95468 
.95478 
.95488 
.95498 

.09009 
.09011 
.09013 
.09015 

+    12' 

49 
50 
51 

8.93063 
.93073 
.93084 
.93094 

.08534 
.08536 
.08538 
.08530 

8.93681 
.93692 
.93702 
.93712 

.08646 
.08648 
.08650 
.08653 

8.94295 
.94305 
.94315 
.94326 

.08769 
.08771 
.08773 
.08775 

8.94904 
.94914 
.94924 
.94934 

.08893 
.08895 
.08897 
.08899 

8.95508 
.95518 
.95528 
.95538 

.09017 
.09019 
.09033 
.09034^ 

12 
11 
10 
9 
8 
7 
6 
5 

+   13' 

53 

54 
55 

8.93104 
.93115 
.93125 
.93135 

.08533 
.08534 
.08536 
.08538 

8.93722 
.93733 
.93743 
.93753 

.08654 
.08656 
.08658 
.08660 

8.94336 
.94346 
.94356 
.94366 

.08777 
.08779 
.08781 
.08783 

8.94944 
.94954 
.94965 
.94975 

.08901 
.08903 
.08905 
.08907 

8.95548 
.95558 
.95568 
.95578 

8.95588 
.95598 
.95608 
.95618 

.09036 
.09038 
.09030 
.09033 

+    14' 

57 
58 
59 

8.93146 
.93156 
.93166 
.93177 

.08540 
.08543 
.08544 
.08546 

8.93764 
.93774 
.93784 
.93794 

.08663 
.08664 
.08666 
.08668 

8.94376 
.94387 
.94397 
.94407 

.08785 
.08788 
.08790 
.08793 

8.94985 
.94995 
.95005 
.95015 

.08909 
.08911 
.08914 
.08916 

.09034 
.09036 
.09038 
.09040 

4 
3 
2 
1 

+    15' 

8.93187 

.08548 

8.93805 

.08071 

8.94417  j  .08794 

8.95025 

.08918 

8.95628   .09043 

0 

21^  44"^         1 

21h4Sm          I 

21h  42m 

2lh  41m         1 

21h40m 

TABLE  45.                  [Page  839 

Haversinea. 

s 

2^2(ym^°(y 

2h  2m  35°  15' 

2h22rnS5°W    | 

2h2Sm35°i5'    | 

2h  24^  36°  0'  1 

s 

60 
59 
58 

57 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

8.95628 
.95638 
.95648 
.95658 

.09043 
.09044 
.09047 
.09049 

8.96227 
.96237 
.96247 
.96257 

.09168 
.09170 
.09173 
.09174 

8.96821 
.96831 
.96841 
.96851 

.09294 
.09296 
.09298 
.09301 

8.97411 
.97421 
.97431 
.97441 

.09421 
.09423 
.09436 
.09438 

8.97997 
.98006 
.98016 
.98026 

.09549 
.09551 
.09553 
.09556 

+    r 

5 
6 

7 

8.95668 
.95678 
.95688 
.95698 

.09051 
.09053 
.09055 
.09057 

8.96267 
.96277 
.96287 
.96297 

.09176 
.09178 
.09181 
.09183 

8.96861 
.96871 
.96881 
.96890 

.09303 
.09305 
.09307 
.09309 

8.97450 
.97460 
.97470 
.97480 

.09430 
.09432 
.09434 
.09436 

8.98035 
.98045 
.98055 
.98065 

.09558 
.09560 
.09563 
.09564 

56 
55 
54 
53 

52 
51 
50 
49 
48 
47 
46 
45 

+   2^ 

9 

10 

11 

8.95709 
.95719 
.95729 
.95739 

.09059 
.09061 
.09063 
.09065 

8.96307 
.96317 
.96326 
.96336 

.09185 
.09187 
.09189 
.09191 

8.96900 
.96910 
.96920 
.96930 

.09311 
.09313 
.09315 
.09317 

8.97489 
.97499 
.97509 
.97519 

.09438 
.09440 
.09443 
.09445 

8.98074 
.98084 
.98094 
.98103 

.09566 
.09568 
.09571 
.09573 

+   3' 

IS 
14 
15 

8.95749 
.95759 
.95769 
.95779 

.09067 
.09070 
.09072 
.09074 

8.96346 
.96356 
.96366 
.96376 

.09193 
.09195 
.09197 
.09199 

8.96940 
.96950 
.96959 
.96969 

.09320 
.09322 
.09324 
.09326 

8.97529 
.97538 
.97548 
.97558 

.09447 
.09449 
.09451 
.09453 

8.98113 
.98123 
.98132 
.98142 

.09575 
.09577 
.09579 
.09581 

+   4^ 
17 
18 
19 

8.95789 
.95799 
.95809 
.95819 

.09076 
.09078 
.03080 
.09083 

8.96386 
.96396 
.96406 
.96416 

.09303 
.09204 
.09306 
.09308 

8.96979 
.96989 
.96999 
.97009 

.09338 
.09330 
.09333 
.09334 

8.97568 
.97577 
.97587 
.97597 

.09455 
.09457 
.09460 
.09463 

8.98152 
.98162 
.98171 
.98181 

.09583 
.09586 

.09588 
.09590 

44 
43 
42 
41 

+   5' 
21 
29 
23 

8.95828 
.95838 
.95848 
.95858 

.09084 
.09086 
.09088 
.09090 

8.96426 
.96436 
.96446 
.96455 

.09210 
.09212 
.09314 
.09316 

8.97018 
.97028 
.97038 
.97048 

.09337 
.09339 
.09341 
.09343 

8.97607 
.97617 
.97626 
.97636 

.09464 
.09466 
.09468 
.09470 

8.98191 
.98200 
.98210 
.98220 

.09593 
.09594 
.09596 
.09598 

40 
39 
38 

37 

+   6' 

25 
26 
27 

8.95868 
.95878 
.95888 
.95898 

.09093 
.09095 
.09097 
.09099 

8.96465 
.96475 
.96485 
.96495 

.09318 
.09330 
.09223 
.09225 

8.97058 
.97068 
.97077 
.97087 

.09345 
.09347 
.09349 
.09351 

8.97646 
.97656 
.97665 
.97675 

.09473 
.09474 
.09477 
.09479 

8.98229 
.98239 
.98249 
.98259 

.09601 
.09603 
.09605 
.09607 

36 
35 
34 
33 

+    r 

29 
SO 
31 

8.95908 
.95918 
.95928 
.95938 

.09101 
.09103 
.09105 
.09107 

8.96505 
.96515 
.96525 
.96535 

.09227 
.09229 
.09231 
.09333 

8.97097 
.97107 
.97117 
.97127 

.09353 
.09356 
.09358 
.09360 

8.97685 
.97695 
.97704 
.97714 

.09481 
.09483 
.09485 
.09487 

8.98268 
.98278 
.98288 
.98297 

.09609 
.09611 
.09613 
.09616 

32 
31 
30 
29 

+   8' 
SS 
34 
35 

8.95948 
.95958 
.95968 
.95978 

.09109 
.09111 
.09113 
.09116 

8.96545 
.96555 
.96564 
.96574 

.09235 
.09237 
.09239 
.09242 

8.97136 
.97146 
.97156 
.97166 

.09362 
.09364 
.09366 
.09368 

8.97724 
.97734 
.97743 
.97753 

.09489 
.09493 
.09494 
.09496 

8.98307 
.98317 
.98326 
.98336 

.09618 
.09630 
.09622 
.09624 

28 

27 
26 
25 

+   9^ 

37 
38 
39 

8.95988 
.95998 
.96008 
.96018 

.09118 
.09120 
.09122 
.09124 

8.96584 
.96594 
.96604 
.96614 

.09244 
.09246 
.092*8 
.09250 

8.97176 
.97186 
.97195 
.97205 

.09370 
.09372 
.09375 
.09377 

8.97763 
.97773 
.97782 
.97792 

.09498 
.09500 
.09503 
.09504 

8.98346 
.98355 
.98365 
.98375 

.09626 
.09638 
.09631 
.09633 

24 
23 

22 
21 

+  W 

41 
42 
43 

8.96028 
.96038 
.96048 
.96058 

.09126 
.09128 
.09130 
.09132 

8.96624 
.96634 
.96644 
.96653 

.09252 
.09254 
.09256 
.09258 

8.97215 
.97225 
.97235 
.97244 

.09379 
.09381 
.09383 
.09385 

8.97802 
.97812 
.97821 
.97831 

.09506 
.09509 
.09511 
.09513 

8.98384 
.98394 
.98404 
.98413 

.09635 
.09837 
.09639 
.09641 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

47 

8.96068 
.96078 
.96088 
.96098 

.09134 
.09136 
.09139 
.09141 

8.96663 
.96673 
.96683 
.96693 

.09260 
.09263 
.09265 
.09267 

8.97254 
.97264 
.97274 
.97284 

.09387 
.09389 
.09392 
.09394 

8.97841 
.97851 
.97860 
.97870 

.09515 
.09517 
.09519 
.09531 

8.98423 
.98433 
.98442 
.98452 

.09643 
.09646 
.09648 
.09650 

+  13' 

5i 

8.96108 
.96118 
.96128 
.96138 

.09143 
.09145 
.09147 
.09149 

8.96703 
.96713 
.96723 
.96733 

.09269 
.09271 
.09273 
.09275 

8.97294 
.97303 
.97313 
.97323 

.09396 
.09398 
.09400 
.09403 

8.97880 
.97890 
.97899 
.93909 

.09534 
.09536 
.09538 
.09530 

8.98462 
.98471 
.98481 
.98491 

.09652 
.09654 
.09656 
.09658 

+  13' 

53 
54 
55 

8.96148 
.96158 
.96167 
.96177 

.09151 
.09153 
.09155 
.09157 

8.96742 
.96752 
.96762 
.96772 

.09277 
.09280 
.09282 
.09284 

8.97333 
.97343 
.97352 
.97362 

.09404 
.09406 
.09409 
.09411 

8.97919 
.97928 
.97938 
.9y948 

.09533 
.09534 
.09536 
.09538 

8.98500 
.98510 
.98520 
.98529 

.09661 
.09663 
.09665 
.09667 

+  14' 

57 
58 
59 

8.96187 
.96197 
.96207 
.96217 

.09160 
.09162 
.09164 
.09166 

8.96782 
.96792 
.96802 
.96812 

.09286 
.09288 
.09290 
.09292 

8.97372 
.97382 
.97392 
.97401 

.09413 
.09115 
.09417 
.09419 

8.97958 
.97967 
.97977 
.97987 

.09541 
.09543 
.09545 
.09547 

8.98539 
.98549 
.98558 
.98568 

.09669 
.09671 
.09673 
.09676 

4 
3 

2 
1 

+  15' 

8.96227 

.09168 

8.96821 

.09294 

8.97411 

.09431 

8.97997 

.09549 

8.98578 

.09678 

0 

21h  S9m 

21hS8^ 

21h  37m 

21h  S6m 

21h  35m 

Page  840]                  TABLE  45. 

Haversines. 

s 

2h  25m  36°  15' 

2^  26m  36°  30'' 

2h  27^  36°  45' 

2h  28m  37°  Q/ 

2h  29m  37°  15/ 

s 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

8.98578 
.98587 
.98597 
.98606 

.09678 
.09680 
.09683 
.09684 

8.99154 
.99164 
.99173 
.99183 

.09807 
.09809 
.09811 
.09814 

8.99727 
.99736 
.99746 
.99755 

.09937 
.09939 
.09952 
.09944 

9.00295 
.00305 
.00314 
.00324 

.10068 
.10070 
.10073 
.10075 

9.00860 
.00869 
.00878 
.00888 

.10200 
.10202 
.10204 
.10206 

60 
59 
58 
57 

+   1" 

5 
6 

7 

8.98616 
.98626 
.98635 
.98645 

.09686 
.09689 
.09691 
.09693 

8.99193 
.99202 
.99212 
.99221 

.09816 
.09818 
.09820 
.09822 

8.99765 
.99774 
.99784 
.99793 

.09946 
.09948 
.09950 
.09953 

9.00333 
.00342 
.00352 
.00361 

.10077 
.10079 
.10081 
.10C34 

9.00897 
.00906 
.00916 
.00925 

.10209 
.10211 
.10213 
.10215 

56 
55 
54 
53 

+  V 

9 

10 

11 

8.98655 
.98664 
.98674 
.98684 

.09695 
.09697 
.09699 
.09701 

8.99231 
.99240 
.99250 
.99260 

.09824 
.09827 
.09829 
.09831 

8.99803 
.99812 
.99822 
.99831 

.09955 
.09957 
.09959 
.09961 

9.00371 
.00380 
.00390 
.00399 

.10086 
.10688 
.10090 
.10092 

9.00935 
.00944 
.00953 
.00963 

.10218 
.10220 
.10222 
.10224 

52 
51 
50 
49 

+   3' 

IS 
14 
15 

8.98693 
.98703 
.98712 
.98722 

.09704 
.09706 
.09708 
.09710 

8.99269 
.99279 
.99288 
.99298 

.09833 
.09835 
.09837 
.09840 

8.99841 
.99850 
.99860 
.99869 

8.99879 
.99888 
.99898 
.99907 

.09963 
.09966 
.09968 
.09970 

9.00408 
.00418 
.00427 
.00437 

.10095 
.10097 
.10099 
.10101 

9.00972 
.00981 
.00991 
.01000 

.10226 
.10228 
.10231 
.10233 

48 
47 
46 
45 

+   4' 
17 
18 
19 

8.98732 
.98741 
.98751 
.98761 

.09712 
.09714 
.09717 
.09719 

8.99307 
.99317 
.99327 
.99336 

.09842 
.09844 
.09846 
.09848 

.09972 
.09974 
.09977 
.09979 

9.00446 
.00456 
.00465 
.00474 

.10103 
.10105 
.10108 
.10110 

9.01009 
.01019 
.01028 
.01037 

.10235 
.10237 
.10240 
.10242 

U 
43 
42 
41 

+   5' 

^^ 

+  6' 

25 
26 
27 

8.98770 
.98780 
.98790 
.98799 

.09721 
.09723 
.09725 
.09727 

8.99346 
.99355 
.99365 
.99374 

.09850 
.09853 
.09855 
.09857 

8.99917 
.99926 
.99936 
.99945 

.09981 
.09983 
.09985 
.09987 

9.00484 
.00493 
.00503 
.00512 

.10112 
.10114 
.10116 
.10119 

9.01047 
.01056 
.01065 
.01075 

.10244 
.10246 
.10248 
.10251 

40 
39 
38 
37 

8.98809 
.98818 
.98828 
.98838 

.09729 
.09732 
.09734 
.09736 

8.99384 
.99393 
.99403 
.99412 

.09859 
.09861 
.09863 
.09866 

8.99955 
.99964 
.99974 
.99983 

.09990 
.09992 
.09994 
.09996 

9.00522 
.00531 
.00540 
.00550 

.10121 
.10123 
.10125 
.10127 

9.01084 
.01094 
.01103 
01112 

.10253 
.10255 
.10257 
.10259 

36 
35 
34 
33 

+    r 

29 
30 
31 

8.98847 
.98857 
.98866 
.98876 

.09738 
.09740 
.09742 
.09745 

8.99422 
.99432 
.99441 
.99451 

.09868 
.09870 
.09872 
.09874 

8.99993 

9.00002 

.00012 

.00021 

.09998 
.10000 
.10003 
.10005 

9.00559 
.00569 
.00578 
.00587 

.10130 
.10132 
.10134 
.10136 

9.01122 
.01131 
.01140 
.01150 

.10262 
.10264 
.10266 
.10268 

32 
31 
30 
29 

+   8' 

33 
34 
35 

8.98886 
.98895 
.98905 
.98915 

.09747 
.09749 
.09751 
.09753 

8.99460 
.99470 
.99479 
.99489 

.09876 
.09879 
.09881 

.09883 

9.00031 
.00040 
.00049 
.00059 

.10007 
.10009 
.10011 
.10014 

9.00597 
.00606 
.00616 
.00625 

.10138 
.10141 
.10143 
.10145 

9.01159 
.01168 
.01178 
.01187 

.10270 
.10273 
.10275 
.10277 

28 
27 
26 
25 

+   r 

59 

8.98924 
.98934 
.98943 
.98953 

.09755 
.09757 
.09760 
.09762 

8.99498 
.99508 
.99517 
.99527 

.09885 
.09887 
.09890 
.09892 

9.00068 
.00078 
.00087 
.00097 

.10016 
.10018 
.10020 
.10022 

9.00634 
.00644 
.00653 
.00663 

.10147 
.10149 
.10152 
.10154 

9.01196 
.01206 
.01215 
.01224 

.10279 
.10281 
.10284 
.10286 

24 
23 

22 
21 

+  W 

41 
42 
43 

8.98963 
.98972 
.98982 
.98991 

.09764 
.09766 
.09768 
.09770 

8.99536 
.99546 
.99556 
.99565 

.09894 
.09896 
.09898 
.09900 

9.00106 
.00116 
.00125 
.00135 

.10025 
.10027 
.10029 
.10031 

9.00672 
.00681 
.00691 
.00700 

.10156 
.10158 
.10160 
.10163 

9.01234 
.01243 
.01252 
.01262 

.10288 
.10290 
.10293 
.10295 

20 
19 
18 
17 

+  ir 

45 
46 
47 

8.99001 
.99011 
.99020 
.99030 

.09773 
.09775 
.09777 
.09779 

8.99575 
.99584 
.99594 
.99603 

.09903 
.09905 
.09907 
.09909 

9.00144 
.00154 
.00163 
.00172 

.10033 
.10035 
.10038 
.10040 
.10042 
.10044 
.10046 
.10049 

9.00710 
.00719 
.00728 
.00738 

.10165 
.10167 
.10169 
.10171 
.10174 
.10176 
.10178 
.10180 

9.01271 
.01280 
.01289 
.01299 

9.01308 
.01317 
.01327 
.01336 

.10297 
.10299 
.10301 
.10304 

16 
15 
14 
13 

+  W 

49 
50 
51 

8.99039 
.99049 
.99058 
.99068 

.09781 
.09783 
.09786 
.09788 

8.99613 
.99622 
.99632 
.99641 

.09911 
.09913 
.09916 
.09918 
.09920 
.09922 
.09924 
.09926 

9.00182 
.00191 
.00201 
.00210 

9.00747 
.00756 
.00766 
.00775 

.10306 
.10308 
.10310 
.10312 

12 

11 

10 

9 

+  13' 

53 
54 
55 

8.99078 
.99087 
.99097 
.99106 

.09790 
.09792 
.09794 
.09796 

8.99651 
.99660 
.99670 
.99679 

9.00220 
.00229 
.00239 
.00248 

.10051 
.10053 
.10055 
.10057 

9.00785 
.00794 
.00803 
.00813 

.10182 
.10184 
.10187 
.10189 

9.01345 
.01355 
.01364 
.01373 

.10315 
.10317 
.10319 
.10321 

8 
7 
6 
5 

+  W 

57 
58 
59 

8.99116 
.99126 
.99135 
.99145 

.09799 
.09801 
.09803 
.09805 

8.99689 
.99698 
.99708 
.99717 

.09929 
.09931 
.09933 
.09935 

9.00258 
.00267 
.00276 
.00286 

9.00295 

.10059 
.10C62 
.10064 
.10066 

9.00822 
.00831 
.00841 
.00850 

.10191 
.10193 
.10196 
.10198 

9.01383 
.01392 
.01401 
.01411 

.10323 
.10326 
.10328 
.10330 

4 
S 
2 
1 

+  15' 

8.99154 

.09807 

8.99727 

.09937 

.10068 

9.00860 

.10200 

9.01420  1  .10332 

0 

21h  spn, 

£lh  S3m 

21h  32m 

21h  Sim 

21h30m 

TABLE  45.                 [Page  841 

Haversines. 

s 

2^  SOm  37°  W 

2h  31^  37°  45' 

2^  32m  38°  0' 

2^  33m  38°  15' 

2hS4^3S°W 

s 

60 
59 
58 
51 
56 
55 
54 
53 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.01420 
.01429 
.01438 
.01448 

.10333 
.10335 
.10337 
.10339 

9.01976 
.01985 
.01995 
.02004 

.10466 
.10468 
.10470 
.10473 

9.02528 
.02538 
.02547 
.02556 

.10599 
.10603 
.10604 
.10606 

9.03077 
.03086 
.03095 
.03104 

.10734 
.10736 
.10739 
.10741 

9.03621 
.03630 
.03639 
.03648 

.10870 
.10873 
.10874 
.10876 

+    r 

5 
6 
1 

9.01457 
.01466 
.01476 
.01485 

.10341 
.10343 
.10346 
.10348 

9.02013 
.02022 
.02031 
.02041 

.10474 
.10477 
.10479 
.10481 

9.02565 
.02574 
.02583 
.02593 

.10608 
.10611 
.10613 
.10615 

9.03113 
.03122 
.03131 
.03141 

.10743 
.10745 
.10748 
.10750 

9.03657 
.03667 
.03676 
.03685 

.10879 
.10881 
.10883 
.10885 

+   2' 

9 

10 

11 

9.01494 
.01504 
.01513 
.01522 

.10350 
.10353 
.10354 
.10357 

9.02050 
.02059 
.02068 
.02078 

.10483 
.10486 
.10488 
.10490 

9.02602 
.02611 
.02620 
.02629 

.10017 
.10630 
.10633 
.10634 

9.03150 
.03159 
.03168 
.03177 

.10753 
.10754 
.10757 
.10759 

9.03094 
.03703 
.03712 
.03721 

.10888 
.10890 
.10893 
.10895 

62 
51 
50 
49 
48 
41 
46 
45 

+      3^ 

13 
14 
15 

9.01531 
.01541 
.01550 
.01559 

.10359 
.10361 
.10363 
.10366 

9.02087 
.02096 
.02105 
.02115 

.10493 
.10494 
.10497 
.10199 

9.02638 
.02648 
.02657 
.02666 

.10636 
.10639 
.10631 
.10633 

9.03186 
.03195 
.03204 
.03213 

.10761 
.10763 
.10766 
.10768 

9.03730 
.03739 
.03748 
.03757 

.10897 
.10899 
.10901 
.10904 

+   4' 
11 
18 
19 

9.01569 
.01578 
.01587 
.01596 

.10368 
.10370 
.10373 
.10374 

9.02124 
.02133 
.02142 
.02151 

.10501 
.10503 
.10506 
.10508 

9.02675 
.02684 
.02693 
.02702 

.10635 
.10638 
.10640 
.10643 

9.03222 
.03231 
.03241 
.03250 

.10770 
.10773 
.10775 
.10777 

9.03766 
.03775 
.03784 
.03793 

.10906 
.10908 
.10910 
.10913 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
21 
26 
25 

24 
23 
22 
21 

+      5' 
21 
22 
23 

9.01606 
.01615 
.01624 
.01634 

.10377 
.10379 
.10381 
.10383 

9.02161 
.02170 
.02179 
.02188 

.10510 
.10513 
.10515 
.10517 

9.02712 
.02721 
.02730 
.02739 

.10644 
.10647 
.10649 
.10651 

9.03259 
.03268 
.03277 
.03286 

.10779 
.10781 
.10784 
.10786 

9.03802 
.03811 
.03820 
.03829 

.10915 
.10917 
.10919 
.10923 

+      6^ 

25 
26 
21 

9.01643 
.01652 
.01661 
.01671 

.10386 
.10388 
.10390 
.10393 

9.02197 
.02207 
.02216 
.02225 

.10519 
.10531 
.10533 
.10536 

9.02748 
.02757 
.02767 
.02776 

.10653 
.10655 
.10658 
.10660 

9.03295 
.03304 
.03313 
.03322 

.10788 
.10796 
.10793 
.10795 

9.03838 
.03847 
.03856 
.03865 

.10934 
.10926 
.10939 
.10931 

+    r 

29 
30 
31 

9.01680 
.01689 
.01698 
.01708 

.10394 
.10397 
.10399 
.10401 

9.02234 
.02244 
.02253 
.02262 

.10538 
.10530 
.10533 
.10535 

9.02785 
.02794 
.02803 
.02812 

.10663 
.10664 
.10667 
.10669 

9.03331 
.03340 
.03350 
.03359 

.10797 
.10799 
.10802 
.10804 

9.03874 
.03883 
.03892 
.03901 

.10933 
.10935 
.10938 
.10940 

+     8' 
S3 
34 
35 

9.01717 
.01726 
.01736 
.01745 

.10403 
.10405 
.10408 
.10410 

9.02271 
.02280 
.02290 
.02299 

.10537 
.10539 
.10541 
.10544 
.10546 
.10548 
.10550 
.10553 

9.02821 
.02830 
.02840 
.02849 

.10671 
.10673 
.10676 
.10678 

9.03368 
.03377 
.03386 
.03395 

.10806 
.10809 
.10811 
.10813 

9.03910 
.03919 
.03928 
.03937 

.10943 
.10944 
.10947 
.10949 

+    r 

31 
38 
39 

9.01754 
.01763 
.01773 
.01782 

.10413 
.10414 
.10417 
.10419 

9.02308 
.02317 
.02326 
.02336 

9.02858 
.02867 
.02876 
.02885 

.10680 
.10683 
.10685 
.10687 

9.03404 
.03413 
.03422 
.03431 

.10815 
.10818 
.10830 
.10833 

9.03946 
.03955 
.03964 
.03973 

.10951 
.10953 
.10956 
.10958 

+    W 

41 
42 
43 

9.01791 
.01800 
.01810 
.01819 

.10431 
.10433 
.10435 
.10438 

9.02345 
.02354 
.02363 
.02372 

.10555 
.10557 
.10559 
.10561 

9.02894 
.02904 
.02913 
.02922 

.10689 
.10691 
.10694 
.10696 

9.03440 
.03449 
.03458 
.03467 

.10834 
.10837 
.10839 
.10831 

9.03982 
.03991 
.04000 
.04009 

.10960 
.10963 
.10965 
.10967 

20 
19 
18 
11 
16 
15 
14 
13 

+  11' 

45 
46 
47 

9.01828 
.01837 
.01847 
.01856 

.10430 
.10433 
.10434 
.10436 

9.02381 
.02391 
.02400 
.02409 

.10564 
.10566 
.10568 
.10570 

9.02931 
.02940 
.02949 
.02958 

.10698 
.10700 
.10703 
.10705 

9.03476 
03486 
.03495 
.03504 

.10833 
.10836 
.10838 
.10840 

9.04018 
.04027 
.04036 
.04045 

.10969 
.10973 
.10974 
.10976 

+  13' 

49 
50 
51 

9.01865 
.01874 
.01884 
.01893 

.10439 
.10441 
.10443 
.10445 

9.02418 
.02427 
.02437 
.02446 

.10573 
.10575 
.10577 
.10579 

9.02967 
.02977 
.02986 
.02995 

.10707 
.10709 
.10713 
.10714 

9.03513 
.03522 
.03531 
.03540 

.10843 
.10845 
.10847 
.10849 

9.04054 
.04063 
.04072 
.04081 

.10978 
.10981 
.10983 
.10985 

12 

11 

10 

9 

+  13^ 

53 
54 
55 

9.01902 
.01911 
.01921 
.01930 

.10448 
.10450 
.10453 
.10454 

9.02455 
.02464 
.02473 
.02483 

.10583 
.10584 
.10586 
.10588 

9.03004 
.03013 
.03022 
.03031 

.10716 
.10718 
.10731 
.10723 

9.03549 
.03558 
.03567 
.03576 

.10851 
.10854 
.10856 
.10858 

9.04090 
.04099 
.04108 
.04117 

.10988 
.10990 
.10992 
.10994 

8 
1 
6 
5 

+  14^ 

51 
58 
59 

9.01939 
01948 
.01958 
.01967 

.10457 
.10459 
.10461 
.10463 

9.02492   .10591 
.02501   .10593 
.02510   .10595 
.02519   .10597 

9.03040 
.03050 
.03059 
.03068 

.10725 
.10727 
.10730 
.10733 

9.03585 
.03594 
.03603 
.03612 

.10861 
.10863 
.10865 

.10867 

9.04126 
.04135 
.04144 
.04153 

.10997 
.10999 
.11001 
.11004 

4 
3 
2 
1 

+  15^ 

9.01976 

.10466 

9.02528  1  .10599 

9.03077 

.10734 

9.03621 

.10870 

9.04162 

.11006 

0 

21h  29m 

21h  28^ 

2in  27m 

2in  26m 

21h  £5m 

Page  842] 


TABLE   45. 

Haversines. 


+    r 

5 

6 

7 


+      V 

9 

10 

11 


+      3^ 

13 
14 
15 


+      4' 
17 
18 
19 


+      5^ 
21 


+      6^ 

25 
26 
27 


+    r 

29 
30 
31 


2^  35m  38°  45^         2h  36m  39°  (/         2^  ST"i  39°  15^        jgft  55m  39°  3©/ 


Log.  Hav.  Nat.  Ilav 


9.04162 
.04171 
.04180 
.04189 


9.04198 
.04207 
.04216 
.04225 


9.04234 
.04243 
.04252 
.04261 


9.04270 
.04279 
.04288 
.04297 


9.04306 
.04315 
.04324 
.04333 


9.04341 
.04350 
.04359 
.04368 

9.04377 
.04386 
.04395 
.04404 


.llOOG 
.11008 
.11010 
.11013 


.11015 
.11017 
.11019 
.11032 


.11034 
.11036 
.11039 
.11031 


.11033 
.11033 
.11038 
.11040 


.11043 
.11044 
.11047 
.11049 


+   8^ 


+  9^ 

37 


+  W 

41 


+  11^ 

45 
46 
47 


+    1%' 

49 
50 
51 


+  ir 

53 
54 
55 

+  w 

57 

58 
59 


+  W 


9.04413 
.04422 
.04431 
.04440 


9.04449 
.04458 
.04467 
.04476 


9.04485 
.04494 
.04503 
.04512 


9.04520 
.04529 
.04538 
.04547 


9.04556 
.04565 
.04574 
.04583 


.04592 
.04601 
.04610 
.04619 


.04628 
.04637 
.04646 
.04654 


9.04663 
.04672 
.04681 
.04690 


.11051 
.11054 
.11056 
.11058 


.11063 
.11065 
.11067 


Log.  Hav.  Nat.  Hav 


9.04699 
.04708 
.04717 
.04726 


9.04735 
.04744 
.04753 
.04761 


9.04770 
.04779 
.04788 
.04797 


9.04806 
.04815 
.04824 
.04833 


9.04842 
.04851 
.04859 
.04868 


9.04877 
.04886 
.04895 
.04904 


.11143 
.11145 
.11147 
.11150 


.11153 
.11154 
.11156 
.11159 


.11161 
.11163 
.11166 
.11168 


.11170 
.11173 
.11175 
.11177 


.11179 
.11183 
.11184 
11186 


.11060  9.04913 


.11070 
.11073 
.11074 
.11076 


.11079 
.11081 
.11083 
.11086 


.11088 
.11090 
.11093 
.11095 


.11097 
.11099 
.11103 
.11104 


.11106 
.11108 
.11111 
.11113 


.11115 
.11117 
.11130 
.11133 


.11134 
.11137 
.11139 
.11131 


9.04699 


.11134 
.11136 
.11138 
.11140 


.11143 


.04922 
.04931 
.04939 


9.04948 
.04957 
.04966 
.04975 


9.04984 
.04993 
.05002 
.05011 


9.05019 
.05028 
.05037 
.05046 


9.05055 
.05064 
.05073 
.05082 


9.05090 
.05099 
.05108 
.05117 


9.05126 
.05135 
.05144 
.05153 


9.05161 
.05170 
.05179 
.05188 


9.05197 
.05206 
.05215 
.05223 


.11189 
.11191 
.11193 
.11195 


.11198 
.11300 
.11303 
.11305 


Log.  Hav.  Nat.  Hav 


9.05232 
.05241 
.05250 
.05259 


9.05268 
.05277 
.05285 
.05294 


9.05303 
.05312 
.05321 
.05330 


9.05339 
.05347 
.05356 
.05365 


9.05374 
.05383 
.05392 
.05400 


9.05409 
.05418 
.05427 
.05436 


.11380 
.11383 
.11385 
.11387 


.11390 
.11393 
.11394 
.11396 


.11399 
.11301 
.11303 
.11306 


.11308 
.11310 
.11313 
.11315 


.11317 
.11330 
.11333 
.11334 


.11307 
.11309 
.11311 
.11314 


.11316 
.11318 
.11331 
.11333 


.11335 
.11338 
.11330 
.11333 


.11334 
.11337 
.11339 
.11341 


.11344 
.11346 
.11348 
.11351 


.11353 
.11355 
.11357 
.11260 


.11363 
.11364 
.11367 
.11269 


21h  24m 


9.05232 


.11371 
.11374 
.11376 
.11378 


.11380 


21^  23^ 


9.05445 
.05453 
.05462 
.05471 


9.05480 
.05489 
.05498 
.05506 


9.05515 
.05524 
.05533 
.05542 


9.05551 
.05559 
.05568 
.05577 


9.05586 
.05595 
.05603 
.05612 


9.05621 
.05630 
.05639 
.05648 


9.05656 
.05665 
.05674 
.05683 


9.05692 
.05700 
.05709 
.05718 


.11336 
.11339 
.11331 
.11333 


.11336 
.11338 
.11340 
.11343 


.11345 
.11347 
.11349 
.11353 


.11354 
.11356 
.11359 
.11361 


.11363 
.11366 
.11368 
.11370 


.11373 
.11375 
.11377 
.11379 


.11383 
.11384 
.11386 
.11389 


Log.  Hav.  Nat.  Hav 


9.05762 
.05771 
.05780 
.05788 


9.05797 
.05806 
.05815 
.05823 


9.05832 
.05841 
.05850 
.05859 


9.05867 
.05876 
.05885 
.05894 


9.05903 
.05911 
.05920 
.05929 


.11419 
.11431 
.11433 
.11436 


.11438 
.11430 
.11433 
.11435 


.11437 
.11440 
.11443 
.11444 


.11447 
.11449 
.11451 
.11453 


9.05938 
.05946 
.05955 
.05964 


9.05973 
.05982 
.05990 
.05999 


9.06008 
.06017 
.06025 
.06034 


9.06043 
.06052 
.06060 
.06069 


9.06078 
.06087 
.06095 
.06104 


9.06113 
.06122 
.06131 
.06139 


.11391 
.11393 
.11396 
.11398 


9.05727 
.05736 
.05744 
.05753 


9.05762 


.11400 
.11403 
.11405 
.11407 


.11410 
.11413 
.11414 
.11416 


.11419 


21h  22in 


9.06148 
.06157 
.06166 
.06174 


9.06183 
.06192 
.06201 
.06209 


.11456 
.11458 
.11460 
.11463 


.11465 
.11467 
.11470 
.11473 
:il474 
.11477 
.11479 
.11481 


.11484 
.11486 
.11488 
.11491 


.11493 
.11495 
.11498 
.11500 


.11503 
.11504 
.11507 
.11509 


2h  39m  39°  45^ 


Log.  Hav.  Nat.  Hav 


9.06288 
.06297 
.06305 
.06314 


9.06323 
.06332 
.06340 
.06349 


9.06358 
.06367 
.06375 
.06384 


9.06393 
.06401 
.06410 
.06419 


9.06428 
.06436 
.06445 
.06454 


9.06462 
.06471 
.06480 
.06489 


9.06497 
.06506 
.06515 
.06523 


9.06532 
.06541 
.06550 
.06558 


9.06567 
.06576 
.06584 
.06593 


.11511 
.11514 
.11516 
.11518 


.11531 
.11523 
.11535 
^11538 
.11530 
.11533 
.11535 
.11537 


9.06218 
.06227 
.06235 
.06244 


9.06253 
.06262 
.06270 
.06279 


9.06288 


.11539 
.11542 
.11544 
.11546 


.11549 
.11551 
.11553 
.11556 


.11558 


21h  21m 


9.06602 
.06611 
.06619 
.06628 


9.06637 
.06645 
.06654 
.06663 


.11558 
.11560 
.11563 
.11565 


.11567 
.11569 
.11572 
.11574 


.11577 
.11579 
.11581 
.11584 


.11586 
.11588 
.11590 
.11593 


.11595 
.11597 
.11600 
.11602 
.11604 
.11607 
.11609 
.11611 


.11614 
.11616 
.11618 
.11621 
.11623 
.11625 
.11638 
.11630 


.11632 
.11635 
.11637 
.11639 


9.06671 
.06680 
.06689 
.06697 


9.06706 
.06715 
.06724 
.06732 


9.06741 
.06750 
.06758 
.06767 


9.06776 
.06784 
.06793 
.06802 


9.06810 


.11642 
.11644 
.11646 
^11649 
.11651 
.11653 
.11656 
.11658 


.11660 
.11663 
.11665 
.11667 


.11670 
.11672 
.11674 
.11677 


.11679 
.11681 
.11684 
.11686 


.11688 
.11691 
.11693 
.11695 


.11698 


21h  20m 


TABLE  45.                 [Page  843 

Haveraines. 

s 

2h40mM°0'    1 

2h4imiO°  15^    1 

2h  42m  40°  30' 

2h43mM°i5'    | 

2hUm^V^    1 

s 

Log.  Ilav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.06810 
.06819 
.06828 
.06836 

.11698 
.11700 
.11703 
.11705 

9.07329 
.07338 
.07346 
.07355 

.11838 
.11841 
.11843 
.11845 

9.07845 
.07853 
.07862 
.07870 

9.07879 
.07887 
.07896 
.07905 

.11980 
.11982 
.11984 
.11987 
.11989 
.11992 
.11994 
.11996 

9.08357 
.08365 
.08374 
.08382 

.12122 
.13134 
.13137 
.13129 

9.08865 
.08874 
.08882 
.08890 

.13365 
.13367 
.13369 
.13373 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

+    r 

5 
6 

7 

9.06845 
.06854 
.06862 
.06871 

.11707 
.11709 
.11713 
.11714 
.11710 
.11719 
.11721 
.11724 

9.07364 
.07372 
.07381 
.07390 

.11848 
.11850 
.11852 
.11855 

9.08391 
.08399 
.08408 
.08416 

9.08425" 
.08433 
.08442 
.08450 

.12131 
.12134 
.12136 
.12138 

9.08899 
.08907 
.08916 
.08924 

.13374 
.13376 
.13379 
.12281 
.12284 
.12286 
.12288 
.12291 

+    r 

9 
10 
11 

9.06880 
.06888 
.06897 
.06906 

9.07398 
.07407 
.07415 
.07424 

.11857 
.11860 
.11862 
.11864 

9.07913 
.07922 
.07930 
.07939 

.11999 
.12001 
.12003 
.12006 

.12141 
.12143 
.12146 
.12148 

9.08933 
.08941 
.08949 
.08958 

+  3' 

13 
14 
15 

+      i' 
17 
18 
19 

9.06914 
.06923 
.06932 
.06940 
'9.06949 
.06958 
.06966 
.06975 

9.06984 
.06992 
.07001 
.07010 

.11736 
.11738 
.11731 
.11733 
.11735 
.11738 
.11740 
.11743 
.11745 
.11747 
.11749 
.11752 

9.07433 
.07441 
.07450 
.07458 

.11867 
.11869 
.11871 
.11874 

9.07947 
.07956 
.07964 
.07973 

9.07981 
.07990 
.07999 
.08007 

.12008 
.12010 
.13013 
.13015 
.13018 
.12020 
.12022 
.12025 
.12027 
.12029 
.12032 
.12034 

9.08459 

.08467 
.08475 
.08484 

.12150 
.12153 
.12155 
.12157 

9.08966 
.08975 
.08983 
.08992 

.12293 
.13396 
.13398 
.13300 
.13303 
.13305 
.13307 
.13310 
.13313 
.13315 
.13317 
.13319 
.13333 
.13334 
.13337 
.12329 
.12331 
.13334 
.13336 
.12339 
.13341 
.12343 
.13346 
.13348 

9.07467 
.07476 
.07484 
.07493 

9.07501 
.07510 
.07519 
.07527 

.11876 
.11878 
.11881 
.11883 

9.08492 
.08501 
.08509 
.08518 

9.08526 
.08535 
.08543 
.08552 

.12160 
.12162 
.12165 
.12167 
.12169 
.13172 
.13174 
.13176 

9.09000 
.09009 
.09017 
.09025 

9.09034 
.09042 
.09051 
.09059 

9.09068 
.09076 
.09084 
.09093 

9.09101 
.09110 
.09118 
.09126 

9.09135 
.09143 
.09152 
.09160 

9.09169 
.09177 
.09185 
.09194 

9.09202 
.09211 
.09219 
.09227 

+      5' 
21 

22 
23 

.11885 

.11888 
.11890 
.11892 

9.08016 
.08024 
.08033 
.08041 

+      6' 

25 
26 
27 

9.07018 
.07027 
.07036 
.07044 

9^07053' 
.07062 
.07070 
.07079 

.11754 
.11756 
.11759 
.11761 
.11763 
.11766 
.11768 
.11770 
.11773 
.11775 
.11777 
.11780 

9.07536 
.07544 
.07553 
.07562 

9.07570 
.07579 
.07587 
.07596 

9.07605 
.07613 
.07622 
.07630 

.11895 
.11897 
.11900 
.11902 
.11904 
.11907 
.11909 
.11911 

9.08050 
.08058 
.08067 
.08075 

9.08084 
.08092 
.08101 
.08110 

.12036 
.12039 
.12041 
.12044 
.12046 
.12048 
.12051 
.12053 

9.08560 
.08569 
.08577 
.08586 

.12179 
.12181 
.12184 
.12186 
.12188 
.12191 
.12193 
.12195 
.13198 
.13300 
.13203 
.13305 
.13307 
.13310 
.13313 
.13314 
.13317 
.12219 
.12233 
.13324 

+    r 

29 
SO 
31 

9.08594 
.08603 
.08611 
.08620 

9.08628 
.08637 
.08645 
.08654 

+   8' 

33 
34 
35 

9.07088 
.07096 
.07105 
.07113 

9.07122 
.07131 
.07139 
.07148 

.11914 
.11916 
.11918 
.11921 

9.08118 
.08127 
.08135 
.08144 

.12055 
.12058 
.12060 
.12062 

+      9' 

37 
38 
39 

.11782 
.11784 
.11787 
.11789 

9.07639 
.07647 
.07656 
.07665 

.11923 
.11925 
.11928 
.11930 

9.08152 
.08161 
.08169 
.08178 

.12065 
.12067 
.12070 
.12073 

9.08662 
.08671 
.08679 
.08687 

.12351 
.12353 
.12355 
.12358 

24 
23 

22 
21 

+  10' 

41 
42 
43 

9.07157 
.07165 
.07174 
.07183 

.11791 
.11794 
.11796 
.11798 

9.07673 
.07682 
.07690 
.07699 

9.07708 
.07716 
.07725 
.07733 

.11933 
.11935 
.11937 
.11940 
.11942 
.11944 
.11947 
.11949 

9.08186 
.08195 
.08203 
.08212 

.12074 
.12077 
.12079 
.12081 

9.08696 
.08704 
.08713 
.08721 

.12360 
.12363 
.12365 
.12367 

20 
19 
18 
17 

+    11^ 

45 
46 
47 

9.07191 
.07200 
.07208 
.07217 

.11801 
.11803 
.11806 
.11808 

9.08220 
.08229 
.08237 
.08246 

.12084 
.12086 
.12089 
.12091 

9.08730 

.08738 
.08747 
.08755 

.12226 
.12229 
.12231- 
.12233 

9.09236 
.09244 
.09253 
.09261 

.12370 
.12372 
.12374 
.12377 
.12379 
.13383 
.13384 
.12386 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

+    12' 

49 
60 
51 

9.07226 
.07234 
.07243 
.07252 

9.07260 
.07269 
.07277 
.07286 

.11810 
.11813 
.11815 
.11817 
.11830 
.11833 
.11834 
.11837 

9.07742 
.07750 
.07759 
.07768 

9.07776" 
.07785 
.07793 
.07802 

.11951 
.11954 
.11956 
.11958 

9.08254 
.08263 
.08271 
.08280 

.12093 
.12096 
.12098 
.13100 

9.08764 
.08772 
.08781 
.08789 

.12236 
.12238 
.12241 
.12243 

9.09269 
.09278 
.09286 
.09295 

+    13' 

53 

54 

55 

+    14' 

57 
'58 
59 

.11961 
.11963 
.11966 
.11968 

9.08288 
.08297 
.08306 
.08314 

.13103 
.12105 
.12108 
.12110 

9.08797 
.08806 
.08814 
.08823 

.12245 
.12248 
.12250 
.12253 

9.09303 
.09311 
.09320 
.09328 

.12389 
.12391 
.12394 
.12396 

9.07295 
.07303 
.07312 
.07321 

.11839 
.11831 
.11834 
.11836 
.11838 

9.07810 
.07819 
.07827 
.07836 

.11970 
.11973 
.11975 
.11977 

9.08323 
.08331 
.08340 
.08348 

.12112 
.13115 
.13117 
.13119 

9.08831 
.08840 
.08848 
.08857 

.13355 
.13257 
.12260 
.12262 

9.09337 
.09345 
.09353 
.09362 

.13398 
.12401 
.12403 
.12406 

4 
S 

2 

1 

+    15' 

9.07329 

9.07845 

.11980 

9.08357 

.12122 

9.08865 

.12365 

9.09370  1  .13408 

0 

£2h  19m 

21h  ism 

21h  nm 

21h  16m 

21h  15m 

21594°— 14- 


-46 


Page  844] 

TABLE  45. 

Haversines. 

s 

2h45m 

41°  W 

2h46m 

41°  30^ 

2^47^ 

41°  45^ 

2h48m 

42°  0^ 

2h  49m  43°  15/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.09370 
.09379 
.09387 
.09395 

.12408 
.12410 
.12413 
.12416 

9.09872 
.09880 
.09889 
.09897 

.12552 
.12555 
.12557 
.12559 

9.10371 
.10379 
.10387 
.10395 

.12697 
.12700 
.12702 
.12704 

9.10866 
.10874 
.10882 
.10891 

.12843 
.12845 

.12848 
.12850 

9.11358 
.11366 
.11374 
.11382 

.12989 
.12992 
.12994 
.12996 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.09404 
.09412 
.09421 
.09429 

.12418 
.12420 
.12422 
.12425 

9.09905 
.09914 
.09922 
.09930 

.12562 
.12564 
.12567 
.12569 

9.10404 
.10412 
.10420 
.10429 

.12707 
.12709 
.12712 
.12714 

9.10899 
.10907 
.10915 
.10923 

.12852 
.12855 
.12857 
.12860 

9.11391 
.11399 
.11407 
.11415 

.12999 
.13001 
.13004 
.13006 

56 

55 
54 
53 

+      2^ 

9 

10 

11 

9.09437 
.09446 
.09454 
.09462 

.12427 
.12430 
.12432 
.12434 

9.09939 
.09947 
.09955 
.09964 

.12572 
.12574 
.12576 
.12579 

9.10437 
.10445 
.10453 
.10462 

.12717 
.12719 
.12721 
.12724 

9.10932 
.10940 
.10948 
.10956 

.12862 
.12865 
.12867 
.12870 

9.11423 
.11431 
.11440 
.11448 

.13009 
.13011 
.13014 
.13016 

52 
51 
50 
49 

+   3^ 

13 
14 
15 

9.09471 
.09479 
.09488 
.09496 

.12437 
.12439 
.12442 
.12444 

9.09972 
.09980 
.09989 
.09997 

.13581 
.12584 
.12586 

.12588 

9.10470 
.10478 
.10486 
.10495 

.12726 
.12729 
.12731 
.12733 

9.10965 
.10973 
.10981 
.10989 

.12872 
.12874 

.12877 
.12879 

9.11456 
.11464 
.11472 
.11480 

.13018 
.13021 
.13023 
.13026 

48 
47 
46 
45 

+   *^ 
17 
18 
19 

9.09504 
.09513 
.09521 
.09529 

.12446 
.12449 
.12451 
.12454 

9.10005 
.10014 
.10022 
.10030 

.12591 
.12593 
.12596 
.12598 

9.10503 
.10511 
.10519 
.10528 

.12736 
.12738 
.12741 
.12743 

9.10997 
.11006 
.11014 
.11022 

.12882 
.12884 
.12887 
.12889 

9.11489 
.11497 
.11505 
.11513 

.13028 
.13031 
.13033 
.13036 

44 
43 
42 
41 

+   5' 

21 

22 
23 

9.09538 
.09546 
.09555 
.09563 

.12456 
.12458 
.12461 
.12463 

9.10039 
.10047 
.10055 
.10064 

.12600 
.12603 
.12605 
.12608 

9.10536 
.10544 
.10553 
.10561 

.12746 
.12748 
.12750 
.12753 

9.11030 
.11038 
.11047 
.11055 

.12891 
.12894 
.12896 
.12899 

9.11521 
.11529 
.11538 
.11546 

.13038 
.13041 
.13043 
.13045 

40 
39 
38 
37 

+      6^ 

25 
26 

27 

9.09571 
.09580 
.09588 
.09596 

.12466 
.12468 
.12470 
.12473 

9.10072 
.10080 
.10088 
.10097 

.12610 
.12613 
.12615 
.12617 

9.10569 
.10577 
.10586 
.10594 

.12755 
.12758 
.12760 
.12763 

9.11063 
.11071 
.11079 
.11088 

.12901 
.12904 
.12906 
.12909 

9.11554 
.11562 
.11570 
.11578 

.13048 
.13050 
.13053 
.13055 

36 
35 
34 
33 
32 
31 
30 
29 

+    r 

29 
30 
31 

9.09605 
.09613 
.09622 
.09630 

.12475 
.12478 
.12480 
.12482 

9.10105 
.10113 
.10122 
.10130 

.12620 
.12622 
.12625 
.12627 

9.10602 
.10610 
.10619 
.10627 

.12765 
.12767 
.12770 
.12772 

9.11096 
.11104 
.11112 
.11120 

.12911 
.12913 
.12916 
.12918 

9.11586 
.11595 
.11603 
.11611 

.13058 
.13060 
.13063 
.13065 

+   8^ 
S3 
34 
35 

9.09638 
.09647 
.09655 
.09663 

.12485 
.12487 
.12490 
.12492 

9.10138 
.10147 
.10155 
.10163 

.12629 
.12632 
.12634 
.12637 

9.10635 
.10643 
.10652 
.10660 

.12775 
.12777 
.12780 
.12782 

9.11129 
.11137 
.11145 
.11153 

.12921 
.12923 
.12926 
.12928 

9.11619 
.11627 
.11635 
.11643 

.13067 
.13070 
.13072 
.13075 

28 
27 
26 
25 

+   0^ 

37 
38 
39 

9.09672 
.09680 
.09688 
.09697 

.12494 
.12497 
.12499 
.12502 

9.10172 
.10180 
.10188 
.10196 

.12639 
.12641 
.12644 
.12646 

9.10668 
.10676 
.10685 
.10693 

.12784 
.12787 
.12789 
.12792 

9.11161 
.11170 
.11178 
.11186 

.12930 
.12933 
.12935 
.12938 

9.11652 
.11660 
.11668 
.11676 

.13077 
.13080 
.13082 
.13085 

24 

23 
22 
21 

+  10^ 

41 
42 
43 

9.09705 
.09713 
.09722 
.09730 

.12504 
.12506 
.12509 
.12511 

9.10205 
.10213 
.10221 
.10230 

.12649 
.12651 
.12654 
.12656 

9.10701 
.10709 
.10718 
.10726 

.12794 
.12797 
.12799 
.12801 

9.11194 
.11202 
.11211 
.11219 

.12940 
.12943 
.12945 
.12948 

9.11684 
.11692 
.11700 
.11709 

.13087 
.13090 
.13092 
.13095 

20 
19 
18 
17 

+  11^ 

45 
46 
47 

9.09739 
.09747 
.09755 
.09764 

.12514 
.12516 
.12519 
.12521 

9.10238 
.10246 
.10255 
.10263 

.12658 
.12661 
.12663 
.12666 

9.10734 
.10742 
.10751 
.10759 

.12804 
.12806 
.12809 
.12811 

9.11227 
.11235 
.11243 
.11252 

.12950 
.12952 
.12955 
.12957 

9.11717 
.11725 
.11733 
.11741 

.13097 
.13099 
.13102 
.13104 

16 
15 
14 
IS 

+  12^ 

49 
50 
51 

9.09772 
.09780 
.09789 
.09797 

.12523 
.12526 
.12528 
.12531 

9.10271 
.10279 
.10288 
.10296 

.12668 
.12671 
.12673 
.12675 

9.10767 
.10775 
.10784 
.10792 

.12814 
.12816 
.12818 
.12821 

9.11260 
.11268 
.11276 
.11284 

.12960 
.12962 
.12965 
.12967 

9.11749 
.11757 
.11766 
.11774 

.13107 
.13109 
.13112 
.13114 

12 
11 
10 
9 
8 
7 
6 
5 

+  13^ 

54 
55 

9.09805 
.09814 
.09822 
.09830 

.12533 
.12536 
.12538 
.12540 

9.10304 
.10313 
.10321 
.10329 

.12678 
.12680 
.12683 
.12685 

9.10800 
.10808 
.10816 
.10825 

.12823 
.12826 

.12828 
.12831 

9.11292 
.11301 
.11309 
.11317 

.12970 
.12972 
.12974 
.12977 

9.11782 
.11790 
.11798 
.11806 

.13116 
.13119 
.13121 
.13124 

+  14^ 

57 
58 

59 

9.09839 
.09847 
.09856 
.09864 

.12543 
.12545 
.12547 
.12550 

9.10337 
.10346 
.10354 
.10362 

.12687 
.12690 
.12692 
.12695 

9.10833 
.10841 
.10849 
.10858 

.12833 
.12836 

.12838 
.12840 

9.11325 
.11333 
.11342 
.11350 

.12979 
.12982 
.12984 
.12987 

9.11814 
.11822 
.11831 
.11839 

.13126 
.13129 
.13131 
.13134 

4 
3 

2 
1 

+    W 

9.09872 

.12552 

9.10371 

.12697 

9.10866 

.12843 

9.11358 

.12989 

9.11847 

.13136 

0 

21^ 

14m 

21h 

13m 

21h  12m 

21f>' 

lim 

21h 

lOm 

TABLE  45.                  [Page  846 
Haversines. 

s 

£h  50^  42°  SCK 

2h  Sim  43°  45/ 

2h  52m.  43°  0" 

2h  53m  43°  15' 

2h  54m  43°  30^ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.11847 
.11855 
.11863 
.11871 

.13136 
.13139 
.13141 
.13143 

9.12332 
.12341 
.12349 
.12357 

.13284 
.13286 
.13289 
.13291 

9.12815 
.12823 
.12831 
.12839 

.13432 
.13435 
.13437 
.13440 

9.13295 
.13303 
.13311 
.13319 

.13581 
.13584 
.13586 
.13589 

9.13771 
.13779 
.13787 
.13795 

.13731 
.13734 
.13736 
.13739 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.11879 
.11887 
.11895 
.11904 

.13146 
.13148 
.13151 
.13153 

9.12365 
.12373 
.12381 
.12389 

.13294 
.13296 
.13299 
.13301 

9.12847 
.12855 
.12863 
.12871 

.13442 
.13445 
.13447 
.13450 

9.13326 
.13334 
.13342 
.13350 

9.13358 
.13366 
.13374 
.13382 

.13591 
.13594 
.13596 
.13599 

9.13803 
.13811 
.13819 
.13827 

.13741 
.13744 
.13746 
.13749 

56 
55 
54 
53 

+      r 

9 

10 

11 

9.11912 
.11920 
.11928 
.11936 

.13156 
.13158 
.13161 
.13163 

9.12397 
.12405 
.12413 
.12421 

.13304 
.13306 
.13309 
.13311 

9.12879 
.12887 
.12895 
.12903 

.13452 
.13455 
.13457 
.13460 

.13601 
.13604 
.13607 
.13609 

9.13834 
.13842 
.13850 
.13858 

.13751 
.13754 
.13756 
.13759 

52 
51 
50 
49 

+     3' 

13 
14 
15 

9.11944 
.11952 
.11960 
.11968 

.13166 
.13168 
.13171 
.13173 

9.12429 
.12437 
.12445 
.12453 

.13314 
.13316 
.13318 
.13321 

9.12911 
.12919 
.12927 
.12935 

.13462 
.13465 
.13467 
.13470 

9.13390 
.13398 
.13406 
.13414 

.13611 
.13614 
.13616 
.13619 

9.13866 
.13874 
.13882 
.13890 

.13761 
.13764 
.13766 
.13769 

48 
47 
46 
45 

17 
18 
19 

9.11977 
.11985 
.11993 
.12001 

.13175 
.13178 
.13180 
.13183 

9.12461 
.12470 
.12478 
.12486 

.13323 
.13326 
.13328 
.13331 

9.12943 
.12951 
.12959 
.12967 

.13472 
.13474 
.13477 
.13479 

9.13422 
.13430 
.13438 
.13446 

.13621 
.13624 
.13626 
.13629 

9.13898 
.13906 
.13913 
.13921 

9.13929 
.13937 
.13945 
.13953 

.13771 
.13774 
.13776 
.13779 

44 
43 
42 
41 
40 
39 
38 
37 

+     5^ 

21 

22 
23 

9.12009 
.12017 
.12025 
.12033 

.13185 
.13188 
.13190 
.13193 

9.12494 
.12502 
.12510 
.12518 

.13333 
.13336 
.13338 
.13341 

9.12975 
.12983 
.12991 
.12999 

.13482 
.13484 
.13487 
.13489 

9.13454 
.13462 
.13470 
.13478 

.13631 
.13634 
.13636 
.13639 

.13781 
.13784 
.13786 
.13789 

+      6' 

25 
26 

27 

9.12041 
.12050 
.12058 
.12066 

.13195 
.13198 
.13200 
.13203 

9.12526 
.12534 
.12542 
.12550 

.13343 
.13346 
.13348 
.13351 

9.13007 
.13015 
.13023 
.13031 

.13492 
.13494 
.13497 
.13499 

9.13486 
.13494 
.13501 
.13509 

.13641 
.13644 
.13646 
.13649 

9.13961 
.13969 
.13977 
.13985 

.13791 
.13794 
.13796 
.13799 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.12074 
.12082 
.12090 
.12098 

.13205 
.13207 
.13210 
.13212 

9.12558 
.12566 
.12574 
.12582 

.13353 
.13356 
.13358 
.13360 

9.13039 
.13047 
.13055 
.13063 

.13502 
.13504 
.13507 
.13509 

9.13517 
.13525 
.13533 
.13541 

.13651 
.13654 
.13656 
.13659 

9.13992 
.14000 
.14008 
.14016 

.13801 
.13804 
.13806 
.13809 

32 
31 
30 
29 

+     8' 
33 
34 
35 

9.12106 
.12114 
.12122 
.12130 

.13215 
.13217 
.13220 
.13222 
.13225 
.13227 
.13230 
.13232 

9.12590 
.12598 
.12606 
.12614 

9.12622 
.12630 
.12638 
.12647 

.13363 
.13365 
.13368 
.13370 
.13373 
.13375 
.13378 
.13380 

9.13071 
.13079 
.13087 
.13095 

9.13103 
.13111 
.13119 
.13127 

.13512 
.13514 
.13517 
.13519 
.13522 
.13524 
.13527 
.13529 

9.13549 
.13557 
.13565 
.13573 

.13661 
.13664 
.13666 
.13669 

9.14024 
.14032 
.14040 
.14048 

.13811 
.13814 
.13816 
.13819 

28 

27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 

+    r 

37 
38 
39 

9.12139 
.12147 
.12155 
.12163 

9.13581 
.13589 
.13597 
.13605 

.13671 
.13674 
.13676 
.13679 

9.14056 
.14063 
.14071 
.14079 

.13822 
.13824 
.13827 
.13829 

+    W 

41 
42 
43 

9.12171 
.12179 
.12187 
.12195 

.13235 
.13237 
.13239 
.13242 

9.12655 
.12663 
.12671 
.12679 

.13383 
.13385 
.13388 
.13390 

9.13135 
.13143 
.13151 
.13159 

.13532 
.13534 
.13537 
.13539 

9.13613 
.13621 
.13628 
.13636 

.13681 
.13684 
.13686 
.13689 

9.14087 
.14095 
.14103 
.14111 

.13832 
.13834 
.13837 
.13839 

+  ir 

45 
46 

47 

9.12203 
.12211 
.12219 
.12228 

.13244 
.13247 
.13249 
.13252 

9.12687 
.12695 
.12703 
.12711 

.13393 
.13395 
.13398 
.13400 

9.13167 
.13175 
.13183 
.13191 

.13542 
.13544 
.13547 
.13549 

9.13644 
.13652 
.13660 
.13668 

.13691 
.13694 
.13696 
.13699 

9.14119 
.14127 
.14134 
.14142 

.13842 
.13844 
.13847 
.13849 

16 
15 
14 
IS 

+    12' 

49 

50 

51 
+    13' 

53 

54 

55 
+    14' 

57 

58 

59 

9.12236 
.12244 
.12252 
.12260 

.13254 
.13257 
.13259 
.13262 

9.12719 
.12727 
.12735 
.12743 

.13403 
.13405 
.13408 
.13410 

9.13199 
.13207 
.13215 
.13223 

913231 
.13239 
.13247 
.13255 

.13552 
.13554 
.13557 
.13559 

9.13676 
.13684 
.13692 
.13700 

.13701 
.13704 
.13706 
.13709 

9.14150 
.14158 
.14166 
.14174 

.13852 
.13854 
.13857 
.13859 

12 

11 

10 

9 

9.12268 
.12276 
.12284 
.12292 

.13264 
.13267 
.13269 
.13272 

9.12751 
.12759 
.12767 
.12775 

.13412 
.13415 
.13417 
.13420 

.13562 
.13564 
.13567 
.13569 

9.13708 
.13716 
.13724 
.13732 

.13711 
.13714 
.13716 
.13719 

9.14182 
.14190 
.14197 
.14205 

.13862 
.13864 
.13867 
.13869 

8 
7 
6 
5 

4 
S 

2 
1 
0 

9.12300 
.12308 
.12316 
.12324 

.13274 
.13276 
.13279 
.13281 
.13284 

9.12783 
.12791 
.12799 
.12807 

9.12815 

.13422 
.13425 
.13427 
.13430 
.13432 

9.13263 
.13271 
.13279 
.13287 

.13571 
.13574 
.13576 
.13579 

9.13739 
.13747 
.]3755 
.13763 

.13721 
.13724 
.13726 
.13729 

9.14213 
.14221 
.14229 
.14237 

.13872 
.13874 
.13877 
.13879 

+  15' 

9.12332 

9.13295   .13581 

9.13771 

.13731 

9.14245 

.13882 

21h9m 

glhSm 

2lh  7m 

21fi6m 

21h5m          1 

h 


Page  846] 

TABLE  45. 
Haveraines. 

s 

^ft  55-m  43°  45' 

2h  56m  44°  0' 

2h  57m  44°  15' 

2h  58m  44°  W 

2h  59m 

44°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.14245 
.14252 
.14260 
.14268 

.13883 
.13884 

.13887 
.13889 

9.14715 
.14723 
.14731 
.14739 

.14033 
.14035 
.14038 
.14041 

9.15183 
.15190 
.15198 
.15206 

.14185 
.14187 
.14190 
.14192 

9.15647 
.15655 
.15663 
.15670 

.14337 
.14340 
.14343 
.14345 

9.16109 
.16117 
.16124 
.16132 

.14491 
.14493 
.14496 
.14498 

60 
59 

58 
57 

+    r 

5 
6 

7 

9.14276 
.14284 
.14292 
.14300 

.13892 
.13894 
.13897 
.13899 

9.14746 
.14754 
.14762 
.14770 

.14043 
.14046 
.14048 
.14051 

9.15214 
.15221 
.15229 
.15237 

.14195 
.14198 
.14200 
.14203 

9.15678 
.15686 
.15694 
.15701 

.14348 
.14350 
.14353 
.14355 

9.16140 
.16147 
.16155 
.16163 

.14501 
.14504 
.14506 
.14509 

56 
55 

54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 

+   2^ 

9 

10 

11 

9.14307 
.14315 
.14323 
.14331 

.13903 
.13904 
.13907 
.13909 

9.14778 
.14785 
.14793 
.14801 

.14053 
.14056 
.14058 
.14061 

9.15245 
.15253 
.15260 
.15268 

.14305 
.14208 
.14210 
.14213 

9.15709 

.15717 
.15724 
.15732 

.14358 
.14360 
.14363 
.14366 
.14368 
.14371 
.14373 
.14376 

9.16170 
.16178 
.16186 
.16193 

.14511 
.14514 
.14516 
.14519 

+   3^ 

13 
14 
15 

9.14339 
.14347 
.14355 
.14362 

.13913 
.13914 
.13917 
.13930 

9.14809 
.14817 
.14824 
.14832 

.14063 
.14066 
.14068 
.14071 

9.15276 
.15284 
.15291 
.15299 

.14215 
.14218 
.14220 
.14223 
.14236 
.14328 
.14331 
.14333 

9.15740 
.15748 
.15755 
.15763 

9.16201 
.16209 
.16216 
.16224 

.14521 
.14524 
.14537 
.14539 

+   4' 
17 
18 
19 

9.14370 
.14378 
.14386 
.14394 

.13933 
.13935 
.13937 
.13930 

9.14840 
.14848 
.14856 
.14863 

.14073 
.14076 
.14079 
.14081 

9.15307 
.15315 
.15322 
.15330 

9.15771 
.15778 
.15786 
.15794 

.14378 
.14381 
.14383 
.14386 

9.16232 
.16239 
.16247 
.16255 

.14533 
.14534 
.14537 
.14539 

+  5^ 

22 
23 

9.14402 
.14410 
.14417 
.14425 

.13933 
.13935 
.13937 
.13940 

9.14871 
.14879 
.14887 
.14895 

.14084 
.14086 
.14089 
.14091 

9.15338 
.15346 
.15353 
.15361 

.14336 
.14238 
.14241 
.14243 

9.15802 
.15809 
.15817 
.15825 

.14388 
.14391 
.14394 
.14396 

9.16262 
.16270 
.16278 
.16285 

.14543 
.14545 
.14547 
.14550 

+   6^ 

26 
27 

9.14433 
.14441 
.14449 
.14457 

.13943 
.13945 
.13947 
.13950 

9.14902 
.14910 
.14918 
.14926 

.14094 
.14096 
.14099 
.14101 

9.15369 
.15377 
.15384 
.15392 

.14246 
.14248 
.14251 
.14253 

9.15832 
.15840 
.15848 
.15855 

.14399 
.14401 
.14404 
.14406 

9.16293 
.16301 
.16308 
.16316 

.14553 
.14555 
.14557 
.14560 

36 
35 
34 
33 

+    r 

30 
31 

9.14465 
.14472 
.14480 
.14488 

.13953 
.13955 
.13957 
.13960 

9.14934 
.14941 
.14949 
.14957 

.14104 
.14106 
.14109 
.14111 

9.15400 

.15408 
.15415 
.15423 

.14256 
.14259 
.14261 
.14264 

9.15863 
.15871 
.15879 
.15886 

.14409 
.14411 
.14414 
.14417 

9.16324 
.16331 
.16339 
.16346 

.14563 
.14565 
.14568 
.14570 

32 
31 
30 
29 

+   8^ 

34 
35 

9.14496 
.14504 
.14512 
.14519 

.13963 
.13965 
.13967 
.13970 

9.14965 
.14973 
.14980 
.14988 

.14114 
.14116 
.14119 
.14133 

9.15431 
.15439 
.15446 
.15454 

.14266 
.14269 
.14271 
.14274 

9.15894 
.15902 
.15909 
.15917 

.14419 
.14433 
.14434 
.14427 

9.16354 
.16362 
.16369 
.16377 

.14573 
.14575 
.14578 
.14580 

28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 

+   9^ 

38 
39 

9.14527 
.14535 
.14543 
.14551 

.13973 
.13975 
.13977 
.13980 

9.14996 
.15004 
.15012 
.15019 

.14134 
.14137 
.14139 
.14133 

9.15462 
.15470 
.15477 
.15485 

.14276 
.14279 
.14281 
.14284 

9.15925 
.15932 
.15940 
.15948 

.14429 
.14432 
.14434 
.14437 

9.16385 
.16392 
.16400 
.16408 

.14583 
.14586 

.14588 
.14591 

+  ir 

42 
43 

9.14559 
.14566 
.14574 
.14582 

.13983 
.13985 

.13988 
.13990 

9.15027 
.15035 
.15043 
.15050 

.14134 
.14137 
.14139 
.14143 

9.15493 
.15500 
.15508 
.15516 

.14287 
.14289 
.14292 
.14294 

9.15955 
.15963 
.15971 
.15978 

.14440 
.14442 
.14445 
.14447 

9.16415 
.16423 
.16431 
.16438 

.14593 
.14596 
.14598 
.14601 

+  11^ 

46 
47 

9.14590 
.14598 
.14606 
.14613 

.13993 
.13995 
.13998 
.14000 

9.15058 
.15066 
.15074 
.15082 

.14144 
.14147 
.14149 
.14153 
.14154 
.14157 
.14160 
.14163 

9.15524 
.15531 
.15539 
.15547 

.14297 
.14299 
.14303 
.14304 

9.15986 
.15994 
.16002 
.16009 

.14450 
.14452 
.14455 
.14457 

9.16446 
.16453 
.16461 
.16469 

.14604 
.14606 
.14609 
.14611 

+  12^ 

49 
50 
51 

9.14621 
.14629 
.14637 
.14645 

.14003 
.14005 
.14008 
.14010 

9.15089 
.15097 
.15105 
.15113 

9.15555 
.15562 
.15570 

.15578 

.14307 
.14309 
.14313 
.14315 

9.16017 
.16025 
.16032 
.16040 

.14460 
.14463 
.14465 
.14468 

9.16476 
.16484 
.16492 
.16499 

.14614 
.14616 
.14619 
.14633 

12 

11 

10 

9 

+  13^ 

5^ 
54 
55 

9.14653 
.14660 
.14668 
.14676 

.14013 
.14015 
.14018 
.14030 

9.15120 
.15128 
.15136 
.15144 

.14165 
.14167 
.14170 
.14172 

9.15585 
.15593 
.15601 
.15609 

.14317 
.14330 
.14333 
.14335 

9.16048 
.16055 
.16063 
.16071 

.14470 
.14473 
.14475 
.14478 

9.16507 
.16515 
.16522 
.16530 

.14634 
.14637 
.14639 
.14633 

8 
7 
6 
5 

+  14' 

57 
58 
59 

9.14684 
.14692 
.14699 
.14707 

.14033 
.14035 
.14038 
.14030 

9.15152 
.15159 
.15167 
.15175 

.14175 
.14177 
.14180 
.14183 

9.15616 
.15624 
.15632 
.15640 

.14327 
.14330 
.14332 
.14335 

9.16078 
.16086 
.16094 
.16101 

.14480 
.14483 
.14486 
.14488 

9.16537 
.16545 
.16553 
.16560 

.14634 
.14637 
.14639 
.14643 

4 
3 

2 
1 
0 

+  15' 

9.14715 

.14033 

9.15183 

.14185 

9.15647 

.14337 

9.16109 

.14491 

9.16568 

.14645 

21^ 

^m 

21hsm 

21^ 

2m 

21^ 

im 

21^ 

Om 

TABLE  45. 

Haveraines. 

[Page  847 

s 

3h  am  45°  0^ 

Sh  im  45°  15' 

Sh  2m  45°  3^ 

Sh  .5"»  45°  W 

Shpn 

46°  0' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.16568 
.16576 
.16583 
.16591 

.11645 
.14647 
.14650 
.14653 

9.17024 
.17032 
.17039 
.17047 

.14799 
.14803 
.14804 
.14807 

9.17477 
.17485 
.17492 
.17500 

.14955 
.14957 
.14960 
.14963 

9.17928 
.17935 
.17943 
.17950 

.15110 
.15113 
.15116 
.15118 

9.18376 
.18383 
.18390 
.18398 

.15367 
.15370 
.15272 
.15275 

60 
59 
58 
57 

+  V 

5 
6 

7 

9.16598 
.16606 
.16614 
.16621 

.14655 
.14658 
.14660 
.14663 

9.17054 
.17062 
.17069 
.17077 

.14810 
.14813 
.14815 
.14817 

9.17507 
.17515 
.17522 
.17530 

.14965 
.14968 
.14970 
.14973 

9.17958 
.17965 
.17973 
.17980 

.15131 
.15133 
.15136 
.16129 

9.18405 
.18413 
.18420 
.18428 

.15278 
.15380 
.15383 
.15285 

56 
55 
54 
63 

+      r 

9 

10 

11 

9.16629 
.16637 
.16644 
.16652 

.14665 
.14668 
.14670 
.14673 

9.17085 
.17092 
.17100 
.17107 

.14830 
.14833 
.14835 
.14838 

9.17538 
.17545 
.17553 
.17560 

.14975 
.14978 
.14981 
.14983 

9.17988 
.17995 
.18003 
.18010 

.15131 
.15134 
.15137 
.15139 

9.18435 
.18443 
.18450 
.18457 

.15288 
.15291 
.15293 
.15296 

52 
51 
50 
49 

+      y 

13 
14 
15 

9.16659 
.16667 
.16675 
.16682 

.14676 
.14678 
.14681 
.14683 

9.17115 
.17122 
.17130 
.17138 

.14830 
.14833 
.14835 
.14838 

9.17568 
.17575 
.17583 
.17590 

.14986 
.14988 
.14991 
.14993 

9.18018 
.18025 
.18033 
.18040 

.15142 
.15144 
.15147 
.15150 

9.18465 
.18472 
.18480 
.18487 

.16298 
.15301 
.16304 
.16306 

48 
47. 
46 
45 

+     i' 
17 
18 
19 

9.16690 
.16697 
.16705 
.16713 

.14686 
.14688 
.14691 
.14693 

9.17145 
.17153 
.17160 
.17168 

.14841 
.14843 
.14846 

.14848 

9.17598 
.17605 
.17613 
.17620 

.14996 
.14999 
.15001 
.15004 

9.18048 
.18055 
.18062 
.18070 

.16153 
.15156 
.16157 
.15160 

9.18495 
.18502 
.18509 
.18517 

.16309 
.16312 
.16314 
.16316 

U 
43 
42 
41 

+     5' 

21 

22 
23 

9.16720 
.16728 
.16735 
.16743 

.14696 
.14699 
.14701 
.14704 

9.17175 
.17183 
.17191 
.17198 

.14851 
.14853 
.14856 
.14859 

9.17628 
.17635 
.17643 
.17650 

.15006 
.15009 
.15013 
.15014 

9.18077 
.18085 
.18092 
.18100 

.16163 
.15165 
.15168 
.15170 

9.18524 
.18532 
.18539 
.18547 

.15319 
.16322 
.16325 
.16327 

40 
39 
38 
37 

+      6' 

25 

26 

27 

9.16751 
.16758 
.16766 
.16774 

.14706 
.14709 
.14713 
.14714 

9.17206 
.17213 
.17221 
.17228 

.14861 
.14864 
.14866 
.14869 

9.17658 
.17665 
.17673 
.17680 

.15017 
.15019 
.15033 
.15035 

9.18107 
.18115 
.18122 
.18130 

.15173 
.16176 
.16178 
.16181 

9.18554 
.18561 
.18569 
.18576 

.15330 
.15333 
.16335 
.16337 

S6 
35 
34 
33 

+    r 

29 
SO 
31 

9.16781 
.16789 
.16796 
.16804 

.14717 
.14719 
.14733 
.14734 

9.17236 
.17243 
.17251 
.17259 

.14873 
.14874 
.14877 
.14879 

9.17688 
.17695 
.17703 
.17710 

.15037 
.15030 
.15032 
.15035 

9.18137 
.18145 
.18152 
.18160 

.16183 
.16186 
.16189 
.16191 

9.18584 
.18591 
.18598 
.18606 

.16340 
.16343 
.16346 
.16348 

32 
31 
SO 
29 

+      S' 
S3 
34 
35 

9.16812 
.16819 
.16827 
.16834 

.14737 
.14730 
.14733 
.14735 

9.17266 
.17274 
.17281 
.17289 

.14883 
.14885 
.14887 
.14890 

9.17718 
.17725 
.17733 
.17740 

.15038 
.15040 
.15043 
.15045 

9.18167 
.18174 
.18182 
.18189 

.16194 
.15197 
.15199 
.16202 

9.18613 
.18621 
.18628 
.18636 

.16361 
.16353 
.16356 
.16359 

28 
27 
26 
25 

+       9' 

37 
38 
39 

9.16842 
.16850 
.16857 
.16865 

.14737 
.14740 
.14743 
.14745 

9.17296 
.17304 
.17311 
.17319 

.14893 
.14895 
.14898 
.14900 

9.17748 
.17755 
.17763 
.17770 

.15048 
.15051 
.15053 
.15056 

9.18197 
.18204 
.18212 
.18219 

.15204 
.15207 
.16210 
.16212 

9.18643 
.18650 
.18658 
.18665 

.15361 
.16364 
.16367 
.16369 

24 
23 
22 
21 

+    W 

41 
42 
43 

9.16872 
.16880 
.16887 
.16895 

.14748 
.14750 
.14753 
.14755 

9.17327 
.17334 
.17342 
.17349 

.14903 
.14905 
.14908 
.14910 

9.17778 
.17785 
.17793 
.17800 

.15058 
.15061 
.15064 
.15066 

9.18227 
.18234 
.18242 
.18249 

.16216 
.15317 
.15330 
.15322 

9.18673 
.18680 
.18687 
.18695 

.16372 
.15374 
.15377 
.15379 

20 
19 
18 
17 

+    11' 

45 
46 

47 

9.16903 
.16910 
.16918 
.16925 

.14758 
.14760 
.14763 
.14766 

9.17357 
.17364 
.17372 
.17379 

.14913 
.14916 
.14918 
.14931 

9.17808 
.17815 
.17823 
.17830 

.15069 
.15071 
.15074 
.15077 

9.18256 
.18264 
.18271 
.18279 

.15225 
.16228 
.15330 
.16233 

9.18702 
.18710 
.18717 
.18724 

.16382 
.16386 
.16388 
.16390 

16 
15 
14 
IS 

+  13' 

49 
50 
51 

9.16933 
.16941 
.16948 
.16956 

.14768 
.14771 
.14773 
.14776 

9.17387 
.17394 
.17402 
.17409 

.14933 
.14936 
.14939 
.14931 

9.17838 
.17845 
.17853 
.17860 

.15079 
.15083 
.15084 
.15087 

9.18286 
.18294 
.18301 
.18309 

.15236 
.15238 
.15241 
.15244 

9.18732 
.18739 
.18747 
.18754 

.15393 
.15395 
.15398 
.15401 

12 
11 
10 
9 
8 
7 
6 
5 

+  13^ 

53 
64 
55 

9.16963 
.16971 
.16979 
.16986 

.14779 
.14781 
.14784 
.14786 

9.17417 
.17425 
.17432 
.17440 

.14934 
.14936 
.14939 
.14943 

9.17868 
.17875 
.17883 
.17890 

.15090 
.15093 
.15095 
.15097 

9.18316 
.18324 
.18331 
.18338 

.15246 
.16349 
.15251 
.16254 

9.18762 
.18769 
.18776 
.18784 

.15403 
.15406 
.15409 
.15411 

+    W 

57 
58 
59 

9.16994 
.17001 
.17009 
.17016 

.14789 
.14791 
.14794 
.14797 

9.17447 
.17455 
.17462 
.17470 

.14944 
.14947 
.14949 
.14953 

9.17898 
.17905 
.17913 
.17920 

.15100 
.15103 
.15105 
.15108 

9.18346 
.18353 
.18361 
.18368 

.15257 
.15259 
.15263 
.15364 

9.18791 
.18798 
.18806 
.18813 

.15414 
.15416 
.15419 
.15423 

4 
S 

2 
1 

+  15^ 



9.17024 

.14799 

9.17477 

.14955 

9.17928 

.15110 

9.18376 

.15367 

9.18821 

.15424 

0 

20h 

59m 

20^  58^ 

20^  57m 

20h  56"» 

20h  55m 

Page  848] 

TABLE  45. 

Haversinea. 

s 

3h  5m  46°  15' 

3h  em  46°  30' 

3^  im  46°  45' 

3h  gm  470  (K 

3h  9m  47°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.18821 
.18828 
.18835 
.18843 

.15424 
.15427 
.15430 
.15432 

9.19263 
.19270 
.19278 
.19285 

.15582 
.15585 

.15588 
.15590 

9.19703 
.19710 
.19717 
.19725 

.15741 
.15743 
.15746 
.15748 

9.20140 
.20147 
.20154 
.20162 

.15900 
.15903 
.15905 
.15908 

9.20574 
.20582 
.20589 
.20596 

.16060 
.16063 
.16065 
.16068 

60 
59 
58 

51 

+    r 

5 
6 

1 

9.18850 

.18858 
.18865 
.18872 

.15435 
.15437 
.15440 
.15443 

9.19292 
.19300 
.19307 
.19315 

.15593 
.15595 
.15598 
.15601 

9.19732 
.19739 

.19747 
.19754 

.15751 
.15754 
.15757 
.15759 

9.20169 
.20176 
.20184 
.20191 

.15911 
.15913 
.15916 
.15919 

9.20603 
.20611 
.20618 
.20625 

.16071 
.16073 
.16076 
.16079 

56 

55 
54 
53 

+      2' 

9 

10 

11 

9.18880 
.18887 
.18895 
.18902 

.15445 
.15448 
.15451 
.15453 

9.19322 
.19329 
.19337 
.19344 

.15603 
.15606 
.15609 
.15611 

9.19761 
.19769 
.19776 
.19783 

.15762 
.15765 
.15767 
.15770 

9.20198 
.20205 
.20213 
.20220 

.15921 
.15924 
.15927 
.15929 
.15932 
.15935 
.15937 
.15940 

9.20632 
.20639 
.20647 
.20654 

.16081 
.16084 
.16087 
.16089 

52 
51 
50 
49 

+   3' 

.  IS 
14 
15 

9.18909 
.18917 
.18924 
.18932 

.15456 
.15458 
.15461 
.15464 

9.19351 
.19359 
.19366 
.19373 

.15614 
.15617 
.15619 
.15622 

9.19790 
.19798 
.19805 
.19812 

.15773 
.15775 
.15778 
.15781 

9.20227 
.20234 
.20242 
.20249 

9.20661 
.20668 
.20675 
.20683 

.16092 
.16095 
.16097 
.16100 

48 
41 
46 
45 

+   4' 
11 
18 
19 

9.18939 
.18946 
.18954 
.18961 

.15466 
.15469 
.15472 
.15474 

9.19381 
.19388 
.19395 
.19403 

.15625 
.15627 
.15630 
.15632 

9.19820 
.19827 
.19834 
.19842 

.15783 
.15786 
.15789 
.15791 

9.20256 
.20263 
.20271 
.20278 

.15943 
.15945 
.15948 
.15951 

9.20690 
.20697 
.20704 
.20712 

.16103 
.16105 
.16108 
.16111 

44 
43 
42 
41 

+  5' 
21 
22 
23 

9.18968 
.18976 
.18983 
.18991 

.15477 
.15479 
.15482 
.15485 

9.19410 
.19417 
.19425 
.19432 

.15635 
.15638 
.15640 
.15643 

9.19849 
.19856 
.19863 
.19871 

.15794 
.15796 
.15799 
.15802 

9.20285 
.20292 
.20300 
.20307 

.15953 
.15956 
.15959 
.15961 

9.20719 
.20726 
.20733 
.20740 

.16113 
.16116 
.16119 
.16121 

40 
39 
38 
31 

+   6' 

25 
26 
21 

9.18998 
.19005 
.19013 
.19020 

.15487 
.15490 
.15493 
.15495 

9.19439 
.19447 
.19454 
.19461 

.15646 
.15648 
.15651 
.15654 

9.19878 
.19885 
.19893 
.19900 

.15804 
.15807 
.15810 
.15812 

9.20314 
.20321 
.20329 
.20336 

.15964 
.15967 
.15969 
.15972 

9.20748 
.20755 
.20762 
.20769 

.16124 
.16127 
.16129 
.16132 

36 

35 
34 
33 

+    r 

29 
30 
31 

9.19027 
.19035 
.19042 
.19050 

.15498 
.15501 
.15503 
.15506 

9.19469 
.19476 
.19483 
.19491 

.15656 
.15659 
.15662 
.15664 

9.19907 
.19914 
.19922 
.19929 

.15815 
.15818 
.15820 
.15823 

9.20343 
.20350 
.20358 
.20365 

.15975 
.15977 
.15980 
.15983 

9.20776 
.20784 
.20791 
.20798 

.16135 
.16137 
.16140 
.16143 

32 
31 
SO 
29 

+   8' 
33 

34 
35 

9.19057 
.19064 
.19072 
.19079 

.15509 
.15511 
.15514 
.15516 

9.19498 
.19505 
.19513 
.19520 

.15667 
.15670 
.15672 
.15675 

9.19936 
.19944 
.19951 
.19958 

.15826 

.15828 
.15831 
.15834 

9.20372 
.20379 
.20386 
.20394 

.15985 

.15988 
.15991 
.15993 

9.20805 
.20812 
.20820 
.20827 

.16146 
.16148 
.16151 
.16154 

28 

21 
26 

25 

+   9' 

31 
38 
39 

9.19086 
.19094 
.19101 
.19109 

.15519 
.15522 
.15524 
.15527 

9.19527 
.19535 
.19542 
.19549 

.15677 
.15680 
.15683 
.15685 

9.19965 
.19973 
.19980 
.19987 

.15836 
.15839 
.15842 
.15844 

9.20401 
.20408 
.20415 
.20423 

.15996 
.15999 
.16001 
.16004 

9.20834 
.20841 
.20848 
.20856 

.16156 
.16159 
.16162 
.16164 

24 
23 

22 
21 

+  10' 

41 
42 
43 

9.19116 
.19123 
.19131 
.19138 

.15530 
.15532 
.15535 
.15537 

9.19557 
.19564 
.19571 
.19579 

.15688 
.15691 
.15693 
.15696 

9.19995 
.20002 
.20009 
.20016 

.15847 
.15850 
.15852 
.15855 

9.20430 
.20437 
.20444 
.20452 

.16007 
.16009 
.16012 
.16015 

9.20863 
.20870 
.20877 
.20884 

.16167 
.16170 
.16172 
.16175 

20 
19 
18 
11 

+    11' 

45 
46 
41 

9.19145 
.19153 
.19160 
.19167 

.15540 
.15543 
.15545 
.15548 

9.19586 
.19593 
.19600 
.19608 

.15699 
.15701 
.15704 
.15706 

9.20024 
.20031 
.20038 
.20045 

.15858 
.15860 
.15863 
.15866 

9.20459 
.20466 
.20473 
.20481 

.16017 
.16020 
.16023 
.16025 

9.20891 
.20899 
.20906 
.20913 

.16178 
.16180 
.16183 
.16186 

16 
15 
14 
IS 
12 
11 
10 
9 

+  12' 

49 
50 
51 

9.19175 
.19182 
.19190 
.19197 

.15551 
.15553 
.15556 
.15559 

9.19615 
.19622 
.19630 
.19637 

.15709 
.15712 
.15714 
.15717 

9.20053 
.20060 
.20067 
.20075 

.15868 
.15871 
.15874 
.15876 

9.20488 
.20495 
.20502 
.20509 

.16028 
.16031 
.16033 
.16036 

9.20920 
.20927 
.20935 
.20942 

.16188 
.16191 
.16194 
.16196 

+    13' 

53 
54 
55 

9.19204 
.19212 
.19219 
.19226 

.15561 
.15564 
.15566 
.15569 

9.19644 
.19652 
.19659 
.19666 

.15720 
.15722 
.15725 
.15728 

9.20082 
.20089 
.20096 
.20104 

.15879 
.15881 

.15884 
.15887 

9.20517 
.20524 
.20531 
.20538 

.16039 
.16041 
.16044 
.16047 

9.20949 
.20956 
.20963 
.20971 

.16199 
.16202 
.16204 
.16207 

8 
1 
6 
5 

+  14' 

51 
58 
59 

9.19234 
.19241 
.19248 
.19256 

9.19263 

.15572 
.15574 
.15577 
.15580 
.15582 

9.19674 
.19681 
.19688 
.19696 

.15730 
.15733 
.15736 
.15738 

9.20111 
.20118 
.20125 
.20133 

.15889 
.15892 
.15895 
.15898 

9.20546 
.20553 
.20560 
.20567 

.16049 
.16052 
.16055 
.16057 

9.20978 
.20985 
.20992 
.20999 

.16210 
.16212 
.16215 
.16218 

4 
3 

2 
1 

+    15' 

9.19703 

.15741 

9.20140 

.15900 

9.20574 

.16060 

9.21006 

.16220 

0 

20h 

54m 

20h  53m 

20^  52m 

20h  5m 

20^50m 

Page  860]                  TABLE  45. 

Haversines. 

s 

Sh  urn  48°  45' 

S\  16^  49°  0' 

Sh  J7m  49°  15/ 

3h  igm  49°  30^ 

Sh  19m  49°  45/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.23128 
.23135 
.23142 
.23149 

.17033 
.17035 
.17038 
.17041 

9.23545 
.23552 
.23559 
.23566 

.17197 
.17200 
.17203 
.17205 

9.23960 
.23967 
.23974 
.23981 

.17362 
.17365 
.17368 
.17370 

9.24372 
.24379 
.24386 
.24393 

.17528 
.17530 
.17533 
.17536 

9.24782 
.24789 
.24796 
.24803 

.17694 
.17697 
.17699 
.17702 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
4S 
47 
46 
45 

44 
43 
42 
41 

+    r 

5 
6 
7 

9.23156 
.23163 
.23170 
.23177 

.17044 
.17046 
.17049 
.17053 

9.23573 
.23580 
.23587 
.23594 

.17208 
.17211 
.17214 
.17216 

9.23988 
.23994 
.24001 
.24008 

.17373 
.17376 
.17379 
.17381 

9.24400 
.24406 
.24413 
.24420 

.17539 
.17541 
.17644 
.17547 

9.24809 
.24816 
.24823 
.24830 

.17706 
.17708 
.17710 
.17713 

+      V 

9 

10 

11 

9.23184 
.23191 
.23198 
.23205 

.17055 
.17057 
.17060 
.17063 

9.23601 
.23608 
.23615 
.23622 

.17219 
.17222 
.17225 
.17227 

9.24015 
.24022 
.24029 
.24036 

.17384 
.17387 
.17390 
.17392 

9.24427 
.24434 
.24441 
.24448 

.17550 
.17562 
.17556 
.17658 

9.24837 
.24843 
.24850 
.24857 

.17716 
.17719 
.17722 
.17724 

+      3' 

13 

14 
15 

9.23212 
.23219 
.23226 
.23233 

.17066 
.17068 
.17071 
.17074 

9.23629 
.23635 
.23642 
.23649 

.17230 
.17233 
.17235 
.17238 

9.24043 
.24050 
.24056 
.24063 

.17395 
.17398 
.17401 
.17403 

9.24454 
.24461 
.24468 
.24475 

.17561 
.17663 
.17566 
.17569 

9.24864 
.24871 
.24877 
.24884 

.17727 
.17730 
.17733 
.17736 

+      i' 
17 
18 
19 

9.23240 
.23247 
.23254 
.23261 

.17076 
.17079 
.17082 
.17085 

9.23656 
.23663 
.23670 
.23677 

.17241 
.17244 
.17246 
.17249 

9.24070 
.24077 
.24084 
.24091 

.17406 
.17409 
.17412 
.17414 

9.24482 
.24489 
.24495 
.24502 

.17672 
.17675 
.17577 
.17680 

9.24891 
.24898 
.24905 
.24911 

.17738 
.17741 
.17744 
.17746 

+  h' 

21 
22 
23 

9.23268 
.23275 
.23282 
.23289 

.17087 
.17090 
.17093 
.17096 

9.23684 
.23691 
.23698 
.23705 

.17252 
.17255 
.17257 
.17260 

9.24098 
.24105 
.24111 
.24118 

.17417 
.17420 
.17423 
.17425 

9.24509 
.24516 
.24523 
.24530 

.17583 
.17586 

.17588 
.17591 

9.24918 
.24925 
.24932 
.24939 

.17749 
.17752 
.17756 
.17758 

40 
39 
38 
37 

+   6' 

25 
26 

27 

9.23295 
.23302 
.23309 
.23316 

.17098 
.17101 
.17104 
.17107 

9.23712 
.23718 
.23725 
.23732 

.17263 
.17266 
.17268 
.17271 

9.24125 
.24132 
.24139 
.24146 

.17428 
.17431 
.17434 
.17436 

9.24536 
.24543 
.24550 
.24557 

.17594 
.17697 
.17600 
.17602 

9.24945 
.24952 
.24959 
.24966 

.17760 
.17763 
.17766 
.17769 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.23323 
.23330 
.23337 
.23344 

.17109 
.17112 
.17115 
.17117 

9.23739 
.23746 
.23753 
.23760 

.17274 
.17277 
.17279 
.17282 

9.24153 
.24160 
.24166 
.24173 

.17439 
.17442 
.17445 
.17447 

9.24564 
.24571 
.24577 
.24584 

.17606 
.17608 
.17611 
.17613 

9.24973 
.24979 
.24986 
.24993 

.17772 
.17774 
.17777 
.17780 

32 
31 
30 
29 

+   8' 
33 
34 
35 

9.23351 
.23358 
.23365 
.23372 

.17120 
.17123 
.17126 
.17128 

9.23767 
.23774 
.23781 
.23788 

.17285 

.17288 
.17290 
.17293 

9.24180 
.24187 
.24194 
.24201 

.17450 
.17453 
.17456 
.17458 

9.24591 
.24598 
.24605 
.24612 

.17616 
.17619 
.17622 
.17624 

9.25000 
.25007 
.25013 
.25020 

.17783 
.17785 

.17788 
.17791 

28 
27 
26 
25 

24 
23 
22 
21 

+   9' 

37 
38 
39 

9.23379 
.23386 
.23393 
.23400 

.17131 
.17134 
.17137 
.17139 

9.23794 
.23801 
.23808 
.23815 

.17296 
.17299 
.17301 
.17304 

9.24208 
.24215 
.24221 
.24228 

.17461 
.17464 
.17467 
.17470 

9.24618 
.24625 
.24632 
.24639 

.17627 
.17630 
.17633 
.17636 

9.25027 
.25034 
.25040 
.25047 

.17794 
.17797 
.17799 
.17802 

+  10' 

41 
42 
43 

9.23407 
.23414 
.23421 
.23427 

.17142 
.17145 
.17148 
.17150 

9.23822 
.23829 
.23836 
.23843 

.17307 
.17310 
.17313 
.17316 

9.24235 
.24242 
.24249 
.24256 

.17472 
.17475 
.17478 
.17481 

9.24646 
.24653 
.24659 
.24666 

.17638 
.17641 
.17644 
.17647 

9.25054 
.25061 
.25068 
.25074 

.17805 
.17808 
.17811 
.17813 

20 
19 
18 
17 

+  ir 

45 
46 
47 

9.23434 
.23441 
.23448 
.23455 

.17153 
.17156 
.17159 
.17161 

9.23850 
.23857 
.23863 
.23870 

.17318 
.17321 
.17323 
.17326 

9.24263 
.24269 
.24276 
.24283 

.17483 
.17486 
.17489 
.17492 

9.24673 
.24680 

.24687 
.24694 

.17649 
.17662 
.17656 
.17658 

9.25081 
.25088 
.25095 
.25102 

.17816 
.17819 
.17822 
.17824 

16 
15 
14 
13 

+  13' 

49 
50 
51 

9.23462 
.23469 
.23476 
.23483 

.17164 
.17167 
.17170 
.17172 

9.23877 
.23884 
.23891 
.23898 

.17329 
.17332 
.17335 
.17337 

9.24290 
.24297 
.24304 
.24311 

.17494 
.17497 
.17500 
.17503 

9.24700 
.24707 
.24714 
.24721 

.17661 
.17663 
.17666 
.17669 

9.25108 
.25115 
.25122 
.25129 

.17827 
.17830 
.17833 
.17836 

12 
11 
10 
9 
8 
7 
6 
5 

4 
3 
2 
1 
0 

+  13' 

53 
54 
55 

9.23490 
.23497 
.23504 
.23511 

.17175 
.17178 
.17181 
.17183 

9.23905 
.23912 
.23919 
.23926 

.17340 
.17343 
.17346 
.17348 

9.24317 
.24324 
.24331 
.24338 

.17505 
.17508 
.17611 
.17614 

9.24728 
.24734 
.24741 
.24748 

.17672 
.17674 
.17677 
.17680 

9.25135 
.25142 
.25149 
.25156 

.17838 
.17841 
.17844 
.17847 

+  14' 

57 
58 
59 

9.23518 
.23525 
.23532 
.23538 

.17186 
.17189 
.17192 
.17194 

9.23932 
.23939 
.23946 
.23953 

.17351 
.17354 
.17367 
.17359 

9.24345 
.24352 
.24359 
.24365 

.17517 
.17519 
.17522 
.17626 

9.24755 
.24762 
.24768 
.24775 

.17683 
.17686 

.17688 
.17691 

9.25163 
.25169 
.25176 
.25183 

.17849 
.17862 
.17866 

.17868 

+  16' 

9.23545 

.17197 

9.23960 

.17362 

9.24372 

.17628 

9.24782 

.17694 

9.25190 

.17861 

20^44'^ 

20h43m 

20h  42m         1 

20h  41m          1 

20^  40m          1 

TABLE  45.                  [Page  851 

Haversines. 

s 

5A  :?0n»  50°  (K 

3^  21m  50°  15' 

Sh  22m  50°  30' 

3^  23m  60°  45' 

3h  24m  51°  (K 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.lXat.  Hav. 

Log.  Hav 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav 

Nat.  Hav. 

s 

0 

1 
2 
3 

9.25190 
.25196 
.25203 
.25210 

.17861 
.17863 
.17866 
.17869 

9.25595 
.25602 
.25608 
.25615 

.18028 
.18031 
.18034 
.18036 

9.25998 
.26005 
.26011 
.26018 

.18196 
.18199 
.18202 
.18205 

9.26398 
.26405 
.26412 
.26418 

.18365 
.18368 
.18370 
.18373 

9.26797 
.26804 
.26810 
.26817 

.18534 
.18537 
.18540 
.18542 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.25217 
.25224 
.25230 
.25237 

.17872 
.17875 

.17877 
.17880 

9.25622 
.25629 
.25635 
.25642 

.18039 
.18042 
.18045 
.18048 

9.26025 
.26031 
.26038 
.26045 

.18207 
.18210 
.18213 
.18216 
.18219 
.18221 
.18224 
.18227 
.18230 
.18233 
.18235 
.18238 

9.26425 
.26432 
.26438 
.26445 

.18376 
.18379 
.18382 
.18384 

9.26823 
.26830 
.26837 
.26843 

.18545 

.18548 
.18551 
.18554 

56 
55 
54 
53 

+      -i' 

9 

10 

11 

9.25244 
.25251 
.25257 
.25264 

.17883 
.17886 
.17888 
.17891 

9.25649 
.25655 
.25662 
.25669 

.18050 
.18053 
.18056 
.18059 

9.26051 
.26058 
.26065 
.26071 

9.26078 
.26085 
.26091 
.26098 

9.26452 
.26458 
.26465 
.26472 

.18387 
.18390 
.18393 
.18396 

9.26850 
.26856 
.26863 
.26870 

9.26876 
.26883 
.26890 
.26896 

.18557 
.18559 
.18562 
.18565 
.18568 
.18571 
.18574 
.18576 

52 
51 
50 
49 
48 
47 
46 
45 

+   3' 

13 
14 
15 

9.25271 
.25278 
.25284 
.25291 

.17894 
.17897 
.17900 
.17902 

9.25676 
.25682 
.25689 
.25696 

.18062 
.18064 
.18067 
.18070 

9.26478 
.26485 
.26492 
.26498 

.18399 
.18401 
.18404 
.18407 

+   4' 
17 
18 
19 

9.25298 
.25305 
.25311 
.25318 

.17905 
.17908 
.17911 
.17914 

9.25703 
.25709 
.25716 
.25723 

.18073 
.18076 
.18078 
.18081 

9.26105 
.26112 
.26118 
.26125 

.18241 
.18244 
.18247 
.18249 

9.26505 
.26512 
.26518 
.26525 

.18410 
.18413 
.18415 
.18418 

9.26903 
.26909 
.26916 
.26923 

.18579 

.18582 
.18585 
.18588 

44 
43 

42 
41 

+      6' 

21 

22 
23 

9.25325 
.25332 
.25339 
.25345 

.17916 
.17919 
.17922 
.17925 

9.25729 
.25736 
.25743 
.25750 

9.25756^ 
.25763 
.25770 
.25776 

.18084 
.18087 
.18090 
.18092 
.18095 
.18098 
.18101 
.18104 

9.26132 
.26138 
.26145 
.26152 

9.26158 
.26165 
.26172 
.26178 

.18252 
.18255 

.18258 
.18261 
.18263 
.18266 
.18269 
.18272 

9.26532 
.26538 
.26545 
.26551 

9.26558 
.26565 
.26571 
.26578 

.18421 
.18424 
.18427 
.18430 
.18432 
.18435 
.18438 
.18441 

9.26929 
.26936 
.26942 
.26949 

.18591 
.18593 
.18596 
.18599 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.25352 
.25359 
.25366 
.25372 

.17928 
.17930 
.17933 
.17936 

9.26956 
.26962 
.26969 
.26975 

.18602 
.18605 
.18608 
.18610 

36 
35 
34 
33 
32 
31 
30 
29 

+    r 

29 
30 
31 

9.25379 
.25386 
.25393 
.25399 

.17939 
.17941 
.17944 
.17947 

9.25783 
.25790 
.25797 
.25803 

.18106 
.18109 
.18112 
.18115 

9.26185 
.26192 
.26198 
.26205 

.18275 
.18277 

.18280 
.18283 

9.26585 
.26591 
.26598 
.26605 

.18444 
.18446 
.18449 
.18452 

9.26982 
.26989 
.26995 
.27002 

.18613 
.18616 
.18619 
.18622 

+     S' 
33 
34 
35 

9.25406 
.25413 
.25420 
.25426 

.17950 
.17953 
.17955 
.17958 

9.25810 
.25817 
.25823 
.25830 

.18118 
.18120 
.18123 
.18126 

9.26212 
.26218 
.26225 
.26232 

.18286 
.18289 
.18292 
.18294 

9.26611 
.26618 
.26625 
.26631 

9.26638 
.26644 
.26651 
.26658 

.18455 
.18458 
.18461 
.18463 
.18466 
.18469 
.18472 
.18475 

9.27008 
.27015 
.27022 
.27028 

.18624 
.18627 
.18630 
.18633 

28 
27 
26 
25 

+      JK 

37 
38 
39 

9.25433 
.25440 
.25447 
.25453 

.17961 
.17964 
.17967 
.17969 

9.25837 
.25844 
.25850 
.25857 

.18129 
.1S132 
.18134 
.18137 

9.26238 
.26245 
.26252 
.26259 

.18297 
.18300 
.18303 
.18306 

9.27035 
.27041 
.27048 
.27055 

.18636 
.18639 
.18641 
.18644 

24 
23 
22 
21 
20 
19 
18 

n 

+    W 

41 

42 
43 

9.25460 
.25467 
.25474 
.25480 

.17972 
.17975 
.17978 
.17981 

9.25864 
.25870 
.25877 
.25884 

.18140 
.18143 
.18146 
.18148 

9.26265 
.26272 
.26279 
.26285 

.18308 
.18311 
.18314 
.18317 

9.26664 
.26671 
.26678 
.26684 

.18478 
.18480 
.18483 
.18486 

9.27061 
.27068 
.27074 
.27081 

.18647 
.18650 
.18653 
.18656 

+  11^ 

45 
46 
47 

9.25487 
.25494 
.25500 
.25507 

.17983 
.17986 
.17989 
.17992 

9.25891 
.25897 
.25904 
.25911 

.18151 
.18154 
.18157 
.18160 

9.26292 
.26299 
.26305 
.26312 

.18320 
.18323 
.18325 
.18328 

9.26691 
.26697 
.26704 
.26711 

.18489 
.18492 
.18494 
.18497 

9.27088 
.27094 
.27101 
.27107 

.18658 
.18661 
.18664 
.18667 

16 

15 

14 

13 

12 

It 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 

+  12' 

49 
50 
51 

9.25514 
.25521 
.25528 
.25534 

.17995 
.17997 
.18000 
.18003 

9.25917 
.25924 
.25931 
.25938 

.18162 
.18165 
.18168 
.18171 

9.26319 
.26325 
.26332 
.26339 

.18331 
.18334 
.18337 
.18339 

9.26717 
.26724 
.26731 
.26737 

.18500 
.18503 
.18506 
.18509 

9.27114 
.27121 
.27127 
.27134 

.18670 
.18673 
.18675 
.18678 

+  13' 

53 
54 
55 

9.25541 
.25548 
.25544 
.25561 

.18006 
.18008 
.18011 
.18014 

9.25944 
.25951 
.25958 
.25964 

.18174 
.18176 
.18179 
.18182 

9.26345 
.26352 
.26359 
.26365 

.18342 
.18345 
.18348 
.18351 

9.26744 
.26751 
.26757 
.26764 

.18511 
.18514 
.18517 
.18520 

9.27140 
.27147 
.27154 
.27160 

.18681 
.18684 
.18687 
.18690 

+  14' 

57 
58 
59 

9.25568 
.25575 
.25581 
.25588 

.18017 
.18020 
.18022 
.18025 

9.25971 
.25978 
.25984 
.25991 

.18185 
.18188 
.18190 
.18193 

9.26372 
.26378 
.26385 
.26392 

.18353 
.18356 
.18359 
.18362 

9.26770 
.26777 
.26784 
.26790 

.18523 
.18526 
.18528 
.18531 

9.27167 
.27173 
.27180 
.27186 

.18692 
.18695 
.18698 
.18701 

+    15' 

9.22595 

.18028 

9.25998 

.18196 

9.26398 

.18365 

9.26797 

.18534 

9.27193 

.18704 

0 

20^  39m 

20h  38m 

20^  S7m          J    20^  36m          1 

20^  35m         1 

Page  862] 

TABLE  45. 

Haversines. 

s 

3h  25m  51°  15' 

3h  26m  51°  30' 

Sh  27m  51°  45' 

3^  28m  52°  0' 

3h  29m  52°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.27193 
.27200 
.27206 
.27213 

.18704 
.18707 
.18710 
.18712 

9.27587 
.27594 
.27600 
.27607 

.18874 
.18877 
.18880- 
.18883 

9.27979 
.27985 
.27992 
.27998 

.19045 
.19048 
.19051 
.19054 

9.28368 
.28375 
.28381 
.28388 

.19217 
.19220 
.19223 
.19226 

9.28756 
.28762 
.28769 

.28775 

.19389 
.19392 
.19395 
.19398 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.27219 
.27226 
.27233 
.27239 

.18715 

.18718 
.18721 
.18724 

9.27613 
.27620 
.27626 
.27633 

.18886 
.18888 
.18891 
.18894 

9.28005 
.28011 
.28018 
.28024 

.19057 
.19060 
.19062 
.19065 

9.28394 
.28401 
.28407 
.28414 

.19228 
.19231 
.19234 
.19237 

9.28782 
.28788 
.28794 
.28801 

.19401 
.19404 
.19406 
.19409 

56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+      2^ 

9 

10 

11 

9.27246 
.27252 
.27259 
.27265 

.18727 
.18729 
.18732 
.18735 

9.27639 
.27646 
.27652 
.27659 

.18897 
.18900 
.18903 
.18906 

9.28031 
.28037 
.28044 
.28050 

.19068 
.19071 
.19074 
.19077 

9.28420 
.28427 
.28433 
.28440 

.19240 
.19243 
.19246 
.19248 

9.28807 
.28814 
.28820 

.28827 

.19412 
.19415 
.19418 
.19421 

+      3' 

13 
14 
15 

9.27272 
.27279 

.27285 
.27292 

.18738 
.18741 
.18744 
.18746 

9.27666 
.27672 
-.27679 
.27685 

.18908 
.18912 
.18914 
.18917 

9.28057 
.28063 
.28070 
.28076 

.19080 
.19082 
.19085 
.19088 

9.28446 
.28453 
.28459 
.28465 

.19251 
.19254 
.19257 
.19260 

9.28833 
.28840 
.28846 
.28852 

.19424 
.19427 
.19429 
.19432 

+      i' 
17 
18 
19 

9.27298 
.27305 
.27311 
.27318 

.18749 
.18752 
.18755 

.18758 

9.27692 
.27698 
.27705 
.27711 

.18920 
.18923 
.18926 
.18928 

9.28083 
.28089 
.28096 
.28102 

.19091 
.19094 
.19097 
.19100 

9.28472 
.28478 
.28485 
.28491 

.19263 
.19266 
.19269 
.19271 

9.28859 
.28865 
.28872 
.28878 

.19435 
.19438 
.19441 
.19444 

44 
43 
42 
41 

+      5^ 
21 
22 
23 

9.27325 
.27331 
.27338 
.27344 

.18761 
.18763 
.18766 
.18769 

9.27718 
.27724 
.27731 
.27737 

.18931 
.18934 
.18937 
.18940 

9.28109 
.28115 
.28122 
.28128 

.19102 
.19105 
.19108 
.19111 

9.28498 
.28504 
.28511 
.28517 

.19274 
.19277 
.19280 
.19283 

9.28885 
.28891 
.28897 
.28904 

.19447 
.19450 
.19452 
.19455 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.27351 
.27357 
.27364 
.27371 

.18772 
.18775 

.18778 
.18780 

9.27744 
.27751 

.27757 
.27764 

.18943 
.18945 
.18948 
.18951 

9.28135 
.28141 
.28148 
.28154 

.19114 
.19117 
.19120 
.19122 

9.28524 
.28530 
.28537 
.28543 

.19286 
.19289 
.19291 
.19294 

9.28910 
.28917 
.28923 
.28930 

.19458 
.19461 
.19464 
.19467 

36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

+    r 

29 
30 
31 

9.27377 
.27384 
.27390 
.27397 

.18783 
.18786 
.18789 
.18792 

9.27770 

.27777 
.27783 
.27790 

.18954 
.18957 
.18960 
.18963 

9.28161 
.28167 
.28174 
.28180 

.19125 
.19128 
.19131 
.19134 

9.28549 
.28556 
.28562 
.28569 

.19297 
.19300 
.19303 
.19306 

9.28936 
.28942 
.28949 
.28955 

.19470 
.19473 
.19475 
.19478 

+      8' 
S3 
34 
35 

9.27403 
.27410 
.27417 
.27423 

.18795 
.18797 
.18800 
.18803 

9.27796 
.27803 
.27809 
.27816 

.18965 
.18968 
.18971 
.18974 

9.28187 
.28193 
.28200 
.28206 

.19137 
.19140 
.19142 
.19145 

9.28575 
.28582 
.28588 
.28595 

.19309 
.19311 
.19314 
.19317 

9.28962 
.28968 
.28974 
.28981 

.19481 
.19484 
.19487 
.19490 

+      9' 

37 
38 
39 

9.27430 
.27436 
.27443 
.27449 

.18806 
.18809 
.18812 
.18815 

9.27822 
.27829 
.27835 
.27842 

.18977 
.18980 
.18983 
.18985 

9.28213 
.28219 
.28226 
.28232 

.19148 
.19151 
.19154 
.19157 

9.28601 
.28608 
.28614 
.28620 

.19320 
.19323 
.19326 
.19329 

9.28987 
.28994 
.29000 
.29007 

.19493 
.19496 
.19499 
.19501 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
IS 
12 
11 
10 
9 

+  10' 

41 
42 
43 

9.27456 
.27463 
.27469 
.27476 

.18817 
.18820 
.18823 
.18826 

9.27848 
.27855 
.27861 
.27868 

.18988 
.18991 
.18994 
.18997 

9.28239 
.28245 
.28252 
.28258 

.19160 
.19163 
.19165 
.19168 

9.28627 
.28633 
.28640 
.28646 

.19332 
.19335 
.19337 
.19340 

9.29013 
.29019 
.29026 
.29032 

.19504 
.19507 
.19510 
.19513 

+  11^ 

45 
46 
47 

9.27482 
.27489 
.27495 
.27502 

.18829 
.18832 
.18834 
.18837 

9.27875 
.27881 
.27888 
.27894 

.19000 
.19002 
.19005 
.19008 

9.28265 
.28271 

.28278 
.28284 

.19171 
.19174 
.19177 
.19180 

9.28653 
.28659 
.28666 
.28672 

.19343 
.19346 
.19349 
.19352 

9.29039 
.29045 
.29051 
.29058 

.19516 
.19519 
.19522 
.19524 

+  13' 

49 
50 
51 

9.27508 
.27515 
.27522 
.27528 

.18840 
.18843 
.18846 
.18849 

9.27901 
.27907 
.27914 
.27920 

.19011 
.19014 
.19017 
.19020 

9.28291 
.28297 
.28304 
.28310 

.19183 
.19185 
.19188 
.19191 

9.28679 
.28685 
.28691 
.28698 

.19355 
.19358 
.19360 
.19363 

9.29064 
.29071 
.29078 
.29084 

.19527 
.19530 
.19533 
.19536 

+    13' 

53 

54 
55 

9.27535 
.27541 
.27548 
.27554 

.18852 
.18854 
.18857 
.18860 

9.27927 
.27933 
.27940 
.27946 

.19022 
.19025 
.19028 
.19031 

9.28317 
.28323 
.28330 
.28336 

.19194 
.19197 
.19200 
.19203 

9.28704 
.28711 
.28717 

.28724 

.19366 
.19369 
.19372 
.19375 

9.29090 
.29096 
.29103 
.29109 

.19539 
.19542 
.19545 
.19548 

8 
7 
6 
5 

4 
3 

2 
1 

+    14' 

57 
58 
59 

9.27561 
.27567 
.27574 
.27580 

.18863 
.18866 
.18869 

.18871 

9.27953 
.27959 
.27966 
.27972 

9.27979 

.19034 
.19037 
.19040 
.19042 

9.28342 
.28349 
.28355 
.28362 

.19205 
.19208 
.19211 
.19214 

9.28730 
.28737 
.28743 
.28749 

.19378 
.19381 
.19383 
.19386 

9.29116 
.29122 
.29128 
.29135 

.19550 
.19553 
.19556 
.19559 

+    16' 

9.27587 

.18874 

.19045 

9.28368 

.19217 

9.28756 

.19389 

9.29141 

.19562 

0 

20Ji 

S4m 

20h  ssm 

201^ 

32m 

20h  Sim 

20h30m 

TABLE  45.                  [Page  863 

Haversines. 

s 

3^  30m  52°  30' 

3^  31^  52°  45' 

3^  32m  53°  (K 

3h  33VI  63°  15' 

5ft  34m  53°  30' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 

■     2 

S 

9.29141 
.29148 
.29154 
.29160 

.19563 
.19565 
.19568 
.19571 

9.29524 
.29531 
.29537 
.29543 

.19735 
.19738 
.19741 
.19744 

9.29906 
.29912 
.29918 
.29925 

.19909 
.19912 
.19915 
.19918 

9.30285 
.30291 
.30207 
.30303 

.20084 
.20087 
.20090 
.20093 

9.30662 
.30668 
.30674 
.30680 

.30359 
.30363 
.30365 
.30368 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.29167 
.29173 
.29180 
.29186 

.19573 
.19576 
.19579 
.19583 

9.29550 
.29556 
.29563 
.29569 

.19747 
.19750 
.19753 
.19756 

9.29931 
.29937 
.29943 
.29950 

.19931 
.19924 
.19927 
.19930 

9.30310 
.30316 
.30322 
.30329 

.20095 
.30098 
.30101 
.20104 

9.30687 
.30693 
.30699 
.30705 

.30371 
.30273 
.30376 
.20279 

56 
55 
54 
53 
52 
51 
50 
49 

+      -i' 

9 

10 

11 

9.29192 
.29199 
.29205 
.29212 

.19585 
.19588 
.19591 
.19594 
.19597 
.19599 
.19603 
.19605 
.19608 
.19611 
.19614 
.19617 

9.29575 
.29582 
.29588 
.29594 

.19758 
.19761 
.19764 
.19767 

9.29956 
.29962 
.29969 
.29975 

.19933 
.19935 
.19938 
.19941 

9.30335 
.30341 
.30348 
.30354 

.20107 
.30110 
.20113 
.20116 

9.30712 
.30718 
.30724 
.30730 

.20383 
.30385 
.30288 
.30391 

+      3' 

13 
14 
15 

9.29218 
.29224 
.29231 
.29237 

9.29601 
.29607 
.29614 
.29620 

9.29626 
.29633 
.29639 
.29645 

.19770 
.19773 
.19776 
.19779 

9.29981 
.29988 
.29994 
.30000 

.19944 
.19947 
.19950 
.19953 

9.30360 
.30366 
.30373 
.30379 

.20119 
.20122 
.20125 
.20127 

9.30737 
.30743 
.30749 
.30755 

.30394 
.30397 
.30300 
.30303 

48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

17 
18 
19 

9.29244 
.29250 
.29256 
.29263 

.19783 
.19785 
.19787 
.19790 

9.30007 
.30013 
.30019 
.30026 

.19956 
.19959 
.19963 
.19964 

9.30385 
.30392 
.30398 
.30404 

.20130 
.20133 
.20136 
.20139 

9.30762 
.30768 
.30774 
.30780 

.20306 
.20309 
.20312 
.20314 

+     6' 
21 
22 
23 

9.29269 
.29276 
.29282 
.29288 

.19630 
.19633 
.19635 
.19638 

9.29652 
.29658 
.29664 
.29671 

.19793 
.19796 
.19799 
.19803 
.19805 
.19808 
.19811 
.19814 

9.30032 
.30038 
.30045 
.30051 

.19967 
.19970 
.19973 
.19976 

9.30410 
.30417 
.30423 
.30429 

.20142 
.20145 
.20148 
.20151 

9.30787 
.30793 
.30799 
.30805 

.20317 
.20320 
.20323 
.20326 

+   6' 

25 
26 

27 

9.29295 
.29301 
.29307 
.29314 

.19631 
.19634 
.19637 
.19640 
.19643 
.19646 
.19649 
.19651 

9.29677 
.29683 
.29690 
.29696 

9.30057 
.30064 
.30070 
.30076 

.19979 
.19982 
.19985 
.19988 

9.30436 
.30442 
.30448 
.30454 

.20154 
.20157 
.30160 
.30162 

9.30812 
.30818 
.30824 
.30830 

.20339 
.20333 
.30335 
.30338 

+    r 

29 
30 
31 

9.29320 
.29327 
.29333 
.29339 

9.29703 
.29709 
.29715 
.29722 

.19816 
.19819 
.19832 
.19825 

9.30083 
.30089 
.30095 
.30102 

.19991 
.19994 
.19996 
.19999 
.20002 
.20005 
.20008 
.20011 

9.30461 
.30467 
.30473 
.30480 

.20165 
.30168 
.20171 
.30174 

9.30837 
.30843 
.30849 
.30855 

.20341 
.20344 
.30347 
.30350 

32 
31 
SO 
29 
28 
27 
26 
25 

+   8' 
33 
34 
35 

9.29346 
.29352 
.29359 
.29365 

.19654 
.19657 
.19660 
.19663 

9.29728 
.29734 
.29741 
.29747 

.19838 
.19831 
.19834 
.19837 
.19840 
.19843 
.19845 
.19848 

9.30108 
.30114 
.30121 
.30127 

9.30133 
.30139 
.30146 
.30152 

9.30486 
.30492 
.30498 
.30505 

.30177 
.30180 
.20183 
.20186 

9.30862 
.30868 
.30874 
.30880 

.30353 
.20355 
.20358 
.20361 

+      9' 

37 
38 
39 

9.29371 
.29378 
.29384 
.29391 

.19666 
.19669 
.19672 
.19675 

9.29753 
.29760 
.29766 
.29772 

.30014 
.30017 
.30020 
.30033 

9.30511 
.30517 
.30524 
.30530 

.20189 
.20192 
.20195 
.20198 

9.30887 
.30893 
.30899 
.30905 

.20364 
.20367 
.20370 
.20373 

24 
23 
22 
21 

+  10' 

41 

42 
43 

9.29397 
.29403 
.29410 
.29416 

.19677 
.19680 
.19683 
.19686 

9.29779 
.29785 
.29791 
.29798 

.19851 
.19854 
.19857 
.19860 

9.30158 
.30165 
.30171 
.30177 

.30036 
.30038 
.30031 
.20034 

9.30536 
.30542 
.30549 
.30555 

.20200 
.20203 
.20206 
.20209 

9.30912 
.30918 
.30924 
.30930 

.20376 
.20379 
.20382 
.20385 

20 
19 
18 
17 

+  11^ 

45 
46 

47 

9.29422 
.29429 
.29435 
.29442 

.19689 
.19693 
.19695 
.19698 

9.29804 
.29810 
.29817 
.29823 

9.29829 
.29836 
.29842 
.29848 

.19863 
.19866 
.19869 
.19873 
.19874 
.19877 
.19880 
.19883 
.19886 
.19889 
.19892 
.19895 

9.30184 
.30190 
.30196 
.30203 

9.30209 
.30215 
.30222 
.30228 

9.30234' 
.30240 
.30247 
.30253 

.30037 
.30040 
.30043 
.30046 

9.30561 
.30567 
.30574 
.30580 

.20212 
.20315 
.30318 
.20221 

9.30937 
.30943 
.30949 
.30955 

.30388 
.30391 
.20393 
.30396 

16 
15 
14 
IS 
12 
11 
10 
9 

+  13' 

49 
50 
51 

9.29448 
.29454 
.29461 
.29467 

.19701 
.19703 
.19706 
.19709 

.30049 
.30053 
.30055 
.30058 

9.30586 
.30593 
.30599 
.30605 

.30334 
.30337 
.20330 
.30333 
.30335 
.30338 
.30341 
.30244 

9.30962 
.30968 
.30974 
.30980 

.20399 
.20402 
.20405 
.20408 

+  13' 

53 
54 
55 

9.29473 
.29480 
.29486 
.29493 

.19713 
.19715 
.19718 
.19731 

9.29855 
.29861 
.29867 
.29874 

.30060 
.30063 
.30066 
.30069 

9.30611 
.30618 
.30624 
.30630 

9.30987 
.30993 
.30999 
.31005 

.20411 
.20414 
.20417 
.20420 

8 
7 
6 
5 

+  U' 

57 
58 
59 

9.29499 
.29505 
.29512 
.29518 

.19734 
.19737 
.19730 
.19733 

9.29880 
.29886 
.29893 
.29899 

.19898 
.19901 
.19903 
.19906 

9.30259 
.30266 
.30272 
.30278 

.30073 
.30075 
.20078 
.30081 

9.30636 
.30643 
.30649 
.30655 

.30347 
.30350 
.30353 
.30356 

9.31012 
.31018 
.31024 
.31030 

.20423 
.20426 
.20429 
.20432 

4 
3 

2 

1 

"+  15' 

9.29524 

.19735 

9.29906 

.19909 

9.30285 

.30084 

9.30662 

.30359 

9.31036 

.20435 

0 

20^  29"^ 

20^28rn 

20^  27-m 

20^  26m 

20Ti  25^ 

Page  864]                  TABLE  45. 

Haversines. 

s 

5^  35m  53°  45' 

S^  36m  54°  0' 

Sh  37m  54°  15/ 

3^  38m  54°  30^ 

3^  39m  54°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.31036 
.31043 
.31049 
.31055 

.30435 
.30437 
.30440 
.30443 
.30446 
.30449 
.30453 
.30455 

9.31409 
.31416 
.31422 
.31428 

.30611 
.30614 
.30617 
.30630 

9.31780 
.31786 
.31793 
.31799 

.30788 
.30790 
.30793 
.30796 

9.32149 
.32155 
.32161 
.32168 

.30965 
.30968 
.30971 
.30974 

9.32516 
.32522 
.32528 
.32534 

.31143 
.31146 
.31149 
.31153 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.31061 
.31068 
.31074 
.31080 

9.31434 
.31440 
.31447 
.31453 

9.31459 
.31465 
.31471 
.31478 

.30633 
.30636 
.30639 
.30631 
.30634 
.30637 
.30640 
.30643 

9.31805 
.31811 
.31817 
.31823 

.30799 
.30803 
.30805 
.30808 

9.32174 
.32180 
.32186 
.32192 

.30977 
.30980 
.30983 
.30986 
.30989 
.30991 
.30994 
.30997 

9.32541 
.32547 
.32553 
.32559 

.31155 
.31158 
.31161 
.31164 

56 

55 
54 
53 

+   2' 

9 

10 

11 

9.31086 
.31093 
.31099 
.31105 

.30458 
.30461 
.30464 
.30467 

9.31830 
.31836 
.31842 
.31848 

.30811 
.30814 
.30817 
.30830 

9.32198 
.32204 
.32210 
.32217 

9.32565 
.32571 
.32577 
.32583 

.31167 
.31169 
.31173 
.31175 

52 
51 
50 
49 

+   3' 

IS 
14 
15 

9.31111 
.31117 
.31124 
.31130 

.30470 
.30473 
.30476 
.30479 

9.31484 
.31490 
.31496 
.31502 

.30646 
.30649 
.30653 
.30655 

9.31854 
.31860 
.31867 
.31873 

.30833 
.30836 
.30839 
.30833 

9.32223 
.32229 
.32235 
.32241 

.31000 
.31003 
.31006 
.31009 

9.32589 
.32595 
.32601 
.32608 

.31178 
.31181 
.31184 
.31187 

48 
47 
46 
45 

+  ^' 
17 
18 
19 

9.31136 
.31142 
.31149 
.31155 

.30481 
.30484 
.30487 
.30490 

9.31508 
.31515 
.31521 
.31527 

.30658 
.30661 
.30664 
.30667 

9.31879 
.31885 
.31891 
.31897 

.30835 
.30838 
.30841 
.30844 

9.32247 
.32253 
.32259 
.32266 

.31013 
.31015 
.31018 
.31031 

9.32614 
.32620 
.32626 
.32632 

9.32638 
.32644 
.32650 
.32656 

.31190 
.31193 
.31196 
.31199 

44 
43 
42 
41 

+      5' 
21 

22 
23 

9.31161 
.31167 
.31173 
.31180 

.30493 
.30496 
.30499 
.30503 

9.31533 
.31539 
.31546 
.31552 

.30670 
.30673 
.30675 
.30678 

9.31903 
.31910 
.31916 
.31922 

.30847 
.30850 
.30853 
.30855 

9.32272 
.32278 
.32284 
.32290 

.31034 
.31037 
.31030 
.31033 
.31036 
.31039 
.31043 
.31045 

.31303 
.31305 
.31308 
.31311 

40 
39 
38 
37 

+      6' 

25 
26 
27 

9.31186 
.31192 
.31198 
.31205 

.30505 
.30508 
.305^11 
.30514 

9.31558 
.31564 
.31570 
.31577 

.30681 
.30684 
.30687 
.30690 

9.31928 
.31934 
.31940 
.31947 

.30858 
.30861 
.30864 
.30867 

9.32296 
.32302 
.32308 
.32315 

9.32662 
.32668 
.32675 
.32681 

.31314 
.31317 
.31330 
.31333 

36 
35 
34 
S3 

+    r 

29 
30 
SI 

9.31211 
.31217 
.31223 
.31229 

.30517 
.30530 
.30533 
.30535 

9.31583 
.31589 
.31595 
.31601 

.30693 
.30696 
.30699 
.30703 

9.31953 
.31959 
.31965 
.31971 

.30870 
.30873 
.30876 
.30879 

9.32321 
.32327 
.32333 
.32339 

.31048 
.31051 
.31054 
.31057 

9.32687 
.32693 
.32699 
.32705 

.31336 
.31339 
.31333 
.31335 

32 
31 
30 
29 

+   8' 
SS 
34 
35 

9.31236 
.31242 
.31248 
.31254 

.30538 
.30531 
.30534 
.30537 

9.31607 
.31614 
.31620 
.31626 

.30705 
.30708 
.30711 
.30714 

9.31977 
.31983 
.31990 
.31996 

.30883 
.30885 
.30888 
.30891 

9.32345 
.32351 
.32357 
.32363 

.31060 
.31063 
.31066 
.31069 

9.32711 
.32717 
.32723 
.32729 

.31338 
.31341 
.31344 
.31347 

28 

27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 

+      9' 

37 
S8 
39 

9.31260 
.31267 
.31273 
.31279 

.30540 
.30543 
.30546 
.30549 

9.31632 
.31638 
.31644 
.31651 

.30717 
.30730 
.30733 
.30736 

9.32002 
.32008 
.32014 
.32020 

.30894 
.30897 
.30900 
.30903 

9.32370 
.32376 
.32382 
.32388 

.31073 
.31074 
.31077 
.31080 

9.32735 
.32741 
.32748 
.32754 

.31350 
.31353 
.31356 
.31359 

+  W 

41 
42 
43 

9.31285 
.31291 
.31298 
.31304 

.30553 
.30555 
.30558 
.30561 

9.31657 
.31663 
.31669 
.31675 

.30739 
.30731 
.30734 
.30737 

9.32026 
.32033 
.32039 
.32045 

.30906 
.30909 
.30913 
.30915 

9.32394 
.32400 
.32406 
.32412 

.31083 
.31086 
.31089 
.31093 

9.32760 
.32766 
.32772 
.32778 

.31363 
.31365 
.31368 
.31371 

+    ir 

45 
46 
47 

9.31310 
.31316 
.31323 
.31329 

.30564 
.30567 
.30570 
.30573 

9.31682 
.31688 
.31694 
.31700 

.30740 
.30743 
.30746 
.30749 

9.32051 
.32057 
.32063 
.32069 

.30918 
.30930 
.30933 
.30936 

9.32418 
.32425 
.32431 
.32437 

.31095 
.31098 
.31101 
.31104 

9.32784 
.32790 
.32796 
.32802 

.31374 
.31377 
.31380 
.31383 

16 
15 
14 
IS 

+  13' 

49 
50 
51 

9.31335 
.31341 
.31347 
.31354 

.30575 
.30578 
.30581 
.30584 

9.31706 
.31712 
.31719 
.31725 

.30753 
.30755 
.30758 
.30761 

9.32076 
.32082 
.32088 
.32094 

.30939 
.30933 
.30935 
.30938 

9.32443 
.32449 
.32455 
.32461 

.31107 
.31110 
.31113 
.31116 

9.32808 
.32814 
.32820 
.32827 

.31385 

.31388 
.31391 
.31394 

12 

11 

10 

9 

+    13' 

5S 
54 
55 

9.31360 
.31366 
.31372 
.31378 

.30587 
.30590 
.30593 
.20596 

9.31731 
.31737 
.31743 
.31749 

.30764 
.30767 
.30770 
.30773 

9.32100 
.32106 
.32112 
.32119 

.30941 
.30944 
.30947 
.30950 
.30953 
.30956 
.30959 
.30963 

9.32467 
.32473 
.32480 
.32486 

.31119 
.31123 
.31135 
.31138 

9.32833 
.32839 
.32845 
.32851 

.31397 
.31300 
.31303 
.31306 

8 
7 
6 
5 

4 
S 
2 
1 

+    14' 

57 
58 
59 

9.31385 
.31391 
.31397 
.31403 

.30599 
.30603 
.30605 
.30608 

9.31756 
.31762 
.31768 
.31774 

.30776 
.30779 
.30783 
.30785 

9.32125 
.32131 
.32137 
.32143 

9.32149 

9.32492 
.32498 
.32504 
.32510 

.31131 
.31134 
.31137 
.31140 
.31143 

9.32857 
.32863 
.32869 
.32875 

.31309 
.31313 
.31315 
.31318 

+    15' 

9.31409 

.20611 

9.31780 

.30788 

.30965 

9.32516 

9.32881 

.31331 

0 

20h  24'^ 

20^  23'm 

20^  22^ 

20h  21m 

20^  20"^ 

TABLE  45.                 [Page  866 

Haversines. 

s 

Sh  40m  65"»  r 

Sh  41m  550  15/ 

Sh  42m  55°  30' 

3h  4Sm  65°  45' 

S^  44™  56°  0' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Ha  v. 

Nat.  Hav. 

0 

1 
2 
3 

9.32881 
.32887 
.32893 
.32899 

.31331 
.31334 
.31337 
.31330 

9.33244 
.33250 
.33256 
.33262 

.31500 
.31503 
.31506 
.31509 

9.33605 
.33611 
.33617 
.33623 

.31680 
.31683 
.31686 
.31689 

9.33965 
.33971 
.33976 
.33982 

.31860 
.31863 
.31866 
.31869 

9.34322 
.34328 
.34334 
.34340 

.33040 
.33043 
.33046 
.33049 

60 
59 
58 

57 

+  V 

5 
6 
7 

9.32905 
.32911 
.32918 
.32924 

.31333 
.31336 
.31339 
.31343 

9.33268 
.33274 
.33280 
.33286 

.31513 
.31515 
.31518 
.31531 

9.33629 
.33635 
.33641 
.33647 

.31693 
.31695 
.31698 
.31701 

9.33988 
.33994 
.34000 
.34006 

.31873 
.31875 

.31878 
.31881 

9.-34346 
.34352 
.34358 
.34363 

.33053 
.33055 
.33058 
.33061 

56 
55 
54 
53 

+      ^' 

9 

10 

11 

9.32930 
.32936 
.32942 
.32948 

.31345 
.31348 
.31351 
.31354 

9.33292 
.33298 
.33305 
.33311 

.31534 
.31537 
.31530 
.31533 

9.33653 
.33659 
.33665 
.33671 

.31704 
.31707 
.31710 
.31713 

9.34012 
.34018 
.34024 
.34030 

.31884 
.31887 
.31890 
.31893 

9.34369 
.34375 
.34381 
.34387 

.33064 
.33067 
.33071 
.33074 

52 
51 
50 
49 

+   3' 

IS 
14 
15 

9.32954 
.32960 
.32966 
.32972 

.31357 
.31360 
.31363 
.31366 

9.33317 
.33323 
.33329 
.33335 

.31536 
.31539 
.31543 
.31545 

9.33677 
.33683 
.33689 
.33695 

.31716 
.31719 
.31733 
.31735 

9.34036 
.34042 
.34048 
.34054 

.31896 
.31899 
.31903 
.31905 

9.34393 
.34399 
.34405 
.3441 1 

.33077 
.33080 
.33083 

.33086 

48 
47 
46 
45 

+   *^ 
17 
18 
19 

9.32978 
.32984 
.32990 
.32996 

.31369 
.31373 
.31375 
.31378 

9.33341 
.33347 
.33353 
.33359 

.31548 
.31551 
.31554 
.31557 

9.33701 
.33707 
.33713 
.33719 

.31738 
.31731 
.31734 
.31737 

9.34060 
.34066 
.34072 
.34078 

.31908 
.31911 
.31914 
.31917 

9.34417 
.34423 
.34429 
.34435 

.33089 
.33093 
.33096 
.33098 

44 
43 
42 
41 

+   5^ 
21 

22 
23 

9.33002 
.33008 
.33014 
.33021 

.31381 
.31384 
.31387 
.31390 
.31393 
.31396 
.31399 
.31403 

9.33365 
.33371 
.33377 
.33383 

9.33389 
.33395 
.33401 
.33407 

.31560 
.31563 
.31566 
.31569 

9.33725 
.33731 
.33737 
.33743 

.31740 
.31743 
.31746 
.31749 

9.34084 
.34090 
.34096 
.34102 

.31930 
.31933 
.31936 
.31939 

9.34441 
.34446 
.34452 
.34458 

.33101 
.22104 
.33107 
.33110 

40 
39 
38 
37 

+      6' 

25 
26 
27 

9.33027 
.33033 
.33039 
.33045 

.31573 
.31575 
.31578 
.31581 

9.33749 
.33755 
.33761 
.33767 

.31753 
.31756 
.31768 
.31761 

9.34108 
.34114 
.34120 
.34126 

.31933 
.31936 
.31938 
.31941 

9.34464 
.34470 
.34476 
.34482 

.32113 
.33116 
.33119 
.33133 

36 
35 
34 
33 

+    r 

29 
SO 
31 

9.33051 
.33057 
.33063 
.33069 

.31405 
.31408 
.31411 
.31414 

9.33413 
.33419 
.33425 
.33431 

.31584 
.31687 
.31590 
.31593 

9.33773 
.33779 
.33785 
.33791 

.31764 
.31767 
.31770 
.31773 

9.34132 
.34137 
.34143 
.34149 

.31944 
.31947 
.31960 
.31963 

9.34488 
.34494 
.34500 
.34506 

.32125 
.22128 
.22131 
.33134 

32 
SI 
30 
29 

+   8' 
33 
34 
35 

9.33075 
.33081 
.33087 
.33093 

.31417 
.31430 
.31433 
.31436 

9.33437 
.33443 
.33449 
.33455 

.31596 
.31599 
.31603 
.31605 

9.33797 
.33803 
.33809 
.33815 

.31776 
.31779 
.31783 
.31786 

9.34155 
.34161 
.34167 
.34173 

.31966 
.31969 
.31963 
.31965 

9.34512 
.34518 
.34524 
.34529 

.33137 
.32140 
.33143 
.33146 

28 
27 
26 
25 

+    r 

37 
38 
39 

9.33099 
.33105 
.33111 
.33117 

.31439 
.31431 
.31434 
.31437 

9.33461 
.33467 
.33473 
.33479 

.31608 
.31611 
.31614 
.31617 

9.33821 
.33827 
.33833 
.33839 

.31788 
.31791 
.31794 
.31797 

9.34179 
.34185 
.34191 
.34197 

.31968 
.31971 
.31974 
.31977 

9.34535 
.34541 
.34547 
.34553 

.32149 
.22152 
.22155 
.33158 

24 
23 
22 
21 
20 
19 
18 
17 

+    W 

41 
42 
43 

9.33123 
.33129 
.33135 
.33142 

.31440 
.31443 
.31446 
.31449 

9.33485 
.33491 
.33497 
.33503 

.31630 
.31633 
.31636 
.31639 

9.33845 
.33851 
.33857 
.33863 

.31800 
.31803 
.31806 
.31809 
.31813 
.31815 
.31818 
.31831 

9.34203 
.34209 
.34215 
.34221 

.31980 
.31983 
.31986 
.31989 

9.34559 
.34565 
.34571 
.34577 

.33161 
.32164 
.22167 
.22170 

+    ir 

45 
46 
47 

9.33148 
.33154 
.33160 
.33166 

.31453 
.31455 
.31458 
.31461 

9.33509 
.33515 
.33521 
.33527 

.31633 
.31635 
.31638 
.31641 

9.33869 
.33875 
.33881 
.33887 

9.33893 
.33899 
.33905 
.33911 

9.34227 
.34233 
.34239 
.34245 

.31993 
.31996 
.31998 
.33001 

9.34583 
.34589 
.34595 
.34600 

.33173 
.33176 
.33179 
.33183 

16 
15 
14 
13 
12 
11 
10 
9 

+  ir 

49 
50 
51 

9.33172 
.33178 
.33184 
.33190 

.31464 
.31467 
.31470 
.31473 

9.33533 
.33539 
.33545 
.33551 

.31644 
.31647 
.31650 
.31653 

.31834 
.31837 
.31830 
.31833 

9.34251 
.34256 
.34262 
.34268 

.33004 
.33007 
.33010 
.33013 

9.34606 
.34612 
.34618 
.34624 

9.34630 
.34636 
.34642 
.34648 

.33185 

.33188 
.32191 
.33194 

+    13' 

53 
54 
55 

9.33196 
.33202 
.33208 
.33214 

.31476 
.31479 
.31483 
.31485 

9.33557 
.33563 
.33569 
.33575 

.31656 
.31659 
.31663 
.31665 

9.33917 
.33923 
.33929 
.33935 

.31836 
.31839 
.31843 
.31845 

9.34274 
.34280 
.34286 
.34292 

.33016 
.33019 
.32033 
.33035 

.33197 
.33300 
.33303 
.33306 

8 
7 
6 
5 

+    14' 

57 
58 
59 

9.33220 
.33226 
.33232 
.33238 

.31488 
.31491 
.31494 
.31497 

9.33581 
.33587 
.33593 
.33599 

.31668 
.31671 
.31674 
.31677 

9.33941 
.33947 
.33953 
.33959 

.31848 
.31851 
.31854 
.31857 

9.34298 
.34304 
34310 
.34316 

.33038 
.33031 
.33034 
.33037 

9.34654 
.34660 
.34666 
.34671 

.33309 
.33313 
.33315 
.33318 

4 
3 
2 
1 

+    15' 

9.33244 

.31500 

9.33605 

.31680 

9.33965 

.31860 

9.34322 

.33040 

9.34677   .33331 

0 

20'h  19m 

20fi  18™ 

20^  17™ 

20^ 16m 

20^  15™ 

Page  856]                  TABLE  45. 

Haversines. 

s 

^A  45m  56°  15' 

3h  46m  56°  30' 

JA  47m  56°  45' 

Sh  48m.  57°  (K 

3^  49m  57°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat  .Hav. 

0 
1 

2 
3 

9.34677 
.34683 
.34689 
.34695 

.22221 
.22225 

.22228 
.22231 

9.35031 
.35037 
.35043 
.35049 

.22403 
.22406 
.22409 
.22412 

9.35383 
.35389 
.35394 
.35400 

.22585 

.22588 
.22591 
.22594 

9.35733 
.35738 
.35744 
.35750 

.22768 
.22771 
.22774 
.22777 

9.36081 
.36086 
.36092 
.36098 

.22951 
.22954 
.22957 
.22960 

60 
59 

58 
57 

+    r 

5 
6 

7 

9.34701 
.34707 
.34713 
.34719 

.22234 
.22237 
.22240 
.22243 

9.35054 
.35060 
.35066 
.35072 

.22415 
.22418 
.22421 
.22424 

9.35406 
.35412 
.35418 
.35424 

.22598 
.22601 
.22604 
.22607 

9.35756 
.35762 
.35767 
.35773 

.22780 
.22783 
.22786 
.22789 

9.36104 
.36110 
.36115 
.36121 

.22964 
.22967 
.22970 
.22973 

56 
55 

54 
53 

+      r 

9 

10 

11 

9.34725 
.34730 
.34736 
.34742 

.22246 
.22249 
.22252 
.22255 

9.35078 
.35084 
.35090 
.35096 

.22427 
.22430 
.22433 
.22437 

9.35429 
.35435 
.35441 
.35447 

.22610 
.22613 
.22616 
.22619 

9.35779 
.35785 
.35791 
.35797 

.22792 
.22795 
.22799 
.22802 

9.36127 
.36133 
.36139 
.36144 

.22976 
.22979 
.22982 
.22985 

52 
51 
50 
49 

+     3' 

13 
14 
15 

9.34748 
.34754 
.34760 
.34766 

.22268 
.22261 
.22264 
.22267 

9.35101 
.35107 
.35113 
.35119 

.22440 
.22443 
.22446 
.22449 

9.35453 
.35459 
.35464 
.35470 

.22622 
.22625 
.22628 
.22631 

9.35802 
.35808 
.35814 
.35820 

.22805 
.22808 
.22811 
.22814 

9.36150 
.36156 
.36162 
.36167 

.22988 
.22991 
.22994 
.22997 

48 
47 
46 
45 

+     4' 
17 
18 
19 

9.34772 
.34778 
.34784 
.34789 

.22270 
.22273 
.22276 
.22279 

9.35125 
.35131 
.35137 
.35143 

.22452 
.22455 
.22458 
.22461 

9.35476 
.35482 
.35488 
.35494 

.22634 
.22637 
.22640 
.22643 

9.35826 
.35831 
.35837 
.35843 

.22817 
.22820 
.22823 
.22826 

9.36173 
.36179 
.36185 
.36191 

.23000 
.23003 
.23006 
.23009 

44 
43 
42 
41 

+     5' 
21 
22 
23 

9.34795 
.34801 
.34807 
.34813 

.22282 
.22285 

.22288 
.22291 

9.35148 
.35154 
.35160 
.35166 

.22464 
.22467 
.22470 
.22473 

9.35500 
.35505 
.35511 
.35517 

.22646 
.22649 
.22652 
.22655 

9.35849 
.35855 
.35860 
.35866 

.22829 
.22832 
.22835 

.22838 
.22841 
.22844 
.22847 
.22850 

9.36196 
.36202 
.36208 
.36214 

.23012 
.23016 
.23019 
.23022 

40 
39 
38 
37 

+  6' 

25 
26 
27 

9.34819 
.34825 
.34831 
.34837 

.22294 
.22297 
.22300 
.22303 

9.35172 
.35178 
.35184 
.35189 

.22476 
.22479 
.22482 
.22485 

9.35523 
.35529 
.35535 
.35540 

.22658 
.22661 
.22664 
.22667 

9.35872 
.35878 
.35884 
.35889 

9.36219 
.36225 
.36231 
.36237 

.23025 
.23028 
.23031 
.23034 

36 
So 
34 
33 

+    r 

29 
30 
31 

9.34843 
.34848 
.34854 
.34860 

.22306 
.22309 
.22312 
.22315 

9.35195 
.35201 
.35207 
.35213 

.22488 
.22491 
.22494 
.22497 

9.35546 
.35552 
.35558 
.35564 

.22671 
.22674 
.22677 
.22680 

9.35895 
.35901 
.35907 
.35913 

.22853 

.22857 
.22860 
.22863 
.22866 
.22869 
.22872 
.22875 

9.36243 
.36248 
.36254 
.36260 

.23037 
.23040 
.23043 
.23046 

32 
31 
30 
29 

+     8' 
S3 
34 
35 

9.34866 
.34872 
.34878 
.34884 

.22318 
.22321 
.22324 
.22327 

9.35219 
.35225 
.35230 
.35236 

.22500 
.22503 
.22506 
.22509 

9.35570 
.35575 
.35581 
.35587 

.22683 
.22686 
.22689 
.22692 

9.35918 
.35924 
.35930 
.35936 

9.36266 
.36271 
.36277 
.36283 

.23049 
.23052 
.23055 
.23058 
.23061 
.23065 
.23068 
.23071 

28 
27 
26 
25 

24 
23 

22 
21 

+     9' 

37 
38 
39 

9.34890 
.34896 
.34901 
.34907 

.22330 
.22333 
.22336 
.22340 

9.35242 
.35248 
.35254 
.35260 

.22512 
.22515 
.22518 
.22522 

9.35593 
.35599 
.35604 
.35610 

.22695 
.22698 
.22701 
.22704 

9.35942 
.35947 
.35953 
.35959 

.22878 
.22881 
.22884 
.22887 

9.36289 
.36294 
.36300 
.36306 

+    10' 

41 
42 
43 

9.34913 
.34919 
.34925 
.34931 

.22343 
.22346 
.22349 
.22352 

9.35266 
.35271 
.35277 
.35283 

.22525 
.22528 
.22531 
.22534 

9.35616 
.35622 
.35628 
.35634 

.22707 
.22710 
.22713 
.22716 
.22719 
.22722 
.22725 
.22728 

9.35965 
.35971 
.35976 
.35982 

9.35988 
.35994 
.36000 
.36005 

.22890 
.22893 
.22896 
.22899 

9.36312 
.36318 
.36323 
.36329 

.23074 
.23077 
.23080 
.23083 

20 
19 
18 
17 
16 
15 
14 
13 

+  ir 

45 
46 
47 

9.34937 
.34943 
.34949 
.34954 

.22355 
.22358 
.22361 
.22364 

9.35289 
.35295 
.35301 
.35307 

.22537 
.22540 
.22543 
.22546 

9.35639 
.35645 
.35651 
.35657 

.22902 
.22905 
.22908 
.22912 

9.36335 
.36341 
.36346 
.36352 

.23086 
.23089 
.23092 
.23095 

+    12' 

49 
50 
51 

9.34960 
.34966 
.34972 
.34978 

.22367 
.22370 
.22373 
.22376 

9.35312 
.35318 
.35324 
.35330 

.22549 
.22552 
.22555 
.22558 

9.35663 
.35669 
.35674 
.35680 

.22731 
.22735 
.22738 
.22741 

9.36011 
.36017 
.36023 
.36029 

.22915 
.22918 
.22921 
.22924 

9.36358 
.36364 
.36369 
.36375 

.23098 
.23101 
.23104 
.23107 

12 
11 
10 
9 
8 
7 
6 
5 

+   13' 

53 
54 
55 

9.34984 
.34990 
.34996 
.35002 

.22379 
.22382 
.22385 

.22388 

9.35336 
.35342 
.35348 
.35353 

.22561 
.22564 
.22567 
.22570 

9.35686 
.35692 
.35698 
.35703 

9.35709 
.35715 
.35721 
.35727 

.22744 
.22747 
.22750 
.22753 
.22756 
.22759 
.22762 
.22765 

9.36034 
.36040 
.36046 
.36052 

.22927 
.22930 
.22933 
.22936 

9.36381 
.36387 
.36392 
.36398 

.23110 
.23114 
.23117 
.23120 

+    14' 

57 
58 
59 

9.35007 
.35013 
.35019 
.35025 

.22391 
.22394 
.22397 
.22400 

9.35359 
.35365 
.35371 
.35377 

.22573 
.22576 
.22579 
.22582 

9.36058 
.36063 
.36069 
.36075 

.22939 
.22942 
.22945 
.22948 
^.22951 

9.36404 
.36410 
.36415 
.36421 

.23123 
.23126 
.23129 
.23132 

4 
3 

2 
1 

+  15' 

9.35031 

.22403 

9.35383 

.22585 

9.35733 

.22768 

9.36081 

9.36427 

.23135 

0 

^oh  14m       1 

20'h'  ISin 

20h i£m 

20^ lim 

20Ji  lOm 

TABLE  45.                  [Page  857 
Haversines. 

s 

Sf^5am57°W    1 

sh5msi°w   1 

3^52^5%°^     1 

S^  53m  58°  15' 

3^  54^  58°  30' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat  Hav. 

0 

1 
2 
S 

9.36427 
.36433 
.36439 
.36444 

.23135 
.23138 
.23141 
.23144 

9.36772 
.36777 
.36783 
.36789 

.23319 
.23322 
.23325 
.23329 

9.37114 
.37120 
.37126 
.37131 

.23504 
.23507 
.23510 
.23513 

9.37455 
.37461 
.37467 
.37472 

.23689 
.23692 
.23695 
.23699 

9.37794 
.37800 
.37806 
.37811 

.23875 

.23878 
.23881 

.23884 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.36450 
.36456 
.36462 
.36467 

.23147 
.23150 
.23153 
.23156 
.23160 
.23163 
.23166 
.23169 

9.36794 
.36800 
.36806 
.36812 

.23332 
.23335 
.23338 
.23341 

9.37137 
.37143 
.37148 
.37154 

9.37160 
.37166 
.37171 
.37177 

.23516 
.23519 
.23523 
.23526 
.23529 
.23532 
.23535 
.23538 
.23541 
.23544 
.23547 
.23550 

9.37478 
.37484 
.37489 
.37495 

9.37501 
.37506 
.37512 
.37518 

9.37523 
.37529 
.37535 
.37540 

9.37546 
.37552 
.37557 
.37563 

.23702 
.23705 
.23708 
.23711 
.23714 
.23717 
.23720 
.23723 
.23726 
.23729 
.23733 
.23736 
.23739 
.23742 
.23745 
.23748 

9.37817 
.37823 
.37828 
.37834 

9.37840 
.37845 
.37851 
.37856 

.23887 
.23891 
.23894 
.23897 

56 
55 
54 
53 

+    r 

9 

10 
11 

9.36473 
.36479 
.36485 
.36490 

9.36817 
.36823 
.36829 
.36834 

.23344 
.23347 
.23350 
.23353 

.23900 
.23903 
.23906 
.23909 

52 
51 
50 
49 

+      3" 

13 
14 
15 

9.36496 
.36502 
.36508 
.36513 

.23172 
.23175 
.23178 
.23181 

9.36840 
.36846 
.36852 
.36857 

.23356 
.23359 
.23362 
.23365 

9.37183 
.37188 
.37194 
.37200 

9.37862 
.37868 
.37873 
.37879 

9.37885 
.37890 
.37896 
.37902 

.23912 
.23915 
.23918 
.23922 
.23925 
.23928 
.23931 
.23934 

48 
47 
46 
45 

U 
43 
42 
41 

+     i' 
17 
18 
19 

9.36519 
.36525 
.36531 
.36536 

.23184 
.23187 
.23190 
.23193 

9.36863 
.36869 
.36875 
.36880 

.23368 
.23372 
.23375 
.23378 

9.37205 
.37211 
.37217 
.37222 

.23553 
.23556 
.23560 
.23563 

+     6^ 
21 
22 
23 

9.36542 
.36548 
.36554 
.36559 

.23196 
.23199 
.23203 
.23206 

9.36886 
.36892 
.36897 
.36903 

.23381 
.23384 
.23387 
.23390 
.23393 
.23396 
.23399 
.23402 

9.37228 
.37234 
.37239 
.37245 

.23566 
.23569 
.23572 
.23575 

9.37569 
.37574 
.37580 
.37585 

.23751 
.23754 
.23757 
.23760 

9.37907 
.37913 
.37918 
.37924 

.23937 
.23940 
.23943 
.23946 
.23950 
.23953 
.23956 
.23959 

40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 

+   6' 

25 
26 

27 

9.36565 
.36571 
.36577 
.36582 

.23209 
.23212 
.23215 
.23218 

9.36909 
.36915 
.36920 
.36926 

9.37251 
.37257 
.37262 
.37268 

.23578 
.23581 
.23584 
.23587 

9.37591 
.37597 
.37602 
.37608 

.23764 
.23767 
.23770 
.23773 

9.37930 
.37935 
.37941 
.37947 

+    r 

29 
SO 
31 

9.36588 
.36594 
.36599 
.36605 

.23221 
.23224 
.23227 
.23230 

9.36932 
.36937 
.36943 
.36949 

.23405 
.23409 
.23412 
.23415 

9.37274 
.37279 
.37285 
.37291 

.23590 
.23594 
.23597 
.23600 

9.37614 
.37619 
.37625 
.37631 

9.37636 
.37642 
.37648 
.37653 

.23776 
.23779 
.23782 
.23785 

.23788" 
.23791 
.23795 
.23798 

9.37952 
.37958 
.37963 
.37969 

.23962 
.23965 
.23968 
.23971 

+   8' 
S3 
34 
35 

9.36611 
.36617 
.36622 
.36628 

.23233 
.23236 
.23239 
.23242 

9.36955 
.36960 
.36966 
.36972 

.23418 
.23421 
.23424 
.23427 

9.37296 
.37302 
.37308 
.37313 

.23603 
.23606 
.23609 
.23612 

9.37975 
.37980 
.37986 
.37992 

.23974 
.23977 
.23981 
.23984 

28 
27 
26 
25 

24 
23 

22 
21 
20 
19 
18 
17 
16 
15 
14 
13 

+   9' 

37 
38 
39 

9.36634 
.36640 
.36645 
.36651 

.23246 
.23249 
.23252 
.23255 

9.36977 
.36983 
.36989 
.36995 

.23430 
.23433 
.23436 
.23439 

9.37319 
.37325 
.37330 
.37336 

.23615 
.23618 
.23621 
.23624 

9.37659 
.37665 
.37670 
.37676 

.23801 
.23804 
.23807 
.23810 

9.37997 
.38003 
.38008 
.38014 

.23987 
.23990 
.23993 
.23996 
.23999 
.24002 
.24005 
.24009 
.24012 
.24015 
.24018 
.24021 

+  10' 

41 
42 
43 

9.36657 
.36663 
.366B8 
.36674 

.23258 
.23261 
.23264 
.23267 

9.37000 
.37006 
.37012 
.37017 

.23442 
.23445 
.23449 
.23452 

9.37342 
.37347 
.37353 
.37359 

.23627 
.23631 
.23634 
.23637 

9.37682 
.37687 
.37693 
.37699 

.23813 
.23816 
.23819 
.23822 

9.38020 
.38025 
.38031 
.38037 

9.38042 
.38048 
.38053 
.38059 

+    11^ 

45 

46 

47 

+  ir 

49 
50 
51 

9.36680 
.36686 
.36691 
.36697 

.23270 
.23273 
.23276 
.23279 

9.37023 
.37029 
.37034 
.37040 

1  .23455 
i  .23458 
!  .23461 
1  .23464 

9.37364  1  .23640 
.37370!  .23643 
.37376   .23646 
.37382   .23649 

9.37704 
.37710 
.37715 
.37721 

.23825 
.23829 
.23832 
.23835 

9.36703 
.36708 
.36714 
.36720 

.23282 
.23285 
.23289 
.23392 

9.37046 
.37052 
.37057 
.37063 

.23467 
.23470 
.23473 
.23476 

9.37387 
.37393 
.37399 
.37404 

.23652 
.23055 
.23658 
.23661 

9.37727 
.37732 
.37738 
.37744 

.23838 
.23841 
.23844 
.23847 

9.38065 
.38070 
.38076 
.38081 

9.3808f 
.38093 
.38098 
.38104 

.24024 
.24027 
.24030 
.24033 
.24036 
.24040 
.24043 
.24046 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.36726 
.36731 
.36737 
.36743 

.23295 
.23298 
.23301 
.23304 

9.37069 
.37074 
.37080 
.37086 

i  .23479 
.23482 
.23486 
.23489 

9.37410 
.37416 
.37421 
.37427 

.23665 
.23668 
.23671 
.23674 

9.37749 
.37755 
.37761 
.37766 

.23850 
.23853 
.23856 
.23860 

+    14' 

57 
58 
59 

9.36749 
.36754 
.36760 
.36766 

.23307 
.23310 
.23313 
.23316 

9.37091 
.37097 
.37103 
.37109 

1  .23492 

.23495 

1  .23498 

'    .23501 

9.37433 
.37438 
.37444 
.37450 

.23677 
.23680 
.23683 
.23686 

9.37772 
.37778 
.37783 
.37789 

.23863 
.23866 
.23869 
.23872 

9.38110 
.38115 
.38121 
.38126 

.24049 
.24052 
.24055 
.24058 

4 
3 
2 
1 

+    15' 

9.36772 

.23819 

9.37114   .23504 

9.37455 

.23689 

9.37794 

.23875 

9.38132 

.24061 

0 

20^  9m 

20^  8'm          1    20^  7"» 

20^  6"»     1    20fi  5m 

Page  858] 

TABLE  45. 

Haversines. 

s 

5ft  55m  58°  45' 

Sh  56m  59°  0' 

5ft  57m  59°  15' 

5ft  58^  59°  30' 

5ft  59m  59°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.38132 
.38138 
.38143 
.38149 

.34061 
.34064 
.34068 
.34071 

9.38468 
.38473 
.38479 
.38485 

.34348 
.34351 
.34354 
.34357 

9.38802 
.38807 
.38813 
.38819 

.34435 
.34438 
.34443 
.34445 

9.39134 
.39140 
.39145 
.39151 

.34633 
.34636 
.34639 
.34633 

9.39465 
.39470 
.39476 
.39481 

.34811 
.34814 
.34818 
.34831 

60 

59 
58 
57 

+    r 

5 
6 

7 

9.38154 
.38160 
.38166 
.38171 

.34074 
.34077 
.34080 
.34083 

9.38490 
.38496 
.38501 
.38507 

.34361 
.34364 
.34367 
.34370 

9.38824 
.38830 
.38835 
.38841 

.34448 
.34451 
.34454 
.34457 

9.39156 
.39162 
.39167 
.39173 

.34636 
.34639 
.34643 
.34645 

9.39487 
.39492 
.39498 
.39503 

.34834 

.34837 
.34830 
.34833 

56 
55 
54 
53 

+   3' 

9 

10 

11 

9.38177 
.38182 
.38188 
.38194 

.34086 
.34089 
.34093 
.34096 

9.38512 
.38518 
.38524 
.38529 

.34373 
.34376 
.34379 
.34383 

9.38846 
.38852 
.38857 
.38863 

.34460 
.34463 
.34467 
.34470 

9.39178 
.39184 
.39189 
.39195 

.34648 
.34651 
.34654 
.34658 

9.39509 
.39514 
.39520 
.39525 

.34836 
.34840 
.34843 
.34846 

52 
51 
50 
49 

+  3' 

13 
14 
15 

9.38199 
.38205 
.38210 
.38216 

.34099 
.34103 
.34105 
.34108 

9.38535 
.38540 
.38546 
.38551 

.34386 
.34389 
.34393 
.34395 

9.38868 
.38874 
.38880 
.38885 

.34473 
.34476 
.34479 
.34483 

9.39201 
.39206 
.39212 
.39217 

.34661 
.34664 
.34667 
.34670 

9.39531 
.39536 
.39542 
.39547 

.34849 
.34853 
.34855 

.34858 

48 
47 
46 
45 

+   4' 
17 
18 
19 

9.38222 
.38227 
.38233 
.38239 

.34111 
.34114 
.34117 
.34130 

9.38557 
.38563 
.38568 
.38574 

.34398 
.34301 
.34304 
.34307 

9.38891 
.38896 
.38902 
.38907 

.34485 

.34488 
.34493 
.34495 

9.39223 
.39228 
.39234 
.39239 

.34673 
.34676 
.34680 
.34683 

9.39553 
.39558 
.39564 
.39569 

.34863 
.34865 
.34868 
.34871 

44 
43 
42 
41 

+   5' 

22 
23 

9.38244 
.38250 
.38255 
.38261 

9.38267 
.38272 
.38278 
.38283 

.34134 
.34137 
.34130 
.34133 

9.38579 
.38585 
.38590 
.38596 

.34310 
.34314 
.34317 
.34330 

9.38913 
.38918 
.38924 
.38929 

.34498 
.34501 
.34504 
.34507 

9.39245 
.39250 
.39256 
.39261 

.34686 
.34689 
.34693 
.34695 

9.39575 
.39580 
.39586 
.39591 

.34874 
.34877 
.34880 
.34884 

40 
39 
38 
37 
36 
35 
34 
33 

+   6' 

26 
27 

.34136 
.34139 
.34143 
.34145 

9.38602 
.38607 
.38613 
.38618 

.34333 
.34336 
.34339 
.34333 

9.38935 
.38941 
.38946 
.38952 

.34510 
.34514 
.34517 
.34530 

9.39267 
.39272 
.39278 
.39283 

.34698 
.34701 
.34705 
.34708 

9.39597 
.39602 
.39608 
.39613 

.34887 
.34890 
.34893 
.34896 

+   7' 

30 
31 

9.38289 
.38295 
.38300 
.38306 

.34148 
.34153 
.34155 
.34158 

9.38624 
.38629 
.38635 
.38641 

.34335 
.34339 
.34343 
.34345 

9.38957 
.38963 
.38968 
.38974 

.34533 
.34536 
.34539 
.34533 

9.39289 
.39294 
.39300 
.39305 

.34711 
.34714 
.34717 
.34730 

9.39619 
.39624 
.39630 
.39635 

.34899 
.34903 
.34906 
.34909 

32 
31 
30 
29 

+  8' 

34 
35 

9.38311 
.38317 
.38322 
.38328 

.34161 
.34164 
.34167 
.34170 

9.38646 
.38652 
.38657 
.38663 

.34348 
.34351 
.34354 
.34357 

9.38979 
.38985 
.38990 
.38996 

.34535 
.34539 
.34543 
.34545 

9.39311 
.39316 
.39322 
.39327 

.34733 
.34737 
.34730 
.34733 

9.39641 
.39646 
.39652 
.39657 

.34913 
.34915 
.34918 
.34931 

28 
27 
26 
25 

24 
23 
22 
21 

+   9' 

38 
39 

9.38334 
.38339 
.38345 
.38350 

.34173 
.34176 
.34180 
.34183 

9.38668 
.38674 
.38680 
.38685 

.34360 
.34364 
.34367 
.34370 

9.39002 
.39007 
.39013 
.39018 

.34548 
.34551 
.34554 
.34557 

9.39333 
.39338 
.39344 
.39349 

.34736 
.34739 
.34743 
.34745 

9.39663 
.39668 
.39674 
.39679 

.34934 
.34938 
.34931 
.34934 

+  10^ 

42 
43 

9.38356 
.38362 
.38367 
.38373 

.34186 
.34189 
.34193 
.34195 

9.38691 
.38696 
.38702 
.38707 

.34373 
.34376 
.34379 
.34383 

9.39024 
.39029 
.39035 
.39040 

.34560 
.34564 
.34567 
.34570 

9.39355 
.39360 
.39366 
.39371 

.34749 
.34753 
.34755 
.34758 

9.39685 
.39690 
.39695 
.39701 

.34937 
.34940 
.34943 
.34946 

20 
19 
18 
17 
16 
15 
14 
13 

+  11' 

45 
46 
47 

9.38378 
.38384 
.38390 
.38395 

.34198 
.34301 
.34304 
.34308 

9.38713 
.38719 
.38724 
.38730 

.34385 

.34388 
.34393 
.34395 

9.39046 
.39051 
.39057 
.39062 

.34573 
.34576 
.34579 
.34583 

9.39377 
.39382 
.39388 
.39393 

.34761 
.34764 
.34767 
.34770 

9.39706 
.39712 
.39717 
.39723 

.34950 
.34953 
.34956 
.34959 

+  13' 

49 
50 
51 

9.38401 
.38406 
.38412 
.38418 

.34311 
.34314 
.34317 
.34330 

9.38735 
.38741 
.38746 
.38752 

.34398 
.34401 
.34404 
.34^07 

9.39068 
.39073 
.39079 
.39085 

.34586 
.34589 
.34593 
.34595 

9.39399 
.39404 
.39410 
.39415 

.34774 
.34777 
.34780 
.34783 

9.39728 
.39734 
.39739 
.39745 

.34963 
.34965 
.34969 
.34973 
.34975 
.34978 
.34981 
.34984 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.38423 
.38429 
.38434 
.38440 

.34333 
.34336 
.34339 
.34333 

9.38757 
.38763 
.38769 
.38774 

.34410 
.34413 
.34417 
.34430 

9.39090 
.39096 
.39101 
.39107 

.34598 
.34601 
.34604 
.34607 

9.39421 
.39426 
.39432 
.39437 

.34786 
.34789 
.34793 
.34796 

9.39750 
.39756 
.39761 
.39767 

+  14' 

57 
58 
59 

9.38445 
.38451 
.38457 
.38462 

.34336 
.34339 
.34343 
.34345 

9.38780 
.38785 
..38791 
.38796 

.34433 
.34436 
.34439 
.34433 

9.39112 
.39118 
.39123 
.39129 

.34611 
.34614 
.34617 
.34630 

9.39443 
.39448 
.39454 
.39459 

.34799 
.34803 
.34805 
.34808 

9.39772 
.39778 
.39783 
.39789 

.34987 
.34991 
.34994 
.34997 

4 
S 
2 
1 
0 

+  15' 

9.38468 

.34348 

9.38802 

.34435 

9.39134 

.34633 

9.39465 

.34811 

9.39794 

.35000 

20h 

4m 

20h  sm 

20^2'^ 

f  Oft  i"* 

20^  0^ 

TABLE  45.                  [Page  859 

Haversines. 

s 

4h  Qm  60°  V 

4^  im  60°  15' 

4h  2m  60°  30^ 

4n  sm  60°  45' 

4h  4^  61°  0' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.39794 
.39799 
.39805 
.39810 

.25000 
.25003 
.25006 
.25009 

9.40121 
.40127 
.40132 
.40138 

.25189 
.25192 
.25195 
.25199 

9.40447 
.40453 
.40458 
.40463 

.25379 
.25382 
.25385 

.25388 

9.40771 
.40777 
.40782 
.40787 

.25569 
.25572 
.25575 
.25578 

9.41094 
.41099 
.41105 
.41110 

.25760 
.25763 
.25766 
.25769 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.39816 
.39821 
.39827 
.39832 

.25013 
.25016 
.25019 
.25022 

9.40143 
.40149 
.40154 
.40159 

.25202 
.25205 
.25208 
.25211 

9.40469 
.40474 
.40480 
.40485 

.25391 
.25395 
.25398 
.25401 

9.40793 
.40798 
.40804 
.40809 

.25582 
.25585 

.25588 
.25591 

9.41115 
.41121 
.41126 
.41131 

.25772 
.25775 
.25779 
.25782 

56 
55 

54 
53 

+  r 

9 

10 

11 

9.39838 
.39843 
.39849 
.39854 

.25025 
.25028 
.25032 
.25035 

9.40165 
.40170 
.40176 
.40181 

.25214 
.25218 
.25221 
.25224 

9.40490 
.40496 
.40501 
.40507 

.25404 
.25407 
.25410 
.25414 

9.40814 
.40820 
.40825 
.40831 

.25594 
.25597 
.25601 
.25604 

9.41137 
.41142 
.41147 
.41153 

.25785 

.25788 
.25791 
.25795 

52 
51 
50 
49 

+   3^ 

13 
14 
15 

9.39860 
.39865 
.39871 
.39876 

.25038 
.25041 
.25044 
.25047 

9.40187 
.40192 
.40198 
.40203 

.25227 
.25230 
.25233 
.25237 

9.40512 
.40518 
.40523 
.40528 

.25417 
.25420 
.25423 
.25426 

9.40836 
.40841 
.40847 
.40852 

.25607 
.25610 
.25613 
.25617 

9.41158 
.41163 
.41169 
.41174 

.25798 
.25801 
.25804 
.25807 

48 
47 
46 
45 

+     i' 
17 
18 
19 

9.39881 
.39887 
.39892 
.39898 

.25050 
.25054 
.25057 
.25060 

9.40208 
.40214 
.40219 
.40225 

.25240 
.25243 
.25246 
.25249 

9.40534 
.40539 
.40545 
.40550 

.25429 
.25433 
.25436 
.25439 

9.40858 
.40863 
.40868 
.40874 

.25620 
.25623 
.25626 
.25629 

9.41180 
.41185 
.41190 
.41196 

.25810 
.25814 
.25817 
.25820 

U 
43 
42 
41 

+     5^ 
21 
22 
23 

9.39903 
.39909 
.39914 
.39920 

.25063 
.25066 
.25069 
.25072 

9.40230 
.40236 
.40241 
.40246 

.25252 
.25255 
.25259 
.25262 

9.40555 
.40561 
.40566 
.40572 

.25442 
.25445 
.25448 
.25452 

9.40879 
.40884 
.40890 
.40895 

.25632 
.25636 
.25639 
.25642 

9.41201 
.41206 
.41212 
.41217 

.25823 
.25826 
.25830 
.25833 

40 
39 
38 
37 
36 
35 
34 
S3 
32 
31 
SO 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 

+   r 

25 
26 
27 

9.39925 
.39931 
.39936 
.39942 

.25076 
.25079 
.25082 
.25085 
.25088 
.25091 
.25095 
.25098 

9.40252 
.40257 
.40263 
.40268 

.25265 
.25268 
.25271 
.26274 

9.40577 
.40582 
.40588 
.40593 

.25455 
.25458 
.25461 
.25464 

9.40900 
.40906 
.40911 
40917 

.25645 
.25648 
.25651 
.25655 

9.41222 
.41228 
.41233 
.41238 

.25836 
.25839 
.25842 
.25845 
.25849 
.25852 
.25855 
.25858 

+    r 

29 
SO 
31 

9.39947 
.39952 
.39958 
.39963 

9.40274 
.40279 
.40284 
.40290 

.25278 
.25281 
.25284 
.25287 

9.40599 
.40604 
.40609 
.40615 

.25467 
.25471 
.25474 
.25477 

9.40922 
.40927 
.40933 
.40938 

.25658 
.25661 
.25664 
.25667 

9.41244 
.41249 
.41254 
.41260 

+     8' 
33 
34 
35 

9.39969 
.39974 
.39980 
.39985 

.25101 
.25104 
.25107 
.25110 

9.40295 
.40301 
.40306 
.40312 

.25290 
.25293 
.25297 
.25300 

9.40620 
.40626 
.40631 
.40636 

.25480 
.25483 
.25487 
.25490 

9.40943 
.40949 
.40954 
.40960 

.25671 
.25674 
.25677 
.25680 

9.41265 
.41270 
.41276 
.41281 

.25861 
.25865 
.25868 
.25871 

+     9" 

37 
38 
39 

9.39991 
.39996 
.40002 
.40007 

.25113 
.25117 
.25120 
.25123 

9.40317 
.40322 
.40328 
.40333 

.25303 
.25306 
.25309 
.25312 

9.40642 
.40647 
.40653 
.40658 

.25493 
.25496 
.25499 
.25502 

9.40965 
.40970 
.40976 
.40981 

.25683 
.25686 
.25690 
.25693 

9.41287 
.41292 
.41297 
.41303 

.25874 
.25877 

.25880 

.25884 

+  w 

41 
42 
43 

9.40012 
.40018 
.40023 
.40029 

.25126 
.25129 
.25132 
.25136 

9.40339 
.40344 
.40350 
.40355 

.25316 
.25319 
.25322 
.25325 

9.40663 
.40669 
.40674 
.40680 

.25506 
.25509 
.25512 
.25515 

9.40986 
.40992 
.40997 
.41003 

.25696 
.25699 
.25702 
.25705 

9.41308 
.41313 
.41319 
.41324 

.25887 
.25890 
.25893 
.25896 

+  11' 

45 
46 
47 

9.40034 
.40040 
.40045 
.40051 

.25139 
.25142 
.25145 
.25148 

9.40360 
.40366 
.40371 
.40377 

.25328 
.25331 
.25335 
.25338 

9.40685 
.40690 
.40696 
.40701 

.25518 
.25521 
.25525 
.25528 

9.41008 
.41013 
.41019 
.41024 

.25709 
.25712 
.25715 
.25718 

9.41329 
.41335 
.41340 
.41345 

.25900 
.25903 
.25906 
.25909 

~+    12' 

49 
50 
51 

9.40056 
.40062 
.40067 
.40072 

.25151 
.25154 
.25158 
.25161 

9.40382 
.40388 
.40393 
.40398 

.25341 
.25344 
.25347 
.25350 

9.40707 
.40712 
.40717 
.40723 

.25531 
.25534 
.25537 
.25540 

9.41029 
.41035 
.41040 
.41046 

.25721 
.25724 
.25728 
.25731 

9.41351 
.41356 
.41361 
.41367 

.25912 
.25915 
.25919 
.25922 

12 

11 

10 

9 

+  m 

53 
54 
55 

9.40078 
.40083 
.40089 
.40094 

.25164 
.25167 
.25170 
.25173 

9.40404 
.40409 
.40415 
.40420 

.25354 
.25357 
.25360 
.25363 

9.40728 
.40734 
.40739 
.40744 

.25544 
.25547 
.25550 
.25553 

9.41051 
.41056 
.41062 
.41067 

.25734 
.25737 
.25740 
.25744 

9.41372 
.41377 
.41383 
.41388 

.25925 
.25928 
.25931 
.25935 

8 
7 
6 
5 

+    U' 

57 
58 
59 

9.40100 
.40105 
.40111 
.40116 

.25177 
.25180 
.25183 
.25186 

9.40425 
.4043] 
.40436 
.40442 

.25366 
.25369 
.25372 
.25376 

9.40750 
.40755 
.40761 
.40766 

.25556 
.25559 
.25563 
.25566 

9.41072 
.41078 
.41083 
.41088 

.25747 
.25750 
.25753 
.25756 

9.41393 
.41399 
.41404 
.41409 

.25938 
.25941 
.25944 
.25947 

4 
S 
2 
1 

+    W 

9.40121 

.25189 

9.40447 

.25379 

9.40771 

.25569 

9.41094 

.25760 

9.41415 

.25951 

0 

19^  59m 

19^  58m 

19h  57m 

19^  56^ 

19h  55m 

21594°— 14 47 


Page  860]                 TABLE  45. 

Haversines. 

s 

4h  5m  61°  15' 

4^  em  61°  30' 

4^  7m  61°  45' 

4h  8m  62°  0' 

4h  9m  62°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

9.41415 
.41420 
.41425 
.41431 

.35951 
.25954 
.25957 
.25960 

9.41734 
.41739 
.41745 
.41750 

.26142 
.26145 
.26148 
.26152 

9.42052 
.42057 
.42062 
.42068 

.26334 
.26337 
.26340 
.36344 

9.42368 
.42373 
.42378 
.42384 

.26526 
.26530 
.26533 
.26536 

9.42682 
.42688 
.42693 
.42698 

.26719 
.26722 
.36726 
.26729 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.41436 
.41441 
.41447 
.41452 

.25963 
.25966 
.25970 
.25973 

9.41755 
.41761 
.41766 
.41771 

.26155 
.26158 
.26161 
.26164 

9.42073 
.42078 
.42083 
.42089 

.36347 
.36350 
.26353 
.36356 

9.42389 
.42394 
.42399 
.42405 

.26539 
.26543 
.26546 
.26549 

9.42703 
.42709 
.42714 
.42719 

.26732 
.26735 
.26739 
.26742 

56 
55 
54 
53 

+   2^ 

>  9 
10 
11 

9.41457 
.41463 
.41468 
.41473 

.25976 
.25979 
.25982 
.25986 

9.41776 
.41782 
.41787 
.41792 

.26168 
.26171 
.26174 
.26177 

9.42094 
.42099 
.42105 
.42110 

.36360 
.36363 
.26366 
.36369 

9.42410 
.42415 
.42420 
.42426 

.26552 
.26555 
.26559 
.26562 

9.42724 
.42730 
.42735 
.42740 

.26745 
.26748 
.26751 
.26755 

52 
51 
50 
49 

+     3' 

13 
14 
15 

9.41479 
.41484 
.41489 
.41495 

.25989 
.25992 
.25995 
.25998 

9.41798 
.41803 
.41808 
.41814 

.26180 
.26184 
.26187 
.36190 

9.42115 
.42120 
.42126 
.42131 

.36373 
.36376 
.26379 
.26382 

9.42431 
.42436 
.42441 
.42447 

.26565 
.26568 
.36571 
.26575 

9.42745 
.42750 
.42756 
.42761 

.26758 
.26761 
.26764 
.26768 

48 
47 
46 
45 

+   4' 
17 
18 
19 

9.41500 
.41505 
.41511 
.41516 

.26002 
.26005 
.26008 
.26011 

9.41819 
.41824 
.41829 
.41835 

.26193 
.36196 
.26200 
.26203 

9.42136 
.42141 
.42147 
.42152 

.26385 
.26389 
.36392 
.26395 

9.42452 
.42457 
.42462 
.42468 

.36578 
.36581 
.26584 
.26587 

9.42766 
.42771 

.42777 
.42782 

.26771 
.26774 
.36777 
.26780 

44 
43 
42 
41 

+     5' 
21 
22 
23 

9.41521 
.41527 
.41532 
.41537 

.26014 
.26017 
.26021 
.26021 

9.41840 
.41845 
.41851 
.41856 

.26206 
.26209 
.36313 
.36316 

9.42157 
.42163 
.42168 
.42173 

.26398 
.26402 
.26405 
.36408 

9.42473 
.42478 
.42483 
.42489 

.26591 
.26594 
.26597 
.26600 

9.42787 
.42792 
.42797 
.42803 

.26784 
.26787 
.26790 
.26793 

40 
39 
38 
37 

+     6' 

25 
26 
27 

9.41543 
.41548 
.41553 
.41559 

.26027 
.26030 
.26033 
.26037 

9.41861 
.41867 
.41872 
.41877 

.26219 
.36333 
.26225 
.36338 

9.42178 
.42184 
.42189 
.42194 

.26411 
.26414 
.36417 
.26421 

9.42494 
.42499 
.42504 
.42510 

.26604 
.26607 
.26610 
.26613 

9.42808 
.42813 
.42818 
.42824 

.26797 
.26800 
.26803 
.26806 

36 
35 
34 
S3 

+    r 

29 
SO 
31 

9.41564 
.41569 
.41575 
.41580 

.26040 
.26043 
.26046 
.26049 

9.41882 
.41888 
.41893 
.41898 

.26232 
.36335 
.26238 
.26241 

9.42199 
.42205 
.42210 
.42215 

.26424 
.26427 
.26430 
.26433 

9.42515 
.42520 
.42525 
.42531 

.26616 
.26620 
.26623 
.36626 

9.42829 
.42834 
.42839 
.42844 

.26809 
.26813 
.26816 
.26819 

32 
31 
SO 
29 

+     S' 
33 
34 
35 

9.41585 
.41590 
.41596 
.41601 

.26053 
.26056 
.26059 
.26062 

9.41904 
.41909 
.41914 
.41920 

.26244 
.26248 
.26251 
.26254 

9.42221 
.42226 
.42231 
.42236 

.26437 
.26440 
.26443 
.26446 

9.42536 
.42541 
.42546 
.42552 

.26629 
.26632 
.26636 
.26639 

9.42850 
.42855 
.42860 
.42865 

.26832 
.26826 
.26829 
.26832 

28 
27 
26 

25 

+      V 

37 
38 
39 

9.41606 
.41612 
.41617 
.41622 

.26065 
.26069 
.36072 
.26075 

9.41925 
.41930 
.41935 
.41941 

.26257 
.26260 
.36264 
.26267 

9.42242 
.42247 
.42252 
.42257 

.26449 
26453 
.26456 
.26459 

9.42557 
.42562 
.42567 
.42573 

.26642 
.26645 
.26649 
.26652 

9.42870 
.42876 
.42881 
.42886 

.26835 
.26838 
.26842 
.26845 

24 
23 
22 
21 

+  W 

41 
42 
43 

9.41628 
.41633 
41638 
.41644 

.26078 
.26081 
.26085 
.26088 

9.41946 
.41951 
.41957 
.41962 

.26270 
.36373 
.36376 
.26280 

9.42263 
.42268 
.42273 
.42278 

.26462 
.26465 
.26469 
.26473 

9.42578 
.42583 
.42588 
.42593 

.26655 
.26658 
.26661 
.26665 

9.42891 
.42897 
.42902 
.42907 

.26848 
.26851 
.26855 

.26858 

20 
19 
18 
17 

+  11' 

45 
46 
47 

9.41649 
.41654 
.41660 
.41665 

.26091 
.26094 
.26097 
.26101 

9.41967 
.41972 
.41978 
.41983 

.26283 
.26286 
.36389 
.26292 

9.42284 
.42289 
.42294 
.42300 

.26475 
.26478 
.26481 
.26485 

9.42599 
.42604 
.42609 
.42614 

.26668 
.26671 
.26674 
.26677 

9.42912 
.42917 
.42923 
.42928 

.26861 
.26864 
.26867 
.26871 

16 
15 
14 
13 

49 
50 
51 

9.41670 
.41676 
.41681 
.41686 

.26104 
.26107 
.26110 
.26113 

9.41988 
.41994 
.41999 
.42004 

.36296 
.26299 
.36302 
.26305 

9.42305 
.42310 
.42315 
.42321 

.26488 
.36491 
.36494 
.26498 

9.42620 
.42625 
.42630 
.42635 

.26681 
.26684 
.26687 
.26690 

9.42933 
.42938 
.42943 
.42949 

.26874 
.26877 

.26880 
.26883 

12 

11 

10 

9 

+  13' 

53 
54 
55 

9.41692 
.41697 
.41702 
.41707 

.26117 
.26120 
.26123 
.26126 

9.42009 
.42015 
.42020 
.42025 

.26308 
.26312 
.26315 
.26318 

9.42326 
.42331 
.42336 
.42342 

.26501 
.26504 
.26507 
.26510 

9.42641 
.42646 
.42651 
.42656 

.26694 
.26697 
.26700 
.26703 

9.42954 
.42959 
.42964 
.42969 

.26887 
.26890 
.26893 
.26896 

8 
7 
6 
5 

+    ir 

57 
58 
59 

9.41713 
.41718 
.41723 
.41729 

.26129 
.26133 
.36136 
.26139 

9.42031 
.42036 
.42041 
.42046 

.26321 
.26324 
.26328 
.26331 

9.42347 
.42352 
.42357 
.42363 

.26514 
.26517 
.26520 
.26523 

9.42662 
.42667 
.42672 
.42677 

.26706 
.26710 
.26713 
.26716 

9.42975 
.42980 
.42985 
.42990 

.26900 
.36903 
.36906 
.36909 

4 
3 
2 
1 

+   W 

9.41734 

.26142 

9.42052 

.26334 

9.42368 

.26536 

9.42682 

.26719 

9.42996 

.36913 

0 

19Ji  54™' 

19h  53m 

19^  52m 

i9ft  5lm 

19^  50m         1 

TABLE  45.                  [Page  861 

Haversines. 

s 

4hl0m&i°W 

4h  11m  62°  45' 

4^  12^  63°  0' 

4^  13m  63°  15' 

4h  14"^  63°  W 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.42996 
.43001 
.43006 
.43011 

.26913 
.26916 
.26919 
.26922 

9.43307 
.43312 
.43317 
.43323 

.27106 
.27110 
.27113 
.27116 

9.43617 
.43622 
.43627 
.43632 

.27300 
.27304 
.27307 
.27310 

9.43926 
.43931 
.43936 
.43941 

.27495 
.27498 
.27502 
.27505 

9.44232 
.44238 
.44243 
.44248 

.27690 
.27693 
.27697 
.27700 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 

+    r 

5 
6 

7 

9.43016 
.43022 
.43027 
.43032 

.26925 
.26929 
.26932 
.26935 

9.43328 
.43333 
.43338 
.43343 

.27119 
.27122 
.27126 
.27129 

9.43638 
.43643 
.43648 
.43653 

.27313 
.27317 
.27320 
.27323 

9.43946 
.43951 
.43956 
.43961 

.27508 
.27511 
.27515 
.27518 

9.44253 

.44258 
.44263 
.44268 

.27703 
.27706 
.27710 
.27713 

+   2^ 

9 

10 

11 

9.43037 
.43042 
.43048 
.43053 

.26938 
.26942 
.26945 
.26948 

9.43348 
.43354 
.43359 
.43364 

.27132 
.27135 
.27139 
.27142 

9.43658 
.43663 
.43669 
.43674 

.27326 
.27330 
.27333 
.27336 

9.43967 
.43972 
.43977 
.43982 

.27521 
.27524 
.27528 
.27531 

9.44273 

.44278 
.44283 
.44289 

.27716 
.27719 
.27723 
.27726 

+   3^ 

13 
14 
15 

9.43058 
.43063 
.43068 
.43074 

.26951 
.26955 
.26958 
.26961 

9.43369 
.43374 
.43380 
.43385 

.27145 
.27148 
.27152 
.27155 

9.43679 
.43684 
.43689 
.43694 

.27339 
.27343 
.27346 
.27349 

9.43987 
.43992 
.43997 
.44002 

.27534 
.27537 
.27541 
.27544 

9.44294 
.44299 
.44304 
.44309 

.27729 
.27732 
.27736 
.27739 

48 
47 
46 
45 

17 
18 
19 

9.43079 
.43084 
.43089 
.43094 

.26964 
.26967 
.26971 
.26974 

9.43390 
.43395 
.43400 
.43405 

.27158 
.27161 
.27165 
.27168 

9.43699 
.43705 
.43710 
.43715 

.27352 
.27356 
.27359 
.27362 

9.44008 
.44013 
.44018 
.44023 

.27547 
.27550 
.27554 
.27557 

9.44314 
.44319 
.44324 
.44329 

.27742 
.27745 
.27749 
.27752 

44 
43 
42 
41 

+      5' 
21 
22 
23 

9.43100 
.43105 
.43110 
.43115 

.26977 
.26980 
.26984 
.26987 

9.43411 
.43416 
.43421 
.43426 

.27171 
.27174 
.27177 
.27181 

9.43720 
.43725 
.43730 
.43735 

.27365 
.27369 
.27372 
.27375 

9.44028 
.44033 
.44038 
.44043 

.27560 
.27563 
.27567 
.27570 

9.44334 
.44340 
.44345 
.44350 

.27755 
.27758 
.27762 
.27765 

40 
39 
38 
S7 
36 
35 
34 
S3 

+      6' 

25 
26 
27 

9.43120 
.43126 
.43131 
.43136 

.26990 
.26993 
.26996 
.27000 

9.43431 
.43436 
.43442 
.43447 

.27184 
.27187 
.27190 
.27194 

9.43741 
.43746 
.43751 
.43756 

.27378 
.27382 
.27385 

.27388 

9.44048 
.44054 
.44059 
.44064 

.27573 
.27576 
.27580 
.27683 

9.44355 
.44360 
.44365 
.44370 

.27768 
.27772 
.27775 

.27778 

+    r 

29 
SO 
31 

9.43141 
.43146 
.43151 
43157 

.27003 
.27006 
.27009 
.27013 

9.43452 
.43457 
.43462 
.43467 

.27197 
.27200 
.27203 
.27207 

9.43761 
.43766 
.43771 
.43777 

.27391 
.27394 
.27398 
.27401 

9.44069 
.44074 
.44079 
.44084 

.27586 
.27589 
.27593 
.27596 

9.44375 
.44380 
.44385 
.44390 

.27781 

.27785 
.27788 
.27791 

S2 
SI 
30 
29 

+   8' 
S3 
34 
S5 

9.43162 
.43167 
.43172 
.43177 

.27016 
.27019 
.27022 
.27025 

9.43473 
.43478 
.43483 
.43488 

.27210 
.27213 
.27216 
.27220 

9.43782 
.43787 
.43792 
.43797 

.27404 
.27407 
.27411 
.27414 

9.44089 
.44095 
.44100 
.44105 

.27599 
.27602 
.27606 
.27609 

9.44396 
.44401 
.44406 
.44411 

.27794 
.27798 
.27801 
.27804 

28 
27 
26 
25 

+   9^ 

37 
38 
39 

9.43183 
.43188 
.43193' 
.43198 

.27029 
.27032 
.27035 
.27038 

9.43493 
.43498 
.43504 
.43509 

.27223 
.27226 
.27229 
.27232 

9.43802 
.43807 
.43813 
.43818 

.27417 
.27420 
.27424 
.27427 

9.44110 
.44115 
.44120 
.44125 

.27612 
.27615 
.27619 
.27622 

9.44416 
.44421 
.44426 
.44431 

.27807 
.27811 
.27814 
.27817 

24 
23 
22 
21 

+  W 

41 

42 
43 

9.43203 
.43209 
.43214 
.43219 

.27042 
.27045 
.27048 
.27051 

9.43514 
.43519 
.43524 
.43529 

.27236 
.27239 
.27242 
.27245 

9.43823 
.43828 
.43833 
.43838 

.27430 
.27433 
.27437 
.27440 

9.44130 
.44135 
.44141 
.44146 

.27625 
.27628 
.27632 
.27635 

9.44436 
.44441 
.44446 
.44452 

.27820 
.27824 

.27827 
.27830 

20 
19 
18 
17 

+  n' 

45 
46 
47 

9.43224 
.43229 
.43234 
.43240 

.27055 
.27058 
.27061 
.27064 

9.43535 
.43540 
.43545 
.43550 

.27249 
.27252 
.27255 
.27258 

9.43843 
.43849 
.43854 
.43859 

.27443 
.27446 
.27450 
.27453 

9.44151 
.44156 
.44161 
.44166 

.27638 
.27641 
.27645 
.27648 

9.44457 
.44462 
.44467 
.44472 

.27833 
.27837 
.27840 
.27843 

16 
15 
14 
IS 

+    ir 

49 
50 
51 

9.43245 
.43250 
.43255 
.43260 

.27068 
.27071 
.27074 
.27077 

9.43555 
.43560 
.43565 
.43571 

.27262 
.27265 
.27268 
.27271 

9.43864 
.43869 
.43874 
.43879 

.27456 
.27459 
.27463 
.27466 

9.44171 
44176 
.44181 
.44187 

.27651 
.27654 
.27658 
.27661 

9.44477 
.44482 
.44487 
.44492 

.27846 
.27850 
.27853 
.27856 

12 

11 

10 

9 

+    W 

53 

54 
55 

9.43266 
.43271 
.43276 
.43281 

.27080 
.27084 
.27087 
.27090 

9.43576 
.43581 
.43586 
.43591 

.27275 

.27278 
.27281 
.27284 

9.43884 
.43890 
.43895 
.43900 

.27469 
.27472 
.27476 
.27479 

9.44192 
.44197 
.44202 
.44207 

.27664 
.27667 
.27671 
.27674 

9.44497 
.44502 
.44507 
.44513 

.27859 
.27863 
.27866 
.27869 

8 
7 
6 
6 

4 
S 
2 
1 
0 

+    W 

57 
58 
59 

9.43286 
.43291 
.43297 
.43302 

.27093 
.27097 
.27100 
.27103 

9.43596 
.43602 
.43607 
.43612 

.27288 
.27291 
.27294 
.27297 

9.43905 
.43910 
.43915 
.43920 

.27482 
.27485 
.27489 
.27492 

9.44212 
.44217 
.44222 
.44227 

.27677 
.27680 
.27684 
.27687 

9.44518 
.44523 
.44528 
.44533 

.27873 
.27876 
.27879 

.27882 

+  W 

9.43307 

.27106 

9.43617 

.27300 

9.43926 

.27495 

9.44232 

.27690 

9.44538 

.27886 

19^  49m 

19h48m, 

ign  47m 

19^46^ 

19h45m 

Page  862]                 TABLE  45. 

Haversinea. 

s 

4h  15m  63°  45' 

4h  16m  64°  0' 

4h  17m  64°  15' 

4h  18m  64°  3^ 

4h  19m  64°  45' 

3 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.44538 
.44543 
.44548 
.44553 

.27886 

.27889 
.27892 
.27895 

9.44842 
.44847 
.44852 
.44857 

.28081 

.38085 
.28088 
.28091 

9.45144 
.45149 
.45155 
.45160 

.28278 
.28281 
.28284 
.28288 

9.45446 
.45451 
.45456 
.45461 

.28474 
.28478 
.28481 
.28484 

9.45745 
.45750 
.45755 
.45760 

.28672 
.28675 

.28678 
.28681 

60 
59 

58 
57 

+      y 

5 
6 

7 

9.44558 
.44563 
.44568 
.44573 

.27899 
.27902 
.27905 
.27908 

9.44862 
.44867 
.44872 

.44877 

.28095 
.28098 
.28101 
.28104 

9.45165 
.45170 
.45175 
.45180 

.28291 
.38394 
.38397 
.38301 

9.45466 
.45471 
.45476 
.45481 

.38488 
.38491 
.38494 
.38497 

9.45765 
.45770 
.45775 
.45780 

.28685 
.38688 
.38691 
.28695 

56 
55 
54 
53 

+      V 

9 

10 

11 

9.44579 
.44584 
.44589 
.44594 

.27912 
.27915 
.27918 
.27921 

9.44882 
.44887 
.44892 
.44898 

.28108 
.28111 
.28114 
.28117 

9.45185 
.45190 
.45195 
.45200 

.38304 
.38307 
.38310 
.38314 

9.45486 
.45491 
.45496 
.45501 

.38501 
.38504 
.38507 
.38511 

9.45785 
.45790 
.45795 
.45800 

.28698 
.28701 
.28704 

.28708 

52 
51 
50 
49 

+   3' 
13 
14 
15 

9.44599 
.44604 
.44609 
.44614 

.27925 
.27928 
.27931 
.27935 

9.44903 
.44908 
.44913 
.44918 

.28121 
.28124 
.28127 
.28130 

9.45205 
.45210 
.45215 
.45220 

.28317 
.28320 
.28324 
.28337 

9.45506 
.45511 
.45516 
.45521 

.38514 
.38517 
.38530 
.28524 

9.45805 
.45810 
.45815 
.45820 

.28711 
.28714 

.28718 
.28721 

48 
47 
46 
45 

+   *' 
17 
18 
19 

9.44619 
.44624 
.44629 
.44634 

.27938 
.27941 
.27944 
.27948 

9.44923 
.44928 
.44933 
.44938 

.28134 
.28137 
.28140 
.28144 

9.45225 
.45230 
.45235 
.45240 

.28330 
.28333 
.28337 
.28340 

9.45526 
.45531 
.45536 
.45541 

.28527 
.28530 
.28534 
.28537 

9.45825 
.45830 
.45835 
.45840 

.28724 

.28727 
.28731 
.38734 

44 
43 
42 
41 

+   5' 
21 

22 
23 

9.44639 
.44645 
.44650 
.44655 

.27951 
.27954 
.27957 
.27961 

9.44943 
.44948 
.44953 
.44958 

.28147 
.28150 
.28153 
.28157 

9.45245 
.45250 
.45255 
.45260 

.28343 
.28347 
.28350 
.28353 

9.45546 
.45551 
.45556 
.45561 

.28540 
.28543 
.28547 
.38550 

9.45845 
.45850 
.45855 
.45860 

.38737 
.38741 
.28744 

.28747 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.44660 
.44665 
.44670 
.44675 

.27964 
.27967 
.27970 
.37974 

9.44963 
.44968 
.44973 
.44978 

.38160 
.38163 
.38166 
.38170 

9.45265 
.45270 
.45275 
.45280 

.28356 
.28360 
.28363 
.28366 

9.45566 
.45571 
.45576 
.45581 

.38553 

.38557 
.38560 
.28563 

9.45865 
.45870 
.45875 
.45879 

.28751 
.28754 

.28757 
.28760 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.44680 
.44685 
.44690 
.44695 

.27977 
.27980 
.27983 
.27987 

9.44983 
.44988 
.44993 
.44998 

.38173 
.38176 
.28180 

.28183 

9.45285 
.45290 
.45295 
.45300 

.28369 
.28373 
.28376 
.28379 

9.45586 
.45591 
.45596 
.45601 

.28566 
.28570 
.28573 
.38576 

9.45884 
.45889 
.45894 
.45899 

.28764 
.28767 
.28770 
.28774 

32 
31 
30 
29 
28 
27 
26 
25 

+   8' 
33 
34 
35 

9.44700 
.44705 
.44710 
.44715 

.27990 
.27993 
.37997 
.28000 

9.45003 
.45009 
.45014 
.45019 

.28186 
.28189 
.28193 
.28196 

9.45305 
.45310 
.45315 
.45320 

.28383 
.28386 
.28389 
.28392 

9.45606 
.45610 
.45615 
.45620 

.38580 

.38583 
.38586 
.28589 

9.45904 
.45909 
.45914 
.45919 

.38777 
.38780 

.28783 
.28787 

+  9^ 

37 
38 
39 

9.44721 
.44726 
.44731 
.44736 

.28003 
.28006 
.28010 
.28013 

9.45024 
.45029 
.45034 
.45039 

.28199 
.28202 
.28206 
.28309 

9.45325 
.45330 
.45335 
.45340 

.28396 
.38399 
.28402 
.28406 

9.45625 
.45630 
.45635 
.45640 

.28593 
.28596 
.28599 
.28603 

9.45924 
.45929 
.45934 
.45939 

.28790 
.28793 
.28797 
.38800 

24 

23 
22 
21 

41 

42 
43 

9.44741 
.44746 
.44751 
.44756 

.28016 
.28019 
.28023 
.28026 

9.45044 
.45049 
.45054 
.45059 

.28213 
.38316 
.38319 
.38223 

9.45345 
.45350 
.45355 
.45360 

.28409 
.28412 
.28415 
.28419 

9.45645 
.45650 
.45655 
.45660 

.28606 
.28609 
.28612 
.28616 

9.45944 
.45949 
.45954 
.45959 

.38803 

.38807 
.38810 
.38813 

20 
19 
18 
17 

+  11^ 

45 
46 
47 

9.44761 
.44766 
.44771 
.44776 

.28039 
.38033 
.38036 
.38039 

9.45064 
.45069 
.45074 
.45079 

.28235 
.38239 
.28232 
.28235 

9.45365 
.45370 
.45375 
.45380 

.28423 
.38435 
.38439 
.28432 

9.45665 
.45670 
.45675 
.45680 

.28619 
.28633 
.38626 
.38639 

9.45964 
.45969 
.45974 
.45979 

.28816 
.28820 

.38833 
.38836 

16 
15 
14 
13 

+  n' 

49 
50 
51 

9.44781 
.44786 
.44791 
.44796 

.28042 
.28046 
.28049 
.28052 

9.45084 
.45089 
.45094 
.45099 

.38338 
.38342 
.28245 

.28248 

9.45385 
.45390 
.45395 
.45400 

.28435 
.28438 
.38442 
.28445 

9.45685 
.45690 
.45695 
.45700 

.38633 
.28635 
.28639 
.28642 

9.45984 
.45989 
.45994 
.45999 

.38830 
.28833 
.28836 
.28839 

12 
11 
10 
9 
8 
7 
6 
5 

+    13' 

53 
54 
55 

9.44801 
.44807 
.44812 
.44817 

.28055 
.28059 
.28062 
.38065 

9.45104 
.45109 
.45114 
.45119 

.28253 
.28255 
.28358 
.38361 

9.45405 
.45410 
.45415 
.45420 

.28448 
.28451 
.28455 

.38458 

9.45705 
.45710 
.45715 
.45720 

.38645 
.38649 
.28652 
.28655 

9.46004 
.46009 
.46014 
.46019 

.28843 
.28846 
.28849 

.28853 

+    1¥ 

57 
58 
59 

9.44822 
.44827 
.44832 
.44837 

.38068 
.28072 
.28075 

.28078 

9.45124 
.45129 
.45134 
.45139 

.38265 
.28268 
.28271 
.28274 

9.45426 
.45431 
.45436 
.45441 

.28461 
.28465 
.28468 
.28471 

9.45725 
.45730 
.45735 
.45740 

.28658 
.28663 
.28665 
.28668 

9.46023 
.46028 
.46033 
.46038 

.28856 
.28859 
.38863 
.38866 

4 
3 
2 
"1 
0 

+  15' 

9.44842 

.28081 

9.45144 

.28278 

9.45446 

.28474 

9.45745 

.38672 

9.46043 

.28869 

I9I1  44m 

IQJi  43m 

19h  42m 

19n  41m 

19h4&m         1 

TABLE  45.                 [Page  863 

Haversines. 

s 

41^  2(y>n  65°  (K 

4h  21m  65°  15^ 

4h  22m  65°  W 

41^  23m  65°  45' 

4^  24^  66°  C 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.46043 
.46048 
.46053 
.46058 

.28869 

.28872 
.38876 

.28879 

9.46340 
.46345 
.46350 
.46355 

.29067 
.29070 
.29074 
.29077 

9.46635 
.46640 
.46645 
.46650 

.29265 
.29269 
.29272 
.29275 

9.46929 
.46934 
.46939 
.46944 

.29464 
.29467 
.29471 
.29474 

9.47222 
.47227 
.47231 
.47236 

.29663 
.29666 
.29670 
.29673 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.46063 
.46068 
.46073 
.46078 

.28882 
.28886 
.28889 
.28892 

9.46360 
.46365 
.46370 
.46375 

.29080 
.29084 
.29087 
.29090 

9.46655 
.46660 
.46665 
.46670 

.29279 
.29282 
.29285 
.29289 
.29292 
.29295 
.29298 
.29302 

9.46949 
.46954 
.46959 
.46963 

9.46968 
.46973 
.46978 
.46983 

.29477 
.29481 
.29484 
.29487 

9.47241 
.47246 
.47251 
.47256 

.29676 
.29680 
.29683 
.29686 
.29690 
.29693 
.29696 
.29700 

56 
55 
64 
53 
52 
51 
50 
49 
48 
47 
46 
45 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
SO 
29 
28 
27 
26 
25 

24 
23 
22 
21 

+     3' 

9 

10 

11 

9.46083 
.46088 
.46093 
.46098 

.28895 
.28899 
.28902 
.28905 

9.46380 
.46384 
.46389 
.46394 

.29093 
.29097 
.29100 
.29103 

9.46675 
.46680 
.46684 
.46689 

.29491 
.29494 
.29497 
.29501 

9.47261 
.47266 
.47270 
.47275 

+   3^ 

IS 
14 
15 

9.46103 
.46108 
.46113 
.46118 

.28909 
.28912 
.28915 
.28918 

9.46399 
.46404 
.46409 
.46414 

.29107 
.29110 
.29113 
.29117 

9.46694 
.46699 
.46704 
.46709 

.29305 
.29308 
.29312 
.29315 

9.46988 
.46993 
.46998 
.47003 

.29504 
.29507 
.29510 
.29514 

9.47280 
.47285 
.47290 
.47295 

.29703 
.29706 
.29710 
.29713 

+     i' 
17 
18 
19 

9.46123 
.46128 
.46132 
.46137 

.28922 
.28925 

.28928 
.28932 

9.46419 
.46424 
.46429 
.46434 

.29120 
.29123 
.29126 
.29130 

9.46714 
.46719 
.46724 
.46729 

.29318 
.29322 
.29325 
.29328 

9.47007 
.47012 
.47017 
.47022 

.29517 
.29520 
.29524 
.29527 

9.47300 
.47304 
.47309 
.47314 

.29716 
.29720 
.29723 
.29726 

+      5' 

21 

22 
23 

9.46142 
.46147 
.46152 
.46157 

.28935 
.28938 
.28942 
.28945 

9.46439 
.46444 
.46448 
.46453 

.29133 
.29136 
.29140 
.29143 

9.46733 
.46738 
.46743 
.46748 

.29332 
.29335 
.29338 
.29341 

9.47027 
.47032 
.47037 
.47042 

.29530 
.29534 
.29537 
.29540 

9.47319 
.47324 
.47329 
.47334 

.29730 
.29733 
.29736 
.2974* 
.29743 
.29746 
.29750 
.29753 

+      6^ 

25 
26 

27 

9.46162 
.46167 
.46172 
.46177 

.28948 
.28952 
.28955 

.28958 

9.46458 
.46463 
.46468 
.46473 

9.46478 
.46483 
.46488 
.46493 

9.46498 
.46503 
.46508 
.46512 

.29146 
.29150 
.29153 
.29156 

9.46753 
.46758 
.46763 
.46768 

.29345 
.29348 
.29351 
.29355 

9.47046 
.47051 
.47056 
.47061 

.29544 
.29547 
.29550 
.29554 

9.47338 
.47343 
.47345 
.47353 

+    r 

29 
SO 
31 

9.46182 
.46187 
.46192 
.46197 

.28961 
.28965 
.28968 
.28971 

.29160 
.29163 
.29166 
.29169 
.29173 
.29176 
.29179 
.29183 

9.46773 
.46778 
.46782 
.46787 

9.46792 
.46797 
.46802 
.46807 

.29358 
.29361 
.29365 
.29368 
.29371 
.29375 
.29378 
.29381 

9.47066 
.47071 
.47076 
.47081 

.29557 
.29560 
.29564 
.29567 

9.47358 
.47363 
.47367 
.47372 

.29756 
.29760 
.29763 
.29766 

+     8' 
33 
34 
35 

9.46202 
.46207 
.46212 
.46217 

.28975 

.28978 
.28981 

.28985 

9.47085 
.47090 
.47095 
.47100 

.29570 
.29573 
.29577 
.29580 

9.47377 
.47382 
.47387 
.47392 

.29770 
.29773 
.29776 
.29779 

+     9^ 

37 
38 
39 

9.46222 
.46226 
.46231 
.46236 

.28988 
.28991 
.28994 
.28998 

9.46517 
.46522 
.46527 
.46532 

.29186 
.29189 
.29193 
.29196 

9.46812 
.46817 
.46822 
.46827 

.29385 
.29388 
.29391 
.29394 

9.47105 
.47110 
.47115 
.47120 

.29583 
.29587 
.29590 
.29593 

9.47397 
.47401 
.47406 
.47411 

.29783 
.29786 
.29789 
.29793 

+  W 

41 
42 
43 

9.46241 
.46246 
.46251 
.46256 

.29001 
.29004 
.29008 
.29011 

9.46537 
.46542 
.46547 
.46552 

.29199 
.29202 
.29206 
.29209 

9.46831 
.46836 
.46841 
.46846 

.29398 
.29401 
.29404 
.29408 

9.47124 
.47129 
.47134 
.47139 

.29597 
.29600 
.29603 
.29607 

9.47416 
.47421 
.47426 
.47431 

.29796 
.29799 
.29803 
.29806 
.29809 
.29813 
.29816 
.29819 

20 
19 
18 
17 
16 
15 
14 
13 

+  ir 

45 
46 

47 

9.46261 
.46266 
.46271 
.46276 

.29014 
.29017 
.29021 
.29024 

9.46557 
.46562 
.46567 
.46571 

.29212 
.29216 
.29219 
.29222 

9.46851 
.46856 
.46861 
.46866 

.29411 
.29414 
.29418 
.29421 

9.47144 
.47149 
.47154 
.47159 

.29610 
.29613 
.29617 
.29620 

9.47435 
.47440 
.47445 
.47450 

+  n' 

49 
50 
51 

9.46281 
.46286 
.46291 
.46296 

.29027 
.29031 
.29034 
.29037 

9.46576 
.46581 
.46586 
.46591 

.29226 
.29229 
.29232 
.29236 

9.46871 
.46875 
.46880 
.46885 

.29424 
.29428 
.29431 
.29434 

9.47163 
.47168 
.47173 
.47178 

.29623 
.29627 
.29630 
.29633 

9.47455 
.47460 
.47464 
.47469 

.29823 
.29826 
.29829 
.29833 

12 
11 
10 
9 
8 
7 
6 
5 

+  13^ 

53 
54 
55 

9.46301 
.46305 
.46310 
.46315 

.29041 
.29044 
.29047 
.29051 

9.46596 
.46601 
.46606 
.46611 

.29239 
.29242 
.29245 
.29249 

9.46890 
.46895 
.46900 
.46905 

.29438 
.29441 
.29444 
.29447 

9.47183 
.47188 
.47193 
.47197 

.29637 
.29640 
.29643 
.29647 

9.47474 
.47479 
.47484 
.47489 

.29836 
.29839 
.29843 
.29846 

+  W 

57 
58 
59 

9.46320 
.46325 
.46330 
.46335 

.29054 
.29057 
.29060 
.29064 

9.46616 
.46621 
.46626 
.46630 

.29252 
.29255 
.29259 
.29262 

9.46910 
.46915 
.46919 
.46924 

.29451 
.29454 
.29457 
.29461 

9.47202 
.47207 
.47212 
.47217 

.29650 
.29653 
.29657 
.29660 

9.47493 
.47498 
.47503 
.47508 

.29849 
.29853 
.29856 
.29859 

4 
3 

2 

1 

+  15^ 

9.46340 

.29067 

9.46635 

.29265 

9.46929 

.29464 

9.47222 

.29663 

9.47513 

.29863 

0 

19^  39m 

19h 38m 

19h  37m 

19^3&n 

19h  SSm         1 

Page864J                  TABLE  45. 

Haversinea. 

s 

4'^  25^'  66°  15' 

4^  26^  66°  Sr 

4h  27m  66°  45' 

4h  28m  67°  C 

4h  29m  67°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.47513 
.47518 
.47523 
.47527 

.39863 
.39866 
.29869 
.29873 

9.47803 
.47807 
.47812 
.47817 

.30063 
.30066 
.30069 
.30073 

9.48091 
.48096 
.48101 
.48105 

.30263 
.30266 
.30269 
.30273 

9.48378 
.48383 
.48387 
.48392 

.30463 
.30467 
.30470 
.30473 

9.48664 
.48668 
.48673 
.48678 

.30664 
.30668 
.30671 
.30675 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+    r 

5 
6 
7 

9.47532 
.47537 
.47542 
.47547 

.29876 
.29879 
.29883 
.29886 

9.47822 
.47827 
.47831 
.47836 

.30076 
.30079 
.30083 
.30086 

9.48110 

.48115 
.48120 
.48124 

.30276 
.30280 
.30283 
.30286 

9.48397 
.48402 
.48407 
.48411 

.30477 
.30480 
.30484 
.30487 

9.48683 
.48687 
.48692 
.48697 

9.48702 
.48706 
.48711 
.48716 

.30678 
.30681 
.30685 
.30688 
.30691 
.30695 
.30698 
.30701 

+     3' 

9 

10 

11 

9.47552 
.47556 
.47561 
.47566 

.29889 
.29893 
.29896 
.29899 

9.47841 
.47846 
.47851 
.47856 

.30089 
.30093 
.30096 
.30099 

9.48129 
.48134 
.48139 
.48144 

.30290 
.30293 
.30296 
.30300 

9.48416 
.48421 
.48426 
.48430 

.30490 
.30494 
.30497 
.30500 

+     3^ 

13 
14 
15 

9.47571 
.47576 
.47581 
.47585 

.29903 
.29906 
.29909 
.29913 

9.47860 
.47865 
.47870 

.47875 

.30103 
.30106 
.30109 
.30113 

9.48148 
.48153 
.48158 
.48163 

.30303 
.30306 
.30310 
.30313 

9.48435 
.48440 
.48445 
.48449 

.30504 
.30507 
.30510 
.30514 

9.48720 
.48725 
.48730 
.48735 

.30705 
.30708 
.30711 
.30715 

+  4^ 
17 
18 
19 

9.47590 
.47595 
.47600 

.47605 

.29916 
.29919 
.29923 
.29926 

9.47880 
.47884 
.47889 
.47894 

.30116 
.30119 
.30123 
.30126 

9.48168 
.48172 
.48177 
.48182 

.30316 
.30320 
.30323 
.30326 

9.48454 
.48459 
.48464 
.48468 

.30517 
.30520 
.30524 
.30527 

9.48739 

.48744 
.48749 
.48754 

.30718 
.30721 
.30725 
.30728 

U 
43 
42 
41 

+     5' 

21 
22 
23 

9.47610 
.47614 
.47619 
.47624 

.29929 
.29933 
.29936 
.29939 

9.47899 
.47904 
.47908 
.47913 

.30129 
.30133 
.30136 
.30139 

9.48187 
.48192 
.48196 
.48201 

.30330 
.30333 
.30336 
.30340 

9.48473 

.48478 
.48483 
.48488 

.30530 
.30534 
.30537 
.30540 

9.48758 
.48763 
.48768 
.48773 

.30732 
.30735 
.30738 
.30742 

40 
39 
38 
37 

+     6' 

25 
26 
27 

9.47629 
.47634 
.47639 
.47643 

.29943 
.29946 
.29949 
.29953 

9.47918 
.47923 
.47928 
.47933 

.30143 
.30146 
.30149 
.30153 

9.48206 
.48211 
.48215 
.48220 

.30343 
.30346 
.30350 
.30353 

9.48492 
.48497 
.48502 
.48507 

.30544 
.30547 
.30551 
.30554 

9.48777 
.48782 
.48787 
.48792 

.30745 
.30748 
.30752 
.30755 

36 
35 
34 
33 
32 
31 
SO 
29 
28 
27 
26 
25 

+    r 

29 
SO 
31 

9.47648 
.47653 
.47658 
.47663 

.29956 
.29959 
.29963 
.29966 

9.47937 
.47942 
.47947 
.47952 

.30156 
.30159 
.30163 
.30166 

9.48225 
.48230 
.48235 
.48239 

.30356 
.30360 
.30363 
.30366 

9.48511 
.48516 
.48521 
.48526 

.30557 
.30561 
.30564 
.30567 

9.48796 
.48801 
.48806 
.48811 

.30758 
.30762 
.30765 
.30768 

+     S' 
33 
34 
35 

9.47668 
.47672 
.47677 
.47682 

.29969 
.29973 
.29976 
.29979 

9.47957 
.47961 
.47966 
.47971 

.30169 
.30173 
.30176 
.30179 

9.48244 
.48249 
.48254 
.48258 

.30370 
.30373 
.30376 
.30380 

9.48530 

.48535 
.485^^0 
.48545 

.30571 
.30574 
.30577 
.30581 

9.48815 
.48820 
.48825 
.48830 

.30772 
.30775 
.30779 
.30782 

+  9' 

37 
38 
39 

9.47687 
.47692 
.47697 
.47701 

.29983 
.29986 
.29989 
.29993 

9.47976 
.47981 
.47985 
.47990 

.30183 
.30186 
.30189 
.30193 

9.48263 
.48268 
.48273 
.48278 

.30383 
.30386 
.30390 
.30393 

9.48549 
.48554 
.48559 
.48564 

.30584 
.30587 
.30591 
.30594 

9.48834 
.48839 
.48844 
.48848 

.30785 
.30789 
.30792 
.30795 

24 
23 

22 
21 

+  W 

41 

42 
43 

9.47706 
.47711 
.47716 
.47721 

.29996 
.29999 
.30003 
.30006 

9.47995 
.48000 
.48005 
.48009 

.30196 
.30199 
.30203 
.30206 

9.48282 
.48287 
.48292 
.48297 

.30397 
.30400 
.30403 
.30407 

9.48568 
.48573 
.48578 
.48583 

.30597 
.30601 
.30804 
.30607 

9.48853 

.48858 
.48863 
.48867 

.30799 
.30802 
.30805 
.30809 

20 
19 
18 
17 

+  11' 

45 
46 

47 

9.47725 
.47730 
.47735 
.47740 

.30009 
.30013 
.30016 
.30019 

9.48014 
.48019 
.48024 
.48029 

.30209 
.30213 
.30216 
.30219 

9.48302 
.48306 
.48311 
.48316 

.30410 
.30413 
.30417 
.30420 

9.48587 
.48592 
.48597 
.48602 

.30611 
.30614 
.30618 
.30621 

9.48872 
.48877 
.48882 
.48886 

.30812 
.30815 
.30819 
.30823 

16 
15 
14 
13 
12 
11 
10 
9 

+    12' 

49 
50 
51 

9.47745 
.47750 
.47754 
.47759 

.30023 
.30026 
.30029 
.30033 

9.48033 
.48038 
.48043 
.48048 

.30223 
.30226 
.30229 
.30233 

9.48321 
.48325 
.48330 
.48335 

.30423 
.30427 
.30430 
.30433 

9.48607 
.48611 
.48616 
.48621 

.30624 
.30628 
.30631 
.30634 

9.48891 
.48896 
.48901 
.48905 

.30826 
.30829 
.30832 
.30836 

+  13^ 

53 
54 
55 

9.47764 
.47769 

.47774 
.47778 

.30036 
.30039 
.30043 
.30046 

9.48053 
.48057 
.48062 
.48067 

.30236 
.30239 
.30243 
.30246 

9.48340 
.48344 
.48349 
.48354 

.30437 
.30440 
.30443 
.30447 

9.48626 
.48630 
.48635 
.48640 

.30638 
.30641 
.30644 
.30648 

9.48910 
.48915 
.48919 
.48924 

.30839 
.30842 
.30846 
.30849 

8 
7 
6 
5 

+    U' 

57 
58 
59 

9.47783 
.47788 
.47793 
.47798 

.30049 
.30053 
.30056 
.30059 

9.48072 
.48077 
.48081 
.48086 

.30249 
.30253 
.30256 
.30259 

9.48359 
.48364 
.48368 
.48373 

.30450 
.30453 
.30457 
.30460 

9.48645 
.48649 
.48654 
.48659 

.30651 
.30655 
.30658 
.30661 

9.48929 
.48934 
.48938 
.48943 

.30852 
.30856 
.30859 
.30862 

4 
3 

2 
1 

+  16' 

9.47803 

.30063 

9.48091 

.30263 

9.48378 

.30463 

9.48664 

.30664 

9.48948 

.30866 

0 

19Ji  34^ 

19h  SSm 

19h  s^ 

19^  Sim 

igf^  som 

TABLE  45.                 [Page  866 

Haversines. 

s 

4^S0m%l°W 

4^^  Sim  67"  45' 

.^ft  S2m  68°  C 

4hSsm6S''W 

4^  S4m  68"  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

9.48948 
.48953 
.48957 
.48962 

.30866 
.30869 
.30873 
.30876 

9.49231 
.49235 
.49240 
.49245 

.31068 
.31071 
.31074 
.31078 

9.49512 
.49517 
.49522 
.49226 

.31270 
.31273 
.31276 
.31280 

9.49793 
.49797 
.49802 
.49807 

.31472 
.31475 
.31479 
.31482 

9.50072 
.50076 
.50081 
.50085 

.31676 
.31678 
.31682 
.31685 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.48967 
.48971 
.48976 
.48981 

.30879 
.30883 
.30886 
.30889 

9.49250 
.49254 
.49259 
.49264 

.31081 
.31084 
.31088 
.31091 

9.49531 
.49536 
.49540 
.49545 

.31283 
.31287 
.31290 
.31293 

9.49811 
.49816 
.49821 
.49825 

.31486 
.31489 
.31492 
.31496 

9.50090 
.50095 
.50099 
.50104 

.31688 
.31693 
.31695 
.31699 

56 
55 
54 
53 

+      3^ 

9 

10 

11 

9.48986 
.48990 
.48995 
.49000 

.30893 
.30896 
.30899 
.30903 

9.49268 
.49273 
.49278 
.49282 

.31095 
.31098 
.31101 
.31105 

9.49550 
.49554 
.49559 
.49564 

.31297 
.31300 
.31303 
.31307 

9.49830 
.49835 
.49839 
.49844 

.31499 
.31503 
.31506 
.31509 

9.50109 
.50113 
.50118 
..50123 

.31703 
.31705 
.31709 
.31712 

52 
51 
50 
49 

+   3' 

IS 
14 
15 

9.49004 
.49009 
.49014 
.49019 

.30906 
.30910 
.30913 
.30916 

9.49287 
.49292 
.49297 
.49301 

.31108 
.31111 
.31115 
.31118 

9.49568 
.49573 
.49578 
.49583 

.31310 
.31314 
.31317 
.31320 

9.49849 
.49853 
.49858 
.49862 

.31513 
.31516 
.31619 
.31523 

9.50127 
.50132 
.50136 
.50141 

.31716 
.31719 
.31722 
.31726 

48 
47 
46 
45 

+   4^ 
17 
18 
19 

9.49023 
.49028 
.49033 
.49038 

.30920 
.30923 
.30926 
.30930 

9.49306 
.49311 
.49315 
.49320 

.31121 
.31125 
.31128 
.31132 

9.49587 
.49592 
.49597 
.49601 

.31324 
.31327 
.31330 
.31334 

9.49867 
.49872 
.49876 
.49881 

.31526 
.31530 
.31533 
.31536 

9.50146 
.50150 
.50155 
.50160 

.31729 
.31732 
.31736 
.31739 

44 
43 
42 
41 

+   6' 
21 
22 
23 

9.49042 
.49047 
.49052 
.49056 

.30933 
.30936 
.30940 
.30943 

9.49325 
.49329 
.49334 
.49339 

.31135 
.31138 
.31142 
.31145 

9.49606 
.49611 
.49615 
.49620 

.31337 
.31341 
.31344 
.31347 

9.49886 
.49890 
.49895 
.49900 

.31540 
.31543 
.31546 
.31550 

9.50164 
.50169 
.50174 
.50178 

.31742 
.31746 
.31749 
.31753 

40 
39 
38 
37 

+   6' 

25 
26 

27 

9.49061 
.49066 
.49071 
.49075 

.30946 
.30950 
.30953 
.30957 

9.49344 
.49348 
.49353 
.49358 

.31148 
.31152 
.31155 
.31158 

9.49625 
.49629 
.49634 
.49639 

.31351 
.31354 
.31357 
.31361 

9.49904 
.49909 
.49914 
.49918 

.31553 
.31557 
.31560 
.31563 

9.50183 
.50187 
.50192 
.50197 

.31756 
.31760 
.31763 
.31766 

36 
35 
34 
SS 

+    r 

29 
SO 
31 

9.49080 
.49085 
.49089 
.49094 

.30960 
.30963 
.30967 
.30970 

9.49362 
.49367 
.49372 
.49376 

.31162 
.31165 
.31169 
.31172 

9.49643 
.49648 
.49653 
.49657 

.31364 
.31367 
.31371 
.31374 

9.49923 
.49928 
.49932 
.49937 

.31567 
.31670 
.31573 
.31677 

9.50201 
.50206 
.50211 
.50215 

.31770 
.31773 
.31776 
.31780 

32 
31 
SO 
29 

+      8' 

S3 
34 
35 

9.49099 
.49104 
.49108 
.49113 

.30973 
.30977 
.30980 
.30983 

9.49381 
.49386 
.49390 
.49395 

.31175 
.31179 
.31182 
.31185 

9.49662 
.49667 
.49671 
.49676 

.31378 
.31381 
.31384 
.31388 

9.49942 
.49946 
.49951 
.49956 

.31680 
.31684 
.31587 

.31590 

9.50220 
.50224 
.50229 
.50234 

.31783 
.31787 
.31790 
.31793 

28 

27 
26 
25 

+   9' 

37 
38 
39 

9.49118 
.49122 
.49127 
.49132 

.30987 
.30990 
.30994 
.30997 

9.49400 
.49405 
.49409 
.49414 

.31189 
.31102 
.3119G 
.31199 

9.49681 
.49685 
.49690 
.49695 

.31391 
.31394 
.31398 
.31401 

9.4y9C0 
.49965 
.49969 
.49974 

.31694 
.31597 
.31601 
.31604 

9.50238 
.50243 
.50248 
.50252 

.31797 
.31800 
.31804 
.31807 

24 
23 
22 
21 
20 
19 
18 
17 

+  W 

41 

42 
43 

9.49137 
.49141 
.49146 
.49151 

.31000 
.31004 
.31007 
.31010 

9.49419 
.49423 
.49428 
.49433 

.31302 
.31206 
.31209 
.31212 

9.49699 
.49704 
.49709 
.49713 

.31405 
.31408 
.31411 
.31415 

9.49979 
.49983 
.49988 
.49993 

.31607 
.31611 
.31614 
.31617 

9.50257 
.50261 
.50266 
.50271 

.31810 
.31814 
.31817 
.31820 

+  ir 

45 
46 

47 

9.49155 
.49160 
.49165 
.49170 

.31014 
.31017 
.31020 
.31024 

9.49437 

.49442 
.49447 
.49451 

.31216 
.31219 
.31222 
.31226 

9.49718 
.49723 
.49727 
.49732 

.31418 
.31431 
.31435 
.31428 

9.49997 
.50002 
.50007 
.50011 

.31621 
.31C24 
.31628 
.31631 

9.50275 
.50280 
.50284 
.50289 

.31824 
.31827 
.31831 
.31834 

16 
15 
14 
13 

+    W 

49 
50 
51 

9.49174 
.49179 
.49184 
.49188 

.31027 
.31031 
.31034 
.31037 

9.49456 
.49461 
.49465 
.49470 

.31229 
.31233 
.31236 
.31239 

9.49737 
.49741 
.49746 
.49751 

.31432 
.314.35 
.31438 
.31442 

9.50016 
.50021 
.50025 
.50030 

.31634 
.31638 
.31641 
.31644 

9.50294 
.50298 
.50303 
.50308 

.31837 
.31841 
.31844 
.31848 

12 

11 

10 

9 

+  13' 

5S 
54 
55 

9.49193 
.49198 
.49202 
.49207 

.31041 
.31044 
.31047 
.31051 

9.49475 
.49480 
.49484 
.49489 

.31243 
.31246 
.31249 
.31253 

9.49755 
.49760 
.49765 
.49769 

.31445 
.31448 
.31452 
.31455 

9.50034 
.50039 
.50044 
.50048 

.31648 
.31651 
.31655 
.31658 

9.50312 
.50317 
.50.322 
.50326 

.31851 
.31854 
.31858 
.31861 

8 
7 
6 
5 

+  14' 

57 
58 
59 

9.49212 
.49217 
.49221 
.49226 

.31054 
.31057 
.31061 
.31064 

9.49494 
.49498 
.49503 
.49508 

.31256 
.31260 
.31263 
.31266 

9.49774 
.49779 
.49783 
.49788 

.31459 
.31462 
.31465 
.31469 

9.50053 
.50058 
.50062 
.50067 

.31661 
.31665 
.31668 
.31672 

9.50331 
.50335 
.50340 
.50345 

.31865 
.31868 
.31871 
.31876 

4 
3 

2 

1 

+  15' 

9.49231 

.31068 

9.49512 

.31270 

9.49793 

.31472 

9.50072 

.31675 

9.50349 

.31878 

0 

19^  29^ 

lOh  2Sm 

19h  27m 

19^  26m 

i9^  25m 

Page  866]                  TABLE  45. 

Haversines, 

s 

4h  35m  68°  45' 

4h  SG-m  69°  0' 

4h  37m  69°  15' 

4Ji  38m  69°  30' 

4h  39m  69°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3. 

9.50349 
.50354 
.50358 
.50363 

.31878 
.31881 
.31885 

.31888 

9.50626 
.50630 
.50635 
.50639 

.32082 
.32085 
.32088 
.32092 

9.50901 
.50905 
.50910 
.50914 

.33285 
.32289 
.32292 
.32296 

9.51174 
.51179 
.51184 
.51188 

.32490 
.32493 
.33496 
.33500 

9.51447 
.51452 
.51456 
.51461 

.33694 
.32698 
.32701 
.32704 

60 
59 
58 
57 
66 
65 
64 
63 
52 
61 
50 
49 

+    r 

5 
6 

7 

9.50368 
.50372 
.50377 
.50382 

.31892 
.31895 
.31898 
.31902 

9.50644 
.50649 
.50653 
.50658 

.32095 
.32099 
.32102 
.32105 

9.50919 
.50924 
.50928 
.50933 

.33299 
.32302 
.32306 
.32309 

9.51193 
.51197 
.51202 
.51206 

.33503 
.32507 
.32510 
.32513 

9.51465 
.51470 
.51474 
.51479 

.32708 
.32711 
.32715 
.32718 

+      V 

9 

10 

11 

9.50386 
.50391 
.50395 
.50400 

.31905 
.31909 
.31912 
.31915 

9.50662 
.50667 
.50672 
.50676 

.32109 
.32112 
.32116 
.32119 

9.50937 
.50942 
.50946 
.50951 

.32313 
.33316 
.32319 
.32323 

9.51211 
.51215 
.51220 
.51225 

.32517 
.33530 
.33524 
.32527 

9.51483 
.51488 
.51492 
.51497 

.32721 
.32735 
.33728 
.33732 

+  3' 

13 
14 
15 

9.50405 
.50409 
.50414 
.50418 

.31919 
.31922 
.31926 
.31929 

9.50681 
.50685 
.50690 
.50694 

.32132 
.32126 
.32129 
.32133 

9.50956 
.50960 
.50965 
.50969 

.32326 
.32330 
.32333 
.32336 

9.51229 
.51234 
.51238 
.51243 

.32531 
.32534 
.32537 
.32541 

9.51501 
.51506 
.51510 
.51515 

.32735 
.32738 
.32743 
.33745 

48 
47 
46 
45 

44 

■43 

42 

41 

+  4' 
17 
18 
19 

9.50423 
.50428 
.50432 
.50437 

.31932 
.31936 
.31939 
.31942 

9.50699 
.50704 
.50708 
.50713 

.32136 
.32139 
.32143 
.32146 

9.50974 
.50978 
.50983 
.50988 

.32340 
.32343 
.32347 
.32350 

9.51247 
.51252 
.51256 
.51261 

.33544 
.32547 
.32551 
.32554 

9.51519 
.51524 
.51529 
.51533 

.33749 
.32762 
.32756 
.33759 

+  5' 

21 
22 
23 

9.50442 
.50446 
.50451 
.50455 

.31946 
.31949 
.31953 
.31956 

9.50717 
.50722 
.50727 
.50731 

.32150 
.33153 
.32156 
.32160 

9.50992 
.50997 
.51001 
.51006 

.32353 
.32357 
.32360 
.32364 

9.51265 
.51270 
.51275 
.51279 

.32558 
.32561 
.32565 
.32568 

9.51538 
.51542 
.51547 
.51551 

.33762 
.33766 
.33769 
.33773 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.50460 
.50465 
.50469 
.50474 

.31959 
.31963 
.31966 
.31970 

9.50736 
.50740 
.50745 
.50750 

.33163 
.32166 
.32170 
.32173 

9.51010 
.51015 
.51019 
.51024 

.33367 
.33370 
.32374 
.33377 

9.51284 
.51288 
.51293 
.51297 

.33571 
.33575 

.32578 
.32582 

9.51556 
.51560 
.51565 
.51569 

.33776 
.33779 
.33783 
.33786 

36 

36 
34 
33 

+    r 

29 
30 
31 

9.50478 
.50483 
.50488 
.50492 

.31973 
.31976 
.31980 
.31983 
.31987 
.31990 
.31993 
.31997 

9.50754 
.50759 
.50763 
.50768 

.32177 
.33180 
.32183 
.32187 

9.51029 
.51033 
.51038 
.51042 

.33381 
.32384 

.32388 
.32391 

9.51302 
.51306 
.51311 
.51315 

.32585 

.33588 
.32592 
.33595 

9.51574 
.51578 
.51583 
.51587 

.33790 
.33793 
.33797 
.33800 

32 
31 
SO 
29 

+   8' 
33 
34 
35 

9.50497 
.50501 
.50506 
.50511 

9.50772 
.50777 
.50782 
.50786 

.32190 
.32194 
.32197 
.32200 

9.51047 
.51051 
.51056 
.51061 

.33394 
.32398 
.32401 
.33405 

9.51320 
.51325 
.51329 
.51334 

.33599 
.33602 
.33605 
.32609 

9.51592 
.51596 
.51601 
.51605 

.33803 
.32807 
.33810 
.33814 

28 
27 
26 
25 

+   9^ 

37 
38 
39 

9.50515 
.50520 
.50524 
.50529 

.32000 
.32004 
.32007 
.32010 

9.50791 
.50795 
.50800 
.50805 

.33304 
.33207 
.33211 
.32214 

9.51065 
.51070 
.51074 
.51079 

.33408 
.32411 
.32415 
.33418 

9.51338 
.51343 
.51347 
.51352 

.32612 
.32616 
.32619 
.32633 

9.51610 
.51614 
.51619 
.51623 

.33817 
.33830 
.33834 
.32837 

24 
28 
22 
21 
20 
19 
18 
11 

+  10' 

41 
42 
43 

9.50534 
.50538 
.50543 
.50547 

.32014 
.32017 
.32021 
.32024 

9.50809 
.50814 
.50818 
.50823 

.32217 
.33331 
.33334 
.32228 

9.51083 
.51088 
.51092 
.51097 

.33422 
.33435 
.33438 
.32432 

9.51356 
.51361 
.51365 
.51370 

.33636 
.33639 
.33633 
.33636 

9.51628 
.51633 
.51637 
.51642 

.33831 
.33834 
.33838 
.33841 

+  11^ 

45 
46 
47 

9.50552 
.50557 
.50561 
.50566 

.32027 
.32031 
.32034 
.32037 

9.50827 
.50832 
.50837 
.50841 

.32231 
.33335 
.33338 
.33341 

9.51102 
.51106 
.51111 
.51115 

.33435 
.33438 
.32442 
.32445 

9.51374 
.51379 
.51384 
.51388 

.33640 
.32643 
.32646 
.32650 

9.51646 
.51651 
.51655 
.51660 

.33844 
.33848 
.33851 
.33855 

16 

15 

14 

IS 

12 

11 

10 

9 

8 

7 

6 

5 

+   12' 

49 
50 
61 

9.50570 
.50575 
.50580 
.50584 

.32041 
.32044 
.32048 
.32051 

9.50846 
.50850 
.50855 
.50860 

.32245 
.32248 
.32251 
.32355 

9.51120 
.51124 
.51129 
.51133 

.32449 
.32452 
.32456 
.33459 

9.51393 
.51397 
.51402 
.51406 

.32653 
.32657 
.32660 
.32663 

9.51664 
.51669 
.51673 
.51678 

.32858 
.32861 
.32865 
.32868 

+  13' 

53 
54 
65 

9.50589 
.50593 
.50598 
.50603 

.32054 
.32058 
.32061 
.32065 

9.50864 
.50869 
.50873 
.50878 

.32258 
.32262 
.32265 
.32268 

9.51138 
.51143 
.31147 
.51152 

.32462 
.32466 
.32469 
.32473 

9.51411 
.51415 
.51420 
.51424 

.32667 
.32670 
.32674 
.32677 

9.51682 
.51687 
.51691 
.51696 

.33873 
.33875 

.33878 
.32882 

+  14' 

57 
58 
69 

9.50607 
.50612 
.50616 
.50621 

.32068 
.32071 
.32075 
.32078 

9.50882 
.50887 
.50892 
.50896 

.33272 
.32275 
.32279 
.32282 

9.51156 
.51161 
.51165 
.51170 

.32476 
.32479 
.32483 
.32486 

9.51429 
.51433 
.51438 
.51442 

.32681 
.33684 
.33687 
.33691 

9.51700 
.51705 
.51709 
.51714 

.32885 
.32889 
.32892 
.33896 

4 

8 

2 
1 

+  15' 

9.50626 

.32082 

9.50901 

.32385 

9.51174 

.33490 

9.51447 

.32694 

9.51718 

.33899 

0 

jgh  24m 

igh  2Sm 

i9h  22m 

19h  21m 

19^  20m. 

TABLE  45.                 [Page  867 

Havereines. 

3 

4A  40TO  70°  r 

4h  41m  70°  15^ 

4h  4pn  70°  30^ 

411 43m  70°  45^ 

4h  44m  710  0/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

9.51718 
.51723 
.51727 
.51732 

.32899 
.32902 
.32906 
.32909 

9.51988 
.51993 
.51997 
.52002 

.33104 
.33108 
.33111 
.33114 

9.52257 
.52261 
.52266 
.52270 

.33310 
.33313 
.33317 
.33320 

9.52525 
.52529 
.52533 
.52538 

.33515 
.33519 
.33522 
.33526 

9.52791 
.52795 
.52800 
.52804 

.33722 
.33725 
.33728 
.33732 

60 
59 
58 
57 
56 
55 
54 
53 

+   1' 

5 
6 
7 

9,51736 
.51741 
.51745 
.51750 

.32913 
.32916 
.32920 
.32923 

9.52006 
.52011 
.52015 
.52020 

.33118 
.33121 
.33125 
.33128 

9.52275 
.52279 
.52284 
.52288 

.33323 
.33327 
.33330 
.33334 

9.52542 
.52547 
.52551 
.52556 

.33529 
.33533 
.33536 
.33540 

9.52809 
.52813 
.52817 
.52822 

.33735 
.33739 
.33742 
.33746 

9 
10 
11 

9.51754 
.51759 
.51763 
.51768 

.32926 
.32930 
.32933 
.32937 

9.52024 
.52029 
.52033 
.52038 

.33132 
.33135 
.33138 
.33142 

9.52293 
.52297 
.52302 
.52306 

.33337 
.33341 
.33344 
.33347 

9.52560 
.52565 
.52569 
.52573 

.33543 
.33546 
.33550 
.33553 

9.52826 
.52831 
.52835 
.52839 

.33749 
.33753 
.33756 
.33759 

52 
51 
50 
49 
48 
47 
46 
45 

+     9" 

IS 
14 
15 

9.51772 
.51777 
.51781 
.51786 

.32940 
.32943 
.32947 
.32950 

9.52042 
.52047 
.52051 
.52056 

.33145 
.33149 
.33152 
.33156 

9.52311 
.52315 
.52320 
.52324 

.33351 
.33354 
.33358 
.33361 

9.52578 
.52582 
.52587 
.52591 

.33557 
.33560 
.33564 
.33567 

9.52844 
.52848 
.52853 

.52857 

.33763 
.33766 
.33770 
.33773 

+     4' 
17 
18 
19 

9.51790 
.51795 
.51799 
.51804 

.32954 
.32957 
.32961 
.32964 

9.52060 
.52065 
.52069 
.52074 

.33159 
.33162 
.33166 
.33169 

9.52328 
.52333 
.52337 
.52342 

.33365 
.33368 
.33371 
.33375 

9.52596 
.52600 
.52605 
.52609 

.33570 
.33574 
.33577 
.33581 

9.52862 
.52866 
.52870 
.52875 

.33777 
.33780 
.33783 
.33787 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 
11 
10 
9 

+  5^ 
21 

22 
23 

9.51808 
.51813 
.51817 
.51822 

.32967 
.32971 
.32974 
.32978 

9.52078 
.52082 
.52087 
.52091 

.33173 
.33176 
.33179 
.33183 

9.52346 
.52351 
.52355 
.52360 

.33378 
.33382 
.33385 
.33389 

9.52G13 
.52618 
.52622 
.52627 

.33584 
.33588 
.33591 
.33594 

9.52879 

.52884 
.52888 
.52893 

.33790 
.33794 
.33797 
.33801 

+  ^ 

25 
26 
27 

9.51826 
.51831 
.51835 
.51840 

.32981 
.32984 
.32988 
.32991 

9.52096 
.52100 
.52105 
.52109 

.33186 
.33190 
.33193 
.33197 

9.52364 
.52369 
.52373 
.52378 

.33392 
.33395 
.33399 
.33402 

9.52631 
.52636 
.52640 
.52645 

.33598 
.33601 
.33605 
.33608 

9.52897 
.52901 
.52906 
.52910 

.33804 
.33808 
.33811 
.33814 

+    r 

29 
SO 
31 

9.51844 
.51849 
.51853 
.51858 

.32995 
.32998 
.33002 
.33005 

9.52114 
.52118 
.52123 
.52127 

.33200 
.33203 
.33207 
.33210 

9.52382 
.52386 
.52391 
.52395 

.33406 
.33409 
.33413 
.33416 

9.52649 
.52653 
.52658 
.52662 

.33612 
.33615 
.33618 
.33622 

9.52915 
.52919 
.52923 
.52928 

.33818 
.33821 
.33825 
.33828 

+  8^ 
33 
34 
35 

9.51862 
.51867 
.51871 
.51876 

.33008 
.33012 
.33015 
.33019 

9.52132 
.52136 
.52141 
.52145 

.33214 
.33217 
.33221 
.33224 

9.52400 
.52404 
.52409 
.52413 

.33419 
.33423 
.33426 
.33430 

9.52667 
.52671 
.52676 
.52680 

.33625 
.33629 
.33632 
.33636 

9.52932 
.52937 
.52941 
.52946 

.33832 
.33835 
.33839 
.33842 

+   r 

37 
38 
39 

9.51880 
.51885 
.51889 
.51894 

.33022 
.33025 
.33029 
.33032 

9.52150 
.52154 
.52159 
.52163 

.33227 
.33231 
.33234 
.33238 

9.52418 
.52422 
.52427 
.52431 

.33433 
.33436 
.33440 
.33444 

9.52684 
.52689 
.52693 
.52698 

.33639 
.33642 
.33646 
.33649 

9.52950 
.52954 
.52959 
.52963 

.33845 
.33849 
.33852 
.33856 

+  W 
41 
42 
43 

9.51898 
.51903 
.51907 
.51912 

.33036 
.33039 
.33043 
.33046 

9.52168 
.52172 
.52177 
.52181 

.33241 
.33245 
.33248 
.33251 

9.52436 
.52440 
.52444 
.52449 

.33447 
.33450 
.33454 
.33457 

9.52702 
.52707 
.52711 

.52715 

.33653 
.33656 
.33660 
.33663 

9.52968 
.52972 
.52976 
.52981 

.33859 
.33863 
.33866 
.33869 

+  11' 

45 
46 
47 

9.51916 
.51921 
.51925 
.51930 

.33049 
.33053 
.33056 
.33060 

9.52185 
.52190 
.52194 
.52199 

.33255 
.33258 
.33262 
.33265 

9.52453 
.52458 
.52462 
.52467 

.33461 
.33464 
.33467 
.33471 

9.52720 
.52724 
.52729 
.52733 

.33667 
.33670 
.33673 
.33677 

9.52985 
.52990 
.52994 
.52999 

.33873 
.33876 
.33880 
.33883 

+  12' 

49 
50 
51 

9.51934 
.51939 
.51943 
.51948 

.33063 
.33067 
.33070 
.33073 

9.52203 
.52208 
.52212 
.52217 

.33269 
.33272 
.33275 
.33279 

9.52471 
.52476 
.52480 
.52484 

.33474 
.33478 
.33481 
.33485 

9.52738 
.52742 
.52747 
.52751 

.33680 
.33684 
.33687 
.33691 

9.53003 
.53007 
.53012 
.53016 

.33887 
.33890 
.33894 
.33897 

+  13' 

5,? 

55 

9.51952 
.51957 
.51961 
.51966 

.33077 
.33080 
.33084 
.33087 

9.52221 
.52226 
.52230 
.52235 

.33282 
.33286 
.33289 
.33293 

9.52489 
.52493 
.52498 
.52502 

.33488 
.33491 
.33495 
.33498 

9.52755 
.52760 
.52764 
.52769 

.33694 
.33698 
.33701 
.33704 

9.53021 
.53025 
.53029 
.53034 

.33900 
.33904 
.33907 
.33911 

8 
7 
6 
5 

+  14' 

57 
55 
59 

9.51970 
.51975 
.51979 
.51984 

.33090 
.33094 
.33097 
.33101 

9.52239 
.52244 
.52248 
.52253 

.33296 
.33299 
.33303 
.33306 

9.52507 
.52511 
.52516 
.52520 

.33502 
.33505 
.33509 
.33512 

9.52773 
.52778 
.52782 
.52786 

.33708 
.33711 
.33715 
.33718 

9.53038 
.53043 
.53047 
.53051 

.33914 
.33918 
.33921 
.33925 

4 
3 

2 

1 

+  15' 

9.51988 

.33104 

9.52257 

.33310 

9.52525 

.33515 

9.52791 

.33722 

9.53056 

.33928 

0 

19h  19m 

jgh  igm 

19h  nm 

19h  lem 

19^ 15m 

V 


Page  868]                 TABLE  45. 

Haversines. 

s 

4h  4Sm  71°  15/ 

471  46m  71°  30/ 

4h  47m  71°  45/ 

4^  48^  72°  r 

4^  49m  72°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.53056 
.53060 
.53065 
.53069 

.33938 
.33931 
.33935 
.33938 

9.53320 
.53324 
.53328 
.53333 

.34135 
.34138 
.34142 
.34145 

9.53582 
.53587 
.53591 
.53595 

.34342 
.34345 
.34349 
.34352 

9.53844 
.53848 
.53852 

.53857 

.34549 
.34553 
.34556 
.34560 

9.54104 
.54108 
.54113 
.54117 

.34757 
.34760 
.34764 
.34767 

60 
59 
58 

57 

+   1^ 

5 

6 

7 

9.53073 
.53078 
.53082 
.53087 

.33913 
.33945 
.33949 
.33953 

9.53337 
.53342 
.53346 
.53350 

.34149 
.34152 
.34155 
.34159 

9.63600 
.53604 
.53609 
.53613 

.34356 
.34359 
.34363 
.34368 

9.53861 
.53865 
.53870 
.53874 

.34563 
.34566 
.34570 
.34573 

9.54121 
.54126 
.54130 
.54134 

.34771 
.34774 
.34778 
.34781 

56 
55 

54 
53 

+     V 

9 

10 

11 

9.53091 
.53096 
.53100 
.53104 

.33956 
.33959 
.33962 
.33966 

9.53355 
.53359 
.53364 
.53368 

.34162 
.34166 
.34169 
.34173 

9.53617 
.53622 
.53626 
.53630 

.34369 
.34373 
.34376 
.34380 

9.53879 
.53883 
.53887 
.53892 

.34577 
.34580 
.34584 
.34587 

9.54139 
.54143 
.54147 
.54152 

.34784 

.34788 
.34791 
.34795 

52 
51 
50 
49 

+     3^ 

13 
14 
15 

9.53109 
.53113 
.53118 
.53122 

.33969 
.33973 
.33976 
.33980 

9.53372 
.53377 
.53381 
.53385 

.34176 
.34180 
.34183 
.34186 

9.53635 
.53639 
.53643 
.53648 

.34383 
.34387 
.34390 
.34394 

9.53896 
.53900 
.53905 
.53909 

.34591 
.34594 
.34598 
.34601 

9.54156 
.54160 
.54165 
.54169 

.34798 
.34802 
.34805 
.34809 
.34812 
.34816 
.34819 
.34833 

48 
47 
46 
45 
44 
43 
42 
41 

+     4^ 
17 
18 
19 

9.53126 
.53131 
.53135 
.53140 

.33983 
.33986 
.33990 
.33993 

9.53390 
.53394 
.53399 
.53403 

.34190 
.34193 
.34197 
.34200 

9.53652 
.53657 
.53661 
.53665 

.34397 
.34400 
.34404 
.34407 

9.53913 
.53918 
.53922 
.53926 

.34604 
.34608 
.34611 
.34615 

9.54173 

.54177 
.54182 
.54186 

+     5^ 
21 
22 
23 

9.53144 
.53148 
.53153 
.53157 

.33997 
.34000 
.34004 
.34007 

9.53407 
.53412 
.53416 
.53421 

.34204 
.34207 
.34211 
.34214 

9.53670 
.53674 
.53678 
.53683 

.34411 
.34414 
.34418 
.34421 

9.53931 
.53935 
.53939 
.53944 

.34618 
.34622 
.34625 
.34629 

9.54190 
.54195 
.54199 
.54203 

.34836 
.34830 
.34833 
.34836 

40 
39 
38 
37 

+      6' 

25 
26 
27 

9.53162 
.53166 
.53170 
.53175 

.34011 
.34014 
.34018 
.34031 

9.53425 
.53429 
.53434 
.53438 

.34218 
.34321 
.34224 
.34228 

9.53687 
.53691 
.53696 
.53700 

.34435 
.34428 
.34432 
.34435 

9.53948 
.53952 
.53957 
.53961 

.34633 
.34636 
.34639 
.34643 

9.54208 
.54212 
.54216 
.54221 

.34840 
.34843 
.34847 
.34850 

36 
35 
34 
33 

+    r 

29 
SO 
31 

9.53179 
.53184 
.53188 
.53192 

.34034 
.34038 
.34031 
.34035 

9.53442 
.53447 
.53451 
.53456 

.34231 
.34235 
.34338 
.34342 

9.53704 
.53709 
.53713 
.53718 

.34439 
.34442 
.34445 
.34449 

9.53966 
.53970 
.53974 
.53978 

.34646 
.34649 
.34653 
.34656 

9.54225 
.54229 
.54234 
.54238 

.34854 

.34857 
.34861 
.34864 

32 
31 
30 
29 

+   8^ 
33 
34 
35 

9.53197 
.53201 
.53206 
.53210 

.34038 
.34043 
.34045 
.34049 

9.53460 
.53464 
.53469 
.53473 

.34245 
.34249 
.34252 
.34256 

9.53722 
.53726 
.53731 
.53735 

.34452 
.34456 
.34459 
.34483 

9.53983 
.53987 
.53991 
.53996 

.34660 
.34663 
.34667 
.34670 

9.54242 
.54247 
.54251 
.54255 

.34868 
.34871 
.34875 

.34878 
.34883 
.34885 
.34888 
.34892 

28 
27 
26 
25 

24 
23 
22 
21 

+  9^ 

37 
38 
39 

9.53214 
.53219 
.53223 
.53228 

.34053 
.34055 
.34059 
.34063 

9.53477 
.53482 
.53486 
.53491 

.34359 
.34262 
.34266 
.34369 

9.53739 
.53744 
.53748 
.53752 

.34466 
.34470 
.34473 
.34477 

9.54000 
.54004 
.54009 
.54013 

.34674 
.34677 
.34681 
.34684 

9.54260 
.54264 
.54268 
.54272 

+    W 

41 
42 
43  ■ 

9.53232 
.53236 
.53241 
.53245 

.34066 
.34069 
.34073 
.34076 

9.53495 
.53499 
.53504 
.53508 

.34273 
.34276 
.34280 
.34383 

9.53757 
.53761 
.53765 
.53770 

.34480 
.34483 
.34487 
.34490 

9.54017 
.54022 
.54026 
.54030 

.34688 
.34691 
.34694 
.34698 

9.54277 
.54281 
.54285 
.54290 

.34895 
.34899 
.34902 
.34906 

20 
19 
18 
17 
16 
15 
14 
13 

+  11^ 

45 
46 
47 

9.53249 
.53254 
.53258 
.53263 

.34080 
.34083 
.34087 
.34090 

9.53512 
.53517 
.53521 
.53526 

.34287 
.34290 
.34293 
.34297 

9.53774 
.53778 
.53783 
.53787 

.34494 
.34497 
.34501 
.34504 

9.54035 
.54039 
.54043 
.54048 

.34701 
.34705 
.34708 
.34712 

9.54294 
.54298 
.54303 
.54307 

.34909 
.34913 
.34916 
.34930 

+  W 

49 
50 
51 

9.53267 
.53271 
.53276 
.53280 

.34093 
.34097 
.34100 
.34104 

9.53530 
.53534 
.53539 
.53543 

.34300 
.34304 
.34307 
.34311 

9.53792 
.53796 
.53800 
.53805 

.34508 
.34511 
.34515 
.34518 

9.54052 
.54056 
.54061 
.54065 

.34715 
.34719 
.34722 
.34726 

9.54311 
.54316 
.54320 
.54324 

.34933 
.34927 
.34930 
.34933 

12 
11 
10 
9 
8 
7 
6 
5 

+    13' 

53 
54 
55 

9.53285 
.53289 
.53293 
.53298 

.34107 
.34111 
.34114 
.34118 

9.53547 
.53552 
.53556 
.53560 

.34314 
.34318 
.34321 
.34325 

9.53809 
.53813 
.53818 
.53822 

.34521 
.34525 
.34528 
.34532 

9.54069 
.54074 
.54078 
.54082 

.34729 
.34733 
.34736 
.34739 

9.54329 
.54333 
.54337 
.54341 

.34937 
.34940 
.34944 
.34947 

+  W 

57 
58 
59 

9.53302 
.53307 
.53311 
.53315 

.34131 
.34124 
.34128 
.34131 

9.53565 
.53569 
.53574 
.53578 

.34328 
.34331 
.34335 
.34338 

9.53826 
.53831 
.53835 
.53839 

.34535 
.34539 
.34542 
.34546 

9.54087 
.54091 
.54095 
.54100 

.34743 
.34746 
.34750 
.34753 

9.54346 
.54350 
.54354 
.54359 

.34951 
.34954 
.34958 
.34961 

4 
3 
2 
1 
0 

+  15' 

9.53320 

.34135 

9.53582 

.34342 

9.53844 

.34549 

9.54104 

.34757 

9.54363 

.34965 

i9h 14m 

19h 13m 

19hipn 

i9h lim 

19hl0m 

TABLE  45.                 [Page  869 

Haversines. 

s 

4^  50m.  72°  w 

4h  5im  72°  45^ 

4h  52m  73°  Q' 

4^  53m  73°  15^ 

4h  54m  73°  3(K 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.54363 
.54367 
.54372 
.54376 

.34965 
.34968 
.34972 
.34975 

9.54621 
.54625 
.54629 
.54634 

.35173 
.35176 
.35180 
.35183 

9.54878 
.54882 
.54886 
.54890 

.35381 
.35385 
.35388 
.35392 

9.55133 
.55137 
.55142 
.55146 

.35590 
.35594 
.35597 
.35601 

9.55387 
.55392 
.55396 
.55400 

.35799 
.35803 
.35806 
.35810 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.54380 
.54385 
.54389 
.54393 

.34979 
.34982 
.34986 
.34989 

9.54638 
.54642 
.54647 
.54651 

.35187 
.35190 
.35194 
.35197 

9.54895 
.54899 
.54903 
.54907 

.35395 
.35399 
.35402 
.35406 

9.55150 
.55154 
.55159 
.55163 

.35604 
.35608 
.35611 
.35615 

9.55404 
.55409 
.55413 
.55417 

.35813 
.35817 
.35820 
.35824 

56 
55 
54 
53 

+  2' 

9 

10 

11 

9.54397 
.54402 
.54406 
.54410 

.34992 
.34996 
.34999 
.35003 

9.54655 
.54659 
.54664 
.54668 

.35201 
.35304 
.35308 
.35311 

9.54912 
.54916 
.54920 
.54924 

.35409 
.35413 
.35416 
.35420 

9.55167 
.55171 
.55176 
.55180 

.35618 
.35622 
.35625 
.35638 

9.55421 
.55425 
.55430 
.55434 

.35827 
.35831 
.35834 
.35838 

52 
51 
50 
49 

+     3' 

13 
14 
15 

9.54415 
.54419 
.54423 
.54428 

.35006 
.35010 
.35013 
.35017 

9.54672 
.54677 
.54681 
.54685 

.35215 
.35218 
.35322 
.35225 

9.54929 
.54933 
.54937 
.54942 

.35423 
.35427 
.35430 
.35434 

9.55184 
.55188 
.55192 
.55197 

.35632 
.35635 
.35639 
.35642 

9.55438 
.55442 
.55447 
.55451 

.35841 
.35845 

.35848 
.35852 

48 
47 
46 
45 

+      4' 
17 
18 
19 

9.54432 
.54436 
.54440 
.54445 

.35020 
.35024 
.35027 
.35031 

9.54689 
.54694 
.54698 
.54702 

.35228 
.35232 
.35235 
.35239 

9.54946 
.54950 
.54954 
.54959 

.35437 
.35441 
.35444 
.35448 

9.55201 
.55205 
.55209 
.55214 

.35646 
.35649 
.35653 
.35656 

9.55455 
.55459 
.55463 
.55468 

.35855 
.35859 
.35862 
.35865 

44 
43 
42 
41 

21 
22 
23 

9.54449 
.54453 
.54458 
.54462 

.35034 
.35038 
.35041 
.35044 

9.54707 
.54711 
.54715 
.54719 

.35242 
.35246 
.35249 
.35253 
.35256 
.35260 
.35263 
.35267 

9.54963 
.54967 
.54971 
.54976 

.35451 
.35454 
.35458 
.35461 

9.55218 
.55222 
.55226 
.55231 

9.55235 
.55239 
.55243 
.55248 

.35660 
.35663 
.35667 
.35670 

9.55472 
.55476 
.55480 
.55485 

.35869 
.35872 
.35876 
.35879 

40 
39 
38 
37 
36 
35 
34 
33 

+   6^ 

25 
26 

27 

9.54466 
.54471 
.54475 
.54479 

.35048 
.35051 
.35055 
.35058 

9.54724 
.54728 
.54732 
.54736 

9.54980 
.54984 
.54988 
.54993 

.35465 
.35468 
.35472 
.35475 

.35674 
.35677 
.35681 
.35684 

9.55489 
.55493 
.55497 
.55501 

.35883 
.35886 
.35890 
.35893 

+    r 

29 
30 
31 

9.54483 
.54488 
.54492 
.54496 

.35062 
.35065 
.35069 
.35072 

9.54741 
.54745 
.54749 
.54754 

.35270 
.35274 
.35377 
.35281 

9.54997 
.55001 
.55005 
.55010 

.35479 
.35482 
.35486 
.35489 

9.55252 
.55256 
.55260 
.55265 

.35688 
.35691 
.35695 
.35698 

9.55506 
.55510 
.55514 
.55518 

.35897 
.35900 
.35904 
.35907 

32 
31 
SO 
29 
28 
27 
26 
25 

+   8^ 
33 
34 
35 

9.51501 
.54505 
.54509 
.54514 

.35076 
.35079 
.35083 
.35086 

9.54758 
.54762 
.54766 
.54771 

.35284 

.35288 
.35291 
.35294 

9.55014 
.55018 
.55022 
.55027 

.35493 
.35496 
.35500 
.35503 

9.55269 
.55273 
.55277 
.55282 

.35702 
.35705 
.35709 
.35712 

9.55523 
.55527 
.55531 
.55535 

.35911 
.35914 
.35918 
.35921 

+  9^ 

37 
38 
39 

9.54518 
.54522 
.54526 
.54531 

.35090 
.35093 
.35097 
.35100 

9.54775 
.54779 
.54784 
.54788 

.35298 
.35301 
.35305 
.35308 

9.55031 
.55035 
.55039 
.55044 

.35507 
.35510 
.35514 
.35517 

9.55286 
.55290 
.55294 
.55298 

.35716 
.35719 
.3^723 
.35726 

9.55539 
.55544 
.55548 
.55552 

.35925 
.35928 
.35932 
.35935 

24 
23 
22 
21 

+  10^ 

41 
42 
43 

9.54535 
.54539 
.54544 
.54548 

.35103 
.35107 
.35110 
.35114 

9.54792 
.54796 
.54801 
.54805 

.35312 
.35315 
.35319 
.35322 

9.55048 
.55052 
.55057 
.55061 

.35521 
.35524 
.35528 
.35531 

9.55303 
.55307 
.55311 
.55315 

.35730 
.35733 
.35737 
.35740 

9.55556 
.55561 
.55565 
.55569 

.35939 
.35942 
.35946 
.35949 

20 
19 
18 

17 

+  ir 

45 
46 
47 

9.54552 
.54556 
.54561 
.54565 

.36117 
.35121 
.35124 
.35128 

9.54809 
.54813 
.54818 
.54822 

.35326 
.35329 
.35333 
.35336 

9.55065 
.55069 
.55074 
.55078 

.35534 
.35538 
.35541 
.35545 

9.55320 
.55324 
.55328 
.55332 

.35743 
.35747 
.35750 
.35754 

9.55573 
.55577 
.55582 
.55586 

.35953 
.35956 
.35960 
.35963 

16 
15 
14 
13 

+    12' 

49 
50 
51 

9.54569 
.54574 
.54578 
.54582 

.35131 
.35135 
.35138 
.35142 

9.54826 
.54831 
.54835 
.54839 

.35340 
.35343 
.35347 
.35350 

9.55082 
.55086 
.55091 
.55095 

.35548 
.35552 
.35555 
.35559 

9.55337 
.55341 
.55345 
.55349 

.35757 
.35761 
.35764 
.35768 

9.55590 
.55594 
.55598 
.55603 

.35967 
.35970 
.35974 
.35977 

12 

11 

10 

9 

+  13^ 

53 
54 
55 

9.54587 
.54591 
.54595 
.54599 

.35145 
.35149 
.35152 
.35156 

9.54843 
.54848 
.54852 
.54856 

.35354 
.35357 
.35361 
.35364 

9.55099 
.55103 
.55108 
.55112 

.35562 
.35566 
.35569 
.35573 

9.55354 
.55358 
.55362 
.55366 

.35771 
.35775 
.35778 
.35782 

9.55607 
.55611 
.55615 
.55620 

.35981 
.35984 
.35988 
.35991 

8 
7 
6 
5 

4 
3 

2 

1 

57 
58 
59 

9.54604 
.54608 
.54612 
.54617 

.35159 
.35162 
.35166 
.35169 

9.54860 
.54865 
.54869 
.54873 

.35368 
.35371 
.35374 
.35378 

9.55116 
.55120 
.55125 
.55129 

.35576 
.35580 
.35583 
.35587 

9.55370 
.55375 
.55379 
.55383 

.35785 
.35789 
.35792 
.35796 

9.5562'4 
.55628 
.55632 
.55636 

.35995 
.35998 
.36002 
.36005 

+  15' 

9.54621 

.35173 

9.54878 

.35381 

9.55133 

.35590 

9.55387 

.35799 

9.55641 

.36009 

0 

19^  9m 

19h  8m 

m  7m 

19h6Jn 

19h5m 

Page  870]                  TABLE  45. 

Havereines. 

s 

^A  55m  73°  45' 

4h  56m  74°  0' 

4h  57m  740  15/ 

4h  58m  740  3(K 

4^  59m  74°  45' 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.j  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

s 

0 
1 

2 
S 

9.55641 
.55645 
.55649 
.55653 

.36009 
.36012 
.36016 
.36019 

9.55893 
.55897 
.55901 
.55905 

.36318 
.36333 
.36335 
.36339 

9.56144 
.56148 
.56152 
.56156 

.36438 
.36431 
.36435 
.36438 

9.56393 
.56397 
.56402 
.56406 

.36638 
.36643 
.36645 
.36649 

9.56642 
.56646 
.56650 
.56654 

.36848 
.36853 
.36855 
.36859 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.55657 
.55662 
.55666 
.55670 

.36033 
.36036 
.36030 
.36033 

9.55909 
.55914 
.55918 
.55922 

.36333 
.36336 
.36339 
.36343 

9.56160 
.56164 
.56169 
.56173 

.36443 
.36445 
.36449 
.36453 

9.56410 
.56414 
.56418 
.56422 

.36653 
.36656 
.36659 
.36663 

9.56658 
.56663 
.56667 
.56671 

.36862 
.36866 
.36869 
.36873 

56 
55 
54 
53 

+  2' 

9 

10 

11 

9.55674 
.55678 
.55683 
.55687 

.36036 
.36040 
.36043 
.36047 

9.55926 
.55930 
.55935 
.55939 

.36346 
.36350 
.36353 
.36357 

9.56177 
.56181 
.56185 
.56189 

.36456 
.36459 
.36463 
.36466 

9.56426 
.56431 
.56435 
.56439 

.36666 
.36670 
.36673 
.36677 

9.56675 
.56679 
.56683 
.56687 

.36877 
.36880 
.36884 
.36887 

52 
51 
50 
49 

+     3' 

IS 
14 
15 

9.55691 
.55695 
.55699 
.55704 

.36050 
.36054 
.36057 
.36061 

9.55943 
.55947 
.55951 
.55955 

.36360 
.36364 
.36367 
.36371 

9.56194 
.56198 
.56202 
.56206 

.36470 
.36473 
.36477 
.36480 

9.56443 
.56447 
.56451 
.56456 

.36680 
.36684 
.36687 
.36691 

9.56692 
.56696 
.56700 
.56704 

.36891 
.36894 
.36898 
.36901 

48 
47 
46 
45 

+  4' 
17 
18 
19 

9.55708 
.55712 
.55716 
.55721 

.36064 
.36068 
.38071 
.36075 

9.55960 
.55964 
.55968 
.55972 

.36374 
.36378 
.36381 
.36385 

9.56210 
.56214 
.56219 
.56223 

.36484 
.36487 
.36491 
.36494 

9.56460 
.56464 
.56468 
.56472 

.36694 
.36698 
.36701 
.36705 

9.56708 
.56712 
.56716 
.56720 

.36905 
.36908 
.36913 
.36915 

44 
43 
42 
41 

+      r 
21 
22 
2S 

9.55725 
.55729 
.55733 
.55737 

.36078 
.36083 
.36085 
.36089 

9.55976 
.55981 
.55985 
.55989 

.36288 
.36393 
.36295 
.36299 

9.56227 
.56231 
.56235 
.56239 

.36498 
.36501 
.36505 
.36508 

9.56476 
.56480 
.56485 
.56489 

.36708 
.36713 
.36715 
.36719 

9.56725 
.56729 
.56733 
.56737 

9.56741 
.56745 
.56749 
.56753 

.36919 
.36922 
.36926 
.36939 
.36933 
.36936 
.36940 
.36943 

40 
39 
38 
37 
36 
35 
34 
33 

+     6' 

25 

26 
27 

9.55742 
.55746 
.55750 
.55754 

.36093 
.36096 
.36099 
.36103 

9.55993 
.55997 
.56001 
.56006 

.36303 
.36306 
.36309 
.36313 

9.56244 
.56248 
.56252 
.56256 

.36512 
.36515 
.36510 
.36522 

9.56493 
.56497 
.56501 
.56505 

.36733 
.36736 
.36729 
.36733 

+    r 

29 
SO 
SI 

9.55758 
.55763 
.55767 
.55771 

.36106 
.36110 
.36113 
.36117 

9.56010 
.56014 
.56018 
.56022 

.36316 
.36320 
.36323 
.36327 

9.56260 
.56264 
.56269 
.56273 

.36526 
.36529 
.36533 
.36536 

9.56509 
.56514 
.56518 
.56522 

.36736 
.36740 
.36743 
.36747 

9.56758 
.56762 
.56766 
.56770 

.36947 
.36950 
.36954 
.36957 

32 
31 
30 
29 

+     S' 
SS 
S4 
S5 

9.55775 
.55779 
.55784 
.55788 

.36130 
.36134 
.36137 
.36131 

9.56027 
.56031 
.56035 
.56039 

.36330 
.36334 
.36337 
.36341 

9.56277 
.56281 
.56285 
.56289 

.36540 
.36543 
.36547 
.36551 

9.56526 
.56530 
.56534 
.56538 

.36750 
.36754 
.36757 
.36761 

9.56774 
.56778 
.56782 
.56786 

.36961 
.36964 
.36968 
.36971 

28 
27 
26 
25 

+     9' 

S7 
38 
39 

9.55792 
.55796 
.55800 
.55805 

.36134 
.36138 
.36141 
.36145 

9.56043 
.56047 
.56052 
.56056 

.36344 
.36348 
.36351 
.36355 

9.56294 
.56298 
.56302 
.56306 

.36554 
.36558 
.36561 
.36565 

9.56543 
.56547 
.56551 
.56555 

.36764 
.36768 
.36771 
.36775 

9.56791 
.56795 
.56799 
.56803 

.36975 
.36978 
.36983 
.36985 

24 
23 
22 
21 

+  10' 

41 
42 
43 

9.55809 
.55813 
.55817 
.55821 

.36148 
.36153 
.36155 
.36159 

9.56060 
.56064 
.56068 
.56073 

.36358 
.36363 
.36365 
.36368 

9.56310 
.56314 
.56318 
.56323 

.36568 
.36572 
.36575 
.36579 

9.56559 
.56563 
.56567 
.56572 

.36778 
.36782 
.36785 
.36789 

9.56807 
.56811 
.56815 
.56819 

.36989 
.36993 
.36996 
.36999 
.37003 
.37006 
.37010 
.37013 

20 
19 
18 

n 

16 
15 
14 
IS 
12 
11 
10 
9 

+  11' 

45 
46 
47 

9.55826 
.55830 
.55834 
.55838 

.36163 
.36166 
.36169 
.36173 

9.56077 
.56081 
.56085 
.56089 

.36373 
.36376 
.36379 
.36383 

9.56327 
.56331 
.56335 
.56339 

.36582 
.36586 
.36589 
.36593 

9.56576 
.56580 
.56584 
.56588 

.36792 
.36796 
.36799 
.36803 

9.56824 
.56828 
.56832 
.56836 

+  13' 

49 
50 
51 

9.55842 
.55846 
.55851 
.55855 

.36176 
.36180 
.36183 
.36187 

9.56093 
.56098 
.56102 
.56106 

.36386 
.36389 
.36393 
.36396 

9.56343 
.56348 
.56352 
.56356 

.36596 
.36600 
.36603 
.36607 
.36610 
.36614 
.36617 
.36631 

9.56592 
.56596 
.56601 
.56605 

.36806 
.36810 
.36813 
.36817 

9.56840 
.56844 
.56848 
.56852 

.37017 
.37030 
.37034 
.37037 

+    13' 

53 
54 
55 

9.55859 
.55863 
.55867 
.55872 

.36190 
.36194 
.36197 
.36301 

9.56110 
.56114 
.56118 
.56123 

.36400 
.36403 
.36407 
.36410 

9.56360 
.56364 
.56368 
.56373 

9.56609 
.56613 
.56617 
.56621 

.36820 
.36834 
.36837 
.36831 

9.56856 
.56861 
.56865 
.56869 

.37031 
.37034 
.37038 
.37041 
.37045 
.37049 
.37053 
.37055 

8 
7 
6 
5 

4 
3 
2 
1 

+  14' 

57 
58 
59 

9.55876 
.55880 
.55884 
.55888 

.36304 
.36308 
.36311 
.36215 

9.56127 
.56131 
.56135 
.56139 

.36414 
.36417 
.36431 
.36434 

9.56377 
.56381 
.56385 
.56389 

.36634 
.36638 
.36631 
.36635 

9.56625 
.56630 
.56634 
.56638 

.36834 
.36838 
.36841 
.36845 

9.56873 
.56877 
.56881 
.56885 

+   15' 

9.55893 

.36318 

9.56144 

.36438 

9.56393 

.36638 

9.56642 

.36848 

9.56889 

.37059 

0 

19h  4m 

igh  sm 

ighpn          1 

19h  im           1 

ighom 

TABLE  45.                 [Page  871 

Haversines. 

s 

5A  Orm  75°  C 

5*  Jn»  75°  15' 

5fc  2^  75°  3(K 

5h  Sm  75°  45' 

5h  4m  76°  0' 

s 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.56889 
.56893 
.56898 
.56902 

.37059 
.37063 
.37066 
.37070 

9.57136 
.57140 
.57144 
.57148 

.37270 
.37273 
.37277 
.37280 

9.57381 
.57385 
.57389 
.57393 

.37481 
.37485 

.37488 
.37492 

9.57625 
.57629 
.57633 
.57637 

.37692 
.37696 
.37699 
.37703 

9.57868 
.57872 
.57876 
.57881 

.37904 
.37907 
.37911 
.37914 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.56906 
.56910 
.56914 
.56918 

.37073 
.37077 
.37080 
.37084 

9.57152 
.57156 
.57160 
.57165 

.37284 
.37287 
.37291 
.37295 

9.57397 
.57402 
.57406 
.57410 

.37495 
.37499 
.37502 
.37506 

9.57642 
.57646 
.57650 
.57654 

.37706 
.37710 
.37713 
.37717 

9.57885 
.57889 
.57893 
.57897 

.37918 
.37922 
.37925 
.37029 

56 
55 
54 
53 

52 
51 
50 
49 
48 
47 
46 
45 

+     V 

9 

10 

11 

9.56922 
.56926 
.56931 
.56935 

.37087 
.37091 
.37094 
.37098 

9.57169 
.57173 
.57177 
.57181 

.37298 
.37302 
.37305 
.37309 

9.57414 
.57418 
.57422 
.57426 

.37509 
.37513 
.37516 
.37520 

9.57658 
.57662 
.57666 
.57670 

.37721 
.37724 
.37728 
.37731 

9.57901 
.57905 
.57909 
.57913 

.37932 
.37936 
.37939 
.37943 

+  3' 

13 
14 
15 

9.56939 
.56943 
.56947 
.56951 

.37101 
.37105 
.37108 
.37113 

9.57185 
.57189 
.57193 
.57197 

.37312 
.37316 
.37319 
.37323 

9.57430 
.57434 
.57438 
.57442 

.37523 
.37527 
.37530 
.37534 

9.57674 
.57678 
.57682 
.57686 

.37735 
.37738 
.37742 
.37745 

9.57917 
.57921 
.57925 
.57929 

.37946 
.37950 
.37953 
.37957 

+   4' 
17 
18 
19 

9.56955 
.56959 
.56963 
.56968 

.37U5 
.37119 
.37122 
.37126 

9.57201 
.57205 
.57210 
.57214 

.37326 
.37330 
.37333 
.37337 

9.57446 
.57450 
.57454 
.57459 

.37537 
.37541 
.37544 
.37548 

9.57690 
.57694 
.57698 
.57702 

.37749 
.37752 
.37756 
.37759 

9.57933 
.57937 
.57941 
.57945 

.37960 
.37964 
.37967 
.37971 

44 
43 
42 
41 

+  5' 
21 

22 
23 

9.56972 
.56976 
.56980 
.56984 

.37129 
.37133 
.37136 
.37140 

9.57218 
.57222 
.57226 
.57230 

.37340 
.37344 
.37347 
.37351 

9.57463 
.57467 
.57471 
.57475 

.37551 
.37555 
.37558 
.37562 

9.57706 
.57711 
.57715 
.57719 

.37763 
.37766 
.37770 
.37773 

9.57949 
.57953 
.57957 
.57961 

.37974 
.37978 
.37982 
.37985 

40 
39 
38 
37 

+   6' 

25 
26 

27 

9.56988 
.56992 
.56996 
.57000 

.37143 
.37147 
.37150 
.37154 

9.57234 
.57238 
.57242 
.57246 

.37354 
.37358 
.37361 
.37365 

9.57479 
.57483 
.57487 
.57491 

.37566 
.37569 
.37573 
.37576 

9.57723 
.57727 
.57731 
.57735 

.37777 
.37780 
.37784 

.37788 

9.57965 
.57969 
.57973 
.57977 

9.57981 
.57986 
.57990 
.57994 

.37989 
.37992 
.37996 
.37999 

36 
35 
34 
S3 

+    r 

29 
30 
31 

9.57005 
.57009 
.57013 
.57017 

.37157 
.37161 
.37164 
.37168 

9.57250 
.57255 
.57259 
.57263 

.37368 
.37372 
.37375 
.37379 

9.57495 
.57499 
.57503 
.57507 

.37580 
.37583 
.37587 
.37590 

9.57739 
.57743 
.57747 
.57751 

.37791 
.37794 
.37798 
.37802 

.38003 
.38006 
.38010 
.38013 

32 
31 
30 
29 

+     8' 
33 
34 
35 

9.57021 
.57025 
.57029 
.57033 

.37171 
.37175 
.37179 
.37182 

9.57267 
.57271 
.57275 
.57279 

.37382 
.37386 
.37389 
.37393 

9.57511 
.57516 
.57520 
.57524 

.37594 
.37597 
.37601 
.37604 

9.57755 
.57759 
.57763 
.57767 

.37805 
.37809 
.37812 
.37816 

9.57998 
.58002 
.58006 
.58010 

.38017 
.38020 
.38024 
.38027 

28 
27 
26 
25 

+  9^ 

37 
38 
39 

9.57037 
.57042 
.57046 
.57050 

.37186 
.37189 
.37193 
.37196 

9.57283 
.57287 
.57291 
.57295 

.37397 
.37400 
.37404 
.37407 

9.57528 
.57532 
.57536 
.57540 

.37608 
.37611 
.37615 
.37618 

9.57771 

.57775 
.57779 
.57783 

.37819 
.37823 
.37826 
.37830 

9.58014 
.58018 
.58022 
.58026 

.38031 
.38034 
.38038 
.38042 

24 
23 
22 
21 

+    W 
41 

42 
43 

9.57054 
.57058 
.57062 
.57066 

.37200 
.37203 
.37207 
.37210 

9.57299 
.57304 
.57308 
.57312 

.37411 
.37414 
.37418 
.37421 

9.57544 
.57548 
.57552 
.57556 

.37622 
.37625 
.37629 
.37632 

9.57787 
.57792 
.57796 
.57800 

.37833 
.37837 
.37840 
.37844 

9.58030 
.58034 
.58038 
.58042 

.38045 
.38049 
.38052 
.38056 

20 
19 
18 
17 

+  11' 

45 
46 
47 

9.57070 
,57074 
.57078 
.57083 

.37214 
.37217 
.37221 
.37224 

9.57316 
.57320 
.57324 
.57328 

.37425 
.37428 
.37432 
.37435 

9.57560 
.57564 
.57568 
.57572 

.37636 
.37639 
.37643 
.37647 

9.57804 
.57808 
.57812 
.57816 

.37847 
.37851 
.37855 

.37858 

9.58046 
.58050 
.58054 
.58058 

9.58062 
.58066 
.58070 
.58074 

.38059 
.38063 
.38066 
.38070 

16 
15 
14 
13 

+  12' 

49 
50 
51 

9.57087 
.57091 
.57095 
.57099 

.37228 
.37231 
.37235 
.37238 

9.57332 
.57336 
.57340 
.57344 

.37439 
.37442 
.37446 
.37449 

9.57577 

.57581 

•  .57585 

.57589 

.37650 
.37654 
.37657 
.37661 

9.57820 
.57824 
.57828 
.57832 

.37862 
.37865 
.37869 
.37872 

.38073 
.38077 
.38080 
.38084 

12 

11 

10 

9 

+  13' 

53 
54 
55 

9.57103 
.57107 
.57111 
.57115 

.37242 
.37245 
.37249 
.37252 

9.57348 
.57353 
.57357 
.57361 

.37453 
.37456 
.37460 
.37463 

9.57593 
.57597 
.57601 
.57605 

.37664 
.37668 
.37671 
.37675 

9.57836 
.57840 
.57844 
.57848 

.37876 
.37879 
.37883 
.37886 

9.58078 
.58082 
.58086 
.58090 

.38087 
.38091 
.38095 
.38098 

8 
7 
6 
5 

+  W 

57 
58 
59 

9.57119 
.57124 
.57128 
.57132 

.37256 
.37259 
.37263 
.37266 

9.57365 
.57369 
.57373 
.57377 

.37467 
.37470 
.37474 
.37477 

9.57609 
.57613 
.57617 
.57621 

.37678 
.37682 
.37685 
.37689 

9.57852 
.57856 
.57860 
.57864 

.37890 
.37893 
.37897 
.37900 

9.58094 
.58098 
.58102 
.58106 

.38102 
.38105 
.38109 
.38112 

4 
3 

2 

1 

+  15' 

9.57136 

.37270 

9.57381 

.37481 

9.57625 

.37692 

9.57868 

.37904 

9.58110 

.38116 

0 

18T^59m 

18^58:^ 

18h  57m 

18}i56m 

18^  55m 

Page  872]                 TABLE  45. 

Haversines, 

8 

Sh  5m  U°  15'     1 

5ft  em  76°  W 

5h  7m  76°  45' 

5h  gm  77°  O' 

5h  gm  77°  W 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

9.58110 
.58114 
.58118 
.58122 

.38116 
.38119 
.38123 
.38126 

9.58351 
.58355 
.58359 
.58363 

.38328 
.38331 
.38335 
.38338 

9.58591 
.58595 
.58599 
.58603 

.38540 
.38544 
.38547 
.38551 

9.58830 
.58834 
.58838 
.58842 

.38752 
.38756 
.38760 
.38763 

9.59068 
.59072 
.59076 
.59079 

.38965 
.38969 
.38972 
.38976 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.58126 
.58131 
.58135 
.58139 

.38130 
.38133 
.38137 
.38140 

9.58367 
.58371 
.58375 
.58379 

.38342 
.38345 
.38349 
.38352 

9.58607 
.58611 
.58615 
.58619 

.38554 

.38558 
.38561 
.38565 

9.58846 
.58850 
.58854 
.58858 

.38767 
.38770 
.38774 

.38777 

9.59083 
.59087 
.59091 
.59095 

.38979 
.38983 
.38986 
.38990 

56 
55 
54 
53 

+     It'' 

9 

10 

11 

9.58143 
.58147 
.58151 
.58155 

.38144 
.38148 
.38151 
.38155 

9.58383 
.58387 
.58391 
.58395 

.38356 
.38360 
.38363 
.38367 

9.58623 
.58627 
.58631 
.58635 

.38568 
.38572 
.38575 
.38579 

9.58862 
..58866 
.58870 

.58874 

.38781 
.38784 
.38788 
.38791 

9.59099 
.59103 
.59107 
.59111 

.38994 
.38997 
.39001 
.39004 

52 
51 
50 
49 

+     3' 

IS 
14 
15 

9.58159 
.58163 
.58167 
.58171 

.38158 
.38162 
.38165 
.38169 

9.58399 
.58403 
.58407 
.58411 

.38370 
.38374 
.38377 
.38381 

9.58639 
.58643 
.58647 
.58651 

.38582 
.38586 
.38590 
.38593 

9.58878 
.58882 
.58885 
.58889 

.38795 
.38799 
.38802 
.38806 

9.59115 
.59119 
.59123 
.59127 

.39008 
.39011 
.39015 
.39018 

48 
47 
46 
45 

+     4' 
17 
18 
19 

9.58175 
.58179 
.58183 
.58187 

.38172 
.38176 
.38179 
.38183 

9.58415 
.58419 
.58423 
.58427 

.38384 

.38388 
.38391 
.38395 

9.58655 
.58659 
.58663 
.58667 

.38597 
.38600 
.38604 
.38607 

9.58893 
.58897 
.58901 
.58905 

.38809 
.38813 
.38816 
.38820 

9.59131 
.59135 
.59139 
.59143 

.39022 
.39025 
.39029 
.39033 

44 
43 
42 
41 

+  5' 

21 
22 
2S 

9.58191 
.58195 
.58199 
.58203 

.38186 
.38190 
.38193 
.38197 

9.58431 
.58435 
.58439 
.58443 

.38398 
.38402 
.38406 
.38409 

9.58671 
.58675 
.58679 
.58683 

.38611 
.38614 
.38618 
.38621 

9.58909 
.58913 
.58917 
.58921 

.38823 

.38827 
.38830 
.38834 

9.59147 
.59151 
.59155 
.59158 

.39036 
.39040 
.39043 
.39047 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.58207 
.58211 
.58215 
.58219 

.38200 
.38204 
.38208 
.38211 

9.58447 
.58451 
.58455 
.58459 

.38413 
.38416 
.38420 
.38423 

9.58687 
.58691 
.58695 
.58699 

.38625 
.38628 
.38632 
.38636 

9.58925 
.58929 
.58933 
.58937 

.38837 
.38841 

.38845 
.38848 

9.59162 
.59166 
.59170 
.59174 

.39050 
.39054 
.39057 
.39061 

36 
35 
34 
SS 

+    r 

29 
SO 
SI 

9.58223 
.58227 
.58231 
.58235 

.38215 
.38218 
.38222 
.38225 

9.58463 
.58467 
.58471 
.58475 

.38427 
.38430 
.38434 
.38437 

9.58703 
.58707 
.58711 
.58715 

.38639 
.38643 
.38646 
.38650 

9.58941 
.58945 
.58949 
.58953 

.38852 

.38855 
.38859 
.38862 

9.59178 
.59182 
.59186 
.59190 

.39064 
.39068 
.39072 
.39075 

S2 
31 
SO 
29 

+     8' 
SS 
S4 
S5 

9.58239 
.58243 
.58247 
.58251 

.38229 
.38232 
.38236 
.38239 

9.58479 
.58483 
.58487 
.58491 

.38441 
.38444 
.38448 
.38451 

9.58719 
.58723 
.58727 
.58731 

.38653 
.38657 
.38660 
.38664 

9.58957 
.58961 
.58965 
.58969 

.38866 
.38869 

.38873 
.38876 

9.59194 
.59198 
.59202 
.59206 

.39079 
.39082 
.39086 
.39089 

28 
27 
26 
25 

+     9' 

S7 
S8 
S9 

9.58255 
.58259 
.58263 
.58267 

.38243 
.38246 
.38250 
.38254 

9.58495 
.58499 
.58503 
.58507 

.38455 
.38459 
.38462 
.38466 

9.58735 
.58739 
.58742 
.58746 

9.58750 
.58754 
.58758 
.58762 

.38667 
.38671 
.38675 
.38678 

9.58973 
.58977 
.58981 
.58985 

.38880 
.38884 
.38887 
.38891 

9.59210 
.59214 
.59218 
.59222 

.39093 
.39096 
.39100 
.39103 

24 
23 
22 
21 

+  W 

41 
42 
4S 

9.58271 
.58275 
.58279 
.58283 

.38257 
.38261 
.38264 
.38268 

9.58511 
.58515 
.58519 
.58523 

.38469 
.38473 
.38476 
.38480 

.38682 

.38685 
.38689 
.38692 

9.58989 
.58992 
.58996 
.59000 

.38894 

.38898 
.38901 
.38905 

9.59225 
.59229 
.59233 
.59237 

.39107 
.39111 
.39114 
.39118 

20 
19 
18 
17 

+   11' 

45 
46 
47 

9.58287 
.58291 
.58295 
.58299 

.38271 
.38275 

.38278 
.38282 

9.58527 
.58531 
.58535 
.58539 

.38483 

.38487 
.38490 
.38494 

9.58766 

.58770 
.58774 
.58778 

.38696 
.38699 
.38703 
.38706 

9.59004 
.59008 
.59012 
.59016 

.38908 
.38912 
.38915 
.38919 

9.59241 
.59245 
.59249 
.59253 

.39121 
.39125 
.39128 
.39132 

16 
15 
14 
13 

49 
50 
51 

9.58303 
.58307 
.58311 
.58315 

.38285 
.38289 
.38292 
.38296 

9.58543 
.58547 
.58551 
.58555 

.38498 
.38501' 
.38505 
.38508 

9.58782 
.58786 
.58790 
.58794 

.38710 
.38713 
.38717 
.38721 

9.59020 
.59024 
.59028 
.59032 

.38923 
.38926 
.38930 
.38933 

9.59257 
.59261 
.59265 
.59269 

.39135 
.39139 
.39143 
.39146 

U 

11 

10 

9 

+  13' 

5S 
54 
55 

9.58319 
.58323 
.58327 
.58331 

.38299 
.38303 
.38307 
.38310 

9.58559 
.58563 
.58567 
.58571 

.38512 
.38515 
.38519 
.38522 

9.58798 
.58802 
.58806 
.58810 

.38724 
.38728 
.38731 
.38735 

9.59036 
.59040 
.59044 
.59048 

.38937 
.38940 
.38944 
.38947 

9.59273 
.59277 
.59281 
.59285 

.39150 
.39153 
.39157 
.39160 

8 
7 
6 
5 

+  W 

57 
58 
59 

9.58335 
.58339 
.58343 
.58347 

.38314 
.38317 
.38321 
.38324 

9.58575 
.58579 
.58583 
.58587 

.38526 
.38529 
.38533 
.38536 

9.58814 
.58818 
.58822 
.58826 

.38738 
.38742 
.38745 
.38749 

9.59052 
.59056 
.59060 
.59064 

.38951 
.38954 
.38958 
.38962 

9.59289 
.59292 
.59296 
.59300 

.39164 
.39167 
.39171 
.39174 

4 
S 

2 

1 

+  W 

9.58351 

.38328 

9.58591 

.38540 

9.58830 

.38752 

9.59068 

.38965 

9.59304 

.39178 

0 

18h  54"^ 

18^  5Sm 

18h62m 

18^  5im 

18h50m 

TABLE  45.                  [Page  873 
Havereines. 

s 

5hlom71°3(/ 

5ft  nm  77°  45' 

5h  12m  78°  C 

5A  ISm  78°  15' 

5ft  14m  78°  30' 

8 

60 
59 

58 
57 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

9.59304 
.59308 
.59312 
.59316 

.39178 
.39182 
.39185 
.39189 

9.59540 
.59544 
.59548 
.59552 

.39391 
.39395 
.39398 
.39402 

9.59774 
.59778 
.59782 
.59786 

.39604 
.39608 
.39612 
.39615 

9.60008 
.60012 
.60016 
.60020 

.39818 
.39821 
.39825 
.39829 

9.60240 
.60244 
.60248 
.60252 

.40032 
.40035 
.40039 
.40042 

+    r 

5 
6 

7 

9.59320 
.59324 
.59328 
.59332 

.39193 
.39196 
.39199 
.39203 

9.59556 
.59559 
.59563 
.59567 

.39405 
.39409 
.39412 
.39416 

9.59790 
.59794 
.59798 
.59802 

.39619 
.30622 
.39626 
.39629 

9.60023 
.60027 
.60031 
.60035 

.39832 
.39836 
.39839 
.39843 

9.60256 
.60260 
.60263 
.60267 

.40046 
.40049 
.40053 
.40057 

56 
55 
54 
53 

+      -y 

9 

10 

11 

9.59336 
.59340 
.59344 
.59348 

.39206 
.39210 
.39214 
.39217 

9.59571 
.59575 
.59579 
.59583 

.39420 
.39423 
.39427 
.39430 

9.59806 
.59809 
.59813 
.59817 

.39633 
.39636 
.39640 
.39844 

9.60039 
.60043 
.60047 
.60051 

.39846 
.39850 
.39854 
.39857 

9.60271 
.60275 
.60279 
.60283 

.40060 
.40064 
.40067 
.40071 

52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
S8 
37 

+     3' 

IS 
14 
15 

+  4' 
17 
18 
19 

9.59351 
.59355 
.59359 
.59363 

.39221 
.39224 
.39228 
.39231 

9.59587 
.59591 
.59595 
.59599 

.39434 
.39437 
.39441 
.39444 

9.59821 
.59825 
.59829 
.59833 

.39647 
.39651 
.39654 
.39658 

9.60054 
.60058 
.60062 
.60066 

.39861 
.39864 
.39868 
.39871 

9.60287 
.60291 
.60294 
.60298 

.40074 
.40078 
.40081 
.40085 

9.59367 
.59371 
.59375 
.59379 

.39235 
.39238 
.39242 
.39245 

9.59602 
.59606 
.59610 
.59614 

.39448 
.39451 
.39455 
.39459 

9.59837 
.59841 
.59845 
.59848 

.39661 
.39665 
.39668 
.39672 

9.60070 
.60074 
.60078 
.60082 

.39875 
.39878 

.39882 
.39886 

9.60302 
.60306 
.60310 
.60314 

.40089 
.40092 
.40096 
.40099 

+  5' 
21 

22 
23 

9.59383 
.59387 
.59391 
.59395 

.39249 
.39253 
.39256 
.39260 

9.59618 
.59622 
.59626 
.59630 

.39462 
.3946G 
.39469 
.39473 

9.59852 
.59856 
.59860 
.59864 

.39676 
.39679 
.39683 
.39686 

9.60085 
.60089 
.60093 
.60097 

.39889 
.39893 
.39896 
.39900 

9.60318 
.60321 
.60325 
.60329 

.40103 
.40106 
.40110 
.40114 

+   6' 

25 
26 
27 

9.59399 
.59403 
.59406 
.59410 

.39263 
.39267 
.39270 
.39274 

9.59634 
.59638 
.59642 
.59646 

.39476 
.39480 
.39484 
.39487 

9.59868 
.59872 
.59876 
.59880 

.39690 
.39693 
.39697 
.39700 

9.60101 
.60105 
.60109 
.60113 

.39903 
.39907 
.39910 
.39914 

9.60333 
.60337 
.60341 
.60345 

.40117 
.40121 
.40124 
.40128 

36 
35 
34 
33 

32 
31 
30 
29 

28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 

+    r 

29 
SO 
SI 

9.59414 
.59418 
.59422 
.59426 

.39277 
.39281 
.39285 
.39288 

9.59649 
.59653 
.59657 
.59661 

.39491 
.39494 
.39498 
.39501 

9.59883 
.59887 
.59891 
.59895 

.39704 
.39708 
.39711 
.39715 

9.60116 
.60120 
.60124 
.60128 

.39918 
.39921 
.39925 
.39928 

9.60348 
.60352 
.60356 
.60360 

.40131 
.40135 
.40139 
.40142 

+   8' 
SS 
34 
35 

9.59430 
.59434 
.59438 
.59442 

.39292 
.39295 
.39299 
.39302 

9.59665 
.59669 
.59673 
.59677 

.39505 
.39508 
.39512 
.39516 

9.59899 
.59903 
.59907 
.59911 

.39718 
.39722 
.39725 
.39729 

9.60132 
.60136 
.60140 
.60144 

.39932 
.39935 
.39939 
.39943 

9.60364 
.60368 
.60372 
.60375 

.40146 
.40149 
.40153 
.40156 

+  9^ 

37 
38 
39 

9.59446 
.59450 
.59454 
.59458 

.39306 
.39309 
.39313 
.39317 

9.59681 
.59685 
.59688 
.59692 

.39519 
.39523 
.39526 
.39530 

9.59915 
.59918 
.59922 
.59926 

.39732 
.39736 
.39739 
.39743 

9.60147 
.60151 
.60155 
.60159 

.39946 
.39950 
.39953 
.39957 

9.60379 
.60383 
.60387 
.60391 

.40160 
.40163 
.40167 
.40171 

+    W 

41 
42 
43 

9.59461 
.59465 
.59469 
.59473 

.39320 
.39324 
.39327 
.39331 

9.59696 
.59700 
.59704 
.59708 

.39533 
.39537 
.39540 
.39544 

9.59930 
.59934 
.59938 
.59942 

.39746 
.39750 
.39754 
.39757 

9.60163 
.60167 
.60171 
.60175 

.39960 
.39964 
.39967 
.39971 

9.60395 
.60399 
.60402 
.60406 

.40174 
.40178 
.40181 
.40185 

+  ir 

45 
46 

47 

9.59477 
.59481 
.59485 
.59489 

.39334 
.39338 
.39341 
.39345 

9.59712 
.59716 
.59720 
.59724 

.39548 
.39551 
.39555 
.39558 

9.59946 
.59950 
.59953 
.59957 

.39761 
.39765 
'39768 
.39772 

9.60178 
.60182 
.60186 
.60190 

.39975 
.39978 
.39982 
.39985 

9.60410 
.60414 
.60418 
.60422 

.40188 
.40192 
.40196 
.40199 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

+    ir 

49 
50 
61 

9.59493 
.59497 
.59501 
.59505 

.39348 
.39352 
.39356 
.39359 

9.59728 
.59731 
.59735 
.59739 

.39562 
.39565 
.39569 
.39572 

9.59961 
.59965 
.59969 
.59973 

.39775 
.39779 
.39782 
.39786 

9.60194 
.60198 
.60202 
.60206 

.39989 
.39992 
.39996 
.40000 

9.60426 
.60429 
.60433 
.60437 

.40203 
.40206 
.40210 
.40213 

+    13' 

53 
54 
55 

9.59508 
.59512 
.59516 
.59520 

.39363 
.39366 
.39370 
.39373 

9.59743 
.59747 
.59751 
.59755 

.39576 
.39580 
.39583 
.39587 

9.59977 
.59981 
.59985 
.59988 

.39789 
.39793 
.39796 
.39800 

9.60209 
.60213 
.60217 
.60221 

.40003 
.40007 
.40010 
.40014 

9.60441 
.60445 
.60449 
.60452 

.40217 
.40220 
.40224 
.40228 

+  14' 

57 
58 
59 

9.59524 
.59528 
.59532 
.59536 

.39377 
.39380 
.39384 
.39388 

9.59759 
.59763 
.59767 
.59770 

.39590 
.39594 
.39597 
.39601 

9.59992 
.59996 
.60000 
.60004 

.39803 
.39807 
.39811 
.39814 

9.60225 
.60229 
.60233 
.60236 

.40017 
.40021 
.40024 
.40028 

9.60456 
.60460 
.60464 
.60468 

.40231 
.40235 
.40238 
.40242 

4 
3 
2 
1 

+  15' 

9.59540 

.39391 

9.59774 

.39604 

9.60008 

.39818 

9.60240 

.40032 

9.60472 

.40245 

0 

18h  49m 

18^48^ 

I8JI'  47m 

18^  4&^ 

18^  45^n 

Page  874]                  TABLE  45. 

Haversines. 

s 

5h  15m  78°  45^ 

5h  16m  79°  0^ 

5h  17m  79°  15^ 

5h  18m  79°  30^ 

5h  igm  79°  45/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.60472 
.60476 
.60479 
.60483 

.40345 
.40349 
.40353 
.40356 

9.60702 
.60706 
.60710 
.60714 

.40460 
.40463 
.40467 
.40470 

9.60931 
.60935 
.60939 
.60943 

.40674 
.40677 
.40681 
.40685 

9.61160 
.61164 
.61167 
.61171 

.40888 
.40893 
.40895 
.40899 

9.61387 
.61391 
.61395 
.61399 

.41103 
.41106 
.41110 
.41114 

60 
59 
58 
57 

+  1' 

5 
6 

7 

9.60487 
.60491 
.60495 
.60499 

.40360 
.40363 
.40367 
.40370 

9.60717 
.60721 
.60725 
.60729 

.40474 
.40477 
.40481 
.40485 

9.60947 
.60951 
.60954 
.60958 

.40688 
.40693 
.40695 
.40699 

9.61175 
.61179 
.61183 
.61186 

.40903 
.40906 
.40910 
.40913 

9.61402 
.61406 
.61410 
.61414 

.41117 
.41131 
.41134 
.41138 

56 
55 
54 
53 

+  ■  3^ 

9 

10 

11 

9.60502 
.60506 
.60510 
.60514 

.40374 
.40377 
.40381 
.40385 

9.60733 
.60737 
.60740 
.60744 

.40488 
.40493 
.40495 
.40499 

9.60962 
.60966 
.60970 
.60973 

.40703 
.40706 
.40710 
.40713 

9.61190 
.61194 
.61198 
.61202 

.40917 
.40930 
.40934 
.40938 

9.61417 
.61421 
.61425 
.61429 

.41131 
.41135 
.41139 
.41143 

52 
51 
50 
49 

+  3^ 

13 
14 
15 

9.60518 
.60522 
.60526 
.60529 

.40388 
.40393 
.40395 
.40399 

9.60748 
.60752 
.60756 
.60760 

.40503 
.40506 
.40510 
.40513 

9.60977 
.60981 
.60985 
.60989 

.40717 
.40730 
.40734 
.40737 

9.61205 
.61209 
.61213 
.61217 

.40931 
.40935 
.40938 
.40943 

9.61433 
.61436 
.61440 
.61444 

.41146 
.41149 
.41153 
.41156 

48 

47 
46 
45 

+  4^ 

n 

18 
19 

9.60533 
.60537 
.60541 
.60545 

.40303 
.40306 
.40310 
.40313 

9.60763 
.60767 
.60771 
.60775 

.40517 
.40530 
.40534 
.40537 

9.60992 
.60996 
.61000 
.61004 

.40731 
.40735 
.40738 
.40743 

9.61221 
.61224 
.61228 
.61232 

.40945 
.40949 
.40953 
.40956 

9.61448 
.61451 
.61455 
.61459 

.41160 
.41164 
.41167 
.41171 

44 
43 
42 
41 

+   5^ 

22 

23 

9.60549 
.60552 
.60556 
.60560 

.40317 
.40330 
.40334 
.40338 

9.60779 
.60783 
.60786 
.60790 

.40531 
.40535 
.40538 
.40543 

9.61008 
.61012 
.61015 
.61019 

.40745 
.40749 
'40753 
.40756 

9.61236 
.61240 
.61243 
.61247 

.40960 
.40963 
.40967 
.40970 

9.61463 
.61467 
.61470 
.61474 

.41174 
.41178 
.41183 
.41185 

40 
39 
38 
37 

+   6^ 

^7 

9.60564 
.60568 
.60572 
.60576 

.40331 
.40335 
.40338 
.40343 

9.60794 
.60798 
.60802 
.60805 

.40545 
.40549 
.40553 
.40556 

9.61023 
.61027 
.61031 
.61034 

.40760 
.40763 
.40767 
.40770 

9.61251 
.61255 
.61258 
.61262 

.40974 
.40978 
.40981 
.40985 

9.61478 
.61482 
.61485 
.61489 

.41189 
.41193 
.41196 
.41199 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.60579 
.60583 
.60587 
.60591 

.40345 
.40349 
.40353 
.40356 

9.60809 
.60813 
.60817 
.60821 

.40560 
.40563 
.40567 
.40570 

9.61038 
.61042 
.61046 
.61050 

.40774 
.40777 
.40781 
.40785 

9.61266 
.61270 
.61274 
.61277 

.40988 
.40993 
.40996 
.40999 

9.61493 
.61497 
.61500 
.61504 

.41303 
.41307 
.41310 
.41314 

32 
31 
SO 
29 

+  8^ 
33 
34 
35 

9.60595 
.60599 
.60602 
.60606 

.40360 
.40363 
.40367 
.40370 

9.60825 
.60828 
.60832 
.60836 

.40574 
.40577 
.40581 
.40585 

9.61053 
.61057 
.61061 
.61065 

.40788 
.40793 
.40795 
.40799 

9.61281 
..61285 
.61289 
.61293 

.41003 
.41006 
.41010 
.41013 

9.61508 
.61512 
.61516 
.61519 

.41317 
.41331 
.41335 
.41338 

28 
27 
26 
25 

+     9^ 

37 
38 
39 

9.60610 
.60614 
.60618 
.60622 

.40374 
.40377 
.40381 
.40385 

9.60840 
.60844 
.60847 
.60851 

.40588 
.40593 
.40595 
.40599 

9.61069 
.61072 
.61076 
.61080 

.40803 
.40806 
.40810 
.40813 

9.61296 
.61300 
.61304 
.61308 

.41017 
.41031 
.41034 
.41038 

9.61523 
.61527 
.61531 
.61534 

.41333 
.41335 
.41239 
.41342 

24 
23 
22 
21 

+  w 

41 
42 
43 

9.60625 
.60629 
.60633 
.60637 

.40388 
.40393 
.40395 
.40399 

9.60855 
.60859 
.60863 
.60867 

.40603 
.40606 
.40610 
.40613 

9.61084 
.61088 
.61091 
.61095 

.40817 
.40830 
.40834 
.40837 

9.61312 
.61315 
.61319 
.61323 

.41031 
.41035 
.41039 
.41043 

9.61538 
.61542 
.61546 
.61549 

.41346 
.41250 
.41353 
.41357 

20 
19 
18 
17 

+  11' 

■45 

47 

9.60641 
.60645 
.60648 
.60652 

.40403 
.40406 
.40410 
.40413 

9.60870 
.60874 
.60878 
.60882 

.40617 
.40630 
.40634 
.40637 

9.61099 
.61103 
.61107 
.61110 

.40831 
.40835 
.40838 
.40843 

9.61327 
.61330 
.61334 
.61338 

.41046 
.41049 
.41053 
.41056 

9.61553 
.61557 
.61561 
.61565 

.41260 
.41264 
.41267 
.41371 

16 
15 
14 
13 

+  12^ 

49 

5i 

9.60656 
.60660 
.60664 
.60668 

.40417 
.40430 
.40434 
.40437 

9.60886 
.60890 
.60893 
.60897 

.40631 
.40635 
.40638 
.40643 

9.61114 
.61118 
.61122 
.61126 

.40845 
.40849 
.40853 
.40856 

9.61342 
.61346 
.61349 
.61353 

.41060 
.41063 
.41067 
.41071 

9.61568 
.61572 
.61576 
.61580 

.41375 
.41378 
.41383 
.41385 

12 

11 

10 

9 

+  13^ 

53 
54 
55 

9.60671 
.60675 
.60679 
.60683 

.40431 
.40434 
.40438 
.40443 

9.60901 
.60905 
.60909 
.60912 

.40645 
.40649 
.40653 
.40656 

9.61129 
.61133 
.61137 
.61141 

.40860 
.40863 
.40867 
.40870 

9.61357 
.61361 
.61364 
.61368 

.41074 
.41078 
.41083 
.41085 

9.61583 
.61587 
.61591 
.61595 

.41389 
.41393 
.41396 
.41300 

8 

7 
6 
5 

57 
55 
59 

9.60687 
.60691 
.60694 
.60698 

.40445 
.40449 
.40453 
.40456 

9.60916 
.60920 
.60924 
.60928 

.40660 
.40663 
.40667 
.40670 

9.61145 
.61148 
.61152 
.61156 

.40874 
.40878 
.40881 

.40885 

9.61372 
.61376 
.61380 
.61383 

.41089 
.41093 
.41096 
.41099 

9.61598 
.61602 
.61606 
.61610 

.41303 
.41307 
.41310 
.41314 

4 
3 
2 
1 

+  15^ 

9.60702 

.40460 

9.60931 

.40674 

9.61160 

.40888 

9.61387 

.41103 

9.61614 

.41318 

0 

18h44m 

18fi  43^ 

18^42^ 

18h  4im 

18h4am         1 

TABLE  45.                 [Page  875 

Haversinea. 

s 

5fe  20'^  80°  (K 

5h  21m  80°  15^ 

5h  2pn  80°  30^ 

5h  23m  80°  45' 

5^^  24'^  81°  O' 

3 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.61614 
.61617 
.61621 
.61625 

.41318 
.41331 
.41325 
.41338 

9.61839 
.61843 
.61846 
.61850 

.41533 
.41536 
.41540 
.41543 

9.62063 
.62067 
.62071 
.62074 

.41748 
.41751 
.41755 
.41758 

9.62287 
.62290 
.62294 
.62298 

.41963 
.41966 
.41970 
.41974 

9.62509 
.62513 
.62516 
.62520 

.42178 
.42182 
.42185 
.42189 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.61629 
.61632 
.61636 
.61640 

.41332 
.41335 
.41339 
.41343 

9.61854 
.61858 
.61861 
.61865 

.41547 
.41550 
.41554 
.41558 

9.62078 
.62082 
.62086 
.62089 

.41762 
.41766 
.41769 
.41773 

9.62301 
.62305 
.62309 
.62313 

.41977 
.41981 
.41984 
.41988 

9.62524 
.62527 
.62531 
.62535 

.42193 
.42196 
.42200 
.42303 

56 
55 
54 
53 

+      r 

9 

10 

11 

9.61644 
.61647 
.61651 
.61655 

.41346 
.41350 
.41353 
.41357 

9.61869 
.61873 
.61876 
.61880 

.41561 
.41565 
.41568 
.41572 

9.62093 
.62097 
.62100 
.62104 

.41776 
.41780 
.41783 
.41787 

9.62316 
.62320 
.62324 
.62327 

.41992 
.41995 
.41999 
.42002 

9.62538 
.62542 
.62546 
.62550 

.42307 
.43311 
.43314 
.42218 

52 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42 
41 

+  K 

13 
14 
15 

9.61659 
.61662 
.61666 
.61670 

.41361 
.41364 
.41368 
.41371 

9.61884 
.61888 
.61891 
.61895 

.41576 
.41579 
.41583 
.41586 

9.62108 
.62112 
.62115 
.62119 

.41791 
.41794 
.41798 
.41801 

9.62331 
.62335 
.62338 
.62342 

.42006 
.42010 
.42013 
.42017 

9.62553 
.62557 
.62561 
.62564 

.42221 
.42225 
.42239 
.42333 

+     i' 
17 
18 
19 

9.61674 
.61677 
.61681 
.61685 

.41375 
.41378 
.41382 
.41386 

9.61899 
.61903 
.61906 
.61910 

.41590 
.41593 
.41597 
.41601 

9.62123 
.62127 
.62130 
.62134 

.41805 
.41809 
.41812 
.41816 

9.62346 
.62350 
.62353 
.62357 

.42020 
.42024 
.42027 
.42031 

9.62568 
.62572 
.62575 
.62579 

.42236 
.43339 
.43343 
.43347 

+  5' 
21 

22 
23 

9.61689 
.61692 
.61696 
.61700 

.41389 
.41393 
.41396 
.41400 

9.61914 
.61917 
.61921 
.61925 

.41604 
.41608 
.41611 
.41615 

9.62138 
.62141 
.62145 
.62149 

.41819 
.41823 
.41827 
.41830 

9.62361 
.62364 
.62368 
.62372 

.42035 
.42038 
.42042 
.42045 

9.62583 
.62586 
.62590 
.62594 

.43350 
.42254 
.42257 
.42261 

40 
39 
38 
37 
36 
35 
34 
33 

+      6^ 

25 
26 
27 

9.61704 
.61708 
.61711 
.61715 

.41404 
.41407 
.41411 
.41414 

9.61929 
.61932 
.61936 
.61940 

.41619 
.41622 
.41626 
.41629 

9.62153 
.62156 
.62160 
.62164 

.41834 
.41837 
.41841 
.41844 

9.62376 
.62379 
.62383 
.62387 

.42049 
.42053 
.42056 
.42060 

9.62598 
.62601 
.62605 
.62609 

.42264 
.43368 
.43373 
.43375 

+    r 

29 
30 
31 

9.61719 
.61723 
.61726 
.61730 

.41418 
.41421 
.41425 
.41429 

9.61944 
.61947 
.61951 
.61955 

.41633 
.41636 
.41640 
.41644 

9.62168 
.62171 
.62175 
.62179 

.41848 
.41852 
.41855 
.41859 

9.62390 
.62394 
.62398 
.62402 

.42063 
.42067 
.42071 
.42074 

9.62612 
.62616 
.62620 
.62623 

.43379 
.43383 
.43386 
.43290 

32 
31 
30 
29 
28 
27 
26 
25 

24 
23 

22 
21 

+   8' 
33 
34 
35 

9.61734 
.61738 
.61741 
.61745 

.41432 
.41436 
.41439 
.41443 

9.61959 
.61962 
.61966 
.61970 

.41647 
.41651 
.41654 
.41658 

9.62182 
.62186 
.62190 
.62194 

.41862 
.41866 
.41870 
.41873 

9.62405 
.62409 
.62413 
.62416 

.42078 
.42081 
.42085 
.42089 

9.62627 
.62631 
.62634 
.62638 

.42293 
.42297 
.42300 
.42304 

+   9^ 

37 
38 
39 

9.61749 
.61753 
.61756 
.61760 

.41447 
.41450 
.41454 
.41457 

9.61974 
.61977 
.61981 
.61985 

.41662 
.41665 
.41669 
.41672 

9.62197 
.62201 
.62205 
.62208 

.41877 
.41880 
.41884 

.41888 

9.62420 
.62424 
.62427 
.62431 

.42092 
.42096 
.42099 
.42103 

9.62642 
.62646 
.62649 
.62653 

.42308 
.42311 
.42315 
.42318 

+  W 

41 
42 
43 

9.61764 
.61768 
.61771 
.61775 

.41461 
.41464 
.41468 
.41472 

9.61989 
.61992 
.61996 
.62000 

.41676 
.41679 
.41683 
.41687 

9.62212 
.62216 
.62220 
.62223 

.41891 
.41895 
.41898 
.41902 

9.62435 
.62439 
.62442 
.62446 

.42106 
.42110 
.42114 
.42117 

9.62657 
.62660 
.62664 
.62668 

.43323 
.43336 
.43339 
.43333 

20 
19 
18 
17 

+  11^ 

45 
46 

47 

9.61779 
.61783 
.61786 
.61790 

.41475 
.41479 
.41482 
.41486 

9.62003 
.62007 
.62011 
.62015 

.41690 
.41694 
.41697 
.41701 

9.62227 
.62231 
.62234 
.62238 

.41905 
.41909 
.41913 
.41916 

9.62450 
.62453 
.62457 
.62461 

.42121 
.42124 
.42128 
.42132 

9.62671 
.62675 
.62679 
.62682 

.43336 
.43340 
.42344 
.42347 

16 
15 
14 
IS 

49 
50 
51 

9.61794 
.61798 
.61801 
.61805 

.41490 
.41493 
.41497 
.41500 

9.62018 
.62022 
.62026 
.62030 

.41705 
.41708 
.41712 
.41715 

9.62242 
.62246 
.62249 
.62253 

.41920 
.41923 
.41927 
.41931 

9.62464 
.62468 
.62472 
.62476 

.42135 
.42139 
.42142 
.42146 

9.62686 
.62690 
.62693 
.62697 

.42351 
.42354 
.42358 
.42361 

12 

11 

10 

9 

+  13^ 

53 
54 
55 

9.61809 
.61813 
.61816 
.61820 

.41504 
.41507 
.41511 
.41515 

9.62033 
.62037 
.62041 
.62045 

.41719 
.41722 
.41726 
.41730 

9.62257 
.62261 
.62264 
.62268 

.41934 
.41938 
.41941 
.41945 

9.62479 
.62483 
.62487 
.62490 

.42150 
.42153 
.42157 
.42160 

9.62701 
.62704 
.62708 
.62712 

.42365 
.42369 
.43372 
.42376 

8 
7 
6 
5 

+  W 

57 
58 
59 

9.61824 
.61828 
.61831 
.61835 

.41518 
.41522 
.41525 
.41529 

9.62048 
.62052 
.62056 
.62059 

.41733 
.41737 
.41740 
.41744 

9.62272 
.62275 
.62279 
.62283 

.41949 
.41952 
.41956 
.41959 

9.62494 
.62498 
.62501 
.62505 

.42164 
.42168 
.42171 
.42175 

9.62716 
.62719 
.62723 
.62727 

.42379 
.42383 
.42387 
.42390 

4 
S 

2 
1 

+  15^ 

9.61839 

.41533 

9.62063 

.41748 

9.62287 

.41963 

9.62509 

.42178 

9.62730 

.42394 

0 

18h  39m 

18^  38m 

J8h  37m         1 

18^S6m 

18^  35-^ 

21594°— 14- 


-48 


TABLE  45.                  [Page  877 
Haversines. 

s 

5^50^82°  30' 

5h  3lm  82°  45' 

5ft  32m  83°  0' 

5^  33m  83°  15' 

5h  34m  83°  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav 

0 
1 

2 
3 

9.63823 
.63826 
.63830 
.63833 

.43474 
.43477 
.43481 
.43485 

9.64038 
.64042 
.64046 
.64049 

.43690 
.43694 
.43697 
.43701 

9.64253 
.64256 
.64260 
.64264 

.43907 
.43910 
.43914 
.43917 

9.64467 
.64470 
.64474 
.64477 

.44123 
.44127 
.44130 
.44134 

9.64679 
.64683 
.64686 
.64690 

.44340 
.44343 
.44347 
.44351 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.63837 
.63841 
.63844 
.63848 

.43488 
.43492 
.43495 
.43499 

9.64053 
.64056 
.64060 
.64063 

.43704 
.43708 
.43712 
.43715 

9.64267 
.64271 
.64274 
.64278 

.43921 
.43925 
.43928 
.43932 

9.64481 
.64484 
.64488 
.64492 

.44138 
.44141 
.44145 
.44148 

9.64694 
.64697 
.64701 
.64704 

.44354 
.44358 
.44362 
.44365 

56 
55 
54 
53 

+    r 

9 
10 
11 

9.63851 
.63855 
.63859 
.63862 

.43503 
.43506 
.43510 
.43513 

9.64067 
.64071 
.64074 
.64078 

.43719 
.43723 
.43726 
.43730 

9.64281 
.64285 
.64289 
.64292 

.43935 
.43939 
.43943 
.43946 

9.64495 
.64499 
.64502 
.64506 

.44152 
.44156 
.44159 
.44163 

9.64708 
.64711 
.64715 
.64718 

.44369 
.44372 
.44376 
.44380 

52 
51 
50 
49 
48 
47 
46 
45 

+     3' 

13 
14 
15 

9.63866 
.63869 
.63873 
.63877 

.43517 
.43521 
.43524 
.43528 

9.64081 
.64085 
.64088 
.64092 

.43733 
.43737 
.43741 
.43744 

9.64296 
.64299 
.64303 
.64306 

.43950 
.43953 
.43957 
.43961 

9.64509 
.64513 
.64516 
.64520 

.44166 
.44170 
.44174 
.44177 

9.64722 
.64725 
.64729 
.64732 

.44383 
.44387 
.44390 
.44394 

+  4^ 
17 
18 
19 

9.63880 
.63884 
.63887 
.63891 

.43531 
.43535 
.43539 
.43542 

9.64096 
.64099 
.64102 
.64106 

.43748 
.43751 
.43755 
.43759 

9.64310 
.64314 
.64317 
.64321 

.43964 
.43968 
.43972 
.43975 

9.64523 
.64527 
.64531 
.64534 

.44181 
.44185 
.44188 
.44192 

9.64736 
.64740 
.64743 
.64747 

.44398 
.44401 
.44405 
.44408 

U 
43 
42 
41 

+     5' 
21 
22 
23 

9.63895 
.63898 
.63902 
.63905 

.43546 
.43549 
.43553 
.43557 

9.64110 
.64113 
.64117 
.64121 

.43762 
.43766 
.43769 
.43773 

9.64324 
.64328 
.64331 
.64335 

.43979 
.43982 
.43986 
.43990 

9.64538 
.64541 
.64545 
.64548 

.44195 
.44199 
.44203 
.44206 

9.64750 
.64754 
.64757 
.64761 

.44412 
.44416 
.44419 
.44423 

40 
39 
38 
37 

+      8' 

25 
26 

27 

9.63909 
.63913 
.63916 
.63920 

.43560 
.43564 
.43567 
.43571 

9.64124 
.64128 
.64131 
.64135 

.43777 
.43780 
.43784 
.43787 

9.64339 
.64342 
.64346 
.64349 

.43993 
.43997 
.44000 
.44004 
.44008 
.44011 
.44015 
.44018 

9.64552 
.64555 
.64559 
.64563 

9.64566 
.64570 
.64573 
.64577 

.44210 
.44213 
.44217 
.44221 

9.64764 
.64768 
.64771 
.64775 

.44427 
.44430 
.44434 
.44437 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.63923 
.63927 
.63931 
.63934 

.43575 
.43578 
.43582 
.43585 

9.64139 
.64142 
.64146 
.64149 

.43791 
.43795 
.43798 
.43802 

9.64353 
.64356 
.64360 
.64363 

.44224 
.44228 
.44231 
.44235 

9.64778 
.64782 
.64785 
.64789 

.44441 
.44445 
.44448 
.44452 

32 
31 

30 
29 

+   8' 
33 
34 
35 

9.63938 
.63941 
.63945 
.63949 

.43589 
.43593 
.43596 
.43600 

9.64153 
.64156 
.64160 
.64164 

.43805 
.43809 
.43813 
.43816 

9.64367 
.64371 
.64374 
.64378 

.44022 
.44026 
.44029 
.44033 

9.64580 
.64584 
.64587 
.64591 

.44239 
.44242 
.44246 
.44250 

9.64793 
.64796 
.64800 
.64803 

.44455 
.44459 
.44463 
.44466 

28 
27 
26 
25 

+   9' 

37 
38 
39 

9.63952 
.63956 
.63959 
.63963 

.43603 
.43607 
.43611 
.43614 

9.64167 
.64171 
.64174 
.64178 

.43820 
.43824 
.43827 
.43831 

9.64381 
.64385 
.64388 
.64392 

.44036 
.44040 

•44U44 

.44047 

9.64594 
.64598 
.64602 
.64605 

.44253 
.44257 
.44260 
.44264 

9.64807 
.64810 
.64814 
.64817 

.44470 
.44474 
.44477 
.44481 

24 
23 
22 
21 

+  10' 

41 
42 
43 

9.63966 
.63970 
.63974 
.63977 

.43618 
.43622 
.43625 
.43629 

9.64181 
.64185 
.64189 
.64192 

.43834 
.43838 
.43842 
.43845 

9.64396 
.64399 
.64403 
.64406 

.44051 
.44055 
.44058 
.44062 

9.64609 
.64612 
.64616 
.64619 

.44268 
.44271 
.44275 
.44278 

9.64821 
.64824 
.64828 
.64831 

.44484 

.44488 
.44492 
.44495 

20 
19 
18 
17 

+  ir 

45 
46 
■^7 

9.63981 
.63984 
.63988 
.63992 

.43632 
.43636 
.43640 
.43643 

9.64196 
.64199 
.64203 
.64206 

9.64210 
.64214 
.64217 
.64221 

.43849 
.43852 
.43856 
.43860 
.43863 
.43867 
.43870 
.43874 

9.64410 
.64413 
.64417 
.64420 

.44065 
.44069 
.44073 
.44076 

9.64623 
.64626 
.64630 
.64633 

.44282 
.44286 
.44289 
.44293 

9.64835 
.64838 
.64842 
.64845 

.44499 
.44502 
.44506 
.44510 

16 
15 
14 
13 

+  12' 

49 
50 
51 

9.63995 
.63999 
.64002 
.64006 

.43647 
.43650 
.43654 
.43658 

9.64424 
.64428 
.64431 
.64435 

.44080 
.44083 
.44087 
.44091 

9.64637  1  .44296 
.64640   .44300 
.64644   .44304 
.64648   .44307 

9.64849 
.64852 
.64856 
.64860 

.44513 
.44517 
.44521 
.44524 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.64010 
.64013 
.64017 
.64020 

.43661 
.43665 
.43668 
.43672 

9.64224 
.64228 
.64231 
.64235 

.43878 
.43881 

.43885 
.43888 

9.64438 
.64442 
.64445 
.64449 

.44094 
.44098 
.44101 
.44105 

9.64651 
.64655 
.64658 
.64662 

.44311 
.44315 
.44318 
.44322 

9.64863 
.64867 
.64870 
.64874 

.44528 
.44531 
.44535 
.44539 

+    14' 

57 
68 
59 

9.64024 
.64028 
.64031 
.64035 

.43676 
.43679 
.43683 
.43686 

9.64239 
.64242 
.64246 
.64249 

.43892 
.43896 
.43899 
.43903 

9.64452 
.64456 
.64460 
.64463 

.44109 
.44112 
.44116 
.44120 

9.64665 
.64669 
.64672 
.64676 

.44325 
.44329 
.44333 
.44336 

9.64877 
.64881 
.64884 
.64888 

.44542 
.44546 
.44549 
.44553 

4 
S 
2 
1 

+    15' 

9.64038 

.43690 

9.64253 

.43907 

9.64467 

.44123 

9.64679 

.44340 

9.64891 

.44557 

0 

18h 29m 

18J>'2S^ 

18h  27m 

18^  26m 

18h  25m 

Page  878]                 TABLE  45. 

Haversines. 

s 

5h  35m  83°  45' 

5A  36m  84°  C 

5h  37m  84°  15' 

5h  38m  84°  3^ 

5h  39m  84°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.64891 
.64895 
.64898 
.64902 

.M557 
.44560 
.44564 
.44568 

9.65102 
.65106 
.65109 
.65113 

.44774 
.44777 
.44781 
.44784 

9.65312 
.65316 
.65319 
.65323 

.44991 
.44994 
.44998 
.45001 

9.65521 
.65525 
.65528 
.65532 

.45308 
.45311 
.45315 
.45319 

9.65729 
.65733 
.65736 
.65740 

.45435 
.45439 
.45433 
.45436 

60 
59 
58 

57 

+    r 

5 

6 

7 

9.64905 
.64909 
.64912 
.64916 

.44571 
.44575 
.44578 
.44583 

9.65116 

1.65120 

.65123 

.65127 

-.44788 
.44793 
.44795 
.44799 

9.65326 
.65330 
.65333 

♦.65337 

.45005 
.45009 
.45013 
.45016 

9.65535 
.65539 
.65542 
.65546 

.45333 
.45336 
.45339 
.45333 

9.65743 
.65747 
.65750 
.65754 

.45439 
.45443 
.45447 
.45450 

56 
55 
54 
53 

+     V 

9 

10 

11 

9.64919 
.64923 
.64926 
.64930 

.44586 
.44589 
.44593 
.44596 

9.65130 
.65134 
.65137 
.65141 

.44803 
.44806 
.44810 
.44813 

9.65340 
.65344 
.65347 
.65351 

.45030 
.45033 
.45037 
.45030 

9.65549 
.65553 
.65556 
.65559 

.45337 
.45340 
.45244 
.45348 

9.65757 
.65761 
.65764 
.65767 

.45454 
.45458 
.45461 
.45465 

52 
51 
50 
49 

+      r 

13 
14 
15 

9.64934 
.64937 
.64941 
.64944 

.44600 
.44604 
.44607 
.44611 

9.65144 
.65148 
.65151 
.65155 

.44817 
.44831 
.44834 

.44838 

9.65354 
.65358 
.65361 
.65365 

.45034 
.45038 
.45041 
.45045 

9.65563 
.65566 
.65570 
.65573 

.45351 
.45335 
.45358 
.45362 

9.65771 
.65774 
.65778 
.65781 

.45468 
.45472 
.45476 
.45479 

48 
47 
46 

45 

44 
43 
42 
41 

+      4' 
17 
18 
19 

9.64948 
.64951 
.64955 
.64958 

.44614 
.44618 
.44623 
.44635 

9.65158 
.65162 
.65165 
.65169 

.44831 
.44835 
.44839 
.44843 

9.65368 
.65372 
.65375 
.65378 

.45048 
.45053 
.45056 
.45059 

9.65577 
.65580 
.65584 
.65587 

.45266 
.45269 
.45273 
.45276 

9.65785 
.65788 
.65792 
.65795 

.45483 
.45486 
.45490 
.45494 

+     5' 
21 
22 
23 

9.64962 
.64965 
.64969 
.64972 

.44639 
.44633 
.44636 
.44640 

9.65172 
.65176 
.65179 
.65183 

.44846 
.44850 
.44853 
.44857 

9.65382 
.65385 
.65389 
.65392 

.45063 
.45067 
.45070 
.45074 

9.65591 
.65594 
.65598 
.65601 

.45280 
.45284 

.45287 
.45391 

9.65799 
.65802 
.65806 
.65809 

.45497 
.45501 
.45505 
.45508 

40 
39 
38 

37 

+     6' 

25 
26 

27 

9.64976 
.64979 
.64983 
.64986 

.44643 
.44647 
.44651 
.44654 

9.65186 
.65190 
.65193 
.65197 

.44860 
.44864 
.44868 
.44871 

9.65396 
.65399 
.65403 
.65406 

.45077 
.45081 
.45085 

.45088 

9.65605 
.65608 
.65612 
.65615 

.45395 
.45398 
.45303 
.45305 

9.65812 
.65816 
.65819 
.65823 

.45513 
.45515 
.45519 
.45523 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.64990 
.64993 
.64997 
.65000 

.44658 
.44661 
.44665 
.44669 

9.65200 
.65204 
.65207 
.65211 

.44875 

.44878 
.44883 
.44886 

9.65410 
.65413 
.65417 
.65421 

.45093 
.45096 
.45099 
.45103 

9.65619 
.65622 
.65625 
.65629 

.45309 
.45313 
.45316 
.45330 

9.65826 
.65830 
.65833 
.65837 

.45526 
.45530 
.45534 
.45537 

32 
31 
SO 

29 

+     8' 
33 
34 
35 

9.65004 
.65007 
.65011 
.65014 

.44673 
.44676 
.44680 
.44683 

9.65214 
.65218 
.65221 
.65225 

.44889 
.44893 
.44897 
.44900 

9.65424 
.65427 
.65431 
.65434 

.45106 
.45110 
.45114 
.45117 

9.65632 
.65636 
.65639 
.65643 

.45334 
.45337 
.45331 
.45334 

9.65840 
.65844 
.65847 
.65850 

.45541 
.45544 
.45548 
.45553 

28 
27 
26 
25 

+     9^ 

37 
38 
39 

9.65018 
.65021 
.65025 
.65028 

.44687 
.44690 
.44694 
.44698 

9.65228 
.65232 
.65235 
.65239 

.44904 
.44907 
.44911 
.44915 

9.65438 
.65441 
.65445 
.65448 

.45131 
.45134 
.45138 
.45133 

9.65646 
.65650 
.65653 
.65657 

.45338 
.45343 
.45345 
.45349 

9.65854 
.65857 
.65861 
.65864 

.45555 
.45559 
.45563 
.45566 

24 
23 
22 
21 

+    W 

41 
42 
43 

9.65032 
.65035 
.65039 
.65043 

.44701 
.44705 
.44708 
.44713 

9.65242 
.65246 
.65249 
.65253 

.44918 
.44933 
.44935 
.44939 

9.65452 
.65455 
.65459 
.65462 

.45135 
.45139 
.45143 
.45146 

9.65660 
.65664 
.65667 
.65671 

.45353 
.45356 
.45360 
.45363 

9.65868 
.65871 
.65875 
.65878 

.45570 
.45573 
.45577 
.46581 

20 
19 
18 
17 
16 
15 
14 
13 

+   11' 

45 
46 
47 

9.65046 
.65050 
.65053 
.65057 

.44716 
.44719 
.44733 
.44737 

9.65256 
.65260 
.65263 
.65267 

.44933 
.44936 
.44940 
.44944 

9.65466 
.65469 
.65473 
.65476 

.45150 
.45153 
.45157 
.45161 

9.65674 
.65677 
.65681 
.65684 

.45367 
.45371 
.45374 
.45378 

9.65881 
.65885 
.65888 
.65892 

.45584 

.45f88 
.45592 
.45595 

+  ly 

49 
50 
51 

9.65060 
.65064 
.65067 
.65071 

.44730 
.44734 
.44737 
.44741 

9.65270 
.65274 
.65277 
.65281 

.44947 
.44951 
.44954 
.44958 

9.65480 
.65483 
.65486 
.65490 

.45164 
.45168 
.45173 
.45175 

9.65688 
.65691 
.65695 
.65698 

.45381 
.45385 
.45389 
.45393 

9.65895 
.65899 
.65902 
.65906 

.45599 
.45603 
.45606 
.45610 

12 

11 

10 

9 

+  13' 

53 

54 
55 

9.65074 
.65078 
.65081 
.65085 

.44745 
.44748 
.44753 
.44755 

9.65284 
.65288 
.65291 
.65295 

.44963 
.44965 
.44969 
.44973 

9.65493 
.65497 
.65500 
.65504 

.45179 
.45183 
.45186 
.45190 

9.65702 
.65705 
.65709 
.65712 

.45396 
.45400 
.45403 
.45407 

9.65909 
.65913 
.65916 
.65919 

.45613 
.45617 
.45630 
.45634 

8 
7 
6 
5 

+  ir 

57 
58 
59 

9.65088 
.65092 
.65095 
.65099 

.44759 
.44763 
.44766 
.44770 

9.65298 
.65302 
.65305 
.65309 

.44976 
.44980 
.44983 
.44987 

9.65507 
.65511 
.65514 
.65518 

.45193 
.45197 
.45300 
.45304 

9.65716 
.65719 
.65722 
.65726 

.45410 
.45414 
.45418 
.45431 

9.65923 
.65926 
.65930 
.65933 

.45628 
.45631 
.45635 
.45639 

4 
3 
2 
1 

+  W 

9.65102 

.44774 

9.65312 

.44991 

9.65521 

.45308 

9.65729 

.45435 

9.65937 

.45643 

0 

iSh  24^ 

ish 23m 

18^  22m 

18h  2im 

18^  20m 

TABLE  45.                  [Page  879 

Haversines. 

s 

5ft  4^  85°  (K  1 

5h  41"^  85°  15' 

5h  42^  85°  Sr 

5h  43m  85°  45' 

5A^'n86°0'  1 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

s 

0 
1 

2 
S 

9.65937 
.65940 
.65944 
.65947 

.45642 
.45646 
.45649 
.45653 

9.66143 
.66146 
.66150 
.66153 

.45860 
.45863 
.45867 
.45870 

9.66348 
.66352 
.66355 
.66359 

.46077 
.46081 
.46084 
.46088 

9.66553 
.66556 
.66560 
.66563 

.46295 
.46298 
.46302 
.46305 

9.66757 
.66760 
.66763 
.66767 

.46512 
.46516 
.46519 
.46523 

60 
59 
58 
57 
56 
55 
54 
53 

+    r 

5 
6 

7 

9.65950 
.65954 
.65957 
.65961 

.45657 
.45660 
.45664 
.45668 

9.66157 
.66160 
.66164 
.66167 

.45874 

.45878 
.45881 

.45885 

9.66362 
.66366 
.66369 
.66372 

.46092 
.46095 
.46099 
.46102 

9.66567 
.66570 
.66573 
.66577 

.46309 
.46313 
.46316 
.46320 

9.66770 
.66774 
.66777 
.66780 

.46527 
.46530 
.46534 
.46538 

+  3' 

9 

10 

11 

9.65964 
.65968 
.65971 
.65975 

.45671 
.45675 
.45678 
.45682 

9.66170 
.66174 
.66177 
.66181 

.45889 
.45892 
.45896 
.45899 

9.66376 
.66379 
.66383 
.66386 

.46106 
.46110 
.46113 
.46117 

9.66580 
.66584 
.66587 
.66590 

.46324 
.46327 
.46331 
.46334 

9.66784 
.66787 
.66791 
.66794 

.46541 
.46545 
.46548 
.46552 

52 
51 
50 
49 

1^ 
14 
15 

9.65978 
.65981 
.65985 
.65988 

.45686 
.45689 
.45693 
.45697 

9.66184 
.66188 
.66191 
.66194 

.45903 
.45907 
.45910 
.45914 

9.66389 
.66393 
.66396 
.66400 

.46121 
.46124 
.46128 
.46131 

9.66594 
.66597 
.66601 
.66604 

.46338 
.46342 
.46345 
.46349 

9.66797 
.66801 
.66804 
.66807 

.46556 
.46559 
.46563 
.46567 

48 
47 
46 
45 

+     4^ 
17 
18 
19 

9.65992 
.65995 
.65999 
.66002 

.45700 
.45704 
.45707 
.45711 

9.66198 
.66201 
.66205 
.66208 

.45918 
.45921 
.45925 
.45928 

9.66403 
.66407 
.66410 
.66413 

.46135 
.46139 
.46142 
.46146 

9.66607 
.66611 
.66614 
.66618 

.46353 
.46356 
.46360 
.46363 

9.66811 
.66814 
.66818 
.66821 

.46570 
.46574 
.46577 
.46581 

44 
43 
42 
41 

+     5' 
21 
22 
2S 

9.66006 
.66009 
.66012 
.66016 

.45715 
.45718 
.45722 
.45726 

9.66212 
.66215 
.66218 
.66222 

.45932 
.45936 
.45939 
.45943 

9.66417 
.66420 
.66424 
.66427 

.46150 
.46153 
.46157 
.46161 

9.66621 
.66624 
.66628 
.66631 

.46367 
.46371 
.46374 
.46378 

9.66824 
.66828 
.66831 
.66835 

.46585 

.46588 
.46592 
.46596 

40 
39 
38 
37 

+   6' 

25 
26 

27 

9.66019 
.66023 
.66026 
.66030 

.46729 
.45733 
.45736 
.45740 

9.66225 
.66229 
.66232 
.66236 

.45947 
.45950 
.45954 
.45957 

9.66430 
.66434 
.66437 
.66441 

.46164 
.46168 
.46171 
.46175 

9.66635 
.66638 
.66641 
.66645 

.46382 
.46385 
.46389 
.46392 

9.66838 
.66841 
.66845 
.66848 

.46599 
.46603 
.46606 
.46610 

36 
*65 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 

+    r 

29 
SO 
SI 

9.66033 
.66037 
.66040 
.66043 

.45744 
.45747 
.45751 
.45755 

9.66239 
.66242 
.66246 
.66249 

.45961 
.45965 
.45968 
.45972 

9.66444 
.66447 
.66451 
.66454 

.46179 
.46182 
.46186 
.46189 

9.66648 
.66652 
.66655 
.66658 

.46396 
.46400 
.46403 
.46407 

9.66851 
.66855 
.66858 
.66862 

.46614 
.46617 
.46621 
.46625 

+   8^ 
SS 
S4 
S5 

9.66047 
.66050 
.66054 
.66057 

.45758 
.45762 
.45765 
.45769 

9.66253 
.66256 
.66260 
.66263 

.45976 
.45979 
.45983 
.45986 

9.66458 
.66461 
.66464 
.66468 

.46193 
.46197 
.46200 
.46204 

9.66662 
.66665 
.66669 
.66672 

.46411 
.46414 
.46418 
.46421 

9.66865 
.66868 
.66872 
.66875 

.46628 
.46632 
.46636 
.46639 

+     9^ 

S7 
S8 
S9 

9.66061 
.66064 
.66067 
.66071 

.45773 
.45776 
.45780 
.45783 

9.66266 
.66270 
.66273 
.66277 

.45990 
.45994 
.45997 
.46001 

9.66471 
.66475 
.66478 
.66482 

.46208 
.46211 
.46215 
.46218 

9.66675 
.66679 
.66682 
.66685 

.46425 
.46429 
.46432 
.46436 

9.66878 
.66882 
.66885 
.66889 

.46643 
.46646 
.46650 
.46654 

+    1(K 

41 
42 
4S 

9.66074 
.66078 
.66081 
.66085 

.45787 
.45791 
.45794 
.45798 

9.66280 
.66284 
.66287 
.66290 

.46005 
.46008 
.46012 
.46015 

9.66485 
.66488 
.66492 
.66495 

.46222 
.46226 
.46229 
.46233 

9.66689 
.66692 
.66696 
.66699 

.46440 
.46443 
.46447 
.46451 

9.66892 
.66895 
.66899 
.66902 

.46657 
.46661 
.46665 
.46668 

+  11' 

45 
46 
47 

9.66088 
.66092 
.66095 
.66098 

.45802 
.45805 
.45809 
.45812 

9.66294 
.66297 
.66301 
.66304 

.46019 
.46023 
.46026 
.46030 

9.66499 
.66502 
.66505 
.66509 

.46237 
.46240 
.46244 
.46247 

9.66702 
.66706 
.66709 
.66713 

.46454 
.46458 
.46461 
.46465 

9.66905 
.66909 
.66912 
.66916 

.46672 
.46675 
.46679 
.46683 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

49 
50 
51 

9.66102 
.66105 
.66109 
.66112 

.45816 
.45820 
.45823 
.45827 

9.66307 
.66311 
.66314 
.66318 

.46034 
.46037 
.46041 
.46044 

9.66512 
.66516 
.66519 
.66522 

.46251 
.46255 
.46258 
.46262 

9.66716 
.66719 
.66723 
.66726 

.46469 
.46472 
.46476 
.46480 

9.66919 
.66922 
.66926 
.66929 

.46686 
.46690 
.46694 
.46697 

+    W 

53 
54 
55 

9.66116 
.66119 
.66122 
.66126 

.45831 
.45834 

.45838 
.45841 

9.66321 
.66325 
.66328 
.66331 

.46048 
.46052 
.46055 
.46059 

9.66526 
.66529 
.66533 
.66536 

.46266 
.46269 
.46273 
.46276 

9.66730 
.66733 
.66736 
.66740 

.46483 
.46487 
.46490 
.46494 

9.66932 
.66936 
.66939 
.66943 

.46701 
.46704 
.46708 
.46712 

+  14' 

57 
58 
59 

9.66129 
.66133 
.66136 
.66140 

.45845 
.45849 
.45852 
.45856 

9.66335 
.66338 
.66342 
.66345 

.46063 
.46066 
.46070 
.46073 

9.66539 
.66543 
.66546 
.66550 

.46280 
.46284 
.46287 
.46291 

9.66743 
.66747 
.66750 
.66753 

.46498 
.46501 
.46505 
.46509 

9.66946 
.66949 
.66953 
.66956 

.46715 
.46719 
.46723 
.46726 

4 
3 
2 
1 

+  15' 

9.66143 

.45860 

9.66348 

.46077 

9.66553 

.46295 

9.66757 

.46512 

9.66959 

.46730 

0 

18^ 19m 

18^  18m 

18^  17m 

18^  16m 

18^  15m 

Page  880]                  TABLE  45. 

Haversines. 

s 

5ft  45™  86°  15' 

5ft  46"»  86°  30' 

5ft  47m  86°  45' 

5ft  4^  87°  0' 

5ft  ^9™  87°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.66959 
.66963 
.66966 
.66970 

.46730 
.46733 
.46737 
.46741 

9.67161 
.67165 
.67168 
.67171 

.46948 
.46951 
.46955 
.46958 

9.67362 
.67366 
.67369 
.67372 

.47165 
.47169 
.47173 
.47176 

9.67562 
.67566 
.67569 
.67572 

.47383 
.47387 
.47390 
.47394 

9.67762 
.67765 
.67768 
.67772 

.47601 
.47605 
.47608 
.47612 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.66973 
.66976 
.66980 
.66983 

.46744 
.46748 
.46752 
.46755 

9.67175 
.67178 
.67181 
.67185 

.46962 
.46966 
.46969 
.46973 

9.67376 
.67379 
.67382 
.67386 

.47180 
.47184 
.47187 
.47191 

9.67576 
.67579 
.67582 
.67586 

.47398 
.47401 
.47405 
.47409 

9.67775 
.67778 
.67782 
.67785 

.47616 
.47619 
.47623 
.47627 

66 

65 
54 
63 

+      r 

9 

10 

11 

9.66986 
.66990 
.66993 
.66997 

.46759 
.46762 
.46766 
.46770 

9.67188 
.67192 
.67195 
.67198 

.46977 
.46980 
.46984 
.46987 

9.67389 
.67392 
.67396 
.67399 

.47194 
.47198 
.47202 
.47205 

9.67589 
.67592 
.67596 
.67599 

.47412 
.47416 
.47420 
.47423 

9.67788 
.67792 
.67795 
.67798 

.47630 
.47634 
.47637 
.47641 

52 
51 
50 
49 

+  3' 

13 
14 
15 

9.67000 
.67003 
.67007 
.67010 

.46773 
.46777 
.46781 
.46784 

9.67202 
.67205 
.67208 
.67212 

.46991 
.46995 
.46998 
.47002 

9.67402 
.67406 
.67409 
.67412 

.47209 
.47213 
.47216 
.47220 

9.67602 
.67606 
.67609 
.67612 

.47427 
.47430 
.47434 
.47438 

9.67801 
.67805 
.67808 
.67811 

.47645 
.47648 
.47652 
.47656 

48 
47 
46 
45 

17 
18 
19 

9.67013 
.67017 
.67020 
.67023 

.46788 
.46792 
.46795 
.46799 

9.67215 
.67218 
.67222 
.67225 

.47006 
.47009 
.47013 
.47017 

9.67416 
.67419 
.67422 
.67426 

.47223 
.47227 
.47231 
.47234 

9.67616 
.67619 
.67622 
.67626 

.47441 
.47445 
.47449 
.47452 

9.67815 
.67818 
.67821 
.67825 

9.67828 
.67831 
.67835 
.67838 

.47659 
.47663 
.47666 
.47670 

44 
43 
42 
41 

+  5' 

21 

22 
23 

9.67027 
.67030 
.67034 
.67037 

.46802 
.46806 
.46810 
.46813 

9.67228 
.67232 
.67235 
.67238 

.47020 
.47024 
.47027 
.47031 

9.67429 
.67432 
.67436 
.67439 

.47238 
.47242 
.47245 
.47249 

9.67629 
.67632 
.67636 
.67639 

.47456 
.47459 
.47483 
.47467 

.47674 
.47677 
.47681 
.47685 

40 
39 
38 
37 
36 
36 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

+  6' 

«5 
26 

27 

9.67040 
.67044 
.67047 
.67050 

.46817 
.46821 
.46824 
.46828 

9.67242 
.67245 
.67249 
.67252 

.47035 
.47038 
.47042 
.47046 

9.67443 
.67446 
.67449 
.67452 

.47252 
.47256 
.47260 
.47263 

9.67642 
.67646 
.67649 
.67652 

.47470 
.47474 
.47478 
.47481 

9.67841 
.67844 
.67848 
.67851 

.47688 
.47692 
.47696 
.47699 

+    r 

29 
30 
31 

9.67054 
.67057 
.67060 
.67064 

.46831 
.46835 
.46839 
.46842 

9.67255 
.67259 
.67262 
.67265 

.47049 
.47053 
.47056 
.47060 

9.67456 
.67459 
.67462 
.67466 

.47267 
.47271 
.47274 

.47278 

9.67656 
.67659 
.67662 
.67666 

.47485 

.47489 
.47492 
.47496 

9.67854 
.67858 
.67861 
.67864 

.47703 
.47706 
.47710 
.47714 
.47717 
.47721 
.47725 
.47728 

+   8' 
33 
34 
35- 

9.67067 
.67071 
.67074 
.67077 

.46846 
.46850 
.46853 
.46857 

9.67269 
.67272 
.67275 
.67279 

.47064 
.47067 
.47071 
.47075 

9.67469 
.67472 
.67476 
.67479 

.47282 
.47285 
.47289 
.47292 

9.67669 
.67672 
.67675 
.67679 

.47499 
.47503 
.47507 
.47510 

9.67868 
.67871 
.67874 
.67878 

+   9' 

37 
38 
39 

9.67081 
.67084 
.67087 
.67091 

.46860 
.46864 
.46868 
.46871 

9.67282 
.67285 
.67289 
.67292 

.47078 
.47082 
.47086 
.47089 

9.67483 
.67486 
.67489 
.67493 

.47296 
.47300 
.47303 
.47307 

9.67682 
.67685 
.67689 
.67692 

.47514 
.47518 
.47521 
.47525 

9.67881 
.67884 
.67887 
.67891 

.47732 
.47735 
.47739 
.47743 

24 
23 
22 
21 
20 
19 
18 
17 

+  lO' 

41 
42 
43 

9.67094 
.67097 
.67101 
.67104 

.46875 
.46879 

.46882 
.46886 

9.67295 
.67299 
.67302 
.67305 

.47093 
.47096 
.47100 
.47104 

9.67496 
.67499 
.67503 
.67506 

.47311 
.47314 
.47318 
.47321 

9.67695 
.67699 
.67702 
.67705 

.47528 
.47532 
.47536 
.47539 

9.67894 
.67897 
.67901 
.67904 

.47746 
.47750 
.47754 
.47757 

+  11' 

45 
46 
47 

9.67108 
.67111 
.67114 
.67118 

.46890 
.46893 
.46897 
.46900 

9.67309 
.67312 
.67315 
.67319 

.47107 
.47111 
.47115 
.47118 

9.67509 
.67512 
.67516 
.67519 

.47325 
.47329 
.47332 
.47336 

9.67709 
.67712 
.67715 
.67719 

.47543 
.47547 
.47550 
.47554 

9.67907 
.67911 
.67914 
.67917 

.47761 
.47765 
.47768 
.47772 

16 
16 
14 
13 
12 
11 
10 
9 

+  12' 

49 
50 
51 

9.67121 
.67124 
.67128 
.67131 

.46904 
.46908 
.46911 
.46915 

9.67322 
.67326 
.67329 
.67332 

.47122 
.47125 
.47129 
.47123 

9.67522 
.67526 
.67529 
.67532 

.47340 
.47343 
.47347 
.47351 

9.67722 
.67725 
.67729 
.67732 

.47558 
.47561 
.47565 
.47568 

9.67920 
.67924 
.67927 
.67930 

.47775 
.47779 
.47783 
.47786 

+  13' 

53 
54 
55 

9.67134 
.67138 
.67141 
.67145 

.46919 
.46922 
.46926 
.46929 

9.67336 
.67339 
.67342 
.67346 

.47136 
.47140 
.47144 
.47147 

9.67536 
.67539 
.67542 
.67546 

.47354 
.47358 
.47361 
.47365 

9.67735 
.67738 
.67742 
.67745 

.47572 
.47576 
.47579 
.47583 

9.67934 
.67937 
.67940 
.67944 

.47790 
.47794 
.47797 
.47801 

8 
7 
6 
5 

+  14' 

57 
55 
59 

9.67148 
.67151 
.67155 
.67158 

.46933 
.46937 
.46940 
.46944 

9.67349 
.67352 
.67356 
.67359 

.47151 
.47155 
.47158 
.47162 

9.67549 
.67552 
.67556 
.67559 

.47369 
.47372 
.47376 
.47380 

9.67748 
.67752 
.67755 
.67758 

.47587 
.47590 
.47594 
.47597 

9.67947 
.67950 
.67953 
.67957 

.47805 
.47808 
.47812 
.47815 

4 
3 

2 
1 

+  15' 

9.67161 

.46948 

9.67362 

.47165 

9.67562 

.47383 

9.67762 

.47601 

9.67960 

.47819 

0 

18h 14^ 

15ft 13m 

18  ft  /^w 

ISh 11m 

Igh  lO-m         1 

TABLE  45.                 [Page  881 

Haversines. 

s 

5h  50m  87°  30' 

5h  Sm  87°  45' 

5h  52m  88°  0' 

5ft  53m  88°  15' 

5fc  54™  88°  30' 

s 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Ilav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

9.67960 
.67963 
.67967 
.67970 

.47819 
.47833 
.47826 
.47830 

9.68158 
.68161 
.68164 
.68167 

.48037 
.48041 
.48044 
.48048 

9:68354 
.68358 
.68361 
.68364 

.48255 
.48259 
.48262 
.48266 

9.68550 
.68553 
.68557 
.68560 

.48473 
.48477 
.48480 

.48484 

9.68745 
.68748 
.68751 
.68755 

.48691 
.48695 
.48698 
.48702 

60 
59 
58 

57 

+    r 

5 

6 

7 

9.67973 
.67977 
.67980 
.67983 

.47834 
.47837 
.47841 
.47844 

.47848 
.47852 
.47855 
.47850 

9.68171 
.68174 
.68177 
.68181 

.48053 
.48055 
.48059 
.48062 

9.68367 
.68371 
.68374 
.68377 

.48269 
.48273 

.48277 
.48280 

9.68563 
.68566 
.68570 
.68573 

.48488 
.48491 
.48495 
.48499 

9.68758 
.68761 
.68764 
.68768 

.48706 
.48709 
.48713 
.48717 

56 
55 
54 
53 
52 
51 
50 
49 

+     V 

9 

10 

11 

9.67986 
.67990 
.67993 
.67996 

9.68184 
.68187 
.68190 
.68194 

9.68197 
.68200 
.68204 
.68207 

.48066 
.48070 
.48073 
.48077 

9.68380 
.68384 
.68387 
.68390 

.48284 
.48288 
.48291 
.48295 

9.68576 
.68579 
.68583 
.68586 

.48502 
.48506 
.48509 
.48513 

9.68771 
.68774 
.68777 
.68781 

.48720 
.48724 

.48728 
.48731 

+  3' 

13 
14 
15 

9.68000 
.68003 
.68006 
.68010 

.47863 
.47866 
.47870 
.47874 

.48081 
.48084 

.48088 
.48092 

9.68393 
.68397 
.68400 
.68403 

.48299 
.48302 
.48306 
.48310 

9.68589 
.68592 
.68596 
.68599 

.48517 
.48520 
.48524 

.48528 

9.68784 
.68787 
.68790 
.68794 

.48735 

.48738 
.48742 
.48746 

48 
47 
46 
45 

+  4' 
17 
18 
19 

9.68013 
.68016 
.68019 
.68023 

.47877 
.47881 
.47884 
.47888 

9.68210 
.68213 
.68217 
.68220 

.48095 
.48099 
.48102 
.48106 

9.68407 
.68410 
.68413 
.68416 

.48313 
.48317 
.48320 
.48324 

9.68602 
.68605 
.68609 
.68612 

.48531 
.48535 
.48538 
.48542 

9.68797 
.68800 
.68803 
.68806 

.48749 
.48753 
.48757 
.48760 

U 
43 
42 
41 

+  5' 
21 

22 
23 

9.68026 
.68029 
.68033 
.68036 

.47892 
.47895 
.47899 
.47903 

9.68223 
.68227 
.68230 
.68233 

.48110 
.48113 
.48117 
.48121 

9.68420 
.68423 
.68426 
.68429 

.48328 
.48331 
.48335 
.48339 

9.68615 
.68618 
.68622 
.68625 

.48546 
.48549 
.48553 
.48557 

9.68810 
.68813 
.68816 
.68820 

.48764 
.48767 
.48771 
.48775 

40 
39 
38 
37 
36 
35 
34 
S3 

+  6' 

25 
26 

27 

9.68039 
.68042 
.68046 
.68049 

.47906 
.47910 
.47913 
.47917 

9.68236 
.68240 
.68243 
.68246 

.48124 
.48128 
.48131 
.48135 

9.68433 
.68436 
.68439 
.68442 

.48342 
.48346 
.48350 
.48353 

9.68628 
.68631 
.68635 
.68638 

.48560 
.48564 

.48568 
.48571 

9.68823 
.68826 
.68829 
.68832 

.48778 
.48782 
.48786 
.48789 

+    r 

29 
30 
31 

9.68052 
.68056 
.68059 
.68062 

.47921 
.47924 
.47928 
.47932 

9.68249 
.68253 
.68256 
.68259 

.48139 
.48142 
.48146 
.48150 

9.68446 
.68449 
.68452 
.68456 

.48357 
.48360 
.48364 
.48368 

9.68641 
.68644 
.68648 
.68651 

.48575 

.48578 
.48582 
.48586 

9.68836 
.68839 
.68842 
.68845 

.48793 
.48797 
.48800 
.48804 

32 
31 
30 
29 
28 
27 
26 
25 

+     8' 
33 
34 
35 

9.68066 
.68069 
.68072 
.68075 

.47935 
.47939 
.47943 
.47946 

9.68263 
.68266 
.68269 
.68272 

.48153 
.48157 
.48161 
.48164 

9.68459 
.68462 
.68465 
.68469 

.48371 
.48375 
.48379 

.48382 

9.68654 
.68657 
.68661 
.68664 

.48589 
.48593 
.48597 
.48600 

9.68849 
.68852 
.68855 
.68858 

.48807 
.48811 

.48815 
.48818 

+    r 

37 
38 
39 

9.68079 
.68082 
.68085 
.68089 

.47950 
.47953 
.47957 
.47961 

9.68276 
.68279 
.68282 
.68286 

.48168 
.48171 
.48175 
.48179 

9.68472 
.68475 
.68478 
.68482 

.48386 
.48389 
.48393 
.48397 

9.68667 
.68670 
.68674 
.68677 

.48604 
.48608 
.48611 
.48615 

9.68862 
.68865 
.68868 
.68871 

.48822 
.48826 
.48829 
.48833 

24 
23 
22 
21 
20 
19 
18 
17 

-f  W 
41 

42 
43 

9.68092 
.68095 
.68098 
.68102 

.47964 
.47968 
.47972 
.47975 

9.68289 
.68292 
.68295 
.68299 

.48182 
.48186 
.48190 
.48193 

9.68485 
.68488 
.68491 
.68495 

.48400 
.48404 
.48408 
.48411 

9.68680 
.68683 
.68687 
.68690 

.48618 
.48622 
.48626 
.48629 

9.68875 
.68878 
.68881 
.68884 

.48837 
.48840 

.48844 
.48847 

+  11' 

45 
46 
47 

9.68105 
.68108 
.68112 
.68115 

.47979 
.47983 
.47986 
.47990 

9.68302 
.68305 
.68308 
.68312 

.48197 
.48201 
.48204 

.48208 

9.68498 
.68501 
.68504 
.68508 

.48415 
.48419 
.48422 
.48426 

9.68693 
.68696 
.68700 
.68703 

.48633 
.48637 
.48640 
.48644 

9.68887 
.68891 
.68894 
.68897 

.48851 
.48855 
.48858 
.48862 

16 
15 
14 
13 
12 
11 
10 
9 

+  n' 

49 
50 
51 

9.68118 
.68121 
.68125 
.68128 

.47993 
.47997 
.48001 
.48004 

9.68315 
.68318 
.68322 
.68325 

.48211 
.48215 
.48219 
.48222 

9.68511 
.68514 
.68517 
.68521 

.48429 
.48433 
.48437 
.48440 

9.68706 
.68709 
.68713 
.68716 

.48648 
.48651 
.48655 
.48658 

9.68900 
.68904 
.68907 
.68910 

.48866 
.48869 

.48873 
.48877 

+  13' 

53 
54 

55 

9.68131 
.68135 
.68138 
.68141 

.48008 
.48012 
.48015 
.48019 

9.68328 
.68331 
.68335 
.68338 

.48226 
.48230 
.48233 
.48237 

9.68524 
.68527 
.68531 
.68534 

.48444 
.48448 
.48451 
.48455 

9.68719 
.68722 
.68726 
.68729 

.48662 
.48666 
.48669 
.48673 

9.68913 
.68917 
.68920 
.68923 

.48880 
.48884 
.48887 
.48891 

8 
7 
6 
5 

+    14' 

57 
58 
59 

9.68144 
.68148 
.68151 
.68154 

.48022 
.48026 
.48030 
.48033 

9.68341 
.68344 
.68348 
.68351 

.48241 
.48244 

.48248 
.48251 

9.68537 
.68540 
.68544 
.68547 

.48459 
.48462 
.48466 
.48469 

9.68732 
.68735 
.68739 
.68742 

.48677 
.48680 

.48684 
.466S8 

9.68926 
.68929 
.68933 
.68936 

.48895 

.48898 
.48902 
.48906 

4 
3 

2 

1 

+    15' 

9.68158 

.48037 

9.68354 

.48255 

9.68550 

.48473 

9.68745 

.48691 

9.68939 

.48909 

0 

18h9m 

IghS^ 

15A7TO 

18^  em 

18h5m 

Page  882]                 TABLE  45. 

Haversines. 

s 

5A  55TO  88°  45' 

6h  S&m  89°  r 

5ft  57m  89°  15' 

5ft  55W  89°  30' 

5ft  59m  89°  45' 

s 

Log.  Hav. 

Nat.  Hav, 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

I-og.  Hav. 

Nat.  Hav. 

0 
1 
2 
S 

9.68939 
.68942 
.68946 
.68949 

.48909 
.48913 
.48917 
.48930 

9.69132 
.69136 
.69139 
.69142 

.49137 
.49131 
.49135 
.49138 

9.69325 
.69328 
.69331 
.69334 

.49346 
.49349 
.49353 
.49356 

9.69516 
.69520 
.69523 
.69526 

.49564 
.49567 
.49571 
.49575 

9.69707 
.69710 
.69713 
.69717 

.49782 
.49785 
.49789 
.49793 

60 
59 
58 
57 

+  y 

5 

6 
7 

9.68952 
.68955 
.68958 
.68962 

.48934 
.48937 
.48931 
.48935 

9.69145 
.69148 
.69152 
.69155 

.49143 
.49146 
.49149 
.49153 

9.69338 
.69341 
.69344 
.69347 

.49360 
.49364 
.49367 
.49371 

9.69529 
.69532 
.69535 
.69539 

.49578 
.49583 
.49585 
.49589 

9.69720 
.69723 
.69726 
.69729 

.49796 
.49800 
.49804 
.49807 

56 
65 
54 
5S 

+  2^ 

9 

10 

11 

9.68965 
.68968 
.68971 
.68975 

.48938 
.48942 
.48946 
.48949 

9.69158 
.69161 
.69164 
.69168 

.49156 
.49160 
.49164 
.49167 

9.69350 
.69354 
.69357 
.69360 

.49375 
.49378 
.49383 
.49386 

9.69542 
.69545 
.69548 
.69551 

.49593 
.49596 
.49600 
.49604 

9.69732 
.69736 
.69739 
.69742 

.49811 
.49815 
.49818 
.49822 

52 
51 
50 
49 

+  3^ 

IS 
14 
15 

9.68978 
.68981 
.68984 
.68988 

.48953 
.48957 
.48960 
.48964 

9.69171 
.69174 
.69177 
.69181 

.49171 
.49175 
.49178 
.49182 

9.69363 
.69366 
.69370 
.69373 

.49389 
.49393 
.49396 
.49400 

9.69555 
.69558 
.69561 
.69564 

.49607 
.49611 
.49615 
.49618 

9.69745 
.69748 
.69751 
.69755 

.49835 
.49839 
.49833 
.49836 

48 
47 
46 
45 

44 
43 
42 
41 

+     4' 
17 
18 
19 

9.68991 
.68994 
.68997 
.69000 

.48967 
.48971 
.48975 

.48978 

9.69184 
.69187 
.69190 
.69193 

.49186 
.49189 
.49193 
.49196 

9.69376 
.69379 
.69382 
.69386 

.49404 
.49407 
.49411 
.49415 

9.69567 
.69570 
.69574 
.69577 

.49632 
.49635 
.49639 
.49633 

9.69758 
.69761 
.69764 
.69767 

.49840 
.49844 
.49847 
.49851 

+  ^ 
21 
22 
2S 

9.69004 
.69007 
.69010 
.69013 

.48983 
.48986 
.48989 
.48993 

9.69197 
.69200 
.69203 
.69206 

.49300 
.49304 
.49307 
.49311 

9.69389 
.69392 
.69395 
.69398 

.49418 
.49433 
.49436 
.49439 

9.69580 
.69583 
.69586 
.69590 

.49636 
.49640 
.49644 
.49647 

9.69770 
.69774 
.69777 
.69780 

.49855 
.49858 
.49863 
.49865 

40 
39 
38 
37 

+  6' 

25 
26 
27 

9.69017 
.69020 
.69023 
.69026 

.48997 
.49000 
.49004 
.49007 

9.69209 
.69213 
.69216 
.69219 

.49315 
.49318 
.49333 
.49326 

9.69402 
.69405 
.69408 
.69411 

.49433 
.49436 
.49440 
.49444 

9.69593 
.69596 
.69599 
.69602 

.49851 
.49655 
.49658 
.49663 

9.69783 
.69786 
.69789 
.69793 

.49869 
.49873 
.49876 
.49880 

36 
35 
S4 
33 

+    r 

29 
SO 
SI 

9.69029 
.69033 
.69036 
.69039 

.49011 
.49015 
.49018 
.49033 

9.69222 
.69225 
.69229 
.69232 

.49339 
.49233 
.49336 
.49340 

9.69414 
.69417 
.69421 
.69424 

.49447 
.49451 
.49455 
.49458 

9.69605 
.69609 
.69612 
.69615 

.49665 
.49869 
.49673 
.49676 

9.69796 
.69799 
.69802 
.69805 

.49884 
.49887 
.49891 
.49895 

32 
31 
SO 
29 

+  8' 
5-5 
S4 
S5 

9.69042 
.69046 
.69049 
.69052 

.49036 
.49039 
.49033 
.49036 

9.69235 
.69238 
.69242 
.69245 

.49244 
.49247 
.49251 
.49355 

9.69427 
.69430 
.69433 
.69437 

.49463 
.49465 
.49469 
.49473 

9.69618 
.69621 
.69625 
.69628 

.49680 
.49684 
.49687 
.49691 

9.69808 
.69812 
.69815 
.69818 

.49898 
.49903 
.49905 
.49909 

28 
27 
26 
25 

+  9^ 

S7 
S8 
S9 

9.69055 
.69058 
.69062 
.69065 

.49040 
.49044 
.49047 
.49051 

9.69248 
.69251 
.69254 
.69258 

.49358 
.49362 
.49366 
.49369 

9.69440 
.69443 
.69446 
.69449 

.49476 
.49480 
.49484 
.49487 

9.69631 
.69634 
.69637 
.69640 

.49695 
.49898 
.49703 
.49705 

9.69821 
.69824 
.69827 
.69831 

.49913 
.49916 
.49930 
.49934 

24 
23 
22 
21 

+    W 

41 
42 
4S 

9.69068 
.69071 
.69074 
.69078 

.49055 
.49058 
.490  i3 
.49066 

9.69261 
.69264 
.69267 
.69270 

.49273 
.49276 
.49380 
.49284 

9.69453 
.69456 
.69459 
.69462 

.49491 
.49495 
.49498 
.49503 

9.69644 
.69647 
.69650 
.69653 

.49709 
.49713 
.49716 
.49730 

9.69834 
.69837 
.69840 
.69843 

.49937 
.49931 
.49935 
.49938 

20 
19 
18 
17 

+  11' 

45 
46 

47 

9.69081 
.69084 
.69087 
.69091 

.49069 
.49073 
.49076 
.49080 

9.69274 
.69277 
.69280 
.69283 

.49287 
.49291 
.49295 
.49298 

9.69465 
.69469 
.69472 
.69475 

.49506 
.49509 
.49513 
.49516 

9.69656 
.69659 
.69663 
.69666 

.49734 
.49727 
.49731 
.49735 

9.69846 
.69850 
.69853 
.69856 

.49943 
.49945 
.49949 
.49953 

16 
15 
14 
IS 

+    12' 

49 
50 
51 

9.69094 
.69097 
.69100 
.69103 

.49084 
.49087 
.49091 
.49095 

9.69286 
.69290 
.69293 
.69296 

.49302 
.49306 
.49309 
.49313 

9.69478 
.69481 
.69484 
.69488 

.49530 
.49524 
.49527 
.49531 

9.69669 
.69672 
.69675 
.69678 

.49738 
.49743 
.49745 
.49749 

9.69859 
.69862 
.69865 
.69869 

.49956 
.49960 
.49964 
.49967 

12 

11 

10 

9 

+  13' 

5S 
54 
55 

9.69107 
.69110 
.69113 
.69116 

.49098 
.49103 
.49106 
.49109 

9.69299 
.69302 
.69306 
.69309 

.49316 
.49330 
.49334 
.49337 

9.69491 
.69494 
.69497 
.69500 

.49535 
.49538 
.49542 
.49545 

9.69682 
.69685 
.69688 
.69691 

.49753 
.49756 
.49760 
.49764 

9.69872 
.69875 
.69878 
.69881 

.49971 
.49975 
.49978 
.49983 

8 
7 
6 
5 

+  14' 

57 
58 
59 

9.69120 
.69123 
.69126 
.69129 

.49113 
.49116 
.49130 
.49134 

9.69312 
.69315 
.69318 
.69322 

.49331 
.49335 
.49338 
.49343 

9.69504 
.69507 
.69510 
.69513 

.49549 
.49553 
.49556 
.49560 

9.69694 
.69698 
.69701 
.69704 

.49767 
.49771 
.49775 

.49778 

9.69884 
.69888 
.69891 
.69894 

.49985 
.49989 
.49993 
.49997 

4 
3 
2 
1 

+  16' 

9.69132 

.49137 

9.69325 

.49346 

9.69516 

.49564 

9.69707 

.49783 

9.69897 

.50000 

0 

18h4m 

18^  Sm, 

18h2m 

iShim 

IShQm 

TABLE  45.                  [Page  883 

Haversines. 

s 

6A  Oni  90°  (K   1 

6Aim90°15'  1 

6h  2m  90°  SO' 

6h  sm  90°  45'  | 

6h  4m  91°  (K  1 

8 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

9.69897 
.69900 
.69903 
.69906 

.50000 
.50004 
.50007 
.50011 

9.70086 
.70089 
.70092 
.70096 

.50218 
.50222 
.50225 
.50229 

9.70274 
.70277 
.70281 
.70284 

.50436 
.50440 
.50444 
.50447 

9.70462 
.70465 
.70468 
.70471 

.50654 
.50658 
.50662 
.50665 

9.70648 
.70652 
.70655 
.70658 

.50873 
.50876 

.50880 
.50884 

60 
59 
68 
57 

+  y 

5 
6 
7 

9.69910 
.69913 
.69916 
.69919 

.50015 
.50018 
.50022 
.50025 

9.70099 
.70102 
.70105 
.70108 

.50233 
.50236 
.50240 
.50244 

9.70287 
.70290 
.70293 
.70296 

.60451 
.50455 
.60458 
.50462 

9.70474 
.70477 
.70480 
.70484 

.50669 
.50673 
.60676 
.50680 

9.70661 
.70664 
.70667 
.70670 

.60887 
.50891 
.50894 
.50898 

56 
55 
54 
5S 
52 
51 
50 
49 

+  V 

9 

10 

11 

9.69922 
.69925 
.69929 
.69932 

.50029 
.50033 
.50036 
.50040 

9.70111 
.70114 
.70118 
.70121 

.50247 
.50251 
.50255 
.50258 

9.70299 
.70303 
.70306 
.70309 

.50465 
.50469 
.60473 
.50476 

9.70487 
.70490 
.70493 
.70496 

.50684 
.60687 
.50691 
.50694 

9.70673 
.70670 
.70679 
.70683 

.50902 
.50906 
.50909 
.60913 

+      3' 

IS 
14 
15 

9.69935 
.69938 
.69941 
.69944 

.50044 
.50047 
.50051 
.50055 

9.70124 
.70127 
.70130 
.70133 

.50262 
.50265 
.50269 
.50273 

9.70312 
.70315 
.70318 
.70321 

.50480 
.50484 
.50487 
.50491 

9.70499 
.70502 
.70505 
.70509 

.60698 
.50702 
.50706 
.60709 

9.70686 
.70689 
.70692 
.70695 

.50916 
.60920 
.60924 
.60927 

48 
47 
46 
45 

44 
4S 
42 
41 
40 
39 
38 
37 

+   *' 
17 
18 
19 

9.69948 
.69951 
.69954 
.69957 

.50058 
.50062 
.50065 
.50069 

9.70136 
.70140 
.70143 
.70146 

.50276 
.50280 
.50284 
.50287 

9.70324 
.70328 
.70331 
.70334 

.50495 
.50498 
.50502 
.50505 

9.70512 
.70515 
.70518 
.70521 

.60713 
.50716 
.50720 
.50724 

9.70698 
.70701 
.70704 
.70707 

.50931 
.50934 
.60938 
.50942 
.60946 
.50949 
.60953 
.50956 

+  6' 
21 
22 
2S 

9.69960 
.69963 
.69966 
.69970 

.50073 
.50076 
.50080 
.50084 

9.70149 
.70152 
.70155 
.70158 

.50291 
.50295 
.50298 
.50302 

9.70337 
.70340 
.70343 
.70346 

.50509 
.50513 
.50616 
.50620 

9.70524 
.70527 
.70530 
.70533 

.50727 
.60731 
.60734 
.50738 

9.70710 
.70714 
.70717 
.70720 

+  ^ 

25 
26 

27 

9.69973 
.69976 
.69979 
.69982 

.50087 
.50091 
.50095 
.50098 

9.70161 
.70165 
.70168 
.70171 

.50305 
.50309 
.50313 
.50316 

9.70349 
.70353 
.70356 
.70359 

.60524 
.50627 
.60531 
.50534 

9.70537 
.70540 
.70543 
.70546 

.50742 
.50745 
.50749 
.60753 

9.70723 
.70726 
.70729 
.70732 

.50960 
.50964 
.50967 
.50971 

36 
35 
34 
33 
32 
31 
30 
29 

+    r 

29 
SO 
SI 

9.69985 
.69988 
.69992 
.69995 

.50102 
.50105 
.50109 
.50113 

9.70174 
.70177 
.70180 
.70183 

.50320 
.50324 
.50327 
.50331 

9.70362 
.70365 
.70368 
.70371 

.50538 
.60542 
.50546 
.50649 

9.70549 
.70552 
.70555 
.70558 

.60756 
.60760 
.50764 
.60767 

9.70735 
.70738 
.70741 
.70745 

.60974 
.60978 
.60982 
.50985 

+   8' 
S3 
S4 
S5 

9.69998 
.70001 
.70004 
.70007 

.50116 
.50120 
.50124 
.50127 

9.70187 
.70190 
.70193 
.70196 

.50335 
.50338 
.50342 
.50345 

9.70374 
.70378 
.70381 
.70384 

.60653 
.60666 
.60560 
.50564 

9.70561 
.70565 
.70568 
.70571 

.50771 
.60774 
.50778 
.50782 

9.70748 
.70751 
.70754 
.70757 

.50989 
.50993 
.50996 
.51000 

28 
27 
26 
25 

+     9^ 

S7 
S8    ■ 
S9 

9.70011 
.70014 
.70017 
.70020 

.50131 
.50135 
.5013S 
.50142 

9.70199 
.70202 
.70205 
.70209 

.50349 
.50353 
.50356 
.50360 

9.70387 
.70390 
.70393 
.70396 

.50567 
.50571 
.50674 
.50678 

9.70574 
.70577 
.70580 
.70583 

.50785 
.50789 
.60793 
.50796 

9.70760 
.70763 
.70766 
.70769 

.51004 
.61007 
.51011 
.51014 

24 

23 
22 
21 

+  W 

41 
42 
4S 

9.70023 
.70026 
.70029 
.70033 

.50145 
.50149 
.50153 
.50156 

9.70212 
.70215 
.70218 
.70221 

.50364 
.50367 
.50371 
.50375 

9.70399 
.70402 
.70406 
.70409 

.60682 
.60585 
.50589 
.50693 

9.70586 
.70589 
.70593 
.70596 

.60800 
.50804 
.50807 
.50811 

9.70772 
.70775 
.70779 

.70782 

.51018 
.51022 
.51026 
.61029 

20 
19 
18 
17 

+    ir 

45 
46 
47 

9.70036 
.70039 
.70042 
.70045 

.50160 
.50164 
.50167 
.50171 

9.70224 
.70227 
.70230 
.70234 

.50378 
.50382 
.50385 
.50389 

9.70412 
.70415 
.70418 
.70421 

.50596 
.50600 
.60604 
.60607 

9.70599 
.70602 
.70605 
.70608 

.50814 
.50818 
.50822 
.60826 

9.70785 
.70788 
.70791 
.70794 

.51033 
.51036 
.61040 
.61043 

16 
15 
14 
IS 

+  nt' 

49 
50 
51 

9.70048 
.70051 
.70055 
.70058 

.50175 
.50178 
.50182 
.50185 

9.70237 
.70240 
.70243 
.70246 

.50393 
.50396 
.50400 
.50404 

9.70424 
.70427 
.70431 
.70434 

.60611 
.60614 
.60618 
.50622 

9.70611 
.70614 
.70617 
.70620 

.50829 
.50833 
.50836 
.60840 

9.70797 
.70800 
.70803 
.70806 

.51047 
.51061 
.51064 
.51068 

12 

11 

10 

9 

+  13' 

5S 
54 
55 

9.70061 
.70064 
.70067 
.70070 

.50189 
.50193 
.50196 
.50200 

9.70249 
.70252 
.70256 
.70259 

.50407 
.50411 
.50415 
.50418 

9.70437 
.70440 
.70443 
.70446 

.50626 
.60629 
.50633 
.50636 

9.70624 
.70627 
.70630 
.70633 

.50844 
.60847 
.50851 
.50854 

9.70809 
.70813 
.70816 
.70819 

.61062 
.51065 
.61069 
.51073 

8 
7 
6 
5 

4-  W 

57 
58 
59 

9.70074 
.70077 
.70080 
.70083 

.50204 
.50207 
.50211 
.50215 

9.70262 
.70265 
.70268 
.70271 

.60422 
.50425 
.50429 
.50433 

9.70449 
.70452 
.70456 
.70459 

.60640 
.50644 
.50647 
.60661 

9.70636 
.70639 
.70642 
.70645 

.50868 
.50862 
.50865 
.50869 

9.70822 
.70825 
.70828 
.70831 

.61076 
.51080 
.51083 
.61087 

4 
3 
2 
1 

+  15' 

9.70086 

.50218 

9.70274 

.50436 

9.70462 

.50654 

9.70648 

.50873 

9.70834 

.51091 

0 

17h  59m 

17n  58m 

17h  57m 

17h  56m 

17h  55^ 

Page  884]                 TABLE  45. 

Haversines. 

s 

6ft  .5TO  91°  15^ 

6h  em  91°  30' 

eh  Tm  91°  45' 

en  gm  92°  (y 

6h  gm  92°  15/ 

s 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 

3 

9.70834 
.70837 
.70840 
.70843 

.51091 
.51094 
.51098 
.51102 

9.71019 
.71022 
.71025 
.71028 

.51309 
.51312 
.51316 
.51320 

9.71203 
.71206 
.71210 
.71213 

.51527 
.51531 
.51534 
.51538 

9.71387 
.71390 
.71393 
.71396 

.51745 
.51749 
.51752 
.51756 

9.71569 
.71572 
.71575 
.71579 

.51963 
.51967 
.51970 
.51974 

60 
59 
58 
57 

+   1' 

5 
6 

7 

9.70847 
.70850 
.70853 
.70856 

.51105 
.51109 
.51113 
.51116 

9.71032 
.71035 
.71038 
.71041 

.51323 
.51327 
.51331 
.51334 

9.71216 
.71219 
.71222 
.71225 

.51541 
.51545 
.51549 
.51552 

9.71399 
.71402 
.71405 
.71408 

.51760 
.51763 
.51767 
.51770 

9.71582 
.71585 
.71588 
.71591 

.51978 
.51981 
.51985 
.51988 

56 
55 

64 
53 

+   3' 
9 

10 
11 

9.70859 
.70862 
.70865 
.70868 

.51120 
.51123 
.51127 
.51131 

9.71044 
.71047 
.71050 
.71053 

.51338 
.51342 
.51345 
.51349 

9.71228 
.71231 
.71234 
.71237 

.51556 
.51560 
.51563 
.51567 

9.71411 
.71414 
.71417 
.71420 

.51774 
.51778 
.51781 
.51785 

9.71594 
.71597 
.71600 
.71603 

.51992 
.51996 
.51999 
.52003 

52 
51 
50 
49 

+  3' 

13 
14 
15 

9.70871 
.70874 
.70877 
.70881 

.51134 
.51138 
.51142 
.51145 

9.71056 
.71059 
.71062 
.71065 

.51352 
.51356 
.51360 
.51363 

9.71240 
.71243 
.71246 
.71249 

.51571 
.51574 
.51578 
.51581 

9.71423 
.71426 
.71430 
.7H33 

.51789 
.51792 
.51796 
.51799 

9.71606 
.71609 
.71612 
.71615 

.62007 
.62010 
.52014 
.52018 

48 
47 
46 
45 

+   r 
17 
18 
19 

9.70884 
.70887 
.70890 
.70893 

.51149 
.51153 
.51156 
.51160 

9.71068 
.71072 
.71075 
.71078 

.51367 
.51371 
.51374 
.51378 

9.71252 
.71255 
.71259 
.71262 

.51585 
.51589 
.51592 
.51596 

9.71436 
.71439 
.71442 
.71445 

.51803 
.51807 
.51810 
.51814 

9.71618 
.71621 
.71624 
.71627 

.52021 
.52025 
.52028 
.62032 

44 
43 
42 
41 

+  5' 
f5 

9.70896 
.70899 
.70902 
.70905 

.51163 
.51167 
.51171 
.51174 

9.71081 
.71084 
.71087 
.71090 

.51382 
.51385 
.51389 
.51392 

9.71265 
.71268 
.71271 
.71274 

.51600 
.51603 
.51607 
.51611 

9.71448 
.71451 
.71454 
.71457 

.51818 
.51821 
.51825 
.51829 

9.71630 
.71633 
.71636 
.71639 

.52036 
.52039 
.52043 
.52047 

40 
39 
38 
37 
36 
35 
34 
33 

+   6' 

;g7 

9.70908 
.70911 
.70914 
.70918 

.51178 
.51182 
.51185 
.51189 

9.71093 
.71096 
.71099 
.71102 

.51396 
.51400 
.51403 
.51407 

9.71277 
.71280 
.71283 
.71286 

.51614 
.51618 
.51621 
.51625 

9.71460 
.71463 
.71466 
.71469 

.51832 
.51836 
.51839 
.51843 

9.71642 
.71645 
.71648 
.71651 

.52050 
.52054 
.52057 
.52061 

+    r 

29   . 
SI  '' 

9.70921 
.70924 
.70927 
.70930 

.51193 
.51198 
.51200 
.51203 

9.71105 
.71108 
.71111 
.71114 

.51411 
.51414 
.51418 
.51422 

9.71289 
.71292 
.71295 
.71298 

.51629 
.51632 
.51636 
.51640 

9.71472 
.71475 
.71478 
.71481 

.51847 
.51850 
.51854 
.51858 

9.71654 
.71657 
.71660 
.71663 

.62065 
.52068 
.52072 
.52076 

32 
31 
30 
29 

+     8' 

34  I 
35 

9.70933 
.70936 
.70939 
.70942 

.51207 
.51211 
.51214 
.51218 

9.71118 
.71121 
.71124 
.71127 

.51425 
.51429 
.51432 
.51436 

9.71301 
.71304 
.71307 
.71311 

.51643 
.51647 
.51650 
.51654 

9.71484 
.71487 
.71490 
.71493 

.51861 
.51865 
.51869 
.51872 

9.71666 
.71670 
.71673 
.71676 

.52079 
.52083 
.62087 
.52090 

28 
27 
26 
25 

+  ^ 

37  s 

38 

39 

9.70945 
.70948 
.70951 
.70955 

.51222 
.51225 
.51229 
.51233 

9.71130 
.71133 
.71136 
.71139 

.51440 
.51443 
.51447 
.51451 

9.71314 
.71317 
.71320 
.71323 

.51658 
.51661 
.51665 
.51669 

9.71496 
.71500 
.71503 
.71506 

.51876 
.51879 
.51883 

.51887 

9.71679 
.71682 
.71685 
.71688 

.62094 
.62097 
.62101 
.52105 

24 
23 

22 

21 

+  W 

41 
42 
43 

9.70958 
.70961 
.70964 
.70967 

.51236 
.51240 
.51243 
.51247 

9.71142 
.71145 
.71148 
.71151 

.51454 
.51458 
.51462 
.51465 

9.71326 
.71329 
.71332 
.71335 

.51672 
.51676 
.51680 
.51683 

9.71509 
.71512 
.71515 
.71518 

.51890 
.51894 
.51898 
.51901 

9.71691 
.71694 
.71697 
.71700 

.62108 
.52112 
.52116 
.52119 

20 
19 
18 
17 

+  tr 

45 
46 
47 

9.70970 
.70973 
.70976 
.70979 

.51251 
.51254 
.51258 
.51262 

9.71154 
.71157 
.71161 
.71164 

.51469 
.51472 
.51476 
.51480 

9.71338 
.71341 
.71344 
.71347 

.51687 
.51690 
.51694 
.51698 

9.71521 
.71524 
.71527 
.71530 

.51905 
.51908 
.51912 
.51916 

9.71703 
.71706 
.71709 
.71712 

.53123 
.52126 
.52130 
.62134 

16 
15 
14 
13 
12 
11 
10 
9 

+  12' 

50 
5i 

9.70982 
.70985 
.70988 
.70992 

.51265 
.51269 
.51273 
.51276 

9.71167 
.71170 
.71173 
.71176 

.51483 
.51487 
.51491 
.51494 

9.71350 
.71353 
.71356 
.71359 

.51701 
.51705 
.51709 
.51712 

9.71533 
.71536 
.71539 
.71542 

.51919 
.51923 
.51927 
.51930 

9.71715 
.71718 
.71721 

.71724 

.52137 
.62141 
.52145 
.52148 

+  13' 

53 
54 

55 

9.70995 
.70998 
.71001 
.71004 

.51380 
.51283 
.51287 
.51291 

9.71179 
.71182 
.71185 
.71188 

.514d8 
.51501 
.51505 
.51508 

9.71362 
.71365 
.71369 
.71372 

.51716 
.51720 
.51723 
.51727 

9.71545 
.71548 
.71551 
.71554 

.51934 
.51938 
.51941 
.51945 

9.71727 
.71730 
.71733 
.71736 

.52152 
.52156 
.62159 
.53163 

i8 
'.7 
'6 
'5 

4 
3 

0 

f 

+  14' 

57 
55 
59 

9.71007 
.71010 
.71013 
.71016 

.51294 
.51298 
.51302 
.51305 

9.71191 
.71194 
.71197 
.71200 

.51512 
.51516 
.51520 
.51523 

9.71375 
.71378 
.71381 
.71384 

.51730 
.51734 
.51738 
.51741 

9.71557 
.71560 
.71563 
.71566 

.61948 
.61952 
.51956 
.51959 

9.71739 
.71742 
.71745 
.71748 

.53166 
.53170 
.53174 
.53177 

4-  16' 

9.71019 

.51309 

9.71203 

.51527 

9.71387 

.51745 

9.71569 

.51963 

9.71751 

.52181 

17h  54'^ 

171).  5Sm 

27A5fTO 

17h  5im 

17h50m    ■> 

TABLE  45.                 [Page  886 

Havereines. 

s 

6h  lom  93°  SiK 

6h  im  92°  45' 

6A  12m  93°  0' 

6h  13m  93°  15' 

6h  14m  930  3(K 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.71751 
.71754 
.71757 
.71760 

.52181 
.52185 
.52188 
.52192 

9.71932 
.71935 
.71938 
.71941 

.52399 
.52403 
.52406 
.52410 

9.72112 
.72115 
.72118 
.72121 

.52617 
.52620 
.52624 
.52628 

9.72292 
.72295 
.72298 
.72301 

.52835 
.52838 
.52842 
.52846 

9.72471 

.72474 
.72476 
.72479 
9.72482 
.72485 
.72488 
.72491 

.53052 
.53056 
.53060 
.53063 

60 
59 
58 

57 

+   1' 

5 
6 

7 

9.71763 
.71766 
.71769 
.71772 

.52196 
.52199 
.52203 
.52206 

9.71944 
.71947 
.71950 
.71953 

.52413 
.52417 
.52421 
.52424 

9.72124 
.72127 
.72130 
.72133 

.52631 
.52635 
.52639 
.52642 

9.72304 
.72307 
.72310 
.72313 

.52849 
.52853 
.52856 
.52860 

.53067 
.53071 
.53074 
.53078 

56 
55 
54 
53 

+   3' 

9 

10 

11 

9.71775 
.71778 
.71781 
.71784 

.52210 
.52214 
.52217 
.52221 

9.71956 
.71959 
.71962 
.71965 

.52428 
.52432 
.52435 
.52439 

9.72136 
.72139 
.72142 
.72145 

.52646 
.52649 
.52653 
.52657 

9.72316 
.72319 
.72322 
.72325 

.52864 
.52867 
.52871 
.52875 

9.72494 
.72497 
.72500 
.72503 

9.72506 
.72509 
.72512 
.72515 

.53081 
.53085 
.53089 
.53092 
.53096 
.53100 
.53103 
.53107 

52 
51 
50 
49 
48 
47 
46 
45 

+   3^ 

13 
14 
15 

9.71787 
.71791 
.71794 
.71797 

.52225 
.52228 
.52232 
.52235 

9.71968 
.71971 
.71974 
.71977 

.52442 
.52446 
,52450 
.52453 

9.72148 
.72151 
.72154 
.72157 

.52660 
.52664 
.52668 
.52671 

9.72328 
.72331 
.72334 
.72337 

.52878 
.52882 
.52885 
.52889 

+   4' 
17 
18 
19 

9.71800 
.71803 
.71806 
.71809 

.52239 
.52243 
.52246 
.52250 

9.71980 
.71983 
.71986 
.71989 

.52457 
.52461 
.52464 
.52468 

9.72160 
.72163 
.72166 
.72169 

.52675 
.52679 
.52682 
.52686 

9.72340 
.72343 
.72346 
.72349 

.52893 

.52896 
.52900 
.52904 

9.72518 
.72521 
.72524 
.72527 

.53110 
.53114 
.53118 
.53121 

44 
43 
42 
41 

+  5' 

^/ 

22 
23 

9.71812 
.71815 
.71818 
.71821 

.52254 
.52257 
.52261 
.52264 
.52268 
.52272 
.52275 
.52279 
.52283 
.52286 
.52290 
.52294 

9  71992 
.71995 
.71998 
.72001 

9.72004 
.72007 
.72010 
.72013 

.52472 
.52475 
.52479 
.52482 

9.72172 
.72175 
.72178 
.72181 

.52689 
.52693 
.52697 
.52700 

9.72352 
.72354 
.72357 
.72360 

.52907 
.52911 
.52915 
.52918 

9.72530 
.72533 
.72536 
.72539 

.53125 
.53129 
.53132 
.53136 

40 
39 
38 
37 

+  6' 

^7 

9.71824 
.71827 
.71830 
.71833 

.52486 
.52490 
.52493 
.52497 

9.72184 
.72187 
.72190 
.72193 

.52704 
.52708 
.52711 
.52715 

9.72363 
.72366 
.72369 
.72372 

.62922 
.52925 
.52929 
.52933 

9.72542 
.72545 
.72548 
.72551 

.53140 
.53143 
.53147 
.53150 

36 
35 
34 
S3 

+    r 

29 
30 
31 

9.71836 
.71839 
.71842 
.71845 

9.72016 
.72019 
.72022 
.72025 

.52501 
.52504 
.52508 
.52511 

9.72196 
.72199 
.72202 
.72205 

.52718 
.52722 
.52726 
.52729 

9.72375 
.72378 
.72381 
.72384 

.52936 
.52940 
.52944 
.52947 

9.72554 
.72557 
.72560 
.72563 

.53154 
.53158 
.53161 
.53165 

32 
31 
30 
29 

+     8' 
33 
34 
35 

9.71848 
.71851 
.71854 
.71857 

.52297 
.52301 
.52304 
.52308 

9.72028 
.72031 
.72034 
.72037 

.52515 
.52519 
.52522 
.52526 

9.72208 
.72211 
.72214 
.72217 

.52733 
.52737 
.52740 
.52744 

9.72387 
.72390 
.72393 
.72396 

.52951 
.52954 
.52958 
.52962 

9.72565 
.72568 
.72571 
.72574 

.53169 
.53172 
.53176 
.53179 

28 
27 
26 

25 

+  9' 

59 

9.71860 
.71863 
.71866 
.71869 

.52312 
.52315 
.52319 
.52323 

9.72040 
.72043 
.72046 
.72049 

.52530 
.52533 
.52537 
.52541 

9.72220 
.72223 
.72226 
.72229 

.52748 
.52751 
.52755 
.52758 

9.72399 
.72402 
.72405 
.72408 

.52965 
.52969 
.52973 
.52976 

9.72577 
.72580 
.72583 
.72586 

.53183 
.53187 
.53190 
.53194 

24 
23 
22 
21 

+  10^ 

41 
42 
43 

9.71872 
.71875 
.71878 
.71881 

.52326 
.52330 
.52334 
.52337 

9.72052 
.72055 
.72058 
.72061 

.52544 
.52548 
.52551 
.52555 

9.72232 
.72235 
.72238 
.72241 

.52762 
.52768 
.52769 
.52773 

9.72411 
.72414 
.72417 
.72420 

.52980 
.52983 
.52987 
.52991 

9.72589 
.72592 
.72595 
.72598 

.53198 
.53201 
.53205 
.53208 

20 
19 
18 

17 

+   11' 

45 
46 

47 

9.71884 
.71887 
.71890 
.71893 

.52341 
.52344 
.52348 
.52352 

9.72064 
.72067 
.72070 
.72073 

.52559 
.52562 
.52566 
.52570 

9.72244 
.72247 
.72250 
.72253 

.52776 
.52780 
.52784 
.52787 

9.72423 
.72426 
.72429 
.72432 

.52994 
.52998 
.53002 
.53005 

9.72601 
.72604 
.72607 
.72610 

.53212 
.53216 
.53219 
.53223 
.53227 
.53230 
.53234 
.53238 

16 
15 
14 
13 

12 

11 

10 

9 

+  ir 

49 
50 
51 

9.71896 
.71899 
.71902 
.71905 

.52355 
.52359 
.52363 
.52366 

9.72076 
.72079 
.72082 
.72085 

.52573 
.52577 
.52580 
.52584 

9.72256 
.72259 
.72262 
.72265 

.52791 
.52795 
.52798 
.52802 

9.72435 
.72438 
.72441 
.72444 

.53009 
.53013 
.53016 
.53020 

9.72613 
.72616 
.72619 
.72622 

+    13' 

53 
54 
55 

9.71908 
.71911 
.71914 
.71917 

.52370 
.52373 
.52377 
.52381 

9.72088 
.72091 
.72094 
.72097 

.52588 
.52591 
.52595 
.52599 

9.72268 
.72271 
.72274 

.72277 

.52806 
.52809 
.52813 
.52816 

9.72447 
.72450 
.72453 
.72456 

.53023 
.53027 
.53031 
.53034 

9.72625 
.72628 
.72631 
.72634 

.53241 
.53245 
.53248 
.53252 

8 
7 
6 
5 

+    14' 

57 
58 
59 

9.71920 
.71923 
.71926 
.71929 

.52384 
.52388 
.52392 
.52395 

9.72100 
.72103 
.72106 
.72119 

.52602 
.52606 
.52610 
.52613 

9.72280 
.72283 
.72286 
.72289 

.52820 
.52824 
.52827 
.52831 

9.72459 
.72462 
.72465 
.72468 

.53038 
.53042 
.53045 
.53049 

9.72637 
.72640 
.72642 
.72645 

.55256 
.53259 
.53263 
.53267 

4 
3 
2 

1 

+   15' 

9.71932 

.52399 

9.72112 

.52617 

9.72292 

.52835 

9.72471 

.53052 

9.72648 

.53270 

0 

17h49m 

17^  48m 

17h  47m 

171^46^ 

17^45^ 

Page  886]                  TABLE  45. 

Haversines. 

s 

6J^  15m  93°  45/ 

6h  16m  94°  0' 

6fe  17m  94°  15/ 

6h  18m  94°  30' 

6h  19m  94°  45 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
S 

9.72648 
.72651 
.72654 
.72657 

.53:370 
.53274 
.53277 
.53281 

9.72825 
.72828 
.72831 
.72834 

.53488 
.53491 
.53496 
.53499 

9.73002 
.73005 
.73008 
.73011 

.63705 
.63709 
.63713 
.63716 

9.73177 
.73180 
.73183 
.73186 

.53923 
.53927 
.63930 
.53934 

9.73352 
.73355 
.73358 
.73361 

.54140 
.54144 
.54148 
.64161 

60 
59 
58 

57 

+    r 

5 
6 

7 

9.72660 
.72663 
.72666 
.72669 

.53285 

.53288 
.53292 
.53296 

9.72837 
.72840 
.72843 
.72846 

.53502 
.53606 
.53610 
.63513 

9.73014 
.73016 
.73019 
.73022 

.53720 
.63724 
.63727 
.63731 

9.73189 
.73192 
.73195 
.73198 

.53937 
.63941 
.53945 
.53948 

9.73364 
.73367 
.73370 
.73373 

.54155 
.54159 
.64162 
.64166 

56 
56 
54 
53 

+   3" 
.  9 

10 

11 

9.72672 
.72675 
.72678 
.72681 

.53299 
.53303 
.53306 
.53310 

9.72849 
.72852 
.72855 
.72858 

.63617 
.63620 
.53524 
.53528 

9.73025 
.73028 
.73031 
.73034 

.53734 
.63738 
.63742 
.53746 

9.73201 
.73204 
.73207 
.73209 

.53952 
.63966 
.53969 
.53963 

9.73375 
.73378 
.73381 
.73384 

.54169 
.54173 
.54177 
.54180 

52 
51 
50 
49 

+      3' 

13 
14 
15 

9.72684 
.72687 
.72690 
.72693 

.53314 
.53317 
.53321 
.53325 

9.72861. 
.72864 
.72867 
.72870 

.63531 
.63535 
.53639 
.63642 

9.73037 
.73040 
.73043 
.73046 

.63749 
.63753 
.53756 
.53760 

9.73212 
.73215 
.73218 
.73221 

.63966 
.63970 
.53974 
.53977 

9.73387 
.73390 
.73393 
.73396 

.64184 

.64188 
.64191 
.64195 

48 
47 
46 
45 

+   4" 
17 
18 
19 

9.72696 
.72699 
.72702 
.72705 

.53328 
.53332 
.53335 
.53339 

9.72873 
.72876 

.72878 
.72881 

.63646 
.63549 
.53553 
.53667 

9.73049 
.73052 
.73055 
.73057 

.53763 
.53767 
.63771 
.63774 

9.73224 
.73227 
.73230 
.73233 

.63981 
.53985 
.53988 
.63992 

9.73399 
.73402 
.73404 
.73407 

.64198 
.64202 
.64206 
.64209 

44 
43 
42 
41 
40 
39 
38 
37 

+   5' 
21 

22 
23 

9.72708 
.72710 
.72713 
.72716 

.53343 
.53346 
.53350 
.53354 

9.72884 
.72887 
.72890 
.72893 

.53660 
.53664 
.63668 
.63571 

9.73060 
.73063 
.73066 
.73069 

.63778 
.63782 
.53786 
.53789 

9.73236 
.73239 
.73242 
.73244 

.63996 
.63999 
.64003 
.64006 

9.73410 
.73413 
.73416 
.73419 

.54213 
.64217 
.54220 
.64224 

+     6' 

25 
26 
27 

9.72719 

.72722 
.72725 
.72728 

.63357 
.53361 
.53364 
.53368 

9.72896 
.72899 
.72902 
.72905 

.63575 
.53579 
.53682 
.53686 

9.73072 
.73075 
.75078 
.73081 

.53792 
.53796 
.63800 
.63803 

9.73247 
.73250 
.73253 
.73256 

.54010 
.64014 
.64017 
.54021 

9.73422 
.73425 
.73428 
.73431 

.64227 
.54231 
.54236 
.54238 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.72731 
.72734 
.72737 
.72740 

.53372 
.53375 
..53379 
.53383 

9.72908 
.72911 
.72914 
.72917 

.63689 
.53593 
.63597 
.53600 

9.73084 
.73087 
.73090 
.73093 

.63807 
.53811 
.63814 
.53818 

9.73259 
.73262 
.73265 
.73268 

.54024 
.54028 
.54032 
.54035 

9.73433 
.73436 
.73439 
.73442 

.54242 
.64245 
.64249 
.64253 

32 
31 
SO 
29 

+      S' 
33 

34 
35 

9.72743 
.72746 
.72749 
.72752 

.53386 
.53390 
.53394 
.53397 

9.72920 
.72923 
.72926 
.72928 

.63604 
.53608 
.53611 
.53616 

9.73096 
.73098 
.73101 
.73104 

.53821 
.53825 
.53829 
.63832 

9.73271 
.73274 
.73277 
.73280 

.54039 
.64043 
.64046 
.64050 

9.73445 
.73448 
.73451 
.73454 

.64266 
.54260 
.54264 
.54267 

28 
27 
26 
25 

+      9" 

37 
38 
39 

9.72755 
.72758 
.72761 
.72764 

.53401 
.53404 
.53408 
.53412 

9.72931 
.72934 
.72937 
.72940 

.63618 
.53622 
.53626 
.63629 

9.73107 
.73110 
.73113 
.73116 

.63836 
.53840 
.53843 
.53847 

9.73282 
.73285 
.73288 
.73291 

.64063 
.54057 
.64061 
.64064 

9.73457 
.73460 
.73462 
.73465 

.54271 
.54274 
.64278 
.54282 

24 
2S 
22 
21 

+  10' 

41 
42 
43 

9.72767 

.72770 
.72772 
.72775 

.53415 
.53419 
.53423 
.53426 

9.72943 
.72946 
.72949 
.72952 

.63633 
.63637 
.63640 
.63644 

9.73119 
.73122 
.73125 
.73128 

.63850 
.63854 

.53858 
.53861 

9.73294 
.73297 
.73300 
.73303 

.54068 
.54072 
.64075 
.54079 

9.73468 
.73471 
.73474 
.73477 

.64285 
.64289 
.64293 
.54296 

20 
19 
18 
17 

+  11" 

45 
46 

47 

9.72778 
.72781 
.72784 
.72787 

.53430 
.53433 
.63437 
.53441 

9.72955 
.72958 
.72961 
.72964 

.63647 
.53651 
.53665 
.63658 

9.73131 
.73134 
.73136 
.73139 

.63865 
.53869 
.53872 
.63876 

9.73306 
.73309 
.73311 
.73314 

.64082 
.64086 
.64090 
.54093 

9.73480 
.73483 
.73486 
.73489 

.64300 
.54303 
.54307 
.54311 

16 
15 
14 
13 

+  n' 

49 
50 
51 

9.72790 
.72793 
.72796 
.72799 

.53444 
.53448 
.53452 
.53455 

9.72967 
.72970 
.72972 
.72975 

.53662 
.53666 
.63669 
.63673 

9.73142 
.73145 
.73148 
.73151 

.53879 
.63883 

.63887 
.63890 

9.73317 
.73320 
.73323 
.73326 

.64097 
.54101 
.54104 
.64108 

9.73491 
.73494 
.73497 
.73500 

.64314 
.54318 
.64322 
.64326 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.72802 
.72805 
.72808 
.72811 

.53459 
.63462 
.63466 
.53470 

9.72978 
.72981 
.72984 
.72987 

.53676 
.63680 
.63684 
.63687 

9.73154 
.73157 
.73160 
.73163 

.63894 
.63898 
.53901 
.53905 

9.73329 
.73332 
.73335 
.73338 

.64111 
.54116 
.54119 
.64122 

9.73503 
.73506 
.73509 
.73512 

.54329 
.54332 
.64336 
.64340 

+  ir 

57 
58 
59 

9.72814 
.72817 
.72820 
.72823 

.63473 
.63477 
.53481 
.53484 

9.72990 
.72993 
.72996 
.72999 

.63691 
.53696 
.63698 
.53702 

9.73166 
.73169 
.73172 
.73174 

.63908 
.63912 
.63916 
.53919 

9.73341 
.73343 
.73346 
.73349 

.54126 
.54130 
.54133 
.54137 

9.73515 
.73517 
.73520 
.73523 

.64343 
.64347 
.54361 
.54364 

4 
3 

2 

0 

+  15' 

9.72825 

.63488 

9,73002 

.63705 

9.73177 

.53923 

9.73352 

.54140 

9.73526 

.54358 

17h  44m 

nh  4sm      1 

17h  42m 

17h  41m 

17h  40m          1 

TABLE  45.                 [Page  887 

Haversines. 

3 

6^20"*  95"  C  1 

6f^  21m  95*  15' 

6h  22m  95°  3r 

6h  2Sm  96°  45' 

6h  24^  96°  0' 

3 

60 
59 
58 
57 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.73526 
.73529 
.73532 
.73535 

.54358 
.54361 
.54365 
.54369 

9.73699 
.73702 
.73705 
.73708 

.54575 
.54579 
.54582 
.54586 

9.73872 
.73875 
.73878 
.73881 

.54792 
.54796 
.54800 
.54803 

9.74044 
.74047 
.74049 
.74052 

.55009 
.55013 
.55017 
.55020 

9.74215 
.74218 
.74220 
.74223 

.55226 
.56230 
.66234 
.65237 

+    r 

5 
6 

7 

9.73538 
.73541 
.73544 
.73546 

.54372 
.54376 
.54380 
.54383 

9.73711 
.73714 
.73717 
.73720 

.54590 
.54593 
.54597 
.54600 

9.73883 
.73886 
.73889 
.73892 

.54807 
.54810 
.54814 
.54818 

9.74055 
.74058 
.74061 
.74064 

.55024 
.55028 
.55031 
.55035 

9.74226 
.74229 
.74232 
.74235 

.55241 
.66245 
.55248 
.55252 

56 

55 
54 
53 
52 
51 
50 
49 

+  r 

9 

10 

11 

9.73549 
.73552 
.73555 
.73558 

.54387 
.54390 
.54394 
.54398 

9.73722 
.73725 
.73728 
.73731 

.54604 
.54608 
.54611 
.54615 

9.73895 
.73898 
.73901 
.73903 

.54821 
.54825 

.54828 
.54832 

9.74067 
.74069 
.74072 
.74075 

.55038 
.55042 
.55046 
.55049 

9.74237 
.74240 
.74243 
.74246 

.55265 
.65259 
.65263 
.55266 

+      3' 

13 
14 
15 

9.73561 
.73564 
.73567 
.73570 

.54401 
.54405 
.54409 
.54412 

9.73734 
.73737 
.73740 
.73743 

.54619 
.54622 
.54626 
.54629 

9.73906 
.73909 
.73912 
.73915 

.54836 
.54839 
.54843 
.54847 

9.74078 
.74081 
.74084 
.74087 

.55053 
.55056 
.55060 
.55064 

9.74249 
.74252 
.74254 
.74257 

.55270 
.55273 
.55277 
.55281 

48 
41 
46 
45 

+     4' 
11 
18 
19 

9.73572 
.73575 
.73578 
.73581 

.54416 
.54419 
.54423 
.54427 

9.73746 
.73748 
.73751 
.73754 

.54633 
.54637 
.54640 
.54644 

9.73918 
.73921 
.73924 
.73926 

.54850 
.54854 
.54857 
.54861 

9.74089 
.74092 
.74095 
.74098 

.55067 
.55071 
.55075 
.55078 

9.74260 
.74263 
.74266 
.74269 

.55284 
.55288 
.66292 
.55295 

U 
43 
42 
41 

+     5' 
21 

22 
23 

9.73584 
.73587 
.73590 
.73593 

.54430 
.54434 
.54437 
.54441 

9.73757 
.73760 
.73763 
.73766 

.54647 
.54651 
.54655 
.54658 

9.73929 
.73932 
.73935 
.73938 

.54865 
.54868 
.54872 
.54876 

9.74101 
.74104 
.74106 
.74109 

.55082 
.55085 
.55089 
.55093 

9.74272 
.74274 
.74277 
.74280 

.55299 
.55302 
.55306 
.56310 

40 
39 
38 
31 

+      6' 

25 
26 
21 

9.73596 
.73598 
.73601 
.73604 

.54445 
.54448 
.54452 
.54456 

9.73769 
.73771 
.73774 
.73777 

.54662 
.54666 
.54669 
.54673 

9.73941 
.73944 
.73946 
.73949 

.54879 
.54883 
.54886 
.54890 

9.74112 
.74115 
.74118 
.74121 

.55096 
.55100 
.55103 
.55107 

9.74283 
.74286 
.74289 
.74291 

.55313 
.55317 
.66320 
.55324 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.73607 
.73610 
.73613 
.73616 

.54459 
.54463 
.54466 
.54470 

9.73780 
.73783 
.73786 
.73789 

.54676 
.54680 
.54684 
.54687 

9.73952 
.73955 
.73958 
.73961 

.54894 
.54897 
.54901 
.54904 

9.74124 
.74126 
.74129 
.74132 

.55111 
,65114 
.66118 
.65122 

9.74294 
.74297 
.74300 
.74303 

.56328 
.66331 
o65336 
.55339 

32 
31 
30 
29 

+  8' 
33 
34 
35 

9.73619 
.73622 
,73624 
.73627 

.54474 
.54477 
.54481 
.54485 

9.73792 
.73794 
.73797 
.73800 

.54691 
.54695 
.54698 
.54702 

9.73964 
.73967 
.73969 
.73972 

.54908 
.54912 
.54915 
.54919 

9.74135 
.74138 
.74141 
.74144 

.65125 
.65129 
.65132 
.55136 

9.74306 
.74308 
.74311 
.74314 

.55342 
.55346 
.55349 
.55353 

28 
21 
26 
25 

+  ^ 

31 
38 
39 

9.73630 
.73633 
.73636 
.73639 

.54488 
.54492 
.54495 
.54499 

9.73803 
.73806 
.73809 
.73812 

.54705 
.54709 
.54713 
.54716 

9.73975 
.73978 
.73981 
.73984 

.54923 
.54926 
.54930 
.54933 

9.74146 
.74149 
.74152 
.74155 

.55140 
.65143 
.66147 
.56150 

9.74317 
.74320 
.74323 
.74325 

.55357 
.66360 
.66364 
.56367 

24 
23 
22 
21 

+  W 

41 

42 
43 

9.73642 
.73645 
.73648 
.73650 

.54503 
.54506 
.54510 
.54514 

9.73815 
.73817 
.73820 
.73823 

.54720 
.54724 
.54727 
.54731 

9.73987 
.73989 
.73992 
.73995 

.54937 
.54941 
.54944 
.54948 

9.74158 
.74161 
.74163 
.74166 

.55154 
.55158 
.55161 
.55165 

9.74328 
.74331 
.74334 
.74337 

.55371 
.55375 
.65378 
.55382 

20 
19 
18 
11 

+    11' 

45 
46 
41 

9.73653 
.73656 
.73659 
.73662 

.54517 
.54521 
.54524 
.54528 

9.73826 
.73829 
.73832 
.73835 

.54734 
.54738 
.54742 
.54745 

9.73998 
.74001 
.74004 
.74007 

.54952 
.54955 
.54959 
.54963 

9.74169 
.74172 
.74175 
.74178 

.66169 
.66172 
.65176 
.56179 

9.74340 
.74342 
.74345 
.74348 

.55386 
.55389 
.55393 
.56396 

16 
15 
14 
13 

+    13' 

49 
50 
51 

9.73665 
.73668 
.73671 
.73674 

.54532 
.54535 
.54539 
.54542 

9.73838 
.73840 
.73843 
.73846 

.54749 
.54752 
.54756 
.54760 

9.74009 
.74012 
.74015 
.74018 

.54966 
.54970 
.54973 
.54977 

9.74181 
.74183 
.74186 
.74189 

.55183 
.55187 
.66190 
.66194 

9.74351 
.74354 
.74357 
.74359 

.55400 
.55404 
.66407 
.56411 

12 

11 

10 

9 

+   13' 

53 
54 
55 

9.73676 
.73679 
.73682 
.73685 

.54546 
.54550 
.54553 
.54557 

9.73849 
.73852 
.73855 
.73858 

.54763 
.54767 
.54771 
.54774 

9.74021 
.74024 
.74027 
.74029 

.54980 
.54984 
.54988 
.54991 

9.74192 
.74195 
.74198 
.74200 

.65197 
.56201 
.55206 
.55208 

9.74362 
.74365 
.74368 
.74371 

.55414 
.55418 
.66422 
.66426 

8 
1 
6 
5 

+    14' 

51 
58 
59 

9.73688 
.73691 
.73694 
.73697 

.54561 
.54564 
.54568 
.54571 

9.73860 
.73863 
.73866 
.73869 

.54778 
.54781 
.54785 
.54789 

9.74032 
.74035 
.74038 
.74041 

.54995 
.54999 
.55002 
.55006 

9.74203 
.74206 
.74209 
.74212 

.55212 
.55216 
.55219 
.55223 

9.74374 
.74376 
.74379 

.74382 

.55429 
.66433 
.66436 
.66440 

4 
3 

2 
1 

+  15' 

9.73699 

.54575 

9.73872 

.54792 

9.74044 

.55009 

9.74215 

.55226 

9.74385 

.55443 

0 

llh  39m 

llhssm 

llh  Sim 

17h  36m 

nh  35m 

Page  888]                  TABLE  45. 

Haversines. 

s 

6A  25m  96°  W 

6ft  26^  96°  30' 

6ft  27m  96°  45' 

6ft  28m  97°  0' 

6ft  29m  97°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.74385 
.74388 
.74391 
.74393 

.55443 
.55447 
.55451 
.55454 

9.74554 
.74557 
.74560 
.74563 

.55660 
.55664 
.55667 
.55671 

9.74723 
.74726 
.74729 
.74732 

.55877 
.55880 
.55884 
.55888 

9.74891 
.74894 
.748a7 
.74900 

.56093 
.56097 
.56101 
.56104 

9.75059 
.75061 
.75064 
.75067 

.56319 
.56314 
.56317 
.56321 

60 
59 
58 
57 

+  r 

5 
6 

7 

9.74396 
.74399 
.74402 
.74405 

.55458 
.55461 
.55465 
.55469 

9.74566 
.74569 
.74571 
.74574 

.55675 
.55678 
.55682 
.55685 

9.74734 
.74737 
.74740 
.74743 

.55891 
.55895 
.55899 
.55902 

9.74902 
.74905 
.74908 
.74911 

.56108 
.56112 
.56115 
.56119 

9.75070 
.75072 
.75075 
.75078 

.56324 
.56328 
.56332 
.56335 

56 
55 
54 
53 

+  ^' 

9 

10 

11 

9.74408 
.74410 
.74413 
.74416 

.55473 
.55476 
.55479 
.55483 

9.74577 
.74580 
.74583 
.74585 

.55689 
.55693 
.55696 
.55700 

9.74746 
.74748 
.74751 
.74754 

.55906 
.55909 
.55913 
.55917 

9.74914 
.74916 
.74919 
.74922 

.56122 
.56126 
.56130 
.56133 

9.75081 
.75084 
.75086 
.75089 

.56339 
.56342 
.56346 
.56350 

52 
51 
50 
49 

+  3' 

13 
14 
15 

9.74419 
.74422 
.74425 
.74427 

.55487 
.55490 
.55494 
.55498 

9.74588 
.74591 
.74594 
.74597 

.55704 
.55707 
.55711 
.55714 

9.74757 
.74760 
.74762 
.74765 

.55920 
.55924 
.55927 
.55931 

9.74925 
.74928 
.74930 
.74933 

.56137 
.56140 
.56144 
.56147 

9.75092 
.75095 
.75097 
.75100 

.56353 
.56357 
.56360 
.56364 

48 
47 
46 
45 

17 
18 
19 

9.74430 
.74433 
.74436 
.74439 

.55501 
.55505 
.55508 
.55512 

9.74600 
.74602 
.74605 
.74608 

.55718 
.55722 
.55725 
.55729 

9.74768 
.74771 
.74774 
.74776 

.55935 
.55938 
.55942 
.55945 

9.74936 
.74939 
.74941 
.74944 

.56151 
.56155 
.56158 
.56162 

9.75103 
.75106 
.75109 
.75111 

.56368 
.56371 
.56375 
.56378 

44 
43 
42 
41 

+  5' 
21 

22 
23 

9.74442 

.74444 
.74447 
.74450 

.55516 
.55519 
.55523 
.55526 

9.74611 
.74614 
.74616 
.74619 

.55732 
.55736 
.55740 
.55743 

9.74779 
.74782 
.74785 
.74788 

.55949 
.55953 
.55956 
.55960 

9.74947 
.74950 
.74953 
.74955 

.56166 
.56169 
.56173 
.56176 

9.75114 
.75117 
.75120 
.75122 

.56382 
.56386 
.56389 
.56393 

40 
39 
38 
37 

+      6' 

25 
26 

27 

9.74453 
.74456 
.74458 
.74461 

.55530 
.55534 
.55537 
.55541 

9.74622 
.74625 
.74628 
.74630 

.55747 
.55750 
.55754 
.55758 

9.74791 
.74793 
.74796 
.74799 

.55964 
.55967 
.55971 
.55974 

9.74958 
.74961 
.74964 
.74967 

.56180 
.56184 
.56187 
.56191 

9.75125 
.75128 
.75131 
.75134 

.56397 
.56400 
.56404 
.56407 

36 
35 
34 
33 

+    r 

29 
30 
31 

9.74464 
.74467 
.74470 
.74473 

.55545 
.55548 
.55552 
.55555 

9.74633 
.74636 
.74639 
.74642 

.55761 
.55765 
.55769 
.55772 

9.74802 
.74805 
.74807 
.74810 

.55978 
.55982 
.55985 
.55989 

9.74969 
.74972 
.74975 
.74978 

.56195 
.56198 
.56202 
.56205 

9.75136 
.75139 

.75142 
.75145 

.56411 
.56415 
.56418 
.56422 

32 
31 
30 
29 
28 
27 
26 
25 

+   8^ 
33 
34 
35 

9.74475 
.74478 
.74481 
.74484 

.55559 
.55563 
.55566 
.55570 

9.74645 
.74647 
.74650 
.74653 

.55776 
.55779 
.55783 

.55787 

9.74813 
.74816 
.74819 
.74821 

.55992 
.55996 
.56000 
.56003 

9.74981 
.74983 
.74986 
.74989 

.56209 
.56213 
.56216 
.56220 

9.75147 
.75150 
.75153 
.75156 

.56425 
.56429 
.56433 
.56436 

+   9' 

37 
38 
39 

9.74487 
.74490 
.74492 
.74495 

.55573 
.55577 
.55581 
.55584 

9.74656 
.74659 
.74661 
.74664 

.55790 
.55794 
.55797 
.55801 

9.74824 
.74827 
.74830 
.74833 

.56007 
.56010 
.56014 
.56018 

9.74992 
.74994 
.74997 
.75000 

.56223 
.56227 
.56231 
.56234 

9.75159 
.75161 
.75164 
.75167 

.56440 
.56443 
.56447 
.56451 

24 
23 

22 
21 

+  10^ 

41 
42 
43 

9.74498 
.74501 
.74504 
.74506 

.55588 
.55592 
.55595 
.55599 

9.74667 
.74670 
.74673 
.74675 

.55805 
.55808 
.55812 
.55815 

9.74835 
.74838 
.74841 
.74844 

.56021 
.56025 
.56029 
.56032 

9.75003 
.75006 
.75008 
.75011 

.56238 
.56241 
.56245 
.56249 

9.75170 

.75172 
.75175 
.75178 

.56454 
.56458 
.56461 
.56465 

20 
19 
IS 
17 
16 
15 
14 
13 
12 
11 
10 
9 

+  11^ 

45 
46 
47 

9.74509 
.74512 
.74515 
.74518 

.55603 
.55606 
.55610 
.55613 

9.74678 
.74681 
.74684 
.74687 

.55819 
.55823 
.55826 
.55830 

9.74846 
.74849 
.74852 
.74855 

.56036 
.56039 
.56043 
.56047 

9.75014 
.75017 
.75020 

.75022 

.56252 
.56256 
.56259 
.56263 

9.75181 
.75183 
.75186 
.75189 

.56469 
.56472 
.56476 
.56479 

49 
50 
51 

9.74521 
.74523 
.74526 
.74529 

.55617 
.55620 
.55624 
.55628 

9.74690 
.74692 
.74695 
.74698 

.55834 
.55837 
.55841 
.55844 

9.74858 
.74860 
.74863 
.74866 

.56050 
.56054 
.56057 
.56061 

9.75025 
.75028 
.75031 
.75033 

.56267 
.56270 
.56274 
.56277 

9.75192 
.75195 
.75197 
.75200 

.56483 
.56487 
.56490 
.56494 

+  13^ 

53 
54 
55 

9.74532 
.74535 
.74538 
.74540 

.55631 
.55635 
.55638 
.55642 

9.74701 
.74704 
.74706 
.74709 

.55848 
.55852 
.55855 
.55859 

9.74869 

.74872 
.74874 
.74877 

.56065 
.56068 
.56072 
.56075 

9.75036 
.75039 
.75042 
.75045 

.56281 
.56285 
.56288 
.56292 

9.75203 
.75206 
.75208 
.75211 

.56497 
.56501 
.56505 
.56508 

8 
7 
6 
5 

+  W 

57 
58 
59 

9.74543 
.74546 
.74549 

.74552 

.55646 
.55649 
.55653 
.55657 

9.74712 
.74715 
.74718 
.74720 

.55862 
.55866 
.55870 
.55873 

9.74880 
.74883 
.74886 
.74888 

.56079 
.56083 
.56086 
.56090 

9.75047 
.75050 
.75053 
.75056 

.56296 
.56299 
.56303 
.56306 

9.75214 
.75217 
.75220 
.75222 

.56512 
.56516 
.56519 
.56523 

4 
3 
2 
1 

+  15' 

9.74554 

.55660 

9.74723 

.55877 

9.74891 

.56093 

9.75059 

.56310 

9.75225 

.56526 

0 

i7A  34'^ 

17^  33m 

17^  3pn 

i7ft  3im 

i7ft  30^ 

TABLE  45. 

Haversines. 

[Page  889 

s 

6 A  SOm  97°  3(K 

eft  3im  97°  45' 

6h  32m  98°  0' 

6^  3Sm  98°  15' 

6h  34m 

98°3(K 

8 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav, 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.75225 
.75228 
.75231 
.75233 

.56526 
.56530 
.56534 
.56537 

9.75391 
.75394 
.75396 
.75399 

.56743 
.58746 
.56750 
-56753 
.56757 
.56761 
.56764 
.56768 

9.75556 
.75559 
.75561 
.75564 

9.75567 
.75570 
.75572 
.75575 

.56959 
.58962 
.56966 
.56969 

9.75720 
.75723 
.75726 
.75729 

9.75731 
.75734 
.75737 
.75739 

9.75742" 
.75745 
.75748 
.75750 

.57175 
.57178 
.67182 
.57185 
.57189 
.57193 
.57196 
.57200 
.57203 
.57207 
.57211 
.57214 
.57218 
.57221 
.57225 
.57229 

9.75884 
.75887 
.75889 
.75892 

9.75895 
.75898 
.75900 
.75903 

.57390 
.57394 
.57398 
.67401 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.75236 
.75239 
.75242 
.75244 

.56541 
.56544 
.56.548 
.56552 

9.75402 
.75405 
.75407 
.75410 

.56973 
.56977 
.56980 
.56984 

.57406 
.57408 
.57412 
.57416 

56 
55 

54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
36 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 

'24 
23 
22 
21 

+  3' 

9 

10 

11 

9.75247 
.75250 
.75253 
.75256 

.56555 
.58559 
.56562 
.56566 

9.75413 
.75416 
.75418 
.75421 

9.75424 
.75427 
.75429 
.75432 

9.75435 
.75438 
.75440 
.75443 

9.75446 
.75449 
.75452 
.75454 

.56771 
.56775 
.56779 
.56782 
.56786 
.56739 
.56793 
.56797 

9.75578 
.75581 
.75583 
.75586 

9.75589 
.75592 
.75594 
.75597 

.56987 
.56991 
.56994 
.56998 

9.75906 
.75908 
.75911 
.75914 

.57419 
.67423 
.57426 
.57430 
.67434 
.57437 
.57441 
.57444 
.67448 
.57462 
.57456 
.57459 
.67462 
.57466 
.57470 
.57473 
.57477 
.67480 
.57484 
.57488 

+     3^ 

13 
14 
15 

9.75258 
.75261 
.75264 
.75267 

.56570 
.56573 
.56577 
.56580 

.57002 
.57005 
.57009 
.57012 
.57016 
.57020 
.57023 
.57027 
.57031 
.57034 
.57038 
.57041 
.57045 
.57049 
.57052 
.57056 
.57059 
.57063 
.57067 
.57070 
.57074 
.57077 
.57081 
.57085 
.57088 
.57092 
.57095 
.57099 

9.75753 
.75756 
.75759 
.75761 

9.75764 
.75767 
.75770 
.75772 

9.75917 
.75919 
.75922 
.75925 

9.75927 
.75930 
.75933 
.75936 

9.75938 
.75941 
.75944 
.75947 

+  4' 
17 
18 
19 

9.75269 
.75272 
.75275 
.75278 

.56584 

.56588 
.56591 
.56595 
.56598 
.56602 
.56606 
.56609 

.56800 
.56804 
.56807 
.56811 

9.75600 
.75603 
.75605 
.75608 

9.75611 
.75614 
.75616 
.75619 

9.75622 
.75625 
.75627 
.75630 

9.75633 
.75636 
.75638 
.75641 

9.75644 
.75646 
.75649 
.75652 

9.75655 
.75657 
.75660 
.75663 

.57232 
.57236 
.57239 
.57243 
.57247 
.57250 
.67254 
.57267 

+     5' 
21 
22 
23 

9.75280 
.75283 
.75286 
.75289 

.56815 
.56818 
.56822 
.56825 

9.75775 
.75778 
.75780 
.75783 

9.75786 
.75789 
.75791 
.75794 

+      6' 

25 
26 

27 

9.75291 
.75294 
.75297 
.75300 

.56613 
.56616 
.56620 
.56624 

9.75457 
.75460 
.75463 
.75465 

.56829 
.56833 
.56836 
.56840 
.56843 
.56847 
.56851 
.56854 
.56858 
.56861 
.56865 
.56869 

.67261 
.57265 
.57268 
.57272 

9.75949 
.75952 
.75955 
.75957 

+    r 

29 
30 
31 

9.75303 
.75305 
.75308 
.75311 

.56627 
.56631 
.56634 
.56638 

9.75468 
.75471 
.75474 
.75476 

9.75797 
.75800 
.75802 
.75805 

9.75808 
.75810 
.75813 
.75816 

9.75819 
.75821 
.75824 
.75827 

.57275 
.57279 
.57283 
.57286 
.57290 
.57293 
.57297 
.57301 
.57304 
.57308 
.57311 
.57315 

9.75960 
.75963 
.75966 
.75968 

9.75971" 
.75974 
.75976 
.75979 

9.75982 
.75985 
.75987 
.75990 

.57491 
.67496 
.57498 
.57602 
.57506 
.57509 
.57613 
.57516 
.57520 
.57524 
.57527 
.57531 

+   8' 
33 
34 
35 

9.75314 
.75316 
.75319 
.75322 

.56642 
.56645 
.56649 
.56652 

9.75479 

.75482 
.75485 
.75487 

+    r 

37 
38 
39 

9.75325 
.75327 
.75330 
.75333 

.56656 
.56660 
.56663 
.56667 

9.75490 
.75493 
.75496 
.75498 

.56872 
.56876 
.56879 
.56883 

+    W 

41 
42 
43 

9.75336 
.75338 
.75341 
.75344 

.56670 
.56674 
.56678 
.56681 

9.75501 
.75504 
.75507 
.75509 

.56887 
.56890 
.56894 
.56897 

9.75666 
.75668 
.75671 
.75674 

.57103 
.57106 
.57110 
.57114 

9.75S30 
.75832 
.75835 
.75838 

.67318 
.57322 
.57326 
.57329 

9.75993 
.75995 
.75998 
.76001 

.57534 
.57538 
.57541 
.57545 

20 
19 
18 
17 

+  11' 

45 
46 
47 

9.75347 
.75350 
.75352 
.75355 

.56685 
.56689 
.56692 
.56696 

9.75512 
.75515 
.75518 
.75520 

.56901 
.56905 
.56908 
.56912 
.56915 
.56919 
.56923 
.56926 
.56930 
.56933 
.56937 
.56941 

9.75677 
.75679 
.75682 
.75685 

9.75688 
.75690 
.75693 
.75696 

.57117 
.57121 
.57124 
.57128 
.57131 
.57135 
.57139 
.57142 
.57146 
.57149 
.57153 
.57157 

9.75840 

.75843 
.75846 
.75849 

.57333 
.57337 
.57340 
.57344 
.57347 
.57351 
.57355 
.57358 
.57362 
.57365 
.57369 
.57373 

9.76004 
.76006 
.76009 
.76012 

9.76014 
.76017 
.76020 
.76023 

9.76025' 
.76028 
.76031 
.76033 

.57649 
.57552 
.57556 
.57559 
.57563 
.57567 
.57570 
.57574 
.57577 
.57581 
.57586 
.57588 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 

+  n' 

49 
50 
51 

9.75358 
.75361 
.75363 
.75366 

9.75369 
.75372 
.75374 
.75377 

'9.75380' 
.75383 
.75385 
.75388 

9.75391 

.56699 
.56703 
.56707 
.56710 
.56714 
.56717 
.56721 
.56725 
.56728 
.56732 
.56735 
.56739 

9.75523 
.75526 
.75529 
.75531 

9.75534 
.75537 
.75540 
.75542 

9.75851 
.75854 
.75857 
.75859 

9.75862 
.75865 
.75868 
.75870 

9.75873 
.75876 
.75879 
.75881 

+  13^ 

53 
54 
55 

9.75698 
.75701 
.75704 
.75707 

57 
58 
59 

9.75545 
.75548 
.75550 
.75553 

.56944 
.56948 
.56951 
.56955 

9.75709 
.75712 
.75715 
.75718 

.57160 
.57164 
.57167 
.57171 

.57376 
.57380 
.57383 
.57387 
.57390 

9.76036 
.76039 
.76041 
.76044 

.57592 
.57696 
.57599 
.57603 

+  15' 

.56743 

9.75556 

.56959 

9.75720 

.67175 

9.75884 

9.76047 

.57606 

0 

— 

nh  29m 

J7h  28m 

17h  27m 

17h 

26m                    I7h 

25m 

Page  890]                  TABLE  45. 

Haversines. 

s 

6ft  55m  98°  45^ 

6ft  36^  99°  0^ 

6ft  37m  99°  15^ 

6ft  55™  99°  30^ 

6ft  39m  99°  45' 

3 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 

2     ■ 
3 

9.76047 
.76050 
.76052 
.76055 

.57606 
.57610 
.57613 
.57617 

9.76209 
.76212 
.76215 
.76217 

.57833 
.57835 
.57839 
.57833 

9.76371 
.76373 
.76376 
.76379 

.58037 
.58041 
.58044 
.58048 

9.76531 
.76534 
.76537 
.76539 

.58353 
.58356 
.58260 
.58363 

9 

76691 
76694 
76697 
76699 

.58467 
.58471 
.58475 

.58478 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+    r 

5 
6 

7 

9.76058 
.76060 
.76063 
.76066 

.57631 
.57634 
.57638 
.57631 

9.76220 
.76223 
.76225 
.76228 

.57836 
.57840 
.57843 

.57847 

9.76381 
.76384 
.76387 
.76389 

.58051 
.58055 
.58059 
.58063 

9.76542 
.76545 
.76547 
.76550 

.58367 
.58370 
.58374 

.58377 

9 

76702 
76705 
76707 
76710 

.58483 
.58485 
.58489 
.58493 
.58496 
.58500 
.58503 
.58507 

+  2' 

9 

10 

11 

9.76069 
.76071 
.76074 
.76077 

.57635 
.57639 
.57643 
.57646 

9.76231 
.76233 
.76236 
.76239 

.57850 
.57854 

.57858 
.57861 

9.76392 
.76395 
.76397 
.76400 

.58066 
.58069 
.58073 
.58077 

9.76553 
.76555 
.76558 
.76561 

.58381 
.58285 
.58388 
.58393 

9 

76713 
.76715 
.76718 
.76721 

+  3^ 

13 
14 
15 

9.76079 

.76082 
.76085 
.76088 

.57649 
.57653 
.57656 
.57660 

9.76241 
.76244 
-.76247 
.76250 

.57865 
.57868 
.57873 
.57876 

9.76403 
.76405 
.76408 
.76411 

.58080 
.58084 
.58087 
.58091 

9.76563 
.76566 
.76569 
.76571 

.58395 
.58399 
.58303 
.58306 

9 

.76723 
.76726 
.76729 
.76731 

.58510 
.58514 

.58518 
.58531 

+  4' 
17 
18 
19 

9.76090 
.76093 
.76096 
.76098 

.57664 
.57667 
.57671 
.57675 

9.76252 
.76255 
.76258 
.76260 

.57879 
.57883 

.57886 
.57890 

9.76414 
.76416 
.76419 

.76422 

.58095 
.58098 
.58103 
.58105 

9.76574 
.76577 
.76579 
.76582 

.58310 
.58313 
.58317 
.58331 

9 

.76734 
.76737 
.76739 
.76742 

.58535 

.58538 
.58533 
.58536 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 

+  5' 

22 
23 

9.76101 
.76104 
.76106 
.76109 

.57678 
.57683 
.57685 
.57689 

9.76263 
.76266 
.76268 
.76271 

.57894 
.57897 
.57901 
.57904 

9.76424 
.76427 
.76430 
.76432 

.58109 
.58113 
.58116 
.58130 

9.76585 
.76587 
.76590 
.76593 

.58334 
.58338 
.58331 
.58335 

9 

.76745 
.76747 
.76750 
.76753 

.58539 
.58543 
.58546 
.58550 

+   6^ 

27 

9.76112 
.76115 
.76117 
.76120 

.57693 
.57696 
.57700 
.57703 

9.76274 
.76276 
.76279 
.76282 

.57908 
.57911 
.57915 
.57919 

9.76435 
.76438 
.76440 
.76443 

.58133 
.58137 
.58130 
.58134 

9.76595 
.76598 
.76601 
.76603 

.58338 
.58343 
.58346 
.58349 

9 

.76755 
.76758 
.76761 
.76763 

.58553 
.58557 
.58561 
.58564 

+   7' 
31 

9.76123 
.76125 
.76128 
.76131 

.57707 

.57710 
.57714 
.57718 

9.76285 
.76287 
.76290 
.76293 

.57933 
.57936 
.57939 
.57933 

9.76446 
.76448 
.76451 
.76454 

.58138 
.58141 
.58145 
.58148 

9.76606 
.76609 
.76611 
.76614 

.58353 
.58356 
.58360 
.58364 

9 

.76766 
.76769 
.76771 
76774 

.58568 
.58571 
.58575 
.58579 

+  8^ 

54 
35 

9.76134 
.76136 
.76139 
.76142 

.57731 
.57735 

.57738 
.57733 

9.76296 
.76298 
.76301 
.76303 

.57937 
.57940 
.57944 
.57947 

9.76456 
.76459 
.76462 
.76464 

.58153 
.58156 
.58159 
.58163 

9.76617 
.76619 
.76622 
.76625 

.58367 
.58371 
.58374 

.58378 

9 

76777 
76779 
.76782 
76784 

.58583 
.58586 
.58589 
.58593 

28 
27 
26 
25 

24 
23 
22 
21 

+  9^ 

57 
55 
39 

9.76144 
.76147 
.76150 
.76152 

.57736 
.57739 
.57743 
.57746 

9.76306 
.76309 
.76311 
.76314 

.57951 
.57955 
.57958 
.57963 

9.76467 
.76470 
.76473 
.76475 

.58166 
.58170 
.58173 
.58177 

9.76627 
.76630 
.76633 
.76635 

.58381 

.58385 
.58389 
.58393 

9 

76787 
76790 
76792 
76795 

.58596 
.58600 
.58604 
.58607 

+  1(K 

43 

9.76155 
.76158 
.76161 
.76163 

.57750 
.57753 
.57757 
.57761 

9.76317 
.76320 
.76322 
.76325 

.57965 
.57969 
.57973 
.57976 

9.76478 
.76481 
.76483 
.76486 

.58181 
.58184 

.58188 
.58191 

9.76638 
.76641 
.76643 
.76646 

.58396 
.58399 
.58403 
.58407 

9 

76798 
76800 
76803 
76806 

.58611 
.58614 
.58618 
.58633 

20 
19 
18 
17 

+  11^ 

45 
46 
47 

9.76166 
.76169 
.76171 
.76174 

.57764 
.57768 
.57771 
.57775 

9.76328 
.76330 
.76333 
.76336 

.57980 
.57983 
.57987 
.57990 

9.76489 
.76491 
.76494 
.76497 

.58195 
.58199 
.58303 
.58306 

9.76649 
.76651 
.76654 
.76657 

.58410 
.58414 
.58417 
.58421 

9 

76808 
76811 
76814 
76816 

.58625 
.58639 
.58633 
.58636 

16 
15 
14 
13 

+  12^ 

49 
50 
51 

9.76177 
.76179 
.76182 
.76185 

.57779 
.57783 
.57786 
.57789 

9.76338 
.76341 
.76344 
.76346 

.57994 
.57998 
.58001 
.58005 

9.76499 
.76502 
.76505 
.76507 

.58309 
.58313 
.58317 
.58330 

9.76659 
.76662 
.76665 
.76667 

.58424 

.58438 
.58433 
.58435 

9 

76819 
76822 
76824 
76827 

.58639 
.58643 
.58647 
.58650 

12 
11 
10 
9 
8 
7 
6 
5 

+  13^ 

55 
54 
55 

9.76188 
.76190 
.76193 
.76196 

.57793 
.57797 
.57800 
.57804 

9.76349 
.76352 
.76354 
.76357 

.58008 
.58013 
.58016 
.58019 

9.76510 
.76513 
.76515 
.76518 

.58334 
.58237 
.58331 
.58334 

9.76670 
.76673 
.76675 
.76678 

.58439 
.58443 
.58446 
.58450 

9 

76830 
76832 
76835 
76838 

.58654 
.58657 
.58661 
.58665 

+  14^ 

57 
55 
59 

9.76198 
.76201 
.76204 
.76206 

.57807 
.57811 
.57815 

.57818 

9.76360 
.76363 
.76365 
.76368 

.58033 
.58036 
.58030 
.58034 

9.76521 
.76523 
.76526 
.76529 

.58338 
.58343 
.58345 
.58349 

9.76681 
.76683 
.76686 
.76689 

.58453 
.58457 
.58460 
.58464 

9 

76840 
76843 
76845 
76848 

.58668 
.58671 
.58675 
.58679 

4 
3 
2 
1 

+  15^ 

9.76209 

.57833 

9.76371 

.58037 

9.76531 

.58253 

9.76691 

.58467 

9. 

76851 

.58682 

0 

nh  24m         1 

17h  2Sm 

17h  22^ 

17h  2m 

J7h  20m         1 

TABLE  45.                  [Page  891 

Haversinea. 

s 

6A  40™  100°  C 

6h  41^  100°  15' 

6h  42m  100°  30' 

6h  43m  100°  45' 

6h  44m  101°  0' 

s 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.l  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.76851 
.76853 
.76856 
.76859 

.586S2 
.58686 
.58690 
.58693 

9.77009 
.77012 
.77015 
.77017 

9.77020 
.77023 
.77025 
.77028 

.58897 
.58901 
.58904 
.58908 

9.77167 
.77170 
.77173 
.77175 

.59112 
.59115 
.59119 
.59123 

9.77325 
.77327 
.77330 
.77333 

.59326 
.59330 
.59333 
.59337 
.59340 
.59344 
.59348 
.59351 

9.77481 
.77484 
.77486 
.77489 

9.77492 
.77494 
.77497 
.77499 

9.77502 
.77505 
.77507 
.77510 

.59540 
.59544 
.59548 
.59551 

60 
59 

58 
67 

+   1^ 

5 
6 

7 

9.76861 
.76864 
.76867 
.76869 

.58697 
.58700 
.58701 
.58707 

.58911 
.58915 
.58919 
.58922 

9.77178 
.77181 
.77183 
.77186 

.59126 
.59130 
.59133 
.59137 

9.77335 
.77338 
.77340 
.77343 

.59555 
.59558 
.59562 
.59565 
.59569 
.59573 
.59576 
.59580 
.59583 
.59587 
.59590 
.59594 
.59598 
.59601 
.59605 
.59608 
.59613 
.59615 
.59619 
.59633 
.59636 
.59630 
.59633 
.59637 

56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+   2' 

9 
10 
11 

9.76872 
.76875 
.76877 
.76880 

.58711 
.58714 

.58718 
.58723 

9.77031 
.77033 
.77036 
.77038 

.58926 
.58929 
.58933 
.58937 
.58940 
.58944 
'  .58947 
.58951 
.58954 
.58858 
.58962 
.58965 

9.77188 
.77191 
.77194 
.77196 

9.77199 
.77202 
.77204 
.77207 

.59140 
.59144 
.59148 
.59151 

9.77346 
.77348 
.77351 
.77353 

.59355 
.59358 
.59363 
.59365 

+  y 

13 
14 
15 

9.76883 
.76885 
.76888 
.76891 

.58725 
.58729 
.58733 
.58736 

9.77041 
.77044 
.77046 
.77049 

.59155 
.59158 
.59163 
.59165 

9.77356 
.77359 
.77361 
.77364 

.59369 
.59373 
.59376 
.59380 

9.77512 
.77515 
.77518 
.77520 

+      i' 
17 
18 
19 

9.76893 
.76896 
.76898 
.76901 

.58740 
.58743 
.58747 
.58750 

9.77052 
.77054 
.77057 
.77060 

9.77209 
.77212 
.77215 
.77217 

.59169 
.59173 
.59176 
.59180 

9.77366 
.77369 
.77372 
.77374 

.59383 
.59387 
.59391 
.59394 
.59398 
.59401 
.59405 
.59408 

9.77523 

.77525 
.77528 
.77531 
9.77533 
.77536 
.77538 
.77541 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
S3 

+   5' 
21 
22 
23 

9.76904 
.76906 
.76909 
.76912 

.58754 

.58758 
.58761 
.58765 

9.77062 
.77065 
.77067 
.77070 

.58969 
.58972 
.58976 
.58979 

9.77220 
.77223 
.77225 
.77228 

.59183 
.59187 
.59190 
.59194 
.59198 
.59201 
.59205 
.59308 

9.77377 
.77380 
.77382 
.77385 

+   6' 

25 
26 

27 

9.76914 
.76917 
.76920 
.76922 

.58768 
.58772 
.58776 
.58779 

9.77073 
.77075 
.77078 
.77081 

.58983 

.58987 
.58990 
.58994 

9.77230 
.77233 
.77236 
.77238 

9.77387 
.77390 

1  .77393 
.77395 

.59412 
.59416 
.59419 
.59423 
.59426 
.59430 
.59433 
.59437 

9.77544 
.77546 
.77549 
.77551 

9.77554 
.77557 
.77559 
.77562 

+    r 

29 
30 
31 

9.76925 
.76928 
.76930 
.76933 

.58783 
.58786 
.58790 
.58793 

9.77083 
.77086 
.77089 
.77091 

.58997 
.59001 
.59005 
.59008 

9.77241 
.77243 
.77246 
.77249 

.59212 
.59215 
.59319 
.59223 

9.77398 
.77400 
.77403 
.77406 

.59640 
.59644 
.59648 
.59651 
.59655 
.59658 
.59663 
.59665 

32 
31 
30 
29 
28 
27 
26 
25 

+   8' 
33 
34 
35 

9.76936 
.76938 
.76941 
.76943 

.58797 
.58801 

.58864 
.58808 

9.77094 
.77096 
.77099 
.77102 

.59012 
.59015 
.59019 
.59022 

9.77251 

.77254 
.77257 
.77259 

.59226 
.59230 
.59233 
.59237 
.59240 
.59244 
.59248 
.59251 

9.77408 
.77411 
.77413 
.77416 

.59440 
.59444 
.59448 
^9451 

9.77564 
.77567 
.77570 
.77572 

+   9^ 

57 
38 
39 

9.76946 
.76949 
.76951 
.76954 

.58811 
.58815 

.58818 
.58822 

9.77104 
.77107 
.77110 
.77112 

.59026 
.59030 
.59033 
.59037 

9.77262 
.77264 
.77267 
.77270 

9.77419 
.77421 
.77424 
.77427 

.59455 
.59458 
.59462 
.59465 

9.77575 

.77577 
.77580 
.77583 

.59669 
.59673 
.59676 
.59680 
.59683 
.59687 
.59690 
.59694 

24 
23 
22 
21 
20 
19 
18 
17 

+  W 

41 
42 
43 

9.76957 
.76959 
.76962 
.76965 

.58826 
.58829 
.58833 
.58836 
.58840 
.58843 
.58847 
.58851 

9.77115 
.77117 
.77120 
.77123 

.59040 
.59044 
.59047 
.59051 

9.77272 

.77275 
.77278 
.77280 

.59255 
.59258 
.59263 
.59365 

9.77429 
.77432 
.77434 
.77437 

.59469 
.59473 
.59476 
.59480 

9.77585 
.77588 
.77590 
.77593 

+  11' 

45 
46 

47 

9.76967 
.76970 
.76972 
.76975 

9.77125 
.77128 
.77131 
.77133 

.59055 
.59058 
.59062 
.59065 

9.77283 

.77285 
.77288 
.77291 

.59369 
.59373 
.59376 
.59380 

9.77440 
.77442 

.77445 
.77447 

.59483 
.59487 
.59490 
.59494 

9.77596 
.77598 
.77601 
.77603 

.59697 
.59701 
.59705 
.59708 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

+  12' 

49 
50 
51 

9.76978 
.76980 
.76983 
.76986 

.58854 
.58858 
.58861 

.58865 

9.77136 
.77139 
.77141 
.77144 

.59069 
.59072 
.59076 
.59080 

9.77293 
.77296 
.77298 
.77301 

.59283 
.59387 
.59390 
.59294 

9.77450 
.77453 
.77455 
.77458 

.59498 
.59501 
.59505 
.59508 

9.77606 
.77609 
.77611 
.77614 

.59713 
.59715 
.59719 
.59733 
.59736 
.59730 
.59733 
.59737 

+  13' 

53 
54 
55 

9.76988 
.76991 
.76994 
.76996 

.58869 

.58872 
.58876 
.58879 

9.77146 
.77149 
.77152 
.77154 

.59083 
.59087 
.59090 
.59094 

9.77304 
.77306 
.77309 
.77312 

.59298 
.59301 
.59305 
.59308 

9.77460 
.77463 
.77466 
.77468 

.59512 
.59515 
.59519 
.59533 

9.77616 
.77619 
.77622 
.77624 

+    14' 

57 
55 
59 

9.76999 
.77002 
.77004 
.77007 

.58883 
.58886 
.58890 
.58894 

9.77157 
.77160 
.77162 
.77165 

.59097 
.59101 
.59105 
.59108 

9.77314 
.77317 
.77319 
.77322 

.59312 
.59315 
.59319 
.59323 

9.77471 
.77473 
.77476 
.77479 

.59526 
.59530 
.59533 
.59537 

9.77627 
.77629 
.77632 
.77634 

.59740 
.59744 
.59747 
.59751 

4 
3 

2 

1 

+  15' 

9.77009 

.58897 

9.77167 

.59112 

9.77325   .59326 

9.77481   .59540 

9.77637 

.59755 

0 

ijh igm 

17hi8m 

17h  17m 

17hl6m 

17h  15m 

_ 

21594°— 14- 


49 


Page  892] 

TABLE  45. 

Haversines. 

s 

6h45m 

101°  15' 

6h46m 

101°  30' 

6h  47m 

101°  45' 

6h  48m, 

103°  0' 

6h  49m 

103°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav 

Nat.  Hav 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.77637 
.77640 
.77642 
.77645 

.59755 
.59758 
.59763 
.59765 

9.77792 

.77795 
.77797 
.77800 

.59968 
.59973 
.59976 
.59979 

9.77947 
.77949 
.77952 
.77954 

.60183 
.60185 
.60189 
.60193 

9.78101 
.78103 
.78106 
.78108 

.60396 
.60399 
.60403 
.60406 

9.78254 
.78256 
.78259 
.78261 

.60609 
.60613 
.60616 
.60630 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.77647 
.77650 
.77653 
.77655 

.59769 
.59773 
.59776 

.59779 

9.77803 
.77805 
.77808 
.77810 

.59983 
.59986 
.59990 
.59993 

9.77957 
.77960 
.77962 
.77965 

.60196 
.60300 
.60303 
.60307 

9.78111 
.78113 
.78116 
.78118 

.60410 
.60414 
.60417 
.60430 

9.78264 
.78266 
.78269 
.78271 

.60633 
.60637 
.60630 
.60634 

56 
55 
54 
53 
62 
51 
50 
49 

+   2^ 

9 

10 

11 

9.77658 
.77660 
.77663 
.77666 

.59783 
.59787 
.59790 
.59794 

9.77813 
.77815 
.77818 
.77821 

.59997 
.60000 
.60004 
.60008 

9.77967 
.77970 
.77972 
.77975 

.60311 
.60314 
.60318 
.60331 

9.78121 
.78124 
.78126 
.78129 

.60434 
.60438 
.60431 
.60435 

9.78274 

.78277 
.78279 
.78282 

.60637 
.60641 
.60644 
.60648 

+  3' 

IS 

14 
15 

9.77668 
.77671 
.77673 
.77676 

.59797 
.59801 
.59804 
.59808 

9.77823 

.77826 
.77828 
.77831 

.60011 
.60015 
.60018 
.60033 

9.77978 
.77980 
.77983 
.77985 

.60335 
.60338 
.60333 
.60335 

9.78131 
.78134 
.78136 
.78139 

.60438 
.60443 
.60445 
.60449 

9.78284 
.78287 
.78289 
.78292 

.60653 
.60655 
.60659 
.60663 

48 
47 
46 
45 

+     4^ 
17 
18 
19 

9.77679 
.77681 
.77684 
.77686 

.59813 
.59815 
.59819 
.59833 

9.77834 
.77836 
.77839 
.77841 

.60035 
.60039 
.60033 
.60036 

9.77988 
.77990 
.77993 
.77996 

.60339 
.60343 
.60346 
.60350 

9.78141 
.78144 
.78147 
.78149 

.60453 
.60456 
.60460 
.60463 

9.78294 
.78297 
.78299 
.78302 

.60666 
.60669 
.60673 
.60676 

44 
43 
42 
41 
40 
39 
38 
37 

+   5^ 
21 

22 
23 

9.77689 
.77691 
.77694 
.77697 

.59836 
.59839 
.59833 
.59837 

9.77844 
.77846 
.77849 
.77852 

.60040 
.60043 
.60047 
.60050 

9.77998 
.78001 
.78003 
.78006 

.60353 
.60357 
.60360 
.60364 

9.78152 
.78154 
.78157 
.78159 

.60467 
.60470 
.60474 
.60477 

9.78305 
.78307 
.78310 
.78312 

.60680 
.60684 
.60687 
.60691 

+   6^ 

26 

27 

9.77699 
.77702 
.77704 
.77707 

.59840 
.59844 
.59847 
.59851 

9.77854 
.77857 
.77859 
.77862 

.60054 
.60057 
.60061 
.60065 

9.78008 
.78011 
.78013 
.78016 

.60368 
.60371 
.60375 
.60378 

9.78162 
.78164 
.78167 
.78170 

.60481 
.60484 
.60488 
.60493 

9.78315 
.78317 
.78320 

.78322 

.60694 
.60698 
.60701 
.60705 

36 
35 
34 
S3 

+   r 

30 
31 

9.77710 

.77712 
.77715 
.77717 

.59854 
.59858 
.59861 
.59865 

9.77864 
.77867 
.77870 
.77872 

.60068 
.60073 
.60075 
.60079 

9.78019 

.78021 
.78024 
.78026 

.60383 
.60385 
.60389 
.60393 

9.78172 

.78175 
.78177 
.78180 

.60495 
.60499 
.60503 
.60506 

9.78325 
.78327 
.78330 
.78332 

.60708 
.60713 
.60715 
.60719 

32 
31 
30 
29 

+   8' 

34 
35 

9.77720 
.77723 
.77725 
.77728 

.59869 
.59873 
.59876 
.59879 

9.77875 
.77877 
.77880 

.77882 

.60083 
.60086 
.60090 
.60093 

9.78029 
.78031 
.78034 
.78037 

.60396 
.60300 
.60303 
.60307 

9.78182 
.78185 
.78187 
.78190 

.60509 
.60513 
.60516 
.60530 

9.78335 
.78338 
.78340 
.78343 

.60733 
.60736 
.60730 
.60733 

28 
27 
26 

25 

+   9' 

57 
38 
39 

9.77730 
.77733 
.77735 
.77738 

.59883 
.59886 
.59890 
.59894 

9.77885 
.77888 
.77890 
.77893 

.60097 
.60100 
.60104 
.60107 

9.78039 
.78042 
.78044 
.78047 

.60310 
.60314 
.60317 
.60331 

9.78192 
.78195 
.78198 
.78200 

.60534 
.60537 
.60531 
.60534 

9.78345 
.78348 
.78350 
.78353 

.60737 
.60740 
.60744 
.60747 

24 

23 
22 
21 

+  1(K 

42 
43 

9.77741 

.77743 
.77746 
.77748 

.59897 
.59901 
.59904 
.59908 

9.77895 
.77898 
.77900 
.77903 

.60111 
.60114 
.60118 
.60133 

9.78049 
.78052 
.78054 
.78057 

.60334 
.60338 
.60333 
.60335 

9.78203 
.78205 
.78208 
.78210 

.60538 
.60541 
.60545 
.60548 

9.78355 
.78358 
.78360 
.78363 

.60751 
.60755 
.60758 
.60763 

20 
19 
18 
17 

+  ir 

45 
46 
47 

9.77751 

.77754 
.77756 
.77759 

.59911 
.59915 
.59919 
.59933 

9.77906 
.77908 
.77911 
.77913 

.60135 
.60139 
.60133 
.60136 

9.78060 
.78062 
.78065 
.78067 

.60339 
.60343 
.60346 
.60349 

9.78213 

.78215 
.78218 
.78221 

.60553 
.60556 
.60559 
.69563 

9.78365 
.78368 
.78371 
.78373 

.60765 
.60769 
.60773 
.60776 

16 
15 
14 
13 

+  12' 

50 
51 

9.77761 
.77764 
.77766 
.77769 

.59936 
.59939 
.59933 
.59936 

9.77916 
.77918 
.77921 
.77924 

.60139 
.60143 
.60146 
.60150 

9.78070 
.78072 
.78075 
.78077 

.60353 
.60356 
.60360 
.60364 

9.78223 
.78226 
.78228 
.78231 

.60566 
.60570 
.60573 
.60577 

9.78376 
.78378 
.78.381 
.78383 

.60779 
.60783 
.60786 
.60790 

12 

11 

10 

9 

+  13^ 

55 
54 
55 

9.77772 

.77774 
.77777 
.77779 

.59940 
.59943 
.59947 
.59951 

9.77926 
.77929 
.77931 
.77934 

.60154 
.60157 
.60161 
.60164 

9.78080 
.78083 
.78085 
.78088 

.60367 
.60371 
.60374 
.60378 

9.78233 
.78236 
.78238 
.78241 

.60580 
.60584 
.60588 
.60591 

9.78386 
.78388 
.78391 
.78393 

.60794 
.60797 
.60801 
.60804 

8 
7 
6 
5 

+  14^ 

57 
58 
59 

9.77782 
.77785 
.77787 
.77790 

.59954 
.59958 
.59961 
.59965 

9.77936 
.77939 
.77942 
.77944 

.60168 
.60171 
.60175 
.60179 

9.78090 
.78093 
.78095 
.78098 

.60381 
.60385 
.60388 
.60393 

9.78243 
.78246 
.78249 
.78251 

.60595 
.60598 
.60603 
.60605 

9.78396 
.78398 
.78401 
.78404 

.60808 
.60811 
.60815 
.60818 

4 
3 
2 
1 
0 

+  15' 

9.77792 

.59968 

9.77947 

.60183 

9.78101 

.60396 

9.78254 

.60609 

9.78406 

.60833 

17h 

14m 

ijh 

13m 

17h  12m 

17h  urn 

17h  10m         1 

TABLE  45.                 [Page  893 

Haversines. 

s 

6/1  50m  103°  W   1 

6^  51^  102°  45'  1 

6/i  5;?™  103°  0'  | 

6ft  55"t  103°  15'  1  6ft  54"»  103°  30'  | 

s 

Log.  Hav. 

Nat.  Hav. 

Hav.Log. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.78406 
.78409 
.78411 
.78414 

.60823 
.60825 
.60829 
.60833 

9.78558 
.78560 
.78563 
.78565 

.61035 
.61038 
.61042 
.61046 

9.78709 
.78711 
.78714 
.78716 

.61248 
.61251 
.61255 
.61258 

9.78859 
.78862 
.78864 
.78867 

.61460 
.61464 
.61467 
.61471 

9.79009 
.79011 
.79014 
.79016 

.61672 
.61676 
.61679 
.61683 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 

+    r 

5 
6 
7 

9.78416 
.78419 
.78421 
.78424 

.60836 
.60840 
.60843 
.60847 

9.78568 
.78570 
.78573 
.78575 

.61049 
.61053 
.61056 
.61060 
.61063 
.61067 
.61070 
.61074 

9.78719 
.78721 
.78724 
.78726 

.61262 
.61265 
.61269 
.61272 

9.78869 
.78872 
.78874 
.78877 

.61474 
.61478 
.61481 
.61485 

9.79019 
.79021 
.79024 
.79026 

.61686 
.61690 
.61693 
.61697 

+  2^ 
9 

10 
11 

9.78426 
.78429 
.78431 
.78434 

.60850 
.60854 
.60857 
.60861 

9.78578 
.78581 
.78583 
.78586 

9.78729 
.78731 
.78734 
.78737 

.61276 
.61279 
.61283 
.61287 

9.78879 
.78882 
.78884 
.78887 

.61488 
.61492 
.61495 
.61499 

9.79029 
.79031 
.79034 
.79036 

.61701 
.61704 
.61708 
.61711 

+   3' 

13 
14 
15 

9.78436 
.78439 
.78442 
.78444 

.60865 
.60868 
.60872 
.60875 

9.78588 
.78591 
.78593 
.78596 

.61077 
.61081 
.61085 
.61088 

9.78739 

.78742 
.78744 
.78747 

.61290 
.61294 
.61297 
.61301 

9.78889 
.78892 
.78894 
.78897 

.61502 
.61506 
.61510 
.61513 

9.79039 
.79041 
.79044 
.79046 

.61715 
.61718 
.61722 
.61725 

48 
47 
46 
45 

+   *^ 
17 
18 
19 

9.78447 
.78449 
.78452 
.78454 

.60879 
.60882 
.60886 
.60889 

9.78598 
.78601 
.78603 
.78606 

.61092 
.61095 
.61099 
.61102 

9.78749 
.78752 
.78754 
.78757 

.61304 
.61308 
.61311 
.61315 

9.78899 
.78902 
.78904 
.78907 

.61517 
.61520 
.61524 
.61527 

9.79049 
.79051 
.79054 
.79056 

.61729 
.61732 
.61736 
.61739 

44 
43 
42 
41 

+  5' 
21 

22     ■ 
23 

9.78457 
.78459 
.78462 
.78464 

.60893 
.60897 
.60900 
.60904 

9.78608 
.78611 
.78013 
.78616 

.61106 
.61109 
.61113 
.61116 

9.78759 
.78762 
.78764 
.78767 

.61318 
.61322 
.61325 
.61329 

9.78909 

.78912 
.78914 
.78917 

.61531 
.61534 
.61538 
.61541 

9.79059 
.79061 
.79064 
.79066 

.61743 
.61747 
.61750 
.61754 

40 
39 
38 

37 

+   6' 

25 
26 
27 

9.78467 
.78469 
.78472 
.78474 

.60907 
.60911 
.60914 
.60918 

9.78618 
.78621 
.78623 
.78626 

.61120 
.61124 
.61127 
.61131 

9.78769 

.78772 
.78774 
.78777 

.61333 
.61336 
.61340 
.61343 

9.78919 
.78922 
.78924 
.78927 

.61545 
.61548 
.61552 
.61556 

9.79069 
.79071 
.79074 
.79076 

.61757 
.61761 
.61764 
.61768 

36 
35 
34 
S3 

+    r 

29 
SO 
31 

9.78477 
.78479 
.78482 
.78485 

.60921 
.60925 
.60928 
.60932 

9.78628 
.78631 
.78633 
.78636 

.61184 
.61138 
.61141 
.61145 

9.78779 
.78782 
.78784 
.78787 

.61347 
.61350 
.61354 
.61357 

9.78929 
.78932 
.78934 
.78937 

.61559 
.61563 
.61566 
.61570 

9.79079 
.79081 
.79084 
.79086 

.61771 
.61775 
.61778 
.61782 

32 
31 
30 
29 

+   8' 
S3 
34 
35 

9.78487 
.78490 
.78492 
.78495 

.60936 
.60939 
.60943 
.60946 

9.78638 
.78641 
.78643 
.78646 

.61148 
.61152 
.61155 
.61159 

9.78789 
.78792 
.78794 
.78797 

.61361 
.61364 
.61368 
.61372 

9.78939 
.78942 
.78944 
.78947 

.61573 
.61577 
.61580 
.61584 

9.79089 
.79091 
.79094 
.79096 

.61785 
.61789 
.61792 
.61796 

28 
27 
26 
25 

24 
23 
22 
21 

+   9' 

37 
38 
39 

9.78497 
.78500 
.78502 
.78505 

.60950 
.60953 
.60957 
.60960 

9.78649 
.78651 
.78654 
.78656 

.61163 
.61166 
.61170 
.61173 

9.78799 
.78802 
.78804 
.78807 

.61375 
.61379 
.61382 
.61386 

9.78949 
.78952 
.78954 
.78957 

.61587 
.61591 
.61594 
.61598 

9.79099 
.79101 
.79103 
.79106 

.61800 
.61803 
.61807 
.61810 

+  W 

41 
42 
43 

9.78507 
.78510 
.78512 
.78515 

.60964 
.60967 
.60971 
.60975 

9.78659 
.78661 
.78664 
.78666 

.61177 
.61180 
.61184 
.61187 

9.78809 
.78812 
.78814 
.78817 

.61389 
.61393 
.61396 
.61400 

9.78959 
.78962 
.78964 
.78967 

.61602 
.61605 
.61609 
.61612 

9.79108 
.79111 
.79113 
.79116 

.61814 
.61817 
.61821 
.61824 

20 
19 
18 
17 

45 
46 
47 

9.78517 
.78520 
.78522 
.78525 

.60978 
.60982 
.60985 
.60989 

9.78669 
.78671 
.78674 
.78676 

.61191 
.61194 
.61198 
.61201 

9.78819 
.78822 
.78824 
.78827 

.61403 
.61407 
.61410 
.61414 

9.78969 
.78972 
.78974 
.78977 

.61616 
.61619 
.61623 
.61626 

9.79118 
.79121 
.79123 
.79126 

.61828 
.61831 
.61835 
.61838 

16 
15 
14 
13 

+  13' 

51 

9.78528 
.78530 
.78533 
.78535 

.60992 
.60996 
.60999 
.61003 

9.78679 
.78681 
.78684 
.78686 

.61205 
.61209 
.61212 
.61216 

9.78829 
.78832 
.78834 
.78837 

.61418 
.61421 
.61425 
.61428 

9.78979 

.78982 
.78984 
.78987 

.61630 
.61633 
.61637 
.61640 

9.79128 
.79131 
.79133 
.79136 

.61842 
.61845 
.61849 
.61853 

12 

11 

10 

9 

+  13' 

55 
54 
55 

9.78538 
.78540 
.78543 
.78545 

.61007 
.61010 
.61014 
.61017 

9.78689 
.78691 
.78694 
.78696 

.61219 
.01223 
.61226 
.61230 

9.78839 

.78842 
.78844 
.78847 

.61432 
.61435 
.61439 
.61442 

9.78989 
.78992 
.78994 
.78997 

.61644 
.61648 
.61651 
.61655 

9.79138 
.79141 
.79143 
.79146 

.61856 
.61860 
.61863 
.61867 

8 
7 
6 
5 

+  14' 

57 
5S 
59 

9.78548 
.78550 
.78553 
.78555 

.61021 
.61024 
.61028 
.61032 

9.78699 
.78701 
.78704 
.78706 

.61233 
.61237 
.61240 
.61244 

9.78849 

.78852 
.78854 
.78857 

.61446 
.61449 
.61453 
.61456 

9.78999 
.79002 
.79004 
.79007 

.61658 
.61662 
.61665 
.61669 

9.79148 
.79151 
.79153 
.79156 

.61870 
.61874 
.61877 
.61881 

4 
3 
2 
1 

+  15' 

9.78558  1  .61035 

9.78709 

.61248 

9.78859 

.61460 

9.79009 

.61672 

9.79158 

.61884 

0 

17^  9m 

i7ft  sm 

nh  Tm 

nn&m, 

irhsm 

Page  894]                  TABLE  45. 

Haversines. 

s 

6ft  55"*  103°  45' 

6ft  56m  104°  r 

6h  5jm  104°  15^ 

6h  58m  104°  30' 

6h  59m  104°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.79158 
.79161 
.79163 
.79165 

.618S4 

.61888 
.61891 
.61895 

9.79306 
.79309 
.79311 
.79314 

.63096 
.63100 
.63103 
.63107 
.63110 
.63114 
.63117 
.63131 

9.79454 
.79457 
.79459 
.79462 

9.79464 
.79466 
.79469 
.79471 

.63308 
.63311 
.63315 
.62318 

9.79601 
.79604 
.79606 
.79609 

.62519 
.62522 
.63526 
.63530 

9.79748 
.79750 
.79752 
.79755 

.62730 
.63734 
.63737 
.63741 

60 
59 
58 
57 
66 
55 
64 
63 
62 
61 
60 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

32 
31 
SO 
29 
28 
27 
26 
25 

+    r 

5 
6 

7 

9.79168 
.79170 
.79173 
.79175 

.61898 
.61903 
.61905 
.61909 

9.79316 
.79319 
.79321 
.79324 

.63333 
.63335 
.63339 
.63333 
.63336 
.63339 
.63343 
.63346 

9.79611 
.79613 
.79616 
.79618 

.63533 
.63537 
.62540 
.63544 

9.79757 
.79760 
.79762 
.79765 

.63744 
.62748 
.62751 
.62755 
.63758 
.62762 
.63765 
.62769 

+   2' 

9 

10 

11 

9.79178 
.79180 
.79183 
.79185 

.61913 
.61916 
.61930 
.61933 

9.79326 
.79329 
.79331 
.79334 

.63134 
.63138 
.63131 
.63135 

9.79474 
.79476 
.79479 
.79481 

9.79621 
.79623 
.79626 
.79628 

.63547 
.63551 
.63554 
.63558 

9.79767 
.79770 
.79772 
.79774 

+  3' 

13 

u 

15 

9.79188 
.79190 
.79193 
.79195 

.61927 
.61930 
.61931 
.61937 

9.79336 
.79339 
.79341 
.79343 

.63138 
.63143 
.63145 
.63149 

9.79484 
.79486 
.79489 
.79491 

.63350 
.63353 
.63357 
.63361 

9.79631 
.79633 
.79635 
.79638 

.63561 
.63565 
.62568 
.63573 

9.79777 
.79779 
.79782 
.79784 

.63773 
.63776 
.62779 
.62783 

+   4' 
17 
18 
19 

9.79198 
.79200 
.79203 
.79205 

.61941 
.61944 
.61948 
.61951 

9.79346 
.79348 
.79351 
.79353 

.62153 
.62156 
.62160 
.62163 

9.79493 
.79496 
.79498 
.79501 

.63364 
.63368 
.63371 
.63375 

9.79640 
.79643 
.79645 
.79648 

9.79650 
.79653 
.79655 
.79657 

.63575 
.63579 
.63582 
.62586 
.62589 
.62593 
.62596 
.62600 

9.79787 
.79789 
.79791 
.79794 

.63786 
.63790 
.63793 
.63797 

+   5' 

21 

22 
23 

9.79208 
.79210 
.79213 
.79215 

.61955 
.61958 
.61963 
.61966 

9.79356 
.79358 
.79361 
.79363 

.62167 
.62170 
.62174 
.62177 

9.79503 
.79506 
.79508 
.79511 

.62378 
.62382 
.62385 
.62389 

9.79796 
.79799 
.79801 
.79804 

.63800 
.63804 
.62807 
.63811 

+  6' 

25 
26 

27 

9.79217 
.79220 
.79222 
.79225 

.61969 
.61973 
.61976 
.61980 

9.79366 
.79368 
.79371 
.79373 

.62181 
.62184 
.62188 
.62191 

9.79513 
.79516 
.79518 
.79520 

.62393 
.63396 
.63399 
.63403 

9.79660 
.79662 
.79665 
.79667 

.62603 
.63607 
.63611 
.63614 
.63618 
.63631 
.63635 
.63638 

9.79806 
.79808 
.79811 
.79813 

9.79816 
.79818 
.79821 
.79823 

.62814 
.63818 
.62822 
.63825 
.62829 
.63833 
.62836 
.62839 

+    r 

29 
30 
31 

9.79227 
.79230 
.79232 
.79235 

.61983 
.61987 
.61990 
.61994 

9.79376 
.79378 
.79380 
.79383 

.62195 
.62198 
.62303 
.63205 

9.79523 

.79525 
.79528 
.79530 

.63406 
.63410 
.63413 
.63417 

9.79670 
.79672 
.79674 
.79677 

+     8' 
33 
34 
35 

9.79237 
.79240 
.79242 
.79245 

.61997 
.62001 
.63004 
.63008 

9.79385 
.79388 
.79390 
.79393 

.62209 
.62213 
.62216 
.62220 

9.79533 
.79535 
.79538 
.79540 

.63430 
.63434 
.62427 
.62431 

9.79679 
.79682 
.79684 
.79687 

.63633 
.63635 
.63639 
.63643 

9.79825 
.79828 
.79830 
.79833 

.62843 
.63846 
.63850 
.62853 

+  9" 

37 
38 
39 

9.79247 
.79250 
.79252 
.79255 

.63011 
.63015 
.63018 
.63032 

9.79395 
.79398 
.79400 
.79403 

.62223 
.62227 
.62230 
.62234 

9.79542 
.79545 
.79547 
.79550 

.62434 
.62438 
.62442 
.62445 

9.79689 
.79692 
,79694 
.79696 

.63646 
.62649 
.63653 
.63656 

9.79835 
.79838 
.79840 
.79842 

.62857 
.63860 
.63864 
.63867 

24 
23 
22 
21 

+    W 

41 
42 
43 

9.79257 
.79260 
.79262 
.79264 

.62026 
.62029 
.62033 
.62036 

9.79405 
.79407 
.79410 
.79412 

.62237 
.62241 
.62244 
.62348 

9.79552 
.79555 
.79557 
.79560 

.62449 
.63453 
.63456 
.63459 

9.79699 
.79701 
.79704 
.79706 

.63680 
.63663 
.63687 
.63670 

9.79845 
.79847 
.79850 
.79852 

.63871 
.63874 
.63878 
.63881 

.63885 
.63888 
.63893 
.63895 

20 
19 
18 
17 
16 
15 
14 

+  ir 

45 
46 

47 

9.79267 
.79269 
.79272 
.79274 

.62040 
.62043 
.62047 
.63050 

9.79415 
.79417 
.79420 
.79422 

.63251 
.63355 
.63358 
.63363 

9.79562 
.79565 
.79567 
.79569 

.63463 
.63466 
.63470 
.63473 
.63477 
.63480 
.63484 
.62487 

9.79709 
.79711 
.79714 
.79716 

.62874 
.63677 
.63681 
.63684 

9.79855 
.79857 
.79859 
.79862 

+  n' 

49 
50 
51 

9.79277 
.79279 
.79282 
.79284 

.62054 
.62057 
.62061 
.62064 

9.79425 
.79427 
.79430 
.79432 

.63365 
.63369 
.62272 
.62276 

9.79572 
.79574 
.79577 
.79579 

9.79718 
.79721 
.79723 
.79726 

.62688 
.62691 
.62695 
.62698 

9.79864 
.79867 
.79869 
.79872 

.63899 
.63902 
.62906 
.62909 
.63913 
.63916 
.63930 
.63933 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.79287 
.79289 
.79292 
.79294 

.62068 
.63071 
.63075 
.63078 

9.79434 
.79437 
.79439 
.79442 

.62379 
.63383 
.63387 
.63290 

9.79582 
.79584 
.79587 
.79589 

9.79591 
.79594 
.79596 
.79599 

.63491 
.63494 
.63498 
.63501 

9.79728 
.79731 
.79733 
.79735 

.62703 
.62706 
.62709 
.62713 

9.79874 
.79876 
.79879 
.79881 

+  14' 

57 
58 
59 

9.79297 
.79299 
.79301 
.79304 

.63083 
.63086 
.63089 
.63093 

9.79444 
.79447 
.79449 
.79452 

.63394 
.63397 
.63301 
.63304 

.63505 
.63508 
.63512 
.63515 

9.79738 
.79740 
.79743 
.79745 

.62716 
.62720 
.62723 
.62727 

9.79884 
.79886 
.79888 
.79891 

.63937 
.63930 
.63934 
.63937 

4 
S 
2 
1 

+  15' 

9.79306 

.63096 

9.79454 

.63308 

9.79601 

.63519 

9.79748 

.62730 

9.79893 

.63941 

0 

171^  4m 

17^  3m 

17^  2m 

i7him 

17h0m 

TABLE  45.                  [Page  895 

Haversines. 

s 

7A  Om  105°  0' 

7ft  im  105°  15' 

7h  2m  105°  3r 

7ft  3m  105°  45' 

7ft  4^  106°  0' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0- 
1 

2 
3 

9.79893 
.79896 
,79898 
.79901 

.62941 
.63944 
.63948 
.62951 

9.80038 
.80041 
.80043 
.80046 

9.80048 
.80050 
.80053 
.80055 

.63153 
.63155 
.63159 
.63162 
.63166 
.63169 
.63173 
.63176 

9.80183 
.80185 
.80188 
.80190 

.63363 
.63365 
.63369 
.63373 

9.80.327 
.80329 
.80331 
.80334 

.63573 
.63576 
.63579 
.63583 
.63586 
.63590 
.63593 
.63597 

9.80470 
.80472 
.80474 
.80477 

.63782 
.63785 
.63789 
.63792 

60 
59 
58 
57 

+    r 

5 
6 

7 

9.79903 
.79905 
.79908 
.79910 

.63955 
.63958 
.63963 
.63965 

9.80192 
.80195 
.80197 
.80200 

.63376 
.63379 
.63383 
.63386 

9.80336 
.80339 
.80341 
.80343 

9.80479 
.80482 
.80484 
.80486 

.63796 
.63799 
.63803 
.63806 

56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

32 
31 
30 

29 
28 

27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 

+  2' 

9 

10 

11 

9.79913 
.79915 
.79918 
.79920 

.63969 
.63973 
.63976 
.63980 

9.80058 
.80060 
.80063 
.80065 

.63180 
.63183 
.63187 
.63190 

9.80202 
.80204 
.80207 
.80209 

.63390 
.63393 
.63397 
.63400 

9.80346 
.80348 
.80351 
.80353 

9.80355" 
.80358 
.80360 
.80362 

9.80365 
.80367 
.80370 
.80372 

.63600 
.63604 
.63607 
.63611 
.63614 
.63618 
.63631 
.63635 
.63638 
.63633 
.63035 
.63639 
.63642 
.63646 
.63649 
.63653 
.63656 
.63660 
.63663 
.63666 
.63670 
.63673 
.63677 
.63680 
.63684 
.63687 
.63691 
.63694 

9.80489 
.80491 
.80494 
.80496 

9.80498 
.80501 
.80503 
.80505 

9.80508 
.80510 
.80513 
.80515 

9.80517 
.80520 
.80522 
.80524 

9.80527 
.80529 
.80532 
.80534 

9.80536 
.80539 
.80541 
.80543 

9.80546 
.80548 
.80551 
.80553 

.63810 
.63813 
.63817 
.63820 
.63834 
.63837 
.63831 
.63834 
.63838 
.63841 
.63845 
.63848 
.63853 
.63855 
.6:J859 
.63862 
.63866 
.63869 
.63873 
.63876 
.63880 
.63883 
.63887 
.63890 

+  3' 

13 
14 
15 

9.79922 
.79925 
.79927 
.79930 

.63983 
.62987 
.63990 
.63994 

9.80067 
.80070 
.80072 
.80075 

9.80077 
.80079 
.80082 
.80084 

.63194 
.63197 
.63201 
.63204 
.63208 
.63211 
.63215 
.63218 
.63233 
.63225 
.63239 
.63333 
.63336 
.63339 
.63343 
.63346 
.63350 
.63353 
.63357 
.63360 

9.80212 
.80214 
.80216 
.80219 

.63404 
.63407 
.63411 
.63414 

+   *' 
17 
18 
19 

9.79932 
.79935 
.79937 
.79939 

.63997 
.63001 
.63004 
.63008 

9.80221 
.80224 
.80226 
.80228 

.63418 
.63431 
.63435 
.63438 

+     5' 

21 

22 
23 

9.79942 
.79944 
.79947 
.79949 

.63011 
.63015 
.63018 
.63033 

9.80087 
.80089 
.80091 
.80094 

9.80096 
.80099 
.80101 
.80103 

9.80106 
.80108 
.80111 
.80113 

9.80116 
.80118 
.80120 
.80123 

9.80231 
.80233 
.80236 
.80238 

9.80240 
.80243 
.80245 
.80248 

9.80250 
.80252 
.80255 
.80257 

9.80260 
.80262 
.80264 
.80267 

9.80269 
.80272 
.80274 
.80276 

9.80279 
.80281 
.80284 
.80286 

.63433 
.63435 
.63439 
.63443 
.63446 
.63450 
.63453 
.63457 
.63460 
.63464 
.63467 
.63471 

9.80374 
.80377 
.80379 
.80382 

9.80384 
.80386 
.80389 
.80391 

9.80393 
.80396 
.80398 
.80401 

9.80403 
.80405 
.80408 
.80410 

25 
26 
27 

9.79951 
.79954 
.79956 
.79959 

.63035 
.63039 
.63033 
.63036 

+    r 

29 
30 
31 

9.79961 
.79964 
.79966 
.79968 

.63039 
.63043 
.63046 
.63050 

+   8' 
33 
34 
35 

9.79971 
.79973 
.79976 
.79978 

.63053 
.63057 
.63060 
.63064 

.63364 
.63367 
.63371 
.63374 

.63474 
.63478 
.63481 
.63485 
.63488 
.63493 
.63495 
.63499 

.63894 
.63897 
.63901 
.63904 
.63908 
.63911 
.63915 
.63918 
.63922 
.63925 
.63929 
.63932 

+  9' 

37 
38 
39 

9.79980 
.79983 
.79985 
.79988 

.63067 
.63071 
.63074 
.63078 
.63081 
.63085 
.63088 
.63093 

9.80125 
.80128 
.80130 
.80132 

9.80135" 
.80137 
.80140 
.80142 

.63378 
.63381 
.63385 
.63388 

9.80413 
.80415 
.80417 
.80420 

9780422 
.80424 
.80427 
.80429 

9.80432 
.80434 
.80436 
.80439 

.63698 
.63701 
.63705 
.63708 

9.80555 
.80558 
.80560 
.80562 

+  10' 

41 
42 
43 

9.79990 
.79993 
.79995 
.79997 

.63393 
.63295 
.63299 
.63302 

.63503 
.63506 
.63509 
.63513 

.63713 
.63715 
.63719 
.63722 
.63726 
.63729 
.63733 
.63736 

9.80565 
.80567 
.80570 
.80572 

+  11' 

45 
46 
47 

9.80000 
.80002 
.80005 
.80007 

.63095 
.63099 
.63103 
.63106 

9.80144 
.80147 
.80149 
.80152 

.63306 
.63309 
.63313 
.63316 

9.80288 
.80291 
.80293 
.80296 

.63516 
.63530 
.63533 
.63537 

9.80574 
.80577 
.80579 
.80581 

9.80584 
.80586 
.80589 
.80591 

.63936 
.63939 
.63943 
.6394fi 
.63950 
.63953 
.63957 
.63960 

16 
15 
14 
13 
12 
11 
10 
9 

+  13' 

49 
50 
51 

9.80009 
.80012 
.80014 
.80017 

.63109 
.63113 
.63116 
.63120 

9.80154 
.80156 
.80159 
.80161 

.63320 
.63323 
.63327 
.63330 

9.80298 
.80300 
.80303 
.80305 

.63530 
.63534 
.63537 
.63541 

9.80441 
.80444 
.80446 
.80448 

.63740 
.63743 
.63747 
.63750 

+    13^ 

53 
54 
55 

9.80019 
.80022 
.80024 
.80026 

.63133 
.63127 
.63131 
.63134 

9.80164 
.80166 
.80168 
.80171 

.63334 
.63337 
.63341 
.63344 

9.80307 
.80310 
.80312 
.80315 

.63544 
.63548 
.63551 
.63555 

9.80451 
.80453 
.80455 
.80458 

.63754 
.63757 
.63761 
.63764 
.63768 
.63771 
.63775 
.63778 

9.80593 
.80596 
.80598 
.80600 

.63964 
.63967 
.63971 
.63974 

8 
7 
6 
5 

+    U' 

57 
58 
59 

9.80029 
.80031 
.80034 
.80036 

.63138 
.63143 
.63145 
.63148 

9.80173 
.80176 
.80178 
.80180 

.63348 
.63351 
.63355 
.63358 

9.80317 
.80319 
.80322 
.80324 

.63558 
.63563 
.63565 
.63569 

9.80460 
.80463 
.80465 
.80467 

9.80603 
.80605 
.80607 
.80610 

.63977 
.63981 
.63984 
.63988 

4 
3 

2 
1 
0 

+    W 

9.80038 

.63153 

9.80183 

.63363 

9.80327 

.63573 

9.80470 

.63782 

9.80612 

.63991 

16h  59m 

16Ji  58m 

16^  57m 

left  56m 

16h  55m 

1  Page  896] 

TABLE  45. 
Haversine.s. 

7h  5m  106°  15' 

7h  em  106°  30' 

7h  7m  106°  45' 

7h  gm  107°  0' 

7h  gm  107°  15' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 

2 
S 

9.80612 
.80615 
.80617 
.80619 

.63991 
.63995 
.63998 
.64003 

9.80754 
.80756 
.80759 
.80761 

.64201 
.64204 
.64308 
.64211 

9.80895 
.80898 
.80900 
.80902 

.64410 
.64413 
.64417 
.64430 

9.81036 
.81038 
.81040 
.81043 

.64619 
.64622 
.64626 
.64629 

9.81176 
.81178 
.81180 
.81183 

.64827 
.64831 
.64834 
.64838 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.80622 
.80624 
.80626 
.80629 

.64005 
.64009 
.64012 
.64016 

9.80763 
.80766 
.80768 
.80771 

.64215 
.64218 
.64222 
.64225 

9.80905 
.80907 
.80909 
.80912 

.64434 
.64437 
.64431 
.64434 

9.81045 
.81047 
.81050 
.81052 

.64632 
.64636 
.64639 
.64643 

9.81185 
.81187 
.81190 
.81192 

.64841 
.64844 
.64848 
.64851 

56 
55 
54 
53 

+     V 

9 

10 

11 

9.80631 
.80634 
.80636 
.80638 

.64019 
.64023 
.64026 
.64030 

9.80773 
.80775 
.80778 
.80780 

.64229 
.64232 
.64236 
.64239 

9.80914 
.80916 
.80919 
.80921 

.64438 
.64441 
.64445 
.64448 

9.81054 
.81057 
.81059 
.81081 

.64646 
.64650 
.64653 
.64657 

9.81194 
.81197 
.81199 
.81201 

.64855 
.64858 
.64862 
.64865 

52 
51 
50 
49 

+      y 

13 
14 
15 

9.80641 
.80643 
.80645 
.80648 

.64033 
.64037 
.64040 
.64044 

9.80782 
.80785 
.80787 
.80789 

.64343 
.64246 
.64250 
.64253 

9.80923 
.80926 
.80928 
.80930 

.64453 
.64455 
.64459 
.64463 

9.81064 
.81066 
.81068 
.81071 

.64660 
.64664 
.64667 
.64671 

9.81204 
.81206 
.81208 
.81211 

.64869 
.64873 
.64876 
.64879 

48 
47 
46 
45 

+  4^ 
17 
18 
19 

9.80650 
.80652 
.80655 
.80657 

.64047 
.64051 
.64054 
.64058 

9.80792 
.80794 
.807% 
.80799 

.64257 
.64260 
.64384 
.64367 

9.80933 
.80935 
.80937 
.80940 

.64466 
.64469 
.64472 
.64476 

.81073 
.81075 
.81078 
.81080 

.64674 
.64678 
.64681 
.64685 

9.81213 
.81215 

.81217 
.81220 

.64883 
.64886 
.64890 
.64893 

44 
43 
42 
41 

+     5' 
21 
22 
23 

9.80660 
.80662 
.80664 
.80667 

.64061 
.64065 
.64068 
.64072 

9.80801 
.80804 
.80806 
.80808 

.64370 
.64374 
.64377 
.64381 

9.80942 
.80944 
.80947 
.80949 

.64479 
.64483 
.64486 
.64490 

9.81082 
.81085 
.81087 
.81089 

.64688 
.64692 
.64695 
.64699 

9.81222 
.81224 
.81227 
.81229 

.64897 
.64900 
.64903 
.64907 

40 
39 
38 
37 

+      <r 

25 
26 
27 

9.80669 
.80671 
.80674 
.80676 

.64075 
.64079 
.64082 
.64086 

9.80811 
.80813 
.80815 
.80818 

.64384 
.64388 
.64391 
.64395 

9.80952 
.80954 
.80956 
.80959 

.64493 
.64497 
.64500 
.64504 

9.81092 
.81094 
.81096 
.81099 

.64702 
.64705 
.64709 
.64712 

9.81231 
.81234 
.81236 
.81238 

.64910 
.64914 
.64917 
.64931 

36 

35 
34 
33 

+    r 

29 
30 
31 

9.80678 
.80681 
.80683 
.80686 

.64089 
.64093 
.64096 
.64100 

9.80820 
.80822 
.80825 
.80827 

.64398 
.64303 
.64305 
.64309 

9.80961 
.80963 
.80966 
.80968 

.64507 
.64511 
.64514 
.64518 

9.81101 
.81103 
.81106 
.81108 

.64716 
.64719 
.64723 
.64726 

9.81241 
.81243 
.81245 
.81248 

.64924 
.64938 
.64931 
.64935 

32 
31 
30 
29 

+   8^ 
33 
34 
35 

9.80688 
.80690 
.80693 
.80695 

.64103 
.64107 
.64110 
.64114 

9.80829 
.80832 
.80834 
.80836 

.64313 
.64316 
.64319 
.64333 

9.80970 
.80973 
.80975 
.80977 

.64521 
.64525 
.64528 
.64532 

9.81110 
.81113 
.81115 
.81117 

.64730 
.64733 
.64737 
.64740 

9.81250 
.81252 
.81255 
.81257 

.64938 
.64943 
.64945 
.64949 

28 
27 
26 
25 

24 
23 
22 
21 

+      r 

37 
38 
39 

9.80697 
.80700 
.80702 
.80704 

.64117 
.64121 
.64124 
.64128 

9.80839 
.80841 
.80844 
.80846 

.64336 
.64330 
.64333 
.64337 

9.80980 
.80982 
.80984 
.80987 

.64535 
.64539 
.64542 
.64546 

9.81120 
.81122 
.81124 
.81127 

.64744 
.64747 
.64751 
.64754 

9.81259 
.81262 
.81264 
.81266 

.64953 
.64956 
.64959 
.64963 

+  W 

41 
42 
43 

9.80707 
.80709 
.80712 
.80714 

.64131 
.64135 
.64138 
.64142 

9.80848 
.80851 
.80853 
.80855 

.64340 
.64344 
.64347 
.64351 

9.80989 
.80991 
.80994 
.80996 

.64549 
.64552 
.64556 
.64559 

9.81129 
.81131 
.81134 
.81136 

.64758 
.64761 
.64765 
.64768 

9.81269 
.81271 
.81273 
.81276 

.64966 
.64969 
.64973 
.64976 

20 
19 
18 
17 

+    11' 

45 
46 
47 

9.80716 
.80719 
.80721 
.80723 

.64145 
.64148 
.64152 
.64155 

9.80858 
.80860 
.80862 
.80865 

.64354 
.64358 
.64361 
.64365 

9.80998 
.81001 
.81003 
.81005 

.64563 
.64566 
.64570 
.64573 

9.81138 
.81141 
.81143 
.81145 

.64772 
.64775 
.64778 
.64782 

9.81278 
.81280 
.81282 
.81285 

.64980 
.64983 
.64987 
.64990 

16 
15 

14 
13 

+  ir 

49 
50 
51 

9.80726 
.80728 
.80730 
.80733 

.64159 
.64162 
.64166 
.64169 

9.80867 
.80869 
.80872 
.80874 

.64368 
.64373 
.64375 
.64378 

9.81008 
.81010 
.81012 
.81015 

.04577 
.64580 
.64584 
.64587 

9.81148 
.81150 
.81152 
.81155 

.64785 
.64789 
.64792 
.64796 

9.81287 
.81289 
.81292 
.81294 

.64994 
.64997 
.65001 
.65004 

12 

11 

10 

9 

+    W 

53 

54 
55 

9.80735 
.80738 
.80740 
.80742 

.64173 
.64176 
.64180 
.64183 

9.80876 
.80879 
.80881 
.80883 

.64383 
.64385 
.64389 
.64393 

9.81017 
.81019 
.81022 
.81024 

.64591 
.64594 
.64598 
.64601 

9.81157 
.81159 
.81162 
.81164 

.64799 
.64803 
.64806 
.64810 

9.81296 
.81299 
.81301 
.81303 

.65008 
.65011 
.65014 
.65018 

8 
7 
6 
5 

+    W 

57 
58 
59 

9.80745 
.80747 
.80749 
.80752 

.64187 
.64190 
.64194 
.64197 

9.80886 
.80888 
.80891 
.80893 

.64396 
.64399 
.64403 
.64406 

9.81026 
.81029 
.81031 
.81033 

.64605 
.64608 
.64612 
.64615 

9.81166 
.81169 
.81171 
.81173 

.64813 
.46817 
.64820 
.64824 

9.81306 
.81308 
.81310 
.81313 

.65031 
.65035 
.65038 
.65033 
.65035 

4 
3 
2 
1 
0 

+  W 

9.80754 

.64301 

9.80895 

.64410 

9.81036 

.64619 

9.81176 

.64827 

9.81315 

16Ji 

54m 

16h  53m 

16^ 

52m 

16^ 

Sim 

i6»  50m 

TABLE  45.                  [Page  897 

Haversines. 

3 

7ft  lom  107°  SO' 

7ft  nm  107°  45' 

7ft  ipn  108°  r 

7h  iSm  108°  15' 

7ft  14m  108°  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 

2 
3 

9.81315 
.81317 
.81320 
.81322 

.65035 
.65039 
.65042 
.65046 

9 

81454 
81456 
81458 
81460 

.65243 
.65247 
.65250 
.65254 

9.81592 
.81594 
.81596 
.81598 

.65451 
.65454 
.65458 
.65461 

9.81729 
.81731 
.81733 
.81736 

.65658 
.65662 
.65665 
.65668 

9.81866 
.81868 
.81870 
.81872 

.65865 
.65869 
.65872 
.65876 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 

+    r 

5 
6 

7 

+   2' 

9 

10 

11 

9.81324 
.81326 
.81329 
.81331 

.65049 
.65053 
.65056 
.65060 

9 

81463 
81465 
81467 
81470 

.65257 
.65261 
.65264 
.65267 

9.81601 
.81603 
.81605 
.81608 

.65465 
.65468 
.65472 
.65475 

9.81738 
.81740 
.81743 
.81745 

.65672 
.65675 
.65679 
.65682 

9.81875 
.81877 
.81879 
.81882 

.65879 

.65882 
.65886 
.65889 

9.81333 
.81336 
.81338 
.81340 

.65063 
.65066 
.65070 
.65073 

9 

81472 
81474 
81477 
81479 

.65271 
.65274 
.65278 
.65281 

9.81610 
.81612 
.81614 
.81617 

.65479 
.65482 
.65485 
.65489 

9.81747 
.81749 
.81752 
.81754 

.65686 
.65689 
.65693 
.65696 

9.81884 
.81886 
.81888 
.81891 

.65893 
.65896 
.65900 
.65903 
.65907 
.65910 
.65914 
.65917 

+     3' 

13 
14 
15 

9.81343 
.81345 
.81347 
.81350 

.65077 
.65080 
.65084 
.65087 

9 

81481 
81483 
81486 
81488 

.65285 
.65288 
.65292 
.65295 

9.81619 
.81621 
.81624 
.81626 

.65492 
.65496 
.65499 
.65503- 

9.81756 
.81759 
.81761 
.81763 

.65700 
.65703 
.65707 
.65710 

9.81893 
.81895 
.81897 
.81900 

+  i' 
17 
18 
19 

9.81352 
.81354 
.81357 
.81359 

.65091 
.65094 
.65098 
.65101 

9 

81490 
81493 
81495 
81497 

.65299 
.65302 
.65306 
.65309 

9.81628 
.81631 
.81633 
.81635 

.65506 
.65510 
.65513 
.65516 

9.81765 
.81768 
.81770 
.81772 

.65713 
.65717 
.65720 
.65724 

9.81902 
.81904 
.81907 
.81909 

.65920 
.65924 
.65927 
.65931 

+     5' 
21 
22 
23 

9.81361 
.81364 
.81366 
.81368 

.65105 
.65108 
.65112 
.65115 

9 

81500 
81502 
81505 
81507 

.65312 
.65316 
.65319 
.65323 
.65326 
.65330 
.65333 
.65337 

9.81637 
.81640 
.81642 
.81644 

.65520 
.65523 
.65527 
.65530 

9.81775 
.81777 
.81779 
.81781 

.65727 
.65731 
.65734 
.65738 

9.81911 
.81913 
.81916 
.81918 

.65934 
.65938 
.65941 
.65944 

+      6' 

25 
26 

27 

9.81370 
.81373 
.81375 
.81377 

.65118 
.65122 
.65125 
.65129 

9 

81509 
81511 
81513 
81516 

9.81647 
.81649 
.81651 
.81653 

.65534 
.65537 
.65541 
.65544 

9.81784 
.81786 
.81788 
.81791 

.65741 
.65744 
.65748 
.65751 

9.81920 
.81922 
.81925 
.81927 

.65948 
.65951 
.05955 
.65958 

36 
35 
34 
S3 

+    r 

29 
30 
31 

9.81380 
.81382 
.81384 
.81387 

.65132 
.65136 
.65139 
.65143 

9 

81518 
81520 
81523 
81525 

.65340 
.65344 
.65347 
.65351 

9.81656 
.81658 
.81660 
.81663 

.65548 
.65551 
.65555 
.65558 

9.81793 
.81795 
.81797 
.81800 

.65755 
.65758 
.65762 
.65765 

9.81929 
.81931 
.81934 
.81936 

.65962 
.65985 
.65969 
.65972 

32 
31 
30 
29 

+   8' 
33 
34 
35 

9.81389 
.81391 
.81394 
.81396 

.65146 
.65150 
.65153 
.65157 

9 

81527 
81530 
81532 
81534 

.65354 
.65357 
.65361 
.65364 

9.81665 
.81667 
.81669 
.81672 

.65561 
.65565 
.65568 
.65572 

9.81802 
.81804 
.81806 
.81809 

.65769 
.65772 
.65776 
.65779 

9.81938 
.81941 
.81943 
.81945 

.65976 
.65979 
.65982 
.65986 

28 
27 
26 
25 

24 
23 

22 
21 

+  9^ 

37 
38 
39 

9.81398 
.81400 
.81403 
.81405 

.65160 
.65164 
.65167 
.65171 

9 

81536 
81539 
81541 
81543 

.65368 
.65372 
.65375 
.65378 

9.81674 
.81676 
.81679 
.81681 

.65575 
.65579 
.65582 
.65586 

9.81811 
.81813 
.81816 
.81818 

.65782 
.65786 
.65789 
.65793 

9.81947 
.81950 
.81952 
.81954 

.65989 
.65993 
.65996 
.66000 

+    W 

41 
42 
43 

9.81407 
.81410 
.81412 
.81414 

.65174 
.65177 
.65181 
.65184 

9 

81546 
81548 
81550 
81552 

.65382 
.65385 
.65389 
.65392 

9.81683 
.81685 
.81688 
.81690 

.65589 
.65593 
.65596 
.65599 

9.81820 
.81822 
.81825 
.81827 

.65796 
.65800 
.65803 
.65807 

9.81956 
.81959 
.81961 
.81963 

.66003 
.66006 
.66010 
.66013 

20 
19 
18 
17 

+    ir 

45 
46 
47 

9.81417 
.81419 
.81421 
.81424 

.65188 
.65191 
.65195 
.65198 

9 

81555 
81557 
81559 
81562 

.65396 
.65399 
.65402 
.65406 

9.81692 
.81695 
.81697 
.81699 

.65603 
.65606. 
.65610 
.65613 

.81829 
.81832 
.81834 
.81836 

.65810 
.65813 
.65817 
.65820 

9.81965 
.81968 
.81970 

.81972 

.66017 
.66020 
.66024 
.66027 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 

2 

1 

+    12^ 

49 
50 
51 

9.81426 
.81428 
.81430 
.81433 

.65202 
.65205 
.65209 
.65212 

9 

81564 
81566 
81569 
81571 

.65409 
.65413 
.65416 
.65420 

9.81701 
.81704 
.81706 
.81708 

.65617 
.65620 
.65624 
.65627 

9.81838 
.81841 
.81843 
.81845 

.65824 
.65827 
.65831 
.65834 

9.81975 
.81977 
.81979 
.81981 

.66031 
.66034 
.66038 
.66041 

+    13^ 

53 
54 
55 

9.81435 
.81437 
.81440 
.81442 

.65216 
.65219 
.65222 
.65226 

9 

81573 
81575 
81578 
81580 

.65423 
.65427 
.65430 
.65434 

9.81711 
.81713 
.81715 
.81717 

.65630 
.65634 
.65637 
.65641 

9.81847 
.81850 
.81852 
.81854 

.65838 
.65841 
.65845 
.65848 

9.81984 
.81986 
.81988 
.81990 

.66044 
.66048 
.66051 
.66055 

+    W 

57 
58 
59 

9.81444 
.81447 
.81449 
.81451 

.65229 
.65233 
.65236 
.65240 

9 

81582 
81585 
81587 
81589 

.65437 
.65440 
.65444 
.65447 

9.81720 
.81722 
.81724 
.81727 

.65644 
.55648 
.65651 
.65655 

9.81857 
.81859 
.81861 
.81863 

.65851 
.65855 

.65858 
.65862 

9.81993 
.81995 
.81997 
.81999 

.66058 
.66062 
.66065 
.66068 

+  15^ 

9.81454 

.65243 

9 

81592 

.65451 

9.81729 

.65658 

9.81866 

.65865 

9.82002 

.66072 

0 

len  49m 

16h  4Sm 

ten  47W 

16^  46m 

ifift  45m 

Page  898] 

TABLE  45. 

Haversines. 

s 

7h  15m  108°  45' 

7h  16m  109°  0' 

7k  17m  109°  15' 

7h  igm  109°  30' 

7h  igm  109°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.82002 
.82004 
.82006 
.82009 

.66073 
.66075 
.66079 
.66083 

9.82137 
.82139 
.82142 
.82144 

.66378 
.66283 
.66385 
.66389 

9.82272 

.82274 
.82277 
.82279 

.66485 
.66488 
.66491 
.66495 

9.82406 
.82409 
.82411 
.82413 

.66690 
.66694 
.66697 
.66701 

9.82540 
.82542 
.82544 
.82547 

9.82549 
.82551 
.82553 
.82555 

.66896 
.66899 
.66903 
.66906 

60 
59 
58 
57 

+       r 

5 
6 

7 

9.82011 
.82013 
.82015 
.82018 

.66086 
.66089 
.66093 
.66096 

9.82146 
.82148 
.82151 
.82153 

.66393 
.66396 
.66299 
.66303 

9.82281 
.82283 
.82286 

.82288 

.66498 
.66502 
.66505 
.66508 

9.82415 
.82417 
.82420 

.82422 

.66704 
.66707 
.66711 
.66714 

.66910 
.66913 
.66916 
.66930 

56 
55 
54 
53 

+   2^ 

9 

10 

11 

9.82020 
.82022 
.82024 
.82027 

.66100 
.66103 
.66106 
.66110 

9.82155 
.82157 
.82160 
.82162 

.66306 
.66309 
.66313 
.66316 

9.82290 
.82292 
.82294 
.82297 

.66512 
.66515 
.66519 
.66522 

9.82424 
.82426 
.82429 
.82431 

.66718 
.66721 
.66735 
.66738 

9.82558 
.82560 
.82562 

.82564 

.66933 
.66937 
.66930 
.66933 
.66937 
.66940 
.66944 
.66947 

52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
S3 
32 
31 
30 
29 
28 
27 
26 
25 

+   3' 

13 
14 
15 

9.82029 
.82031 
.82033 
.82036 

.66113 
.66117 
.66130 
.66134 

9.82164 
.82166 
.82169 
.82171 

.66330 
.66333 
.66337 
.66330 

9.82299 
.82301 
.82303 
.82306 

.66526 
.66539 
.66533 
.66536 

9.82433 
.82435 
.82438 
.82440 

.66731 
.66735 
.66738 
.66743 

9.82567 
.82569 
.82571 
.82573 

+      4' 
17 
18 
19 

9.82038 
.82040 
.82042 
.82045 

.66137 
.66130 
.66134 
.66137 

9.82173 
.82175 
.82178 
.82180 

.66333 
.66337 
.66340 
.66344 

9.82308 
.82310 
.82312 
.82315 

.66539 
.66543 
.66546 
.66550 

9.82442 
.82444 
.82446 
.82449 

.66745 
.66749 
.66752 
.66755 
.66759 
.66763 
.66766 
.66769 

9.82575 
.82578 
.82580 
.82582 

9.82584 
.82587 
.82589 
.82591 

9.82593 
.82595 
.82598 
.82600 

9782602" 
.82604 
.82606 
.82609 

.66951 
.66954 
.66957 
.66961 

+      5' 
21 

22 
23 

9.82047 
.82049 
.82051 
.82054 

.66141 
.66144 
.66148 
.66151 

9.82182 
.82184 
.82187 
.82189 

.66347 
.66351 
.66354 
.66357 

9.82317 
.82319 
.82321 
.82324 

.66553 
.66557 
.66560 
.66563 

9.82451 
.82453 
.82455 
.82458 

.66964 
.66968 
.66971 
.66975 
.G6978 
.66981 
.66985 
.66988 
.66993 
.66995 
.66998 
.67002 
.67005 
.67009 
.67013 
.67016 

+   6' 

25 
26 

27 

9.82056 
.82058 
.82061 
.82063 

.66155 
.66158 
.66161 
.66165 

9.82191 
.82193 
.82196 
.82198 

.66361 
.66364 
.66368 
.66371 

9.82326 
.82328 
.82330 
.82333 

.66567 
.66570 
.66574 
.66577 

9.82460 
.82462 
.82464 
.82467 

.66773 
.66776 
.66779 
.66783 

+    r 

29 
30 
31 

9.82065 
.82067 
.82070 
.82072 

.66168 
.66173 
.66175 
.66179 

9.82200 
.82202 
.82205 
.82207 

.66375 
.66378 
.66383 
.66385 

9.82335 
.82337 
.82339 
.82341 

.66581 
.66584 
.66587 
.66591 

9.82469 
.82471 
.82473 
.82475 

.66786 
.66790 
.66793 
.66797 

+   8' 
33 
34 

35 

9.82074 
.82076 
.82079 
.82081 

.66183 
.66186 
.66189 
.66193 

9.82209 
.82211 
.82214 
.82216 

.66388 
.66392 
.66395 
.66399 
.66402 
.66406 
.66409 
.66412 
.66416 
.66419 
.66423 
.66426 

9.82344 
.82346 
.82348 
.82350 

.66594 
.66598 
.66601 
.66605 

9.82478 
.82480 
.82482 
.82484 

.66800 
.66803 
.66807 
.66810 

9.82611 
.82613 
.82615 
.82618 

9.82620 
.82622 
.82624 
.82627 

+      9" 

37 
38 
39 

9.82083 
.82085 
.82088 
.82090 

.66196 
.66199 
.66303 
.66306 

9.82218 
.82220 
.82223 
.82225 

9.82227 
.82229 
.82232 
.82234 

9.82353 
.82355 
.82357 
.82359 

.66608 
.66611 
.66615 
.66618 

9.82487 
.82489 
.82491 
.82493 

.66814 
.66817 
.66831 
.66834 
.66837 
.66831 
.66834 
.66838 

.67019 
.67032 
.67026 
.67029 

24 
23 
22 
21 

+    W 

41 
42 
43 

9.82092 
.82094 
.82097 
.82099 

.66310 
.66313 
.66317 
.66330 

9.82362 
.82364 
.82366 
.82368 

.66622 
.66625 
.66629 
.66632 

9.82495 
.82498 
.82500 
.82502 

9.82629 
.82631 
.82633 
.82635 

.67033 
.67036 
.67039 
.67043 

20 
19 
18 
17 
16 
15 
14 
13 

+  ir 

45 
46 
47 

9.82101 
.82103 
.82106 
.82108 

.66333 
.66337 
.66330 
.66334 

9.82236 
.82238 
.82241 
.82243 

.66430 
.66433 
.66436 
.66440 

9.82371 
.82373 
.82375 
.82377 

.66635 
.66639 
.66642 
.66646 

9.82504 
.82507 
.82509 
.82511 

.66841 
.66844 
.66848 
.66851 

9.82638 
.82640 
.82642. 
.82644 

.67046 
.67050 
.67053 
.67057 

+    12' 

49 
50 
51 

9.82110 
.82112 
.82115 
.82117 

.66337 
.66341 
.66344 
.66347 

9.82245 
.82247 
.82250 
.82252 

.66443 
.66447 
.66450 
.66454 

9.82380 
.82382 
.82384 
.82386 

.66649 
.66653 
.66656 
.66659 

9.82513 
.82515 
.82518 
.82520 

.66855 

.66858 
.66862 
.66865 

9.82646 
.82649 
.82651 
.82653 

.67060 
.67063 
.67067 
.67070 

12 

11 

10 

9 

+  13' 

53 
54 
55 

9.82119 
.82121 
.82124 
.82126 

.66351 
.66354 
.66258 
.66361 

9.82254 
.82256 
.82259 
.82261 

.66457 
.66460 
.66464 
.66467 

9.82388 
.82391 
.82393 
.82395 

.66663 
.66666 
.66670 
.66673 

9.82522 
.82524 
.82527 
.82529 

.66868 
.66872 
.66875 
.66879 

9.82655 
.82657 
.82660 
.82662 

.67074 
.67077 
.67081 
.67084 

8 
7 
6 
5 

57 
58 
59 

9.82128 
.82130 
.82133 
.82135 

.66265 
.66268 
.66373 
.66375 

9.82263 
.82265 
.82268 
.82270 

.66471 
.66474 
.66478 
.66481 

9.82397 
.82400 
.82402 
.82404 

.66677 
.66680 
.66683 
.66687 

9.82531 
.82533 
.82535 
.82538 

.66882 
.66886 
.66889 
.66892 

9.82664 
.82666 
.82668 
.82671 

.67087 
.67091 
.67094 
.67098 

4 
3 
2 
1 
0 

+  15' 

9.82137 

.66378 

9.82272 

.66485 

9.82406 

.66690 

9.82540 

.66896 

9.82673 

.67101 

16^ 

44m 

16h  43m 

16h 

42m 

16^ 

41m 

le'i 

40m 

TABLE  45.                  [Page  899 
Haversines. 

s 

7A  20m  110°  0' 

7h  21^  110°  15' 

7h22m  110°  30' 

7ft  23m  110°  45' 

7A^4mlU°0'  1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.82673 
.82675 
.82677 
.82680 

.67101 
.67104 
.67108 
.67111 

9.82805 
.82807 
.82810 
.82812 

9.82814 
.82816 
.82818 
.82821 

.67306 
.67309 
.67313 
.67316 

9.82937. 
.82939 
.82941 
.82944 

.67510 
.67514 
.67517 
.67531 
.67534 
.67537 
.67531 
.67534 

9.83068 
.83070 
.83073 
.83075 

9.83077 
.83079 
.83081 
.83083 

.67715 
.67718 
.67731 
.67735 

9.83199 
.83201 
.83203 
.83205 

.67918 
.67933 
.67925 
.67929 

60 
59 

58 
57 

+    r 

5 
6 

7 

9.82682 
.82684 
.82686 
.82688 

.67115 
.67118 
.67123 
.67135 

.67330 
.67333 
.67336 
.67330 

9.82946 
.82948 
.82950 
.82952 

.67738 
.67733 
.67735 
.67738 

9.83207 
.83210 
.83212 
.83214 

.67933 
.67935 
.67939 
.67943 

56 
55 
54 
53 
52 
51 
50 
49 

+     V 

9 

10 

11 

9.82691 
.82693 
.82695 
.82697 

.67128 
.67132 
.67135 
.67139 
.67142 
.67145 
.67149 
.67152 

9.82823 
.82825 
.82827 
.82829 

.67333 
.67337 
.67340 
.67343 

9.82955 
.82957 
.82959 
.82961 

.67538 
.67541 
.67544 
.67548 

9.83086 
.83088 
.83090 
.83092 

9.83094 
.83097 
.83099 
.83101 

.67743 
.67745 
.67749 
.67753 

9.83216 
.83218 
.83220 
.83223 

.67946 
.67949 
.67953 
.67956 

+     3' 

13 
14 
15 

9.82699 
.82702 
.82704 
.82706 

9.82832 
.82834 
.82836 
.82838 

.67347 
.67350 
.67354 
.67357 

9.82963 
.82966 
.82968 
.82970 

.67551 
.67555 
.67558 
.67561 

.67755 
.67759 
.67763 
.67766 
.67769 
.67773 
.67776 
.67779 

9.83225 
.83227 
.83229 
.83231 

9.83233 
.83236 
.83238 
.83240 

.67959 
.67963 
.67966 
.67969 
.67973 
.67976 
.67979 
.67983 

48 
47 
46 
45 

44 
43 
42 
41 

+     4' 

17 
18 
19 

9.82708 
.82710 
.82713 
.82715 

.67156 
.67159 
.67163 
.67166 

9.82840 
.82843 
.82845 
.82847 

.67360 
.67364 
.67367 
.67371 
.67374 
.67377 
.67381 
.67384 

9.82972 
.82974 
.82976 
.82979 

.67565 
.67568 
.67573 
.67575 

9.83103 
.83105 
.83107 
.83110 

+  5' 
21 

22 
23 

9.82717 
.82719 
.82722 
.82724 

.67169 
.67173 
.67176 
.67180 

9.82849 
.82851 
.82854 
.82856 

9.82981 
.82983 
.82985 
.82987 

.67578 
.67582 
.67585 
.67589 
.67593 
.67595 
.67599 
.67603 
.67606 
.67609 
.67613 
.67616 
.67619 
.67623 
.67636 
.67630 

9.83112 
.83114 
.83116 
.83118 

.67783 
.67786 
.67789 
.67793 

9.83242 
.83244 
.83246 
.83249 

9.83251 
.83253 
.83255 
.83257 

9.83259 
.83262 
.83264 
.83266 

.67986 
.67990 
.67993 
.67996 
.68000 
.68003 
.68007 
.68010 

40 
39 
38 
37 
36 
35 
34 
33 

H-   6' 

25 
26 

27 

9.82726 
.82728 
.82730 
.82733 

.67183 
.67186 
.67190 
.67193 

9.82858 
.82860 

.82862 
.82805 

.67388 
.67391 
.67395 
.67398 
.67401 
.67405 
.67408 
.67413 

9.82990 
.82992 
.82994 
.82996 

9.83120 
.83123 
.83125 
.83127 

.67796 
.67800 
.67803 
.67806 

+    r 

29 
30 
31 

9.82735 
.82737 
.82739 
.82741 

.67197 
.67200 
.67203 
.67207 

9.82867 
.82869 
.82871 
.82873 

9.82998 
.83001 
.83003 
.83005 

9.83129 
.83131 
.83134 
.83136 

.67810 
.67813 
.67817 
.67830 

.68013 
.68017 
.68030 
.68024 

32 
31 
30 
29 
28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 

+   8' 
33 
34 
35 

9.82744 
.82746 
.82748 
.82750 

.67210 
.67214 
.67217 
.67221 

9.82876 
.82878 
.82880 
.82882 

9.82884 
.82887 
.82889 
.82891 

.67415 
.67418 
.67433 
.67435 
.67439 
.67433 
.67435 
.67439 

9.83007 
.83009 
.83011 
.83014 

9.83138 
.83140 
.83142 
.83144 

.67833 
.67837 
.67830 
.67834 

9.83268 
.83270 
.83272 
.83275 

.68027 
.68030 
.68034 
.68037 

+  9^ 

37 
38 
39 

9.82752 
.82755 
.82757 
.82759 

.67224 
.67227 
.67231 
.67234 

9.83016 
.83018 
.83020 
.83022 

.67633 
.67636 
.67640 
.67643 

9.83147 
.83149 
.83151 
.83153 

.67837 
.67840 
.67844 
.67847 

9.83277 
.83279 
.83281 
.83283 

.68041 
.68044 
.68047 
.68051 

+  w 

41 
42 
43 

9.82761 
.82763 
.82766 
.82768 

.67238 
.67241 
.67244 
.67248 

9.82893 
.82895 
.82898 
.82900 

9.82902 
.82904 
.82906 
.82909 

.67442 
.67446 
.67449 
.67452 

9.83025 
.83027 
.83029 
.83031 

.67647 
.67650 
.67653 
.67657 

9.83155 
.83157 
.83160 
.83162 

9.83164 
.83166 
.83168 
.83170 

.67850 
.67854 
.67857 
.67861 

9.83285 
.83288 
.83290 
.83292 

.68054 
.68058 
.68061 
.68064 

+  ir 

45 
46 
47 

9.82770 

.82772 
.82774 
.82777 

.67251 
.67255 
.67258 
.67261 

.67456 
.67459 
.67463 
.67466 
.67469 
.67473 
.67476 
.67480 

9.83033 
.83035 
.83038 
.83040 

.67660 
.67664 
.67667 
.67670 

.67864 
.67868 
.67871 
.67874 

9.83294 
.83296 
.83298 
.83301 

9.83303" 
.83305 
.83307 
.83309 

.68068 
.68071 
.68074 
.68078 

16 
15 
14 
13 

+  13' 

49 
50 
51 

9.82779 
.82781 
.82783 
.82785 

.67265 
.67368 
.67272 
.67275 

9.82911 
.82913 
.82915 
.82917 

9.83042 
.83044 
.83046 
.83049 

.67674 
.67677 
.67681 
.67684 

9.83173 
.83175 
.83177 
.83179 

9.83181 
.83184 
.83186 
.83188 

.67878 
.67881 

.67884 
.67888 

.68081 
.68085 
.68088 
.68091 

12 
11 
10 
9 
8 
7 
6 
5 

+  13' 

53 
54 
55 

9.82788 
.82790 
.82792 
.82794 

.67379 
.67282 
.67285 
.67289 

9.82920 
.82922 
.82924 
.82926 

.67483 
.67487 
.67490 
.67493 

9.83051 
.83053 
.83055 
.83057 

.67687 
.67691 
.67694 
.67698 

.67891 
.67895 
.67898 
.67901 

9.83311 
.83314 
.83316 
.83318 

.68095 
.68098 
.68102 
.68105 

+  14' 

57 
58 
59 

9.82796 
.82799 
.82801 
.82803 

.67393 
.67396 
.67399 
.67303 

9.82928 
.82930 
.82933 
.82935 

.67497 
.67500 
.67504 
.67507 

9.83059 
.83062 
.83064 
.83066 

.67701 
.67704 
.67708 
.67711 

9.83190 
.83192 
.83194 
.83197 

.67905 
.67908 
.67913 
.67915 

9.83320 
.83322 
.83324 
.83327 

.68108 
.68112 
.68115 
.68119 

4 
3 
2 
1 

+  15' 

9.82805 

.67306 

9.82937 

.67510 

9.83068 

.67715 

9.83199 

.67918 

9.83329 

.68122 

0 

ifife  39m 

16^  38m 

16h  STm 

ifift  sem 

16^  35m 

Page  900] 

TABLE  45. 

Haversines. 

s 

7ft  ^5m  111°  W 

7h  26m  111°  3(K 

7fe  27m  111°  45'  1 

7ft  28m  113°  0' 

7ft  29m  113°  15'  1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.83329 
.83331 
.83333 
.83335 

.68123 
.68135 
.68129 
.68133 

9.83458 
.83460 
.83462 
.83464 

.68335 
.68338 
.68333 
.68335 

9.83587 
.83589 
.83591 
.83593 

.68538 
.68531 
.68535 
.68538 

9.83715 
.83717 
.83719 
.83721 

.68730 
.68734 
.68737 
.68740 

9.83842 
.83844 
.83847 
.83849 

.68933 
.68936 
.68939 
.68943 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.83337 
.83339 
.83342 
.83344 

.68135 
.68139 
.68142 
.68116 

9.83467 
.83469 
.83471 
.83473 

.68339 
.68342 
.68345 
.68349 

9.83595 
.83597 
.83600 
.83602 

.68541 
.68545 
.68548 
.68553 

9.83723 
.83725 
.83728 
.83730 

.68744 
.68747 
.68751 
.68754 

9.83851 
.83853 
.83855 
.83857 

.68946 
.68949 
.68953 
.68956 

56 
55 
54 
53 
52 
51 
50 
49 

+      r 

9 

10 

11 

9.83346 
.83348 
.83350 
.83352 

.68149 
.68152 
.68156 
.68159 

9.83475 
.83477 
.83480 
.83482 

.68353 
.68356 
.68359 
.68362 

9.83604 
.83606 
.83608 
.83610 

.68555 
.68558 
.68562 
.68565 

9.83732 
.83734 
.83736 
.83738 

.68757 
.68761 
.68764 
.68767 

9.83859 
.83861 
.83864 
.83866 

.68959 
.68963 
.68966 
.68969 

+  3' 

13 
14 
15 

9.83355 
.83357 
.83359 
.83361 

.68163 
.68166 
.68169 
.68173 

9.83484 
.83486 
.83488 
.83490 

.68366 
.68369 
.68372 
.68376 

9.83612 
.83615 
.83617 
.83619 

.68568 
.68572 
.68575 
.68579 

9.83740 
.83743 
.83745 
.83747 

.68771 
.68774 

.68778 
.68781 

9.83868 
.83870 

.83872 
.83874 

.68973 
.68976 

.68980 
.68983 

48 
47 
46 
45 

+     4' 
17 
18 
19 

9.833.63 
.83365 
.83368 
.83370 

.68176 
.68180 
.68183 
.68186 

9.83492 
.83495 
.83497 
.83499 

.68379 
.68383 
.68386 
.68389 

9.83621 
.83623 
.83625 
.83627 

.68583 
.68585 
.68589 
.68592 

9.83749 
.83751 
.83753 
.83755 

.68784 

.68788 
.68791 
.68794 

9.83876 
.83878 
.83881 
.83883 

.68986 
.68990 
.68993 
.68996 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 

+      5^ 

21 
22 
23 

9.83372 
.83374 
.83376 
.83378 

.68190 
.68193 
.68196 
.68200 

9.83501 
.83503 
.83505 
.83507 

.68393 
.68396 
.68399 
.68403 

9.83630 
.83632 
.83634 
.83636 

9.83638 
.83640 
.83642 
.83644 

.68595 
.68599 
.68602 
.68606 

9.83757 
.83760 
.83762 
.83764 

.68798 
.68801 
.68804 

.68808 

9.83885 
.83887 
.83889 
.83891 

.69000 
.69003 
.69006 
.69010 

+      ^ 
25 
26 

27 

9.83380 
.83383 
.83385 
.83387 

.68303 
.68207 
.68310 
.68313 

9.83510 
.83512 
.83514 
.83516 

.68406 
.68410 
.68413 
.68416 

.68609 
.68612 
.68616 
.68619 

9.83766 
.83768 
.83770 
.83772 

.68811 
.68815 

.68818 
.68831 

9.83893 
.83895 
.83897 
.83900 

9.83902 
.83904 
.83906 
.83908 

.69013 
.69017 
.69030 
.69033 

+    r 

29 
30 
31 

9.83389 
.83391 
.83393 
.83396 

.68317 
.68330 
.68221 
.68227 

9.83518 
.83520 
.83522 
.83525 

.68420 
.68423 
.68427 
.68430 

9.83647 
.83649 
.83651 
.83653 

.68633 
.68636 
.68639 
.68633 

9.83774 
.83777 
.83779 
.83781 

.68825 
.68828 
.68831 
.68835 

.69037 
.69030 
.69033 
.69037 

+   8' 
33 
34 
35 

9.83398 
.83400 
.83402 
.83404 

.68330 
.68334 
.68337 
.68310 

9.83527 
.83529 
.83531 
.83533 

.68433 
.68437 
.68440 
.68443 

9.83655 
.83657 
.83659 
.83662 

.68636 
.68639 
.68643 
.68646 

9.83783 
.83785 
.83787 
.83789 

.68838 
.68842 

.68845 
.68848 

9.83910 
.83912 
.83914 
.83916 

.69040 
.69044 
.69047 
.69050 

28 
27 
26 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

IS 

12 

11 

10 

9 

8 

7 

6 

5 

+  9^ 

37 
38 
39 

9.83406 
.83409 
.83411 
.83413 

.68344 
.68347 
.68351 
.68354 

9.83535 
.83537 
.83540 
.83542 

.68447 
.68450 
.68454 
.68457 

9.83664 
.83666 
.83668 
.83670 

.68649 
.68653 
.68656 
.68660 

9.83791 
.83794 
.83796 
.83798 

.68852 

.68855 
.68858 
.68862 

9.83919 
.83921 
.83923 
.83925 

.69054 
.69057 
.69060 
.69064 

+  W 

41 
42 
43 

9.83415 
.83417 
.83419 
.83421 

.68357 
.68361 
.68364 

.68368 

9.83544 
.83546 
.83548 
.83550 

.68460 
.68464 
.68467 
.68470 

9.83672 
.83674 
.83676 
.83679 

.68663 
.68666 
.68670 
.68673 

9.83800 
.83802 
.83804 
.83806 

.68865 
.68869 

.68872 
.68875 

9.83927 
.83929 
.83931 
.83933 

.69067 
.69070 
.69074 
.69077 

+  ir 

45 
46 
47 

9.83424 
.83426 
.83428 
.83430 

.68371 
.68274 

.68378 
.68381 

9.83552 
.83555 
.83557 
.83559 

.68474 
.68477 
.68481 
.68484 

9.83681 
.83683 
.83685 
.83687 

.68676 
.68680 
.68683 

.68687 

9.83808 
.83811 
.83813 
.83815 

.68879 

.68882 
.68885 
.68889 

9.83935 
.83938 
.83940 
.83942 

.69080 
.69084 
.69087 
.69091 

+  12' 

49 
50 
51 

9.83432 
.83434 
.83436 
.83439 

.68384 
.68388 
.68391 
.68395 

9.83561 
.83563 
.83565 
.83567 

.68487 
.68491 
.68494 
.68497 

9.83689 
.83691 
.83694 
.83696 

.68690 
.68693 
.68697 
.68700 

9.83817 
.83819 
.83821 
.83823 

.68892 
.68895 
.68899 
.68902 

9.83944 
.83946 
.83948 
.83950 

.69094 
.69097 
.69101 
.69104 

+    13^ 

53 
54 
55 

9.83441 
.83443 
.83445 
.83447 

.68398 
.68301 
.68305 
.68308 

9.83570 
.83572 
.83574 
.83576 

.68501 
.68504 
.68508 
.68511 

9.83698 
.83700 
.83702 
.83704 

.68703 
.68707 
.68710 
.68713 

9.83825 
.83828 
.83830 
.83832 

.68906 
.68909 
.68912 
.68916 

9.83952 
.83955 
.83957 
.83959 

.69107 
.69111 
.69114 
.69117 

+    W 

57 
58 
59 

9.83449 
.83452 
.83454 
.83456 

.68313 
.68315 

.68318 
.68333 

9.83578 
.83580 
.83582 
.83585 

.68515 
.68518 
.68521 
.68525 

9.83706 
.83708 
.83711 
.83713 

.68717 
.68730 
.68734 
.68737 

9.83834 
.83836 
.83838 
.83840 

.68919 
.68922 
.68926 
.68939 

9.83961 
.83963 
.83965 
.83967 

9.83969 

.69131 
.69134 
.69137 
.69131 
.69134 

4 
3 
2 
1 
0 

+    IS' 

9.83458 

.68325 

9.83587 

.68528 

9.83715 

.68730 

9.83842 

.68933 

16h 

54™ 

iSh  33m 

16hS2m 

16h  Sim 

U^SOfin 

TABLE  45.                  [Page  901 
Haversines. 

s 

7ft  50TO  112°  W 

7ft  Sim  113°  45' 

7ft5^mll3°(K  1 

7A  3Sm  113°  15'  | 

7ft  34m  113°  W 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Har. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

1 
2 
3 

9.83969 
.83971 
.83974 
.83976 

.69134 
.6913S 
.69141 
.69144 

9.84096 
.84098 
.84100 
.84102 

.69336 
.69339 
.69342 
.69346 

9.84221 
.84223 
.84226 
.84228 

.69537 
.69540 
.69543 
.69547 

9.84346 
.84349 
.84351 
.84353 

.69737 
.69741 
.69744 
.69747 

9.84471 
.84473 
.84475 
.84477 

.69937 
.69941 
.69944 
.69947 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.83978 
.83980 
.83982 
.83984 

.69148 
.69151 
.69154 
.69158 

9.84104 
.84106 
.84108 
.84110 

.69349 
.69352 
.69356 
.69359 

9.84230 
.84232 
.84234 
.84236 

.69550 
.69553 
.69557 
.69560 

9.84355 
.84357 
.84359 
.84361 

.69751 
.69754 
.69757 
.69761 

9.84479 
.84481 
.84483 
.84485 

.69951 
.69954 
.69957 
.69961 

56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+  3' 

9 

10 

11 

9.83986 
.83988 
.83990 
.83992 

.69161 
.69164 
.69168 
.69171 

9.84112 
.84114 
.84117 
.84119 

.69362 
.69366 
.69369 
.69372 

9.84238 
.84240 
.84242 
.84244 

.69563 
.69567 
.69570 
.69573 

9.84363 
.84365 
.84367 
.84369 

.69764 
.69767 
.69771 
.69774 

9.84488 
.84490 
.84492 
.84494 

.69964 
.69967 
.69971 
.69974 

+  3' 

IS 
14 
15 

9.83995 
.83997 
.83999 
.84001 

.69174 
.69178 
.69181 
.69185 

9.84121 
.84123 
.84125 
.84127 

.69376 
.69379 
.69382 
.69386 

9.84246 
.84248 
.84251 
.84253 

.69577 
.69580 
.69583 
.69587 

9.84371 
.84373 
.84376 
.84378 

.69777 
.69781 
.69784 
.69787 

9.84496 
.84498 
.84500 
.84502 

.69977 
.69981 
.69981 
.69987 

+  4' 

17 
18 
19 

9.84003 
.84005 
.84007 
.84009 

.69188 
.69191 
.69195 
.69198 

9.84129 
.84131 
.84133 
.84135 

.69389 
.69393 
.69396 
.69399 

9.84255 
.84257 
.84259 
.84261 

.69590 
.69593 
.69597 
.69600 

9.84380 
.84382 
.84384 
.84386 

.69791 
.69794 
.69797 
.69801 

9.84504 
.84506 
.84508 
.84510 

.69991 
.69994 
.69997 
.70001 

U 
43 
42 
41 

+  5' 

21 

22 
23 

9.84011 
.84014 
.84016 
.84018 

.69301 
.69205 
.69208 
.69211 

9.84138 
.84140 
.84142 
.84144 

.69403 
.69406 
.69409 
.69413 

9.84263 
.84265 
.84267 
.84269 

.69603 
.69607 
.69610 
.69614 

9.84388 
.84390 
.84392 
.84394 

.69804 
.69807 
.69811 
.69814 

9.84512 
.84514 
.84517 
.84519 

.70004 
.70007 
.70011 
.70014 

40 
39 
38 
37 

+  ^ 

25 
26 
27 

9.84020 
.84022 
.84024 
.84026 

.69215 
.69218 
.69221 
.69225 

9.84146 
.84148 
.84150 
.84152 

.69416 
.69419 
.69423 
.69426 

9.84271 
.84274 
.84276 
.84278 

.69617 
.69620 
.69624 
.69627 

9.84396 
.84398 
.84400 
.84403 

.69817 
.69821 
.69834 
.69827 

9.84521 
.84523 
.84525 
.84527 

.70017 
.70021 
.70034 
.70027 

36 
35 
34 
33 

+    r 

29 
SO 
SI 

9.84028 
.84030 
.84033 
.84035 

.69228 
.69232 
.69235 
.69238 

9.84154 
.84156 
.84159 
.84161 

.69429 
.69433 
.69436 
.69439 

9.84280 
.84282 
.84284 
.84286 

.69630 
.69634 
.69637 
.69640 

9.84405 
.84407 
.84409 
.84411 

.69831 
.69834 
.69837 
.69841 

9.84529 
.84531 
.84533 
.84535 

.70031 
.70034 
.70037 
.70041 

32 
31 
30 
29 

28 
27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 

+  8' 
S3 
34 
35 

9.84037 
.84039 
.84041 
.84043 

.69242 
.69245 
.69248 
.69252 

9.84163 
.84165 
.84167 
.84169 

.69443 
.69446 
.69450 
.69453 

9.84288 
.84290 
.84292 
.84294 

.69644 
.69647 
.59650 
.69654 

9.84413 
.84415 
.84417 
.84419 

.69844 
.69847 
.69851 
.69854 

9.84537 
.84539 
.84541 
.84543 

.70044 
.70047 
.70051 
.70054 

+   IK 

55 
59 

9.84045 
.84047 
.84049 
.84051 

.69255 
.69258 
.69262 
.69265 

9.84171 
.84173 
.84175 
.84177 

.69456 
.69460 
.69463 
.69466 

9.84296 
.84299 
.84301 
.84303 

.69657 
.69660 
.69664 
.69667 

9.84421 
.84423 
.84425 
.84427 

.69857 
.69861 
.69864 
.69867 

9.84545 
.84547 
.84550 
.84552 

.70057 
.70061 
.70064 
.70067 

+  10' 

41 

42 
43 

9.84054 
.84056 
.84058 
.84060 

.69268 
.69272 
.69275 
.69279 

9.84179 
.84182 
.84184 
.84186 

.69470 
.69473 
.69476 
.69480 

9.84305 
.84307 
.84309 
.84311 

.69670 
.69674 
.69677 
.69680 

9.84430 
.84432 
.84434 
.84436 

.69871 
.69874 
.69877 
.69881 

9.84554 
.84556 
.84558 
.84560 

.70071 
.70074 
.70077 
.70081 

+    11' 

45 
46 
47 

9.84062 
.84064 
.84066 
.84068 

.69282 
.69285 
.69289 
.69292 

9.84188 
.84190 
.84192 
.84194 

.69483 
.69486 
.69490 
.69493 

9.84313 
.84315 
.84317 
.84319 

.69684 
.69687 
.69690 
.69694 

9.84438 
.84440 
.84442 
.84444 

.69884 
.69887 
.69891 
.69894 

9.84562 
.84564 
.84566 
.84568 

.70084 
.70087 
.70091 
.70094 

16 
15 
14 
13 

+  n' 

49 
50 
51 

9.84070 
.84072 
.84075 
.84077 

.69295 
.69299 
.69302 
.69305 

9.84196 
.84198 
.84200 
.84203 

.69496 
.69500 
.69503 
.69506 

9.84321 
.84324 
.84326 
.84328 

.69697 
.69700 
.69704 
.69707 

9.84446 
.84448 
.84450 
.84452 

.69897 
.69901 
.69904 
.69907 

9.84570 

.84572 
.84574 
.84576 

.70097 
.70101 
.70104 
.70107 

12 
11 
10 
9 
8 
7 
6 
5 

4 
3 
2 
1 

+  13' 

53 
54 
55 

9.84079 
.84081 
.84083 
.84085 

.69309 
.69312 
.69315 
.69319 

9.84205 
.84207 
.84209 
.84211 

.69510 
.69513 
.69516 
.69520 

9.84330 
.84332 
.84334 
.84336 

.69710 
.69714 
.69717 
.69720 

9.84454 
.84456 
.84459 
.84461 

.69911 
.69914 
.69917 
.69921 

9.84578 
.84581 
.84583 
.84585 

.70111 
.70114 
.70117 
.70131 

+  W 

57 
58 
59 

9.84087 
.84089 
.84091 
.84093 

.69322 
.69326 
.69329 
.69332 

9.84213 
.84215 
.84217 
.84219 

.69523 
.69527 
.69530 
.69533 

9.84338 
.84340 
.84342 
.84344 

.69724 
.69727 
.69731 
.69734 

9.84463 
.84465 
.84467 
.84469 

.69924 
.69927 
.69931 
.69934 

9.84587 
.84589 
.84591 
.84593 

.70134 
.70137 
.70131 
.70134 

+  15' 

9.84096 

.69336 

9.84221 

.69537 

9.84346 

.69737 

9.84471 

.69937 

9.84595 

.70137 

0 

16^  29m 

16h  28m 

len  27m 

16h2&m 

16^  25m 

Page  902] 

TABLE  45. 

Haversines. 

s 

rh  35m  113°  45' 

7h  36m  114°  0' 

7h  Sim  114°  15' 

7/1  sS'm  114°  30' 

7h  39m  114°  45^  1 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.84595 
.84597 
.84599 
.84601 

.70137 
.70141 
.70144 
.70147 

9.84718 
.84720 
.84722 
.84724 

.70337 
.70340 
.70343 
.70347 

9.84841 
.84843 
.84845 
.84847 

.70536 
.70539 
.70543 
.70546 

9.84963 
.84965 
.84967 
.84969 

.70735 
.70738 
.70741 
.70745 

9.85085 
.85087 
.85089 
.85091 

.70933 
.70936 
.70940 
.70943 

60 
59 
58 
57 

+  r 

5 
6 

7 

9.84603 
.84605 
.84607 
.84609 

.70151 
.70154 
.70157 
.70161 

9.84726 
.84729 
.84731 
.84733 

.70350 
.70353 
.70357 
.70360 

9.84849 
.84851 
.84853 
.84855 

.70549 
.70553 
.70556 
.70559 

9.84971 
.84973 
.84975 
.84977 

.70748 
.70751 
.70755 

.70758 

9.85093 
.85095 
.85097 
.85099 

.70946 
.70950 
.70953 
.70956 

66 
55 

54 
53 

+    -n' 

9 
10 
11 

9.84611 
.84613 
.84616 
.84618 

.70164 
.70167 
.70171 
.70174 

9.84735 
.84737 
.84739 
.84741 

.70363 
.70367 
.70370 
.70373 

9.84857 
.84859 
.84861 
.84863 

.70563 
.70566 
.70569 
.70573 

9.84979 
.84982 
.84984 
.84986 

.70761 
.70764 
.70768 
.70771 

9.85101 
.85103 
.85105 
.85107 

.70959 
.70963 
.70966 
.70969 

52 
51 
50 
49 
48 
47 
46 
45 

44 
43 
42 
41 

+  3' 

13 
14 
15 

9.84620 
.84622 
.84624 
.84626 

.70177 
.70181 
.70184 
.70187 

9.84743 
.84745 
.84747 
.84749 

.70377 
.70380 
.70383 
.70387 

9.84866 
.84868 
.84870 
.84872 

.70576 
.70579 
.70583 
.70586 

9.84988 
.84990 
.84992 
.84994 

.70774 

.70778 
.70781 
.70784 

9.85109 
.85111 
.85113 
.85115 

.70973 
.70976 
.70979 
.70983 

+  4' 

n 

18 
19 

9.84628 
.84630 
.84632 
.84634 

.70191 
.70194 
.70197 
.70301 

9.84751 
.84753 
.84755 
.84757 

.70390 
.70393 
.70397 
.70400 

9.84874 
.84876 
.84878 
.84880 

.70589 
.70593 
.70596 
.70599 

9.84996 
.84998 
.85000 
.85002 

.70788 
.70791 
.70794 
.70798 

9.85117 
.85119 
.85121 
.85123 

.70986 
.70989 
.70992 
.70996 

+   5^ 
21 

22 
23 

9.84636 
.84638 
.84640 
.84642 

.70204 
.70307 
.70311 
.70314 

9.84759 
.84761 
.84763 
.84765 

.70403 
.70407 
.70410 
.70413 

9.84882 
.84884 
.84886 
.84888 

.70603 
.70606 
.70609 
.70613 

9.85004 
.85006 
.85008 
.85010 

.70801 
.70804 
.70807 
.70811 

9.85125 
.85127 
.85129 
.85131 

.70999 
.71002 
.71006 
.71009 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.84644 
.84646 
.84648 
.84651 

.70317 
.70331 
.70334 
.70337 

9.84767 
.84770 
.84772 
.84774 

.70417 
.70430 
.70433 
.70436 

9.84890 
.84892 
.84894 
.84896 

.70615 
.70619 
.70633 
.70635 

9.85012 
.85014 
.85016 
.85018 

.70814 
.70817 
.70821 
.70824 

9.85133 
.85135 
.85137 
.85139 

.71013 
.71016 
.71019 
.71033 

36 
35 
34 
33 
32 
31 
30 
29 

+    r 

29 
SO 
31 

9.84653 
.84655 
.84657 
.84659 

.70330 
.70334 
.70337 
.70340 

9.84776 
.84778 
.84780 

.84782 

.70430 
.70433 
.70436 
.70440 

9.84898 
.84900 
.84902 
.84904 

.70629 
.70633 
.70635 
.70639 

9.85020 
.85022 
.85024 
.85026 

.70827 
.70831 
.70834 
.70837 

9.85141 
.85143 
.85145 
.85147 

.71025 
.71029 
.71032 
.71035 

+     8^ 
S3 
34 
35 

9.84661 
.84663 
.84665 
.84667 

.70344 
.70347 
.70350 
.70354 

9.84784 
.84786 
.84788 
.84790 

.70443 
.70446 
.70450 
.70453 

9.84906 
.84908 
.84910 
.84912 

.70643 
.70645 
.70649 
.70653 

9.85028 
.85030 
.85032 
.85034 

.70840 
.70844 
.70847 
.70850 

9.85149 
.85151 
.85153 
.85155 

.71039 
.71042 
.71045 
.71049 

28 
27 
26 
25 

+     9^ 

37 
38 
39 

9.84669 
.84671 
.84673 
.84675 

.70357 
.70360 
.70364 
.70367 

9.84792 
.84794 
.84796 
.84798 

.70456 
.70460 
.70463 
.70466 

9.84914 
.84916 
.84919 
.84921 

.70655 
.70659 
.70662 
.70665 

9.85036 
.85038 
.85040 
.85042 

.70854 
.70857 
.70860 
.70864 

9.85158 
.85160 
.85162 
.85164 

.71052 
.71055 
.71058 
.71062 

24 
23 
22 
21 

+    W 

41 
42 
43 

9.84677 
.84679 
.84681 
.84683 

.70370 
.70374 
.70377 
.70380 

9.84800 
.84802 
.84804 
.84806 

.70470 
.70473 
.70476 
.70480 

9.84923 
.84925 
.84927 
.84929 

.70668 
.70673 
.70675 
.70678 

9.85044 
.85046 
.85048 
.85050 

.70867 
.70870 
.70874 

.70877 

9.85166 
.85168 
.85170 
.85172 

.71065 
.71068 
.71072 
.71075 

20 
19 
18 
17 
16 
15 
14 
13 
12 
11 
10 
9 

+  11' 

45 
46 
47 

9.84685 
.84688 
.84690 
.84692 

.70384 
.70387 
.70390 
.70394 

9.84808 
.84810 
.84812 
.84815 

.70483 
.70486 
.70490 
.70493 

9.84931 
.84933 
.84935 
.84937 

.70682 
.70685 
.70688 
.70692 

9.85052 
.85054 
.85057 
.85059 

.70880 

.70884 
.70887 
.70890 

9.85174 
.85176 
.85178 
.85180 

.71078 
.71082 
.71085 

.71088 

+  ir 

49 
50 
51 

9.84694 
.84696 
.84698 
.84700 

.70397 
.70300 
.70304 
.70307 

9.84817 
.84819 
.84821 
.84823 

.70496 
.70499 
.70503 
.70506 

9.84939 
.84941 
.84943 
.84945 

.70695 
.70698 
.70702 
.70705 

9.85061 
.85063 
.85065 
.85067 

.70893 
.70897 
.70900 
.70903 

9.85182 
.85184 
.85186 
.85188 

.71091 
.71095 
.71098 
.71101 

+  13^ 

S3 

54 
55 

9.84702 
.84704 
.84706 
.84708 

.70310 
.70314 
.70311 
.70330 

9.84825 
.84827 
.84829 
.84831 

.70509 
.70513 
.70516 
.70519 

9.84947 
.84949 
.84951 
.84953 

.70708 
.70712 
.70715 
.70718 

9.85069 
.85071 
.85073 
.85075 

.70907 
.70910 
.70913 
.70916 

9.85190 
.85192 
.85,  94 
.85196 

.71105 
.71108 
.71111 
.71114 

8 
7 
6 
5 

+  W 

57 
58 
59 

9.84710 
.84712 
.84714 
.84716 

.70334 
.70337 
.70330 
.70333 

9.84833 
.84835 
.84837 
.84839 

.70533 
.70536 
.70529 
.70533 

9.84955 
.84957 
.84959 
.84961 

.70731 
.70735 
.70739 
.70731 

9.85077 
.85079 
.85081 
.85083 

.70920 
.70923 
.70926 
.70930 

9.85198 
.85200 
.85202 
.85204 

.71118 
.71131 
.71134 
.71128 

4 
3 
2 
1 

+    W 

9.84718 

.70337 

9.84841 

.70536 

9.84963 

.70735 

9.85085 

.70933 

9.85206 

.71131 

0 

16^ 

24'^ 

16^ 

2Sm 

leT^  22m 

16^ 

21m 

len  20m 

TABLE  45.                  [Page  903 
Haversines. 

s 

7^  40^  115°  (K 

7ft  41"^  115°  15' 

7ft  42m  115°  30' 

7ft  43'^  115°  45' 

7ft  U^  116°  V 

s 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
S 

9.85206 
.85208 
.85210 
.85212 

.71131 
.71134 
.71138 
.71141 

9.85326 
.85328 
.85330 
.85332 

.71328 
.71332 
.71335 
.71338 

9.85446 
.85448 
.85450 
.85452 

.71526 
.71529 
.71532 
.71535 

9.85565 
.85567 
.85569 
.85571 

.71722 
.71726 
.71729 
.71732 
.71735 
.71739 
.71742 
.71745 

9.85684 
.85686 
.85688 
.85690 

9.85692 
.85694 
.85696 
.85698 

.71919 
.71922 
.71925 

.71928 

60 
59 
58 
57 
56 
55 
54 
53 

+    r 

5 
6 

7 

9.85214 
.85216 
.85218 
.85220 

.71144 
.71147 
.71151 
.71154 

9.85334 
.85336 
.85338 
.85340 

.71342 
.71345 
.71348 
.71351 

9.85454 
.85456 
.85458 
.85460 

.71539 
.71542 
.71545 
.71549 

9.85573 
.85575 
.85577 
.85579 

.71932 
.71935 
.71938 
.71941 

+      r 

9 

10 

11 

9.85222 
.85224 
.85226 
.85228 

.71157 
.71161 
.71164 
.71167 

9.85342 
.85344 
.85346 
.85348 

9.85350 
.85352 
.85354 
.85356 

.71355 
.71358 
.71361 
.71365 

9.85462 
.85464 
.85466 
.85468 

.71552 
.71555 
.71558 
.71562 

9.85581 
.85583 
.85585 
.85587 

.71748 
.71752 
.71755 
.71758 

9.85700 
.85702 
.85704 
.85706 

.71945 
.71948 
.71951 
.71955 

52 
51 
50 
49 

+   3^ 

IS 
14 
15 

9.85230 
.85232 
.85234 
.85236 

.71170 
.71174 
.71177 
.71180 

.71368 
.71371 
.71374 
.71378 

9.85470 
.85472 
.85474 
.85476 

.71565 
.71568 
.71571 
.71575 

9.85589 
.85591 
.85593 
.85595 

.71762 
.71765 
.71768 
.71771 
.71775 
.71778 
.71781 
.71784 

9.85708 
.85710 
.85712 
.85714 

9.85716 
.85718 
.85720 
.85722 

9.85724 
.85726 
.85727 
.85729 

.71958 
.71961 
.71964 
.71968 
.71971 
.71974 
.71977 
.71981 

48 
47 
46 
45 

44 
43 
42 
41 

+   4' 
17 
18 
19 

9.85238 
.85240 
.85242 
.85244 

.71184 
.71187 
.71190 
.71194 

9.85358 
.85360 
.85362 
.85364 

.71381 
.71384 
.71388 
.71391 

9.85478 
.85480 
.85482 
.85484 

.71578 
.71581 
.71585 

.71588 

9.85597 
.85599 
.85601 
.85603 

+  5^ 
21 

22 
23 

9.85246 
.85248 
.85250 
.85252 

.71197 
.71200 
.71203 
.71207 

9.85366 
.85368 
.85370 
.85372 

.71394 
.71397 
.71401 
.71404 

9.85486 
.85488 
.85490 
.85492 

.71591 
.71594 
.71598 
.71601 

9.85605 
.85607 
.85609 
.85611 

.71788 
.71791 
.71794 
.71798 

.71984 
.71987 
.71990 
.71994 

40 
S9 
38 
37 
S6 
35 
34 
33 

+   6' 

25 
26 
27 

9.85254 
.85256 
.85258 
.85260 

.71210 
.71213 
.71217 
.71220 

9.85374 
.85376 
.85378 
.85380 

.71407 
.71411 
.71414 
.71417 

9.85494 
.85496 
.85498 
.85500 

.71604 
.71608 
.71611 
.71614 

9.85613 
.85615 
.85617 
.85619 

.71801 
.71804 
.71807 
.71811 

9.85731 
.85733 
.85735 
.85737 

.71997 
.72000 
.72003 
.72007 

+    r 

29 
SO 
SI 

9.85262 
.85264 
.85266 
.85268 

.71223 
.71226 
.71230 
.71233 

9.85382 
.85384 
.85386 
.85388 

.71420 
.71424 
.71427 
.71430 

9.85502 
.85504 
.85506 
.85508 

.71617 
.71621 
.71624 
.71627 

9.85621 
.85623 
.85625 
.85627 

.71814 
.71817 

.71820 
.71824 

9.85739 
.85741 
.85743 
.85745 

.72010 
.72013 
.72017 
.72020 

32 
SI 
30 
29 

+   8' 

ss 

S4 
S5 

9.85270 
.85272 
.85274 
.85276 

.71236 
.71240 
.71243 
.71246 

9.85390 
.85392 
.85394 
.85396 

.71434 
.71437 
.71440 
.71443 

9.85510 
.85512 
.85514 
.85516 

.71631 

.71634 

.71637 

.  .71640 

9.85629 
.85631 
.85633 
.85635 

.71827 
.71830 
.71834 
.71837 

9.85747 
.85749 
.85751 
.85753 

.72023 
.72026 
.72030 
.72033 

28 
27 
26 
25 

+   9^ 

S7 
38 
S9 

9.85278 
.85280 
.85282 
.85284 

.71249 
.71253 
.71256 
.71259 

9.85398 
.85400 

.85402 
.85404 

.71447 
.71450 
.71453 
.71456 

9.85518 
.85520 
.85522 
.85524 

.71644 
.71647 
.71650 
.71653 

9.85637 
.85639 
.85641 
.85643 

.71840 
.71843 
.71847 
.71850 

9.85755 
.85757 
.85759 
.85761 

.72036 
.72039 
.72043 
.72046 

24 
23 
22 
21 

+  ir 

41 
42 
43 

9.85286 
.85288 
.85290 
.85292 

.71263 
.71266 
.71269 
.71273 

9.85406 
.85408 
.85410 
.85412 

.71460 
.71463 
.71466 
.71470 

9.85526 
.85528 
.85530 
.85532 

.71657 
.71660 
.71663 
.71667 

9.85645 
.85647 
.85649 
.85651 

.71853 
.71856 
.71860 
.71863 

9.85763 
.85765 
.85767 
.85769 

.72049 
.72052 
.72056 
.72059 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
S 
2 
1 

+  11' 

45 
46 
47 

9.85294 
.85296 
.85298 
.85300 

.71276 
.71279 
.71282 
.71286 

9.85414 
.85416 
.85418 
.85420 

.71473 
.71476 
.71480 
.71483 

9.85534 
.85536 
.85538 
.85540 

.71670 
.71673 
.71676 
.71680 

9.85653 
.85654 
.85656 
.85658 

.71866 
.71870 
.71873 
.71876 

9.85771 
.85773 
.85775 
.85777 

.72062 
.72066 
.72069 
.72072 

+  ir 

49 
50 
51 

9.85302 
.85304 
.85306 
.85308 

.71289 
.71292 
.71296 
.71299 

9.85422 
.85424 
.85426 
.85428 

.71486 
.71489 
.71493 
.71496 

9.85542 
.85544 
.85546 
.85548 

.71683 
.71686 
.71690 
.71693 

9.85660 
.85662 
.85664 
.85666 

.71879 

.71883 
.71886 
.71889 

9.85779 
.85781 
.85783 
.85785 

.72075 
.72079 
.72082 
.72085 

+  13^ 

53 
54 

55 

9.85310 
.85312 
.85314 
.85316 

.71302 
.71305 
.71309 
.71312 

9.85430 
.85432 
.85434 
.85436 

.71499 
.71503 
.71506 
.71509 

9.85550 
.85552 
.85554 
.85555 

.71696 
.71699 
.71703 
.71706 

9.85668 
.85670 
.85672 
.85674 

.71892 
.71896 
.71899 
.71902 

9.85787 
.85788 
.85790 
.85792 

.72088 
.72092 
.72095 
.72098 

+  14' 

57 
58 
59 

9.85318 
.85320 
.85322 
.85324 

.71315 
.71319 
.71322 
.71325 

9.85438 
.85440 
.85442 
.85444 

.71512 
.71516 
.71519 
.71522 

9.85557 
.85559 
.85561 
.85563 

.71709 
.71712 
.71716 
.71719 

9.85676 
.85678 
.85680 
.85682 

.71905 
.71909 
.71912 
.71915 

9.85794 
.85796 
.85798 
.85800 

.72101 
.72105 
.72108 
.72111 

+  15' 

9.85326 

.71328 

9.85446 

.71526 

9.85565 

.71722 

9.85684 

.71919 

9.85802 

.72114 

0 

16h  19m 

leh  ism 

16h  nm 

16^1&n 

16^  15'^ 

— . — 

Page  904]                 TABLE  45. 

Haversines. 

B 
S 

7A  45m  116°  15'  1 

7ft  46"*  116°  30' 

7h  47m  116°  45' 

7ft  48m  117°  0' 

7ft  49m  1170  15/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.85802 
.85804 
.85806 
.85808 

.72114 
.72118 
.72121 
.72124 

9.85920 
.85922 
.85924 
.85926 

.72310 
.72313 
.72316 
.72320 

9.86037 
.86039 
.86041 
.86043 

.72505 
.72508 
.72511 
.72515 

9.86153 
.86155 
.86157 
.86159 

.72700 
.72703 
.72706 
.72709 

9.86269 
.86271 
.86273 
.86275 

.72894 
.72897 
.72900 
.72903 

60 
59 
58 

57 

+  1' 

5 
6 

7 

9.85810 
.85812 
.85814 
.85816 

.72127 
.72131 
.72134 
.72137 

9.85928 
.85930 
.85931 
.85933 

.72323 
.72326 
.72329 
.72333 

9.86045 
.86046 
.86048 
.86050 

.72518 
.72521 
.72524 
.72528 

9.86161 
.86163 
.86165 
.86167 

.72712 
.72716 
.72719 

.72722 

9.86277 
.86279 
.86281 
.86282 

.72907 
.72910 
.72913 
.72916 

56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 

+  r 

9 

10 

11 

9.85818 
.85820 
.85822 
.85824 

.72141 
.72144 
.72147 
.72150 

9.85935 
.85937 
.85939 
.85941 

.72336 
.72339 
.72342 
.72346 

9.86052 
.86054 
.86056 
.86058 

.72531 
.72534 
.72537 
.72541 

9.86169 
.86171 
.86173 
.86174 

.72725 
.72729 
.72732 
.72735 

9.86284 
.86286 
.86288 
.86290 

.72920 
.72923 
.72926 
.72929 

+   3' 

IS 

14 
15 

9.85826 
.85828 
.85830 
.85832 

.72154 
.72157 
.72160 
.72163 

9.85943 
.85945 
.85947 
.85949 

.72349 
.72352 
.72355 
.72359 

9.86060 
.86062 
.86064 
.86066 

.72544 

.72547 
.72550 
.72554 

9.86176 
.86178 
.86180 
.86182 

.72738 
.72742 
.72745 

.72748 

9.86292 
.86294 
.86296 
.86298 

.72^32 
.72936 
.72939 
.72942 

+     4' 
17 
18 
19 

9.85834 
.85836 
.85838 
.85840 

.72167 
.72170 
.72173 
.72176 

9.85951 
.85953 
.85955 
.85957 

.72362 
.72365 
.72368 
.72372 

9.86068 
.86070 
.86072 
.86074 

.72557 
.72560 
.72563 
.72567 

9.86184 
.86186 
.86188 
.86190 

.72751 
.72755 

.72758 
.72761 

9.86300 
.86302 
.86304 
.86306 

.72945 
.72949 
.72953 
.72955 

U 
43 
42 
41 
40 
39 
38 
37 

+  5' 
21 

22 
23 

9.85841 
.85843 
.85845 
.85847 

.72180 
.72183 
.72186 
.72189 

9.85959 
.85961 
.85963 
.85965 

.72375 
.72378 
.72381 
.72385 

9.86076 
.86078 
.86080 
.86081 

.72570 
.72573 
.72576 
.72580 

9.86192 
.86194 
.86196 
.86198 

.72764 
.72768 
.72771 
.72774 

9.86307 
.86309 
.86311 
.86313 

.72958 
.72962 
.72965 
.72968 

+  ^ 

25 
26 

27 

9.85849 
.85851 
.85853 
.85855 

.72193 
.72196 
.72199 
.72202 

9.85967 
.85969 
.85971 
.85972 

.72388 
.72391 
.72394 
.72398 

9.86083 
.86085 
.86087 
.86089 

.72583 
.72586 
.72589 
.72593 

9.86200 
.86201 
.86203 
.86205 

.72777 
.72780 

.72784 
.72787 

9.86315 
.86317 
.86319 
.86321 

.72971 
.72974 
.72978 
.72981 

36 
35 
34 
33 

+    r 

29 
SO 
31 

9.85857 
.85859 
.85861 
.85863 

.72206 
.72209 
.72212 
.72215 

9.85974 
.85976 
.85978 
.85980 

.72401 
.72404 
.72407 
.72411 

9.86091 
.86093 
.86095 
.86097 

.72596 
.72599 
.72602 
.72606 

9.86207 
.86209 
.86211 
.86213 

.72790 
.72793 
.72797 
.72800 

9.86323 
.86325 
.86327 
.86329 

.72984 
.72987 
.72991 
.72994 

32 
31 
SO 
29 

+  8' 
33 
34 
35 

9.85865 
.85867 
.85869 
.85871 

.72219 
.72222 
.72225 
.72229 

9.85982 
.85984 
.85986 
.85988 

.72414 
.72417 
.72420 
.72424 

9.86099 
.86101 
.86103 
.86105 

.72609 
.72612 
.72615 
.72618 

9.86215 
.86217 
.86219 
.86221 

.72803 
.72806 
.72810 
.72813 

9.86331 
.86332 
.86334 
.86336 

.72997 
.73000 
.73004 
.73007 

28 
27 
26 
25 

+   9^ 

37 
38 
39 

9.85873 
.85875 
.85877 
.85879 

.72232 
.72235 
.72238 
.72242 

9.85990 
.85992 
.85994 
.85996 

.72427 
.72430 
.72433 
.72437 

9.86107 
.86109 
.86111 
.86112 

.72622 
.72625 
.72628 
.72631 

9.86223 
.86225 
.86227 
.86229 

.72816 
.72819 
.72823 
.72826 

9.86338 
.86340 
.86342 
.86344 

.73010 
.73013 
.73016 
.73020 

24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 

+    W 

41 

42 
43 

9.85881 
.85883 
.85885 
.85887 

.72245 
.72248 
.72251 
.72255 

9.85998 
.86000 
.86002 
.86004 

.72440 
.72443 
.72446 
.72450 

9.86114 
.86116 
.86118 
.86120 

.72635 
.72638 
.72641 
.72644 

9.86230 
.86232 
.86234 
.86236 

.72829 
.72832 
.72835 
.72839 

9.86346 
.86348 
.86350 
.86352 

.73023 
.73026 
.73029 
73033 

+    11' 

45 
46 
47 

9.85888 
.85890 
.85892 
.85894 

.72258 
.72261 
.72264 
.72268 

9.86006 
.86008 
.86010 
.86011 

.72453 
.72456 
.72459 
.72463 

9.86122 
.86124 
.86126 
.86128 

.72648 
.72651 
.72654 
.72657 

9.86238 
.86240 
.86242 
.86244 

.72842 
.72845 

.72848 
.72852 

9.86354 
.86355 
.86357 
.86359 

.73036 
.73039 
.73042 
.73046 

+    12' 

49 
50 
51 

9.85896 
.85898 
.85900 
.85902 

.72271 
.72274 
.72277 
.72281 

9.86013 
.86015 
.86017 
.86019 

.72466 
.72469 
.72472 
72476 

9.86130 
.86132 
.86134 
.86136 

.72661 
.72664 
.72667 
.72670 

9.86246 
.86248 
.86250 
.86252 

.72855 
.72858 
.72861 
.72865 

9.86361 
.86363 
.86365 
.86367 

.73049 
.73052 
.73055 
.73058 

12 

11 

10 

9 

+  13' 

53 
54 
55 

9.85904 
.85906 
.85908 
.85910 

.72284 

.72287 
.72290 
.72294 

9.86021 
.86023 
.86025 
.86027 

.72479 

.72482 
.72485 
.72489 

9.86138 
.86140 
.86142 
.86143 

.72674 
.72677 
.72680 
.72683 

9.86254 
.86256 
.86257 
.86259 

.72868 
.72871 

.72874 
.72878 

9.86369 
.86371 
.86373 
.86375 

.73062 
.73065 
.73068 
.73071 

8 
7 
6 
5 

+    14' 

57 
58 
59 

9.85912 
.85914 
.85916 
.85918 

.72297 
.72300 
.72303 
72307 

9.86029 
.86031 
.86033 
.86035 

.72492 
.72495 
.72498 
.72502 

9.86145 
.86147 
.86149 
.86151 

.72687 
.72690 
.72693 
.72696 

9.86261 
.86263 
.86265 
.86267 

.72881 
.72884 
.72887 
.72890 

9.86377 
.86379 
.86380 
.86382 

.73076 
.73078 
.73081 
.73084 

4 
3 
2 
1 

+    16' 

9.85920 

.72310 

9.86037 

.72505 

9.86153 

.72700 

9.86269 

.72894 

9.86384 

.73087 

0 

16h  W^ 

16h  ISrn 

16h  12m 

IG^lim 

16^  10^ 

TABLE  45.                 [Page  906 

Havereines. 

s 

7ft  50m  117°  30' 

7A  5im  nT"  45' 

7ft  52m  1180  (/ 

7A  5sm  U8°  15' 

7A  54m  118"  30' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav 

.  Nat.  Hav 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 

2 
3 

9.86384 
.86386 
.86388 
.86390 

.73087 
.73091 
.73094 
.73097 

9.86499 
.86501 
.86503 
.86505 

.73281 
.73384 
.73387 
.73290 

9.86613 
.86615 
.86617 
.86619 

.73474 
.73477 
.73480 
73483 

9.86727 
.86729 
.86730 
.86732 

.73666 
.73669 
.73672 
.73676 

9.86840 
.86842 
.86843 
.86845 

.73858 
.73861 
.73864 
.73868 

60 
59 
58 
57 

■f    r 

6 
6 
7 

9.86392 
.86394 
.86396 
.86398 

.73100 
.73104 
.73107 
.73110 

9.86507 
.86509 
.86510 
.86512 

.73294 
.73297 
.73300 
.73303 

9.86621 
.86623 
.86625 
.86626 

.73486 
.73490 
.73493 
.73496 

9.86734 
.86736 
.86738 
.86740 

.73679 
.73682 
.73685 

.73688 

9.86847 
.86849 
.86851 
.86853 

.73871 
.73874 

.73877 
.73880 

56 
55 
54 
53 
52 
51 
50 
49 

+     ^ 

9 

10 

11 

9.86400 
.86401 
.86403 
.86405 

.73113 
.73116 
.73130 
.73123 

9.86514 
.86516 
.86518 
.86520 

.73306 
.73310 
.73313 
.73316 

9.86628 
.86630 
.86632 
.86654 

.73499 
.73502 
.73506 
.73509 

9.86742 
.86744 
.86746 
.86747 

.73693 
.73695 
.73698 
.73701 

9.86855 
.86857 
.86859 
.86860 

.73884 
.73887 
.73890 
.73893 

+  3' 

IS 
14 
15 

9.86407 
.86409 
.86411 
.86413 

.73126 
.73129 
.73133 
.73136 

9.86522 
.86524 
.86526 
.86528 

.73319 
.73323 
.73326 
.73339 

9.86636 
.86638 
.86640 
.86642 

.73512 
.73515 
.73519 
.73522 

9.86749 
.86751 
.86753 
.86755 

.73704 
.73708 
.73711 
.73714 

9.86862 
.86864 
.86866 
.86868 

.73896 
.73899 
.73903 
.73906 

48 
47 
46 
45 

U 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 

+  4^ 
17 
18 
19 

9.86415 
.86417 
.86419 
.86421 

.73139 
.73142 
.73145 
.73149 

9.86529 
.86531 
.86533 
.86535 

.73332 
.73335 
.73339 
.73342 

9.86643 
.86645 
.86647 
.86649 

.73525 
.73528 
.73531 
.73535 

9.86757 
.86759 
.86761 
.86763 

.73717 
.73720 
.73724 
.73727 

9.86870 
.86872 
.86874 
.86875 

.73909 
.73913 
.73915 
.73919 

+  ^ 

21 
22 
2S 

9.86423 
.86424 
.86426 
.86428 

.73153 
.73155 
.73158 
.73162 

9.86537 
.86539 
.86541 
.86543 

.73345 
.73348 
.73351 
.73355 

9.86651 
.86653 
.86655 
.86657 

.73538 
.73541 
.73544 
.73547 

9.86764 
.86766 
.86768 
.86770 

.73730 
.73733 
.73736 
.73740 

9.86877 
.86879 
.86881 
.86883 

.73933 
.73935 
.73938 
.73931 

+  6^ 

25 
26 
27 

9.86430 
.86432 
.86434 
.86436 

.73165 
.73168 
.73171 
.73174 

9.86545 
.86547 
.86569 
.86550 

.73358 
.73361 
.73364 
.73368 

9.86659 
.86661 
.86662 
.86664 

.73551 
.73554 
.73557 
.73560 

9.86772 
.86774 
.86776 
.86778 

.73743 
.73746 
.73749 
.73752 

9.86885 
.86887 
.86889 
.86890 

.73935 
.73938 
.73941 
.73944 

+    r 

29 
SO 
SI 

9.86438 
.86440 
.86442 
.86444 

.73178 
.73181 
.73184 
.73187 

9.86552 
.86554 
.86556 
.86558 

.73371 
.73374 
.73377 
.73380 

9.86666 
.86668 
.86670 
.86672 

.73563 
.73567 
.73570 
.73573 

9.86780 
.86781 
.86783 
.86785 

.73756 
.73759 
73763 
.73765 

9.86892 
.86894 
.86896 
.86898 

.73947 
.73951 
.73954 
.73957 

32 
31 

30 
29 
28 

27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 

+  8' 
S3 
S4 
S5 

9.86446 
.86447 
.86449 
.86451 

.73191* 
.73194 
.73197 
.73200 

9.86560 
.86562 
.86564 
.86566 

.73384 
.73387 
.73390 
.73393 

9.86674 
.86676 
.86678 
.86679 

.73576 
.73579 
.73583 
.73586 

9.86787 
.86789 
.86791 
.86793 

.73768 
.73772 
.73775 
.73778 

9.86900 
.86902 
.86904 
.86905 

.73960 
.73963 
.73967 
.73970 

+  9^ 

57 
S8 
39 

9.86453 
.86455 
.86457 
.86459 

.73203 
.73207 
.73310 
.73213 

9.86568 
.86569 
.86571 
.86573 

.73396 
.73400 
.73403 
.73406 

9.86681 
.86683 
.86685 
.86687 

.73589 
.73592 
.73595 
.73599 

9.86795 
.86796 
.86798 
.86800 

.73781 
.73784 

.73788 
.73791 

9.86907 
.86909 
.86911 
.86913 

.73973 
.73976 
.73979 
.73983 

+  W 

41 

42 
43 

9.86461 
.86463 
.86465 
.86467 

.73216 
.73220 
.73333 
.73326 

9.86575 
.86577 
.86579 
.86581 

.73409 
.73413 
.73416 
.73419 

9.86689 
.86691 
.86693 
.86695 

.73602 
.73605 
.73608 
.73611 

9.86802 
.86804 
.86806 
.86808 

.73794 
.73797 
.73800 
.73804 

9.86915 
.86917 
.86919 
.86920 

.73986 
.73989 
.73992 
.73995 

+  11^ 

45 
46 

47 

9.86468 
.86470 
.86472 
.86474 

.73339 
.73333 
.73336 
.73339 

9.86583 
.86585 
.86587 
.86588 

.73422 
.73425 
.73429 
.73432 

9.86696 
.86698 
.86700 
.86702 

.73615 
.73618 
.73621 
.73624 

9.86810 
.86812 
.86813 
.86815 

.73807 
.73810 
.73813 
.73816 

9.86922 
.86924 
.86926 
.86928 

.73998 
.74002 
.74005 
.74008 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 

2 
1 
0 

+  13' 

49 
50 
51 

9.86476 
.86478 
.86480 
.86482 

.73342 
.73245 

.73249 
.73253 

9.86590 
.86592 
.86594 
.86596 

.73435 
.73438 
.73441 
.73445 

9.86704 
.86706 
.86708 
.86710 

.73628 
.73631 
.73634 
.73637 

9.86817 
.86819 
.86821 
.86823 

.73820 
.73823 
.73826 
.73829 

9.86930 
.86932 
.86933 
.86935 

.74011 
.74014 
.74018 
.74021 

+  13' 

53 
54 
55 

9.86484 
.86486 
.86488 
.86489 

.73255 
.73258 
.73361 
.73265 

9.86598 
.86600 
.86602 
.86604 

.73448 
.73451 
.73454 
.73458 

9.86712 
.86713 
.86715 
.86717 

.73640 
.73644 
.73647 
.73650 

9.86825 
.86827 
.86828 
.86830 

.73832 
.73836 
.73839 
.73842 

9.86937 
.86939 
.86941 
.86943 

.74034 
.74037 
.74030 
.74033 

+  14' 

57 
58 
59 

9.86491 
.86493 
.86495 
.86497 

.73368 
.73371 
.73274 
.73278 

9.86606 
.86607 
.86609 
.86611 

.73461 
.73464 
.73467 
.73470 

9.86719 
.86721 
.86723 
.86725 

.73653 
.73656 
.73680 
.73663 

9.86832 
.86834 
.86836 
.86838 

.73845 

.73848 
.73853 
.73855 

9.86945 
.86947 
.86948 
.86950 

.74037 
.74040 
.74043 
.74046 

+   15' 

9.86499 

.73381 

9.86613 

.73474 

9.86727 

.73666 

9.86840 

.73858 

9.86952 

.74049 

lehgm 

lehgm 

i6A7'» 

i6h  em 

lehsm 

Page  906]                  TABLE  45. 

Haversines. 

s 

7h  55m  118°  45' 

7A  56m  119°  0'  | 

jh  57m  119°  15' 

7^  58m  119°  30' 

Ih  5om  119°  45' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 
1 
2 
3 

9.86952 
.86954 
.86956 
.86958 

.74049 
.74053 
.74056 
.74059 

9.87064 
.87066 
.87068 
.87070 ' 

.74340 
.74344 
.74247 
.74250 

9.87175 
.87177 
.87179 
.87181 

.74431 
.74434 
.74437 
.74441 

9.87286 
.87288 
.87290 
.87292 

.74621 
.74624 
.74628 
.74631 

9.87396 
.87398 
.87400 
.87402 

.74811 
.74814 
.74817 
.74820 

60 
59 
58 
57 

+    r 

5 
6 
7 

9.86960 
.86962 
.86963 
.86965 

.74063 
.74065 
.74069 
.74073 

9.87072 
.87073 
.87075 
.87077 

.74253 
.74356 
.74360 
.74263 

9.87183 
.87185 
.87187 
.87188 

.74444 
.74447 
.74450 
.74453 

9.87294 
.87295 
.87297 
.87299 

.74634 
.74637 
.74640 
.74643 

9.87404 
.87406 
.87407 
.87409 

.74823 

.74827 
.74830 
.74833 

66 
55 
54 
53 

+      2' 

9 
10 
11 

9.86967 
.86989 
.86971 
.86973 

.74075 
.74078 
.74081 
.74084 

9.87079 
.87081 
.87083 
.87085 

.74266 
.74269 
.74272 
.74275 

9.87190 
.87192 
.87194 
.87196 

.74456 
.74460 
.74463 
.74466 

9.87301 
.87303 
.87305 
.87306 

.74646 
.74650 
.74653 
.74656 

9.87411 
.87413 
.87415 
.87417 

.74836 
.74839 
.74843 
.74846 

62 
61 
50 
49 

+      3^ 

IS 
14 
15 

9.86975 
.86977 
.86978 
.86980 

.74088 
.74091 
.74094 
.74097 

9.87086 
.87088 
.87090 
.87092 

.74279 
.74283 
.74285 

.74288 

9.87198 
.87199 
.87201 
.87203 

.74469 
.74473 
.74475 
.74479 

9.87308 
.87310 
.87312 
.87314 

.74659 
.74662 
.74665 
.74669 

9.87418 
.87420 
.87422 
.87424 

.74849 
.74853 
.74855 

.74858 

48 
47 
46 
45 

+   4^ 
17 
18 
19 

9.86982 
.86984 
.86986 
.86988 

.74100 
.74104 
.74107 
.74110 

9.87094 
.87096 
.87098 
.87100 

.74291 
.74294 
.74298 
.74301 

9.87205 
.87207 
.87209 
.87211 

.74482 
.74485 

.74488 
.74491 

9.87316 
.87318 
.87319 
.87321 

.74673 
.74675 
.74678 
.74681 

9.87426 
.87428 
.87429 
.87431 

.74861 
.74864 
.74868 
74871 

44 
43 
42 
41 

+  ^ 
U 

22 
23 

9.86990 
.86991 
.86993 
.86995 

.74113 
.74116 
.74130 
.74133 

9.87101 
.87103 
.87105 
.87107 

.74304 
.74307 
.74310 
.74314 

9.87212 
.87214 
.87216 
.87218 

.74494 
.74498 
.74501 
.74504 

9.87323 
.87325 
.87327 
.87329 

.74684 

.74688 
.74691 
.74694 

9.87433 
.87435 
.87437 
.87439 

.74874 

.74877 
.74880 

.74883 

40 
39 
38 
37 

+   6' 

25 
26 
27 

9.86997 
.86999 
.87001 
.87003 

.74136 
.74139 
.74133 
.74135 

9.87109 
.87111 
.87112 
.87114 

.74317 
.74320 
.74323 
.74326 

9.87220 

.87222 
.87224 
.87225 

.74507 
.74510 
.74514 
.74517 

9.87330 
.87332 
.87334 
.87336 

.74697 
.74700 
.74703 
.74707 

9.87440 
.87442 
.87444 
.87446 

.74887 
.74890 
.74893 
.74896 

36 
35 
34 
S3 

+    r 

29 
SO 
31 

9.87004 
.87006 
.87008 
.87010 

.74139 
.74143 
.74145 
.74148 

9.87116 
.87118 
.87120 
.87122 

.74329 
.74333 
.74336 
.74339 

9.87227 
.87229 
.87231 
.87233 

.74520 
.74523 
.74526 
.74529 

9.87338 
.87340 
.87341 
.87343 

.74710 
.74713 
.74716 
.74719 

9.87448 
.87450 
.87451 
.8745S 

.74809 
.74902 
.74905 
.74908 

32 
31 
30 
29 

+   8^ 
33 
34 
35 

9.87012 
.87014 
.87016 
.87018 

.74151 
.74155 
.74158 
.74161 

9.87124 
.87125 
.87127 
.87129 

.74342 
.74345 
.74349 
.74352 

9.87235 
.87236 
.87238 
.87240 

.74533 
.74536 
.74539 
.74542 

9.87345 
.87347 
.87349 
.87351 

.74733 
.74726 
.74729 
.74732 

9.87455 
.87457 
.87459 
.87460 

.74912 
.74915 
.74918 
.74931 

28 
27 
26 

25 

+      9^ 

37 
38 
39 

9.87019 
.87021 
.87023 
.87025 

.74164 
.74167 
.74170 
.74174 

9.87131 
.87133 
.87135 
.87137 

.74355 
.74358 
.74361 
.74364 

9.87242 
.87244 
.87246 
.87248 

.74545 
.74548 
.74553 
.74555 

9.87352 
.87354 
.87356 
.87358 

.74735 
.74738 
.74741 
.74744 

9.87462 
.87464 
.87466 
.87468 

.74924 
.74928 
.74931 
.74934 

24 
23 
22 
21 

+  10^ 

41 
42 
43 

9.87027 
.87029 
.87031 
.87032 

.74177 
.74180 
.74183 
.74186 

9.87138 
.87140 
.87142 
.87144 

.74368 
.74371 
.74374 
.74377 

9.87249 
.87251 
.87253 
.87255 

.74558 
.74561 
.74564 
.74567 

9.87360 
.87362 
.87363 
.87365 

.74748 
.74751 
.74754 
.74757 

9.87470 
.87471 
.87473 
.87475 

.74937 
.74940 
.74943 
.74946 

20 
19 
18 
17 

+  11^ 

45 
46 
47 

9.87034 
.87036 
.87038 
.87040 

.74190 
.74193 
.74196 
.74199 

9.87146 
.87148 
.87149 
.87151 

.74380 
.74383 
.74387 
.74390 

9.87257 
.87259 
.87260 
.87262 

.74571 
.74574 
.74577 
.74580 

9.87367 
.87369 
.87371 
.87373 

.74760 
.74763 
.74767 
.74770 

9.87477 
.87479 
.87481 
.87482 

.74950 
.74953 
.74956 
.74959 

16 
16 
14 
IS 
12 
11 
10 
9 

+  n' 

49 
50 
51 

9.87042 
.87044 
.87045 
.87047 

.74302 
.74305 
.74309 
.74313 

9.87153 
.87155 
.87157 
.87159 

.74393 
.74396 
.74399 
.74402 

9.87264 
.87266 
.87268 
.87270 

.74583 
.74586 
.74590 
.74593 

9.87374 
.87376 
.87378 
.87380 

.74773 
.74776 
.74779 

.74783 

9.87484 
.87486 
.87488 
.87490 

.74963 
.74965 
.74969 
.74973 

+  13^ 

53 

54 
55 

9.87049 
.87051 
.87053 
.87055 

9.87057 
.87059 
.87060 
.87062 

.74215 
.74318 
.74331 
.74225 

9.87161 
.87162 
.87164 
.87166 

.74406 
.74409 
.74413 
.74415 

9.87271 
.87273 
.87275 
.87277 

.74596 
.74599 
.74603 
.74605 

9.87382 
.87384 
.87385 
.87387 

.74786 
.74789 
.74793 
.74795 

9.87492 
.87493 
.87495 
.87497 

.74975 
.74978 
.74981 
.74984 

8 
7 

e 

5 

4 
3 
2 
1 

+  W 

57 
58 
59 

.74328 
.74231 
.74234 
.74237 

9.87168 
.87170 
.87172 
.87174 

.74418 
.74422 
.74425 
.74428 

9.87279 
.87281 
.87283 
.87284 

.74609 
.74612 
.74615 
.74618 

9.87389 
.87391 
.87393 
.87395 

.74798 
.74801 
.74805 
.74808 

9.87499 
.87501 
.87502 
.87504 

.74987 
.74991 
.74994 
.74997 

+    16^ 

9.87064 

.74240 

9.87175 

.74431 

9.87286 

.74621 

9.87396 

.74811 

9.87506 

.75000 

0 

lehpn. 

lehsm 

16^2^ 

U^lrn. 

lehom 

TABLE  45.                  [Page  907 

Haversines. 

s   ' 

8%  om  120°  r 

S'*^  120°  30^  1 

8h  4m  121°  r 

8h  em  121°  SO"   1 

5ft  8m  122°  r 

3 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.87506 

0.75000 

9.87724 

0.75377 

9.87939 

0.75752 

9.88153 

0.76125 

9.88364 

0.76496 

60 

2 

.87510 

.75006 

.87727 

.75383 

.87943 

.75758 

.88156 

.76131 

.88367 

.76502 

58 

4+   1 

.87513 

.75013 

.87731 

.75389 

.87947 

.75764 

.88160 

.76137 

.88371 

.76508 

56 

6 

.87517 

.75019 

.87735 

.75396 

.87950 

.75771 

.88163 

.76144 

.88374 

.76514 

54 

8+   3 

9.87521 

0.75025 

9.87738 

0.75402 

9.87954 

0.75777 

9.88167 

0.76150 

9.88378 

0.76521 

52 

10 

.87524 

.75032 

.87742 

.75408 

.87957 

.75783 

.88170 

.76156 

.88381 

.76527 

50 

12+   3 

.87528 

.75038 

.87745 

.75415 

.87961 

.75789 

.88174 

.76162 

.88385 

.76533 

48 

U 

.87532 

.75044 

.87749 

.75421 

.87964 

.75795 

.88177 

.76168 

.88388 

.76539 

46 

16+   4 

9.87535 

0.75050 

9.87753 

0.75427 

9.87968 

0.75802 

9.88181 

0.76175 

9.88392 

0.76545 

44 

18 

.87539 

.75057 

.87756 

.75433 

.87971 

.75808 

.88185 

.76181 

.88395 

.76551 

42 

20+   5 

.87543 

.75063 

.87760 

.75440 

.87975 

.75814 

.88188 

.76187 

.88399 

.76558 

40 

gf 

.87546 

.75069 

.87764 

.75446 

.87979 

.75820 

.88192 

.76193 

.88402 

.76564 

38 

24+   6 

9.87550 

0.75075 

9.87767 

0.75452 

9.87982 

0.75827 

9.88195 

0.76199 

9.88406 

0.76570 

36 

^6 

.87553 

.75082 

.87771 

.75458 

.87986 

.75833 

.88199 

.76205 

.88409 

.76576 

34 

;g5+  7 

.87557 

.75088 

.87774 

.75465 

.87989 

.75839 

.88202 

.76212 

.88413 

.76582 

32 

30 

.87561 

.75094 

.87778 

.75471 

.87993 

.75845 

.88206 

.76218 

.88416 

.76588 

SO 

32+   8 

9.87564 

0.75101 

9.87782 

0.75477 

9.87996 

0.75852 

9.88209 

0.76224 

9.88420 

0.76595 

28 

34 

.87568 

.75107 

.87785 

.75483 

.88000 

.75858 

.88213 

.76230 

.88423 

.76601 

26 

36+   9 

.87572 

.75113 

.87789 

.75490 

.88004 

.75864 

.88216 

.76236 

.88427 

.76607 

24 

5<§ 

.87575 

.75120 

.87792 

.75496 

.88007 
9.88011 

.75870 
0.75876 

.88220 
9.88223 

.76243 
0.76249 

.88430 
9.88434 

.76613 
0.76(il9 

22 
20 

40+10 

9.87579 

0.75126 

9.87796 

0.75502 

4^ 

.87583 

.75132 

.87800 

.75508 

.88014 

.75883 

.88227 

.76255 

.88437 

.76625 

18 

i*+ll 

.87586 

.75138 

.87803 

.75515 

.88018 

.75889 

.88230 

.76261 

.88441 

.76632 

16 

46 

.87590 

.75145 

.87807 

.75521 

.88021 

.75895 

.88234 

.76267 

.88444 

.76638 

14 

48+12 

9.87593 

0.75151 

9.87810 

0.75527 

9.88025 

0.75901 

9.88237 

0.76274 

9.88448 

0.76644 

12 

50 

.87597 

.75157 

.87814 

.75533 

.88029 

.75908 

.88241 

.76280 

.88451 

.76650 

10 

5.2+13 

.87601 

.75164 

.87818 

.75540 

.88032 

.75914 

.88244 

.76286 

.88455 

.76656 

8 

64 

.87604 

.75170 

.87821 

.75546 

.88036 

.75920 

.88248 

.76292 

.88458 

.76662 

6 

56+U 

9.87608 

0.75176 

9.87825 

0.75552 

9.88039 

0.75926 

9.88252 

0.76298 

9.88462 

0.76668 

4 

58 

9.87612 

0.75182 

9.87828 

0.75558 

9.88043 

0.75932 

9.88255 

0.76305 

9.88465 

0.76675 

2 

15h  59m 

15h  57m 

15h  55m 

15h  53m 

15^  5im 

s   ' 
0+15 

8h  im  120°  0" 

8A  3"»  120°  30' 

8h  5m  121°  (y 

8h  im  121°  30^ 

Sh  gm  122°  O' 

s 
60 

9.87615 

0.75189 

9.87832 

0.75565 

9.88046 

0.75939 

9.88259 

0.76311 

9.88469 

0.76681 

2 

.87619 

.75195 

.87835 

.75571 

.88050 

.75945 

.88262 

.76317 

.88472 

.76687 

58 

4+16 

.87623 

.75201 

.87839 

.75577 

.88053 

.75951 

.88266 

.76323 

.88476 

.76693 

56 

6 

.87626 

.75208 

.87843 

.75583 

.88057 

.75957 

.88269 

.76329 

.88479 

.76699 

54 
52 

8+11 

9.87630 

0.75214 

9.87846 

0.75590 

9.88061 

0.75964 

9.88273 

0.76335 

9.88483 

0.76705 

10 

.87633 

.75220 

.87850 

.75596 

.88064 

.75970 

.88276 

.76342 

.88486 

.76711 

50 

if+18 

.87637 

.75226 

.87853 

.75602 

.88068 

.75976 

.88280 

.76348 

.88490 

.76718 

48 

14 

.87641 

.75233 

.87857 

.75608 

.88071 

.75982 

.88283 

.76354 

.88493 

.76724 

46 

16+19 

9.87644 

0.75239 

9.87861 

0.75615 

9.88075 

0.75988 

9.88287 

0.76360 

9.88496 

0.76730 

44 

18 

.87648. 

.75245 

.87864 

.75621 

.88078 

.75995 

.88290 

.76366 

.88500 

.76736 

42 

^0+30 

.87652 

.75251 

.87868 

.75627 

.88082 

.76001 

.88294 

.76373 

.88503 

.76742 

40 

22 

.87655 

.75258 

.87871 

.75633 

.88085 

.76007 

.88297 

.76379 

.88507 

.76748 

38 
36 

24+21 

9.87659 

0.75264 

9.87875 

0.75640 

9.88089 

0.76013 

9.88301 

0.76385 

9.88510 

0.76754 

26 

.87662 

.75270 

.87879 

.75646 

.88092 

.76019 

.88304 

.76391 

.88514 

.76761 

34 

28+22 

.87666 

.75277 

.87882 

.75652 

.88096 

.76026 

.88308 

.76397 

.88517 

.76767 

32 

SO 

.87670 

.75283 

.87886 

.75658 

.88100 

.76032 

.88311 

.76403 

.88521 

.76773 

30 

32+2S 

9.87673 

0.75289 

9.87889 

0.75665 

9.88103 

0.76038 

9.88315 

0.76410 

9.88524 

0.76779 

28 

34 

.87677 

.75295 

.87893 

.75671 

.88107 

.76044 

.88318 

.76416 

.88528 

.76785 

26 

36+2^: 

.87680 

.75302 

.87896 

.75677 

.88110 

.76050 

.88322 

.76422 

.88531 

.76791 

24 

38 

.87684 

.75308 

.87900 

.75683 

.88114 

.76057 

.88325 

.76428 

.88535 

.76V97 

22 
20 

40+25 

9.87688 

0.75314 

9.87904 

0.75690 

9.88117 

0.76063 

9.88329 

0.78434 

9.88528 

0.76804 

42 

.87691 

.75321 

.87907 

.75696 

.88121 

.76069 

.88332 

.76440 

.88542 

.76810 

18 

44+26 

.87695 

.75327 

.87911 

.75702 

.88124 

.76075 

.88336 

.76447 

.88545 

.76816 

16 

46 

.87699 

.75333 

.87914 

.75708 

.88128 

.76082 

.88339 

.76453 

.88549 

.76823 

14 

48+21 

9.87702 

0.75339 

9.87918 

0.75714 

9.88131 

0.76088 

9.88343 

0.76459 

9.88552 

0.76828 

12 

50 

.87706 

.75346 

.87921 

.75721 

.88135 

.76094 

.88346 

.76465 

.88556 

.76834 

10 

5^+28 

.87709 

.75352 

.87925 

.75727 

.88139 

.76100 

.88350 

.76471 

.88559 

.76840 

8 

54 

.87713 

.75358 

.87929 

.75733 

.88142 

.76106 

.88353 

.76477 

.88562 

.76847 

6 

56+29 

9.87717 

0.75364 

9.87932 

0.75739 

9.88146 

0.76113 

9.88357 

0.76484 

9.88566 

0.76853 

4 

58 

.87720 

.75371 

.87936 

.75746 

.88149 

.76119 

.88360 

.76490 

.88569 

.76859 

2 

60+30 

9.87724 

0.75377 

9.87939 

0.75752 

9.88153 

0.76125 

9.88364 

0.76496 

9.88573 

0.76865 

0 

15^  58m 

15h  56^ 

15h  54m 

15T^52:m 

15^  5m 

21594°— 14 50 


Page  908]                  TABLE  45.                         | 

Haversines,                                1 

s    ' 

8^  lOm  133°  30^ 

8hl2mn3°(i'    1 

8h  14^  123°  30^ 

gn  16m  124°  0' 

8h  18m  124°  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Ilav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.88573 

0.76865 

9.88780 

0.77232 

9.88984 

0.77597 

9.89187 

0.77960 

9.89387 

0.78320 

60 

2 

.88576 

.76871 

.88783 

.77238 

.88988 

.77603 

.89190 

.77966 

.89391 

.78326 

68 

4+   1 

.88580 

.76877 

.88787 

.77244 

.88991 

.77609 

.89194 

.77972 

.89394 

.78332 

56 

6 

.88583 

.76883 

.88790 

.77250 

.88995 

.77615 

.89197 

.77978 

.89397 

.78338 

54 

8-\-  2 

9.88587 

0.76890 

9.88793 

0.77256 

9.88998 

0.77621 

9.89200 

0.77984 

9.89400 

0.78344 

62 

10 

.88590 

.76896 

.88797 

.77263 

.89001 

.77627 

.89204 

.77990 

.89404 

.78350 

60 

12-\-   3 

.88594 

.76903 

.88800 

.77369 

.89005 

.77633 

.89207 

.77996 

.89407 

.78356 

48 

U 

.88597 

.76908 

.88804 

.77275 

.89008 

.77639 

.89210 

.78003 

.89411 

.78362 

46 

16+  4 

9.88600 

0.76914 

9.88807 

0.77381 

9.89012 

0.77645 

9.89214 

0.78008 

9.89414 

0.78368 

44 

18 

.88604 

.76920 

.88811 

.77387 

.89015 

.77651 

.89217 

.78014 

.89417 

.78374 

42 

20+   5 

.88607 

.76926 

.88814 

.77293 

.89018 

.77657 

.89221 

.78020 

.89421 

.78380 

40 

22 

.88611 

.76933 

.88817 

.77299 

.89022 

.77664 

.89224 

.78036 

.89424 

.78386 
0.78392 

38 
36 

24+   6 

9.88614 

.076939 

9.88821 

0.77305 

9.89025 

0.77670 

9.89227 

0.78033 

9.89427 

26 

.88618 

.76945 

.88824 

.77311 

.89028 

.77676 

.89231 

.78038 

.89431 

.78398 

34 

£8+   7 

.88621 

.76951 

.88828 

.77317 

.89032 

.77682 

.89234 

.78044 

.89434 

.78404 

32 

SO 

.88625 

.76957 

.88831 

.77333 

.89035 

.77688 

.89237 

.78050 

.89437 

.78410 

SO 

32+   8 

9.88628 

0.76963 

9.88835 

0.77329 

9.89039 

0.77694 

9.89241 

0.78056 

9.89441 

0.78416 

28 

34 

.88632 

.76969 

.88838 

.77336 

.89042 

.77700 

.89244 

.78063 

.89444 

.78422 

26 

36+   9 

.88635 

.76975 

.88841 

.77342 

.89045 

.77706 

.89247 

.78068 

.89447 

.78428 

24 

38 

.88639 

.76981 

.88845 

.77348 

.89049 

.77712 

.89251 

.78074 

.89450 
9.89454 

.78434 

22 

40+19 

9.88642 

0.76988 

.9.88848 

0.77354 

9.89052 

0.77718 

9.89254 

0.78080 

0.78440 

20 

42 

.88645 

.76994 

.88852 

.77360 

.89056 

.77724 

.89257 

.78086 

.89457 

.78446 

18 

44+n 

.88649 

.77000 

.88855 

.77366 

.89059 

.77730 

.89261 

.78093 

.89460 

.78452 

16 

46 

.88652 

.77006 

.88858 

.77372 

.89062 

.77736 

.89264 

.78098 

.89464 

.78458 

14 

48+12 

9.88656 

0.77012 

9.88862 

0.77378 

9.89066 

0.77742 

9.89267 

0.78104 

9.89467 

0.78464 

12 

SO 

.88659 

.77018 

.88865 

.77384 

.89069 

.77748 

.89271 

.78110 

.89470 

.78470 

10 

62+lZ 

.88663 

.77034 

.88869 

.77390 

.89072 

.77754 

.89274 

.78116 

.89474 

.78476 

8 

54 

.88666 

.77030 
0.77036 

.88872 

.77396 

.89076 
9.89079 

.77760 

.89277 

.78133 

.89477 

.78482 
0.78488 

6 
4 

66+U 

9.88670 

9.88876 

0.77403 

0.77766 

9.89281 

0.78138 

9.89480 

68 

9.88673 

0.77043 

9.88879 

0.77409 

9.89083 

0.77772 

9.89284 

0.78134 

.9.89484 

0.78494 

2 

15h  49m 

15^  4Tm 

15^  45m 

15^  43m 

15h  41m 

B        ' 

0+15 

8h  llm  132°  W 

8h  ism  123°  (K 

8h  15m  133°  30^ 

8h  17m  124°  O' 

8h  19m  124°  30^ 

6 

9.88677 

0.77049 

9.88882 

0.77415 

9.89086 

0.77779 

9.89287 

0.78140 

9.89487 

0.78500 

60 

2 

.88680 

.77055 

.88886 

.77412 

.89089 

.77785 

.89291 

.78146 

.89490 

.78506 

58 

4+16 

.88683 

.77061 

.88889 

.77427 

.89093 

.77791 

.89294 

.78153 

.89493 

.78512 

56 

6 

.88687 

.77067 

.88893 

.77433 

.89096 
9.89099 

.77797 

.89298 

.78158 
0.78164 

.89497 

,78518 

54 

8+11 

9.88690 

0.77073 

9.88896 

0.77439 

0.77803 

9.89301 

9.89500 

0.78524 

52 

10 

.88694 

.77079 

.88899 

.77445 

.89102 

.77809 

.89304 

.78170 

.89503 

.78530 

50 

12+1'i 

.88697 

.77085 

.88903 

.77451 

.89106 

.77815 

.89308 

.78176 

.89507 

.78536 

48 

14 

.88701 

.77093 

.88906 

.77457 

.89110 

.77821 

.89311 

.78183 

.89510 

.78542 

46 

16+n 

9.88704 

0.77098 

9.88910 

0.77463 

9.89113 

0.77827 

9.89314 

0.78188 

9.89513 

0.78548 

44 

18 

.88708 

.77104 

.88913 

.77469 

.89116 

.77833 

.89318 

.78194 

.89517 

.78554 

42 

£0+30 

.88711 

.77110 

.88916 

.77475 

.89120 

.77839 

.89321 

.78200 

.89520 

.78560 

40 

22 

.88714 

.77116 

.88920 

.77483 

.89123 

.77845 

.89324 

.78206 

.89523 

.78566 

38 

24+21 

9.88718 

0.77133 

9.88923 

0.77488 

9.89126 

0.77851 

9.89328 

0.78212 

9.89527 

0.78572 

36 

26 

.88721 

.77138 

.88927 

.77494 

.89130 

.77857 

.89331 

.78218 

.89530 

.78577 

34 

28+22 

.88725 

.77134 

.88930 

.77500 

.89133 

.77863 

.89334 

.78224 

.89533 

.78583 

32 

SO 

.88728 

.77140 

.88933 

.77506 

.89137 

.77869 

.89338 

.78230 

.89536 

.78589 

30 

32+23 

9.88732 

0.77147 

9.88937 

0.77512 

9.89140 

0.77875 

9.89341 

0.78336 

9.89540 

0.78595 

28 

34 

.88735 

.77153 

.88940 

.77518 

.89143 

.77881 

.89344 

.78343 

.89543 

.78601 

26 

36+24: 

.88739 

.77159 

.88944 

.77524 

.89147 

.77887 

.89348 

.78248 

.8S546 

.78607 

24 

38 

.88742 

.77165 

.88947 

.77530 

.89150 

.77893 
0.77899 

.89351 

.78254 

.89550 

.78613 
0.78619 

22    - 
20m 

40+25 

9.88745 

0.77171 

9.88950 

0.77536 

9.89153 

9.89354 

0.78260 

9.89553 

42 

.88749 

.77177 

.88954 

.77542 

.89157 

.77905 

.89358 

.78366 

.89556 

.78625 

ism 

44+2% 

.88752 

.77183 

.88957 

.77548 

.89160 

.77911 

.89361 

.78373 

.89559 

.78531 

16m 

46 

.88756 

.77189 

.88961 

.77554 

.89163 

.77917 

.89364 

.78378 

.89563 

.78637 

uM 

48+21 

9.88759 

0.77195 

9.88964 

0.77560 

9.89167 

0.77923 

9.89368 

0.78384 

9.89566 

0.78643 

12  m 

50 

.88763 

.77301 

.88967 

.77567 

.89170 

.77939 

.89371 

.78390 

.89569 

.78649 

lom 

52 +2% 

.88766 

.77208 

.88971 

.77573 

.89174 

.77936 

.89374 

.78396 

.89573 

.78655 

8  ■ 

54 

.88769 

.77314 

.88974 

.77579 

.89177 

.77942 

.89378 

.78303 
0.78308 

.89576 
9.89579" 

.78661 
0.78667 

6 
4 

56+219 

9.88773 

0.77220 

9.88978 

0.77585 

9.89180  i  0.77948 

9.89381 

58 

.88776 

.77226 

.88981 

.77591 

.89184  !  .77954 

.89384 

.78314 

.89583 

.78673 

2 

60+30 

9.88780 

0.77232 

9.88984 

0.77597 

9.89187  0.77960 

9.89387 

0.78320 

9.89586 

0.78679 

'i| 

15^48m 

15h  46^ 

15^44^ 

15h42m 

15h  40m 

J 

TABLE  45.                 [Page  909 

Haversines. 

.  s 

8^  20m  125°  O' 

8^  22m  125°  30' 

8h  24m  126°  0' 

8h  26m  136°  30' 

Sh  28m  127°  (/ 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.89586 

0.78679 

9.89782 

0.79035 

9.89976 

0.79389 

9.90168 

0.79741 

9.90358 

0.80091 

60 

2 

.89589 

.78685 

.89785 

.79041 

.89979 

.79395 

.90171 

.79747 

.90361 

.80097 

58 

4+   1 

.89592 

.78691 

.89789 

.79047 

.89983 

.79401 

.90175 

.79753 

.90365 

.80102 

56 

6 

.89596 

.78697 
0.78703 

.89792 
9.89795 

.79053 

.89986 

.79407 

.90178 

.79759 
0.79765 

.90368 

.80108 
0.80114 

54 
52 

5+  2 

9.89599 

0.79059 

9.89989 

0.79413 

9.90181 

9.90371 

10 

.89602 

.78709 

.89798 

.79065 

.89992 

.79419 

.90184 

.79770 

.90374 

.80120 

50 

12+   3 

.89606 

.78715 

.89802 

.79071 

.89995 

.79425 

.90187 

.79776 

.90377 

.80126 

48 

J4 

.89609 

.78721 

.89805 

.79077 

.89999 

.79430 

.90191 

.79782 

.90380 

.80131 

46 

i6+  4 

9.89612 

0.78726 

9.89808 

0.79082 

9.90002 

0.79436 

9.90194 

0.79788 

9.90383 

0.80137 

44 

25   ■= 

.89615 

.78732 

.89811 

.79088 

.90005 

.79442 

.90197 

.79794 

.90387 

.80143 

42 

fO+  5 

.89619 

.78738 

.89815 

.79094 

.90008 

.79448 

.90200 

.78800 

.90390 

.80149 

40 

22       - 

.89622 

.78744 

.89818 
9.89821 

.79100 
0.79106 

.90012 

.79454 

.90203 

.79805 

.90393 

.80155 
0.80160 

38 
36 

^4+  6 

9.89625 

0.78750 

9.90015 

0.79460 

9.90206 

0.79811 

9.90396 

f6  •". . 

.89628 

.78756 

.89824 

.79112 

.90018 

.79466 

.90210 

.79817 

.90399 

.80166 

34 

28+   7 

.89632 

.78762 

.89828 

.79118 

.90021 

.79471 

.90213 

.79823 

.90402 

.80172 

32 

50  :: 

.89635 

.78768 

.89831 

.79124 

.90024 

.79477 

.90216 

.79829 

.90405 

.80178 

SO 

S2+   8 

9.89638 

0.78774 

9.89834 

0.79130 

9.90028 

0.79483 

9.90219 

0.79835 

9.90409 

0.80184 

28 

5^  ::> 

.89642 

.78780 

.89837 

.79136 

.90031 

.79489 

.90222 

.79840 

.90412 

.80189 

26 

56+  9 

,89645 

.78786 

.89840 

.79142 

.90034 

.79495 

.90225 

.70846 

.90415 

.80195 

24 

S8    "  ■> 

.89648 

.78793 

.89844 

.79148 

.90037 

.79501 

.90229 

.79852 
0.79858 

.90418 

.80201 
0.80207 

22 
20 

^+10 

9.89651 

0.78798 

9.89847 

0.79153 

9.90040 

0.79507 

9.90232 

9.90421 

42 

.89655 

.78804 

.89850 

.79159 

.90044 

.79513 

.90235 

.79864 

.90425 

.80213 

18 

^+11 

.89658 

.78810 

.89853 

.79165 

.90047 

.79519 

.90238 

.79870 

.90428 

.80218 

16 

46 

.89661 

.78816 

.89857 

.79171 

.90050 

.79524 

.90241 

.79875 

.90431 

.80224 

14 

48+1% 

9.89665 

0.78822 

9.89860 

0.79177 

9.90053 

0.79530 

9.90244 

0.79881 

9.90434 

0.80230 

12 

50 

.89668 

.78828 

.89863 

.79183 

.90056 

.79536 

.90248 

.79887 

.90437 

.80236 

10 

62+13 

.89671 

.78834 

.89866 

.79189 

.90060 

.79542 

.90251 

.79899 

.90440 

.80242 

8 

54 

.89674 

.78839 

.89870 

.79195 

.90063 

.79548 
0.79554 

.90254 
9.90257 

.79893 
0.79905 

.90443 

.80247 

6 
4 

56+U 

9.89678 

0.78845 

9.89873 

0.79201 

9.90066 

9.90446 

0.80253 

58 

9.89681  0.78851 

9.89876 

0.79207 

9.90069 

0.79560 

9.90260 

0.79910 

.9.90449 

0.80259 

2 

15A  39m 

15^37^ 

15^  S5m 

15h  SSm 

15h  Sim 

B    -f 
0+15 

8h  21m  125°  0^ 

8h  23m  125°  30^ 

8h  25m  126°  0" 

8h  27m  126°  30^ 

Sh  29m  127°  r 

B 

60 

9.89684 

0.78857 

9.88879  :  0.79212 

.9.90072 

0.79565 

9.90264 

0.79916 

9.90452 

0.80265 

2 

.89687 

.78863 

.89883  i  .79218 

.90076 

.79571 

.90267 

.79922 

.90456 

.80270 

58 

^+16 

.89691 

.78869 

.89886  i  .79224 

.90079 

.79577 

.90270 

.79928 

.90459 

.80276 

56 

6 

.89694 

.78875 

.89889  1  .79230 
9.89892  0.79236 

.90082 

.79583 

.90273 

.79934 

.90462 

.80282 

54 

8+n 

9.89697 

0.78881 

9.90085 

0.79589 

9.90276 

0.79940 

9.90465 

0.80288 

52 

10 

.89701 

.78887 

.89896 

.79242 

.90088 

.79595 

.90279 

.79945 

.90468 

.80294 

50 

12+lS 

.89704 

.78893 

.89899 

.79248 

.90092 

.79601 

.90282 

.79951 

.90471 

.80299 

48 

14 

.89707 

.78899 

.89902 

.79254 

.90095 

.79607 

.90286 

.79957 

.90475 

.80305 

46 

16+19 

9.89710 

0.78905 

9.89905 

0.79260 

9.90098 

0.79612 

9.90289 

0.79963 

9.90478 

0.80311 

44 

18 

.89714 

.78911 

.89908 

.79266 

.90101 

.79618 

.90292 

.79969 

.90481 

.80317 

42 

20+20 

.89717 

.78917 

.89912 

.79271 

.90104 

.79624 

.90295 

.79974 

.90484 

.80323 

40 

22 

.89720 

.78923 

.89915 

.79277 

.90108 

.79630 

.90298 

.79980 

.90487 

.80328 
0.80334 

38 
36 

24+21 

9.89723 

0.78328 

9.89918 

0.79283 

9.90111 

0.79636 

9.90301 

0.79986 

9.90490 

26 

.89727 

.78934 

.89921 

.79289 

.90114 

.79642 

.90305 

.79992 

.90493 

.80340 

34 

28+Zi 

.89730   .78940 

.89925 

.79295 

.90117 

.79648 

.90308 

.79998 

.90496 

.80346 

32 

SO 

.89733 

.78946 

.89928 

.79301 

.90120 

.79653 

.90311 

.80004 

.90499 

.80351 

30 

5^+23 

9.89736 

0.78952 

9.89931 

0.79307 

9.90124 

0.79659 

9.90314 

0.80009 

9.90503 

0.80357 

28 

S4 

.89740 

.78958 

.89934 

.79313 

.90127 

.79665 

.90317 

.80015 

.90506 

.80363 

26 

S6+U 

.89743 

.78364 

.89938 

.79319 

.90130 

.79671 

.90320 

.80021 

.90509 

.80369 

24 

S8 

.89746 

.78970 
0.78976 

.89941 

.79325 

.90133 

.79677 

.90324 

.80027 
0.80033 

.90512 
.990515 

.80375 
0.80380 

22 
20 

40+15 

9.89749 

9.89944 

0.79330 

9.90136 

0.79683 

9.90327 

42 

.89753 

.78982 

.89947 

.79336 

.90140 

.79688 

.90330 

.80038 

.90518 

.80386 

18 

4^+26 

.89756 

.78988 

.89950 

.79342 

.90143 

.79694 

.90333 

.80044 

.90521 

.80392 

16 

46 

.89759 

.78994 

.89954 

.79348 

.90146 

.79700 

.90336 

.80050 

.90524 

.80398 

14 

48+21 

9.89763 

0.79000 

.9.89957 

0.79354 

9.90149 

•0.79706 

9.90339 

0.80056 

9.90527 

0.80403 

12 

50 

.89766 

.79006 

.89960 

.79360 

.90152 

.79712 

.90342 

.80062 

.90531 

.80409 

10 

52+2S 

.89769 

.79911 

.89963 

.79366 

.90356 

.79718 

.90346 

.80068 

.90534 

.80415 

8 

54 

.89772 

.79017 

.89966 
9.89970 

.79372 

.90159 

.79724 
0.79729 

.90349 

.80073 

.90537 

.80421 

6 
4 

56+29 

9.89776 

0.79023 

0.79377 

9.90162 

9.90352 

0.80079 

9.90540 

0.80427 

58 

.89779 

.79029 

.89973 

.79383 

.90165 

.79735 

.90355 

.80085 

.90543 

.80432 

2 

60+30 

9.89782 

0.79035 

9.89976 

0.79389 

9.90168 

0.79741 

9.90358 

0.80091 

9.90546 

0.80438 

0 

15^  38m 

15^  36m 

15A  34m 

15fi  32m 

15hS0m 

Page  910]                  TABLE  45.                         | 

Haversines.                                1 

s 

8h  som  127°  30' 

8^1  3'2m  128°  0' 

gn  34m  128°  30^ 

8h  36m  129°  0' 

8h  38m  129°  30' 

s 

Log.  Ilav.i  Nat.  Ilav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.|  Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

0      0 

9.90546  0.80438 

9.90732 

0.80783 

9.90916 

0.81126 

9.91098 

0.81466 

9.91277  0.81804 

60 

^ 

.90549  1  .80444 

.90735 

.80789 

.90919 

.81131 

.91101 

.81473 

.91280!  .81810 

58 

4+  1 

.90552 

.80450 

.90738 

.80795 

.90922 

.81137 

.91104 

.81477 

.91283 

.81815 

56 

6 

.90556 

.80455 

.90741 

.80800 

.90925 

.81143 

.91107 

.81483 

.91286 

.81831 

54 

8+  2 

9.90559 

0.80461 

9.90744 

0.90806 

9.90928 

0.81148 

9.91110 

0.81489 

9.91289 

0.81836 

52 

10 

.90562 

.80467 

.90747 

.80812 

.90931 

.81154 

.91113 

.81494 

.91292 

.81833 

50 

12^   3 

.90565 

.80473 

.90751 

.80817 

.90934 

.81160 

.91116 

.81500 

.91295 

.81838 

48 

U 

.90568 

.80478 

.90754 

.80823 

.90937 

.81165 

.91119 

.81506 

.91298 

.81843 

46 

16-\-   4 

9.90571 

0.80484 

9.90757 

0.80829 

9.90940 

0.81171 

9.91122 

0.81511 

9.91301 

6.81849 

U 

18 

.90574 

.80490 

.90760 

.80835 

.90943 

.81177 

.91125 

.81517 

.91304 

.81854 

42 

20-\-   5 

.90577 

.80496 

.90763 

.80840 

.90946 

.81183 

.91128 

.81533 

.91307 

.81860 

40 

22 

.90580 

.80503 

.90766 

.80846 

.90949 

.81188 

.91131 

.81538 

.91310 

.81866 
0.81871 

38 
36 

24+   6 

9.90584 

0.80507 

9.90769 

0.80852 

9.90952 

0.81194 

9.91134 

0.81534 

9.91313 

26 

.90587 

.80513 

.90772 

.80858 

.90955 

.81300 

.91137 

.81539 

.91316 

.81877 

34 

28+   7 

.90590 

.80519 

.90775 

.80863 

.90958 

.81205 

.91140 

.81545 

.91319 

.81883 

32 

^0 

.90593 

.80525 

.90778 

.80869 

.90962 

.81211 

.91143  1  .81551 

.91322 

.81888 

30 

32+   8 

9.90596 

0.80530 

9.90781 

0.80875 

9.90965 

0.81217 

9.91146  0.81556 

9.91325 

0.81894 

28 

5-^ 

.90599 

.80536 

.90784 

.80880 

.90968 

.81222 

.91149   .81563 

.91328 

.81899 

26 

56+  9 

.90602 

.80542 

.90787 

.80886 

.90971 

.81228 

.91152   .81568 

.91331 

.81905 

24 

38 

.90605 

.80548 

.90790 

.80892 
0.80898 

.90974 

.81234 

.91155   .81573 

.91334 

.81910 

22 

40+10 

9.90608 

0.80553 

9.90794 

9.90977 

0.81239 

9.91158 

0.81579 

9.91337 

0.81916 

20 

42 

.90611 

.80559 

.90797 

.80903 

.90980 

.81245 

.91161 

.81585 

.91340 

.81933 

18 

U+11 

.90615 

.80565 

.90800 

.80909 

.90983 

.81251 

.91164 

.81590 

.91343 

.81937 

16 

46 

.90618 

.80571 

.90803 

.80915 

.90986 

.81356 

.91167 

.81596 

.91346 

.81933 

14 

48+12 

9.90621 

0.80576 

9.90806 

0.80920 

9.90989 

0.81363 

9.91170 

0.81601 

9.91349 

0.81938 

12 

50 

.90624 

.80582 

.90809 

.80926 

.90992 

.81268 

.91173   .81607 

.91352 

.81944 

10 

52+13 

.90627 

.80588 

.90812 

.80932 

.90995 

.81273 

.91176   .81613 

.91355 

.81950 

8 

54 

.90630 

.80594 

.90815 

.80938 

.90998 

.81279 

.91179 

.81618 

.91358 

.81955 

6 

56+14 

9.90633 

0.80599 

9.90818 

0.80943 

9.91001 

0.81285 

9.91182 

0.81634 

9.91361 

0.81961 

4 

58 

9.90636 

0.80605 

9.90821 

0.80949 

9.91004 

0.81291 

9.91185 

0.81630 

9.91364 

0.81966 

2 

15h  29m 

15h  27m 

15h  25m 

15^  23m 

15h  21-m 

s   ' 
0+16 

8^31^127°  SO' 

Sh  33m  128°  0^ 

8h  35m  128°  30^ 

8h  37m  129°  0" 

8h  39m  129°  30^ 

s 
60 

9.90639 

0.80611 

9.90824 

0.80955 

9.91007 

0.81296 

9.91188 

0.81635 

9.91367 

0.81973 

Jg 

.90642 

.80617 

.90827 

.80960 

.91010 

.81302 

.91191 

.81641 

.91369 

.81978 

58 

4+16 

.90646 

.80622 

.90830 

.80966 

.91013 

.81308 

.91194 

.81647 

.91372 

.81983 

56 

6 

.90646 

.80628 

.90833 

.80972 

.91016 

.81313 

.91197 

.81653 

.91375 

.81989 
0.81994 

54 
52 

8+n 

9.90652 

0.80634 

9.90836 

0.80978 

9.91019 

0.81319 

9.91200 

0.81658 

9.91378 

10 

.90655 

.80640 

.90840 

.80983 

.91022 

.81325 

.91203 

.81663 

.91381 

.83000 

50 

12+18 

.90658 

.80645 

.90843 

.80989 

.91025 

.81330 

.91206 

.81669 

.91384 

.83005 

48 

14 

.90661 

.80651 

.90846 

.80995 

.91028 

.81336 

.91209 

.81675 

.91387 

.83011 

46 

16+19 

9.90664 

0.80657 

9.90849 

0.81000 

9.91031 

0.81343 

9.91212 

0.81680 

9.91390 

0.83017 

44 

18 

.90667 

.80663 

.90852 

.81008 

.91034 

.81347 

.91215 

.81686 

.91393 

.83033 

42 

20+20 

.90670 

.80668 

.90855 

.81012 

.91037 

.81353 

.91218 

.81693 

.91396 

.83038 

40 

22 

.90673 

.80674 

.90858 

.81017 

.91040 
9.91043 

.81359 

.91221 

.81697 

.91399 
9.91402 

.83033 

38 
36 

24+21 

9.90676 

0.80680 

9.90861 

0.81023 

0.81364 

9.91224 

0.81703 

0.83039 

26 

.90680 

.80686 

.90864 

.81029 

.91046 

.81370 

.91227 

.81708 

.91405 

.83045 

34 

28+22 

.90683 

.80691 

.90867 

.81035 

.91049 

.81376 

.91230 

.81714 

.91408 

.83050 

32 

SO 

.90686 

.80697 

.90870 

.81040 

.91052 

.81381 

.91233 

.81730 

.91411 

.83056 

30 

32+23 

9.90689 

0.80703 

9.90873 

0.81046 

9.91055 

0.81387 

9.91236 

0.81735 

9.91414 

0.83061 

28 

34 

.90692 

.80709 

.90876 

.81052 

.91058 

.81393 

.91239 

.8?.731 

.91417 

.83067 

26 

36+24: 

.90695 

.80714 

.90879 

.81057 

.91061 

.81398 

.91242 

.81737 

.91420 

.83073 

24 

38 

.90698 

.80720 

.90882 

.81063 

.91064 

.81404 

.91245 

.81742 

.91423 

.82078 

22 
20 

40+25 

9.90701 

0.80726 

9.90885 

0.81068 

9.91067 

0.81409 

9.91248 

0.81748 

9.91426 

0.82084 

42 

.90704 

.80731 

.90888 

.81074 

.91071 

.81415 

.91251 

.81753 

.91429 

.82089 

18 

U+26 

.90707 

.80737 

.90892 

.81080 

.91074 

.81431 

.91254 

.81759 

.91432 

.83095 

16 

46 

.90710 

.80743 

.90895 

.81086 

.91077 

.81436 

.91257 

.81765 

.91435 

.83100 

14 

48+21 

9.90714 

0.80749 

9.90898 

0.81092 

9.91080 

0.81432 

9.91260 

0.81770 

9.91437 

0.83106 

12 

50 

.90717   .80754 

.90901 

.81097 

.91083 

.81438 

.91263 

.81776 

.91440 

.83113 

10 

52+28 

.90720   .80760 

.90904 

.81103 

.91086 

.81443 

.91265 

.81781 

.91443 

.83117 

8 

54 

.90723 

.80766 
0.80772 

.90907 

.81109 

.91089 

.81449 

.91268 

.81787 
0.81793 

.91446 

.83133 

6 
4 

56+29 

9.90726 

9.90910 

0.81114 

9.91092 

0.81455 

9.91271 

9.91449 

0.83138 

58 

.90729   .80777 

.90913 

.81120 

.91095 

.81460 

.91274 

.81798 

.91452 

.83134 

2 

60+30 

9.90732  0.80783 

9.90916 

0.81126 

9.91098 

0.81466 

9.91277 

0.81804 

9.91455 

0.83139 

0 

/5'^  28m 

15h  26m       n 

15^  24"^         1 

15^  22m         1 

15J>-  20m         1 

TABLE  45.                  [Page  911 

Haversines. 

s    ' 

5A  40''«  130°  0'  1 

8^  42^  130°  30^ 

8h  U^  131°  iy 

8^  46m  131°  30^  | 

8^  4Sm  132°  r 

3 

Log.  Ilav. 

Nat.  Ilav. 

Log.  Hav.  Nat.  nav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

0      0 

9.91455 

0.83139 

9.91631 

0.82472 

9.91805 

0.82803 

9.91976 

0.83131 

9.92146 

0.83457 

60 

2 

.91458 

.83145 

.91634 

.82478 

.91807 

.82808 

.91979 

.83136 

.92149 

.83463 

58 

4+   1 

.91461 

.83151 

.91637 

.82483 

.91810 

.82814 

.91982 

.83142 

.92152 

.83467 

56 

6 

.91464 

.82156 

.91640 
9.91643 

.82489 
0.82495 

.91813 

.82819 
0.82825 

.91985 
9.91988 

.83147 
0.83153 

.92154 

.83473 

54 

52 

8+   3 

9.91467 

0.83163 

9.91816 

9.92157 

0.83478 

10 

.91470 

.83167 

.91645 

.82500 

.91819 

.83830 

.91991 

.83158 

.92160 

.83484 

50 

12+   4 

.91473 

.83173 

.91648 

.82506 

.91822 

.83836 

.91993  i  .83164 

.92163 

.83489 

48 

U 

.91476 

.83178 

.91651 

.82511 

.91825 

.83841 

.91996  j  .83169 

.92166 

.83494 

46 

16+   4 

9.91479 

0.83184 

9.91654 

0.83517 

9.91828 

0.83847 

9.91999  1  0.83175 

9.92169 

0.83500 

44 

18 

.91482 

.83189 

.91657 

.83533 

.91830 

.83853 

.92002 

.83180 

.92171 

.83505 

42 

20+   5 

.91485 

.83195 

.91660 

.83538 

.91833 

.83858 

.92005 

.83185 

.92174 

.83511 

40 

22 

.91488 

.83200 

.91663 
9.91666 

.83533 

.91836 

.83863 

.92008 
9.92010 

.83191 

.92177 

.83516 

38 

24+   6 

9.91490 

0.83306 

0.83539 

9.91839 

0.82869 

0.83196 

9.92180 

0.83531 

36 

26 

.91493 

.83312 

.91669 

.83544 

.91842 

.82874 

.92013 

.83203 

.92183 

.83527 

34 

28+   7 

.91496 

.82217 

.91672 

.82550 

.91845 

.82880 

.92016 

.83307 

.92185 

.83532 

32 

SO 

.91499 

.83333 

.91674 

.83555 

.91848 

.82885 

.92019 

.83313 

.92188 

.83538 

30 

S2+   8 

9.91502 

0.82228 

9.91677 

0.83561 

9.91851 

0.82891 

9.92022 

0.83318 

9.92191 

0.83543 

28 

.54 

.91505 

.82234 

.91680 

.83566 

.91853 

.82896 

.92025 

.83334 

.92194 

.83548 

26 

56+  9 

.91508 

.82240 

.91683 

.83573 

.91856 

.82902 

.92027 

.83329 

.92197 

.83554 

24 

38 

.91511 

.82345 

.91686 

.83577 

.91859 

.83907 

.92030 

.83334 

.92199 
9.92202 

.83559 
0.83564 

22 
20 

40+10 

9.91514 

0.83351 

9.91689 

0.83583 

9.91862 

0.82913 

9.92033 

0.83340 

42 

.91517 

.83356 

.91692 

.83588 

.91865 

.82918 

.92036 

.83345 

.92205 

.83570 

18 

44+11 

.91520 

.82362 

.91695 

.83594 

.91868 

.83934 

.92039 

.83351 

.92208 

.83575 

16 

46 

.91523 

.83367 

.91698 

.83599 

.91871 

.83939 

.92042 

.83356 

.92211 

.83581 

14 

45+13 

9.91526 

0.82273 

9.91701 

0.83605 

9.91874 

0.83934 

9.92044 

0.83263 

9.92213 

0.83586 

12 

50 

.91529 

.82278 

.91703 

.83610 

.91876 

.83940 

.92047 

..83367 

.92216 

.83591 

10 

52+lZ 

.91532 

.82284 

.91706 

.83616 

.91879 

.83945 

.92050 

.83373 

.92219 

.83597 

8 

54 

.91534 

.82290 

.91709 

.83631 

.91882 
9.91885 

.83951 

0:83956 

.92053 
9.92056 

.83378 
0.83383 

.92222 
9.92225 

.83602 

6 

56+14 

9.91537 

0.83395 

9.91712 

0.83627 

0.83608 

4 

58 

9.91540 

0.83301 

9.91715 

0.83632 

9.91888 

0.83963 

9.92059 

0.83389 

9.92227 

0.83613 

2 

15h  igm 

15h  nm 

15^  15m 

15h  13m 

loh  11m 

s   ' 
0+15 

8h  4im  130°  0^ 

8h  4sm  130°  30' 

Sh  45m  131°  0' 

8h  47m  131°  30: 

8h  49m  132°  0' 

s 
60 

9.91543 

0.83306 

9.91718  1  0.82638 

9.91891 

0.83967 

9.92061 

0.83394 

9.92230 

0.83618 

2 

.91546 

.83312 

.91721  1  .82644 

.91894 

.83973 

.92064 

.83300 

.92233 

.83624 

58 

4+ie 

.91549 

.82317 

.91724  i  .82649 

.91896 

.83978 

.92067 

.83305 

.92236 

.83629 

56 

6 

.91552 

.82323 

.91727 

.82655 

.91899 

.83984 

.92070 

.83310 
0.83316 

.92239 

.83635 

54 
52 

8+11 

9.91555 

0.82328 

9.91730 

0.82660 

9.91902 

0.83989 

9.92073 

9.92241 

0.83640 

10 

.91558 

.82334 

.91732 

.82666 

.91905 

.83995 

.92076 

.83331 

.92244 

.83645 

50 

12+1% 

.91561 

.82339 

.91735 

.82671 

.91908 

.83000 

.92078 

.83337 

.92247 

.83651 

48 

14 

.91564 

.83345 

.91738 

.82677 

.91911 

.83006 

.92081 

.83333 

.92250 

.83656 

46 

i6+19 

9.91567 

0.83351 

9.91741 

0.82682 

9.91914 

0.83011 

9.92084 

0.83337 

9.92253 

0.83661 

U 

18 

.91570 

.83356 

.91744 

.82688 

.91916 

.83016 

.92087 

.83343 

.92255 

.83667 

42 

20+29 

.91573 

.83363 

.91747 

.82693 

.91919 

.83033 

.92090 

.83348 

.92258 

.83673 

40 

22 

.91575 

.83367 

.91750 

.83699 

.91922 
9.91925 

.83037 
0.83033 

.92093 
9.92095 

.83354 
0.83359 

.92261 

.83678 

38 
36 

24+21 

9.91578 

0.82373 

9.91753 

0.83704 

9.92264 

0.83683 

26 

.91581 

.83378 

.91756 

.83710 

.91928 

.83038 

.92098 

.83365 

.92266 

.83688 

34 

28+n 

.91584 

.83384 

.91758 

.82715 

.91931 

.83044 

.92101 

.83370 

.92269 

.83694 

32 

SO 

.91587 

.82389 

.91761 

.82721 

.91934 

.83049 

.92104 

.83375 

.92272 

.83699 

30 

S2+29 

9.91590 

0.83395 

9.91764 

0.82726 

9.91936 

0.83055 

9.92107 

0.83381 

9.92275 

0.83704 

28 

S4 

.91593 

.83400 

.91767 

.82732 

.91939 

.83060 

.92109 

.83386 

.92278 

.83710 

26 

36+24: 

.91596 

.83406 

.91770 

.82737 

.91942 

.83066 

.92112 

.83393 

.92280 

.83715 

24 

38 

.91599 

.83412 

.91773 

.82743 

.91945 

.83071 

.92115 

.83397 
0.83402 

.92283 
9.92286 

.83720 
0.83726 

22 
20 

40+25 

9.91602 

0.83417 

9.91776 

0.82748 

9.91948 

0.83077 

9.92118 

42 

.91605 

.83433 

.91779 

.83764 

.91951 

.83083 

.92121 

.83408 

.92289 

.83731 

18 

44+36 

.91608 

.83438 

.91782 

.83759 

.91954 

.83087 

.92124 

.83413 

.92292 

.83737 

16 

46 

.91610 

.83434 

.91784 

.83765 

.91956 

.83093 

.92126 

.83419 

.92294 

.83742 

14 

48+21 

9.91613 

0.83439 

9.91787 

0.82770 

9.91959 

0.83098 

9.92129 

0.83424 

9.92297 

0.83747 

12 

50 

.91616 

.83445 

.91790 

.83776 

.91962 

.83104 

.92132 

.83430 

.92300 

.83753 

10 

5^+38 

.91619 

.83450 

.91793 

.82781 

.91965 

.83109 

.92135 

.83435 

.92303 

.83758 

8 

54 

.91622 

.83456 

.91796 

.82786 

.91968 
9T91971 

.83115 
0.83130 

.92138 
9.92140 

.83440 
0.83446 

.92305 

.83763 

6 

66+29 

9.91625 

0.83461 

9.91799 

0.83792 

9.92308 

0.83769 

4 

58 

.91628 

.82467 

.91802 

.83797 

.91973 

.83126 

.92143 

.83451 

.92311 

.83774 

2 

60+30 

9.91631 

0.82472 

9.91805 

0.83803 

9.91976 

0.83131 

9.92146 

0.83457 

9.92314 

0.83780 

0 

15h  18m 

15h  16m 

J5h  14m 

J5h  12m 

15h  lOm 

Page  912]                 TABLE  45. 

Haversines. 

s    ' 

8h  50m  132°  30' 

5ft  5;?™  133°  0' 

5ft  54™  133°  30^ 

5ft  56m  134°  0' 

5ft  58m  134°  SO' 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

2 

4+  1 
6 

'9.92314 
.92317 
.92319 
.92322 

0.S3780 
.83785 
.83790 
.83796 

0.83801 
.83806 
.83812 
.83817 

0.83832 
.83828 
.83833 
.83838 

0.83844 
.83849 
.83855 
.83860 

0.83865 
.83871 
.83876 
.83881 

9.92480 

.92482 
.92485 
.92488 

0.84100 
.84105 
.84111 
.84116 

9.92643 
.92646 
.92649 
.92652 

0.84418 
.84423 
.84428 
.84434 

0.84439 
.84444 
.84449 
.84455 

0.84460 
.84465 
.84470 
.84476 

9.92805 
.92808 
.92811 
.92813 

0.84733 

.84738 
.84743 
.84749 

9.92965 
.92968 
.92970 
.92973 

0.85045 
.85051 
.85056 
.85061 

60 
58 
66 
54 

8+   2 

10 

12+   3 
14 

16+   4 
18 

20+   5 
22 

9.92325 
.92328 
.92330 
.92333 

9.92336 
.92339 
.92342 
.92344 

9.92491 
.92493 
.92496 
.92499 

9.92502 
.92504 
.92507 
.92510 

0.84121 
.84127 
.84133 
.84137 

0.84142 
.84148 
.84153 
.84158 

9.92654 
.92657 
.92660 
.92662 

9  92665 
.92668 
.92670 
.92673 

9.92816 
.92819 
.92821 
.92824 

9.92827 
.92829 
.92832 
.92835 

0.84754 
.84759 
.84764 
.84770 

0.84775 
.84780 
.84785 
.84790 

9.92975 
.92978 
.92981 
.92984 

9.92986 
.92989 
.92992 
.92994 

0.85066 
.85071 
.85077 
.85083 

0.85087 
.85092 
.85097 
.85102 

62 
60 
48 
46 
44 
42 
40 
38 

24+   6 
26 

28+   7 
30 

32+   8 
34 

36+   9 
38 

9.92347 
.92350 
.92353 
.92355 

9.92358 
.92361 
.92364 
.92366 

9.92512 
.92515 
.92518 
.92521 

9.92523 
.92526 
.92529 
.92532 

0.84164 
.84169 
.84174 
.84180 

0.84185 
.84190 
.84196 
.84301 

9.92676 
.92679 
.92681 
.92684 

9.92687 
.92689 
.92692 
.92695 

0.84481 
.84486 
.84492 
.84497 

0.84502 
.84507 
.84513 
.84518 

9.92837 
.92840 
.92843 
.92845 

9.92848 
.92851 
.92853 
.92856 

0.84796 
.84801 
.84806 
.84811 

0.84817 
.84822 
.84827 
.84832 

9.92997 
.93001 
.93002 
.93005 

9.93007 
.93010 
.93013 
.93015 

0.85108 
.85113 
.85118 
.85123 

0.85128 
.85134 
.85139 
.85144 

36 

34 
32 
30 
28 
26 
24 
22 

40+10 

42 

U+11 

46 

48+12 

50 

52+n 

54 

9.92369 
.92372 
.92375 
.92378 

9.92380 
.92383 
.92386 
.92389 

0.83887 
.83892 
.83897 
.83903 

0.83908 
.83913 
.83919 
.83924 

9.92534 
.92537 
.92540 
.92543 

9.92545 
^2548 
.92551 
.92554 

0.84206 
.84211 
.84217 
.84222 

0.84227 
.84233 
.84238 
.84243 

9.92698 
.92700 
.92703 
.92706 

9.92708 
.92711 
.92714 
.92716 

0.84523 
.84528 
.84534 
.84539 

0.84544 
.84549 
.84555 
.84560 

9.92859 
.92861 
.92864 
.92867 

9.92869 
.92872 
.92875 
.92877 

0.84837 
.84843 

.84848 
.84853 
0.84858 
.84863 
.84869 
.84874 

9.93018 
.93021 
.93023 
.93026 

9.93029 
.93031 
.93034 
.93036 

0.85149 
.85154 
.85159 
.85165 

0.85170 
.85175 
.85180 
.85185 

0.85190 

0.85196 

20 
18 
16 
14 
12 
10 
8 
6 

4 

2 

56+14 
55 

9.92391 
9.92394 

0.83929 
0.83935 

9.92556 
9.92559 

0.84249 
0.84254 

9.92719 
9.92722 

0.84565 
0.84570 

9.92880 
9.92883 

0.84879 

0.84884 

9.93039 
9.93042 

IShgm 

15h7m 

15115m 

15h3m 

Uhlm 

8   ' 

5ft  5m  132°  30' 

5ft  53m  133°  0' 

5ft  55m  133°  30' 

5ft  57TO  134°  0' 

5ft  59m  134°  30' 

s 

0+15 
2 

4+16 
6 

9.92397 
.92400 
.92402 
.92405 

0.83940 
.83945 
.83951 
.83956 

9.92562 
.92564 
.92567 
.92570 

0.84259 
.84264 
.84270 
.84275 

9.92725 
.92727 
.92730 
.92733 

0.84576 

.84581 
.84586 
.84591 

9.92885 
.92888 
.92891 
.92893 

0.84890 
.84895 
.84900 
.84905 

9.93044 
.93047 
.93050 
.93052 

0.85201 
.85206 
.85211 
.85216 

60 
68 
66 
54 

5+17 

io 

12+1% 
14 

16+19 
i5 

fO+20 
22 

9.92408 
.92411 
.92413 
.92416 

9.92419 
.92422 
.92425 
.92427 

0.83961 
.83967 
.83972 
.83977 

0.83983 
.83988 
.83993 
.83999 

9.92573 
.92575 
.92578 
.92581 

9.92584 
.92586 
.92589 
.92592 

0.84280 
.84286 
.84291 
.84296 

0.84302 
.84307 
.84312 
.84317 

9.92735 
.92738 
.92741 
.92743 

9.92746 
.92749 
.92751 
.92754 

0.84597 
.84602 
.84607 
.84612 

0.84618 
.84623 
.84628 
.84633 

9.92896 
.92899 
.92901 
.92904 

9.92907 
.92909 
.92912 
.92915 

0.84910 
.84916 
.84921 
.84926 

0.84931 
.84936 
.84942 
.84947 

9.93055 
.93057 
.93060 
.93063 

9.93065 
.93068 
.93071 
.93073 

0.85221 
.85227 
.85333 
.85337 

0.85343 
.85247 
.85252 
.85358 

62 
50 
48 
46 
44 
42 
40 
38 

24+21 

26 

28+22 

SO 

5^+23 

34 

56+24 

55 

9.92430 
.92433 
.92436 
.92438 

9.92441 
.92444 
.92447 
.92449 

0.84004 
.84009 
.84015 
.84020 

0.84025 
.84031 
.84036 
.84041 

9.92594 
.92597 
.92600 
.92603 

9.92605 
.92608 
.92611 
.92613 

0.84323 
.84328 
.84333 
.84339 

0.84344 
.84349 
.84354 
.84360 

9.92757 
.92760 
.92762 
.92765 

9.92768 
.92770 
.92773 
.92776 

0.84639 
.84644 
.84649 
.84654 

0.84660 
.84665 
.84670 
.84675 

9.92917 
.92920 
.92923 
.92925 

9.92928 
.92931 
.92933 
.92936 

0.84953 
.84957 
.84963 
.84968 

0.84973 
.84978 
.84983 
.84988 

9.93076 
.93079 
.93081 
.93084 

9.93086 
.93089 
.93092 
.93094 

0.85263 
.85268 
.85373 

.85378 
0.85283 
.85288 
.85394 
.85399 

36 
34 
32 
30 
28 
26 
24 
22 

40+25 

42 

44+26 

46 

45+27 

50 

5^+28 

54 

9.92452 
.92455 
.92458 
.92460 

9.92463 
.92466 
.92469 
.92471 

9.92474 
.92477 

9.92480 

0.84047 
.84052 
.84057 
.84063 

0.84068 
.84073 
.84079 
.84084 

0.84089 
.84095 

0.84100 

9.92616 
.92619 
.92622 
.92624 

9.92627 
.92630 
.92633 
.92635 

9.92638 
.92641 

9.92643 

0.84365 
.84370 
.84376 
.84381 

0.84386 
.84391 
.84397 
.84402 

9.92778 
.92781 
.92784 
.92786 

9.92789 
.92792 
.92794 
,92797 

0.84681 
.84686 
.84691 
.84696 

0.84702 
.84707 
.84712 
.84717 

9.92939 
.92941 
.92944 
.92947 

9.92949 
.92952 
.92955 
.92957 

9.92960 
.92962 

9.92965 

0.84994 
.84999 
.85004 
.85009 

0.85014 
.85030 
.85025 
.85030 

9.93097 
.93100 
.93102 
.93105 

9.93107 
.93110 
.93113 
.93115 

0.85304 
.85309 
.85314 
.85319 

0.85324 
.85330 
.85335 
.85340 

0.85345 
.85350 

0.85355 

20 
18 
16 
14 
12 
10 
8 
6 

4 
g 
0 

56+29 

55 

60+30 

0.84407 

.84412 

0.84418 

9.92800 

.92802 

9.92805 

0.84722 

.84728 
0.84733 

0.85035 

.85040 

0.85045 

9.93118 

.93120 

9.93123 

15^  8^ 

15h6m 

15^4.m 

IShgm 

15^  Om 

TABLE  45.                  [Page  913 

Havereines. 

s   ' 

Qhom         135° 

9A  4™    136° 

9h  gm         137° 

9^ 12m       138° 

9hl6m       139°  | 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 
0.85967 

Log.  Hav.  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

I^g.  Hav. 

Nat.  Hav. 

s 
60 

0      0 

9.93123 

0.85355 

9.93433 

9.93736 

0.86568 

9.94030 

0.87157 

9.94318 

0.87735 

4      1 

.93128 

.85366 

.93438 

.85977 

.93741 

.86578 

.94035 

.87167 

.94322 

.87745 

56 

8      2 

.93134 

.85376 

.93443 

.85987 

'.93746 

.86588 

.94040 

.87177 

.94327 

.87755 

52 

12      3 

.93139 

.85386 

.93448 

.85997 

.93751 

.86597 

.94045 

.87186 

.94332 

.87764 

48 

16      4 

9.93144 

0.85396 

9.93454 

0.86007 

9.93755 

0.86607 

9.94050 

0.87196 

9.94336 

0.87774 

U 

20      5 

.93149 

.85407 

.93459 

.86017 

.93760 

.86617 

.94055 

.87206 

.94341 

.87783 

40 

24      6 

.93154 

.85417 

.93464 

.86028 

.93765 

.86627 

.94059 

.87216 

.94346 

.87793 

36 

28      7 

.93160 

.85427 

.93469 

.86038 

.93770 

.86637 

.94064 

.87225 

.94351 

.87802 

32 

32      8 

9.93165 

0.85438 

9.93474 

0.86048 

9.93775 

0.86647 

9.94069 

0.87235 

9.94355 

0.87812 

28 

36      9 

.93170 

.85448 

.93479 

.86058 

.93780 

.86657 

.94074 

.87245 

.94360 

.87821 

24 

40  10 

■  .93175 

.85458 

.93484 

.86068 

.93785 

.86667 

.94079 

.87254 

.94365 

.87831 

20 

-^4  11 

.93181 

.85468 

.93489 

.86078 

.93790 

.86677 

.94084 

.87264 

.94369 

.87840 

16 

48    13 

9.93186 

0.85479 

9.93494 

0.86088 

9.93795 

0.86686 

9.94088 

0.87274 

9.94374 

0.87850 

12 

5^  13 

.93191 

.85489 

.93499 

.86098 

.93800 

.86696 

.94093 

.87283 

.94379 

.87859 

8 

56    14 

9.93196 

0.85499 

9.93504 

0.86108 

9.93805 

0.86706 

9.94098 

0.87293 

9.94383 

0.87869 

4 

14h 59m 

i4h  55m 

14^ 5im 

14h  47m 

14h4,sm 

s   ' 

9h im         135° 

9^  5m        136° 

9fi  9m     137° 

9h ism       138° 

9h  17m       139° 

8 

0  15 

9.93201 

0.85509 

9.93509 

0.86118 

9.93810 

0.86716 

9.94103 

0.87303 

9.94388 

0.87878 

60 

4    16 

.93207 

.85520 

.93515 

.86128 

.93815 

.86726 

.94108 

.87313 

.94393 

.87888 

56 

5  17 

.93212 

.85530 

.93520 

.86138 

.93820 

.86736 

.94112 

.87322 

.94398 

.87897 

52 

12    18 

.93217 

.85540 

.93525 

.86148 

.93825 

.86746 

.94117 

.87332 

.94402 

.87907 

48 

iff  19 

9.93222 

0.85550 

9.93530 

0.86158 

9.93830 

0.86756 

9.94122 

0.87342 

9.94407 

0.87916 

44 

£0  20 

.93227 

.85560 

.93535 

.86168 

.93835 

.86765 

.94127 

.87351 

.94412 

.87926 

40 

24    21 

.93232 

.85571 

.93540 

.86178 

.93840 

.86775 

.94132 

.87361 

.94416 

.87935 

36 

f5  22 

.93238 

.85581 

.93545 

.86189 

.93845 

.88785 

.94137 

.87371 

.94421 

.87945 

32 

S2    23 

9.93243 

0.85591 

9.93550 

0.86199 

9.93849 

0.86795 

9.94141 

0.87380 

9.94426 

0.87954 

28 

56  24 

.93248 

.85601 

.93555 

.86209 

.93854 

.86805 

.94146 

.87390 

.94430 

.87964 

24 

40  25 

.93253 

.85612 

.93560 

.86219 

.93859 

.86815 

.94151 

.87400 

.94435 

.87973 

20 

44  26 

.93258 

.85622 

.93565 

.86229 

.93864 

.86825 

.94156 

.87409 

.94440 

.87983 

16 

4^  27 

9.93264 

0.85632 

9.93570 

0.86239 

9.93869 

0.86834 

9.94161 

0.87419 

9.94444 

0.87992 

12 

52    28 

.93269 

.85642 

.93575 

.86249 

.93874 

.86844 

.94165 

.87428 

.94449 

.88001 

8 

56  29 

9.93274 

0.85652 

9.93580 

0.86259 

9.93879 

0.86854 

9.94170 

0.87438 

9.94454 

0.88011 

4 

14h  58m 

14h 54m 

14hsom 

14h 46m 

14h  42m 

8    ' 

9^  2m         135° 

9h6m         136° 

9h  10m       1370 

9^  14m       138° 

9^  18m       139° 

s 

0    30 

9.93279 

0.85663 

9.93585 

0.86296 

9.93884 

0.86864 

9.94175 

0.87448 

9.94458 

0.88020 

60 

4  31 

.93284 

.85673 

.93590 

.86279 

.93889 

.88874 

.94180 

.87457 

.94463 

.88030 

56 

8    32 

.93289 

.85683 

.93595 

.86289 

.93894 

.86884 

.94184 

.87467 

.94468 

.88039 

52 

J:?  33 

.93295 

.85693 

.93600 

.86299 

.93899 

.86893 

.94189 

.87477 

.94472 

.88049 

48 

i6  34 

9.93300 

0.85703 

9.93605 

0.86309 

9.93904 

0.86903 

9.94194 

0.87486 

9.94477 

0.88058 

U 

20    35 

.93305 

.85713 

.93611 

.86319 

.93908 

.86913 

.94199 

.87496 

.94482 

.88068 

40 

£4  36 

.93310 

.85724 

.93616 

.86329 

.93913 

.86923 

.94204 

.87505 

.94486 

.88077 

36 

28    37 

.93315 

.85734 

.93621 

.86339 

.93918 

.86933 

.94208 

.87515 

.94491 

.88086 

32 

5£  38 

9.93320 

0.85744 

9.93626 

0.86349 

9.93923 

0.86942 

9.94213 

0.87525 

9.94496 

0.88096 

28 

56  39 

.93326 

.85754 

.93631 

.86359 

.93928 

.86952 

.94218 

.87534 

.94500 

.88105 

24 

40    40 

.93331 

.85764 

.93636 

.86369 

.93933 

.86962 

.94223 

.87544 

.94505 

.88115 

20 

44  41 

.93336 

.85774 

.93641 

.86379 

.93938 

.86972 

.94227 

.87554 

.94509 

.88124 

16 

48    42 

9.93341 

0.85785 

9.93646 

0.86389 

9.93943 

0.86982 

9.94232 

0.87563 

9.94514 

0.88133 

12 

52  43 

.93346 

.85795 

.93651 

.86399 

.93948 

.86991 

.94237 

.87573 

.94519 

.88143 

8 

56  44 

9.93351 

0.85805 

9.93656 

0.86409 

9.93952 

0.87001 

9.94242 

0.87582 

9.94523 

0.88152 

4 

14h  sjm 

14h  53m 

14^ 49m 

14h  4.5m 

14h  41m 

s   ' 

9hsm         135° 

9h  7m         136° 

gh  11m       137° 

9h 15m       138° 

9h  19m       139° 

s 

0    45 

9.93356 

0.85815 

9.93661 

0.86419 

9.93957 

0.87011 

9.94246 

0.87592 

9.94528 

0.88162 

60 

4  46 

.93362 

.85825 

.93666 

.86429 

.93962 

.87021 

.94251 

.87602 

.94533 

.88171 

56 

S  47 

.93367 

.85835 

.93671 

.86438 

.93967 

.87030 

.94256 

.87611 

.94537 

.88180 

52 

i^  48 

.93372 

.85846 

.93676 

.86448 

.93972 

.87040 

.94261 

.87621 

.94542 

.88190 

4S 

16    49 

9.93377 

0.85856 

9.93681 

0.86458 

9.93977 

0.87050 

9.94265 

0.87630 

9.94546 

0.88199 

44 

fO  50 

.93382 

.85866 

.93686 

.86468 

.93982 

.87060 

.94270 

.87640 

.94551 

.88209 

40 

24    51 

.93387 

.85876 

.93691 

.86478 

.93987 

.87070 

.94275 

.87649 

.94556 

.88218 

36 

£5  52 

.93392 

.85886 

.93696 

.86488 

.93991 

.87079 

.94280 

.87659 

.94560 

.88227 

32 

52  53 

9.93397 

0.85896 

9.93701 

0.86498 

9.93996 

0.87089 

9.94284 

0.87669 

9.94565 

0.88237 

28 

S6    54 

.93403 

.85906 

.93706 

.86508 

.94001 

.87099 

.94289 

.87678 

.94570 

.88246 

24 

40  55 

.93408 

.85916 

.93711 

.86518 

.94006 

.87109 

.94294 

.87688 

.94574 

.88255 

20 

44    56 

.93413 

.85926 

.93716 

.86528 

.94011 

.87118 

.94299 

.87697 

.94579 

.88265 

16 

45  57 

9.93418 

0.85937 

9.93721 

0.86538 

9.94016 

0.87128 

9.94303 

0.87707 

9.94583 

0.88274 

12 

52  68 

.93423 

.85947 

.93726 

.86548 

.94021 

.87138 

.94308 

.87716 

.94588 

.88284 

8 

66    69 

.93428 

.85957 

.93731 

.86558 

.94026 

.87148 

.94313 

.87726 

.94593 

.88293 

4 

60  60 

9.93433 

0.85967 

9.93736 

0.86568 

9.94030 

0.87157 

9.94318 

0.87735 

9.94597 

0.88302 

0 

14h  567n           1 

J4h  r,2m           1 

14^ 4Sm          1 

14^  44m         i 

14*  40m         1 

Page  914]                 TABLE  45. 

Haversines. 

s   ' 

9h  20m        140° 

9h  24m        141° 

9h  28m        143° 

9h  S2m       143° 

9h  36m        144° 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.94597 

0.88302 

9.94869 

0.88857 

9.95134 

0.89401 

9.96391 

0.89933 

9.95641 

0.90451 

60 

4      1 

.94602 

.88312 

.94874 

.88866 

.95138 

.89409 

.95396 

.89941 

.95645 

.90459 

56 

8      2 

.94606 

.88321 

.94878 

.88876 

.95143 

.89418 

.95400 

.89949 

.95649 

.90468 

52 

12      3 

.94611 

.88330 

.94883 

.88885 

.95147 

.89427 

.95404 

.89958 

.95654 

.90476 

48 

16      4 

9.94616 

0.88340 

9.94887 

0.88894 

9.95151 

0.89436 

9.95408 

0.89967 

9.95658 

0.90485 

44 

20      5 

.94620 

.88349 

.94892 

.88903 

.95156 

.89445 

.95412 

.89976 

.95662 

.90494 

40 

24      6 

.94625 

.88358 

.94896 

.88912 

.95160 

.89454 

.95417 

.89984 

.95666 

.90502 

36 

28      7 

.94629 

.88368 

.94901 

.88921 

.95164 

.89463 

.95421 

.89993 

.95670 

.90511 

32 

S2      8 

9.94634 

0.88377 

9.94905 

0.88930 

9.95169 

0.89473 

9.95425 

0.90003 

9.95674 

0.90519 

28 

S6      9 

.94638 

.88386 

.94909 

.88940 

.95173 

.89481 

.95429 

.90010 

.95678 

.90528 

24 

40    10 

.94643 

.88396 

.94914 

.86949 

.95177 

.89490 

.95433 

.90019 

.95682 

.90537 

20 

^  11 

.94648 

.88405 

.94918 

.88958 

.95182 

.89499 

.95438 

.90028 

.95686 

.90545 

16 

48    12 

9.94652 

0.88414 

9.94923 

0.88967 

9.95186 

0.89508 

9.95442 

0.90037 

9.95690 

0.90553 

12 

5f  13 

.94657 

.88423 

.94927 

.88976 

.95190 

.89517 

.95446 

.90045 

.95694 

.90563 

8 

56    14 

9.94661 

0.88433 

9.94932 

0.88985 

9.95195 

0.89536 

9.95450 

0.90054 

9.95699 

0.90570 

4 

14f>-  S9m 

14^  35m 

14^  3im 

14^  27m 

14h  23m 

s   ' 
0  15 

9h  2im       140° 

9h  25m       141° 

9h  29m        142° 

9h  33m        143° 

9h  37m       144° 

s 
60 

9.94666 

0.88442 

9.94936 

0.88994 

9.95199 

0.89534 

9.95454 

0.90063 

9.95703 

0.90579 

4    16 

.94670 

.88451 

.94941 

.89003 

.95203 

.89543 

.95459 

.90071 

.97507 

.90588 

56 

5  17 

.94675 

.88461 

.94945 

.89012 

.95208 

.89552 

.95463 

.90080 

.95711 

.90596 

52 

12    18 

.94680 

.88470 

.94950 

.89022 

.95212 

.89561 

.95467 

.90089 

.95715 

.90604 

48 

16  19 

9.94684 

0.88479 

9.94954 

0.89031 

9.95216 

0.89570 

9.95471 

0.90097 

9.95719 

0.90613 

U 

^0  30 

.94689 

.88489 

.94958 

.89040 

.95221 

.89579 

.95475 

.90106 

.95723 

.90631 

40 

24    21 

.94693 

.88498 

.94963 

.89049 

.95225 

.89588 

.95480 

.90115 

.95727 

.90630 

36 

:25  22 

.94698 

.88507 

.94967 

.89058 

.95229 

.89597 

.95484 

.90124 

.95731 

.90638 

32 

32    23 

9.94702 

0.88516 

9.94972 

0.89067 

0.95234 

0.89606 

9.95488 

0.90132 

9.95735 

0.90647 

28 

56  24 

.94707 

.88526 

.94976 

.89076 

.95238 

.89614 

.95492 

.90141 

.95739 

.90655 

24 

40  25 

.94711 

.88535 

.94981 

.89085 

.95242 

.89623 

.95496 

.90150 

.95743 

.90664 

20 

44  26 

.94716 

.88544 

.94985 

.89094 

.95246 

.89632 

.95501 

.90158 

.95747 

.90673 

16 

45  27 

9.94721 

0.88553 

9.94989 

0.89103 

9.95251 

0.89641 

9.95505 

0.90167 

9.95751 

0.90680 

12 

62    28 

.94725 

.88563 

.94994 

.89112 

.95255 

.89650 

.95509 

.90176 

.95755 

.90689 

8 

56  29 

9.94730 

0.88572 

9.94998 

0.89121 

9.95259 

0.89659 

9.95513 

0.90184 

9.95759 

0.90697 

4 

Uf)-  38m 

14^  34m 

14^  30m 

14h  26m 

14h  22m 

s   ' 
0    30 

9h  22m       140° 

9h  26m       141° 

9h  som       143° 

9h  34m       143° 

9h  ssm      144° 

s 
60 

9.94734 

0.88581 

9.95003 

0.89130 

9.95264 

0.89668 

9.95517 

0.90193 

9.95763 

0.90706 

4  31 

.94739 

.88590 

.95007 

.89139 

.95268 

.89677 

.95521 

.90201 

.95768 

.90714 

56 

8    32 

.94743 

.88600 

.95011 

.89149 

.95272 

.89685 

.95526 

.90210 

.95772 

.90733 

52 

:?f  33 

.94748 

.88609 

.95016 

.89158 

.95276 

.89694 

.95530 

.90219 

.95776 

.90731 

48 

i6  34 

9.94752 

0.88618 

9.95020 

0.89167 

9.95281 

0.89703 

9.95534 

0.90227 

9.95780 

0.90740 

44 

20    35 

.94757 

.88627 

.95025 

.89176 

.95285 

.89712 

.95538 

.90336 

.95784 

.90748 

40 

^4  36 

.94761 

.88637 

.95029 

.89185 

.95289 

.89721 

.95542 

.90245 

.95788 

.90756 

36 

28    37 

.94766 

.88646 

.95033 

.89194 

.95294 

.89730 

.95546 

.90253 

.95792 

.90765 

32 

5^  38 

9.94770 

0.88655 

9.95038 

0.89203 

9.95298 

0.89738 

9.95550 

0.90262 

9.95796 

0.90773 

28 

56  39 

.94774 

.88664 

.95042 

.89212 

.95302 

.89747 

.95555 

.90371 

.95800 

.90793 

24 

40    40 

.94779 

.88674 

.95047 

.89231 

.95306 

.89756 

.95559 

.90379 

.95804 

.90790 

20 

44  41 

.94784 

.88683 

.95051 

.89230 

.95311 

.89765 

.95563 

.90388 

.95808 

.90798 

16 

48    42 

9.94788 

0.88692 

9.95055 

0.89239 

9.95315 

0.89774 

9.95567 

0.90396 

9.95812 

0.90807 

12 

5;?  43 

.94793 

.88701 

.95060 

.89248 

.95319 

.89783 

.95571 

.90305 

.95816 

.90815 

8 

56  44 

9.94797 

0.88710 

9.95064 

0.89257 

9.95323 

0.89791 

9.95575 

0.90314 

9.95820 

0.90834 

4 

14h  sjm         ! 

i4h  ssm 

14^  29m 

14h  25m         1 

14h  21m 

s   ' 
0    45 

9h23m       140°  1 

9h  27m       141° 

9h  Sim       143° 

9h35m       143°  | 

9h  39m       144° 

s 
60 

9.94802 

0.88720 

9.95069 

0.89266 

9.95328 

0.89800 

9.95579 

0.90322 

9.95824 

0.90832 

4  46 

.94806 

.88729 

.95073 

.89275 

.95332 

.89809 

.95584 

.90331 

.95828 

.90840 

56 

5  47 

.94811 

.88738 

.95077 

.89284 

.95336 

.89818 

.95588 

.90339 

.95832 

.90849 

52 

i;?  48 

.94815 

.88747 

.95082 

.89293 

.95340 

.89827 

.95592 

.90348 

.95836 

.90857 

48 

16    49 

9.94820 

0.88756 

9.95086 

0.89302 

9.75345 

0.89835 

9.95596 

0.90357 

9.95840 

0.90866 

U 

fO  50 

.94824 

.88766 

.95090 

.89311 

.95349 

.89844 

.95600 

.90365 

.95844 

.90874 

40 

24    51 

.94829 

.88775 

.95095 

.89320 

.95353 

.89853 

.95604 

.90374 

.95848 

.90882 

36 

;?5  52 

.94833 

.88784 

.95099 

.89.329 

.95357 

.89862 

.95608 

.90382 

.95852 

.90891 

32 

5^  53 

9.94838 

0.88793 

9.95104 

0.89338 

9.95362 

0.89870 

9.95613 

0.90391 

9  95856 

0.90899 

28 

36    54 

.94842 

.88802 

.95108 

.89347 

.95366 

.89879 

.95617 

.90399 

.95860 

.90907 

24 

40  55 

.94847 

.88811 

.95112 

.89356 

.95370 

.89888 

.95621 

.90408 

.95864 

.90916 

20 

U    56 

.94851 

.88821 

.95117 

.89365 

.95374 

.89897 

.95625 

.90417 

.95868 

.90924 

16 

45  57 

9.94856 

0.88830 

9.95121 

0.89374 

9.95379 

0.89906 

9.95629 

0.90425 

9.95872 

0.90933 

12 

5f  58 

.94860 

.88839 

.95125 

.89383 

.95383 

.89914 

.95633 

.90434 

.95876 

.90941 

8 

56    59 

.94865 

.88848 

.95130 

.89392 

.95387 

.89923 

.95637 

.90442 

.95880 

.90949 

4 

60  60 

9.94869 

0.88857 

9.95134 

0.89401 

9.95391 

0.89932 

9.95641 

0.90451 

9.95884 

0.90958 

0 

14^  36m         1 

14h  S2m         1 

14^  28m         1 

14^  24^         1 

14f>'  20m         1 

TABLE  45.                 [Page  916 

Haversines. 

s   ' 

9h40m       145° 

9h  44^      146° 

9h  48m       147° 

9h  S2m       148° 

9h  56m       149° 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  IJav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.95884 

0.90958 

9.96119 

0.91452 

9.96347 

0.91934 

9.96568 

0.92402 

9.96782 

0.93858 

60 

4      1 

.95888 

.90966 

.96123 

.91469 

.96351 

.91941 

.96572 

.92410 

.96786 

,  .92666 

56 

8      It 

.95892 

.90974 

.96127 

.91468 

.96355 

.91949 

.96576 

.92418 

.96789 

.92873 

52 

12      3 

.95896 

.90983 

.96131 

.91476 

.96359 

.91957 

.96579 

.92426 

.96793 

.92881 

48 

16      4 

9.95900 

0.90991 

9.96135 

0.91484 

9.96362 

0.91965 

9.96583 

0.92433 

9.96796 

0.92888 

44 

20      6 

.95904 

.90999 

.96139 

.91493 

.96366 

.91973 

.96586 

.92441 

.96800 

.93896 

40 

24      6 

.95908 

.91008 

.96142 

.91501 

.96370 

.91981 

.96590 

.92449 

.96803 

.92903 

36 

28      7 

.95912 

.91016 

.96146 

.91509 

.96374 

.91989 

.96594 

.92456 

.96807 

.92911 

32 

5^   8 

9.95916 

0.91024 

9.96150 

0.91517 

9.96377 

0.91997 

9.96597 

0.92464 

9.96810 

0.93918 

28 

S6      9 

.95920 

.91033 

.96154 

.91525 

.96381 

.92005 

.96601 

.92472 

.96814 

.93936 

24 

40  le 

.95924 

.91041 

.96158 

.91533 

.96385 

.92013 

.96604 

.92479 

.96817 

.93933 

20 

■^4  11 

.95928 

.91049 

.96162 

.91541 

.96388 

.92020 

.96608 

.92487 

.96821 

.93941 

16 

48    12 

9.95932 

0.91057 

9.96165 

0.91549 

9.96392 

0.92028 

9.96612 

0.92495 

9.96824 

0.93948 

12 

5^  13 

.95936 

.91066 

.96169 

.91557 

.96396 

.92036 

.96615 

.92502 

.96827 

.93955 

8 

56    14 

9.95939 

0.91074. 

9.96173 

0.91565 

9.96400 

0.92044 

9.96619 

0.92510 

9.96831 

0.93963 

4 

14h  19m 

14h  ism 

14h  11m 

14h7m 

14h  sm 

s   ' 
0  15 

9h  41m       145° 

9h  45m       146° 

9h  49m       147° 

9h  SSm       148° 

9h  S7m       149° 

a 
60 

9.95943 

0.91082 

9.96177 

0.91574 

9.96403 

0.92052 

9.96622 

0.92518 

9.96834 

0.93970 

4    16 

.95947 

.91091 

.96181 

.91582 

.96407 

.92060 

.96626 

.92525 

.96837 

.93978 

56 

5  17 

.95951 

.91099 

.96185 

.91590 

.96411 

.92068 

.96630 

.92533 

.96841 

.93985 

52 

12    18 

.95955 

.91107 

.96188 

.91598 

.96412 

.92076 

.96633 

.92541 

.96845 

.93993 

48 

i6  19 

9.95959 

0.91115 

9.96192 

0.91606 

9.96418 

0.92083 

9.96637 

0.92548 

9.96848 

0.93000 

U 

:?0  30 

.95963 

.91124 

.96196 

.91614 

.96422 

.92091 

.96640 

.92556 

.96852 

.93007 

40 

;?4  21 

.95967 

.91132 

.96200 

.91622 

.96426 

.92099 

.96644 

.92563 

.96855 

.93015 

36 

f<§  22 

.95971 

.91140 

.96204 

.91630 

.96429 

.92107 

.96648 

.92571 

.96859 

.93033 

32 

S2    23 

9.95975 

0.91149 

9.96208 

0.91638 

9.96433 

0.92115 

9.96651 

0.92579 

9.96862 

0.93030 

28 

56  24 

.95979 

.91157 

.96211 

.91646 

.96437 

.92123 

.96655 

.92586 

.96866 

.93037 

24 

40  25 

.95983 

.91165 

.96215 

.91654 

.96440 

.92130 

.96658 

.92594 

.96869 

.93045 

20 

44    26 

.95987 

.91173 

.96219 

.91662 

.96444 

.92138 

.96662 

.93603 

.96873 

.93053 

16 

45  27 

9.95991 

0.91182 

9.96223 

0.91670 

9.96448 

0.92146 

9.96665 

0.93609 

9.96876 

0.93059 

12 

52    28 

.95995 

.91190 

.96227 

.91678 

.96451 

.92154 

.96669 

.93617 

.96879 

.93067 

8 

56  29 

9.95999 

0.91198 

9.96230 

0.91686 

9.96455 

0.92162 

9.96673 

0.92624 

9.96883 

0.93074 

4 

14h  18m 

14h  14m 

14h  10m 

14h6m 

14h2m 

s   ' 
0    30 

9h42m       145°  | 

9h  46m       148° 

9h50m       147° 

9h  Sim       148° 

9h  sSm       149° 

s 
60 

9.96002 

0.91206 

9.96234 

0.91694 

9.96459 

0.92170 

9.96676 

0.92633 

9.96886 

0.93081 

4  31 

.96006 

.91215 

.96238 

.91702 

.96462 

.92177 

.96680 

.93640 

.96890 

.93089 

56 

8    32 

.96010 

.91223 

.96242 

.91710 

.96466 

.92185 

.96683 

.93647 

.96894 

.93096 

52 

i:g  33 

.96014 

.91231 

.96246 

.91718 

.96470 

.92193 

.96687 

.93655 

.96897 

.93104 

48 

:?6  34 

9.96018 

0.91239 

9.96249 

0.91726 

9.96473 

0.92301 

9.96690 

0.93663 

9.96900 

0.93111 

44 

20    35 

.96022 

.91247 

.96253 

.91734 

.96477 

.92209 

.96994 

.93670 

.96904 

.93118 

40 

^4  36 

.96026 

.91256 

.96257 

.91742 

.96481 

.92216 

.96697 

.93678 

.96907 

.93126 

36 

28    37 

.96030 

.91264 

.96261 

.91750 

.96484 

.92224 

.96701 

.93685 

.96910 

.93133 

32 

5^  38 

9.96034 

0.91272 

9.96265 

0.91758 

9.96488 

0.92232 

9.96705 

0.93693 

9.96914 

0.93110 

28 

56  39 

.96038 

.91280 

.96268 

.91766 

.96492 

.92240 

.96708 

.93700 

.96917 

.93148 

24 

40    40 

.96042 

.91289 

.96272 

.91774 

.96495 

.92248 

.96712 

.93708 

.96921 

.93155 

20 

44  41 

.96046 

.91297 

.96276 

.91782 

.96499 

.92255 

.96715 

.93715 

.96924 

.93162 

16 

48    42 

9.96049 

0.91305 

9.96280 

0.91790 

9.96503 

0.92263 

9.96719 

0.93733 

9.96928 

0.93170 

12 

52  44 

.96053 

.91313 

.96283 

.91798 

.96506 

.92271 

.96722 

.93731 

.96931 

.93177 

8 

56  44 

9.96057 

0.91321 

9.96287 

0.91806 

9.96510 

0.92279 

9.96726 

0.93738 

9.96934 

0.93184 

4 

i4h  17m 

14h  ism 

14h  9m 

14hsm 

14h  im          i 

s   ' 
0    45 

9h  43m       1450 

9h  47m       146° 

9h  Sim       147° 

9h  SSm       148° 

9h59m       149°  | 

60 

9.96061 

0.91329 

9.96291 

0.91814 

9.96514 

0.92286 

9.96729 

0.93746 

9.96938 

0.93193 

4  46 

.96065 

.91338 

.96295 

.91822 

.96517 

.92294 

.96733 

.93753 

.96941 

.93199 

56 

5  47 

.96069 

.91346 

.96299 

.91830 

.96521 

.92302 

.96736 

.93761 

.96945 

.93306 

52 

J2  48 

.96073 

.91354 

.96302 

.91838 

.96525 

.92310 

.96740 

.93768 

.96948 

.93314 

48 

16    49 

9.96077 

0.91362 

9.96306 

0.91846 

9.96528 

0.92317 

9.96743 

0.93776 

9,96951 

0.93331 

U 

^0  60 

.96081 

.91370 

.96310 

.91854 

.96532 

.92325 

.96747 

.92783 

.96955 

.93338 

40 

24    51 

.96084 

.91379 

.96314 

.91862 

.96536 

.92333 

.96750 

.93791 

.96958 

.93336 

36 

f5  52 

.96088 

.91387 

.96317 

.91870 

.96539 

.93341 

.96754 

.93798 

.96962 

.93343 

32 

5:?  53 

9.96092 

0.91395 

9.96321 

0.91878 

9.96543 

0.92348 

9.96758 

0.93806 

9.96965 

0.93350 

28 

36    54 

.96096 

.91403 

.96325 

.91886 

.96547 

.92356 

.98761 

.93813 

.96968 

.93358 

24 

40  55 

.96100 

.91411 

.96329 

.91894 

.96550 

.93364 

.96765 

.93831 

.96972 

.93365 

20 

U    56 

.96104 

.91419 

.96332 

.91902 

.96554 

.93373 

.96768 

.93838 

.96975 

.93373 

16 

45  57 

9.96108 

0.91427 

9.96336 

0.91910 

9.96557 

0.93379 

9.96772 

0.92836 

9.96979 

0.93379 

12 

5f  58 

.96112 

.91436 

.96340 

.91918 

.96561 

.92387 

.96775 

.92843 

.96982 

.93387 

8 

50    59 

.96115 

.91444 

.96344 

.91926 

.96565 

.92394 

.96779 

.92851 

.96985 

.93394 

4 

60  60 

9.96119 

0.91452 

9.96347 

0.91934 

9.96568 

0.92402 

9.96782 

0.92858 

9.96989 

0.93301 

0 

14h  16m        ~\ 

14^  12m          1 

14h  8m          1 

14h  4m          1 

Uft  Om          1 

Page  916]                 TABLE  45. 

Haversines. 

s 

iOAOm   150°  1 

lOh  4m       151° 

lOh  8m       153° 

ion  12m     153° 

ion  16m     154°  1 

s 

Lor.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.96989 

0.93301 

9.97188 

0.93731 

9.97381 

0.94147 

9.97566 

0.94550 

9.97745 

0.94940 

60 

4      1 

.96992 

.93309 

.97192 

.93738 

.97384 

.94154 

.97569 

.95557 

.97748 

.94946 

56 

8      3 

.96996 

.93316 

.97195 

.93^45 

.97387 

.94161 

.97572 

.94564 

.97751 

.94952 

52 

12      3 

.96999 

.93333 

.97198 

.93753 

.97390 

.94168 

.97575 

.94570 

.97754 

.94959 

48 

16      4 

9.97002 

0.93330 

9.97201 

0.93759 

9.97393 

0.94175 

9.97578 

0.94577 

9.97756 

0.94965 

44 

W      5 

.97006 

.93338 

.97205 

.93766 

.97397 

.94181 

.97581 

.94583 

.97759 

.94973 

40 

U      6 

.97009 

.93345 

.97208 

.93773 

.97400 

.94188 

.97584 

.94590 

.97762 

.94978 

36 

28      7 

.97012 

.93353 

.97211 

.93780 

.97403 

.94195 

.97587 

.94596 

.97765 

.94984 

32 

5:?   8 

9.97016 

0.93359 

9.97214 

0.93787 

9.97406 

0.94303 

9.97591 

0.94603 

9.97768 

0.94991 

28 

56   9 

.97019 

.93367 

.97218 

.93794 

.97409 

.94209 

.97594 

.94610 

.97771 

.94997 

24 

40    10 

.97022 

.93374 

.97221 

.93801 

.97412 

.94315 

.97597 

.94616 

.97774 

.95003 

20 

44  11 

.97026 

.93381 

.97224 

.93808 

.97415 

.94333 

.97600 

.94623 

.97777 

.95010 

16 

48    13 

9.97029 

0.93388 

9.97227 

0.93815 

9.97418 

0.94339 

9.97603 

0.94639 

9.97780 

0.95016 

12 

5f  13 

.97033 

.93395 

.97231 

.93833 

.97422 

.94336 

.97606 

.94636 

.97783 

.95033 

8 

56  14 

9.97036 

0.93403 

9.97234 

0.93839 

9.97425 

0.94343 

9.97609 

0.94642 

9.97785 

0.95039 

4 

13^  59m 

isJi  55m 

ISh  Sim 

isn  47m 

isn  4sm 

8    ' 

0    15 

10^ im       150° 

lOh  5m       151° 

lOh 9m       153° 

ion  13m     153° 

ion  17m     154° 

s 
60 

9.97039 

0.93410 

9.97237 

0.93836 

9.97428 

0.94349 

9.97612 

0.94649 

9.97788 

0.95035 

4    16 

.97043 

.93417 

.97240 

.93843 

.97431 

.94356 

.97615 

.94655 

.97791 

.95041 

56 

5  17 

.97046 

.93434 

.97244 

.93850 

.97434 

.94363 

.97618 

.94663 

.97794 

.95048 

52 

i^  18 

.97049 

.93433 

.97247 

.93857 

.97437 

.94370 

.97621 

.94669 

.97797 

.95054 

48 

16    19 

9.97052 

0.93439 

9.97250 

0.93864 

9.97440 

0.94376 

9.97624 

0.94675 

9.97800 

0.95060 

44 

;gO  30 

.97056 

.93446 

.97253 

.93871 

.97443 

.94383 

.97627 

.94683 

.97803 

.95066 

40 

24    31 

.97059 

.93453 

.97257 

.93878 

.97447 

.94390 

.97630 

.94688 

.97806 

.95073 

36 

:?«  33 

.97063 

.93460 

.97260 

.93885 

.97450 

.94397 

.97633 

.94695 

.97808 

.95079 

32 

5f  33 

9.97066 

0.93468 

9.97263 

0.93893 

9.97453 

0.94303 

9.97636 

0.94701 

9.97811 

0.95085 

28 

36    34 

.97069 

.93475 

.97266 

.93899 

.97456 

.94310 

.97639 

.94708 

.97814 

.95093 

24 

40  35 

.97073 

.93483 

.97269 

.93906 

.97459 

.94317 

.97642 

.94714 

.97817 

.95098 

20 

U    26 

.97076 

.93489 

.97273 

.93913 

.97462 

.94334 

.97645 

.94731 

.97820 

.95104 

16 

4^  37 

9.97079 

0.93496 

9.97276 

0.93930 

9.97465 

0.94330 

9.97647 

0.94737 

9.97823 

0.95111 

12 

5^  38 

.97083 

.93503 

.97279 

.93937 

.97468 

.94337 

.97650 

.94734 

.97826 

.95117 

8 

56    39 

9.97086 

0.93511 

9.97282 

0.93934 

9.97471 

0.94344 

9.97653 

0.94740 

9.97829 

0.95133 

4 

13^  58m         1 

13h  54m 

13h  50m 

13n  46m 

I3n  42m 

s   ' 
0    30 

10^  2m       150°  j 

lOh  6m       151° 

ion  lOm     153° 

ion  14m     153° 

ion Igm     154° 

3 

60 

9.97089 

0.93518 

9.97285 

0.93941 

9.97474 

0.94351 

9.97656 

0.94747 

9.97831 

0.95139 

4  31 

.97093 

.93535 

.97289 

.93948 

.97478 

.94357 

.97659 

.94753 

.97834 

.95136 

56 

5  33 

.97096 

.93533 

.97292 

.93955 

.97481 

.94364 

.97662 

.94760 

.97837 

.95143 

52 

12    33 

.97099 

.93539 

.97295 

.93963 

.97484 

.94371 

.97665 

.94766 

.97840 

.95148 

48 

i6  34 

9.97103 

0.93546 

9.97298 

0.93969 

9.97487 

0.94377 

9.97668 

0.94773 

9.97843 

0.95154 

44 

20    35 

.97106 

.93554 

.97301 

.93976 

.97490 

.94384 

.97671 

.94779 

.97846 

.95161 

40 

f4  36 

.97109 

.93561 

.97305 

.93983 

.97493 

.94391 

.97674 

.94786 

.97849 

.95167 

36 

;?5  37 

.97113 

.93568 

.97308 

.93989 

.97496 

.94397 

.97677 

.94792 

.97851 

.95173 

32 

S2    38 

9.97116 

0.93575 

9.97311 

0.93996 

9.97499 

0.94404 

9.97680 

0.94799 

9.97854 

0.95179 

28 

56  39 

.97119 

.93583 

.97314 

.94003 

.97502 

.94411 

.97683 

.94805 

.97857 

.95185 

24 

40    40 

.97123 

.93589 

.97317 

.94010 

.97505 

.94418 

.97686 

.94811 

.97860 

.95193 

20 

44  41 

.97126 

.93596 

.97321 

.94017 

.97508 

.94424 

.97689 

.94818 

.97863 

.95198 

16 

45  43 

9.97129 

0.93603 

9.97324 

0.94034 

9.97511 

0.94431 

9.97692 

0.94824 

9.97866 

0.95304 

12 

52    43 

.97132 

.93611 

.97327 

.94031 

.97514 

.94438 

.97695 

.94831 

.97868 

.95310 

8 

56  44 

9.97136 

0.93618 

9.97330 

0.94038 

9.97518 

0.94444 

9.97698 

0.94837 

9.97871 

0.95217 

4 

ISh  57m 

ISh 5Sm 

isn 49m 

13n  45m 

ISh  41m 

0    45 

10^ 3m       150° 

ion  7m       151° 

lOh  llm     153° 

ion  15m     153° 

ion  19m     154° 

s 
60 

9.97139 

0.93635 

9.97333 

0.94045 

9.97521 

0.94451 

9.97701 

0.94844 

9.97874 

0.95233 

4  46 

.97142 

.93633 

.97337 

.94051 

.97524 

.94458 

.97704 

.94850 

.97877 

.95339 

56 

5  47 

.97146 

.93639 

.97340 

.94058 

.97527 

.94464 

.97707 

.94857 

.97880 

.95335 

52 

12    48 

.97149 

.93646 

.97343 

.94065 

.97530 

.94471 

.97710 

.94863 

.97883 

.95341 

48 

i6  49 

9.97152 

0.93653 

9.97346 

0.94073 

9.97533 

0.94477 

9.97713 

0.94869 

9.97885 

0.95348 

44 

20    50 

.97156 

.93660 

.97349 

.94079 

.97536 

.94484 

.97716 

.94876 

.97888 

.95354 

40 

;?4  51 

.97159 

.93667 

.97352 

.94086 

.97539 

.94491 

.97718 

.94882 

.97891 

.95360 

36 

;?5  53 

.97162 

.93674 

.97356 

.94093 

.97542 

.94497 

.97721 

.94889 

.97894 

.95266 

32 

32    53 

9.97165 

0.93683 

9.97359 

0.94099 

9.97545 

0.94504 

9.97724 

0.94895 

9.97897 

0.95272 

28 

56  54 

.97169 

.93689 

.97362 

.94106 

.97548 

.94511 

.97727 

.94901 

.97899 

.95378 

24 

40    55 

.97172 

.93696 

.97365 

.94113 

.97551 

.94517 

.97730 

.94908 

.97902 

.95385 

20 

44  56 

.97175 

.93703 

.97368 

.94130 

.97554 

.94534 

.97733 

.94914 

.97905 

.95391 

16 

45  57 

9.97179 

0.93710 

9.97371 

0.94137 

9.97557 

0.94531 

9.97736 

0.94931 

9.97908 

0.95397 

12 

52    58 

.97182 

.93717 

.97575 

.94134 

.97560 

.94537 

.97739 

.94927 

.97911 

.95303 

8 

56  59 

.97185 

.93734 

.97378 

.94141 

.97563 

.94544 

.97742 

.94933 

.97914 

.95309 

4 

60    60 

9.97188 

093731 

9.97381 

0.94147 

9.97566 

0.94550 

9.97745 

0.94940 

9.97916 

0.95315 

0 

13^  56m         1 

isn  52m 

isn48m 

isn  44m 

isn  40m        1 

TABLE  45.                 [Page  917 

Haversines. 

s    ' 

lOh  2(pn.     155° 

lOh,  24m      156° 

lOh  2Sm     157° 

lOh  32m     158° 

lOhS&n     159°  1 

8 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.;  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

0 

9.97918 

0.95315 

9.98081 

0.95677 

9.98239 

0.96025 

9.98389 

0.96359 

9.98533 

0.96679 

60 

4 

1 

.97919 

.95322 

.98084 

.95683 

.98241 

.96031 

.98392 

.96365 

.98536 

.96684 

56 

8 

2 

.97922 

.95328 

.98086 

.95689 

.98244 

.96037 

.98394 

.96370 

.98538 

.96689 

52 

12 

3 

.97925 

.95334 

.98089 

.95695 

.98246 

.96042 

.98397 

.96376 

.98540 

.96695 

48 

16 

4 

9.97927 

0.95340 

9.98092 

0.95701 

9.98249 

0.96048 

9.98399 

0.96381 

9.98543 

0.96700 

44 

20 

5 

.97930 

.95346 

.98094 

.95707 

.98251 

.96054 

.98402 

.96386 

.98545 

.96705 

40 

24 

6 

.97933 

.95352 

.98097 

.95713 

.98254 

.96059 

.98404 

.96392 

.98547 

.96710 

36 

23 

7 

.97936 

.95358 

.98100 

.95719 

.98256 

.96065 

.98406 

.96397 

.98550 

.96715 

32 

32 

8 

9.97939 

0.95364 

9.98102 

0.95724 

9.98259 

0.96071 

9.98409 

0.96403 

9.98552 

0.96721 

28 

36 

9 

.97941 

.95371 

.98105 

.95730 

.98262 

.96076 

.98411 

.96408 

.98554 

.96726 

24 

40 

10 

.97944 

.95377 

.98108 

.95736 

.98264 

.96082 

.98414 

.96413 

.98557 

.96731 

20 

44 

11 

.97947 

.95383 

.98110 

.95742 

.98267 

.96088 

.98416 

.96419 

.98559 

.96736 

16 

48 

13 

9.97950 

0.95389 

9.98113 

0.95748 

9.98269 

0.96093 

9.98419 

0.96424 

9.98561 

0.96741 

12 

52 

13 

.97953 

.95395 

.98116 

.95754 

.98272 

.96099 

.98421 

.96430 

.98564 

.96746 

8 

56 

14 

9.97955 

0.95401 

9.98118 

0.95760 

9.98274 

0.96104 

9.98424 

0.96435 

9.98566 

0.96752 

4 

jfjft  sgm 

13f>'  35m 

ISh  Sim 

13h  27m 

ISh  23m 

8 
0 

15 

lOh  2im     155° 

lOh  25m     156° 

IQh  29m     151" 

lOh  33m     158° 

IQh  Sim      1590 

s 
60 

9.97958 

0.95407 

9.98121 

0.95766 

9.98277 

0.96110 

9.98426 

0.96440 

9.98568 

0.96757 

4 

16 

.97961 

.95413 

.98124 

.95771 

.98279 

.96116 

.98428 

.96446 

.98570 

.96762 

56 

8 

17 

.97964 

.95419 

.98126 

.95777 

.98282 

.96121 

.98431 

.96451 

.98573 

.96767 

52 

12 

18 

.97966 

.95425 

.98129 

.95783 

.98285 

.96127 

.98433 

.96457 

.98575 

.96772 

48 

16 

19 

9.97969 

0.95431 

9.98132 

0.95789 

9.98287 

0.96133 

9.98436 

0.96462 

9.98577 

0.96777 

44 

20 

20 

.97972 

.95438 

.98134 

.95795 

.98290 

.96138 

.98438 

.96467 

.98580 

.96782 

40 

24 

21 

.97975 

.95444 

.98137 

.95801 

.98292 

.96144 

.98440 

.96473 

.98582 

.96788 

36 

28 

22 

.97977 

.95450 

.98139 

.95806 

.98295 

.96149 

.98443 

.96478 

.98584 

.96793 

32 

52 

23 

9.97980 

0.95456 

9.98142 

0.95812 

9.98297 

0.96155 

9.98455 

0.96483 

9.98587 

0.96798 

28 

36 

24 

.97983 

.95462 

.98145 

.85818 

.98300 

.96161 

.98448 

.96489 

.98589 

.96803 

24 

40 

25 

.97986 

.95468 

.98147 

.95824 

.98302 

.96166 

.98450 

.96494 

.98591 

.96808 

20 

44 

26 

.97988 

.95474 

.98150 

.95830 

.98305 

.96172 

.98453 

.96500 

.98593 

.96813 

16 

48 

27 

9.97991 

0.95480 

9.98153 

0.95836 

9.98307 

0.96177 

9.98455 

0.96505 

9.98596 

0.96818 

12 

52 

28 

.97994 

.95486 

.98155 

.95841 

.98310 

.96183 

.98457 

.96510 

.98598 

.96823 

8 

56 

29 

9.97997 

0.95492 

9.98158 

0.95847 

9.98312 

0.96188 

9.98460 

0.96516 

9.98600 

0.96829 

4 

13^38^ 

13h  54™    1 

13^30m 

ISh  26m 

13h  22m 

8 

0 

30 

lOh  22m     155° 

lOfi  26m      156° 

IQh  30^ 

►  157° 

IQh  34m     158° 

IQh  SSm      159° 

s 
60 

9.97999 

0.95498 

9.98161 

0.95853 

9.98315 

0.96194 

9.98462 

0.96521 

9.98603 

0.96834 

4 

31 

.98002 

.95504 

.98163 

.95859 

.98317 

.96200 

.98465 

.96526 

.98605 

.96839 

56 

8 

32 

.98005 

.95510 

.98166 

.95865 

.98320 

.96205 

.98467 

.96532 

.98607 

.96844 

52 

12 

33 

.98008 

.95516 

.98168 

.95870 

.98322 

.96211 

.98469 

..96537 

.98609 

.96849 

48 

16 

34 

9.98010 

0.95522 

9.98171 

0.95876 

9.98325 

0.96216 

9.98472 

0.96542 

9.98612 

0.96854 

44 

20 

35 

.98013 

.95528 

.98174 

.95883 

.98327 

.96222 

.98474 

.96547 

.98614 

.96859 

40 

24 

36 

.98016 

.95534 

.98176 

.95888 

.98330 

.96237 

.98476 

.96553 

.98616 

.96864 

36 

28 

37 

.98019 

.95540 

.98179 

.95894 

.98332 

.96223 

.98479 

.96558 

.98619 

.96869 

32 

32 

38 

9.98021 

0.95546 

9.98182 

0.95899 

9.98335 

0.96238 

9.98481 

0.96563 

9.98621 

0.96874 

28 

36 

39 

.98024 

.95552 

.98184 

.95905 

.98337 

.96344 

.98484 

.96569 

.98623 

.96879 

24 

40 

40 

.98027 

.95558 

.98187 

.95911 

.98340 

.96249 

.98486 

.96574 

.98625 

.96884 

20 

44 

41 

.98030 

.95564 

.98189 

.95917 

.98342 

.96255 

.98488 

.96579 

.98628 

.96889 

16 

48 

42 

9.98032 

0.95570 

9.98192 

0.95922 

9.98345 

0.96360 

9.98491 

0.96585 

9.98630 

0.96894 

12 

52 

43 

.98035 

.95576 

.98195 

.95928 

.98347 

.96266 

.98493 

.96590 

.98632 

.96899 

8 

56 

44 

9.98038 

0.95582 

9.98197 

0.95934 

9.98350 

0.96272 

9.98496 

0.96595 

9.98634 

0.96905 

4 

ISh  37m 

13>>'  33m 

ISh  29m 

ISh  25m 

ISh  21m         1 

8 
0 

45 

10h23m    155°  1 

J  Oh  21m     156° 

lOh  Sim     157° 

lOh  35m     158° 

IQh  39m     159°  1 

3 
60 

9.98040 

0.95588 

9.98200 

0.95940 

9.98352 

0.96277 

9.98498 

0.96600 

9.98637 

0.96910 

4 

46 

.98043 

.95594 

.98202 

.95945 

.98355 

.96283 

.98500 

.96606 

.98639 

.96915 

56 

8 

47 

.98046 

.95600 

.98205 

.95951 

.98357 

.96288 

.98503 

.96611 

.98641 

.96930 

52 

12 

48 

.98049 

.95606 

.98208 

.95957 

.98360 

.96294 

.98505 

.96616 

.98643 

.96935 

48 

16 

49 

9.98051 

0.95612 

9.98210 

0.95962 

9.98362 

0.96299 

9.98507 

0.96621 

9.98646 

0.96930 

U 

20 

50 

.98054 

.95618 

.98213 

.95968 

.98365 

.96305 

.98510 

.96627 

.98648 

.96935 

40 

24 

51 

.98057 

.95624 

.98215 

.95974 

.98367 

.96310 

.98512 

.96632 

.98650 

.96940 

36 

28 

52 

.98059 

.95630 

.98218 

.95980 

.98370 

.96315 

.98514 

.96637 

.98652 

.96945 

32 

32 

53 

9.98062 

0.95636 

9.98221 

0.95985 

9.98372 

0.96331 

9.98517 

0.96642 

9.98655 

0.96950 

28 

36 

54 

.98065 

.95642 

.98223 

.95991 

.98375 

.96326 

.98519 

.96648 

.98657 

.96955 

24 

40 

55 

.98067 

.95648 

.98226 

.95997 

.98377 

.96332 

.98521 

.96653 

.98659 

.96960 

20 

44 

56 

.98070 

.95654 

.98228 

.96002 

.98379 

.96337 

.98524 

.96658 

.98661 

.96965 

16 

48 

57 

9.98073 

0.95660 

9.98231 

0.96008 

9.98382 

0.96343 

9.98526 

0.96663 

9.98664 

0.96970 

12 

52 

58 

.98076 

.95665 

.98233 

.96014 

.98384 

.96348 

.98529 

.96669 

.98666 

.96975 

8 

56 

59 

.98078 

.95671 

.98236 

.96020 

.98387 

.%354 

.98531 

.96674 

.98668 

.96980 

4 

60 

60 

9.98081 

0.95677 

9.98239 

0.96025 

9.98389 

0.96359 

9.98533 

0.96679 

9.98670 

0.96985 

0 

13h  36^ 

13h  32m 

13h  28m         1 

13h  24m         1 

ISh  gom         1 

Page  918]                  TABLE  45. 

Havereines. 

s    ' 

ion  40m     160° 

IQh  44m     161° 

lOh  48m     163° 

lOh  52m     163° 

lOh  56m     164° 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav.  Nat.  Hav. 

Log.  Hav.:  Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0      0 

9.98670 

0.96985 

9.98801 

0.97276 

9.98924 

0.97553 

9.99041 

0.97815 

9.99151 

0.98063 

60 

4      1 

.98673 

.96990 

.98803 

.97381 

.98926 

.97557 

.99043 

.97819 

.99152 

.98067 

56 

8      1i 

.98675 

.96995 

.98805 

.97385 

.98928 

.97562 

.99044 

.97824 

.99154 

.98071 

52 

12      3 

.98677 

.97000 

.98807 

.97390 

.98930 

.97566 

.99046 

.97828 

.99156 

.98075 

48 

16      4 

9.98679 

0.97005 

9.98809 

0.97395 

9.98932 

0.97571 

9.99048 

0.97832 

9.99158 

0.98079 

44 

20      5 

.98681 

.97009 

.98811 

.97300 

.98934 

.97575 

.99050 

.97836 

.99159 

.98083 

40 

24      6 

.98684 

.97014 

.98813 

.97304 

.98936 

.97580 

.99052 

.97841 

.99161 

.98087 

36 

28      1 

.98686 

.97019 

.98815 

.97309 

.98938 

.97584 

.99054 

.97845 

.99163 

.98091 

32 

S2      8 

9.98688 

0.97024 

9.98817 

0.97314 

9.98940 

0.97589 

9.99056 

0.97849 

9.99165 

0.98095 

28 

S6      9 

.98690 

.97029 

.98819 

.97318 

.98942 

.97593 

.99058 

.97853 

.99166 

.98099 

24 

40    10 

.98692 

.97034 

.98822 

.97333 

.98944 

.97598 

.99059 

.97858 

.99168 

.98103 

20 

^  11 

.98695 

.97039 

.98824 

.97338 

.98946 

.97602 

.99061 

.97862 

.99170 

.98107 

16 

48    13 

9.98697 

0.97044 

9.98826 

0.97333 

9.98948 

0.97606 

9.99063 

0.97866 

9.99172 

0.98111 

12 

5f  13 

.98699 

.97049 

.98828 

.97337 

.98950 

.97611 

.99065 

.97870 

.99173 

.98115 

8 

56    14 

9.98701 

0.97054 

9.98830 

0.97343 

9.98952 

0.97615 

9.99067 

0.97874 

9.99175 

0.98119 

4 

13h 19m 

ISh  lorn 

ISh  11m 

ISh  7m 

ISh  3m 

s   ' 

lOh  4im     160° 

lOh  45m     161° 

lOh  4m     162° 

IQh  53m     163° 

lOh  57m     164° 

s 

0  15 

9.98703 

0.97059 

9.98832 

0.97347 

9.98954 

0.97620 

9.99069 

0.97879 

9.99177 

0.98133 

60 

4    16 

.98706 

.97064 

.98834 

.97351 

.98956 

.97624 

.99071 

.97883 

.99179 

.98137 

56 

5  17 

.98708 

.97069 

.98836 

.97356 

.98958 

.97629 

.99072 

.97887 

.99180 

.98131 

52 

12    18 

.98710 

.97074 

.98838 

.97361 

.98960 

.97633 

.99074 

.97891 

.99182 

.98135 

48 

i6  19 

9.98712 

0.97078 

9.98840 

0.97365 

9.98962 

0.97637 

9.99076 

0.97895 

9.99184 

0.98139 

U 

;?0  20 

.98714 

.97083 

.98842 

.97370 

.98964 

.97643 

.99078 

.97899 

.99186 

.98143 

40 

24    21 

.98717 

.97088 

.98845 

.97374 

.98966 

.97646 

.99080 

.97904 

.99187 

.98146 

36 

^.^  23 

.98719 

.97093 

.98847 

.97379 

.98968 

.97651 

.99082 

.97908 

.99189 

.98150 

32 

32    23 

9.98721 

0.97098 

9.98849 

0.97384 

9.98970 

0.97655 

9.99084 

0.97913 

9.99191 

0.98154 

28 

56  24 

.98723 

.97103 

.98851 

.97388 

.98971 

.97660 

.99085 

.97916 

.99193 

.98158 

24 

40  25 

.98725 

.97108 

.98853 

.97393 

.98973 

.97664 

.99087 

.97930 

.99194 

.98162 

20 

i4  26 

.98728 

.97113 

.98855 

.97398 

.98975 

.97668 

.99089 

.97924 

.99196 

.98166 

16 

45  27 

9.98730 

0.97117 

9.98857 

0.97403 

9.98977 

0.97673 

9.99091 

0.97939 

9.99198 

0.98170 

12 

62    28 

.98732 

.97123 

.98859 

.97407 

.98979 

.97677 

.99093 

.97933 

.99200 

.98174 

8 

56  29 

9.98734 

0.97127 

9.98861 

0.97413 

9.98981 

0.97681 

9.99095 

0.97937 

9.99201 

0.98178 

4 

ISh ism 

13h  14m 

ISh  10m 

ISh  6m 

ISh  2m 

s   ' 

lOh  42m     160° 

lOh  46m     161° 

IQh  50m     162° 

lOh  54'^     163° 

IQh  58m     164° 

s 

0    30 

9.98736 

0.97132 

9.98863 

0.97416 

9.98983 

0.97686 

9.99096 

0.97941 

9.99203 

0.98182 

60 

4  31 

.98738 

.97137 

.98865 

.97431 

.98985 

.97690 

.99098 

.97945 

.99205 

.98185 

56 

8    32 

.98741 

.97143 

.98867 

.97425 

.98987 

.97695 

.99100 

.97949 

.99206 

.98189 

52 

if  33 

.98743 

.97147 

.98869 

.97430 

.98989 

.97699 

.99102 

.97953 

.99208 

.98193 

48 

i6  34 

9.98745 

0.97151 

9.98871 

0.97435 

9.98991 

0.97703 

9.99104 

0.97957 

9.99210 

0.98197 

U 

20    35 

.98747 

.97156 

.98873 

.97439 

.98993 

.97708 

.99106 

.97962 

.99212 

.98301 

40 

;g4  36 

.98749 

.97161 

.98875 

.97444 

.98995 

.97713 

.99107 

.97966 

.99213 

.98205 

36 

28    37 

.98751 

.97166 

.98877 

.97448 

.98997 

.97716 

.99109 

.97970 

.99215 

.98209 

32 

5f  38 

9.98754 

U97171 

9.98880 

0.97453 

9.98999 

0.97721 

9.99111 

0.97974 

9.99217 

0.98212 

28 

56  39 

.98756 

.97176 

.98882 

.97458 

.99001 

.97735 

.99113 

.97978 

.99218 

.98216 

24 

40    40 

.98758 

.97180 

.98884 

.97463 

.99003 

.97729 

.99115 

.97982 

.99220 

.98230 

20 

44  41 

.98760 

.97185 

.98886 

.97467 

.99004 

.97734 

.99116 

.97986 

.99222 

.98334 

16 

48    42 

9.98762 

0.97190 

9.98888 

0.97471 

9.99006 

0.97738 

9.99118 

0.97990 

9.99223 

0.98338 

12 

5:2  43 

.98764 

.97195 

.98890 

.97476 

.99008 

.97742 

.99120 

.97994 

.99225 

.98333 

8 

56  44 

9.98766 

0.97200 

9.98892 

0.97480 

9.99010 

0.97747 

9.99122 

0.97998 

9.99227 

0.98336 

4 

l,3h  17m 

ISh  ism 

ISh  gm 

ISh  5m 

ISh  pn 

s   ' 

lOh  43m     160° 

lOh  47m     161° 

IQh  5lm     162° 

lOh  55m     163° 

lOh  59m     164° 

s 

0  45 

9.98769 

0.97204 

9.98894 

0.97485 

9.99012 

0.97761 

9.99124 

0.98002 

9.99229 

0.98339 

60 

4  46 

.98771 

.97209 

.98896 

.97490 

.99014 

.97755 

.99126 

.98007 

.99230 

.98343 

56 

5  47 

.98773 

.97214 

.98898 

.97494 

.99016 

.97760 

.99127 

.98011 

.99232 

.98347 

52 

if  48 

.98775 

.97219 

.98900 

.97499 

.99018 

.97764 

.99129 

.98015 

.99234 

.98351 

48 

16    49 

9.98777 

0.97224 

9.98902 

0.97503 

9.99020 

0.97768 

9.99131 

0.98019 

9.99235 

0.98355 

44 

fO  50 

98779 

.97238 

.98904 

.97508 

.99022 

.97773 

.99133 

.98033 

.99237 

.98358 

40 

24    51 

.98781 

.97333 

.98906 

.97513 

.99024 

.97777 

.99135 

.98037 

.99239 

.98263 

36 

f5  62 

.98784 

.97338 

.98908 

.97517 

.99026 

.97781 

.99136 

.98031 

.99240 

.98266 

32 

5f  63 

9.98786 

0.97343 

9.98910 

0.97531 

9.99027 

0.97785 

9.99138 

0.98035 

9.99242 

0.98270 

28 

S6    64 

.98788 

.97347 

.98912 

.97526 

.99029 

.97790 

.99140 

.98039 

.99244 

.98374 

24 

40  65 

.98790 

.97353 

.98914 

.97530 

.99031 

.97794 

.99142 

.98043 

.99245 

.98377 

20 

44    66 

.98792 

.97357 

.98916 

.97535 

.99033 

.97798 

.99143 

.98047 

.99247 

.98281 

16 

45  67 

9.98794 

0.97363 

9.98918 

0.97639 

9.99035 

0.97802 

9.99145 

0.98051 

9.99249 

0.98385 

12 

5f  68 

.98796 

.97366 

.98920 

.97544 

.99037 

.97807 

.99147 

.98055 

.99250 

.98389 

8 

56    59 

.98798 

.97371 

.98922 

.97548 

.99039 

.97811 

.99149 

.98059 

.99252 

.98393 

4 

60  60 

9.98801 

0.97376 

9.98924 

0.97553 

9.99041 

0.97815 

9.99151 

0.98063 

9.99254 

0.98396 

0 

ISh  16m 

ISh  12m 

ISh  gm          1 

ISh  4m          1 

ISh  om          1 

TABLE  45.                 [Page  919 

Haversines. 

s    ' 

lin  am       165° 

lin4m       166° 

llhgrn       167° 

llh  12m     168° 

llh  16m     169° 

s 

Log.  Hav. 

Nat.  I  lav. 

Ix)g.  Ilav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  llav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

0 

9.99254 

0.98296 

9.99350 

0.98515 

9.99440 

0.98719 

9.99523 

0.98907 

9.99599 

0.99081 

60 

4 

1 

.99255 

.98300 

.99352 

.98518 

.99441 

.98722 

.99524 

.98910 

.99600 

.99084 

56 

8 

3 

.99257 

.98304 

.99353 

.98522 

.99443 

.98725 

.99526 

.98913 

.99602 

.99087 

52 

12 

3 

.99259 

.98308 

.99355 

.98525 

.99444 

.98728 

.99527 

.98916 

.99603 

.99090 

48 

16 

4 

9.99260 

0.98311 

9.99356 

0.98529 

9.99446 

0.98732 

9.99528 

0.98919 

9.99604 

0.99092 

44 

20 

5 

.99262 

.98315 

.99358 

.98532 

.99447 

.98735 

.99529 

.98922 

.99605 

.99095 

40 

24 

6 

.99264 

.98319 

.99359 

.98536 

.99448 

.98738 

.99531 

.98925 

.99606 

.99098 

36 

28 

7 

.99265 

.98323 

.99361 

.98539 

.99450 

.98741 

.99532 

.98928 

.99608 

.99101 

32 

S2 

8 

9.99267 

0.98326 

9.99362 

0.98543 

9.99451 

0.98745 

9.99533 

0.98931 

9.99609 

0.99103 

28 

36 

9 

.99269 

.98330 

.99364 

.98546 

.99453 

.98748 

.99535 

.98934 

.99610 

.99106 

24 

40 

10 

.99270 

.98334 

.99366 

.98550 

.99454 

.98751 

.99536 

.98937 

.99611 

.99109 

20 

U 

11 

.99272 

.98337 

.99367 

.98553 

.99456 

.98754 

.99537 

.98940 

.99612 

.99112 

16 

48 

12 

9.99274 

0.98341 

9.99369 

0.98557 

9.99457 

0.98757 

9.99539 

0.98943 

9.99614 

0.99114 

12 

52 

13 

.99275 

.98345 

.99370 

.98500 

.99458 

.98761 

.99540 

.98946 

.99615 

.99117 

8 

56 

14 

9.99277 

0.98349 

9.99372 

0.98564 

9.99460 

0.98764 

9.99541 

0.98949 

9.99616 

0.99120 

4 

1 

12h  59m          1 

12h  55m 

12h5lm 

12h  47m 

12h 43m 

s   '1 

llhim       165° 

llhsm       166° 

llhgm       167° 

llh  13m     168° 

llh  17m     169° 

s 

0 

15 

9.99278 

0.98352 

9.99373 

0.98567 

9.99461 

0.98767 

9.99543 

0.98952 

9.99617 

0.99123 

60 

4 

16 

.99280 

.98356 

.99375 

.98571 

.99463 

.98770 

.99544 

.98955 

.99618 

.99125 

56 

8 

17 

.99282 

.98360 

.99376 

.98574 

.99464 

.98774 

.99545 

.98958 

.99620 

.99128 

52 

12 

18 

.99283 

.98363 

.99378 

.98577 

.99465 

.98777 

.99546 

.98961 

.99621 

.99131 

48 

16 

19 

9.99285 

0.98367 

9.99379 

0.98581 

9.99467 

0.98780 

9.99548 

0.98964 

9.99622 

0.99133 

44 

20 

20 

.99287 

.98371 

.99381 

.98584 

.99468 

.98783 

.99549 

.98967 

.99623 

.99136 

40 

24 

21 

.99288 

.98374 

.99382 

.98588 

.99470 

.98786 

.99550 

.98970 

.99624 

.99139 

36 

28 

22 

.99290 

.98378 

.99384 

.98591 

.99471 

.98789 

.99552 

.98973 

.99626 

.99141 

32 

S2 

23 

9.99291 

0.98382 

9.99385 

0.98595 

9.99472 

0.98793 

9.99553 

0.98976 

9.99627 

0.99144 

28 

S6 

24 

.99293 

.98385 

.99387 

.98598 

.99474 

.98796 

.99554 

.98979 

.99628 

.99147 

24 

40 

25 

.99295 

.98389 

.99388 

.98601 

.99475 

.98799 

.99555 

.98982 

.99629 

.99149 

20 

44 

26 

.99296 

.98393 

.99390 

.98605 

.99477 

.98802 

.99557 

.98985 

.99630 

.99152 

16 

48 

27 

9.99298 

0.98396 

9.99391 

0.98608 

9.99478 

0.98805 

9.99558 

0.98987 

9.99631 

0.99155 

12 

52 

28 

.99300 

.98400 

.99393 

.98611 

.99479 

.98809 

.99559 

.98990 

.99633 

.99157 

8 

56 

29 

9.99301 

0.98404 

9.99394 

0.98615 

9.99481 

0.98812 

9.99561 

0.98993 

9.99634 

0.99160 

4 

1 

12h  58m 

12h  54m 

12h  50m 

12h  46m 

12h  42m 

s   '  1 

llh2m       165° 

llhem      166° 

llhiom     167° 

llh  14m     168° 

llh  18m     169° 

s 
60 

0 

30 

9.99303 

0.98407 

9.99396 

0.98619 

9.99482 

0.98815 

9.99562 

0.98996 

9.99635 

0.99163 

4 

31 

.99304 

.98411 

.99397 

.98622 

.99484 

.98818 

.99563 

.98999 

.99636 

.99165 

56 

8 

32 

.99306 

.98415 

.99399 

.98625 

.99485 

.98821 

.99564 

.99002 

.99637 

.99168 

52 

12 

33 

.99308 

.98418 

.99400 

.98629 

.99486 

.98824 

.99566 

.99005 

.99638 

.99171 

48 

16 

34 

9.99309 

0.98422 

9.99402 

0.98632 

9.99488 

0.98827 

9.99567 

0.99008 

9.99639 

0.99173 

44 

20 

35 

.99311 

.98426 

.99403 

.98635 

.99489 

.98830 

.99568 

.99011 

.99641, 

.99176 

40 

24 

36 

.99312 

.98429 

.99405 

.98639 

.99490 

.98834 

.99569 

.99014 

.99642 

.99179 

36 

28 

37 

.99314 

.98433 

.99406 

.98642 

.99492 

.98837 

.99571 

.99016 

.99643 

.99181 

32 

S2 

38 

9.99316 

0.98436 

9.99408 

0.98646 

9.99493 

0.98840 

9.99572 

0.99019 

9.99644 

0.99184 

28 

S6 

39 

.99317 

.98440 

.99409 

.98649 

.99495 

.98843 

.99573 

.99022 

.99645 

.99186 

24 

40 

40 

.99319 

.98444 

.99411 

.98652 

.99496 

.98846 

.99575 

.99025 

.99646 

.99189 

20 

44 

41 

.99320 

.98447 

.99412 

.98656 

.99497 

.98849 

.99576 

.99028 

.99648 

.99193 

16 

48 

42 

9.99322 

0.98451 

9.99414 

0.98659 

9.99499 

0.98852 

9.99577 

0.99031 

9.99649 

0.99194 

12 

52 

43 

.99324 

.98454 

.99415 

.98662 

.99500 

.98855 

.99578 

.99034 

.99650 

.99197 

8 

56 

44 

9.99325 

0.98458 

9.99417 

0.98666 

9.99501 

0.98858 

9.99580 

0.99036 

9.99651 

0.99199 

4 

12h  57m 

12h  53m 

i2h 49m 

12h  45m 

12h  41m 

s   ' 

llhsm       165° 

llhjm       166° 

llh  llm     167° 

llh  15m     168° 

llh  19m     169° 

s 

0 

45 

9.99327 

0.98462 

9.99418 

0.98669 

9.99503 

0.98862 

9.99581 

0.99039 

9.99652 

0.99202 

60 

4 

46 

.99328 

.98465 

.99420 

.98672 

.99504 

.98865 

.99582 

.99042 

.99653 

.99205 

56 

8 

47 

.99330 

.98469 

.99421 

.98676 

.99505 

.98868 

.99583 

.99045 

.99654 

.99207 

52 

12 

48 

.99331 

.98472 

.99422 

.98679 

.99507 

.98871 

.99584 

.99048 

.99655 

.99210 

48 

16 

49 

9.99333 

0.98476 

9.99424 

0.98682 

9.99508 

0.98874 

9.99586 

0.99051 

9.99657 

0.99212 

U 

20 

50 

.99335 

.98479 

.99425 

.98686 

.99510 

.98877 

.99587 

.99053 

99658 

.99215 

40 

24 

51 

.99336 

.98483 

.99427 

.98689 

.99511 

.98880 

.99588 

.99056 

.99659 

.99217 

36 

28 

52 

.99338 

.98487 

.99429 

.98692 

.99512 

.98883 

.99580 

.99059 

.99660 

.99220 

32 

S2 

53 

9.99339 

0.98490 

9.99430 

0.98696 

9.99514 

0.98886 

9.99591 

0.99062 

9.99661 

0.99223 

28 

36 

54 

.99341 

.98494 

.99431 

.98699 

.99515 

.98889 

.99592 

.99065 

.99662 

.99225 

24 

40 

55 

.99342 

.98497 

.99433 

.98702 

.99516 

.98892 

.99593 

.99067 

.99663 

.99228 

20 

U 

56 

.99344 

.98501 

.99434 

.98705 

.99518 

.98895 

.99594 

.99070 

.99664 

.99230 

16 

48 

57 

9.99345 

0.98504 

9.99436 

0.98709 

9.99519 

0.98898 

9.99596 

0.99073 

9.99666 

0.99233 

12 

52 

68 

.99347 

.98508 

.99437 

.98712 

.99520 

.98901 

.99597 

.99076 

.99667 

.99235 

8 

56 

59 

.99349 

.98511 

.99438 

.98715 

.99522 

.98904 

.99598 

.99079 

.99668 

.99238 

4 

60 

60 

9.99350 

0.98515 

9.99440 

0.98719 

9.99523 

0.98907 

9.99599 

0.99081 

9.99669 

0.99240 

0 

12^^  56m 

12h  52m 

12h  48m 

12h  44m 

12h  40m 

Page  920]                  TABLE  45.                         | 

Haversines.                              1 

s    ' 

llh20m       170° 

llh£4m       171° 

llh  28m       172° 

llh  32m       173° 

llh  36m       174° 

s 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav. 

0 

0 

9.99669 

0.99240 

9.99732 

0.99384 

9.997.88 

0.99513 

9.99838 

0.99627 

9.99881 

0.99726 

60 

4 

1 

.99670 

.99243 

.99733 

.99387 

.99789 

.99515 

.99839 

.99639 

.99882 

.99728 

66 

8 

3 

.99671 

.99245 

.99734 

.99389 

.99790 

.99517 

.99839 

.99631 

.99882 

.99729 

62 

12 

3 

.99672 

.99248 

.99735 

.99391 

.99791 

.99519 

.99840 

.99633 

.99883 

.99731 

48 

16 

4 

9.99673 

0.99250 

9.99736 

0.99393 

9.99792 

0.99521 

9.99841 

0.99634 

9.99884 

0.99732 

U 

20 

5 

.99674 

.99253 

.99737 

.99396 

.99793 

.99523 

.99842 

.99636 

.99884 

.99734 

40 

24 

6 

.99675 

.99255 

.99738 

.99398 

.99793 

.99525 

.99842 

.99638 

.99885 

.99735 

36 

28 

7 

.99677 

.99258 

.99739 

.99400 

.99794 

.99527 

.99843 

.99640 

.99885 

.99737 

32 

S2 

8 

9.99678 

0.99260 

9.99740 

0.99402 

9.99795 

0.99539 

9.99844 

0.99641 

9.99886 

0.99738 

28 

S6 

9 

.99679 

.99263 

.99741 

.99405 

.99796 

.99531 

.99845 

.99643 

.99887 

.99740 

24 

40 

10 

.99680 

.99265 

.99742 

.99407 

.99797 

.99533 

.99845 

.99645 

.99887 

.99741 

20 

44 

11 

.99681 

.99268 

.99743 

.99409 

.99798 

.99535 

.99846 

.99647 

.99888 

.99743 

16 

48 

13 

9.99682 

0.99270 

9.99744 

0.99411 

9.99799 

0.99537 

9.99847 

0.99648 

9.99889 

0.99744 

12 

52 

13 

.99683 

.99273 

.99745 

.99414 

.99800 

.99539 

.99848 

.99650 

.99889 

.99746 

8 

56 

U 

9.99684 

0.99275 

9.99746 

0.99416 

9.99800 

0.99541 

9.99848 

0.99652 

9.99890  1  0.99747 

4 

12^  S9m 

12h  s.sm 

12hsim 

12h 27m 

12h 23m 

8 

1 

llh2im       170° 

llfi'25'm       171° 

llh  29m       172° 

llh  33m      173° 

llh  37m       174° 

s 

'^ 

15 

9.99685 

0.99278 

9.99747 

0.99418 

9.99801 

0.99543 

9.99849 

0.99653 

9.99891 

0.99748 

60 

4 

16 

.99686 

.99280 

.99748 

.99420 

.99802 

.99545 

.99850 

.99655 

.99891 

.99750 

66 

8 

17 

.99687 

.99283 

.99748 

.99422 

.99803 

.99547 

.99851 

.99657 

.99892 

.99751 

62 

12 

18 

.99688 

.99285 

.99749 

.99425 

.99804 

.99549 

.99851 

.99659 

.99893 

.99753 

48 

16 

19 

9.99690 

0.99288 

9.99750 

0.99427 

9.99805 

0.99551 

9.99852 

0.99660 

9.99893 

0.99754 

44 

20 

20 

.99691 

.99290 

.99751 

.99429 

.99805 

.99553 

.99853 

.99663 

.99894 

.99756 

40 

24 

21 

.99692 

.99293 

.99752 

.99431 

.99806 

.99555 

.99854 

.99664 

.99894 

.99757 

36 

28 

1% 

.99693 

.99295 

.99753 

.99433 

.99807 

.99557 

.99854 

.99665 

.99895 

.99759 

32 

S2 

23 

9.99694 

0.99297 

9.99754 

0.99436 

9.99808 

0.99559 

9.99855 

0.99667 

9.99896 

0.99760 

28 

36 

24 

.99695 

.99300 

.99755 

.99438 

.99809 

.99561 

.99856 

.99669 

.99896 

.99761 

24 

40 

25 

.99696 

.99302 

.99756 

.99440 

.99810 

.99563 

.99857 

.99670 

.99897 

.99763 

20 

44 

26 

.99697 

.99305 

.99757 

.99442 

.99811 

.99565 

.99857 

.99673 

.99897 

.99674 

16 

48 

27 

9.99698 

0.99307 

9.99758 

0.99444 

9.99811 

0.99567 

9.99858 

0.99674 

9.99898 

0.99766 

12 

52 

28 

.99699 

.99309 

.99759 

.99446 

'  .99812 

.99568 

.99859 

.99675 

.99899 

.99767 

8 

56 

29 

9.99700 

0.99312 

9.99760 

0.99449 

9.99813 

0.99570 

9.99859 

0.99677 

9.99899 

0.99768 

4 

121 38m 

12h  S4m     -* 

...  12h30m   '-*» 

12h  26m 

12h 22m 

8 

t 

llh22m       170° 

llh  26m       171° 

Ilh30m.^.n2° 

llh  34m       173° 

llh  38m       174° 

a 
60 

0 

30 

9.99701 

0.99314 

9.99761 

0.99451 

9.99814 

0.99572 

9.99860 

0.99679 

9.99900 

0.99770 

4 

31 

.99702 

.99317 

.99762 

.99453 

.99815 

.99574 

.99861 

.99680 

.99901 

.99771 

56 

8 

32 

.99703 

.99319 

.99763 

.99455 

.99815 

.99576 

.99862 

.99683 

.99901 

.99773 

62 

12 

33 

.99704 

.99321 

.99764 

.99457 

.99816 

.99578 

.99862 

.99684 

.99902 

.99774 

48 

16 

34 

9.99705 

0.99334 

9.99765 

0.99459 

9.99817 

0.99580 

9.99863 

0.99685 

9.99902 

0.99775 

44 

20 

35 

.99706 

.99326 

.99766 

.99461 

.99818 

.99582 

.99864 

.99687 

.99903 

.99777 

40 

24 

36 

.99707 

.99329 

.99766 

.99464 

.99819 

.99584 

.99864 

.99688 

.99904 

.99778 

36 

28 

37 

.99708 

.99331 

.99767 

.99466 

.99820 

.99585 

.99865 

.99690 

.99904 

.99780 

32 

32 

38 

9.99710 

0.99333 

9.99768 

0.99468 

9.99820 

0.99587 

9.99866 

0.99693 

9.99905 

0.99781 

28 

36 

39 

.99711 

.99336 

.99769 

.99470 

.99821 

.99589 

.99867 

.99693 

.99905 

.99782 

24 

40 

40 

.99712 

.99338 

.99770 

.99472 

.99822 

.99591 

.99867 

.99695 

.99906 

.99784 

20 

U 

41 

.99713 

.99340 

.99771 

.99474 

.99823 

.99593 

.99868 

.99696 

.99906 

.99785 

16 

48 

42 

9.99714 

0.99343 

9.99772 

0.99476 

9.99824 

0.99595 

9.99869 

0.99698 

9.99907 

0.99786 

12 

52 

43 

.99715 

.99345 

.99773 

.99478 

.99824 

.99597 

.99869 

.99700 

.99908 

.99788 

8 

56 

44 

9.99716 

0.99347 

9.99774 

0.99480 

9.99825 

0.99598 

9.99870 

0.99701 

9.99908 

0.99789 

4 

12h  37m         1 

12h  ssm          1 

12h 29m          1 

12h25m         1 

12h 21m 

«   ' 

llh23m       170° 

lift  27m       171° 

llh  Sim       173° 

llh  35m      173° 

llh  39m       171° 

a 
60 

0 

45 

9.99717 

0.99350 

9.99774 

0.99483 

9.99826 

0.99600 

9.99871 

0.99703 

9.99909 

0.99790 

4 

46 

.99718 

.99352 

.99775 

.99485 

.99827 

.99602 

.99871 

.99704 

.99909 

.99792 

56 

8 

47 

.99719 

.99354 

.99776 

.99487 

.99828 

.99604 

.99872 

.99706 

.99910 

.99793 

52 

12 

48 

.99720 

.99357 

.99777 

.99489 

.99828 

.99606 

.99873 

.99708 

.99911 

.99794 

48 

16 

49 

9.99721 

0.99359 

9.99778 

0.99491 

9.99829 

0.99608 

9.99874 

0.99709 

9.99911 

0.99796 

44 

20 

50 

.99722 

.99361 

.99779 

.99493 

.99830 

.99609 

.99874 

.99711 

.99912 

.99797 

40 

24 

51 

.99723 

.99364 

.99780 

.99495 

.99831 

.99611 

.99875 

.99713 

.99912 

.99798 

36 

28 

52 

.99724 

.99366 

.99781 

.99497 

.99832 

.99613 

.99876 

.99714 

.99913 

.99799 

32 

32 

53 

9.99725 

0.99368 

9.99782 

0.99499 

9.99832 

0.99615 

9.99876 

0.99715 

9.99913 

0.99801 

28 

36 

54 

.99726 

.99371 

.99783 

.99501 

.99833 

.99617 

.99877 

.99717 

.99914 

.99802 

24 

40 

55 

.99727 

.99373 

.99784 

.99503 

.99834 

.99618 

.99878 

.99719 

.99915 

.99803 

20 

44 

56 

.99728 

.99375 

.99785 

.99505 

.99835 

.99630 

.99878 

.99730 

.99915 

.99805 

16 

48 

57 

9.99729 

0.99378 

9.99786 

0.99507 

9.99836 

0.99622 

9.99879 

0.99733 

9.99916 

0.99806 

12 

62 

58 

.99730 

.99380 

.99786 

.99509 

.99836 

.99624 

.99880 

.99723 

.99916 

.99807 

8 

56 

59 

.99731 

.99382 

.99787 

.99511 

.99837 

.99626 

.99880 

.99725 

.99917 

.99808 

4 

60 

60 

9.99732 

0.99384 

9.99788 

0.99513 

9.99838 

0.99627 

9.99881 

0.99726 

9.99917 

0.99810 

0 

12h  sem           1 

12h  32m         1 

12h 28m          1 

12h  24m          1 

12h  20m          1 

TABLE  45.                 [Page  921 

Haversines. 

a    ' 

llh40m       175° 

llh44m       176° 

llh  48m       177° 

llh  52m       178° 

llh  56m       179° 

3 

60 

Log.  Ilav 

Nat.  Hav. 

Log.  Hav 

Nat.  Hav. 

Log.  Hav. 

Nat.  Hav 

Log.  Hav. 

Nat.  Hav. 
0.99970 

lyog.  Hav. 
9.99997 

Nat.  Hav. 
0.99992 

0      0 

9.99917 

0.99810 

9.99947 

0.99878 

9.99970 

0.99931 

9.99987 

4       1 

.99918 

.99811 

.99948 

.99879 

.99971 

.99932 

.99987 

.99971 

.99997 

.99993 

56 

8      3 

.99918 

.99812 

.99948 

.99880 

.99971 

.99933 

.99987 

.99971 

.99997 

.99993 

52 

12      3 

.99919 

.99814 

.99948 

.99881 

.99971 

.99934 

.99987 

.99971 

.99997 

.99993 

48 

16      4 

9.99919 

0.99815 

9.99949 

0.99882 

9.99972 

0.99934 

9.99988 

0.99972 

9.99997 

0.99994 

44 

20      5 

.99920 

.99816 

.99949 

.99883 

.99972 

.99935 

.99988 

.99972 

.99997 

.99994 

40 

24      6 

.99921 

.99817 

.99950 

.99884 

.99972 

.99936 

.99988 

.99973 

.99997 

.99994 

86 

28      7 

.99921 

.99819 

.99950 

.99885 

.99973 

.99937 

.99988 

.99973 

.99997 

.99994 

32 

5^   8 

9.99922 

0.99820 

9.99951 

0.99886 

9.99973 

0.99937 

9.99988 

0.99973 

9.99998 

0.99994 

28 

36      9 

.99922 

.99821 

.99951 

.99887 

.99973 

.99938 

.99989 

.99974 

.99998 

.99995 

24 

40  10 

.99923 

.99822 

.99951 

.99888 

.99973 

.99939 

.99989 

.99974 

.99998 

.99995 

20 

■W  11 

.99923 

.99823 

.99952 

.99889 

.99974 

.99940 

.99989 

.99975 

.99998 

.99995 

16 

4S    12 

9.99924 

0.99825 

9.99952 

0.99890 

9.99974 

0.99940 

9.99989 

0.99975 

9.99998 

0.99995 

12 

5;?  13 

.99924 

.99826 

.99953 

.99891 

.99974 

.99941 

.99989 

.99976 

.99998 

.99995 

8 

56    U 

9.99925 

0.99827 

9.99953 

0.99892 

9.99975 

0.99942 

9.99990 

0.99976 

9.99998 

0.99996 

4 

12fi  19m 

12h'  15m 

12h  lim 

12h  7m 

12hsm 

s   ' 

llh4im       175° 

llh  4sm       176° 

llh  49m        177 

llh5Sm       178° 

llh  57m       179° 

s 

0  15 

9.99925 

0.99828 

9.99953 

0.99893 

9.99975 

0.99942 

9.99990 

0.99977 

9.99998 

0.99996 

'W 

4    16 

.99926 

.99829 

.99954 

.99894 

.99975 

.99943 

.99990 

.99977 

.99998 

.99996 

56 

5  17 

.99926 

.99831 

.99954 

.99895 

.99976 

.99944 

.99990 

.99978 

.99998 

.99996 

52 

12    18 

.99927 

.99832 

.99954 

.99896 

.99976 

.99944 

.99990 

.99978 

.99998 

.99996 

48 

i6  19 

9.99927 

0.99833 

9.99955 

0.99897 

9.99976 

0.99945 

9.99991 

0.99978 

9.99998 

0.99996 

44 

«0  20 

.99928 

.99834 

.99955 

.99898 

.99976 

.99946 

.99991 

.99979 

.99999 

.99997 

40 

24    21 

.99928 

.99835 

.99956 

.99899 

.99977 

.99947 

.99991 

.99979 

.99999 

.99997 

36 

«5  22 

.99929 

.99837 

.99956 

.99900 

.99977 

.99947 

.99991 

.99980 

.99999 

.99997 

32 

32    23 

9.99929 

0.99838 

9.99957 

0.99900 

9.99977 

0.99948 

9.99991 

0.99980 

9.99999 

0.99997 

28 

■J6  24 

.99930 

.99839 

.99957 

.99901 

.99978 

.99949 

.99992 

.99981 

.99999 

.99997 

24 

40  25 

.99931 

.99840 

.99958 

.99902 

.99978 

.99949 

.99992 

.99981 

.99999 

.99997 

20 

44  26 

.99931 

.99841 

.99958 

.99903 

.99978 

.99950 

.99992 

.99981 

.99999 

.99998 

16 

4^  27 

9.99932 

0.99842 

9.99958 

0.99904 

9.99978 

0.99950 

9.99992 

0.99982 

9.99999 

0.99998 

12 

52    28 

.99932 

.99844 

.99959 

.99905 

.99979 

.99951 

.99992 

.99982 

.99999 

.99998 

8 

56  29 

9.99933 

0.99845 

9.99959 

0.99906 

9.99979 

0.99952 

9.99992 

0.99982 

9.99999 

0.99998 

4 

12h  18m 

12h  14m 

12h  10m 

12h6m 

12h2m 

8    ' 

llh42m       175° 

llh  46m       176° 

llhSOm       177° 

llh  54m       178° 

llh  58m       179° 

s 
60 

0    30 

9.99933 

0.99846 

9.99959 

0.99907 

9.99979 

0.99952 

9.99993 

0.99983 

9.99999 

0.99998 

4  31 

.99934 

.99847 

.99960 

.99908 

.99980 

.99953 

.99993 

.99983 

.99999 

.99998 

56 

8    32 

.99934 

.99848 

.99960 

.99909 

.99980 

.99954 

.99993 

.99984 

.99999 

.99998 

52 

i;2  33 

.99935 

.99849 

.99961 

.99909 

.99980 

.99954 

.99993 

.99984 

.99999 

.99998 

48 

i6  34 

9.99935 

0.99850 

9.99961 

0.99910 

9.99980 

0.99955 

9.99993 

0.99984 

9.99999 

0.99999 

44 

20    35 

.99935 

.99851 

.99961 

.99911 

.99981 

.99956 

.99993 

.99985 

.99999 

.99999 

40 

;g4  36 

.99936 

.99853 

.99962 

.99912 

.99981 

.99956 

.99994 

.99985 

9.99999 

.99999 

36 

28    37 

.99936 

.99854 

.99962 

.99913 

.99981 

.99957 

.99994 

.99985 

0.00000 

.99999 

32 

5^  38 

9.99937 

0.99855 

9.99963 

0.99914 

9.99981 

0.99957 

9.99994 

0.99986 

0.00000 

0.99999 

28 

56  39 

.99937 

.99856 

.99963 

.99915 

.99982 

.99958 

.99994 

.99986 

.00000 

.99999 

24 

40    40 

.99938 

.99857 

.99963 

.99915 

.99982 

►  .99959 

.99994 

.99986 

.00000 

.99999 

20 

44  41 

.99938 

.99858 

.99964 

.99916 

.99982 

.99959 

.99994 

.99987 

.00000 

.99999 

16 

48    42 

9.99939 

0.99859 

9.99964 

0.99917 

9.99983 

0.99960 

9.99994 

0.99987 

0.00000 

0.99999 

12 

5:2  43 

.99939 

.99860 

.99964 

.99918 

.99983 

.99960 

.99995 

.99987 

.00000 

.99999 

8 

56  44 

9.99940 

0.99861 

9.99965 

0.99919 

9.99983 

0.99961 

9.99995 

0.99988 

0.00000 

0.99999 

4 

12h  17m 

12h ism         1 

12h9m 

12h5m 

12h  im 

s   ' 

llk4sm       175°  j 

llh  47m       176°  1 

llhsim       177° 

llh  55m       178° 

llh  59m       179° 

s 
60 

0    45 

9.99940 

0.99863 

9.99965 

0.99920 

9.99983 

0.99961 

9.99995 

0.99988 

0.00000 

1.00000 

4  46 

.99941 

.99864 

.99965 

.99920 

.99983 

.99962 

.99995 

.99988 

.00000 

.00000 

56 

^  47 

.99941 

.99865 

.99966 

.99921 

.99984 

.99963 

.99995 

.99989 

.00000 

.OGOOO 

52 

1:?  48 

.99942 

.99866 

.99966 

.99922 

.99984 

.99963 

.99995 

.99989 

.00000 

.00000 

48 

16    49 

9.99942 

0.99867 

9.99966 

0.99923 

9.99984 

0.99964 

9.99995 

0.99989 

0.00000 

1.00000 

44 

;20  50 

.99943 

.99868 

.99967 

.99934 

.99984 

.99964 

.99996 

.99990 

.00000 

.00000 

40 

24    51 

.99943 

.99869 

.99967 

.99924 

.99985 

.99965 

.99996 

.99990 

.00000 

.00000 

36 

;g5  52 

.99943 

.99870 

.99968 

.99925 

.99985 

.99965 

.99996 

.99990 

.00000 

.00000 

32 

5:2  53 

9.99944 

0.99871 

9.99968 

0.99926 

9.99985 

0.99966 

9.99996 

0.99991 

0.00000 

1.00000 

28 

36    54 

.99944 

.99872 

.99968 

.99927 

.99985 

.99966 

.99996 

.99991 

.00000 

.00000 

24 

40  55 

.99945 

.99873 

.99969 

.99928 

.99986 

.99967 

.99996 

.99991 

.00000 

.00000 

20 

44    56 

.99945 

.99874 

.99969 

.99928 

.99986 

.99967 

.99996 

.99991 

.00000 

.00000 

16 

4<S  57 

9.99946 

0.99875 

9.99969 

0.99929 

9.99986 

0.99968 

9.99996 

0.99992 

0.00000 

1.00000 

12 

5;g  68 

.99946 

.99876 

.99970 

.99930 

.99986 

.99969 

.99996 

.99992 

.00000 

.00000 

8 

56    59 

.99947 

.99877 

.99970 

.99931   .99987 

.99969 

.99997 

.99992 

.00000 

.00000 

4 

60  60 

9.99947 

0.99878  9.99970 

0.99931  9.99987 

0.99970 

9.99997 

0.99992 

0.00000 

1.00000 

0 

12h  16m          1    i2h  12m          |     i2h  gm           | 

12h  4m          1 

12hom           1 

Page  922]                                            TABLE  46. 

CorrectioDs*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

the  True  Altitude. 

or  of  the  Sun's 

Lower  lAvnh,  to  Find 

HEIGHT  OF  THE  EYE.                                                                            1 

8  Feet. 

9  Feet. 

10  Feet. 

11  Feet. 

12  Feet. 

13  Feet.         1 

Obs.  Alt. 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

O 

>i< 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

COIT. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

o     / 
6  30 

5  29 

10  40 

5  19 

10  50 

5  09 

11  00 

5  00 

11  09 

4  51 

11  18 

4  43 

11  26 

40 

5  39 

10  30 

5  29 

10  40 

5  19 

10  50 

5  10 

10  59 

5  01 

11  08 

4  53 

11  16 

50 

5  49 

10  20 

5  39 

10  30 

5  29 

10  40 

5  20 

10  49 

5  11 

10  58 

5  03 

11  06 

7  00 

5  59 

10  10 

5  49 

10  20 

5  39 

10  30 

5  30 

10  39 

5  21 

10  48 

5  13 

10  56 

10 

6  08 

10  01 

5  58 

10  11 

5  48 

10  21 

5  39 

10  30 

5  30 

10  39 

5  22 

10  47 

20 

6  17 

9  52 

6  07 

10  02 

5  57 

10  12 

5  48 

10  21 

5  39 

10  30 

5  31 

10  38 

7  30 

6  26 

9  43 

6  16 

9  53 

6  06 

10  03 

5  57 

10  12 

5  48 

10  21 

5  40 

10  29 

40 

6  34 

9  35 

6  24 

9  45 

6  14 

9  55 

6  05 

10  04 

5  56 

10  13 

5  48 

10  21 

50 

6  42 

9  27 

6  32 

9  37 

6  22 

9  47 

6  13 

9  56 

6  04 

10  05 

5  56 

10  13 

8  00 

6  50 

9  19 

6  40 

9  29 

6  30 

9  39 

6  21 

9  48 

6  12 

9  57 

6  04 

10  05 

10 

6  57 

9  12 

6  47 

9  22 

6  37 

9  32 

6  28 

9  41 

6  19 

9  50 

6  11 

9  58 

20 

7  04 

9  05 

6  54 

9  15 

6  44 

9  25 

6  35 

9  34 

6  26 

9  43 

6  18 

9  51 

8  30 

7  11 

8  58 

7  01 

9  08 

6  51 

9  18 

6  42 

9  27 

6  33 

9  36 

6  25 

9  44 

40 

7  18 

8  51 

7  08 

9  01 

6  58 

9  11 

6  49 

9  20 

6  40 

9  29 

6  32 

9  37 

50 

7  24 

8  45 

7  14 

8  55 

7  04 

9  05 

6  55 

9  14 

6  46 

9  23 

6  38 

9  31 

9  00 

7  30 

8  39 

7  20 

8  49 

7  10 

8  59 

7  01 

9  08 

6  52 

9  17 

6  44 

9  25 

20 

7  42 

8  27 

7  32 

8  37 

7  22 

8  47 

7  13 

8  56 

7  04 

9  05 

6  56 

9  13 

40 

7  53 

8  16 

7  43 

8  26 

7  33 

8  36 

7  24 

8  45 

7  15 

8  54 

7  07 

9  02 

10  00 

8  04 

8  05 

7  54 

8  15 

7  44 

8  25 

7  35 

8  34 

7  26 

8  43 

7  18 

8  51 

20 

8  14 

7  55 

8  04 

8  05 

7  54 

8  15 

7  45 

8  24 

7  36 

8  33 

7  28 

8  41 

40 

8  23 

7  46 

8  13 

7  56 

8  03 

8  06 

7  54 

8  15 

7  45 

8  24 

7  37 

8  32 

11  00 

8  32 

7  37 

8  22 

7  47 

8  12 

7  57 

8  03 

8  06 

7  54 

8  15 

7  46 

8  23 

30 

8  44 

7  25 

8  34 

7  35 

8  24 

7  45 

8  15 

7  54 

8  06 

8  03 

7  58 

8  11 

12  00 

8  55 

7  14 

8  45 

7  24 

8  35 

7  34 

8  26 

7  43 

8  17 

7  52 

8  09 

8  00 

30 

9  06 

7  03 

8  56 

7  13 

8  46 

7  23 

8  37 

7  32 

8  28 

7  41 

8  20 

7  49 

13  00 

9  16 

6  53 

9  06 

7  03 

8  56 

7  13 

8  47 

7  22 

8  38 

7  31 

8  30 

7  39 

30 

9  25 

6  44 

9  15 

6  54 

9  05 

7  04 

8  56 

7  13 

8  47 

7  22 

8  39 

7  30 

14  00 

9  33 

6  36 

9  23 

6  46 

9  13 

6  56 

9  04 

7  05 

8  55 

7  14 

8  47 

7  22 

15  00 

9  49 

6  20 

9  39 

6  30 

9  29 

6  40 

9  20 

6  49 

9  11 

6  58 

9  03 

7  06 

16  00 

10  02 

6  07 

9  52 

6  17 

9  42 

6  27 

9  33 

6  36 

9  24 

6  45 

9  16 

6  53 

17  00 

10  15 

5  54 

10  05 

6  04 

9  55 

6  14 

9  46 

6  23 

9  37 

6  32 

9  29 

6  40 

18  00 

10  25 

5  44 

10  15 

5  54 

10  05 

6  04 

9  56 

6  13 

9  47 

6  22 

9  39 

6  30 

19  00 

10  35 

5  34 

10  25 

5  44 

10  15 

5  54 

10  06 

6  03 

9  57 

6  12 

9  49 

6  20 

20  00 

10  43 

5  25 

10  33 

5  35 

10  23 

5  45 

10  14 

5  54 

10  05 

6  03 

9  57 

6  11 

22  00 

10  59 

5  09 

10  49 

5  19 

10  39 

5  29 

10  30 

5  38 

10  21 

5  47 

10  13 

5  55 

24  00 

11  12 

4  56 

11  02 

5  06 

10  52 

5  16 

10  43 

5  25 

10  34 

5  34 

10  26 

5  42 

26  00 

11  23 

4  45 

11  13 

4  55 

11  03 

5  05 

10  54 

5  14 

10  45 

5  23 

10  37 

5  31 

28  00 

11  33 

4  35 

11  23 

4  45 

11  13 

4  55 

11  04 

5  04 

10  55 

5  13 

10  47 

5  21 

30  00 

11  41 

4  27 

11  31 

4  37 

11  21 

.  4  47 

11  12 

4  56 

11  03 

5  05 

10  55 

5  13 

32  00 

11  49 

4  19 

11  39 

4  29 

11  29 

4  39 

11  20 

4  48 

11  11 

4  57 

11  03 

5  05 

34  00 

11  56 

4  12 

11  46 

4  22 

11  36 

4  32 

11  27 

4  41 

11  18 

4  50 

11  10 

4  58 

36  00 

12  02 

4  06 

11  52 

4  16 

11  42 

4  26 

11  33 

4  35 

11  24 

4  44 

11  16 

4  52 

38  00 

12  07 

4  01 

11  57 

4  11 

11  47 

4  21 

11  38 

4  30 

11  29 

4  39 

11  21 

4  47 

40  00 

12  12 

3  55 

12  02 

4  05 

11  52 

4  15 

11  43 

4  24 

11  34 

4  33 

11  26 

4  41 

45  00 

12  23 

3  44 

12  13 

3  54 

12  03 

4  04 

11  54 

4  13 

11  45 

4  22 

11  37 

4  30 

50  00 

12  31 

3  35 

12  21 

3  45 

12  11 

3  55 

12  02 

4  04 

11  53 

4  13 

11  45 

4  21 

55  00 

12  38 

3  27 

12  28 

3  37 

12  18 

3  47 

12  09 

3  56 

12  00 

4  05 

11  52 

4  13 

60  00 

12  44 

3  20 

12  34 

3  30 

12  24 

3  40 

12  15 

3  49 

12  06 

3  58 

11  58 

4  06 

65  00 

12  51 

3  13 

12  41 

3  23 

12  31 

3  33 

12  22 

3  42 

12  13 

3  51 

12  05 

3  59 

70  00 

12  56 

3  07 

12  46 

3  17 

12  36 

3  27 

12  27 

3  36 

12  18 

3  45 

12  10 

3  53 

75  00 

13  00 

3  02 

12  50 

3  12 

12  40 

3  22 

12  31 

3  31 

12  22 

3  40 

12  14 

3  48 

80  00 

13  06 

2  56 

12  56 

3  06 

12  46 

3  16 

12  37 

3  25 

12  28 

3  34 

12  20 

3  42 

85  00 

13  10 

2  51 

13  00 

3  01 

12  50 

3  11 

12  41 

3  20 
3  15 

12  32 

3  29 

12  24 

3  37 

90  00 

13  14 

2  46 

13  04 

2  56 

12  54 

3  06 

12  45 

12  36 

3  24 

12  28 

3  32 

1 

Additioi 

TAL  COKR. 

Day  of  Month. 

Jan. 

Feb.     Mar. 

Apr 

May. 

June 

July. 

Aug. 

Sept. 

Oct. 

Noi 

T. 

Dec. 

,f 

r/ 

,f 

„ 

// 

// 

f, 

„ 

tf 

// 

t 

ff 

FOR  SU 

N's  Alt. 

l8ttol5th.... 

+18 

+15 

+8 

0 

-  8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th  to  31st... 

+17 

+12 

+4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*Thec 

orrections  for  theobserved  altitude  of  a  Star  or  Planet  involves  the  di] 

)and  the  refraction; 

and  for  the  observed  altitude 

of  the  Sun 

s  lower  limb,  the  dip,  refraction,  parallax,  and  mean  semidiameter,  wi 

lich  is  taken  as  16'. 

A  supplementary  correction 

taking  acc( 

)unt  of  the  variation  of  the  Sun's  semidiameter  in  the  different  month 

s  of  the  year  is  given 

at  the  foot  of  the  main  table 

TABLE  46. 

[Page  923 

CorrectioDfl  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's 

Lower  Limb,  to  Find 

the  True  Altitude — Continued. 

Ob8.  Alt. 

HEIGHT  OF  THE  EYE.                                                                            1 

14  Feet. 

16  Feet. 

16  Feet. 

17  Feet. 

18  Feet. 

19  Feet.         1 

O 

* 

O 

* 

G 

* 

o 

* 

O 

:*> 

O 

if 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

star's 

Sun's 

star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

0           / 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

/     // 

6  30 

4  35 

11  34 

4  27 

11  42 

4  20 

11  49 

4  13 

11  56 

4  06 

12  03 

3  59 

12  10 

40 

4  45 

11  24 

4  37 

11  32 

4  30 

11  39 

4  23 

11  46 

4  16 

11  53 

4  09 

12  00 

50 

4  55 

11  14 

4  47 

11  22 

4  40 

11  29 

4  33 

11  36 

4  26 

11  43 

4  19 

11  50 

7  00 

5  05 

11  04 

4  57 

11  12 

4  50 

11  19 

4  43 

11  26 

4  36 

11  33 

4  29 

11  40 

10 

5  14 

10  55 

5  06 

11  03 

4  59 

11  10 

4  52 

11  17 

4  45 

11  24 

4  38 

11  31 

20 

5  23 

10  46 

5  15 

10  54 

5  08 

11  01 

5  01 

11  08 

4  54 

11  15 

4  47 

11  22 

7  30 

5  32 

10  37 

5  24 

10  45 

5  17 

10  52 

5  10 

10  59 

5  03 

11  06 

4  56 

11  13 

40 

5  40 

10  29 

5  32 

10  37 

5  25 

10  44 

5  18 

10  51 

5  11 

10  58 

5  04 

11  05 

50 

5  48 

10  21 

5  40 

10  29 

5  33 

10  36 

5  26 

10  43 

5  19 

10  50 

5  12 

10  57 

8  00 

5  56 

10  13 

5  48 

10  21 

5  41 

10  28 

5  34 

10  35 

5  27 

10  42 

5  20 

10  49 

10 

6  03 

10  06 

5  55 

10  14 

5  48 

10  21 

5  41 

10  28 

5  34 

10  35 

5  27 

10  42 

20 

6  10 

9  59 

6  02 

10  07 

5  55 

10  14 

5  48 

10  21 

5  41 

10  28 

5  34 

10  35 

8  30 

6  17 

9  52 

6  09 

10  00 

6  02 

10  07 

5  55 

10  14 

5  48 

10  21 

5  41 

10  28 

40 

6  24 

9  45 

6  16 

9  53 

6  09 

10  00 

6  02 

10  07 

5  55 

10  14 

5  48 

10  21 

50 

6  30 

9  39 

6  22 

9  47 

6  15 

9  54 

6  08 

10  01 

6  01 

10  08 

5  54 

10  15 

9  00 

6  36 

9  33 

6  28 

9  41 

6  21 

9  48 

6  14 

9  55 

6  07 

10  02 

6  00 

10  09 

20 

6  48 

9  21 

6  40 

9  29 

6  33 

9  36 

6  26 

9  43 

6  19 

9  50 

6  12 

9  57 

40 

6  59 

9  10 

6  51 

9  18 

6  44 

9  25 

6  37 

9  32 

6  30 

9  39 

6  23 

9  46 

10  00 

7  10 

8  59 

7  02 

9  07 

6  55 

9  14 

6  48 

9  21 

6  41 

9  28 

6  34 

9  35 

20 

7  20 

8  49 

7  12 

8  57 

7  05 

9  04 

6  58 

9  11 

6  51 

9  18 

6  44 

9  25 

40 

7  29 

8  40 

7  21 

8  48 

7  14 

8  55 

7  07 

9  02 

7  00 

9  09 

6  53 

9  16 

11  00 

7  38 

8  31 

7  30 

8  39 

7  23 

8  46 

7  16 

8  53 

7  09 

9  00 

7  02 

9  07 

30 

7  50 

8  19 

7  42 

8  27 

7  35 

8  34 

7  28 

8  41 

7  21 

8  48 

7  14 

8  55 

12  00 

8  01 

8  08 

7  53 

8  16 

7  46 

8  23 

7  39 

8  30 

7  32 

8  37 

7  25 

8  44 

30 

8  12 

7  57 

8  04 

8  05 

7  57 

8  12 

7  50 

8  19 

7  43 

8  26 

7  36 

8  33 

13  00 

8  22 

7  47 

8  14 

7  55 

8  07 

8  02 

8  00 

8  09 

7  53 

8  16 

7  46 

8  23 

30 

8  31 

7  38 

8  23 

7  46 

8  16 

7  53 

8  09 

8  00 

8  02 

8  07 

7  55 

8  14 

14  00 

8  39 

7  30 

8  31 

7  38 

8  24 

7  45 

8  17 

7  52 

8  10 

7  59 

8  03 

8  06 

15  00 

8  55 

7  14 

8  47 

7  22 

8  40 

7  29 

8  33 

7  36 

8  26 

7  43 

8  19 

7  50 

16  00 

9  08 

7  01 

9  00 

7  09 

8  53 

7  16 

8  46 

7  23 

8  39 

7  30 

8  32 

7  37 

17  00 

9  21 

6  48 

9  13 

6  56 

9  06 

7  03 

8  59 

7  10 

8  52 

7  17 

8  45 

7  24 

18  00 

9  31 

6  38 

9  23 

6  46 

9  16 

6  53 

9  09 

7  00 

9  02 

7  07 

8  55 

7  14 

19  00 

9  41 

6  28 

9  33 

6  36 

9  26 

6  43 

9  19 

6  50 

9  12 

6  57 

9  05 

7  04 

20  00 

9  49 

6  19 

9  41 

6  27 

9  34 

6  34 

9  27 

6  41 

9  20 

6  48 

9  13 

6  55 

22  00 

10  05 

6  03 

9  57 

6  11 

9  50 

6  18 

9  43 

6  25 

9  36 

6  32 

9  29 

6  39 

24  00 

10  18 

5  50 

10  10 

5  58 

10  03 

6  05 

9  56 

6  12 

9  49 

6  19 

9  42 

6  26 

26  00 

10  29 

5  39 

10  21 

5  47 

10  14 

5  54 

10  07 

6  01 

10  00 

6  08 

9  53 

6  15 

28  00 

10  39 

5  29 

10  31 

5  37 

10  24 

5  44 

10  17 

5  51 

10  10 

5  58 

10  03 

6  05 

30  00 

10  47 

5  21 

10  39 

5  29 

10  32 

5  36 

10  25 

5  43 

10  18 

5  50 

10  11 

5  57 

32  00 

10  55 

5  13 

10  47 

5  21 

10  40 

5  28 

10  33 

5  35 

10  26 

5  42 

10  19 

5  49 

34  00 

11  02 

5  06 

10  54 

5  14 

10  47 

5  21 

10  40 

5  28 

10  33 

5  35 

10  26 

5  42 

36  00 

11  08 

5  00 

11  00 

5  08 

10  53 

5  15 

10  46 

5  22 

10  39 

5  29 

10  32 

5  36 

38  00 

11  13 

4  55 

11  05 

5  03 

10  58 

5  10 

10  51 

5  17 

10  44 

5  24 

10  37 

5  31 

40  00 

11  18 

4  49 

11  10 

4  57 

11  03 

6  04 

10  56 

5  11 

10  49 

5  18 

10  42 

5  25 

45  00 

11  29 

4  38 

11  21 

4  46 

11  14 

4  53 

11  07 

5  00 

11  00 

5  07 

10  53 

5  14 

50  00 

11  37 

4  29 

11  29 

4  37 

11  22 

4  44 

11  15 

4  51 

11  08 

4  58 

11  01 

5  05 

55  00 

11  44 

4  21 

11  36 

4  29 

11  29 

4  36 

11  22 

4  43 

11  15 

4  50 

11  08 

4  57 

60  00 

11  50 

4  14 

11  42 

4  22 

11  35 

4  29 

11  28 

4  36 

11  21 

4  43 

11  14 

4  50 

65  00 

11  57 

4  07 

11  49 

4  15 

11  42 

4  22 

11  35 

4  29 

11  28 

4  36 

11  21 

4  43 

70  00 

12  02 

4  01 

11  54 

4  09 

11  47 

4  16 

11  40 

4  23 

11  33 

4  30 

11  26 

4  37 

75  00 

12  06 

3  56 

11  58 

4  04 

11  51 

4  11 

11  44 

4  18 

11  37 

4  25 

11  30 

4  32 

80  00 

12  12 

3  50 

12  04 

3  58 

11  57 

4  05 

11  50 

4  12 

11  43 

4  19 

11  36 

4  26 

85  00 

12  16 

3  45 

12  08 

3  53 

12  01 

4  00 

11  54 

4  07 

11  47 

4  14 

11  40 

4  21 

90  00 

12  20 

3  40 

12  12 

3  48 

12  05 

3  55 

11  58 

4  02 

11  51 

4  09 

11  44 

4  16 

1 

Additional  Core. 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

lune. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

/, 

/, 

,/ 

rr 

„ 

// 

// 

// 

// 

n 

/' 

FOE  Sun's  Alt. 

let  to  15th... - 

+18 

+15 

H 

-8 

0 

-8    - 

-13 

-14 

-11 

-5 

+3 

+  11 

+16 

16thto3l8t... 

+17 

+12 

H 

-4 

-4 

-11    - 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*  The  corrections  for  the  observed  altitude  of  a  Star  or  Pla 

net  involves  the  dip  and  the  refraction; 

and  for  the  observed  altitude 

of  the  Sun's  lower  limb,  the  dip,  refraction,  parallax,  and  me£ 

in  semidiameter,  which  is  taken  as  16'. 

A  supplementary  correction 
Ekt  the  foot  of  the  main  table. 

taking  account  of  the  variation  of  the  Sun's  semidiameter  in  t 

iie  different  months  of  the  year  is  given 

21594°— 14- 


-51 


Page  824] 

TABLE  46. 

Corrections  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun's 

Lower  Limb,  to  Find 

the  True  Altitude — Continued. 

Ob3.  Alt. 

HEIGHT  OF  THE  EYE.                                                                            i 

20  Feet.          j 

21  Feet.         | 

22  Feet.         1 

23  Feet.         1 

24  Feet.         1 

25  Feet.         j 

O 

* 

O 

* 

0 

* 

O 

* 

0 

* 

O 

* 

Sun's 

star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

Star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

o       ' 

6  30 

3  52 

12  17 

3  46 

12  23 

3  39 

12  30 

3  33 

12  36 

3  27 

12  42 

3  21 

12  48 

40 

4  .2 

12  07 

3  56 

12  13 

3  49 

12  20 

3  43 

12  26 

3  37 

12  32 

3.31 

12  38 

50 

4  12 

11  57 

4  06 

12  03 

3  59 

12  10 

3  53 

12  16 

3  47 

12  22 

3  41 

12  28 

7  00 

4  22 

11  47 

4  16 

11  53 

4  09 

12  00 

4  03 

12  06 

3  57 

12  12 

3  51 

12  18 

10 

4  31 

11  38 

4  25 

11  44 

4  18 

11  51 

4  12 

11  57 

4  06 

12  03 

4  00 

12  09 

20 

4  40 

11  29 

4  34 

11  35 

4  27 

11  42 

4  21 

11  48 

4  15 

11  54 

4  09 

12  00 

7  30 

4  49 

11  20 

4  43 

11  26 

4  36 

11  33 

4  30 

11  39 

4  24 

11  45 

4  18 

11  51 

40 

5b 

4  57 

11  12 

4  51 

11  18 

4  44 

11  25 

4  38 

11  31 

4  32 

11  37 

4  26 

11  43 

5  05 

11  04 

4  59 

11  10 

4  52 

11  17 

4  46 

11  23 

4  40 

11  29 

4  34 

11  35 

8  00 

5  13 

10  56 

5  07 

11  02 

5  00 

11  09 

4  54 

11  15 

4  48 

11  21 

4  42 

11  27 

10 

5  20 

10  49 

5  14 

10  55 

5  07 

11  02 

5  01 

11  08 

4  55 

11  14 

4  49 

11  20 

20 

5  27. 

10  42 

5  21 

10  48 

5  14 

10  55 

5  08 

11  01 

5  02 

11  07 

4  56 

11  13 

8  30 

5  34 

10  35 

5  28 

10  41 

5  21 

10  48 

5  15 

10  54 

5  09 

11  00 

5  03 

11  06 

40 

5  41 

10  28 

5  35 

10  34 

5  28 

10  41 

5  22 

10  47 

5  16 

10  53 

5  10 

10  59 

50 

5  47 

10  22 

5  41 

10  28 

5  34 

10  35 

5  28 

10  41 

5  22 

10  47 

5  16 

10  53 

9  00 

5  53 

10  16 

5  47 

10  22 

5  40 

10  29 

5  34 

10  35 

5  28 

10  41 

5  22 

10  47 

20 

6  05 

10  04 

5  59 

10  10 

5  52 

10  17 

5  46 

10  23 

5  40 

10  29 

5  34 

10  35 

40 

6  16 

9  53 

6  10 

9  59 

6  03 

10  06 

5  57 

10  12 

5  51 

10  18 

5  45 

10  24 

10  00 

6  27 

9  42 

6  21 

9  48 

6  14 

9  55 

6  08 

10  01 

6  02 

10  07 

5  56 

10  13 

20 

6  37 

9  32 

6  31 

9  38 

6  24 

9  45 

6  18 

9  51 

6  12 

9  57 

6  06 

10  03 

40 

6  46 

9  23 

6  40 

9  29 

6  33 

9  36 

6  27 

9  42 

6  21 

9  48 

6  15 

9  54 

11  00 

6  55 

9  14 

6  49 

9  20 

6  42 

9  27 

6  36 

9  33 

6  30 

9  39 

6  24 

9  45 

30 

7  07 

9  02 

7  01 

9  08 

6  54 

9  15 

6  48 

9  21 

6  42 

9  27 

6  36 

9  33 

12  00 

7  18 

8  51 

7  12 

8  57 

7  05 

9  04 

6  59 

9  10 

6  53 

9  16 

6  47 

9  22 

30 

7  29 

8  40 

7  23 

8  46 

7  16 

8  53 

7  10 

8  59 

7  04 

9  05 

6  58 

9  11 

13  00 

7  39 

8  30 

7  33 

8  36 

7  26 

8  43 

7  20 

8  49 

7  14 

8  55 

7  08 

9  01 

30 

7  48 

8  21 

7  42 

8  27 

7  35 

8  34 

7  29 

8  40 

7  23 

8  46 

7  17 

8  52 

14  00 

7  56 

8  13 

7  50 

8  19 

7  43 

8  26 

7  37 

8  32 

7  31 

8  38 

7  25 

8  44 

15  00 

8  12 

7  57 

8  06 

8  03 

7  59 

8  10 

7  53 

8  16 

7  47 

8  22 

7  41 

8  28 

16  00 

8  25 

7  44 

8  19 

7  50 

8  12 

7  57 

8  06 

8  03 

8  00 

8  09 

7  54 

8  15 

17  00 

8  38 

7  31 

8  32 

7  37 

8  25 

7  44 

8  19 

7  50 

8  13 

7  56 

8  07 

8  02 

18  00 

8  48 

7  21 

8  42 

7  27 

8  35 

7  34 

8  29 

7  40 

8  23 

7  46 

8  17 

7  52 

19  00 

8  58 

7  11 

8  52 

7  17 

8  45 

7  24 

8  39 

7  30 

8  33 

7  36 

8  27 

7  42 

20  00 

9  06 

7  02 

9  00 

7  08 

8  53 

7  15 

8  47 

7  21 

8  41 

7  27 

8  35 

7  33 

22  00 

9  22 

6  46 

9  16 

6  52 

9  09 

6  59 

9  03 

7  05 

8  57 

7  11 

8  51 

7  17 

24  00 

9  35 

6  33 

9  29 

6  39 

9  22 

6  46 

9  16 

6  52 

9  10 

6  58 

9  04 

7  04 

26  00 

9  46 

6  22 

9  40 

6  28 

9  33 

6  35 

9  27 

6  41 

9  21 

6  47 

9  15 

6  53 

28  00 

9  56 

6  12 

9  50 

6  18 

9  43 

6  25 

9  37 

6  31 

9  31 

6  37 

9  25 

6  43 

30  00 

10  04 

6  04 

9  58 

6  10 

9  51 

6  17 

9  45 

6  23 

9  39 

6  29 

9  33 

6  35 

32  00 

10  12 

5  56 

10  06 

6  02 

9  59 

6  09 

9  53 

6  15 

9  47 

6  21 

9  41 

6  27 

34  00 

10  19 

5  49 

10  13 

5  55 

10  06 

6  02 

10  00 

6  08 

9  54 

6  14 

9  48 

6  20 

36  00 

10  25 

5  43 

10  19 

5  49 

10  12 

5  56 

10  06 

6  02 

10  00 

6  08 

9  54 

6  14 

38  00 

10  30 

5  38 

10  24 

5  44 

10  17 

5  51 

10  11 

5  57 

10  05 

6  03 

9  59 

6  09 

40  00 

10  35 

5  32 

10  29 

5  38 

10  22 

5  45 

10  16 

5  51 

10  10 

5  57 

10  04 

6  03 

45  00 

10  46 

5  21 

10  40 

5  27 

10  33 

5  34 

10  27 

5  40 

10  21 

5  46 

10  15 

5  52 

50  00 

10  54 

5  12 

10  48 

5  18 

10  41 

5  25 

10  35 

5  31 

10  29 

5  37 

10  23 

5  43 

55  00 

11  01 

5  04 

10  55 

5  10 

10  48 

5  17 

10  42 

5  23 

10  36 

5  29 

10  30 

5  35 

60  00 

11  07 

4  57 

11  01 

5  03 

10  54 

5  10 

10  48 

5  16 

10  42 

5  22 

10  36 

5  28 

65  00 

11  14 

4  50 

11  08 

4  56 

11  01 

5  03 

10  55 

5  09 

10  49 

5  15 

10  43 

5  21 

70  00 

11  19 

4  44 

11  13 

4  50 

11  06 

4  57 

11  00 

5  03 

10  54 

5  09 

10  48 

5  15 

75  00 

11  23 

4  39 

11  17 

4  45 

11  10 

4  52 

11  04 

4  58 

10  58 

5  04 

10  52 

5  10 

80  00 

11  29 

4  33 

11  23 

4  39 

11  16 

4  46 

11  10 

4  52 

11  04 

4  58 

10  58 

5  04 

85  00 

11  33 

4  28 

11  27 

4  34 

11  20 

4  41 

11  14 

4  47 

11  08 

4  53 

11  02 

4  59 

90  00 

11  37 

4  23 

11  31 

4  29 

11  24 

4  36 

11  18 

4  42 

11  12 

4  48 

11  06 

4  54 

1 

Additional  Core 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

.    May. 

June. 

July.    Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

ft 

It 

t> 

// 

>> 

II 

II 

II 

II 

II 

II 

" 

FOE  Sun's  Alt. 

1st  to  15th.... 

+18 

+15 

+8 

C 

1     -8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th  to  31st... 

+17 

+12 

+4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*  The  corrections 

for  the  observed  altitude  of  a  Star  or  Planet  involves  the  di] 

~>  and  the  refraction; 

and  for  the  observed  altitude 

of  the  Sun's  lower  IL 

mb,  the  dip,  refraction, parallax,  and  mean semidiametar,  w 

hichistakenas  16'. 

A  supplementary  correction 
I  at  the  toot  of  the  main  table. 

taking  account  of  th 

e  variation  of  the  Sun's  semidiameter  in  the  different  montl 

sof  the  year  is  giver 

TABLE  46. 

[Page  926  1 

Correctiona* 

to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  | 

the  True  Altitude — Continued. 

1 

Obs.  Alt. 

HEIGHT  OF  THE  EYE.                                                                       | 

26  Feet. 

27  Feet. 

28  Feet. 

29  Feet. 

30  Feet.           1 

O 

* 

O 

« 

O 

« 

O 

* 

O 

* 

Sun's 

star's 

Sun's 

star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

6  30 

3  15 

12  54 

3  09 

13  00 

3  04 

/     // 
13  05 

2  58 

13  11 

2  53 

13  16 

40 

3  25 

12  44 

3  19 

12  50 

3  14 

12  55 

3  08 

13  01 

3  03 

13  06 

50 

3  35 

12  34 

3  29 

12  40 

3  24 

12  45 

3  18 

12  51 

3  13 

12  56 

7  00 

3  45 

12  24 

3  39 

12  30 

3  34 

12  35 

3  28 

12  41 

3  23 

12  46 

10 

3  54 

12  15 

3  48 

12  21 

3  43 

12  26 

3  37 

12  32 

3  32 

12  37 

20 

4  03 

12  06 

3  57 

12  12 

3  52 

12  17 

3  46 

12  23 

3  41 

12  28 

7  30 

4  12 

11  57 

4  06 

12  03 

4  01 

12  08 

3  55 

12  14 

3  50 

12  19 

40 

4  20 

11  49 

4  14 

11  55 

4  09 

12  00 

4  03 

12  06 

3  58 

12  11 

50 

4  28 

11  41 

4  22 

11  47 

4  17 

11  52 

4  11 

11  58 

4  06 

12  03  . 

8  00 

4  36 

11  33 

4  30 

11  39 

4  25 

11  44 

4  19 

11  50 

4  14 

11  55 

10 

4  43 

11  26 

4  37 

11  32 

4  32 

11  37 

4  26 

11  43 

4  21 

11  48 

20 

4  50 

11  19 

4  44 

11  25 

4  39 

11  30 

4  33 

11  36 

4  28 

11  41 

8  30 

4  57 

11  12 

4  51 

11  18 

4  46 

11  23 

4  40 

11  29 

4  35 

11  34 

40 

5  04 

11  05 

4  58 

11  11 

4  53 

11  16 

4  47 

11  22 

4  42 

11  27 

50 

5  10 

10  59 

5  04 

11  05 

4  59 

11  10 

4  53 

11  16 

4  48 

11  21 

9  00 

5  16 

10  53 

5  10 

10  59 

5  05 

11  04 

4  59 

11  10 

4  54 

11  15 

20 

5  28 

10  41 

5  22 

10  47 

5  17 

10  52 

5  11 

10  58 

5  06 

11  03 

40 

5  39 

10  30 

5  33 

10  36 

5  28 

10  41 

5  22 

10  47 

5  17 

10  52 

10  00 

5  50 

10  19 

5  44 

10  25 

5  39 

10  30 

5  33 

10  36 

5  28 

10  41 

20 

6  00 

10  09 

5  54 

10  15 

5  49 

10  20 

5  43 

10  26 

5  38 

10  31 

40 

6  09 

10  00 

6  03 

10  06 

5  58 

10  11 

5  52 

10  17 

5  47 

10  22 

11  00 

6  18 

9  51 

6  12 

9  57 

6  07 

10  02 

6  01 

10  08 

5  56 

10  13 

30 

6  30 

9  39 

6  24 

9  45 

6  19 

9  50 

6  13 

9  56 

6  08 

10  01 

12  00 

6  41 

9  28 

6  35 

9  34 

6  30 

9  39 

6  24 

9  45 

6  19 

9  50 

30 

6  52 

9  17 

6  46 

9  23 

6  41 

9  28 

6  35 

9  34 

6  30 

9  39 

13  00 

7  02 

9  07 

6  56 

9  13 

6  51 

9  18 

6  45 

9  24 

6  40 

9  29 

30 

7  11 

8  58 

7  05 

9  04 

7  00 

9  09 

6  54 

9  15 

6  49 

9  20 

14  00 

7  19 

8  50 

7  13 

8  56 

7  08 

9  01 

7  02 

9  07 

6  57 

9  12 

15  00 

7  35 

8  34 

7  29 

8  40 

7  24 

8  45 

7  18 

8  51 

7  13 

8  56 

16  00 

7  48 

8  21 

7  42 

8  27 

7  37 

8  32 

7  31 

8  38 

7  26 

8  43 

17  00 

8  01 

8  08 

7  55 

8  14 

7  50 

8  19 

7  44 

8  25 

7  39 

8  30 

18  00 

8  11 

7  58 

8  05 

8  04 

8  00 

8  09 

7  54 

8  15 

7  49 

8  20 

19  00 

8  21 

7  48 

8  15 

7  54 

8  10 

7  59 

8  04 

8  05 

7  59 

8  10 

20  00 

8  29 

7  39 

8  23 

7  45 

8  18 

7  50 

8  12 

7  56 

8  07 

8  01 

22  00 

8  45 

7  23 

8  39 

7  29 

8  34 

7  34 

8  28 

7  40 

8  23 

7  45 

24  00 

8  58 

7  10 

8  52 

7  16 

8  47 

7  21 

8  41 

7  27 

8  36 

7  32 

26  00 

9  09 

6  59 

9  03 

7  05 

8  58 

7  10 

8  52 

7  16 

8  47 

7  21 

28  00 

9  19 

6  49 

9  13 

6  55 

9  08 

7  00 

9  02 

7  06 

8  57 

7  11 

30  00 

9  27 

6  41 

9  21 

6  47 

9  16 

6  52 

9  10 

6  58 

9  05 

7  03 

32  00 

9  35 

6  33 

9  29 

6  39 

9  24 

6  44 

9  18 

6  50 

9  13 

6  55 

34  00 

9  42 

6  26 

9  36 

6  32 

9  31 

6  37 

9  25 

6  43 

9  20 

6  48 

36  00 

9  48 

6  20 

9  42 

6  26 

9  37 

6  31 

9  31 

6  37 

9  26 

6  42 

38  00 

9  53 

6  15 

9  47 

6  21 

9  42 

6  26 

9  36 

6  32 

9  31 

6  37 

40  00 

9  58 

6  09 

9  52 

6  15 

9  47 

6  20 

9  41 

6  26 

9  36 

6  31 

45  00 

10  09 

5  58 

10  03 

6  04 

9  58 

6  09 

9  52 

6  15 

9  47 

6  20 

50  00 

10  17 

5  49 

10  11 

5  55 

10  06 

6  GO 

10  00 

6  06 

9  55 

6  11 

55  00 

10  24 

5  41 

10  18 

5  47 

10  13 

5  52 

10  07 

5  58 

10  02 

6  03 

60  00 

10  30 

5  34 

10  24 

5  40 

10  19 

5  45 

10  13 

5  51 

10  08 

5  56 

65  00 

10  37 

5  27 

10  31 

5  33 

10  26 

5  38 

10  20 

5  44 

10  15 

5  49 

70  00 

10  42 

5  21 

10  36 

5  27 

10  31 

5  32 

10  25 

5  38 

10  20 

5  43 

75  00 

10  46 

5  16 

10  40 

5  22 

10  35 

5  27 

10  29 

5  33 

10  24 

5  38 

80  00 

10  52 

5  10 

10  46 

5  16 

10  41 

5  21 

10  35 

5  27 

10  30 

5  32 

85  00 

10  56 

5  05 

10  50 

5  11 

10  45 

5  16 

10  39 

5  22 

10  34 

5  27 

90  00 

11  00 

5  00 

10  54 

5  06 

10  49 

5  11 

10  43 

5  17 

10  38 

5  22 

1 

Additionai,  Cc 

EB. 

Day  of  Month. 

Jan. 

Feb. 

Mai 

.     Apr.    ] 

May. 

June 

July. 

-Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

// 

,> 

/ 

// 

^/ 

// 

// 

" 

// 

f' 

// 

FOB  Sun's  Ai 

-T. 

Isl 

t  to  15th.... 

+18 

+15 

+J 

5         0    - 

-  8 

-13 

v-14 

-11 

-5 

+3 

+11 

+16 

16 

thto3l8t... 

+17 

+12 

+^ 

t      -4    - 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*  The  correct 

ons  for  the 

observed  altitude  of  a  £ 

)tar  or  Planet  involves  the  dip  and  the  refraction;  and  for 
t,  and  mean  semidiameter,  which  is  talcen  as  16'.    A  supp 
imeter  in  the  different  months  of  the  year  is  given  at  the  fc 

the  observed  altitude 

of  the  Sun's  lowe 

rlimb,  the 

dip,  refraction,  parallaj 

lementary  correction 

taking  account  of 

the  variati 

on  of  the  Sun'ssemidia 

ot  of  the  main  table. 

Page  926] 

TABLE  46. 

Corrrections  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb, 

to  Find 

the  True  Altitude — Continued. 

HEIGHT  OF  THE  EYE.                                                                       1 

31  Feet. 

32  Feet. 

33  Feet. 

34  Feet.         1 

35  Feet.            1 

Obs.  Alt. 

O 

* 

O 

* 

O 

* 

0 

* 

O 

♦ 

Sun's 

star's 

Sun's 

star's 

Sun's 

star's 

Sun's 

star's 

Sun's 

star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

o        / 

>      n 

/     // 

/     II 

/     i> 

/     // 

/    II 

/     // 

/     // 

/     // 

/      11 

6  30 

2  48 

13  21 

2  42 

13  27 

2  37 

13  32 

2  32 

13  37 

2  27 

13  42 

40 

2  58 

13  11 

2  52 

13  17 

2  47 

13  22 

2  42 

13  27 

2  37 

13  32 

50 

3  08 

13  01 

3  02 

13  07 

2  57 

13  12 

2  52 

13  17 

2  47 

13  22 

7  00 

3  18 

12  51 

3  12 

12  57 

3  07 

13  02 

3  02 

13  07 

2  57 

13  12 

10 

3  27 

12  42 

3  21 

12  48 

3  16 

12  53 

3  11 

12  58 

3  06 

13  03 

20 

3  36 

12  33 

3  30 

12  39 

3  25 

12  44 

3  20 

12  49 

3  15 

12  54 

7  30 

3  45 

12  24 

3  39 

12  30 

3  34 

12  35 

3  29 

12  40 

3  24 

12  45 

40 

3  53 

12  16 

3  47 

12  22 

3  42 

12  27 

3  37 

12  32 

3  32 

12  37 

50 

4  01 

12  08 

3  55 

12  14 

3  50 

12  19 

S  45 

12  24 

3  40 

12  29 

8  00 

4  09 

12  00 

4  03 

12  06 

3  58 

12  11 

3  53 

12  16 

3  48 

12  21 

10 

4  16 

11  53 

4  10 

11  59 

4  05 

12  04 

4  00 

12  09 

3  55 

12  14 

20 

4  23 

11  46 

4  17 

11  52 

4  12 

11  57 

4  07 

12  02 

4  02 

12  07 

8  30 

4  30 

11  39 

4  24 

11  45 

4  19 

11  50 

4  14 

11  55 

4  09 

12  00 

40 

4  37 

11  32 

4  31 

11  38 

4  26 

11  43 

4  21 

11  48 

4  16 

11  53 

50 

4  43 

11  26 

4  37 

11  32 

4  32 

11  37 

4  27 

11  42 

4  22 

11  47 

9  00 

4  49 

11  20 

4  43 

11  26 

4  38 

11  31 

4  33 

11  36 

4  28 

11  41 

20 

5  01 

11  08 

4  55 

11  14 

4  50 

11  19 

4  45 

11  24 

4  40 

11  29 

40 

5  12 

10  57 

5  06 

11  03 

5  01 

11  08 

4  56 

11  13 

4  51 

11  18 

10  00 

5  23 

10  46 

5  17 

10  52 

5  12 

10  57 

5  07 

11  02 

5  02 

11  07 

20 

5  33 

10  36 

5  27 

10  42 

5  22 

10  47 

5  17 

10  52 

5  12 

10  57 

40 

5  42 

10  27 

5  36 

10  33 

5  31 

10  38 

5  26 

10  43. 

5  21 

10  48 

11  00 

5  51 

10  18 

5  45 

10  24 

5  40 

10  29 

5  35 

10  34 

5  30 

10  39 

30 

6  03 

10  06 

5  57 

10  12 

5  52 

10  17 

5  47 

10  22 

5  42 

10  27 

12  00 

6  14 

9  55 

6  08 

10  01 

6  03 

10  06 

5  58 

10  11 

5  53 

10  16 

30 

6  25 

9  44 

6  19 

9  50 

6  14 

9  55 

6  09 

10  00 

6  04 

10  05 

13  00 

6  35 

9  34 

6  29 

9  40 

6  24 

9  45 

6  19 

9  50 

6  14 

9  55 

30 

6  44 

9  25 

6  38 

9  31 

6  33 

9  36 

6  28 

9  41 

6  23 

9  46 

14  00 

6  52 

9  17 

6  46 

9  23 

6  41 

9  28 

6  36 

9  33 

6  31 

9  38 

15  00 

7  08 

9  01 

7  02 

9  07 

6  57 

9  12 

6  52 

9  17 

6  47 

9  22 

16  00 

7  21 

8  48 

7  15 

8  54 

7  10 

8  59 

7  05 

9  04 

7  00 

9  09 

17  00 

7  34 

8  35 

7  28 

8  41 

7  23 

8  46 

7  18 

8  51 

7  13 

8  56 

18  00 

7  44 

8  25 

7  38 

8  31 

7  33 

8  36 

7  28 

8  41 

7  23 

8  46 

19  00 

7  54 

8  15 

7  48 

8  21 

7  43 

8  26 

7  38 

8  31 

7  33 

8  36 

20  00 

8  02 

8  06 

7  56 

8  12 

7  51 

8  17 

7  46 

8  22 

7  41 

8  27 

22  00 

8  18 

7  50 

8  12 

7  56 

8  07 

8  01 

8  02 

8  06 

7  57 

8  11 

24  00 

8  31 

7  37 

8  25 

7  43 

8  20 

7  48 

8  15 

7  53 

8  10 

7  58 

26  00 

8  42 

7  26 

8  36 

7  32 

8  31 

7  37 

8  26 

7  42 

8  21 

7  47 

28  00 

8  52 

7  16 

8  46 

7  22 

8  41 

7  27 

8  36 

7  32 

8  31 

7  37 

30  00 

9  00 

7  08 

8  54 

7  14 

8  49 

7  19 

8  44 

7  24 

8  39 

7  29 

32  00 

9  08 

7  00 

9  02 

7  06 

8  57 

7  11 

8  52 

7  16 

8  47 

7  21 

34  00 

9  15 

6  53 

9  09 

6  59 

9  04 

7  04 

8  59 

7  09 

8  54 

7  14 

36  00 

9  21 

6  47 

9  15 

6  53 

9  10 

6  58 

9  05 

7  03 

9  00 

7  08 

38  00 

9  26 

6  42 

9  20 

6  48 

9  15 

6  53 

9  10 

6  58 

9  05 

7  03 

40  00 

9  31 

6  36 

9  25 

6  42 

9  20 

6  47 

9  15 

6  52 

9  10 

6  57 

45  00 

9  42 

6  25 

9  36 

6  31 

9  31 

6  36 

9  26 

6  41 

9  21 

6  46 

50  00 

9  50 

6  16 

9  44 

6  22 

9  39 

6  27 

9  34 

6  32 

9  29 

6  37 

55  00 

9  57 

6  08 

9  51 

6  14 

9  46 

6  19 

9  41 

6  24 

9  36 

6  29 

60  00 

10  03 

6  01 

9  57 

6  07 

9  52 

6  12 

9  47 

6  17 

9  42 

6  22 

65  00 

10  10 

5  54 

10  04 

6  00 

9  59 

6  05 

9  54 

6  10 

9  49 

6  15 

70  00 

10  15 

5  48 

10  09 

5  54 

10  04 

5  59 

9  59 

6  04 

9  54 

6  09 

75  00 

10  19 

5  43 

10  13 

5  49 

10  08 

5  54 

10  03 

5  59 

9  58 

6  04 

80  00 

10  25 

5  37 

10  19 

5  43 

10  14 

5  48 

10  09 

5  53 

10  04 

5  58 

85  00 

10  29 

5  32 

10  23 

5  38 

10  18 

5  43 

10  13 

5  48 

10  08 

5  53 

90  00 

10  33 

5  27 

10  27 

5  33 

10  22 

5  38 

10  17 

5  43 

10  12 

5  48 

1 

Additional  C( 

)ER. 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

June 

.    July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

// 

„ 

If 

II 

// 

" 

// 

/' 

" 

" 

II 

FOR  Sun's  A 

LT. 

Is 

t  to  15th.... 

+18 

+15 

+8 

0    - 

-  8 

-13 

-14 

-11 

-5 

+3 

+■ 

11 

+16 

16 

th  to  31st. . . 

+17 

+12 

+4 

-4    - 

-11 

-14 

-13 

-  9 

-1 

+7 

+ 

14 

+18 

*  Thecorrect 

onsforthe< 

jhserved  altitude  of  a  S 

tar  or  Planet  involves  the  dip  and  the  refraction;  and  for 
,  and  mean  semidiameter,  which  is  taken  as  16'.    A  supp 
meter  In  the  diflerent  months  of  the  year  is  given  at  the  fc 

the  observe 

d  altitude 

of  the  Sun's  lowe 

r  limb,  the 

lip,  refraction,  parallax 

lementary 

correction 

taking  account  of 

thevarlati( 

)n  of  the  Sun's  semldla 

»ot  of  the  n: 

tain  table. 

TABLE  46. 

[Page  927 

Corrections* 

to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb, 

to  Find 

the  True  Altitude — Continued. 

OBfl.  Alt. 

HEIGHT  OF  THE  EYE.                                                                       1 

36  Feet. 

37  Feet.            1 

38  Feet.           1 

39  Feet. 

40  Feet.          | 

O 

* 

O 

* 

0 

* 

O 

iii 

O 

* 

■   Sun's 

star's 

Sun's 

star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

o        / 

6  30 

t      n 

2  22 

13  47 

2  17 

13  52 

2  13 

13  56 

2  08 

14  01 

2  03 

/     II 
14  06 

40 

2  32 

13  37 

2  27 

13  42 

2  23 

13  46 

2  18 

13  51 

2  13 

13  56 

50 

2  42 

13  27 

2  37 

13  32 

2  33 

13  36 

2  28 

13  41 

2  23 

13  46 

7  GO 

2  52 

13  17 

2  47 

13  22 

2  43 

13  26 

2  38 

13  31 

2  33 

13  36 

10 

3  01 

13  08 

2  56 

13  13 

2  52 

13  17 

2  47 

13  22 

2  42 

13  27 

20 

3  10 

12  59 

3  05 

13  04 

3  01 

13  08 

2  56 

13  13 

2  51 

13  18 

7  30 

3  19 

12  50 

3  14 

12  55 

3  10 

12  59 

3  05 

13  04 

3  00 

13  09 

40 

3  27 

12  42 

3  22 

12  47 

3  18 

12  51 

3  13 

12  56 

3  08 

13  01 

50 

3  35 

12  34 

3  30 

12  39 

3  26 

12  43 

3  21 

12  48 

3  16 

12  53 

8  00 

3  43 

12  26 

3  38 

12  31 

3  34 

12  35 

3  29 

12  40 

3  24 

12  45 

10 

3  50 

12  19 

3  45 

12  24 

.  3  41 

12  28 

3  36 

12  33 

3  31 

12  38 

20 

3  57 

12  12 

3  52 

12  17 

3  48 

12  21 

3  43 

12  26 

3  38 

12  31 

8  30 

4  04 

12  05 

3  59 

12  10 

3  55 

12  14 

3  50 

12  19 

3  45 

12  24 

40 

4  11 

11  58 

4  06 

12  03 

4  02 

12  07 

3  57 

12  12 

3  52 

12  17 

50 

4  17 

11  52 

4  12 

11  57 

4  08 

12  01 

4  03 

12  06 

3  58 

12  11 

9  00 

4  23 

11  46 

4  18 

11  51 

4  14 

11  55 

4  09 

12  00 

4  04 

12  05 

20 

4  35 

11  34 

4  30 

11  39 

4  26 

11  43 

4  21 

11  48 

4  16 

11  53 

40 

4  46 

11  23 

4  41 

11  28 

4  37 

11  32 

4  32 

11  37 

4  27 

11  42 

10  00 

4  57 

11  12 

4  52 

11  17 

4  48 

11  21 

4  43 

11  26 

4  38 

11  31 

20 

5  07 

11  02 

5  02 

11  07 

4  58 

11  11 

4  53 

11  16 

4  48 

11  21 

40 

5  16 

10  53 

5  11 

10  58 

5  07 

11  02 

5  02 

11  07 

4  57 

11  12 

11  00 

5  25 

10  44 

5  20 

10  49 

5  16 

10  53 

5  11 

10  58 

5  06 

11  03 

30 

5  37 

10  32 

5  32 

10  37 

5  28 

10  41 

5  23 

10  46 

5  18 

10  51 

12  00 

5  48 

10  21 

5  43 

10  26 

5  39 

10  30 

5  34 

10  35 

5  29 

10  40 

30 

5  59 

10  10 

5  54 

10  15 

5  50 

10  19 

5  45 

10  24 

5  40 

10  29 

13  00 

6  09 

10  00 

6  04 

10  05 

6  00 

10  09 

5  55 

10  14 

5  50 

10  19 

30 

6  18 

9  51 

6  13 

9  56 

6  09 

10  00 

6  04 

10  05 

5  59 

10  10 

14  00 

6  26 

9  43 

6  21 

9  48 

6  17 

9  52 

6  12 

9  57 

6  07 

10  02 

15  00 

6  42 

9  27 

6  37 

9  32 

6  33 

9  36 

6  28 

9  41 

6  23 

9  46 

16  00 

6  55 

9  14 

6  50 

9  19 

6  46 

9  23 

6  41 

9  28 

6  36 

9  33 

17  00 

7  08 

9  01 

7  03 

9  06 

6  59 

9  10 

6  54 

9  15 

6  49 

9  20 

18  00 

7  18 

8  51 

7  13 

8  56 

7  09 

9  00 

7  04 

9  05 

6  59 

9  10 

19  00 

7  28 

8  41 

7  23 

8  46 

7  19 

8  50 

7  14 

8  55 

7  09 

9  00 

20  00 

7  36 

8  32 

7  31 

8  37 

7  27 

8  41 

7  22 

8  46 

7  17 

8  51 

22  00 

7  52 

8  16 

7  47 

8  21 

7  43 

8  25 

7  38 

8  30 

7  33 

8  35 

24  00 

8  05 

8  03 

8  00 

8  08 

7  56 

8  12 

7  51 

8  17 

7  46 

8  22 

26  00 

8  16 

7  52 

8  11 

7  57 

8  07 

8  01 

8  02 

8  06 

7  57 

8  11 

28  00 

8  26 

7  42 

8  21 

7  47 

8  17 

7  51 

8  12 

7  56 

8  07 

8  01 

30  00 

8  34 

7  34 

8  29 

7  39 

8  25 

7  43 

8  20 

7  48 

8  15 

7  53 

32  00 

8  42 

7  26 

8  37 

7  31 

8  33 

7  35 

8  28 

7  40 

8  23 

7  45 

34  00 

8  49 

7  19 

8  44 

7  24 

8  40 

7  28 

8  35 

7  33 

8  30 

7  38 

36  00 

8  55 

7  13 

8  50 

7  18 

8  46 

7  22 

8  41 

7  27 

8  36 

7  32 

38  00 

9  00 

7  08 

8  55 

7  13 

8  51 

7  17 

8  46 

7  22 

8  41 

7  27 

40  00 

9  05 

7  02 

9  00 

7  07 

8  56 

7  11 

8  51 

7  16 

8  46 

7  21 

45  00 

9  16 

6  51 

9  11 

6  56 

9  07 

7  00 

9  02 

7  05 

8  57 

7  10 

50  00 

9  24 

6  42 

9  19 

6  47 

9  15 

6  51 

9  10 

6  56 

9  05 

7  01 

55  00 

9  31 

6  34 

9  26 

6  39 

9  22 

6  43 

9  17 

6  48 

9  12 

6  53 

60  00 

9  37 

6  27 

9  32 

6  32 

9  28 

6  36 

9  23 

6  41 

9  18 

6  46 

65  00 

9  44 

6  20 

9  39 

6  25 

9  35 

6  29 

9  30 

6  34 

9  25 

6  39 

70  00 

9  49 

6  14 

9  44 

6  19 

9  40 

6  23 

9  35 

6  28 

9  30 

6  33 

75  00 

9  53 

6  09 

9  48 

6  14 

9  44 

6  18 

9  39 

6  23 

9  34 

6  28 

80  00 

9  59 

6  03 

9  54 

6  08 

9  50 

6  12 

9  45 

6  17 

9  40 

6  22 

85  00 

10  03 

5  58 

9  58 

6  03 

9  54 

6  07 

9  49 

6  12 

9  44 

6  17 

90  00 

10  07 

5  53 

10  02 

5  58 

9  58 

6  02 

9  53 

6  07 

9  48 

6  12 

1 

Additional  C 

3RR. 

Day  of  Month.    |  Jan.  1 

Feb. 

Mar. 

Apr. 

May. 

June.  1  July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

,/ 

„ 

,, 

// 

// 

n 

» 

" 

" 

" 

" 

If 

FOE  Sun's  A 

LT. 

Is 

t  to  15th 

+18 

+15 

+8 

0    - 

-  8 

-13 

-14 

-11 

-5 

+3 

+ 

11 

+16 

16 

thto3l8t... 

+17 

+12 

+4 

-4    - 

-11 

-14 

-13 

-  9 

-1 

+7 

+ 

14 

+18 

*  The  correct 

ions  for  the 

observed  altitude  of  a 

3tar  or  Planet  involves  the  dip  and  the  refraction;  and  foi 

theobserv 

ed  altitude 

of  the  Sun's  lowe 

r  limb,  the 

dip,  refraction,  paralla 

t,  and  mean  semidiameter,  which  is  taken  as  16'.    A  sup 

plementary 
oot  of  the  n 

correction 

taking  account  of 

thevariati( 

)n  of  the  Sun's  semidia 

meter  in  the  different  months  of  the  year  is  given  at  the  i 

lain  table. 

Page  928] 

TABLE  46. 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun's 

Lower  Limb,  to  Find 

the  True  Altitude — Continued. 

HEIGHT   OF  THE   EYE.                                                                           1 

41  Feet. 

42  Feet. 

43  Feet. 

44  Feet. 

45  Feet. 

46  Feet.         1 

*-\__        A  T*H 

1 

KjDO,     JVltl.. 

.o 

* 

O 

* 

O 

* 

O 

* 

O 

* 

O 

♦ 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sim's 

Star's 

Sun's 

star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

6  30 

1  58 

/     ft 
14  11 

1  54 

14  15 

1  49 

1      n 

14  20 

1  44 

14  25 

1  39 

14  30 

1  35 

14  34 

40 

2  08 

14  01 

2  04 

14  05 

1  59 

14  10 

1  54 

14  15 

1  49 

14  20 

1  45 

14  24 

50 

2  18 

13  51 

2  14 

13  55 

2  09 

14  00 

2  04 

14  05 

1  59 

14  10 

1  55 

14  14 

7  00 

2  28 

13  41 

2  24 

13  45 

2  19 

13  50 

2  14 

13  55 

2  09 

14  00 

2  05 

14  04 

10 

2  37 

13  32 

2  33 

13  36 

2  28 

13  41 

2  23 

13  46 

2  18 

13  51 

2  14 

13  55 

20 

2  46 

13  23 

2  42 

13  27 

2  37 

13  32 

2  32 

13  37 

2  27 

13  42 

2  23 

13  46 

7  30 

2  55 

13  14 

2  51 

13  18 

2  46 

13  23 

2  41 

13  28 

2  36 

13  33 

2  32 

13  37 

40 

3  03 

13  06 

2  59 

13  10 

2  54 

13  15 

2  49 

13  20 

2  44 

13  25 

2  40 

13  29 

50 

3  11 

12  58 

3  07 

13  02 

3  02 

13  07 

2  57 

13  12 

2  52 

13  17 

2  48 

13  21 

8  00 

3  19 

12  50 

3  15 

12  54 

3  10 

12  59 

3  05 

13  04 

3  00 

13  09 

2  56 

13  13 

10 

3  26 

12  43 

3  22 

12  47 

3  17 

12  52 

3  12 

12  57 

3  07 

13  02 

3  03 

13  06 

20 

3  33 

12  36 

3  29 

12  40 

3  24 

12  45 

3  19 

12  50 

3  14 

12  55 

3  10 

12  59 

8  30 

3  40 

12  29 

3  36 

12  33 

3  31 

]2  38 

3  26 

12  43 

3  21 

12  48 

3  17 

12  52 

40 

3  47 

12  22 

3  43 

12  26 

3  38 

12  31 

3  33 

12  36 

3  28 

12  41 

3  24 

12  45 

50 

3  53 

12  16 

3  49 

12  20 

3  44 

12  25 

3  39 

12  30 

3  34 

12  35 

3  30 

12  39 

9  00 

3  59 

12  10 

3  55 

12  14 

3  50 

12  19 

3  45 

12  24 

3  40 

12  29 

3  36 

12  33 

20 

4  11 

11  58 

4  07 

12  02 

4  02 

12  07 

3  57 

14  12 

3  52 

12  17 

3  48 

12  21 

40 

4  22 

11  47 

4  18 

11  51 

4  13 

11  56 

4  08 

12  01 

4  03 

12  06 

3  59 

12  10 

10  00 

4  33 

11  36 

4  29 

11  40 

4  24 

11  45 

4  19 

11  50 

4  14 

11  55 

4  10 

11  59 

20 

4  43 

11  26 

4  39 

11  30 

4  34 

11  35 

4  29 

11  40 

4  24 

11  45 

4  20 

11  49 

40 

4  52 

11  17 

4  48 

11  21 

4  43 

11  26 

4  38 

11  31 

4  33 

11  36 

4  29 

11  40 

11  00 

5  01 

11  08 

4  57 

11  12 

4  52 

11  17 

4  47 

11  22 

4  42 

11  27 

4  38 

11  31 

30 

5  13 

10  56 

5  09 

11  00 

5  04 

11  05 

4  59 

11  10 

4  54 

11  15 

4  50 

11  19 

12  00 

5  24 

10  45 

5  20 

10  49 

5  15 

10  54 

5  10 

10  59 

5  05 

11  04 

5  01 

11  08 

30 

5  35 

10  34 

5  31 

10  38 

5  26 

10  43 

5  21 

10  48 

5  16 

10  53 

5  12 

10  57 

13  00 

5  45 

10  24 

5  41 

10  28 

5  36 

10  33 

5  31 

10  38 

5  26 

10  43 

5  22 

10  47 

30 

5  54 

10  15 

5  50 

10  19 

5  45 

10  24 

5  40 

10  29 

5  35 

10  34 

5  31 

10  38 

14  00 

6  02 

10  07 

5  58 

10  11 

5  53 

10  16 

5  48 

10  21 

5  43 

10  26 

5  39 

10  30 

15  00 

6  18 

9  51 

6  14 

9  55 

6  09 

10  00 

6  04 

10  05 

5  59 

10  10 

5  55 

10  14 

16  00 

6  31 

9  38 

6  27 

9  42 

6  22 

9  47 

6  17 

9  52 

6  12 

9  57 

6  08 

10  01 

17  00 

6  44 

9  25 

6  40 

9  29 

6  35 

9  34 

6  30 

9  39 

6  25 

9  44 

6  21 

9  48 

]8  00 

6  54 

9  15 

6  50 

9  19 

6  45 

9  24 

6  40 

9  29 

6  35 

9  34 

6  31 

9  38 

19  00 

7  04 

9  05 

7  00 

9  09 

6  55 

9  14 

6  50 

9  19 

6  45 

9  24 

6  41 

9  28 

20  00 

7  12 

8  56 

7  08 

9  00 

7  03 

9  05 

6  58 

9  10 

6  53 

9  15 

6  49 

9  19 

22  00 

7  28 

8  40 

7  24 

8  44 

7  19 

8  49 

7  14 

8  54 

7  09 

8  59 

7  05 

9  03 

24  00 

7  41 

8  27 

7  37 

8  31 

7  32 

8  36 

7  27 

8  41 

7  22 

8  46 

7  18 

8  50 

26  00 

7  52 

8  16 

7  48 

8  20 

7  43 

8  25 

7  38 

8  30 

7  33 

8  35 

7  29 

8  39 

28  00 

8  02 

8  06 

7  58 

8  10 

7  53 

8  15 

7  48 

8  20 

7  43 

8  25 

7  39 

8  29 

30  00 

8  10 

7  58 

8  06 

8  02 

8  01 

8  07 

7  56 

8  12 

7  51 

8  17 

7  47 

8  21 

32  00 

8  18 

7  50 

8  14 

7  54 

8  09 

7  59 

8  04 

8  04 

7  59 

8  09 

7  55 

8  13 

34  00 

8  25 

7  43 

8  21 

7  47 

8  16 

7  52 

8  11 

7  57 

8  06 

8  02 

8  02 

8  06 

36  00 

8  31 

7  37 

8  27 

7  41 

8  22 

7  46 

8  17 

7  51 

8  12 

7  56 

8  08 

8  00 

38  00 

8  36 

7  32 

8  32 

7  36 

8  27 

7  41 

8  22 

7  46 

8  17 

7  51 

8  13 

7  55 

40  00 

8  41 

7  26 

8  37 

7  30 

8  32 

7  35 

8  27 

7  40 

8  22 

7  45 

8  18 

7  49 

45  00 

8  52 

7  15 

8  48 

7  19 

8  43 

7  24 

8  38 

7  29 

8  33 

7  34 

8  29 

7  38 

50  00 

9  00 

7  06 

8  56 

7  10 

8  51 

7  15 

8  46 

7  20 

8  41 

7  25 

8  37 

7  29 

55  00 

9  07 

6  58 

9  03 

7  02 

8  58 

7  07 

8  53 

7  12 

8  48 

7  17 

8  44 

7  21 

60  00 

9  13 

6  51 

9  09 

6  55 

9  04 

7  00 

8  59 

7  05 

8  54 

7  10 

8  50 

7  14 

65  00 

9  20 

6  44 

9  16 

6  48 

9  11 

6  53 

9  06 

6  58 

9  01 

7  03 

8  57 

7  07 

70  00 

9  25 

6  38 

9  21 

6  42 

9  16 

6  47 

9  11 

6  52 

9  06 

6  57 

9  02 

7  01 

75  00 

9  29 

6  33 

9  25 

6  37 

9  20 

6  42 

9  15 

6  47 

9  10 

6  52 

9  06 

6  56 

80  00 

9  35 

6  27 

9  31 

6  31 

9  26 

6  36 

9  21 

6  41 

9  16 

6  46 

9  12 

6  50 

85  00 

9  39 

6  22 

9  35 

6  26 

9  30 

6  31 

9  25 

6  36 

9  20 

6  41 

9  16 

6  45 

90  00 

9  43 

6  17 

9  39 

6  21 

9  34 

6  26 

9  29 

6  31 

9  24 

6  36 

9  20 

6  40 

1 

Additio 

SAL  CORR 

Day  of  Month. 

Jan. 

Feh. 

Mar. 

Apr 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dee. 

II 

„ 

// 

„ 

„ 

// 

II 

II 

II 

II 

II 

II 

FOB  8V 

•n's  Alt. 

l3tt 

x)15th.... 

+18 

+15 

- 

F8 

0 

-  8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th 

to  3l8t... 

+17 

+12 

- 

f-4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*The< 

jorrection. 

>  for  the  oh 

served  altitude  of  a 

Star  or  Pk 

met  involves  the  dip 

and  the  refraction; 

and  for  the  observed  altitude 

of  the  Sun 

s  lower  liu 

Qh,  thedi] 

p,  refraction,  paralla 

X,  and  me 

an  semidiameter,  w 

hichis  takenasie'. 

A  supplementary  correction 
at  the  foot  of  the  main  table. 

taking  accc 

)unt  of  the 

variation 

of  the  Sun's  semidi 

ameter  in 

the  diflerent  mouth 

s  of  the  year  is  given 

TABLE  46. 

[Page  929 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun 'a 

Lower  Limb,  to  Find 

the  True  Altitude — Continued. 

Obs.  Alt. 

HEIGHT  OF  THE  EYE.                                                                           1 

47  Feet. 

48  Feet. 

49  Feet. 

50  Feet. 

51  Feet. 

52  Feet.         1 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

star's 

Sun's 

Star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(  +  ) 

(-) 

(  +  ) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

6  30 

1  31 

/     // 
14  38 

1  27 

14  42 

1  23 

14  46 

1  19 

14  50 

1  15 

/     II 
14  54 

1    II 
1  11 

14  58 

40 

1  41 

14  28 

1  37 

14  32 

1  33 

14  36 

1  29 

14  40 

1  25 

14  44 

1  21 

14  48 

50 

1  51 

14  18 

1  47 

14  22 

1  43 

14  26 

1  39 

14  30 

1  35 

14  34 

1  31 

14  38 

7  00 

2  01 

14  08 

1  57 

14  12 

1  53 

14  16 

1  49 

14  20 

1  45 

14  24 

1  41 

14  28 

10 

2  10 

13  59 

2  06 

14  03 

2  02 

14  07 

1  58 

14  11 

1  54 

14  15 

1  50 

14  19 

20 

2  19 

13  50 

2  15 

13  54 

2  11 

13  58 

2  07 

14  02 

2  03 

14  06 

1  59 

14  10 

7  30 

2  28 

13  41 

2  24 

13  45 

2  20 

13  49 

2  16 

13  53 

2  12 

13  57 

2  08 

14  01 

40 

2  36 

13  33 

2  32 

13  37 

2  28 

13  41 

2  24 

13  45 

2  20 

13  49 

2  16 

13  53 

50 

2  44 

13  25 

2  40 

13  29 

2  36 

13  33 

2  32 

13  37 

2  28 

13  41 

2  24 

13  45 

8  00 

2  52 

13  17 

2  48 

13  21 

2  44 

13  25 

2  40 

13  29 

2  36 

13  33 

2  32 

13  37 

10 

2  59 

13  10 

2  55 

13  14 

2  51 

13  18 

2  47 

13  22 

2  43 

13  26 

2  39 

13  30 

20 

3  06 

13  03 

3  02 

13  07 

2  58 

13  11 

2  54 

13  15 

2  50 

13  19 

2  46 

13  23 

8  30 

3  13 

12  56 

3  09 

13  00 

3  05 

13  04 

3  01 

13  08 

2  57 

13  12 

2  53 

13  16 

40 

3  20 

12  49 

3  16 

12  53 

3  12 

12  57 

3  08 

13  01 

3  04 

13  05 

3  00 

13  09 

50 

3  26 

12  43 

3  22 

12  47 

3  18 

12  51 

3  14 

12  55 

3  10 

12  59 

3  06 

13  03 

9  00 

3  32 

12  37 

3  28 

12  41 

3  24 

12  45 

3  20 

12  49 

3  16 

12  53 

3  12 

12  57 

20 

3  44 

12  25 

3  40 

12  29 

3  36 

12  33 

3  32 

12  37 

3  28 

12  41 

3  24 

12  45 

40 

3  55 

12  14 

3  51 

12  18 

3  47 

12  22 

3  43 

12  26 

3  39 

12  30 

3  35 

12  34 

10  00 

4  06 

12  03 

4  02 

12  07 

3  58 

12  11 

3  54 

12  15 

3  50 

12  19 

3  46 

12  23 

20 

4  16 

11  53 

4  12 

11  57 

4  08 

12  01 

4  04 

12  05 

4  00 

12  09 

3  56 

12  13 

40 

4  25 

11  44 

4  21 

11  48 

4  17 

11  52 

4  13 

11  56 

4  09 

12  00 

4  05 

12  04 

11  00 

4  34 

11  35 

4  30 

11  39 

4  26 

11  43 

4  22 

11  47 

4  18 

11  51 

4  14 

11  55 

30 

4  46 

11  23 

4  42 

11  27 

4  38 

11  31 

4  34 

11  35 

4  30 

11  39 

4  26 

11  43 

12  00 

4  57 

11  12 

4  53 

11  16 

4  49 

11  20 

4  45 

11  24 

4  41 

11  28 

4  37 

11  32 

30 

5  08 

11  01 

5  04 

11  05 

5  00 

11  09 

4  56 

11  13 

4  52 

11  17 

4  48 

11  21 

13  00 

5  18 

10  51 

5  14 

10  55 

5  10 

10  59 

5  06 

11  03 

5  02 

11  07 

4  58 

11  11 

30 

5  27 

10  42 

5  23 

10  46 

5  19 

10  50 

5  15 

10  54 

5  11 

10  58 

5  07 

11  02 

14  00 

5  35 

10  34 

5  31 

10  38 

5  27 

10  42 

5  23 

10  46 

5  19 

10  50 

5  15 

10  54 

15  00 

5  51 

10  18 

5  47 

10  22 

5  43 

10  26 

5  39 

10  30 

5  35 

10  34 

5  31 

10  38 

16  00 

6  04 

10  05 

6  00 

10  09 

5  56 

10  13 

5  52 

10  17 

5  48 

10  21 

5  44 

10  25 

17  00 

6  17 

9  52 

6  13 

9  56 

6  09 

10  00 

6  05 

10  04 

6  01 

10  08 

5  57 

10  12 

18  00 

6  27 

9  42 

6  23 

9  46 

6  19 

9  50 

6  15 

9  54 

6  11 

9  58 

6  07 

10  02 

19  00 

6  37 

9  32 

6  33 

9  36 

6  29 

9  40 

6  25 

9  44 

6  21 

9  48 

6  17 

9  52 

20  00 

6  45 

9  23 

6  41 

9  27 

6  37 

9  31 

6  33 

9  35 

6  29 

9  39 

6  25 

9  43 

22  00 

7  01 

9  07 

6  57 

9  11 

6  53 

9  15 

6  49 

9  19 

6  45 

9  23 

6  41 

9  27 

24  00 

7  14 

8  54 

7  10 

8  58 

7  06 

9  02 

7  02 

9  06 

6  58 

9  10 

6  54 

9  14 

26  00 

7  25 

8  43 

7  21 

8  47 

7  17 

8  51 

7  13 

8  55 

7  09 

8  59 

7  05 

9  03 

28  00 

7  35 

8  33 

7  31 

8  37 

7  27 

8  41 

7  23 

8  45 

7  19 

8  49 

7  15 

8  53 

30  00 

7  43 

8  25 

7  39 

8  29 

7  35 

8  33 

7  31 

8  37 

7  27 

8  41 

7  23 

8  45 

32  00 

7  51 

8  17 

7  47 

8  21 

7  43 

8  25 

7  39 

8  29 

7  35 

8  33 

7  31 

8  37 

34  00 

7  58 

8  10 

7  54 

8  14 

7  50 

8  18 

7  46 

8  22 

7  42 

8  26 

7  38 

8  30 

36  00 

8  04 

8  04 

8  00 

8  08 

7  56 

8  12 

7  52 

8  16 

7  48 

8  20 

7  44 

8  24 

38  00 

8  09 

7  59 

8  05 

8  03 

8  01 

8  07 

7  57 

8  11 

7  53 

8  15 

7  49 

8  19 

40  00 

8  14 

7  53 

8  10 

7  57 

8  06 

8  01 

8  02 

8  05 

7  58 

8  09 

7  54 

8  13 

45  00 

8  25 

7  42 

8  21 

7  46 

8  17 

7  50 

8  13 

7  54 

8  09 

7  58 

8  05 

8  02 

50  00 

8  33 

7  33 

8  29 

7  37 

8  25 

7  41 

8  21 

7  45 

8  17 

7  49 

8  13 

7  53 

55  00 

8  40 

7  25 

8  36 

7  29 

8  32 

7  33 

8  28 

7  37 

8  24 

7  41 

8  20 

7  45 

60  00 

8  46 

7  18 

8  42 

7  22 

8  38 

7  26 

8  34 

7  30 

8  30 

7  34 

8  26 

7  38 

65  00 

8  53 

7  11 

8  49 

7  15 

8  45 

7  19 

8  41 

7  23 

8  37 

7  27 

8  33 

7  31 

70  00 

8  58 

7  05 

8  54 

7  09 

8  50 

7  13 

8  46 

7  17 

8  42 

7  21 

8  38 

7  25 

75  00 

9  02 

7  00 

8  58 

7  04 

8  54 

7  08 

8  50 

7  12 

8  46 

7  16 

8  42 

7  20 

80  00 

9  08 

6  54 

9  04 

6  58 

9  00 

7  02 

8  56 

7  06 

8  52 

7  10 

8  48 

7  14 

85  00 

9  12 

6  49 

9  08 

6  53 

9  04 

6  57 

9  00 

7  01 

8  56 

7  05 

8  52 

7  09 

90  00 

9  16 

6  44 

9  12 

6  48 

9  08 

6  52 

9  04 

6  56 

9  00 

7  00 

8  56 

7  04 

1 

Additio 

NAL  CORB 

Day  of  Month. 

Jan. 

Feh. 

Mar. 

Apr 

.    May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

/, 

// 

,, 

, 

// 

„ 

// 

n 

11 

It 

II 

It 

FOE  St. 

rN's  Alt. 

Ist1 

to  15th.... 

+18 

+15 

+8 

0 

-  8 

-13 

-14 

-11 

-5 

+3 

+  11 

+16 

16th 

I  to  31st... 

+17 

+12 

+4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

♦The 

3orrectlon 

3  for  the  oV 

served  altitude  of  a 

Star  or  Planet  involves  the  dij 

and  the  refraction; 

and  for  the  observed  altitude 

of  the  Sun 

's  lower  lii 

nb.thedi 

p,  refraction,  paralle 

IX,  and  mean  semidiameter,  w 

hich  is  taken  as  16'. 

A  supplementary  conection 
at  the  foot  of  the  main  table. 

taking  ace 

ountof  th 

3  variation 

of  the  Sun's  semid 

ameter  in  the  different  month 

s  of  the  year  is  given 

Page  930] 

TABLE  46. 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun's  Lower  Limb,  to  Find 

the  True  Altitude — Continued .                                                            1 

Obs.  Alt. 

HEIGHT   OF  THE  EYE.                                                                            1 

53  Feet. 

54  Feet. 

55  Feet.         1 

56  Feet. 

57  Feet.         | 

58  Feet.         1 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

6  30 

/     1) 
1  07 

15  02 

1  03 

15  06 

0  59 

15  10 

0  55 

15  14 

0  51 

15  18 

1     II 
0  48 

15  21 

40 

1  17 

14  52 

1  13 

14  56 

1  09 

15  00 

1  05 

15  04 

1  01 

15  08 

0  58 

15  11 

50 

1  27 

14  42 

1  23 

14  46 

1  19 

14  50 

1  15 

14  54 

1  11 

14  58 

1  08 

15  01 

7  00 

1  37 

14  32 

1  33 

14  36 

1  29 

14  40 

1  25 

14  44 

1  21 

14  48 

1  18 

14  51 

10 

1  46 

14  23 

1  42 

14  27 

1  38 

14  31 

1  34 

14  35 

1  30 

14  39 

1  27 

14  42 

20 

1  55 

14  14 

1  51 

.14  18 

1  47 

14  22 

1  43 

14  26 

1  39 

14  30 

1  36 

14  33 

7  30 

2  04 

14  05 

2  00 

14  09 

1  56 

14  13 

1  52 

14  17 

1  48 

14  21 

1  45 

14  24 

40 

2  12 

13  57 

2  08 

14  01 

2  04 

14  05 

2  00 

14  09 

1  56 

14  13 

1  53 

14  16 

50 

2  20 

13  49 

2  16 

13  53 

2  12 

13  57 

2  08 

14  01 

2  04 

14  05 

2  01 

14  08 

8  00 

2  28 

13  41 

2  24 

13  45 

2  20 

13  49 

2  16 

13  53 

2  12 

13  57 

2  09 

14  00 

10 

2  35 

13  34 

2  31 

13  38 

2  27 

13  42 

2  23 

13  46 

2  19 

13  50 

2  16 

13  53 

20 

2  42 

13  27 

2  38 

13  31 

2  34 

13  35 

2  30 

13  39 

2  26 

13  43 

2  23 

13  46 

8  30 

2  49 

13  20 

2  45 

13  24 

2  41 

13  28 

2  37 

13  32 

2  33 

13  36 

2  30 

13  39 

40 

2  56 

13  13 

2  52 

13  17 

2  48 

13  21 

2  44 

13  25 

2  40 

13  29 

2  37 

13  32 

50 

3  02 

13  07 

2  58 

13  11 

2  54 

13  15 

2  50 

13  19 

2  46 

13  23 

2  43 

13  26 

9  00 

3  08 

13  01 

3  04 

13  05 

3  00 

13  09 

2  56 

13  13 

2  52 

13  17 

2  49 

13  20 

20 

3  20 

12  49 

3  16 

12  53 

3  12 

12  57 

3  08 

13  01 

3  04 

13  05 

3  01 

13  08 

40 

3  31 

12  38 

3  27 

12  42 

3  23 

12  46 

3  19 

12  50 

3  15 

12  54 

3  12 

12  57 

10  00 

3  42 

12  27 

3  38 

12  31 

3  34 

12  35 

3  30 

12  39 

3  26 

12  43 

3  23 

12  46 

20 

3  52 

12  17 

3  48 

12  21 

3  44 

12  25 

3  40 

12  29 

3  36 

12  33 

3  33 

12  36. 

40 

4  01 

12  08 

3  57 

12  12 

3  53 

12  16 

3  49 

12  20 

3  45 

12  24 

3  42 

12  27 

11  00 

4  10 

11  59 

4  06 

12  03 

4  02 

12  07 

3  58 

12  11 

3  54 

12  15 

3  51 

12  18 

30 

4  22 

11  47 

4  18 

11  51 

4  14 

11  55 

4  10 

11  59 

4  06 

12  03 

4  03 

12  06 

12  00 

4  33 

11  36 

4  29 

11  40 

4  25 

11  44 

4  21 

11  48 

4  17 

11  52 

4  14 

11  55 

30 

4  44 

11  25 

4  40 

11  29 

4  36 

11  33 

4  32 

11  37 

4  28 

11  41 

4  25 

11  44 

13  00 

4  54 

11  15 

4  50 

11  19 

4  46 

11  23 

4  42 

11  27 

4  38 

11  31 

4  35 

11  34 

30 

5  03 

11  06 

4  59 

11  10 

4  55 

11  14 

4  51 

11  18 

4  47 

11  22 

4  44 

11  25 

14  00 

5  11 

10  58 

5  07 

11  02 

5  03 

11  06 

4  59 

11  10 

4  55 

11  14 

4  52 

11  17 

15  00 

5  27 

10  42 

5  23 

10  46 

5  19 

10  50 

5  15 

10  54 

5  11 

10  58 

5  08 

11  01 

16  00 

5  40 

10  29 

5  36 

10  33 

5  32 

10  37 

5  28 

10  41 

5  24 

10  45 

5  21 

10  48 

17  00 

5  53 

10  16 

5  49 

10  20 

5  45 

10  24 

5  41 

10  28 

5  37 

10  32 

5  34 

10  35 

18  00 

6  03 

10  06 

5  59 

10  10 

5  55 

10  14 

5  51 

10  18 

5  47 

10  22 

5  44 

10  25 

19  00 

6  13 

9  56 

6  09 

10  00 

6  05 

10  04 

6  01 

10  08 

5  57 

10  12 

5  54 

10  15 

20  00 

6  21 

9  47 

6  17 

9  51 

G  13 

9  55 

6  09 

9  59 

6  05 

10  03 

6  02 

10  06 

22  00 

6  37 

9  31 

6  33 

9  35 

6  29 

9  39 

6  25 

9  43 

6  21 

9  47 

6  18 

9  50 

24  00 

6  50 

9  18 

6  46 

9  22 

6  42 

9  26 

6  38 

9  30 

6  34 

9  34 

6  31 

9  37 

26  00 

7  01 

9  07 

6  57 

9  11 

6  53 

9  15 

6  49 

9  19 

6  45 

9  23 

6  42 

9  26 

28  00 

7  11 

8  57 

7  07 

9  01 

7  03 

9  05 

6  59 

9  09 

6  55 

9  13 

6  52 

9  16 

30  00 

7  19 

8  49 

7  15 

8  53 

7  11 

8  57 

7  07 

9  01 

7  03 

9  05 

7  00 

9  08 

32  00 

7  27 

8  41 

7  23 

8  45 

7  19 

8  49 

7  15 

8  53 

7  11 

8  57 

7  08 

9  00 

34  00 

7  34 

8  34 

7  30 

8  38 

7  26 

8  42 

7  22 

8  46 

7  18 

8  50 

7  15 

8  63 

36  00 

7  40 

8  28 

7  36 

8  32 

•    7  32 

8  36 

7  28 

8  40 

7  24 

8  44 

7  21 

8  47 

38  00 

7  45 

8  23 

7  41 

8  27 

7  37 

8  31 

7  33 

8  35 

7  29 

8  39 

7  26 

8  42 

40  00 

7  50 

8  17 

7  46 

8  21 

7  42 

8  25 

7  38 

8  29 

7  34 

8  33 

7  31 

8  36 

45  00 

8  01 

8  06 

7  57 

8  10 

7  53 

8  14 

7  49 

8  18 

7  45 

8  22 

7  42 

8  25 

50  00 

8  09 

7  57 

8  05 

8  01 

8  01 

8  05 

7  57 

8  09 

7  53 

8  13 

7  50 

8  16 

55  00 

8  16 

7  49 

8  12 

7  53 

8  08 

7  57 

8  04 

8  01 

8  00 

8  05 

7  57 

8  08 

60  00 

8  22 

7  42 

8  18 

7  46 

8  14 

7  50 

8  10 

7  54 

8  06 

7  58 

8  03 

8  01 

65  00 

8  29 

7  35 

8  25 

7  39 

8  21 

7  43 

8  17 

7  47 

8  13 

7  51 

8  10 

7  54 

70  00 

8  34 

7  29 

8  30 

7  33 

8  26 

7  37 

8  22 

7  41 

8  18 

7  45 

8  15 

7  48 

75  00 

8  38 

7  24 

8  34 

7  28 

8  30 

7  32 

8  26 

7  36 

8  22 

7  40 

8  19 

7  43 

80  00 

8  44 

7  18 

8  40 

7  22 

8  36 

7  26 

8  32 

7  30 

8  28 

7  34 

8  25 

7  37 

85  00 

8  48 

7  13 

8  44 

7  17 

8  40 

7  21 

8  36 

7  25 

8  32 

7  29 

8  29 

7  32 

90  00 

8  52 

7  08 

8  48 

7  12 

8  44 

7  16 

8  40 

7  20 

8  36 

7  24 

8  33 

7  27 

1 

Additio 

NAL  Core 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

.     May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

n 

// 

„ 

II 

II 

II 

,/ 

„ 

,/ 

„ 

II 

FOR  SX 

Hi's  Alt. 

I8t1 

to  15th.... 

+18 

+15 

+8 

0 

-  8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

IBtll 

I  to  31st... 

+17 

+12 

+4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+  14 

+18 

♦The 

correction 

3  for  the  ol 

)served  altitude  of  a 

Star  or  Planet  involves  the  dij 

)  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun 

's  lower  lii 

■nb,thedi 

p,  refraction,  paralla 

X,  and  mean  semidiameter,  w 

hich  is  taken  as  16'.   A  supplementary  correction 
IS  of  the  year  is  given  at  the  foot  of  the  main  table. 

taking  ace 

cunt  of  th 

evariatior 

I  of  the  Sun's  semid 

lameter  in  the  diilerent  montl 

TABLE  46. 

[Page  931 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun 'a  Lower  Limb,  to  Find 

the  True  Altitude — Continued.                                                            1 

Obs.  Alt. 

HEIGHT  OF  THE  EYE.                                                                            1 

59  Feet. 

60  Feet. 

61  Feet. 

62  Feet. 

63  Feet. 

64  Feet.          1 

O 

>•> 

O 

* 

O 

♦ 

O 

« 

O 

« 

O 

« 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

6  30 

0  44 

/     // 
15  25 

0  40 

/     II 
15  29 

0  36 

/       n 

15  33 

0  32 

15  37 

0  29 

>     II 
15  40 

0  25 

15  44 

40 

0  54 

15  15 

0  50 

15  19 

0  46 

15  23 

0  42 

15  27 

0  39 

15  30 

0  35 

15  34 

50 

1  04 

15  05 

1  00 

15  09 

0  56 

15  13 

0  52 

15  17 

0  49 

15  20 

0  45 

15  24 

7  00 

1  14 

14  55 

1  10 

14  59 

1  06 

15  03 

1  02 

15  07 

0  59 

15  10 

0  55 

15  14 

10 

1  23 

14  46 

1  19 

14  50 

1  15 

14  54 

1  11 

14  58 

1  08 

15  01 

1  04 

15  05 

20 

1  32 

14  37 

1  28 

14  41 

1  24 

14  45 

1  20 

14  49 

1  17 

14  52 

1  13 

14  56 

7  30 

1  41 

14  28 

1  37 

14  32 

1  33 

14  36 

1  29 

14  40 

1  26 

14  43 

1  22 

14  47 

40 

1  49 

14  20 

1  45 

14  24 

1  41 

14  28 

1  37 

14  32 

1  34 

14  35 

1  30 

14  39 

60 

1  57 

14  12 

1  53 

14  16 

1  49 

14  20 

1  45 

14  24 

1  42 

14  27 

1  38 

14  31 

8  00 

2  05 

14  04 

2  01 

14  08 

1  57 

14  12 

1  53 

14  16 

1  50 

14  19 

1  46 

14  23 

10 

2  12 

13  57 

2  08 

14  01 

2  04 

14  05 

2  00 

14  09 

1  57 

14  12 

1  53 

14  16 

20 

2  19 

13  50 

2  15 

13  54 

2  11 

13  58 

2  07 

14  02 

2  04 

14  05 

2  00 

14  09 

8  30 

2  26 

13  43 

2  22 

13  47 

2  18 

13  51 

2  14 

13  55 

2  11 

13  58 

2  07 

14  02 

40 

2  33 

13  36 

2  29 

13  40 

2  25 

13  44 

2  21 

13  48 

2  18 

13  51 

2  14 

13  55 

50 

2  39 

13  30 

2  35 

13  34 

2  31 

13  38 

2  27 

13  42 

2  24 

13  45 

2  20 

13  49 

9  00 

2  45 

13  24 

2  41 

13  28 

2  37 

13  32 

2  33 

13  36 

2  30 

13  39 

2  26 

13  43 

20 

2  57 

13  12 

2  53 

13  16 

2  49 

13  20 

2  45 

13  24 

2  42 

13  27 

2  38 

13  31 

40 

3  08 

13  01 

3  04 

13  05 

3  00 

13  09 

2  56 

13  13 

2  53 

13  16 

2  49 

13  20 

10  00 

3  19 

12  50 

3  15 

12  54 

3  11 

12  58 

3  07 

13  02 

3  04 

13  05 

3  00 

13  09 

20 

3  29 

12  40 

3  25 

12  44 

3  21 

12  48 

3  17 

12  52 

3  14 

12  55 

3  10 

12  59 

40 

3  38 

12  31 

3  34 

12  35 

3  30 

12  39 

3  26 

12  43 

3  23 

12  46 

3  19 

12  50 

11  00 

3  47 

12  22 

3  43 

12  26 

3  39 

12  30 

3  35 

12  34 

3  32 

12  37 

3  28 

12  41 

30 

3  59 

12  10 

3  55 

12  14 

3  51 

12  18 

3  47 

12  22 

3  44 

12  25 

3  40 

12  29 

12  00 

4  10 

11  59 

4  06 

12  03 

4  02 

12  07 

3  58 

12  11 

3  55 

12  14 

3  51 

12  18 

30 

4  21 

11  48 

4  17 

11  52 

4  13 

11  56 

4  09 

12  00 

4  06 

12  03 

4  02 

12  07 

13  00 

4  31 

11  38 

4  27 

11  42 

4  23 

11  46 

4  19 

11  50 

4  16 

11  53 

4  12 

11  57 

30 

4  40 

11  29 

4  36 

11  33 

4  32 

11  37 

4  28 

11  41 

4  25 

11  44 

4  21 

11  48 

14  00 

4  48 

11  21 

4  44 

11  25 

4  40 

11  29 

4  36 

11  33 

4  33 

11  36 

4  29 

11  40 

15  00 

5  04 

11  05 

5  00 

11  09 

4  56 

11  13 

4  52 

11  17 

4  49 

11  20 

4  45 

11  24 

16  00 

5  17 

10  52 

5  13 

10  56 

5  09 

11  00 

5  05 

11  04 

5  02 

11  07 

4  58 

11  11 

17  00 

5  30 

10  39 

5  26 

10  43 

5  22 

10  47 

5  18 

10  51 

5  15 

10  54 

5  11 

10  58 

18  00 

5  40 

10  29 

5  36 

10  33 

5  32 

10  37 

5  28 

10  41 

5  25 

10  44 

5  21 

10  48 

19  00 

5  50 

10  19 

5  46 

10  23 

5  42 

10  27 

5  38 

10  31 

5  35 

10  34 

5  31 

10  38 

20  00 

5  58 

10  10 

5  54 

10  14 

5  50 

10  18 

5  46 

10  22 

5  43 

10  25 

5  39 

10  29 

22  GO 

6  14 

9  54 

6  10 

9  58 

6  06 

10  02 

6  02 

10  06 

5  59 

10  09 

5  55 

10  13 

24  00 

6  27 

9  41 

6  23 

9  45 

6  19 

9  49 

6  15 

9  53 

6  12 

9  56 

6  08 

10  00 

26  00 

6  38 

9  30 

6  34 

9  34 

6  30 

9  38 

6  26 

9  42 

6  23 

9  45 

6  19 

9  49 

28  00 

6  48 

9  20 

6  44 

9  24 

6  40 

9  28 

6  36 

9  32 

6  33 

9  35 

6  29 

9  39 

30  00 

6  56 

9  12 

6  52 

9  16 

6  48 

9  20 

6  44 

9  24 

6  41 

9  27 

6  37 

9  31 

32  00 

7  04 

9  04 

7  00 

9  08 

6  56 

9  12 

6  52 

9  16 

6  49 

9  19 

6  45 

9  23 

34  00 

7  11 

8  57 

7  07 

9  01 

7  03 

9  05 

6  59 

9  09 

6  56 

9  12 

6  52 

9  16 

36  00 

7  17 

8  51 

7  13 

8  55 

7  09 

8  59 

7  05 

9  03 

7  02 

9  06 

6  58 

9  10 

38  00 

7  22 

8  46 

7  18 

8  50 

7  14 

8  54 

7  10 

8  58 

7  07 

9  01 

7  03 

9  05 

40  00 

7  27 

8  40 

7  23 

8  44 

7  19 

8  48 

7  15 

8  52 

7  12 

8  55 

7  08 

8  59 

45  00 

7  38 

8  29 

7  34 

8  33 

7  30 

8  37 

7  26 

8  41 

7  23 

8  44 

7  19 

8  48 

50  00 

7  46 

8  20 

7  42 

8  24 

7  38 

8  28 

7  34 

8  32 

7  31 

8  35 

7  27 

8  39 

55  00 

7  53 

8  12 

7  49 

8  16 

7  45 

8  20 

7  41 

8  24 

7  38 

8  27 

7  34 

8  31 

60  00 

7  59 

8  05 

7  55 

8  09 

7  51 

8  13 

7  47 

8  17 

7  44 

8  20 

7  40 

8  24 

65  00 

8  06 

7  58 

8  02 

8  02 

7  58 

8  06 

7  54 

8  10 

7  51 

8  13 

7  47 

8  17 

70  00 

8  11 

7  52 

8  07 

7  56 

8  03 

8  00 

7  59 

8  04 

7  56 

8  07 

7  52 

8  11 

75  00 

8  15 

7  47 

8  11 

7  51 

8  07 

7  55 

8  03 

7  59 

8  00 

8  02 

7  56 

8  06 

80  00 

8  21 

7  41 

8  17 

7  45 

8  13 

7  49 

8  09 

7  53 

8  06 

7  56 

8  02 

8  00 

85  00 

8  25 

7  36 

8  21 

7  40 

8  17 

7  44 

8  13 

7  48 

8  10 

7  51 

8  06 

7  55 

90  00 

8  29 

7  31 

8  25 

7  35 

8  21 

7  39       8  17 

7  43 

8  14       7  46  1 

8  10 

7  50 

1 

Addition 

f  AL  COKR. 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

May. 

lune. 

July. 

Aug. 

Sept. 

Oct. 

Nov 

.  1  Dec. 

„ 

II 

II 

n 

// 

„ 

II 

II 

II 

II 

1 

1          n 

FOR  Su 

N's  Alt. 

Istt 

ol5th.... 

+18 

+15 

1-8 

0 

-  8    ■ 

-13 

-14 

-11 

-5 

+3 

+1] 

.   +16 

16th 

to  3l8t... 

+  17 

+12 

h4 

-4 

-11    ■ 

-14 

-13 

-  9 

-1 

+7 

+1^ 

[    +18 

*Thec 

orrections  for  the  ob 

served  altitude  of  a 

Star  or  Pla 

net  involves  the  dip 

and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun' 

s  lower  limb,  the  dij 

),  refraction,  paralla 

X,  and  me 

an  semidiameter,  w 

tiich  is  taken  as  16'.  A  supplementary  correction 
3  of  the  year  is  given  at  the  foot  of  the  main  table. 

taking  accc 

)unt  of  the  variation 

of  the  Sun's  semidi 

ameter  in 

the  different  month. 

Page  932] 

TABLE  46. 

Corrections*  to 

be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  f 

the  True  Altitude — Continued.                                                            1 

Obs.  Alt. 

HEIGHT   OF  THE  EYE.                                                                            1 

65  Feet.          1 

66  Feet.          1 

67  Feet.          1 

68  Feet.         1 

69  Feet.          1 

70  Feet.          1 

O 

* 

O 

* 

O 

* 

O 

* 

O 

* 

G 

* 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Sun's 

Star's 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

Corr. 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

(+) 

(-) 

O            1 

6  30 

0  21 

15  48 

0  18 

1     II 
15  51 

0  14 

15  55 

0  10 

15  59 

0  07 

16  02 

0  03 

16  06 

40 

0  31 

15  38 

0  28 

15  41 

0  24 

15  45 

0  20 

15  49 

0  17 

15  52 

0  13 

15  56 

50 

0  41 

15  28 

0  38 

15  31 

0  34 

15  35 

0  30 

15  39 

0  27 

15  42 

0  23 

15  46 

7  00 

0  51 

15  18 

0  48 

15  21 

0  44 

15  25 

0  40 

15  29 

0  37 

15  32 

0  33 

15  36 

10 

1  00 

15  09 

0  57 

15  12 

0  53 

15  16 

0  49 

15  20 

0  46 

15  23 

0  42 

15  27 

20 

1  09 

15  00 

1  06 

15  03 

1  02 

15  07 

0  58 

15  11 

0  55 

15  14 

0  51 

15  18 

7  30 

1  18 

14  51 

1  15 

14  54 

1  11 

14  58 

1  07 

15  02 

1  04 

15  05 

1  00 

15  09 

40 

1  26 

14  43 

1  23 

14  46 

1  19 

14  50 

1  15 

14  54 

1  12 

14  57 

1  08 

15  01 

50 

1  34 

14  35 

1  31 

14  38 

1  27 

14  42 

1  23 

14  46 

1  20 

14  49 

1  16 

14  53 

8  00 

1  42 

14  27 

1  39 

14  30 

1  35 

14  34 

1  31 

14  38 

1  28 

14  41 

1  24 

14  45 

10 

1  49 

14  20 

1  46 

14  23 

1  42 

14  27 

1  38 

14  31 

1  35 

14  34 

1  31 

14  38 

20 

1  56 

14  13 

1  53 

14  16 

1  49 

14  20 

1  45 

14  24 

1  42 

14  27 

1  38 

14  31 

8  30 

2  03 

14  06 

2  00 

14  09 

1  56 

14  13 

1  52 

14  17 

1  49 

14  20 

1  45 

14  24 

40 

2  10 

13  59 

2  07 

14  02 

2  03 

14  06 

1  59 

14  10 

1  56 

14  13 

1  52 

14  17 

50 

2  16 

13  53 

2  13 

13  56 

2  09 

14  00 

2  05 

14  04 

2  02 

14  07 

1  58 

14  11 

9  00 

2  22 

13  47 

2  19 

13  50 

2  15 

13  54 

2  11 

13  58 

2  08 

14  01 

2  04 

14  05 

20 

2  34 

13  35 

2  31 

13  38 

2  27 

13  42 

2  23 

13  46 

2  20 

13  49 

2  16 

13  53 

40 

2  45 

13  24 

2  42 

13  27 

2  38 

13  31 

2  34 

13  35 

2  31 

13  38 

2  27 

13  42 

10  00 

2  56 

13  13 

2  53 

13  16 

2  49 

13  20 

2  45 

13  24 

2  42 

13  27 

2  38 

13  31 

20 

3  06 

13  03 

3  03 

13  06 

2  59 

13  10 

2  55 

13  14 

2  52 

13  17 

2  48 

13  21 

40 

3  15 

12  54 

3  12 

12  57 

3  08 

13  01 

3  04 

13  05 

3  01 

13  08 

2  57 

13  12 

11  00 

3  24 

12  45 

3  21 

12  48 

3  17 

12  52 

3  13 

12  56 

3  10 

12  59 

3  06 

13  03 

30 

3  36 

12  33 

3  33 

12  36 

3  29 

12  40 

3  25 

12  44 

3  22 

12  47 

3  18 

12  51 

12  00 

3  47 

12  22 

3  44 

12  25 

3  40 

12  29 

3  36 

12  33 

3  33 

12  36 

3  29 

12  40 

30 

3  58 

12  11 

3  55 

12  14 

3  51 

12  18 

3  47 

12  22 

3  44 

12  25 

3  40 

12  29 

13  00 

4  08 

12  01 

4  05 

12  04 

4  01 

12  08 

3  57 

12  12 

3  54 

12  15 

3  50 

12  19 

30 

4  17 

11  52 

4  14 

11  55 

4  10 

11  59 

4  06 

12  03 

4  03 

12  06 

3  59 

12  10 

14  00 

4  25 

11  44 

4  22 

11  47 

4  18 

11  51 

4  14 

11  55 

4  11 

11  58 

4  07 

12  02 

15  00 

4  41 

11  28 

4  38 

11  31 

4  34 

11  35 

4  30 

11  39 

4  27 

11  42 

4  23 

11  46 

16  00 

4  54 

11  15 

4  51 

11  18 

4  47 

11  22 

4  43 

11  26 

4  40 

11  29 

4  36 

11  33 

17  00 

5  07 

11  02 

5  04 

11  05 

5  00 

11  09 

4  56 

11  13 

4  53 

11  16 

4  49 

11  20 

18  00 

5  17 

10  52 

5  14 

10  55 

5  10 

10  59 

5  06 

11  03 

5  03 

11  06 

4  59 

11  10 

19  00 

5  27 

10  42 

5  24 

10  45 

5  20 

10  49 

5  16 

10  53 

5  13 

10  56 

5  09 

11  00 

20  00 

5  35 

10  33 

5  32 

10  36 

5  28 

10  40 

5  24 

10  44 

5  21 

10  47 

5  17 

10  51 

22  00 

5  51 

10  17 

5  48 

10  20 

5  44 

10  24 

5  40 

10  28 

5  37 

10  31 

5  33 

10  35 

24  00 

6  04 

10  04 

6  01 

10  07 

5  57 

10  11 

5  53 

10  15 

5  50 

10  18 

5  46 

10  22 

26  00 

6  15 

9  53 

6  12 

9  56 

6  08 

10  00 

6  04 

10  04 

6  01 

10  07 

5  57 

10  11 

28  00 

6  25 

9  43 

6  22 

9  46 

6  18 

9  50 

6  14 

9  54 

6  11 

9  57 

6  07 

10  01 

30  00 

6  33 

9  35 

6  30 

9  38 

6  26 

9  42 

6  22 

9  46 

6  19 

9  49 

6  15 

9  53 

32  00 

6  41 

9  27 

6  38 

9  30 

6  34 

9  34 

6  30 

9  38 

6  27 

9  41 

6  23 

9  45 

34  00 

6  48 

9  20 

6  45 

9  23 

6  41 

9  27 

6  37 

9  31 

6  34 

9  34 

6  30 

9  38 

36  00 

6  54 

9  14 

6  51 

9  17 

6  47 

9  21 

6  43 

9  25 

6  40 

9  28 

6  36 

9  32 

38  00 

6  59 

9  09 

6  56 

9  12 

6  52 

9  16 

6  48 

9  20 

6  45 

9  23 

6  41 

9  27 

40  00 

7  04 

9  03 

7  01 

9  06 

6  57 

9  10 

6  53 

9  14 

6  50 

9  17 

6  46 

9  21 

45  00 

7  15 

8  52 

7  12 

8  55 

7  08 

8  59 

7  04 

9  03 

7  01 

9  06 

6  57 

9  10 

50  00 

7  23 

8  43 

7  20 

8  46 

7  16 

8  50 

7  12 

8  54 

7  09 

8  57 

7  05 

9  01 

55  00 

7  30 

8  35 

7  27 

8  38 

7  23 

8  42 

7  19 

8  46 

7  16 

8  49 

7  12 

8  53 

60  00 

7  36 

8  28 

7  33 

8  31 

7  29 

8  35 

7  25 

8  39 

7  22 

8  42 

7  18 

8  46 

65  00 

7  43 

8  21 

7  40 

8  24 

7  36 

8  28 

7  32 

8  32 

7  29 

8  35 

7  25 

8  39 

70  00 

7  48 

8  15 

7  45 

8  18 

7  41 

8  22 

7  37 

8  26 

7  34 

8  29 

7  30 

8  33 

75  00 

7  52 

8  10 

7  49 

8  13 

7  45 

8  17 

7  41 

8  21 

7  38 

8  24 

7  34 

8  28 

80  00 

7  58 

8  04 

7  55 

8  07 

7  51 

8  11 

7  47 

8  15 

7  44 

8  18 

7  40 

8  22 

85  00 

8  02 

7  59 

7  59 

8  02 

7  55 

8  06 

7  51 

8  10 

7  48 

8  13 

7  44 

8  17 

90  00 

8  06 

7  54 

8  03 

7  57 

7  59 

8  01 

7  55 

8  05 

7  52 

8  08 

7  48 

8  12 

1 

Additio 

NAL  Cork 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

.     May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

„ 

„ 

, 

„ 

„ 

n 

,/ 

„ 

^ 

/, 

1, 

FOE  St 

[N's  Alt. 

Istl 

X)15th.... 

+  18 

+15 

+8 

c 

-   8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th 

to  31st... 

+17 

+12 

+4 

-A 

-11 

-14    -13 

-  9 

-1 

+7 

+14 

+18 

*The( 

jorrection 

5  for  the  olj 

served  altitude  of  a 

Star  or  Planet  involves  the  dip  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun 

s  lower  lii 

nb,  thedi 

p,  refraction,  paralls 

IX,  and  mean  semidiameter,  which  is  taken  as  16'.  A  supplementary  correction 
ameter  in  the  different  months  of  the  year  is  given  at  the  Toot  of  the  main  table. 

taking  ace 

Duntof  th 

B  variation 

of  the  Sun's  semid 

TABLE  46.                                            [Page  933 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  1 

the  True  Altitude— Continued.                                                            1 

Obs.  Alt 

HEIGHT  OF  THE  EYE.                                                                           1 

71  Feet. 

72  Feet. 

73  Feet. 

74  Feet. 

75  Feet. 

76  Feet.         1 

Sun's 
Corr. 
(+) 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

* 

star's 
Corr. 
(-) 

Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

n©, 

Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

4< 

Star's 
Corr. 
(-) 

6  30 

0  00 

16  09 

-0  04 

16  13 

-0  08 

16  17 

-0  11 

16  20 

/     II 
-0  14 

16  23 

-0  17 

16  26 

40 

0  10 

15  59 

+0  06 

16  03 

+0  02 

16  07 

-0  01 

16  10 

-0  04 

16  13 

-0  07 

16  16 

50 

0  20 

15  49 

0  16 

15  53 

0  12 

15  57 

+0  09 

16  00 

+0  06 

16  03 

+0  03 

16  06 

7  00 

0  30 

15  39 

0  26 

15  43 

0  22 

15  47 

1  19 

15  50 

0  16 

15  53 

0  13 

15  56 

10 

0  39 

15  30 

0  35 

15  34 

0  31 

15  38 

1  28 

15  41 

0  25 

15  44 

0  22 

15  47 

20 

0  48 

15  21 

0  44 

15  25 

0  40 

15  29 

1  37 

15  32 

0  34 

15  35 

0  31 

15  38 

7  30 

0  57 

15  12 

0  53 

15  16 

0  49 

15  20 

1  46 

15  23 

0  43 

15  26 

0  40 

15  29 

40 

1  05 

15  04 

1  01 

15  08 

0  57 

15  12 

1  54 

15  15 

0  51 

15  18 

0  48 

15  21 

50 

1  13 

14  56 

1  09 

15  00 

1  05 

15  04 

1  02 

15  07 

0  59 

15  10 

0  56 

15  13 

8  00 

1  21 

14  48 

1  17 

14  52 

1  13 

14  56 

1  10 

14  59 

1  07 

15  02 

1  04 

15  05 

10 

1  28 

14  41 

1  24 

14  45 

1  20 

14  49 

1  17 

14  52 

1  14 

14  55 

1  11 

14  58 

20 

1  35 

14  34 

1  31 

14  38 

1  27 

14  42 

1  24 

14  45 

1  21 

14  48 

1  18 

14  51 

8  30 

1  42 

14  27 

1  38 

14  31 

1  34 

14  35 

1  31 

14  38 

1  28 

14  41 

1  25 

14  44 

40 

1  49 

14  20 

1  45 

14  24 

1  41 

14  28 

1  38 

14  31 

1  35 

14  34 

1  32 

14  37 

50 

1  55 

14  14 

1  51 

14  18 

1  47 

14  22 

1  44 

14  25 

1  41 

14  28 

1  38 

14  31 

9  00 

2  01 

14  08 

1  57 

14  12 

1  53 

14  16 

1  50 

14  19 

1  47 

14  22 

1  44 

14  25 

20 

2  13 

13  56 

2  09 

14  00 

2  05 

14  04 

2  02 

14  07 

1  59 

14  10 

1  56 

14  13 

40 

2  24 

13  45 

2  20 

13  49 

2  16 

13  53 

2  13 

13  56 

2  10 

13  59 

2  07 

14  02 

10  00 

2  35 

13  34 

2  31 

13  38 

2  27 

13  42 

2  24 

13  45 

2  21 

13  48 

2  18 

13  51 

20 

2  45 

13  24 

2  41 

13  28 

2  37 

13  32 

2  34 

13  35 

2  31 

13  38 

2  28 

13  41 

40 

2  54 

13  15 

2  50 

13  19 

2  46 

13  23 

2  43 

13  26 

2  40 

13  29 

2  37 

13  32 

11  00 

3  03 

13  06 

2  59 

13  10 

2  55 

13  14 

2  52 

13  17 

2  49 

13  20 

2  46 

13  23 

30 

3  15 

12  54 

3  11 

12  58 

3  07 

13  02 

3  04 

13  05 

3  01 

13  08 

2  58 

13  11 

12  00 

3  26 

12  43 

3  22 

12  47 

3  18 

12  51 

3  15 

12  54 

3  12 

12  57 

3  09 

13  00 

30 

3  37 

12  32 

3  33 

12  36 

3  29 

12  40 

3  26 

12  43 

3  23 

12  46 

3  20 

12  49 

13  00 

3  47 

12  22 

3  43 

12  26 

3  39 

12  30 

3  36 

12  33 

3  33 

12  36 

3  30 

12  39 

30 

3  56 

12  13 

3  52 

12  17 

3  48 

12  21 

3  45 

12  24 

3  42 

12  27 

3  39 

12  30 

14  00 

4  04 

12  05 

4  00 

12  09 

3  56 

12  13 

3  53 

12  16 

3  50 

12  19 

3  47 

12  22 

15  00 

4  20 

11  49 

4  16 

11  53 

4  12 

11  57 

4  09 

12  00 

4  06 

12  03 

4  03 

12  06 

16  00 

4  33 

11  36 

4  29 

11  40 

4  25 

11  44 

4  22 

11  47 

4  19 

11  50 

4  16 

11  53 

17  00 

4  46 

11  23 

4  42 

11  27 

\% 

11  31 

4  35 

11  34 

4  32 

11  37 

4  29 

11  40 

18  00 

4  56 

11  13 

4  52 

11  17 

11  21 

4  45 

11  24 

4  42 

11  27 

4  39 

11  30 

19  00 

5  06 

11  03 

5  02 

11  07 

4  58 

11  11 

4  55 

11  14 

4  52 

11  17 

4  49 

11  20 

20  00 

5  14 

10  54 

5  10 

10  58 

5  06 

11  02 

5  03 

11  05 

5  00 

11  08 

4  57 

11  11 

22  00 

5  30 

10  38 

5  26 

10  42 

5  22 

10  46 

5  19 

10  49 

5  16 

10  52 

5  13 

10  55 

24  00 

5  43 

10  25 

5  39 

10  29 

5  35 

10  33 

5  32 

10  36 

5  29 

10  39 

5  26 

10  42 

26  00 

5  54 

10  14 

5  50 

10  18 

5  46 

10  22 

5  43 

10  25 

5  40 

10  28 

5  37 

10  31 

28  00 

6  04 

10  04 

6  00 

10  08 

5  56 

10  12 

5  53 

10  15 

5  50 

10  18 

5  47 

10  21 

30  00 

6  12 

9  56 

6  08 

10  00 

6  04 

10  04 

6  01 

10  07 

5  58 

10  10 

5  65 

10  13 

32  00 

6  20 

9  48 

6  16 

9  52 

6  12 

9  56 

6  09 

9  59 

6  06 

10  02 

6  03 

10  05 

34  00 

6  27 

9  41 

6  23 

9  45 

6  19 

9  49 

6  16 

9  52 

6  13 

9  55 

6  10 

9  58 

36  00 

6  33 

9  35 

6  29 

9  39 

6  25 

9  43 

6  22 

9  46 

6  19 

9  49 

6  16 

9  52 

38  00 

6  38 

9  30 

6  34 

9  34 

6  30 

9  38 

6  27 

9  41 

6  24 

9  44 

6  21 

9  47 

40  00 

6  43 

9  24 

6  39 

9  28 

6  35 

9  32 

6  32 

9  35 

6  29 

9  38 

6  26 

9  41 

45  00 

6  54 

9  13 

6  50 

9  17 

6  46 

9  21 

6  43 

9  24 

6  40 

9  27 

6  37 

9  30 

50  00 

7  02 

9  04 

6  58 

9  08 

6  54 

9  12 

6  51 

9  15 

6  48 

9  18 

6  45 

9  21 

55  00 

7  09 

8  56 

7  05 

9  00 

7  01 

9  04 

6  58 

9  07 

6  55 

9  10 

6  52 

9  13 

60  00 

7  15 

8  49 

7  11 

8  53 

7  07 

8  57 

7  04 

9  00 

7  01 

9  03 

6  58 

9  06 

65  00 

7  22 

8  42 

7  18 

8  46 

7  14 

8  50 

7  11 

8  53 

y  08 

8  56 

7  05 

8  59 

70  00 

7  27 

8  36 

7  23 

8  40 

7  19 

8  44 

7  16 

8  47 

7  13 

8  50 

7  10 

8  53 

75  00 

7  31 

8  31 

7  27 

8  35 

7  23 

8  39 

7  20 

8  42 

7  17 

8  45 

7  14 

8  48 

80  00 

7  37 

8  25 

7  33 

8  29 

7  29 

8  33 

7  26 

8  36 

7  23 

8  39 

7  20 

8  42 

85  00 

7  41 

8  20 

7  37 

8  24 

7  33 

8  28 

7  30 

8  31 

7  27 

8  34 

7  24 

8  37 

90  00 

7  45 

8  15 

+7  41 

8  19 

+7  37 

8  23 

+7  34 

8  26 

+7  31 

8  29 

+7  28 

8  32 

1 

Additioi 

vTAL  Core. 

Day  of  Month 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

3ct. 

Nov. 

Dec. 

It 

// 

II 

„ 

„ 

„ 

~ 

II 

„ 

II 

„ 

II 

FOR  SU 

n's  Alt. 

Istt 

ol5th....  +18 

+15 

H 

^8 

0 

-  8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th 

to  31st... +17 

+12 

H 

h4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*Thec 

orrections  for  the  oh 

served  altitude  of  a  K 

StarorPla 

net  invoh 

^es  the  dip  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun' 

s  lower  limb,  the  dij 

3,  refraction,  paralla 

X,  and  me 

an  semidi 

ameter,  which  is  taken  as  16'.  A  supplementary  correction 

taking  accc 

unt  of  the  variation 

of  the  Sun's  semid 

ameter  in 

the  diiier< 

jit  months  of  the  year  is  given  at  the  foot  of  the  main  table. 

Page  934] 

TABLE  46. 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  | 

the  True  Altitude — Continued.                                                            1 

Obs.  Alt. 

HEIGHT   OF  THE  EYE.                                                                            1 

77  Feet. 

78  Feet.        1 

79  Feet.          1 

80  Feet.         1 

81  Feet.          1 

82  Feet.         1 

* 

* 

* 

* 

>K 

ii< 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 

COTI. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

6  30 

-0  21 

16  30 

-0  24 

16  33 

-0  28 

16  37 

-0  31 

16  40 

-0  34 

16  43 

-0  37 

16  46 

40 

-0  11 

16  20 

-0  14 

16  23 

-0  18 

16  27 

-0  21 

16  30 

-0  24 

16  33 

-0  27 

16  36 

50 

-0  01 

16  10 

-0  04 

16  13 

-0  08 

16  17 

-0  11 

16  20 

-0  14 

16  23 

-0  17 

16  26 

7  00 

+Q  09 

16  00 

+0  06 

16  03 

+0  02 

16  07 

-0  01 

16  10 

-0  04 

16  13 

-0  07 

16  16 

10 

0  18 

15  51 

0  15 

15  54 

0  11 

15  58 

+0  08 

16  01 

+0  05 

16  04 

+0  02 

16  07 

20 

0  27 

15  42 

0  24 

15  45 

0  20 

15  49 

0  17 

15  52 

0  14 

15  55 

0  11 

15  58 

7  30 

0  36 

15  33 

0  33 

15  36 

0  29 

15  40 

0  26 

15  43 

0  23 

15  46 

0  20 

15  49 

40 

0  44 

15  25 

0  41 

15  28 

0  37 

15  32 

0  34 

15  35 

0  31 

15  38 

0  28 

15  41 

50 

0  52 

15  17 

0  49 

15  20 

0  45 

15  24 

0  42 

15  27 

0  39 

15  30 

0  36 

15  33 

8  00 

1  00 

15  09 

0  57 

15  12 

0  53 

15  16 

0  50 

15  19 

0  47 

15  22 

0  44 

15  25 

10 

1  07 

15  02 

1  04 

15  05 

1  00 

15  09 

0  57 

15  12 

0  54 

15  15 

0  51 

15  18 

20 

1  14 

14  55 

1  11 

14  58 

1  07 

15  02 

1  04 

15  05 

1  01 

15  08 

0  58 

15  11 

8  30 

1  21 

14  48 

1  18 

14  51 

1  14 

14  55 

1  11 

14  58 

1  08 

15  01 

1  05 

15  04 

40 

1  28 

14  41 

1  25 

14  44 

1  21 

14  48 

1  18 

14  51 

1  15 

14  54 

1  12 

14  57 

50 

1  34 

14  35 

1  31 

14  38 

1  27 

14  42 

1  24 

14  45 

1  21 

14  48 

1  18 

14  51 

9  00 

1  40 

14  29 

1  37 

14  32 

1  33 

14  36 

1  30 

14  39 

1  27 

14  42 

1  24 

14  45 

20 

1  52 

14  17 

1  49 

14  20 

1  45 

14  24 

1  42 

14  27 

1  39 

14  30 

1  36 

14  33 

40 

2  03 

14  06 

2  00 

14  09 

1  56 

14  13 

1  53 

14  16 

1  50 

14  19 

1  47 

14  22 

10  00 

2  14 

13  55 

2  11 

13  58 

2  07 

14  02 

2  04 

14  05 

2  01 

14  08 

1  58 

14  11 

20 

2  24 

13  45 

2  21 

13  48 

2  17 

13  52 

2  14 

13  55 

2  11 

13  58 

2  08 

14  01 

40 

2  33 

13  36 

2  30 

13  39 

2  26 

13  43 

2  23 

13  46 

2  20 

13  49 

2  17 

13  52 

11  00 

2  42 

13  27 

2  39 

13  30 

2  35 

13  34 

2  32 

13  37 

2  29 

13  40 

2  26 

13  43 

30 

2  54 

13  15 

2  51 

13  18 

2  47 

13  22 

2  44 

13  25 

2  41 

13  28 

2  38 

13  31 

12  00 

3  05 

13  04 

3  02 

13  07 

2  58 

13  11 

2  55 

13  14 

2  52 

13  17 

2  49 

13  20 

30 

3  16 

12  53 

3  13 

12  56 

3  09 

13  00 

3  06 

13  03 

3  03 

13  06 

3  00 

13  09 

13  00 

3  26 

12  43 

3  23 

12  46 

3  19 

12  50 

3  16 

12  53 

3  13 

12  56 

3  10 

12  59 

30 

3  35 

12  34 

3  32 

12  37 

3  28 

12  41 

3  25 

12  44 

3  22 

12  47 

3  19 

12  50 

14  00 

3  43 

12  26 

3  40 

12  29 

3  36 

12  33 

3  33 

12  36 

3  30 

12  39 

3  27 

12  42 

15  00 

3  59 

12  10 

3  56 

12  13 

3  52 

12  17 

3  49 

12  20 

3  46 

12  23 

3  43 

12  26 

16  00 

4  12 

11  57 

4  09 

12  00 

4  05 

12  04 

4  02 

12  07 

3  59 

12  10 

3  56 

12  13 

17  00 

4  25 

11  44 

4  22 

11  47 

4  18 

11  51 

4  15 

11  54 

4  12 

11  57 

4  09 

12  00 

18  00 

4  35 

11  34 

4  32 

11  37 

4  28 

11  41 

4  25 

11  44 

4  22 

11  47 

4  19 

11  50 

19  00 

4  45 

11  24 

4  42 

11  27 

4  38 

11  31 

4  35 

11  34 

4  32 

11  37 

4  29 

11  40 

20  00 

4  53 

11  15 

4  50 

11  18 

4  46 

11  22 

4  43 

11  25 

4  40 

11  28 

4  37 

11  31 

22  00 

5  09 

10  59 

5  06 

11  02 

5  02 

11  06 

4  59 

11  09 

4  56 

11  12 

4  53 

11  15 

24  00 

5  22 

10  46 

5  19 

10  49 

5  15 

10  53 

5  12 

10  56 

5  09 

10  59 

5  06 

11  02 

26  00 

5  33 

10  35 

5  30 

10  38 

5  26 

10  42 

5  23 

10  45 

5  20 

10  48 

5  17 

10  51 

28  00 

5  43 

10  25 

5  40 

10  28 

5  36 

10  32 

5  33 

10  35 

5  30 

10  38 

5  27 

10  41 

30  00 

5  51 

10  17 

5  48 

10  20 

5  44 

10  24 

5  41 

10  27 

5  38 

10  30 

5  35 

10  33 

32  00 

5  59 

10  09 

5  56 

10  12 

5  52 

10  16 

5  49 

10  19 

5  46 

10  22 

5  43 

10  25 

34  00 

6  06 

10  02 

6  03 

10  05 

5  59 

10  09 

5  56 

10  12 

5  53 

10  15 

5  50 

10  18 

36  00 

6  12 

9  56 

6  09 

9  59 

6  05 

10  03 

6  02 

10  06 

5  59 

10  09 

5  56 

10  12 

38  00 

6  17 

9  51 

6  14 

9  54 

6  10 

9  58 

6  07 

10  01 

6  04 

10  04 

6  01 

10  07 

40  00 

6  22 

9  45 

6  19 

9  48 

6  15 

9  52 

6  12 

9  55 

6  09 

9  58 

6  06 

10  01 

45  00 

6  33 

9  34 

6  30 

9  37 

6  26 

9  41 

6  23 

9  44 

6  20 

9  47 

6  17 

9  50 

50  00 

6  41 

9  25 

6  38 

9  28 

6  34 

9  32 

6  31 

9  35 

6  28 

9  38 

6  25 

9  41 

55  00 

6  48 

9  17 

6  45 

9  20 

6  41 

9  24 

6  38 

9  27 

6  35 

9  30 

6  32 

9  33 

60  00 

6  54 

9  10 

6  51 

9  13 

6  47 

9  17 

6  44 

9  20 

6  41 

9  23 

6  38 

9  26 

65  00 

7  01 

9  03 

6  58 

9  06 

6  54 

9  10 

6  51 

9  13 

6  48 

9  16 

6  45 

9  19 

70  00 

7  06 

8  57 

7  03 

9  00 

6  59 

9  04 

6  56 

9  07 

6  53 

9  10 

6  50 

9  13 

75  00 

7  10 

8  52 

7  07 

8  55 

7  03 

8  59 

7  00 

9  02 

6  57 

9  05 

6  54 

9  08 

80  00 

7  16 

8  46 

7  13 

8  49 

7  09 

8  53 

7  06 

8  56 

7  03 

8  59 

7  00 

9  02 

85  00 

7  20 

8  41 

7  17 

8  44 

7  13 

8  48 

7  10 

8  51 

7  07 

8  54 

7  04 

8  57 

90  00 

+7  24 

8  36 

+7  21 

8  39 

+7  17 

8  43 

+7  14 

8  46 

+7  11 

8  49 

+7  08 

8  52 

1 

Additio 

NAL  CORB. 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

.    May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

,/ 

„ 

/            tr 

// 

t) 

" 

'1 

II 

" 

" 

FOR  St 

jN's  Alt. 

1st 

to  15th.... 

+18 

+15 

+8 

C 

)   -  8 

-13 

-14 

-11 

-5 

+3 

+11 

+^^ 

16tl 

1  to  31st... 

+17 

+12 

+4 

-4 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*The 

corrections  for  the  ol 

^served  altitude  of  a 

Star  or  Planet  involves  the  dip  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun 

's  lower  limb,  the  di 

p,  refraction,  paralk 

IX,  and  mean  semidiameter,  which  is  taken  as  10'.  A  supplementary  correction 
ameter  in  the  different  months  of  the  year  is  given  at  the  foot  of  the  main  table. 

taking  ace 

ount  of  the  variatior 

1  of  the  Sun's  semid 

TABLE  46.                                             [Page  935 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  1 



the  True  Altitude — Continued. 

HEIGHT  OF  THE  EYE.                                                                            | 

83  Feet. 

84  Feet. 

85  Feet. 

86  Feet. 

87  Feet. 

88  Feet.         1 

Obs.  Alt 

Sun's 
Corr. 

* 
Star's 
Corr. 
(-) 

G 
Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

* 

Star's 

Corr. 

(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

6  30 

-0  41 

/     // 
16  50 

-0  44 

16  53 

-0  47 

16  56 

-0  50 

1     II 
16  59 

-0  63 

17  02 

-0  57 

17  06 

40 

-0  31 

16  40 

-0  34 

16  43 

-0  37 

16  46 

-0  40 

16  49 

-0  43 

16  62 

-0  47 

16  56 

50 

-0  21 

16  30 

-0  24 

16  33 

-0  27 

16  36 

-0  30 

16  39 

-0  33 

16  42 

-0  37 

16  46 

7  00 

-0  11 

16  20 

-0  14 

16  23 

-0  17 

16  26 

-0  20 

16  29 

-0  23 

16  32 

-0  27 

16  36 

10 

-0  02 

16  11 

-0  05 

16  14 

-0  08 

16  17 

-0  11 

16  20 

-0  14 

16  23 

-0  18 

16  27 

20 

+0  07 

16  02 

+0  04 

16  05 

+0  01 

16  08 

-0  02 

16  11 

-0  05 

16  14 

-0  09 

16  18 

7  30 

0  16 

15  53 

0  13 

15  56 

0  10 

15  59 

+0  07 

16  02 

+0  04 

16  05 

0  00 

16  09 

40 

0  24 

15  45 

0  21 

15  48 

0  18 

15  51 

0  15 

15  54 

0  12 

16  67 

+0  08 

16  01 

50 

0  32 

15  37 

0  29 

15  40 

0  26 

15  43 

0  23 

15  46 

0  20 

16  49 

0  16 

16  63 

8  00 

0  40 

15  29 

0  37 

15  32 

0  34 

15  35 

0  31 

15  38 

0  28 

15  41 

0  24 

15  46 

10 

0  47 

15  22 

0  44 

15  25 

0  41 

15  28 

0  38 

15  31 

0  35 

15  34 

0  31 

15  38 

20 

0  54 

15  15 

0  51 

15  18 

0  48 

15  21 

0  45 

15  24 

0  42 

16  27 

0  38 

15  31 

8  30 

1  01 

15  08 

0  58 

15  11 

0  55 

15  14 

0  52 

15  17 

0  49 

16  20 

0  46 

15  24 

40 

1  08 

15  01 

1  05 

15  04 

1  02 

15  07 

0  59 

15  10 

0  56 

15  13 

0  52 

15  17 

50 

1  14 

14  55 

1  11 

14  58 

1  08 

15  01 

1  05 

15  04 

1  02 

15  07 

0  58 

15  11 

9  00 

1  20 

14  49 

1  17 

14  52 

1  14 

14  55 

1  11 

14  58 

1  08 

16  01 

1  04 

15  05 

20 

1  32 

14  37 

1  29 

14  40 

1  26 

14  43 

1  23 

14  46 

1  20 

14  49 

1  16 

14  53 

40 

1  43 

14  26 

1  40 

14  29 

1  37 

14  32 

1  34 

14  35 

1  31 

14  38 

1  27 

14  42 

10  00 

1  54 

14  15 

1  51 

14  18 

1  48 

14  21 

1  45 

14  24 

1  42 

14  27 

1  38 

14  31 

20 

2  04 

14  05 

2  01 

14  08 

1  58 

14  11 

1  55 

14  14 

1  52 

14  17 

1  48 

14  21 

40 

2  13 

13  56 

2  10 

13  59 

2  07 

14  02 

2  04 

14  05 

2  01 

14  08 

1  57 

14  12 

11  00 

2  22 

13  47 

2  19 

13  50 

2  16 

13  53 

2  13 

13  56 

2  10 

13  59 

2  06 

14  03 

30 

2  34 

13  35 

2  31 

13  38 

2  28 

13  41 

2  25 

13  44 

2  22 

13  47 

2  18 

13  51 

12  00 

2  45 

13  24 

2  42 

13  27 

2  39 

13  30 

2  36 

13  33 

2  33 

13  36 

2  29 

13  40 

30 

2  56 

13  13 

2  53 

13  16 

2  50 

13  19 

2  47 

13  22 

2  44 

13  26 

2  40 

13  29 

13  00 

3  06 

13  03 

3  03 

13  06 

3  00 

13  09 

2  57 

13  12 

2  54 

13  15 

2  50 

13  19 

30 

3  15 

12  54 

3  12 

12  57 

3  09 

13  00 

3  06 

13  03 

3  03 

13  06 

2  59 

13  10 

14  00 

3  23 

12  46 

3  20 

12  49 

3  17 

12  52 

3  14 

12  55 

3  11 

12  58 

3  07 

13  02 

15  00 

3  39 

12  30 

3  36 

12  33 

3  33 

12  36 

3  30 

12  39 

3  27 

12  42 

3  23 

12  46 

16  00 

3  52 

12  17 

3  49 

12  20 

3  46 

12  23 

3  43 

12  26 

3  40 

12  29 

3  36 

12  33 

17  00 

4  05 

12  04 

4  02 

12  07 

3  59 

12  10 

3  56 

12  13 

3  53 

12  16 

3  49 

12  20 

18  00 

4  15 

11  54 

4  12 

11  57 

4  09 

12  00 

4  06 

12  03 

4  03 

12  06 

3  69 

12  10 

19  00 

4  25 

11  44 

4  22 

11  47 

4  19 

11  50 

4  16 

11  53 

4  13 

11  66 

4  09 

12  00 

20  00 

4  33 

11  35 

4  30 

11  38 

4  27 

11  41 

4  24 

11  44 

4  21 

11  47 

4  17 

11  61 

22  00 

4  49 

11  19 

4  46 

11  22 

4  43 

11  25 

4  40 

11  28 

4  37 

11  31 

4  33 

11  35 

24  00 

5  02 

11  06 

4  59 

11  09 

4  56 

11  12 

4  53 

11  15 

4  60 

11  18 

4  46 

11  22 

26  00 

5  13 

10  55 

6  10 

10  58 

5  07 

11  01 

5  04 

11  04 

6  01 

11  07 

4  57 

11  11 

28  00 

5  23 

10  45 

5  20 

10  48 

5  17 

10  51 

5  14 

10  54 

5  11 

10  57 

5  07 

11  01 

30  00 

5  31 

10  37 

5  28 

10  40 

5  25 

10  43 

5  22 

10  46 

5  19 

10  49 

5  16 

10  63 

32  00 

5  39 

10  29 

5  36 

10  32 

5  33 

10  35 

5  30 

10  38 

5  27 

10  41 

5  23 

10  46 

34  00 

5  46 

10  22 

5  43 

10  25 

5  40 

10  28 

5  37 

10  31 

5  34 

10  34 

6  30 

10  38 

36  00 

5  52 

10  16 

5  49 

10  19 

5  46 

10  22 

5  43 

10  25 

5  40 

10  28 

5  36 

10  32 

38  00 

5  57 

10  11 

5  54 

10  14 

5  51 

10  17 

5  48 

10  20 

6  45 

10  23 

5  41 

10  27 

40  00 

6  02 

10  05 

5  59 

10  08 

5  56 

10  11 

5  53 

10  14 

5  50 

10  17 

5  46 

10  21 

45  00 

6  13 

9  54 

6  10 

9  57 

6  07 

10  00 

6  04 

10  03 

6  01 

10  06 

5  57 

10  10 

50  00 

6  21 

9  45 

6  18 

9  48 

6  15 

9  51 

6  12 

9  54 

6  09 

9  57 

6  05 

10  01 

55  00 

6  28 

9  37 

6  25 

9  40 

6  22 

9  43 

6  19 

9  46 

6  16 

9  49 

6  12 

9  53 

60  00 

6  34 

9  30 

6  31 

9  33 

6  28 

9  36 

6  25 

9  39 

6  22 

9  42 

6  18 

9  46 

65  00 

6  41 

9  23 

6  38 

9  26 

6  35 

9  29 

6  32 

9  32 

6  29 

9  36 

6  26 

9  39 

70  00 

6  46 

9  17 

6  43 

9  20 

6  40 

9  23 

6  37 

9  26 

6  34 

9  29 

6  30 

9  33 

75  00 

6  50 

9  12 

6  47 

9  15 

6  44 

9  18 

6  41 

9  21 

6  38 

9  24 

6  34 

9  28 

80  00 

6  56 

9  06 

6  53 

9  09 

6  50 

9  12 

6  47 

9  15 

6  44 

9  18 

6  40 

9  22 

85  00 

7  00 

9  01 

6  57 

9  04 

6  54 

9  07 

6  51 

9  10 

6  48 

9  13 

6  44 

9  17 

90  00 

+7  04 

8  56 

+7  01 

8  59 

+6  58 

9  02 

+6  55 

9  05 

+6  62 

9  08 

+6  48 

9  12 

1 

Additio] 

■^AL  Core. 

Day  of  Month 

Jan. 

Feb. 

Mar. 

Apr 

May. 

June. 

July. 

Aug. 

Sept.     ( 

3ct. 

Nov.  1  Dec.  1 

// 

'/ 

" 

'/ 

ti 

" 

" 

II 

" 

" 

" 

FOR  SU 

:sj'3  Alt. 

Istt 

o  15th.. 

.-+18 

+15 

+8 

0 

-  8    - 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16th 

to  31st. 

..+17 

+12 

+4 

-4 

-11    - 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*Thec 

orrections  for  the  oh 

served  altitude  of  a » 

Star  or  Planet  involves  the  dip  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun 

s  lower  limb,  the  di 

p,  refraction,  paralla 

X,  and  mean  semidiameter,  which  is  taken  as  16'.  A  supplementary  correction 

taking  ace 

)unt  of  the  variation 

of  the  Sun's  semid 

ameter  in  the  different  months  of  the  year  is  given  at  the  foot  of  the  main  table. 

Page 

936] 

TABLE  46. 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star  or  of  the  Sun's  Lower  Limb,  to  Find  1 

the  True  Altitude — Continued. 

1 

Obs.  Alt. 

HEIGHT   OF  THE  EYE.                                                                            1 

89  Feet. 

90  Feet. 

91  Feet. 

92  Feet. 

93  Feet. 

94  Feet.         1 

* 

* 

* 

* 

* 

:|c 

Sim's 
Con. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

O 
Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

6  30 

-1  00 

17  09 

-1  03 

17  12 

-1  06 

17  15 

-1  09 

17  18 

-1  12 

17  21 

-1  15 

1     It 
17  24 

40 

-0  60 

16  59 

-0  53 

17  02 

-0  56 

17  05 

-0  59 

17  08 

-1  02 

17  11 

-1  05 

17  14 

50 

-0  40 

16  49 

-0  43 

16  52 

-0  46 

16  55 

-0  49 

16  58 

-0  52 

17  01 

-0  55 

17  04 

7  00 

-0  30 

16  39 

-0  33 

16  42 

-0  36 

16  45 

-0  39 

16  48 

-0  42 

16  51 

-0  45 

16  54 

10 

-0  21 

16  30 

-0  24 

16  33 

-0  27 

16  36 

-0  30 

16  39 

-0  33 

16  42 

-0  36 

16  45 

20 

-0  12 

16  21 

-0  15 

16  24 

-0  18 

16  27 

-0  21 

16  30 

-0  24 

16  33 

-0  27 

16  36 

7  30 

-0  03 

16  12 

-0  06 

16  15 

-0  09 

16  18 

-0  12 

16  21 

-0  15 

16  24 

-0  18 

16  27 

40 

+0  05 

16  04 

+0  02 

16  07 

-0  01 

16  10 

-0  04 

16  13 

-0  07 

16  16 

-0  10 

16  19 

50 

0  13 

15  56 

0  10 

15  59 

+0  07 

16  02 

+0  04 

16  05 

+0  01 

16  08 

-0  02 

16  11 

8  00 

0  21 

15  48 

0  18 

15  51 

0  15 

15  54 

0  12 

15  57 

0  09 

16  00 

+0  06 

16  03 

10 

0  28 

15  41 

0  25 

15  44 

0  22 

15  47 

0  19 

15  50 

0  16 

15  53 

0  13 

15  56 

20 

0  35 

15  34 

0  32 

15  37 

0  29 

15  40 

0  26 

15  43 

0  23 

15  46 

0  20 

15  49 

8  30 

0  42 

15  27 

0  39 

15  30 

0  36 

15  33 

0  33 

15  36 

0  30 

15  39 

0  27 

15  42 

40 

0  49 

15  20 

0  46 

15  23 

0  43 

15  26 

0  40 

15  29 

0  37 

15  32 

0  34 

15  35 

50 

0  55 

15  14 

0  52 

15  17 

0  49 

15  20 

0  46 

15  23 

0  43 

15  26 

0  40 

15  29 

9  00 

1  01 

15  08 

0  58 

15  11 

0  55 

15  14 

0  52 

15  17 

0  49 

15  20 

0  46 

15  23 

20 

1  13 

14  56 

1  10 

14  59 

1  07 

15  02 

1  04 

15  05 

1  01 

15  08 

0  58 

15  11 

40 

1  24 

14  45 

1  21 

14  48 

1  18 

14  51 

1  15 

14  54 

1  12 

14  57 

1  09 

15  00 

10  00 

1  35 

14  34 

1  32 

14  37 

1  29 

14  40 

1  26 

14  43 

1  23 

14  46 

1  20 

14  49 

20 

1  45 

14  24 

1  42 

14  27 

1  39 

14  30 

1  36 

14  33 

1  33 

14  36 

1  30 

14  39 

40 

1  54 

14  15 

1  51 

14  18 

1  48 

14  21 

1  45 

14  24 

1  42 

14  27 

1  39 

14  30 

11  00 

2  03 

14  06 

2  00 

14  09 

1  57 

14  12 

1  54 

14  15 

1  51 

14  18 

1  48 

14  21 

30 

2  15 

13  54 

2  12 

13  57 

2  09 

14  00 

2  06 

14  03 

2  03 

14  06 

2  00 

14  09 

12  00 

2  26 

13  43 

2  23 

13  46 

2  20 

13  49 

2  17 

13  52 

2  14 

13  55 

2  11 

13  58 

30 

2  37 

13  32 

2  34 

13  35 

2  31 

13  38 

2  28 

13  41 

2  25 

13  44 

2  22 

13  47 

13  00 

2  47 

13  22 

2  44 

13  25 

2  41 

13  28 

2  38 

13  31 

2  35 

13  34 

2  32 

13  37 

30 

2  56 

13  13 

2  53 

13  16 

2  50 

13  19 

2  47 

13  22 

2  44 

13  25 

2  41 

13  28 

14  00 

3  04 

13  05 

3  01 

13  08 

2  58 

13  11 

2  55 

13  14 

2  52 

13  17 

2  49 

13  20 

15  00 

3  20 

12  49 

3  17 

12  52 

3  14 

12  55 

3  11 

12  58 

3  08 

13  01 

3  05 

13  04 

16  00 

3  33 

12  36 

3  30 

12  39 

3  27 

12  42 

3  24 

12  45 

3  21 

12  48 

3  18 

12  51 

17  00 

3  46 

12  23 

3  43 

12  26 

3  40 

12  29 

3  37 

12  32 

3  34 

12  35 

3  31 

12  38 

18  00 

3  56 

12  13 

3  53 

12  16 

3  50 

12  19 

3  47 

12  22 

3  44 

12  25 

3  41 

12  28 

19  00 

4  06 

12  03 

4  03 

12  06 

4  00 

12  09 

3  57 

12  12 

3  54 

12  15 

3  51 

12  18 

20  00 

4  14 

11  54 

4  11 

11  57 

4  08 

12  00 

4  05 

12  03 

4  02 

12  06 

3  59 

12  09 

22  00 

4  30 

11  38 

4  27 

11  41 

4  24 

11  44 

4  21 

11  47 

4  18 

11  50 

4  15 

11  53 

24  00 

4  43 

11  25 

4  40 

11  28 

4  37 

11  31 

4  34 

11  34 

4  31 

11  37 

4  28 

11  40 

26  00 

4  54 

11  14 

4  51 

11  17 

4  48 

11  20 

4  45 

11  23 

4  42 

11  26 

4  39 

11  29 

28  00 

5  04 

11  04 

5  01 

11  07 

4  58 

11  10 

4  55 

11  13 

4  52 

11  16 

4  49 

11  19 

30  00 

5  12 

10  56 

5  09 

10  59 

5  06 

11  02 

5  03 

11  05 

5  00 

11  08 

4  57 

11  11 

32  00 

5  20 

10  48 

5  17 

10  51 

5  14 

10  54 

5  11 

10  57 

5  08 

11  00 

5  05 

11  03 

34  00 

5  27 

10  41 

5  24 

10  44 

5  21 

10  47 

5  18 

10  50 

5  15 

10  53 

5  12 

10  56 

36  00 

5  33 

10  35 

5  30 

10  38 

5  27 

10  41 

5  24 

10  44 

5  21 

10  47 

5  18 

10  50 

38  00 

5  38 

10  30 

5  35 

10  33 

5  32 

10  36 

5  29 

10  39 

5  26 

10  42 

5  23 

10  45 

40  00 

5  43 

10  24 

5  40 

10  27 

5  37 

10  30 

5  34 

10  33 

5  31 

10  36 

5  28 

10  39 

45  00 

5  54 

10  13 

5  51 

10  16 

5  48 

10  19 

5  45 

10  22 

5  42 

10  25 

5  39 

10  28 

50  00 

6  02 

10  04 

5  59 

10  07 

5  56 

10  10 

5  53 

10  13 

5  50 

10  16 

5  47 

10  19 

55  00 

6  09 

9  56 

6  06 

9  59 

6  03 

10  02 

6  00 

10  05 

5  57 

10  08 

5  54 

10  11 

60  00 

6  15 

9  49 

6  12 

9  52 

6  00 

9  55 

6  06 

9  58 

6  03 

10  01 

6  00 

10  04 

65  00 

6  22 

9  42 

6  19 

9  45 

6  16 

9  48 

6  13 

9  51 

6  10 

9  54 

6  07 

9  57 

70  00 

6  27 

9  36 

6  24 

9  39 

6  21 

9  42 

6  18 

9  45 

6  15 

9  48 

6  12 

9  51 

75  00 

6  31 

9  31 

6  28 

9  34 

6  25 

9  37 

6  22 

9  40 

6  19 

9  43 

6  16 

9  46 

80  00 

6  37 

9  25 

6  34 

9  28 

6  31 

9  31 

6  28 

9  34 

6  25 

9  37 

6  22 

9  40 

85  00 

6  41 

9  20 

6  38 

9  23 

6  35 

9  26 

6  32 

9  29 

6  29 

9  32 

6  26 

9  35 

90  00 

+6  45 

9  15 

+6  42 

9  18 

+6  39 

9  21 

+6  36 

9  24 

+6  33 

9  27 

+6  30 

9  30 

1 

Additio 

(TAL  Cork. 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr. 

May.   . 

Fune. 

Ju 

y.    Aug. 

Sept.    ( 

Dct. 

Nov 

.    Dec. 

// 

// 

„ 

/, 

f 

// 

//         // 

„ 

n 

>         1, 

roB  Stj 

'n's  Alt. 

Istt 

o  15th.... 

+18 

+15 

+8 

0 

-  8    - 

-13 

-1 

4    -11 

-5 

+3 

+11 

+16 

16th 

to  3l8t.. 

+17 

+12 

+4 

-4 

-11    - 

-14 

-1 

3-9 

-1 

f7 

+  14 

+18 

♦The 

3oiTections  for  the  ot 

served  altitude  of  a 

Star  or  Planet  involves  the  dip  and  the  r< 

sfraction;  and  for  the  observed  altitude 

of  the  Sun 

3  lower  limb,  the  di 

p,  refraction,  paralla 

X,  and  mean  semidiameter,  which  is  tak 

en  as  16'.  A  supplementary  correction 
ir  is  given  at  the  loot  of  the  main  table. 

taking  ace 

}UQt  of  thev  ariation 

of  the  Sun's  semidi 

ameter  in  the  different  months  of  the  yes 

TABLE  46. 

[Page  937 

Corrections*  to  be  Applied  to  the  Observed  Altitude  of  a  Star 

or  of  the  Sun's  Lower  Limb,  to  Find 

the  True  Altitude — Continued.                                                            | 

HEIGHT   OF  THE  EYE.                                                                            1 

95  Feet. 

96  Feet.          1 

97  Feet.         1 

98  Feet.         1 

99  Feet.         1 

100  Feet.        1 

Obs.  Alt. 

oO, 
Sun's 

Corr. 

Star's 
Corr. 
(-) 

„o 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

Sun's 
Corr. 

Star's 
Corr. 
(-) 

«o. 

Sun's 
Corr. 

star's 
Corr. 
(-) 

oO, 
Sun's 

Corr. 

Star's 
Corr. 
(-) 

oO, 
Sun's 

Corr. 

Star's 
Corr. 
(-) 

o           , 

/     // 

/     t, 

/     II 

/     // 

/       n 

/     II 

/     II 

1     II 

/     // 

/     // 

/     II 

/     II 

6  30 

-1  18 

17  27 

-1  21 

17  30 

-1  24 

17  33 

-1  27 

17  36 

-1  30 

17  39 

-1  33 

17  42 

40 

-1  08 

17  17 

-1  11 

17  20 

-1  14 

17  23 

-1  17 

17  26 

-1  20 

17  29 

-1  23 

17  32 

50 

-0  58 

17  07 

-1  01 

17  10 

-1  04 

17  13 

-1  07 

17  16 

-1  10 

17  19 

-1  13 

17  22 

7  00 

-0  48 

16  57 

-0  51 

17  00 

-0  54 

17  03 

-0  57 

17  06 

-1  00 

17  09 

-1  03 

17  12 

10 

-0  39 

16  48 

-0  42 

16  51 

-0  45 

16  54 

-0  48 

16  57 

-0  51 

17  00 

-0  54 

17  03 

20 

-0  30 

16  39 

-0  33 

16  42 

-0  36 

16  45 

-0  39 

16  48 

-0  42 

16  51 

-0  45 

16  54 

7  30 

-0  21 

16  30 

-0  24 

16  33 

-0  27 

16  36 

-0  30 

16  39 

-0  33 

16  42 

-0  36 

16  45 

40 

-0  13 

16  22 

-0  16 

16  25 

-0  19 

16  28 

-0  22 

16  31 

-0  25 

16  34 

-0  28 

16  37 

50 

-0  05 

16  14 

-0  08 

16  17 

-0  11 

16  20 

-0  14 

16  23 

-0  17 

16  26 

-0  20 

16  29 

8  00 

+0  03 

16  06 

0  00 

16  09 

-0  08 

16  12 

-0  06 

16  15 

-0  09 

16  18 

-0  12 

16  21 

10 

0  10 

15  59 

+0  07 

16  02 

+0  04 

16  05 

+0  01 

16  08 

-0  02 

16  11 

-0  05 

16  14 

20 

0  17 

15  52 

0  14 

15  55 

0  11 

15  58 

0  08 

16  01 

+0  05 

16  04 

+0  02 

16  07 

8  30 

0  24 

15  45 

0  21 

15  48 

0  18 

15  51 

0  15 

15  54 

0  12 

15  57 

0  09 

16  00 

40 

0  31 

15  38 

0  28 

15  41 

0  25 

15  44 

0  22 

15  47 

0  19 

15  50 

0  16 

15  53 

50 

0  37 

15  32 

0  34 

15  35 

0  31 

15  38 

0  28 

15  41 

0  25 

15  44 

0  22 

15  47 

9  00 

0  43 

15  26 

0  40 

15  29 

0  37 

15  32 

0  34 

15  35 

0  31 

15  38 

0  28 

15  41 

20 

0  55 

15  14 

0  52 

15  17 

0  49 

15  20 

0  46 

15  23 

0  43 

15  26 

0  40 

15  29 

40 

1  06 

15  03 

1  03 

15  06 

1  00 

15  09 

0  57 

15  12 

0  54 

15  15 

0  51 

15  18 

10  00 

1  17 

14  52 

1  14 

14  55 

1  11 

14  58 

1  08 

15  01 

1  05 

15  04 

1  02 

15  07 

20 

1  27 

14  42 

1  24 

14  45 

1  21 

14  48 

1  18 

14  51 

1  15 

14  54 

1  12 

14  57 

40 

1  36 

14  33 

1  33 

14  36 

1  30 

14  39 

1  27 

14  42 

1  24 

14  45 

1  21 

14  48 

11  00 

1  45 

14  24 

1  42 

14  27 

1  39 

14  30 

1  36 

14  33 

1  33 

14  36 

1  30 

14  39 

30 

1  57 

14  12 

1  54 

14  15 

1  51 

14  18 

1  48 

14  21 

1  45 

14  24 

1  42 

14  27 

12  00 

2  08 

14  01 

2  05 

14  04 

2  02 

14  07 

1  59 

14  10 

1  56 

14  13 

1  53 

14  16 

30 

2  19 

13  50 

2  16 

13  53 

2  13 

13  56 

2  10 

13  59 

2  07 

14  02 

2  04 

14  05 

13  00 

2  29 

13  40 

2  26 

13  43 

2  23 

13  46 

2  20 

13  49 

2  17 

13  52 

2  14 

13  55 

30 

2  38 

13  31 

2  35 

13  34 

2  32 

13  37 

2  29 

13  40 

2  26 

13  43 

2  23 

13  46 

14  00 

2  46 

13  23 

2  43 

13  26 

2  40 

13  29 

2  37 

13  32 

2  34 

13  35 

2  31 

13  38 

15  00 

3  02 

13  07 

2  59 

13  10 

2  56 

13  13 

2  53 

13  16 

2  50 

13  19 

2  47 

13  22 

16  00 

3  15 

12  54 

3  12 

12  57 

3  09 

13  00 

3  06 

13  03 

3  03 

13  06 

3  00 

13  09 

17  00 

3  28 

12  41 

3  25 

12  44 

3  22 

12  47 

3  19 

12  50 

3  16 

12  53 

3  13 

12  56 

18  00 

3  38 

12  31 

3  35 

12  34 

3  32 

12  37 

3  29 

12  40 

3  26 

12  43 

3  23 

12  46 

19  00 

3  48 

12  21 

3  45 

12  24 

3  42 

12  27 

3  39 

12  30 

3  36 

12  33 

3  33 

12  36 

20  00 

3  59 

12  12 

3  53 

12  15 

3  50 

12  18 

3  47 

12  21 

3  44 

12  24 

3  41 

12  27 

22  00 

4  12 

11  56 

4  09 

11  59 

4  06 

12  02 

4  03 

12  05 

4  00 

12  08 

3  57 

12  11 

24  00 

4  25 

11  43 

4  22 

11  46 

4  19 

11  49 

4  16 

11  52 

4  13 

11  55 

4  10 

11  58 

26  00 

4  36 

11  32 

4  33 

11  35 

4  30 

11  38 

4  27 

11  41 

4  24 

11  44 

4  21 

11  47 

28  00 

4  46 

11  22 

4  43 

11  25 

4  40 

11  28 

4  37 

11  31 

4  34 

11  34 

4  31 

11  37 

30  00 

4  54 

11  14 

4  51 

11  17 

4  48 

11  20 

4  45 

11  23 

4  42 

11  26 

4  39 

11  29 

32  00 

5  02 

11  06 

4  59 

11  09 

4  56 

11  12 

4  53 

11  15 

4  50 

11  18 

4  47 

11  21 

34  00 

5  09 

10  59 

5  06 

11  02 

5  03 

11  05 

5  00 

11  08 

4  57 

11  11 

4  54 

11  14 

36  00 

5  15 

10  53 

5  12 

10  56 

5  09 

10  59 

5  06 

11  02 

5  03 

11  05 

5  00 

11  08 

38  00 

5  20 

10  48 

5  17 

10  51 

5  14 

10  54 

5  11 

10  57 

5  08 

11  00 

5  05 

11  03 

40  00 

5  25 

10  42 

5  22 

10  45 

5  19 

10  48 

5  16 

10  51 

5  13 

10  54 

5  10 

10  57 

45  00 

5  36 

10  31 

5  33 

10  34 

5  30 

10  37 

5  27 

10  40 

5  24 

10  43 

5  21 

10  46 

50  00 

5  44 

10  22 

5  41 

10  25 

5  38 

10  28 

5  35 

10  31 

5  32 

10  34 

5  29 

10  37 

55  00 

5  51 

10  14 

5  48 

10  17 

5  45 

10  20 

5  42 

10  23 

5  39 

10  26 

5  36 

10  29 

60  00 

5  57 

10  07 

5  54 

10  10 

5  51 

10  13 

5  48 

10  16 

5  45 

10  19 

5  42 

10  22 

65  00 

6  04 

10  00 

6  01 

10  03 

5  58 

10  06 

5  55 

10  09 

5  52 

10  12 

5  49 

10  15 

70  00 

6  09 

9  54 

6  06 

9  57 

6  03 

10  00 

6  00 

10  03 

5  57 

10  06 

5  54 

10  09 

75  00 

6  13 

9  49 

6  10 

9  52 

6  07 

9  55 

6  04 

9  58 

6  01 

10  01 

5  58 

10  04 

80  00 

6  19 

9  43 

6  16 

9  46 

6  13 

9  49 

6  10 

9  52 

6  07 

9  55 

6  04 

9  58 

85  00 

6  23 

9  38 

6  20 

9  41 

6  17 

9  44 

6  14 

9  47 

6  11 

9  50 

6  08 

9  53 

90  00 

6  27 

9  33 

+6  24 

9  36 

+6  21 

9  39 

+6  18 

9  42 

+6  15 

9  45 

+6  12 

9  48 

1 

Additio 

NAL  Cork 

Day  of  Month. 

Jan. 

Feb. 

Mar. 

Apr 

.    May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

„ 

„ 

„ 

// 

ti 

II 

1, 

// 

II 

" 

II 

FOR  Sr 

in's  Alt. 

Ist 

to  15th.... 

+18 

+15 

+8 

C 

I    -  8 

-13 

-14 

-11 

-5 

+3 

+11 

+16 

16tl 

I  to  31st... 

+17 

+12 

+4 

-A 

-11 

-14 

-13 

-  9 

-1 

+7 

+14 

+18 

*The 

correction 

s  for  the  o 

>served  altitude  of  a 

Star  or  Planet  involves  the  di 
X,  and  mean  semidiameter,  v 

[)  and  the  refraction;  and  for  the  observed  altitude 

of  the  Sun 

's  lower  li 

Hb,  thedi 

p,  refraction,  paralla 

•hich  is  taken  as  16'.  A  supplementary  correction 
s  of  the  year  is  given  at  the  foot  of  the  main  table. 

taking  ace 

ountof th 

8  variation 

of  the  Sun's  semidi 

ameter  in  the  diflerent  month 

Page  938] 

TABLE  47. 

Longitude  Factors. 

F  Is  the  change  in  longitude  due  to  a  change  of  1'  in  latitude. 

Latitude. 

Bear- 

0° 

1° 

2° 

4° 

6° 

8° 

10° 

12° 

Bear- 

ing. 

ing. 

0 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o 

1 

57.29 

57.30 

57.32 

57.43 

57.61 

57.85 

58.17 

58.57 

1 

2 

28.64 

28.64 

28.65 

28.71 

28.79 

28.92 

29.08 

29.28 

2 

3 

19.08 

19.08 

19.09 

19.13 

19.19 

19.27 

19.38 

19.51 

3 

4 

14.30 

14.30 

14.31 

14.34 

14.38 

14.44 

14.52 

14.62 

4 

5 

11.43 

11.43 

11.44 

11.46 

11.49 

11.54 

11.61 

11.69 

5 

6 

9.51 

9.52 

9.52 

9.54 

9.57 

9.61 

9.66 

9.73 

6 

7 

8.14 

8.15 

8.15 

8.16 

8.19 

8.22 

8.27 

8.33 

7 

8 

7.12 

7.12 

7.12 

7.13 

7.15 

7.18 

7.22 

7.27 

8 

10 

5.67 

5.67 

5.68 

5.69 

5.70 

5.73 

5.76 

5.80 

10 

12 

4.71 

4.71 

4.71 

4.72 

4.73 

4.75 

4.78 

4.81 

12 

14 

4.01 

4.01 

4.01 

4.02 

4.03 

4.05 

4.07 

4.10 

14 

16 

3.49 

3.49 

3.49 

3.50 

3.51 

3.52 

3.54 

3.56 

16 

18 

3.08 

3.08 

3.08 

3.08 

3.10 

3.11 

3.13 

3.15 

18 

20 

2.75 

2.75 

2.75 

2.75 

2.76 

2.77 

2.79 

2.81 

20 

n 

2.47 

2.47 

2.48 

2.48 

2.49 

2.50 

2.51 

2.53 

22 

U 

2.25 

2.25 

2.25 

2.25 

2.26 

2.27 

2.28 

2.30 

24 

m 

2.05 

2.05 

2.05 

2.05 

2.06 

2.07 

2.08 

2.10 

26 

28 

1.88 

1.88 

1.88 

1.88 

1.89 

1.90 

1.91 

1.92 

28 

30 

1.73 

1.73 

1.73 

1.74 

1.74 

1.75 

1.76 

1.77 

30 

32 

1.60 

1.60 

1.60 

1.60 

1.61 

1.62 

1.63 

1.64 

32 

34 

1.48 

1.48 

1.48 

1.49 

1.49 

1.50 

1.50 

1.52 

34 

36 

1.38 

1.38 

1.38 

1.38 

1.38 

1.39 

1.40 

1.41 

36 

38 

1.28 

1.28 

1.28 

1.28 

1.29 

1.29 

1.30 

1.31 

38 

40 

1.19 

1.19 

1.19 

1.19 

1.20 

1.20 

1.21 

1.22 

40 

42 

1.11 

1.11 

1.11 

1.11 

1.12 

1.12 

1.13 

1.14 

42 

44 

1.04 

1.04 

1.04 

1.04 

1.04 

1.05 

1.05 

1.06 

44 

46 

.97 

.97 

.97 

.97 

.97 

.98 

.98 

.99 

46 

48 

.90 

.90 

.90 

.90 

.90 

.91 

.91 

.92 

48 

50 

.84 

.84 

.84 

.84 

.84 

.85 

.85 

.86 

50 

52 

.78 

.78 

.78 

.78 

.79 

.79 

.79 

.80 

52 

54 

.73 

.73 

.73 

.73 

.73 

.73 

.74 

.74 

54 

56 

.67 

.67 

.67 

.68 

.  .68 

.68 

.68 

.69 

56 

58 

.63 

.63 

.63 

.63 

.63 

.63 

.63 

.64 

58 

60 

.58 

.58 

.58 

.58 

.58 

.58 

.59 

.59 

60 

62 

.53 

.53 

.53 

.53 

.53 

.54 

.54 

.54 

62 

64 

.49 

.49 

.49 

.49 

.49 

.49 

.50 

.50 

64 

66 

.45 

.45 

.45 

.45 

.45 

.45 

,45 

.46 

66 

68 

.40 

.40 

.40 

.40 

.40 

.41 

.41 

.41 

68 

70 

.36 

.36 

.36 

.36 

.37 

.37 

.37 

.37 

70 

72 

.33 

.33 

.33 

.33 

.33 

.33 

.33 

.33 

72 

74 

.29 

.29 

.29 

.29 

.29 

.29 

.29 

.29 

74 

76 

.25 

.25 

.25 

.25 

.25 

.25 

.25 

.25 

76 

78 

.21 

.21 

.21 

.21 

.21 

.21 

.22 

.22 

78 

80 

.18 

.18 

.18 

.18 

.18 

.18 

.18 

.18 

80 

81 

.16 

.16 

.16 

.16 

.16 

.16 

.16 

.16 

81 

82 

.14 

.14 

.14 

.14 

.14 

.14 

.14 

.14 

82 

83 

.12 

.12 

.12 

.12 

.12 

.12 

.12 

.13 

83 

84 

.10 

.10 

.10 

.10 

.10 

.10 

.11 

.11 

84 

85 

.09 

.09 

.09 

.09 

.09 

.09 

.09 

.09 

85 

86 

.07 

.07 

.07 

.07 

.07 

.07 

.07 

.07 

86 

87 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

87 

88 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.04 

88 

89 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

89 

90 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

90 

0° 

1° 

2° 

4° 

6° 

8° 

10° 

12° 

Co 

rr.  to  Long. = Error  in  Lat.) 

<F. 

TABLE  47. 

[Page 

939 

Longitude  Factors. 

t 

F  la  the  change  in  longitude  due  to  a  change  of  1'  in  latitude. 

Latitude. 

Bear- 

14° 

16° 

18° 

20°              22° 

24° 

26° 

28° 

Bear- 

ing. 

ing. 

0 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o 

1 

59.04 

59.60 

60.24 

60.97 

61.79 

62.71 

63.74 

64.88 

1 

2 

29.51 

29.79 

30.11 

30.47 

30.89 

31.35 

31.86 

32.43 

2 

3 

19.67 

19.85 

20.06 

20.31 

20.58 

20.89 

21.23 

21.61 

3 

4 

14.74 

14.88 

15.04 

15.22 

15.42 

15.65 

15.91 

16.20 

4 

5 

11.78 

11.89 

12.02 

12.16 

12.33 

12.51 

12.72 

12.95 

5 

6 

9.81 

9.90 

10.00 

10.12 

10.26 

10.41 

10.59 

10.78 

6 

7 

8.39 

8.47 

8.56 

8.67 

8.78 

8.91 

9.06 

9.22 

7 

8 

7.33 

7.40 

7.48 

7.57 

7.67 

7.79 

7.92 

8.06 

8 

10 

5.85 

5.90 

5.96 

6.03 

6.12 

6.21 

6.31 

6.42 

10 

12 

4.85 

4.89 

4.95 

5.01 

5.07 

5.15 

5.23 

5.33 

12 

14 

4.13 

4.17 

4.22 

4.27 

4.33 

4.39 

4.46 

4.54 

14 

16 

3.59 

3.63 

3.67 

3.71 

3.76 

3.82 

3.88 

3.95 

16 

18 

3.17 

3.20 

3.24 

3.28 

3.32 

3.37 

3.42 

3.49 

18 

20 

2.83 

2.86 

2.89 

2.92 

2.96 

3.01 

3.06 

3.11 

20 

22 

2.55 

2.58 

2.60 

2.63 

2.67 

2.71 

2.75 

2.80 

22 

24 

2.32 

2.34 

2.36 

2.39 

2.42 

2.46 

2.50 

2.54 

24 

26 

2.11 

2.13 

2.16 

2.18 

2.21 

2.24 

2.28 

2.32 

26 

28 

1.94 

1.96 

1.98 

2.00 

2.03 

2.06 

2.09 

2.13 

28 

30 

1.78 

1.80 

1.82 

1.84 

1.87 

1.90 

1.93 

1.96 

30 

32 

1.65 

1.66 

1.68 

1.70 

1.73 

1.75 

1.78 

1.81 

32 

34 

1.53 

1.54 

1.56 

1.58 

1.60 

1.62 

1.65 

1.68 

34 

36 

1.42 

1.43 

1.45 

1.47 

1.48 

1.51 

1.53 

1.56 

36 

38 

1.32 

1.33 

1.35 

1.36 

1.38 

1.40 

1.42 

1.45 

38 

40 

1.23 

1.24 

1.25 

1.27 

1.28 

1.30 

1.33 

1.35 

40 

42 

1.14 

1.15 

1.17 

1.18 

1.20 

1.22 

1.24 

1.26 

42 

44 

,1.07 

1.08 

1.09 

1.10 

1.12 

1.13 

1.15 

1.17 

44 

46 

1.00 

1.01 

1.02 

1.03 

1.04 

1.06 

1.07 

1.09 

46 

48 

.93 

.94 

.95 

.96 

.97 

.99 

1.00 

1.02 

48 

50 

.87 

.87 

.88 

.89 

.91 

.92 

.93 

.95 

50 

52 

.80 

.81 

.82 

.83 

.84 

.85 

.87 

.88 

52 

54 

.75 

.76 

.76 

.77 

.78 

.79 

.81 

.82 

54 

56 

.69 

.70 

.71 

.72 

.73 

.74 

.75 

.76 

56 

58 

.64 

.65 

.66 

.66 

.67 

.68 

.69 

.71 

58 

60 

.60 

.60 

.61 

.61 

.62 

.63 

.64 

.65 

60 

62 

.55 

.55 

.56 

.57 

.57 

.58 

.59 

.60 

63 

64 

.50 

.51 

.51 

.52 

.53 

.53 

.54 

.55 

64 

66 

.46 

.46 

.47 

.47 

.48 

.49 

.50 

.50 

66 

68 

.42 

.42 

.42 

.43 

.44 

.44 

.45 

.46 

68 

70 

.37 

.38 

.38 

.39 

.39 

.40 

.40 

.41 

70 

73 

.34 

.34 

.34 

.35 

.35 

.36 

.36 

.37 

73 

74 

.30 

.30 

.30 

.31 

.31 

.31 

.32 

.33 

74 

76 

.26 

.26 

.26 

.27 

.27 

.27 

.28 

.28 

76 

78 

.22 

.22 

.22 

.23 

.23 

.23 

.24 

.24 

78 

80 

.18 

.18 

.18 

.19 

.19 

.19 

.20 

.20 

80 

81 

.16 

.16 

.17 

.17 

.17 

.17 

.18 

.18 

81 

82 

.14 

.15 

.15 

.15 

.15 

.15 

.16 

.16 

83 

83 

.13 

.13 

.13 

.13 

.13 

.13 

.14 

.14 

83 

84 

.11 

.11 

.11 

.11 

.11 

.11 

.12 

.12 

84 

85 

.09 

.09 

.09 

.09 

.09 

.10 

.10 

.10 

85 

86 

.07 

.07 

.07 

.07 

.08 

.08 

.08 

.08 

86 

87 

.05 

.05 

.05 

.06 

.06 

.06 

.06 

.06 

87 

88 

.04 

.04 

.04 

.04 

.04 

.04 

.04 

.04 

88 

89 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

89 

90 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

90 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

Coi 

T.  to  Long. = Error  in  Lat.> 

CF. 

21594°— 14- 


Pag 

e940] 

TABLE  47. 

Longitude  Factors. 

F  is  the  change  In  longitude  due  to  a  change  of  1'  in  latitude. 

Latitude. 

Bear- 

30° 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

Bear- 

ing. 

ing. 

o 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o 

1 

66.15 

67.56 

69.10 

70.81 

72.70 

74.79 

77.09 

79.64 

1 

S 

33.07 

33.77 

34.54 

35.40 

36.34 

37.38 

38.53 

39.81 

2 

3 

22.03 

22.50 

23.02 

23.59 

24.21 

24.91 

25.68 

26.53 

3 

4 

16.51 

16.86 

17.25 

17.68 

18.15 

18.67 

19.24 

19.88 

4 

5 

13.20 

13.48 

13.79 

14.13 

14.50 

14.92 

15.38 

15.89 

5 

6 

10.99 

11.22 

11.48 

11.76 

12.07 

12.42 

12.80 

13.23 

6 

7 

9.40 

9.60 

9.82 

10.07 

10.34 

10.63 

10.96 

11.32 

7 

8 

8.22 

8.39 

8.58 

8.79 

9.03 

9.29 

9.57 

9.89 

8 

10 

6.55 

6.69 

6.84 

7.01 

7.20 

7.40 

7.63 

7.88 

10 

13 

5.43 

5.55 

5.67 

5.81 

5.97 

6.14 

6.33 

6.54 

12 

14 

4.63 

4.73 

4.84 

4.96 

5  09 

5.24 

5.40 

5.58 

14 

16 

4.03 

4.11 

4.21 

4.31 

4.43 

4.55 

4.69 

4.85 

16 

18 

3.55 

3.63 

3.71 

3.80 

3.91 

4.02 

4.14 

4.28 

18 

20 

3.17 

3.24 

3.31 

3.40 

3.49 

3.59 

3.70 

3.82 

20 

22 

2.86 

2.92 

2.98 

3.06 

3.14 

3.23 

3.33 

3.44 

22 

24 

2.59 

2.65 

2.71 

2.78 

2.85 

2.93 

3.02 

3.12 

24 

26 

2.37 

2.42 

2.47 

2.53 

2.60 

2.68 

2.76 

2.85 

26 

28 

2.17 

2.22 

2.27 

2.32 

2.39 

2.45 

2.53 

2.61 

28 

30 

2.00 

2.04 

2.09 

2.14 

2.20 

2.26 

2.33 

2.41 

30 

32 

1.85 

1.89 

1.93 

1.98 

2.03 

2.09 

2.15 

2.22 

32 

34 

1.71 

1.75 

1.79 

1.83 

1.88 

1.93 

1.99 

2.06 

34 

36 

.     1.59 

1.62 

1.66 

1.70 

1.75 

1.80 

1.85 

1.91 

36 

38 

1.48 

1.51 

1.54 

1.58 

1.62 

1.67 

1.72 

1.78 

38 

40 

1.38 

1.41 

1.44 

1.47 

1.51 

1.56 

1.60 

1.66 

40 

42 

1.28 

1.31 

1.34 

1.37 

1.41 

1.45 

1.49 

1.54 

42 

44 

1.20 

1.22 

1.25 

1.28 

1.31 

1.35 

1.39 

1.44 

44 

46 

1.11 

1.14 

1.16 

1.19 

1.23 

1.26 

1.30 

1.34 

46 

48 

1.04 

1.06 

1.09 

1.11 

1.14 

1.17 

1.21 

1.25 

48 

50 

.97 

.99 

1.01 

1.04 

1.06 

1.09 

1.13 

1.17 

50 

62 

.90 

.92 

.94 

.97 

.99 

1.02 

1.05 

1.09 

52 

54 

.84 

.86 

.88 

.90 

.92 

.95 

.98 

1.01 

54 

56 

.78 

.79 

.81 

.83 

.86 

.88 

.91 

.94 

56 

58 

.72 

.74 

.75 

.77 

.79 

.82 

.84 

.87 

58 

60 

.67 

.68 

.70 

.71 

.73 

.75 

.78 

.80 

60 

62 

.61 

.63 

.64 

.66 

.67 

.69 

.72 

.74 

62 

64 

.56 

.57 

.59 

.60 

.62 

.64 

.66 

.68 

64 

66 

.51 

.52 

.54 

.55 

.56 

.58 

.60 

.62 

66 

68 

.47 

.48 

.49 

.50 

.51 

.53 

.54 

.56 

68 

70 

.42 

.43 

.44 

.45 

.46 

.47 

.49 

.51 

70 

72 

.37 

.38 

.39 

.40 

.41 

.42 

.44 

.45 

72 

74 

.33 

.34 

.35 

.35 

.36 

.37 

.39 

.40 

74 

76 

.29 

.29 

.30 

.31 

.32 

.32 

.34 

.35 

76 

78 

.24 

.25 

.26 

.26 

.27 

.28 

.29 

.29 

78 

80 

.20 

.21 

.21 

.22 

.22 

.23 

.24 

.24 

80 

81 

.18 

.19 

.19 

.20 

.20 

.21 

.21 

.22 

81 

82 

.16 

.17 

.17 

.17 

.18 

.18 

.19 

.19 

82 

83 

.14 

.14 

.15 

.15 

.16 

.16 

.16 

.17 

83 

84 

.12 

.12 

.13 

.13 

.13 

.14 

.14 

.15 

84 

85 

.10 

.10 

.11 

.11 

.11 

.11 

.12 

.12 

85 

86 

.08 

.08 

.08 

.09 

.09 

.09 

.09 

.10 

86 

87 

.06 

.06 

.06 

.06 

.07 

.07 

.07 

.07 

87 

88 

.04 

.04 

.04 

.04 

.04 

.05 

.05 

.05 

88 

89 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

89 

90 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

90 

30° 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

Corr.  to  Long.=EiTor  in  Lat.xF.                                                                            1 

TABLE  47. 

[Page  941 

Longitude  Factors. 

F  Is  the  cbange  In  longitude  due  to  a  change  of  1'  in  latitude. 

Latitude. 

Bear- 

46° 

48° 

50° 

52° 

54° 

56° 

58° 

60° 

Bear- 

ing. 

ing. 

o 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o' 

1 

82.47 

85.62 

89.13 

93.05 

97.47 

102.5 

108.1 

114.6 

1 

2 

41.22 

42.80 

44.55 

46.51 

48.72 

51.21 

54.04 

67.27 

2 

3 

27.47 

28.52 

29.68 

30.99 

32.46 

34.12 

36.01 

38.16 

3 

4 

20.59 

21.37 

22.25 

23.23 

24.33 

•25.  57 

26.99 

28.60 

4 

5 

16.45 

17.08 

17.78 

18.57 

19.45 

20.44 

21.57 

22.86 

5 

6 

13.70 

14.22 

14.80 

15.45 

16.19 

17.01 

17.95 

19.03 

6 

7 

11.72 

12.17 

12.67 

13.23 

13.86 

14.56 

15.37 

16.29 

7 

8 

10.24 

10.63 

11.07 

11.56 

12.11 

12.72 

13.43 

14.23 

8 

10 

8.16 

8.48 

8.82 

9.21 

9.65 

10.14 

10.70 

11.34 

10 

12 

6.77 

7.03 

7.32 

7.64 

8.00 

8.41 

8.88 

9.41 

12 

14 

5.77 

5.99 

6.24 

6.51 

6.82 

7.17 

7.57 

8.02 

14 

16 

5.02 

5.21 

5.42 

5.66 

5.93 

6.24 

6.58 

6.97 

16 

18 

4.43 

4.60 

4.79 

5.00 

5.24 

5.50 

5.81 

6.15 

18 

20 

3.95 

4.11 

4.27 

4.46 

4.67 

4.91 

5.19 

5.49 

20 

22 

3.56 

3.70 

3.85 

4.02 

4.21 

4.43 

4.67 

4.95 

22 

24 

3.23 

3.36 

3.49 

3.65 

3.82 

4.02 

4.24 

4.49 

24 

26 

2.95 

3.06 

3.19 

3.33 

3.49 

3.66 

3.87 

4.10 

26 

28 

2.71 

2.81 

2.93 

3.05 

3.20 

3.36 

3.55 

3.76 

28 

30 

2.49 

2.59 

2.69 

2.81 

2.95 

3.10 

3.27 

3.46 

30 

32 

2.30 

2.39 

2.49 

2.60 

2.72 

2.86 

3.02 

3.20 

32 

34 

2.13 

2.22 

2.31 

2.41 

2.52 

2.65 

2.80 

2.96 

34 

36 

1.98 

2.06 

2.14 

2.24 

2.34 

2.46 

2.60 

2.75 

36 

38 

1.84 

1.91 

1.99 

2.08 

2.18 

2.29 

2.41 

2.56 

38 

40 

1.71 

1.78 

1.85 

1.94 

2.03 

2.13 

2.25 

2.38 

40 

42 

1.60 

1.66 

1.73 

1.80 

1.89 

1.99 

2.09 

2.22 

42 

44 

1.49 

1.55 

1.61 

1.68 

1.76 

1.85 

1.95 

2.07 

44 

46 

1.39 

1.44 

1.50 

1.57 

1.64 

1.73 

1.82 

1.93 

46 

48 

1.30 

1.35 

1.40 

1.46 

1.53 

1.61 

1.70 

1.80 

48 

50 

1.21 

1.25 

1.31 

1.36 

1.43 

1.50 

1.58 

1.68 

50 

52 

1.12 

1.17 

1.22 

1.27 

1.33 

1.40 

1.47 

1.56 

52 

54 

1.05 

1.09 

1.13 

1.18 

1.23 

1.30 

1.37 

1.45 

54 

56 

.97 

1.01 

1.05 

1.10 

1.15 

1.21 

1.27 

1.35 

56 

58 

.90 

.93 

.97 

1.01 

1.06 

1.12 

1.18 

1.25 

58 

60 

.83 

.86 

.90 

.94 

.98 

1.03 

1.09 

1.15 

60 

62 

.77 

.79 

.83 

.86 

.90 

.95 

1.00 

1.06 

62 

64 

.70 

.73 

.76 

.79 

.83 

.87 

.92 

.97 

64 

66 

.64 

.66 

.69 

.72 

.76 

.79 

.84 

.89 

66 

68 

.58 

.60 

.63 

.65 

.69 

.72 

.76 

.81 

68 

70 

.52 

.54 

.57 

.59 

.62 

.65 

.68 

.73 

70 

72 

.47 

.49 

.51 

.53 

.55 

.58 

.61 

.65 

72 

74 

.41 

.43 

.45 

.46 

.49 

.51 

.54 

.57 

74 

76 

.36 

.37 

.39 

.40 

.42 

.45 

.47 

.50 

76 

78 

.31 

.32 

.33 

.34 

.36 

.38 

.40 

.42 

78 

80 

.25 

.26 

.27 

.29 

.30 

.31 

.33 

.35 

80 

81 

.23 

.24 

.25 

.26 

.27 

.28 

.30 

.32 

81 

82 

.20 

.21 

.22 

.23 

.24 

.25 

.26 

.28 

82 

83 

.18 

.18 

.19 

.20 

.21 

.22 

.23 

.25 

83 

84 

.15 

.16 

.16 

.17 

.18 

.19 

.20 

.21 

84 

85 

.13 

.13 

.14 

.14 

.15 

.16 

.16 

.17 

85 

86 

.10 

.10 

.11 

.11 

.12 

.12 

.13 

.14 

86 

87 

.08 

.08 

.08 

.08 

.09 

.09 

.10 

.10 

87 

88 

.05 

.05 

.05 

.06 

.06 

.06 

.07 

.07 

88 

89 

.02 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

89 

90 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

.00 

90 

46° 

48° 

50° 

52° 

54° 

66° 

58° 

60° 

doi 

T.  to  Long.=Error  in  Lat.X 

r. 

Page  942] 

TABLE  48. 

Latitude  Factors. 

t  is  the  change  in  latitude  due  to  a  change  of  1'  in  longitude. 

Latitude. 

Bear- 

0" 

1° 

3° 

4° 

6° 

8° 

10° 

13° 

Bear- 

ing. 

ing. 

o 

/ 

/ 

/ 

/ 

/ 

/ 

f 

/ 

o 

1 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

1 

3 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

3 

3 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

3 

4 

.07 

.07 

.07 

.07 

.07 

.07 

.07 

.07 

4 

5 

.09 

.09 

.09 

.09 

.09 

.09 

.09 

.09 

5 

6 

.11 

.11 

.11 

.10 

.10 

.10 

.10 

.10 

6 

1 

.12 

.12 

.12 

.12 

.12 

.12 

.12 

.12 

7 

8 

.14 

.14 

.14 

.14 

.14 

.14 

.14 

.14 

8 

10 

.18 

.18 

.18 

.18 

.18 

.17 

.17 

.17 

10 

13 

.21 

.21 

.21 

.21 

.21 

.21 

.21 

.21 

13 

14 

.25 

.25 

.25 

.25 

.25 

.25 

.25 

.24 

14 

16 

.29 

.29 

.29 

.29 

.28 

.28 

.28 

.28 

16 

18 

.32 

.32 

.32 

.32 

.32 

.32 

.32 

.32 

18 

20 

.36 

.36 

.36 

.36 

.36 

.36 

.36 

.36 

30 

33 

.40 

.40 

.40 

.40 

.40 

.40 

.40 

.40 

33 

34 

.44 

.44 

.44 

.44 

.44 

.44 

.44 

.43 

34 

36 

.49 

.49 

.49 

.49 

.49 

.48 

.48 

.48 

36 

38 

.53 

.53 

.53 

.53 

.53 

.53 

.52 

.52 

38 

30 

.58 

.58 

.58 

.57 

.57 

.57 

.57 

.56 

30 

33 

.63 

.63 

.63 

.63 

.62 

.62 

.61 

.61 

33 

34 

.68 

.68 

.68 

.67 

.67 

.67 

.67 

.66 

34 

36 

.72 

.72 

.72 

.72 

.72 

.72 

.71 

.71 

36 

38 

.78 

.78 

.78 

.78 

.78 

.78 

.77 

.76 

38 

40 

.84 

.84 

.84 

.84 

.83 

.83 

.83 

.82 

40 

43 

.90 

.90 

.90 

.90 

.89 

.89 

.88 

.88 

43 

44 

.96 

.96 

.96 

.96 

.96 

.95 

.95 

.94 

44 

46 

1.04 

1.04 

1.04 

1.03 

1.03 

1.03 

1.02 

1.01 

46 

48 

1.11 

1.11 

1.11 

1.11 

1.11 

1.10 

1.10 

1.09 

48 

50 

1.19 

1.19 

1.19 

1.19 

1.19 

1.18 

1.17 

1.17 

50 

53 

1.28 

1.28 

1.28 

1.28 

1.27 

1.27 

1.26 

1.25 

53 

54 

1.38 

1.38 

1.38 

1.37 

1.37 

1.36 

1.36 

1.35 

54 

56 

1.48 

1.48 

1.48 

1.48 

1.47 

1.47 

1.46 

1.45 

56 

58 

1.60 

1.60 

1.60 

1.60 

1.59 

1.58 

1.58 

1.57 

58 

60 

1.73 

1.73 

1.73 

1.73 

1.72 

1.72 

1.71 

1.69 

60 

63 

1.88 

1.88 

1.88 

1.88 

1.87 

1.86 

1.85 

1.84 

63 

64 

2.05 

2.05 

2.05 

2.05 

2.04 

2.03 

2.02 

2.01 

64 

66 

2.25 

2.25 

2.24 

2.24 

2.23 

2.22 

2.21 

2.20 

66 

68 

2.48 

2.48 

2.47 

2.47 

2.46 

2.45 

2.44 

2.42 

68 

70 

2.75 

2.75 

2.75 

2.74 

2.73 

2.72 

2.71 

2.69 

70 

73 

3.08 

3.08 

3.08 

3.07 

3.06 

3.05 

V     3.03 

3.01 

73 

74 

3.49 

3.49 

3.49 

3.48 

3.47 

3.45 

3.43 

3.41 

74 

76 

4.01 

4.01 

4.01 

4.00 

3.99 

3.97 

3.95 

3.92 

76 

78 

4.70 

4.70 

4.70 

4.69 

4.68 

4.66 

4.63 

4.60 

78 

80 

5.67 

5.67 

5.67 

5.66 

5.64 

5.62 

5.59 

5.55 

80 

81 

6.31 

6.31 

6.31 

6.30 

6.28 

6.25 

6.22 

6.18 

81 

83 

7.12 

7.11 

7.11 

7.10 

7.07 

7.05 

7.01 

6.96 

83 

83 

8.15 

8.14 

8.14 

8.13 

8.10 

8.07 

8.02 

7.97 

83 

84 

9.52 

9.51 

9.51 

9.49 

9.46 

9.42 

9.37 

9.31 

84 

85 

11.43 

11.43 

11.42 

11.40 

11.37 

11.32 

11.25 

11.18 

85 

86 

14.30 

14.30 

14.29 

14.27 

14.22 

14.16 

14.08 

13.99 

86 

87 

19.08 

19.08 

19.07 

19.03 

18.98 

18.91 

18.79 

18.66 

87 

88 

28.63 

28. '63 

28.62 

28.57 

28.48 

28.35 

28.20 

28.01 

88 

89 

57.29 

57.28 

57.26 

57.15 

56.98 

56.73 

56.42 

56.04 

89 

0° 

1° 

3° 

4° 

6° 

8° 

10° 

13° 

C< 

)r.  to  Lat.= Error  in  Long.> 

;f. 

TABLE  48. 

Latitude  Factors. 

[Page 

943 

t  is  the  change  in  latitude  due  to  a  change 

3f  1'  in  longitude. 

Latitude. 

Bear- 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

Bear- 

ing. 

ing. 

0 

/ 

f 

/ 

/ 

/ 

/ 

f 

/ 

o 

1 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

0.02 

1 

2 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

2 

3 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

3 

4 

.07 

.07 

.07 

.07 

.06 

.06 

.06 

.06 

4 

5 

.08 

.08 

.08 

.08 

.08 

.08 

.08 

.08 

5 

6 

.10 

.10 

.10 

.10 

.10 

.10 

.09 

.09 

6 

7 

.12 

.12 

.12 

.12 

.11 

.11 

.11 

.11 

7 

8 

.14 

.14 

.13 

.13 

.13 

.13 

.13 

.12 

8 

10 

.17 

.17 

.17 

.17 

.16 

.16 

.16 

.16 

10 

13 

.21 

.20 

.20 

.20 

.20 

.19 

.19 

.19 

12 

14 

.24 

.24 

.24 

.23 

.23 

.23 

.22 

.22 

14 

16 

.28 

.28 

.27 

.27 

.27 

.26 

.26 

.25 

16 

18 

.32 

.31 

.31 

.30 

.30 

.30 

.29 

.29 

18 

20 

.35 

.35 

.35 

.34 

.34 

.33 

.33 

.32 

20 

Zt 

.39 

.39 

.38 

.38 

.38 

.37 

.36 

.36 

22 

U 

.43 

.43 

.42 

.42 

.41 

.41 

.40 

.39 

24 

26 

.47 

.47 

.46 

.46 

.45 

.45 

.44 

.43 

26 

28 

.52 

.51 

.51 

.50 

.49 

.49 

.48 

.47 

28 

30 

.56 

.56 

.55 

.54 

.53 

.53 

.52 

.51 

30 

32 

.61 

.60 

.60 

.59 

.58 

.57 

.56 

.55 

32 

34 

.65 

.65 

.64 

.63 

.63 

.62 

.61 

.59 

34 

36 

.70 

.70 

.69 

.68 

.68 

.66 

.65 

.64 

36 

38 

.76 

.75 

.74 

.74 

.72 

.71 

.70 

.69 

38 

40 

.81 

.81 

.80 

.79 

.78 

.77 

.75 

.74 

40 

42 

.88 

.87 

.85 

.85 

.83 

.82 

.81 

.79 

42 

44 

.93 

.93 

.92 

.91 

.89 

.88 

.87 

.85 

44 

46 

1.01 

1.00 

.99 

.97 

.96 

.95 

.93 

.91 

46 

48 

1.08 

1.07 

1.06 

1.04 

1.03 

1.02 

1.00 

.98 

48 

50 

1.16 

1.15 

1.13 

1.12 

1.10 

1.09 

1.07 

1.05 

50 

52 

1.24 

1.23 

1.22 

1.20 

1.19 

1.17 

1.15 

1.13 

52 

54 

1.34 

1.32 

1.31 

1.29 

1.28 

1.26 

1.24 

1.22 

54 

56 

1.44 

1.43 

1.41 

1.39 

1.38 

1.35 

1.33 

1.31 

56 

58 

1.55 

1.54 

1.52 

1.50 

1.48 

1.46 

1.44 

1.41 

58 

60 

1.68 

1.67 

1.65 

1.63 

1.61 

1.58 

1.56 

1.53 

60 

62 

1.83 

1.81 

1.79 

1.77 

1.74 

1.72 

1.69 

1.66 

62 

64 

1.99 

1.97 

1.95 

1.93 

1.90 

1.87 

1.84 

1.81 

64 

66 

2.18 

2.16 

2.14 

2.11 

2.08 

2.05 

2.02 

1.98 

66 

68 

2.40 

2.38 

2.35 

2.33 

2.30 

2.26 

2.23 

2.18 

68 

70 

2.67 

2.64 

2.61 

2.58 

2.55 

2.51 

2.47 

2.43 

70 

72 

2.99 

2.96 

2.93 

2.89 

2.85 

2.81 

2.77 

2.72 

72 

74 

3.38 

3.35 

3.32 

3.28 

3.23 

3.19 

3.14 

3.08 

74 

76 

3.89 

3.86 

3.81 

3.77 

3.72 

3.66 

3.61 

3.54 

76 

78 

4.56 

4.52 

4.47 

4.42 

4.36 

4.30 

4.23 

4.15 

78 

80 

5.50 

5.45 

5.39 

5.33 

5.26 

5.18 

5.10 

5.01 

80 

81 

6.13 

6.07 

6.01 

5.93 

5.86 

5.77 

5.68 

5.58 

81 

82 

6.90 

6.84 

6.77 

6.69 

6.60 

6.50 

6.40 

6.28 

82 

83 

7.90 

7.83 

7.75 

7.65 

7.55 

7.44 

7.32 

7.19 

83 

84 

9.23 

9.15 

9.05 

8.94 

8.82 

8.69 

8.55 

8.40 

84 

85 

11.09 

10.99 

10.87 

10.74 

10.60 

10.44 

10.26 

10.09 

85 

86 

13.88 

13.75 

13.60 

13.44 

13.26 

13.07 

12.86 

12.63 

86 

87 

18.51 

18.34 

18.15 

17.93 

17.69 

17.43 

17.15 

16.85 

87 

88 

27.78 

27.52 

27.23 

26.91 

26.55 

26.16 

25.74 

25.28 

88 

89 

55.59 

55.07 

54.49 

53.84 

53.12 

52.33 

51.50 

50.58 

89 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

Ck) 

rr.  to  Lat.=Error  in  Long.) 

<f. 

Page  944] 

TABLE  48. 

Latitude  Factors. 

t  is  the  change  to  latitude  due  to  a  change  of  1'  in  longitude. 

Latitude. 

Bear- 
ing. 

30° 

32°^ 

34° 

36° 

38° 

40° 

42° 

44° 

Bear- 
ing. 

o 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o 

1 

0.02 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

1 

2 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

2 

3 

.05 

.05 

.04 

.04 

.04 

.04 

.04 

.04 

3 

4 

.06 

.06 

.06 

.06 

.06 

.05 

.05 

.05 

4 

5 

.08 

.07 

.07 

.07 

.07 

.07 

.07 

.06 

5 

6 

.09 

.09 

.09 

.09 

.08 

.08 

.08 

.08 

6 

7 

.11 

.10 

.10 

.10 

.10 

.09 

.09 

.09 

7 

8 

.12 

.12 

.12 

.11 

.11 

.11 

.10 

.10 

8 

10 

.15 

.15 

.15 

.14 

.14 

.14 

.13 

.13 

10 

13 

.18 

.18 

.18  ■ 

.17 

.17 

.16 

.16 

.15 

12 

14 

.22 

.21 

.21 

.20 

.20 

.19 

.19 

.18 

14 

16 

.25 

.24 

.24 

.23 

.23 

.22 

.21 

.21 

16 

18 

.28 

.28 

.27 

.26 

.26 

.25 

.24 

.23 

18 

20 

.32 

.31 

.30 

.29 

.29 

.28 

.27 

.26 

20 

22, 

.35 

.34 

.34 

.33 

.32 

.31 

.30 

.29 

22 

24 

.39 

.38 

.37 

.36 

.35 

.34 

.33 

.32 

24 

26 

.42 

.41 

.40 

.40 

.38 

.37 

.36 

.35 

26 

28 

.46 

.45 

.44 

.43 

.42 

.41 

.40 

.38 

28 

30 

.50 

.49 

.48 

.47 

.45 

.44 

.43 

.41 

30 

32 

.54 

.53 

.52 

.51 

.49 

.48 

.47 

.45 

32 

34 

.58 

.57 

.56 

.55 

.53 

.52 

.50 

.49 

34 

36 

.63 

.62 

.60 

.59 

.57 

.56 

.54 

.52 

36 

38 

.68 

.66 

.65 

.63 

.62 

.60 

.58 

.56 

38 

40 

.72 

.71 

.69 

.68 

.66 

.64 

.63 

.60 

40 

42 

.78 

.76 

.75 

.73 

.71 

.69 

.67 

.65 

42 

44 

.83 

.82 

.80 

.78 

.76 

.74 

.72 

.69 

44 

46 

.90 

.88 

.86 

.84 

.82 

.79 

.77 

.74 

46 

48 

.96 

.94 

.92 

.90 

.88 

.85 

.83 

.80 

48 

50 

1.03 

1.01 

.99 

.96 

.94 

.91 

.88 

.86 

50 

52 

1.11 

1.09 

1.06 

1.04 

1.01 

.98 

.95 

.92 

52 

54 

1.19 

1.16 

1.14 

1.11 

1.08 

1.05 

1.02 

.99 

54 

56 

1.28 

1.26 

1.23 

1.20 

1.17 

1.14 

1.10 

1.07 

56 

58 

1.39 

1.36 

1.33 

1.30 

1.26 

1.23 

1.19 

1.15 

58 

60 

1.49 

1.47 

1.44 

1.40 

1.37 

1.33 

1.29 

1.25 

60 

62 

1.63 

1.59 

1.56 

1.52 

1.48 

1.44 

1.40 

1.35 

62 

64 

1.78 

1.74 

1.70 

1.66 

1.62 

1.57 

1.52 

1.48 

64 

66 

1.95 

1.91 

1.85 

1.82 

1.77 

1.72 

1.67 

1.62 

66 

68 

2.14 

2.10 

2.05 

2.00 

1.95 

1.90 

1.84 

1.78 

68 

70 

2.38 

2.33 

2.28 

2.22 

2.17 

2.10 

2.04 

1.98 

70 

72 

2.67 

2.61 

2.55 

2.50 

2.43 

2.36 

2.29 

2.21 

72 

74 

3.02 

2.96 

2.89 

2.82 

2.75 

2.67 

2.59 

2.51 

74 

76 

3.47 

3.40 

3.33 

3.25 

3.16 

3.07 

2.98 

2.89 

76 

78 

4.07 

3.99 

3.90 

3.81 

3.71 

3.60 

3.50 

3.38 

78 

80 

4.91 

4.81 

4.70 

4.59 

4.47 

4.34 

4.22 

4.08 

80 

81 

5.47 

5.35 

5.24 

5.11 

4.98 

4.84 

4.69 

4.54 

81 

82 

6.16 

6.03 

5.90 

5.76 

5.61 

5.45 

5.29 

5.12 

82 

83 

7.05 

6.91 

6.75 

6.59 

6.42 

6.24 

6.05 

5.86 

83 

84 

8.24 

8.07 

7.93 

7.70 

7.50 

7.29 

7.07 

6.84 

84 

85 

9.90 

9.69 

9.48 

9.25 

9.01 

8.75 

8.49 

8.22 

85 

86 

12.39 

12.13 

11.86 

11.57 

11.27 

10.95 

10.63 

10.29 

86 

87 

16.52 

16.18 

15.82 

15.44 

15.04 

14.62 

14.18 

13.73 

87 

88 

24.80 

24.28 

23.74 

23.17 

22.56 

21.93 

21.28 

20.60 

88 

89 

49.61 

48.58 

47.50 

46.36 

45.14 

43.98 

42.58 

41.21 

89. 

30° 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

Cc 

rr.  to  Lat.-=  Error  in  Long. 

Xf. 

TABLE  48. 

fPage 

945 

Latitude  Factors. 

f  Is  the  change  In  latitude  due  to  a  change  of  1'  in  longitude. 

Latitude. 

Bear- 
ing. 

46° 

48° 

56°    * 

52° 

54° 

56° 

68° 

60° 

Bear- 
ing. 

o 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

o 

1 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

1 

S 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

.02 

2 

3 

.04 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

3 

4 

.05 

.05 

.04 

.04 

.04 

.04 

.04 

.03 

4 

5 

.06 

.06 

.06 

.05 

.05 

.05 

.05 

.04- 

5 

6 

.07 

.07 

.07 

.06 

.06 

.06 

.06 

.05 

6 

7 

.08 

.08 

.08 

.08 

.07 

.07 

.06 

.06 

7 

8 

.10 

.09 

.09 

.08 

.08 

.08 

.07 

.07 

8 

10 

.12 

.12 

.11 

.11 

.10 

.10 

.09 

.09 

10 

n 

.15 

.14 

.14 

.13 

.13 

.12 

.11 

.11 

12 

14 

.17 

.17 

.16 

.15 

.15 

.14 

.13 

.12 

14 

16 

.20 

.19 

.18 

.18 

.17 

.16 

.15 

.14 

16 

18 

.23 

.22 

.21 

.20 

.19 

.18 

.17 

.16 

18 

20 

•     .25 

.24 

.23 

.22 

.21 

.20 

.19 

.18 

20 

n 

.28 

.27 

.26 

.25 

.24 

.23 

.21 

.20 

22 

u 

.31 

.30 

.29 

.27 

.26 

.25 

.24 

.22 

24 

26 

.34 

.33 

.31 

.30 

.29 

.27 

.26 

.24 

26 

28 

.37 

.36 

.34 

.33 

.31 

.30 

.28 

.27 

28 

30 

.40 

.39 

.37  ■ 

.36 

.34 

.32 

.31 

.29 

30 

32 

.43 

.42 

.40 

.38 

.37 

.35 

.33 

.31 

32 

34 

.47 

.45 

.43 

.41 

.40 

.38 

.36 

.34 

34 

36 

.51 

.49 

.47 

.45 

.43 

.41 

.38 

.36 

36 

38 

.54 

.52 

.50 

.48 

.46 

.44 

.41 

.39 

38 

40 

.58 

.56 

.54 

.52 

.49 

.47 

.44 

.42 

40 

42 

.63 

.60 

.58 

.56 

.53 

.50 

.48 

.45 

42 

44 

.67 

.65 

.62 

.60 

.57 

.54 

.51 

.48 

44 

46 

.72 

.69 

.67 

■       .64 

.61 

.58 

.55 

.52 

46 

48 

.77 

.74 

.71 

.68 

.65 

.62 

.59 

.56 

48 

50 

.83 

.80 

.77 

.73 

.70 

.67 

.63 

.60 

50 

52 

.89 

.86 

.82 

.79 

.75 

.72 

.68 

.64 

52 

54 

.96 

.92 

.88 

.85 

.81 

.77 

.73 

.69 

54 

56 

1.03 

.99 

.95 

.91 

.87 

.83 

.79 

.74 

56 

58 

1.11 

1.07 

1.03 

.99 

.94 

.89 

.85 

.80 

58 

60 

1.20 

1.16 

1.11 

1.07 

1.02 

.97 

.92 

.87 

60 

62 

1.31 

1.26 

1.21 

1.16 

1.11 

1.05 

1.00 

.94 

62 

64 

1.42 

1.37 

1.32 

1.26 

1.20 

1.15 

1.09 

1.03 

64 

66 

1.56 

1.50 

1.44 

1.38 

1.32 

1.26 

1.19 

1.12 

66 

68 

1.72 

1.66 

1.59 

1.52 

1.45 

1.38 

1.31 

1.24 

68 

70 

1.91 

1.84 

1.77 

1.69 

1.61 

1.54 

1.45 

1.37 

70 

72 

2.14 

2.06 

1.99 

1.89 

1.81 

1.72 

1.63 

1.54 

73 

74 

2.42 

2.33 

2.24 

2.15 

2.05 

1.95 

1.85 

1.74 

74 

76 

2.79 

2.68 

2.58 

2.47 

2.36 

2.24 

2.13 

2.01 

76 

78 

3.27 

3.15 

3.02 

2.90 

2.77 

2.63 

2.49 

2.35 

78 

80 

3.94 

3.80 

3.70 

3.49 

3.33 

3.17 

3.01 

2.84 

80 

81 

4.39 

4.23 

4.06 

3.89 

3.71 

3.53 

3.35  • 

3.16 

81 

82 

4.94 

4.76 

4.57 

4.38 

4.18 

3.98 

3.77 

3.56 

82 

83 

5.66 

5.45 

5.24 

5.01 

4.79 

4.56 

4.32 

4.07 

83 

84 

6.61 

6.37 

6.12 

5.86 

5.59 

5.32 

5.04 

4.76 

84 

85 

7.94 

7.65 

7.35 

7.04 

6.72 

6.39 

6.06 

5.72 

85 

86 

9.94 

9.57 

9.19 

8.81 

8.41 

8.00 

7.58 

7.15 

86 

87 

13.26 

12.77 

12.27 

11.75 

11.22 

10.67 

10.11 

9.54 

87 

88 

19.89 

19.16 

18.41 

17.64 

16.83 

16.01 

15.17 

14.32 

88 

89 

39.80 

38.34 

36.83 

35.24 

33.68 

32.04 

30.36 

28.65 

89 

46° 

48° 

50° 

52° 

54° 

56° 

58° 

60° 

CoTT.  to  Lat.= Error  in  Lon 

g.xf. 

o 


i^ 


i 

j 


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